engineering data on mixing ()

Preface This book is a compilation of the engineering data on mixing, which have appeared in the

major technical journals of chemical engineering and bioengineering since 1975. That year marked the beginning of a period of rapid advancement in the science and technology of mixing, with rather reliable results for both theoretical and experimental studies. In addition, we have included some important earlier articles which have been and are still being referred to.

Mixing is a basic technology important in a wide variety of industries. Many numbers of tanks equipped with various types of agitators have been used for mixing all kinds of materials since ancient times. Yet designs of both agitators and tanks still depend primarily on art and experience. In the light of this fact we felt that the data on mixing should be compiled and presented in a systematic manner for assistance in design and analysis of agitated tanks , and to provide easier access to mixing data for various engineering activities. Of course, computer-aided searches of pertinent data bases can be of assistance to chemical engineers and bioengineers in their studies. However, computer surveys of data bases are sometimes time-consuming and often costly. Furthermore inadequate selection of key words can jeopardize the searches. In view of these objections, we offer this book in the hope that it will be useful to those who desire to conduct an efficient and accurate survey of the mixing data of interest to them.

No attempts were made to verify the mixing data given by the various investigators. We have simply indicated the limitations of correlations and data when they are available. The use of uniform units might have been appreciated by users of this book. However, we have elected to use the original units as given by the various authors, lest errors be introduced in the conversion process.

In Chapter 1 we present a variety of results for the experimental measurements of flow patterns in stirred tanks. Most of the measurements were made by using modem Laser-Doppler techniques. This chapter is useful for the prediction of flow patterns in tanks with many different geometries, various types of agitators, and fluids of diverse physical and rheological properties. Here can also be found valuable data for the validation of results obtained by CFD simulations. Chapters 2 through 5 deal with data for traditional chemical engineering subjects. In Chapter 6 we sununarize a number of scale-up relations developed over the years for various systems. They include liquid, solid-liquid, liquid-liquid, gas-liquid, and solid-liquid-gas systems. Chapter 7 provides data related to multiphase processes. We wish to call attention to two sections:

Section 7.4.1 Drop size and drop-size distributions Section 7.4.2 Bubble size and bubble-size distributions

These two subjects have not been treated systematically either in text books or in handbooks on stirred-tank mixing, although the results of both experimental and theoretical investigations have been reported on many occasions. Chapter 8 deals with gas-inducing mechanically agitated systems. The applications of this type of agitation system will become increasingly attractive from the standpoint of rationahzation of stirred-tank operations as well as environmental protection.

A review of this book will reveal many important research subjects that fall in the domain of stirred-tank mixing. We examined over nine hundred technical articles published since 1950. From this activity we could draw two important conclusions: (1) First, about 95% of the results reported in those articles were obtained by employing vessels whose diameters were less than 0.5 m. In industry, vessels with appreciably greater diameters are in daily use, and many more vessels will be designed and fabricated for future use. In view of this fact, much of the accumulated data and associated theory based on small- scale experiments will probably be

VI

inadequate for prediction of the performance of industrial-scale vessels. More data are undoubtedly needed to narrow the gap originating from this mismatch of equipment sizes. More specifically, advanced scale-up techniques, not rules, should be developed for precise prediction. In this respect it would be of great help if industries were cooperative in furnishing unsuccessful, as well as successful, examples of scale-up. (2) Secondly, there is a striking shortage of mixing data for systems in which highly viscous, non-Newtonian fluids are studied. It may be true that conventional agitated tanks are not satisfactory for such fluids. However, the authors of this book feel that many challenges still exist in this area.

In this book we have excluded from consideration two important subjects related to mixing: reactions and crystallization in stirred tanks. Most of the articles treating those subjects were found to place more emphasis on the development of rate expressions for the reactions or crystallization. Here, we have aimed to compile data correlating process parameters with agitated-tank geometry and the physical properties of the relevant fluids. For this reason we feel that reactions and crystallization should be treated differently.

It should be noted that several important journals issued in Russia, in Eastern Europe, and in the People's Republic of China were not considered in our search for mixing data. This is mainly because of difficulties in obtaining the original journals as well as the English-language versions. However, the authors sincerely hope that the pubhcation of this book will encourage other interested persons to compile mixing data published in the geographical regions mentioned above. Perhaps in this way some collaborative efforts will result in a substantially more complete compilation of engineering mixing data.

It is inevitable that errors, omissions, and misunderstandings will arise in a work of this type. The authors will be grateful if readers would take the time and trouble to point these out to us.

The authors would like to thank Professor R. B. Bird of the University of Wisconsin, who aided with advice and suggestions in reviewing and editing the title and preface to this book. Acknowledgment is also made to the staff members of Shinzan Sha, in particular, to Mr. K. Shinoe for his constructive advice during the preparation of the manuscript of this book, and to Ms. H. Tomita for the preparation of the camera-ready manuscript. Without their efforts this book could not have become a reality.

August, 1999

Reiji Mezaki Masafumi Mochizuki

Kohei Ogawa

Chapter 1 . Flow patterns

1.1 Single phase

Peters, D. C. and Smith, J. M., Ttans. Instn. Chem. Engrs., 45, T360 (1967) Fluid Flow in the Region of Anchor Agitator Blades

Experimental apparatus Vessel Type: flat-bottomed Diameter: 12.08 in Height: 18 in

Liquid contained Height: 14 in

Impeller Type: anchor Width of agitator blade: 1.0 in Wall/blade clearance: runs2A 0.125 in runs2C 0.50 in

Working fluids and their physical properties No.

1 lubricating oil 2 lubricating oil 3 glycerol (3% water) 4 silicone oil (MS200) 5 silicone oil (MS200)

6 1% polyacrylamide (aq.) 7 2% 8 4%

Reynolds numbers were computed Flow measurement technique

Photography Results

Tank: 22.9 cm diameter Anchor: 19.5 cm diameter, 2.5 cm wide, 90 rev/min Fluid: Silicone oils, 60 poise and 180 poise

Velocity components perpendicular to radii, along. normal to, and at 30* to agitator blade

^ (poise) 1.5 - 2.5 6.8 - 10.4 5.6 - 9.75 125 - 131 290 ~ 318

n 0.7

0.46 - 0.54 0.30 - 0.38

p (g/cm^) 0.865 0.885 1.25 0.96 0.98

/j(gs" Vcm) p(g/cm^) 2.12 - 2.57 1.01 40.4 - 50.4 1.02 3 0 8 - 4 6 0 1.04

using temperature-corrected viscosity data.

1 ' 1 ' '

t -

t«-

-t-

1 8 «

' ' ' LJ-' f

^^^-^^V^J

Hi)) ^^^Sr/w/y feCX^^^y^vy*!?^^^^

IS^^^^^r^'^^' Velocity profiles and flow patterns (Beckner, J. L., Ph. D. Thesis, 1965. University of Wales)

Chapter 1. Flow pattoms

\'-.

X y

16 p.p.s. (some points at 8 p.p.s.) NiRe)=21A, Run3-2C-10

25.4 p.p.s. (some points at 12.7 p.p.s.) iV(i?«)=105.3, Run3-2C-30

33.4 p.p.s. and 63.4 p.p.s. i\^(/?e)=143.4, Run3-2C-60

Flow patterns with glycerol

1.1 Single phas«

^" . . . • . - A*

• . 7 •.. ' . •M-Ji'.i 'V^ •••.. y

/f.- •

r'' * . > r ; * , .

/ 32.0p.p.s.

N*(Me)=l2.9, Run7-2C-40 64.0 p.p.s (some points at 32 p.p.s.)

iV*(/?^)=25.5, Run7-2C-80

' - -r - ^-. *

/

64.0 p.p.s (some points at 32 p.p.s.) N*(Jie)=3lA, Run7-2C-100

Notation a geometrical constant c clearance between blades and wall D paddle diameter DT tank diameter k usual power law characterization parameter n usual power law characterization parameter N rotational speed of stirrer p density of fluid /i viscosity of fluid

Note: Cxeneralized Reynolds numbers are based on a power law (expression for the shear rate/shear stress relationship as used by Beckner)

Flow patterns with 2% aqueous polyacrylamide, 1 in. blade, 0.5 in clearance

The normal Reynolds number: NiHe)=N^Dpln

The Reynolds nimiber for power-law fluids: N*{Re)=N^~''D^p/[k[a(\-n)Y'\

a=37-120 C/DT

Chapter 1. Plow patterns

Cooper, R. C. and Wolf, D., Can. J. ofChem. Eng., 46,94 (1968) Velocity Profiles and Pumping Capacities for Turbine Type Impellers

Experimental apparatus Vessel Type: flat-bottomed Diameter: 15 in Height: 20 in

Baffle Number: 4 Width: IV2 in

Impeller Type: 6 and 10 bladed turbines Dimension:

Turbine No.

1 2 3 4 5 6 7 8 9

10 11 12

Blade diameter in.

3 4 5 6 9 9 4 4 4 4 4 4

Blade width in.

0.6 0.8 1.0 1.2 1.8 3.6 0.6 1.0 1.2 1.4 1.6 0.8

Blade length in.

0.75 1.0 1.25 1.5 2.25 2.25 1.0 1.0 1.0 1.0 1.0 1.0

No of Blades

6 6 6 6 6 6 6 6 6 6 6

10

Working fluids Water and air

Flow measurement technique Hot-wire anemometry and three-directional pressure measurement

1.1 Siiigl* phas«

Results

J 2 .4 .« .B LO

Normalized radial velocity profiles for various turbine sizes and various rotational speeds in water.

Radial velocity profiles at different radial distances (4-in. turbine in water).

Notation VR radial velocity component W turbine blade width Z vertical distance

Chapter 1. Flow patterns

Bourne, J. R. and Butler, H., Trans. Instn. Chem. Engrs., 47, Til (1969) An Analysis of the Flow Produced by Helical Ribbon Impellers

Experimental apparatus Dimensions of vessels and impellers Type: flat-bottomed Volume: (1) 6 gals (2) 160 gals Geometry

The geometry of the helical ribbon mixer

Summery of principal dimensions

Impeller number

1 2 3 4 5

d (in)

10.303 11.030 11.142 11.370 34.34

d D

0.889 0.952 0.962 0.981 0.954

h D

1.06 1.06 1.06 1.06 1.06

W D

0.108 0.108 0.108 0.108 0.104

s D

0.345 0.345 0.345 0.345 0.345

Zo D

1.22 1.2L' 1.22 1.22 1.22

Working fluids and their physical properties Pseudoplastic fluids:

aqueous solutions of sodium carboxy methyl cellulose (CMC) and hydroxypropyl methyl cellulose (Celacol)

apparent viscosities 1 ~ 500 poise at concentrations up to 3 w/w% and shear rates of 1 -3001/s

1.1 Single phase

Flow-measurement technique Observations of solid tracers and cine-photography

Results

0-15

0-03 L

p-

y

Y

Y

Y U

[ T T" \" I I 1

i xa A* Y4 4*0 D20

20A X40 i AO 20 XS YCO X20 Y40

Y X O30 SX20 • A80 ^20

AAO O30 e+goao 3p V,

• ' 'J , Y20 V«0 O30 V20 30 X a oso aso vioo oso

30o3o ^ 3 0 YIO 030

lOOA S^OW VW 20X O60 vco 0*0

AID

vso

1 1 1 1 i i

I i 1

+ 30 _ X«0

•f20 _

Y l

YS X20

X20 X20

1 J ,„-J.,..J

^

y /

/ o

7

/

/ 0-A 0-6

NOTE > No values of r^/Ni bclwtcn 0 ondOOS

X: Howflex SP D:2'95< Celacol y;2'65%Celacol + :2-3% Celacol A; 2-0% Celacol Y: 1-65% Celacol

o-iep-

0-15

0-09 h

0-03

Y Y Y Y Y V Y Y Y Is

Y Y Y Y y V z

1 1 ' i X-t-

X

xAxo / X /+

/ X X^ /x+

Xf + Xo +

o o x+ X X ^

O y ^ -»ox /

x^l X X

/ / / . .

i 1 ! r---T—

X -t-

X+ X + XO X \ x j X XX + x \ O x \

+ X X X X \ X+ X O X + \ X X + X + \

+ X + X ^ X+ X + X + X

+ X X X X +

X

J l _ . 1 1 J

• r - —

1

\ "H X

\ H

X

X H

\ \

_LAI 0-A 0-6

+ : impeller I X: impeller 2 o: impellers

The distribution of axial fluid velocities in the core for impeller 2 pumping upwards

The distribution of axial fluid velocities in the core for impeUers 1,2 and 5 (6 gal and 160 gal tanks) pumping downwards

Notation d outside diameter of ribbon D inside diameter of tank h height of ribbon N rotational speed of impeUer r radial coordinate Ri inside radius of ribbon 5 pitch of ribbon Vt axial fluid velocity W width of ribbon Zo static height of liquid in tank

Chapter 1. Flowpatt«ms

Takashima, I. and Mochizuki, M.J. Chem. Eng. Japan, 4,66 (1971) Tomographic Observations of the Flow Around Agitator Impeller

Experimental apparatus Vessel Type: flat-bottomed Diameter: 450 mm Height: 600 mm

Liquid contained Height: 520 mm

Baffle Number: 4 Width: 45 mm

Impeller Type: radial flow turbine Diameter: 150 mm Number of impellers: 1 Number of blades on impeller: 8 Width of impeller blade (parallel to shaft): 34 nun Off-bottom clearance: 260 mm

Results

Flow profile in each sectional zone of various types of 8 blades turbine agitator

1.1 Single phas«

Double helical flow model for agitator blade

Notation u tangential velocity at blade tip V absolute velocity of flow observed on the fixed coordinate Vr radial velocity of flow w relative velocity of flow observed on the rotating coordinate *P angle of the blade (see attached figure) Fb circulation of bound vortex around the blade 0 Vr/u flow coefficient CD angular velocity of impeller

Subscript 2 outer point of flow from the impeller

10 Chapter 1. Flow patterns

Murakami, Y., Fujimoto, K., Shimada, T, Yamada, A. and Asano, K.,/. Chem.

Eng. Japan, 5,297 (1972) Evaluation of Performance of Mixing Apparatus for High Viscosity Fluids

Vessel and impeller geometry

Impellers and vessels

(a) anchor (b) paddle (c) helical ribbon (d) mixing apparatus with two agitator axes having multidisks Z>=12.2cm, H=D, rf=0.90D and 0.95A 6=0.1Z), 1)^=6.0 and 9.0 cm, /=0.5/)rf and 0.22Drf

Working fluids and their physical properties Liquid: aqueous solutions of com syrup

Viscosity: about 200 poise Flow measurement technique

Photography Results

t " I I h t I t I 0 0 . 5 1.0 - - * ' V Q XTTnd

Anchor-tangential velocity

ll-H'

h I i i I MM I 0 0 . 5 1 . 0 *"•* V Q ^Tind

Paddle-tangential velocity

RE - 0.07

[ol

1 XjlfUlDK

1 Lfflll^ W?nfK

11

j •

I

Sg /S>KP1

/"^

0 0.5 1.0 "adn

Helical ribbon (velocity profiles)

1.1 Single phase 11

Mixing apparatus with two agitator axes having multidisks (velocity profiles at a section 6 mm apart from the disk at 15 mm space intervals)

^CIRCULAR ANNULUS . KEILSPALT MASCHINEN

CIRCULAR ANNULUS (ROTATING CYLINDER)

ECCENTRIC CYLINDERS

HELICAL RIBBON WITH SCRAPE

MIXER WITH TWO AGITATOR AXES HAVING DISKS

EXTRUDER

\ - C & R REACTOf

|CL>

s Q

0.01 0.02 0.0^ 0.1 0.2

1 -K , C/D, I/D^

Shear characteristics

ELICAL SCREki (NAGATA)

HELICAL SCREW (GRAY)

Notation b blade width of helical ribbon, cm d impeller diameter, cm D vessel diameter, cm Dd disk diameter, cm gr gravitational conversion factor, g cm/G sec^ / distance between disks, cm n rotational speed, 1/sec Pv power consumption/unit volume, Gcm/seccm^ Vb, V2 tangential and axial velocity, cm/sec 77 liquid viscosity, poise K ratio of impeller diameter to vessel diameter

12 Chapter 1. Flow pattoms

Ito, S., Ogawa, K. and Yoshida, N.,/. Chem. Eng. Japan, 8,206 (1975) Turbulence in Impeller Stream in a Stirred Vessel

Experimental apparatus Vessel Type: flat-bottomed Diameter: 312 mm


Baffle Number: 4 Width: 10.4 mm

Impeller Type: a standard six-bladed turbine Diameter: 104 nmi Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 26 nrni Width of impeller blade (parallel to shaft): 20.8 nmi Off-bottom clearance: 156 mm

Working fluids and their physical properties an aqueous solutions of K4Fe (CKk and KaFe (CN)6. The kinematic viscosities of the solutions are the same as that of water

Flow measurement technique Measurement of diffusional mass transfer rate using a multi-electrode

Experimental conditions Impeller speed: 60,90 and 120 rpm

Results

Notation r_ radial position, mm Ui mean velocity of i component, cm/sec UT impeller tip velocity, cm/sec 2 axial position, mm

Subscript r, z, G radial, axial, tangential component

65 75 85 95 105 t15 125 r, mm

Turbulence intensity

1.1 13

Van't Riet, K. and Smith, J. M., Chem. Eng. ScL, 30,1093 (1975) The Trailing Vortex System Produced by Rushton Turbine Agitators

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 44 cm (2) 120 cm

Baffle Number: 2

Impeller Type: six-bladed disc turbine Diameter: (1) 17.6 (2) 48 cm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): Z)/4 Width of impeller blade (parallel to shaft): D/5

Working fluids and their physical properties Fluid: tap water and water/glycerin solutions Tracer: polystyrene particles (diameter 0.5 mm)

Flow measurement technique Photography

Experimental conditions Impeller speed: 5 rps Direction of

R e s u l t s rototion

Schematic thee dimensional view of the trailing vortex pair.

Dirtetion

Schematic two dimensional view of the flow in the stirrer blade region. S, stagnation point.


, Blode

>^<A{»,<9xlO'

500

A/ff,«300

The vortex axis position at different iV)?,.

0

o \ % I .1 (A

c E o

lOh

' ' ' 1 \ I »

^ l-5xlO*</V^,<9xlO*

/V/?,*500

%5-300 Slopc-2

0 5 -1 M I I

I J I I I

The dimensionless angular velocity distribution.

# , Averages for 1.5X 10^< NR, > 9 X 10^; O, Measuring points for 7V)?,=300 ; Z)=17.6cm

10

Dimensionleis rodius from vortex axis. r/Oin\0

Notation D stirrer diameter, m N stirrer speed, 1/sec NRt Reynolds number, pND^/j], dimensionless r radial distance, m 7} dynamic viscosity, Nsec/m^ p density, kg/m^ (o angular velocity, 1/sec

1.1 Single phase 15

Gunkel, A. A. and Weber, M. E.,AIChE Journal, 21,931 (1975) Flow Phenomena in Stirred Tanks Part I. The Impeller Stream

Experimental apparatus Vessel Type: flat-bottomed Diameter: 45.7 cm Height: 45.7 cm

Baffle Number: 4 Width: 0.17

Impeller Type: standard six-bladed disk turbine Diameter: 22.8 cm Number of impellers: 1 Number of blades on impeUer: 6 Length of impeller blade (perpendicular to shaft): //Z)=0.25 Width of impeller blade (parallel to shaft): w/D=0.2 Off-bottom clearance: T/2

Working fluid Air

Flow measurement technique Hot-wire anemometry

Experimental conditions Impeller speed: 200,400,600 and 950 rpm ^^

Results

Notation D E,(n)

I n N T w

impeller diameter one-dimensional energy spectrum in the frequency space length of impeller blade j&requency rate of rotation of impeller tank diameter impeller blade width

10

10"

10'

10"'

10"

10

10-

10

^4-400 rpm, s - l c m , z - 0 . O-O

N-800rpm, s-7cm^

2 - 0 , 0 -0

' N-600rpm, s - 1 cm.

2—0.5 In , 0 - 0

N-200rpm, $-1cm,

2 - 0 ^ 0 - 4 3 '

probe in vertical

plane

23468 10" lrf 10 10^ 10*

n (H2)

One dimensional energy spectra in the impeller stream.


Hiraoka, S., Yamada, I. and Mizoguchi, K.,/. Chem. Eng. Japan, 12,56 (1979) IWo Dimensional Model Analysis of Flow Behavior of Highly Viscous Non-Newtonian Fluid in Agitated Vessel with Paddle Impeller

Dimension of vessel and impeller 0.3 ^d/D< 0.9

Computational conditions 10 < Re {=^DVp/fi)

Computational results

d/D > 0.5 n «o.e

Rcf 0

(p/>*.v)

Non-Newtonian viscosity distribution for paddle of rf/2>=0.5

Notation d impeUer diameter, m D vessel diameter, m K fluid consistency, k g / m (sec)^"** n flow behavior index J? radial coordinate, m Re Reynolds number, DVp/fi, dimensionless V rotational velocity of vessel wall, m / s e c p non-Newtonian viscosity, N s e c / m ^ /Xar apparent viscosity, N s e c / m ^ ft* dimensionless non-Newtonian viscosity, fi/po,

dimensionless p fluid density, kg/w? (o dimensionless vorticity

Non-Newtonian viscosity distributions for different size impellers

^^^\w^^m^ I {(cDw+2)}. N J ^-^mv/DT

Superscript — averaged value

Subscript NN non-Newtonian fluid N Newtonian fluid w vessel wall

1.1 SingI* phase 17

Kuriyama, M., Inomata, H., Aral, K. and Saito, S.,AIChEJoumaU 28,385 (1982) Numerical Solution for the Flow of Highly Viscous Fluid in Agitated Vessel with Anchor Impeller



Impeller Type: anchor Diameter: about 128 mm Height: 115 mm Number of impellers: 1

Working fluids Aqueous solutions of com syrup containing solid-particles as tracers


Experimental conditions Results

i..

: C«tcuUt«d • : ExptrimtnUI

Tangential velocity distributions (Be = 1)

(K 07 0.91.0 r/R H

—: CatcuUted • :Exp«rim«nU(

Radial velocity distributions {Re = 1)

Notation d impeller diameter N rotational speed of impeller U, V velocity components VB tangential velocity of blade tip Re Reynolds number, d Nl v, dimensionless V kinematic viscosity


Mochizuki, M. and Takashima, I., Kagaku Kougaku Ronbunshu, 8,487 (1982) The Flow around Turbine Type Impellers



Impeller Type: six-bladed disk turbine Diameter: 225 mm Disk diameter: 150 mm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 56 mm Width of impeller blade (parallel to shaft): 28,46,56, 75, and 112.5 mm Off-bottom clearance: 225 mm

Working fluid Tap water


Experimental conditions Impeller speed: 62.5 and 99.4 rpm

Results

ry piong V, V,

Velocity diagram of the flow around impeller

1.1 Single phas« 19

I

2/D Part0 (2) 0.250 j , 1 r

0235

^ 9

lil L

T~l r

^-h

O T-n «-

^ T

^

T~1 r-®

i_ai L_

f" •f^f

j<JiJ J L.

4

upper edge btade

B/Ort/2

0 10 0 0 0 10 0 10 0 1-0 0 10

Center of

B/0^1/5

B/DrI/8

Velocity profiles at impeller tip

Tomograms with rotating cameraB/D=l/5, 62.5 rpm

Notation B width of impeller blade D impeller d iameter U2 tangential velocity V absolute velocity of flow z vertical distance along z-axis 0 normalized velocity, v/u2 (p angle of polar coordinate Q) angular velocity of impel le r

Subscripts 1 inner area of impeller 2 outer area of impeller 3 top and bot tom area of impeller r radial component z axial component (p tangential component


Mochizuki, M. and Takashima, L, Kagaku Kougaku Ronbunshu, 10,399 (1984) Distribution of Pressure on the Surface of Blade of Turbine Impeller

Experimental apparatus Vessel Tjrpe: flat-bottomed Diameter: 450 mm



Impeller Type: six-bladed disk turbine Diameter: 225 mm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 56 nmi Width of impeller blade (paraUel to shaft): B/Z)=l/2,1/5, and 1/8 Off-bottom clearance: 225 mm


Flow measurement technique Visualization

Experimental conditions Impeller rotational velocity:

82,104 and 106 rpm Results

Sock surface Front surface

Notation B width of impeller blade, m D impeller diameter, m N impeller rotational speed,

1/min !cl B/D»1/8 N*106rpm

Visualization of flow on the surface of blade with oil film method

1.1 Single phase 21

Kuboi, R. and Nienow, A. W, Chem. Eng. Sci., 41,123 (1986) Intervortex Mixing Rates in High-Viscosity Liquids Agitated by High-Speed Dual Impellers

Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.29 m

Liquid contained Height: 0.29 m

Impeller Type: (1) angled blade (2) disk turbine Number of impellers: 2 Number of blades on impeller: (1) 6 (2) 6

Ct>N

T^ ,x

i> Boffins. 0-lT.

: s ] .

HD»T/2 H l|

6 Blodts

45»

- * 4 D M I

MA OH T 6 Blodts

JL 0/5

T-0-29in

A schematic diagram of the equipment.

Working fluids, their physical properties and experimental conditions Physical properties and experimental conditions

(a) Tunnel G140 com syrup/saturated benzoic acid (mass ratio = 5.7:1) p =1,347 kg/m^ n =1.00 Pas (221C): ^ =1.35 Pas (20^:) Re range: 70^140; speed range =3.3—6.7 rev/s

(b) 0.30% by wt Goodrich Carbopol in water (pH 4.4) p =1,000 kg/m', T =22.27°-^ ; Ui=1.54r°" ; To=20.0 Pa Re range: 85 ~ 150 ; speed range=6.3-^7.5 rev/s

(c) 1.4% by wt Hercules 7H4C CMC in water (neutral) p = 1,000 kg/m', T= 12.2 f" ; t;i=9.82r' ' Re range: 72^190; speed range=4.3~8.0 rev/s

Flow measurement technique Photographs of solid-particle tracers

22

Results

Chapter 1. Plow patterns

Flow patterns with com syrup: (a) upward pumping combination (5 rev/s); (b) downward pumping (three gross vortices (3,33 rev/s)); (c) downward pumping showing the additional fourth small vortex (5 rev/s)

Flow patterns with Carbopol: (a) upward pumping combination (5.3 rev/s); (b) downward pumping combination (5.3 rev/s)

Notation Cb Ci impeller clearance above the base, m D impeller diameter, m H liquid height, m T tank diameter, m

1.1 Single phas* 23

Yianneskis, M., Popiolek, Z. and Whitelaw, J. E.J. Fluid Mech., 175,537 (1987) An Experimental Study of the Steady and Unsteady Flow Characteristics of Stirred Reactors




Impeller Type: six-bladed disk impeller Number of impellers: 1 Number of blades on impeUer: 6 Dimensions:

Impeller Diameter Disk diameter mm mm

Blade width mm

Blade length mm

r/4 r/3 TI2

73.5 98.0

147.0

55.12 73.5

110.25

14.7 19.6 29.4

18.37 24.5 36.75

Off-bottom clearance: 7/4, 7/3 and 7/2 Working fluid

Water Flow measurement technique

Laser-Doppler anemometry Experimental conditions

Temperature: 20 ± 2*C Impeller rotational speed: 300 rpm

Results

Flow visualization at d =42.5''; (a) i>=r/3, C=r/2, N=3Q0 rpm. (b) />=r/3, C=r/4, Ar=300 rpm

Notation T cylinder diameter, nmi

(a) (b)

24 Chapter 1. Flowpatt«ms

Kamiwano, M. Saito, E and Kaminoyama, M., Kagaku Kougaku Ronbunshu,

14,316 (1988) Flow Pattern and Apparent Viscosity of Pseudo-plastic Liquid in a Stirred

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1)0.1 (2)0.2 (3)0.3 (4) 0.4 m

Liquid contained Height: (1)0.1 (2)0.2 (3)0.4 (4) 0.4 m

Impeller Type: six-bladed flat turbine Diameter: (1) 0.05 Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: (1)0.05

Working fluid Pseudoplastic: 1.2 wt% aqueous solution of hydroxyethyl cellulose

Experimental conditions Rotational speed of impeller (1/sec)

(1)16.7 (2)6.88 (3)4.03 (4)2.72 Flow measurement technique

Image sensor velocimetry Results

(2)0.10 (3)0.15 (4) 0.20 m

(2)0.10 (3)0.15 (4) 0.20 m

-Q05

- 0 1 Q05

(a) V, component

(a) Vr component

Distribution of flow velocity expressed by three-dimensional components (D=0.2m, it =6.88 s *)

-I 1.4

V-2 < | l . O ^

(b) lit component

(b) Vet component

Distribution of flow velocity expressed by three-dimensional components (D=0.2 m, «=6.88 s *)

1.1 S ingI * phas«

0

a:

[-{U

-0.6

(c) Vt component

Distribution of flow velocity expressed by three-dimensional components (Z>=0.2 m, n=6.88s~*)

Notation D vessel diameter, m n impeller rotational speed, 1/sec R radius of vessel, m V flow velocity, m/sec Z height of vessel, m

Subscript r, 9t, z axes of cylindrical coordinate

25

Cenler axis of vessel

blade

k » \ V V ... _

[

{ : = : -R=0.lV-

Bottom o( vessel 0.5 m/5

Flow pattern represented by dimensional vector in r-z plane (D=0.2 m, «=6.88 s"*)


Winardi,S., Nakao, S. and Nagase, Y.,/. Chem. Eng. Japan, 21,503, (1988) Pattern Recognition in Flow Visualization around a Paddle Impeller


Liquid contained Height: 400 ram


Impeller Type: four-bladed paddle impeller Diameter: 160 mm Number of impellers: 1 Number of blades on impeller: 4 Width of impeller blade (parallel to shaft): 40 mm Off-bottom clearance: 200 mm

Working fluid Water


Experimental conditions Impeller rotational speed: 120 rpm

Results

// Lli "^^

x>-. -- . - -

\ . 4

; »'' I

**••" ! I i " —1« \ \ i . . . . : J 5 . . . ^ ^

\ \m.y' / I I-jJ / • J I

rrtS

Icl

(a) Discharge pattern, TD (b) Cross pass pattern, TP; x mark

indicates disappearance of a particle from the impeller

(c) Asymmetric Discharge patten, UD (d) Illustration of Weak Discharge

patten, WD (e) Illustration of Weak Cross-pass

patten, WP


Komori, S. and Murakami, Y.,AIChE Journal, 34,932 (1988) Turbulent Mixing in Baffled Stirred Tanks with Vertical-Blade Impellers

Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.29 m Height: 0.7 m

Liquid contained Height:/) and 2Z)

Baffle Number: 4 Width: 0.029 m

Impeller Type: four-bladed paddle Diameter: 0.145 m Number of impellers: 1 and 2 Number of blades on impeller: 4 Blade width: 0.029 m Blade thickness: 0.003 m

^^o^P S H im^ers ^ / ^ ^-/^ A H=2D 2 0.14--1.70 1.0 - 0.5L/Z) B H=2D 2 1.0 0.06-0.90 C H=2D 1 - 0.10-1.50 D H=^D 2 0.10-0.60 0.5 (1.0 - 0.5L/Z)) E H=D 1 z 0.06 - 0.90

Working fluid Water

Flow measurement technique Laser-Doppler velocimetry


28

Results

Chapter 1 . Flow pattoms

2S0

200

*- 150

100

50h

OL

Afl-2.0s'^ on»1.0s*^

o

L/0-0.2

(Al

tlg/D*1.0

1/0-0.3 VI>*^-2 hj,/0«0.425 ^

O O

0.004

O.OOC

0.001 J

0.01

0.02

0.04 ^0.0« ^0.08

0.10 0.20

(Bl (C) (0)

CxpertaenUI Group

(CI

Maximum (highest) mixing efficiency and minimum energy consumption for each experimental group

1 . * » . l

I: . .**-"*. I l l

3,..«V«*>N^^ I

];.......—;;] a::::!!" -*•

\ ''"-'ii 3:»r»»«... . , , . j . ' .* .»%*«.. . ,^, .

in • e.i VD • 0.7

Velocity vectors and flow patterns in a double-impeller tank, H-2D, «=150 rpm (group A) (a) with lowest mixing efficiency, (b) with highest mixing efficiency

1.1 Single phase 29

Velocity vectors and flow patterns in a double-impeller tank, H=2D, «=150 rpm (group B) (a) with lowest mixing efficiency, (b) with highest mixing efficiency

1 1 1 [ 1 11 i 11111 1 1 il 11 {11 i 1 JJWHTTI

'i 11 ^n i 1 i 1 ij i 1 il LTI1111 (IIX1 'ft/ W SMK '1 w iVw 1 m 111iII11 i 111 II 1 ;[illlJIJ||||/|| TTTrTTT^MTtvn jJflTjT m

•lii 'inuiiii^i •llliSlllllli:!!

lUifmTmil^ PW™ 1 iJirm] j 1111 [ I TTl [TtJ 1 !| 1 1111 111 111 I'l ill J1 1111111 1M 1 III \TI\ 3 m l

J iJinJIjLH ^illJITriTnfllll

surtlng Point

Tracer traveling path and lattices which indicate velocity-measiuement points in a double-impeller tank, H==2D, n=150 rpm (group A)

Notation D tank diameter Ettox maximum value of mixing efficiency hb vertical distance between bottom of a tank and center of lower impeller H water depth L vertical distance between double impellers n impeller rotational speed P' 6 energy consumption P- 6mn minimum value of energy consumption P- 6


Wu, H. and Patterson, G. K., Chem. Eng. Scu, 44,2207 (1989) Laser-Doppler Measurements of Turbulent-Flow Parameters in a Stirred Mixer

Experimental apparatus Vessel Type: flat-bottomed Diameter: 27 cm Height: 27 cm

Liquid contained Height: 27 cm

Baffle Number: 4 Width: lO/T

Impeller Type: six-bladed disk turbine Diameter: 9.3 cm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): D/4 Width of impeller blade (parallel to shaft): D/5 Off-bottom clearance: T/3

Working fluid Water


Experimental conditions Impeller speed: 100, 200 and 300 rpm

Results

200 rpm r(cm)

D 5 0 o 6.0 A 7.0 • 7.7 0 9 0 V J0.5

1 ))J3

•^•v> > I > I

Mean radial velocity profiles at various radial positions.

0.1 02 0.3 0.4 09 0.$ 07 08 Ua/U,ip

Mean tangential velocity profiles at various radial positions.

1 .1 S i n g l e p h a s e 31

-^V,o -0.05 0.00 0.05 0.10

Mean axial velocity profiles at various radial positions,

0.15 0.20

- T - -r- -r-r»5cm

total random O O too rpm

000 0.05 0.iO 015 0.20 025 0.30 0.35 Ur'/Uiip

Profile of radial turbulence intensity near the impeller tip.

0.00 0.05 0.10 0.15 0 2 0 0 2 5

Profile of tangential turbulence intensity near the impeller tip.

Notation D impeller diameter r radical coordinate T tank diameter u fluctuation velocity U mean velocity Uiip impeller tip velocity w impeller blade width z axial coordinate

0.30 055

1

1

0.00 0.05 0.10 015 0 2 0 0 2 5 0 3 0 035 u;/u,ip

Profile of axial turbulence intensity near the impeller tip.

Subscripts r, 6,2 radial, tangential, axial

Superscript root-mean-square value


Ranade, V V and Joshi, J. B., Ttam. Instn. Chem. Engrs., 68, Pirt A. 19 (1990) Flow Generated by a Disc Turbine: Part I Experimental

Experimental apparatus Vessel Type: flat-bottomed Diameter: 300 and 500 mm

Baffle Number: 4 Width: r /4

Impeller Type: six-bladed disc turbine Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: H/2

Vessel Impeller diameter, diameter,

r, mm Z), nmi 300 100 500 168

Disc diameter,

mm 67

117

Disc thickness,

mm 2.7 3.7

Blade thickness.

mm 2.0 2.7

Blade width=i)/5. Blade length=Z)/4. Hub diameter=25 mm. Hub height=25 mm. Shaft diameter=19 mm.


Flow measurement technique Laser-Doppler anemometry

Results

0 0*1 0*2 0*1 0*4 0*1 0«l 0*7 0*t 0*1 !•( OIMCMSIONLESS RAOIAL COOHOINATE , ( r- R,)/(l^fl, I

Radial profile of maximum mean radial velocity in the impeller stream.

1.1 Single phase 33

Curve Reference T mm

D mm Measurement Technique

1 2 3 4 5 6 nt work

292 381 290

1,000 270 89

300

101.6 101.6 96.7

333.3 93.0 30.4

100.0

Streak photography Hot wire anemometer Laser Doppler anemometer Hot film anemometer Laser Doppler anemometer Laser Doppler anemometer Laser Doppler anemometer

1. Cutter, L A.. \9&I,AIChEJ, 4:485. 2. Cooper, R. G. and Wolf, D., 1968, CanJCkem EngScu 46:96. 3. Van der Molen, K. and Van Maanen, H. R. E., 1978, Chem Eng Sci, 33:1161. 4. Drbohlav, J., Fort, L, Maca, K. and Placek, J., 1978, CoU Czech Chem Commun, 43:3148. 5. Wu,. H. and Patterson, G. K., 1987. Private Communications. 6. Chen, K. Y, Hajduk, J. C, and Johnson, J. W. 1988, Chem Eng Commun, 72:141.

0»% 0*2 0«} 0>4 0*f 0«« ••? 0*ft OtMCHSIOMLKSS RADIAL COOHOINATE f r - l t | ] / | l | . f l , |

Radial profile of maximum mean tangential velocity in the impeller stream.

Notation D impeller diameter, m H height of vessel, m N impeller rotational speed, 1/sec Q flow rate, mVsec r radial coordinate, m R tank radius, m Ri impeller radius, m T tank diameter, m U mean velocity, m/sec Utip impeller tip velocity, m/sec V tangential mean velocity, m/sec 2 axial coordinate, m

0 0.1 0-2 OO 0*4 0*S 0*1 MMCNStOflLESS RADIAL COORDINATE (r -R| | / (R-R|)

Radial profile of radial pumping capacity.


Kaminoyama, M., Saito, F. and Kamiwano, M.J. Chem. Eng. Japan, 23,214 (1990) Flow Analogy of Pseudoplastic Liquid in Geometrically Similar Stirred Vessels Based on Numerical Analysis

Experimental apparatus Dimensions of vessel and impeller

Vessel type: flat-bottomed Baffle: non-baffle Impeller: (1) six-bladed turbine Number of impeller: (1 )1

analysed region

'fh

P-j

d/DaO.5 H/D-1.0 H/D=0.5

bw/D=OJ bl/D=0.125 ds/O = 0.0^

(a)

onolysed region

Ks20

Ksit I • d/DsO.9 112 H/0=:1,o

bwl/DsO.l bvv2/D=0l

tt»'2 ds/DsQ.O^

(2) paddle (3) anchor (2) 1 (3) 1

onolysed region

.Ks21

H/D«1.0 h 70=0.5

ds/0 = 0.0^

Schematic diagrams of mixers and analyzed regions: (a) turbine impeller mixer; (b) paddle impeller mixer; (c) anchor impeller mixer

1.1 Single phase 35

Working fluid A highly viscous pseudoplastic Ellis liquid


1t

shofl impeller

J = l

vessel wall

O.Sm/5

J=A

(a)

K = l I.OwA

(b)

K=n

Velocity vector distributions in turbine mixer (Z)=0.2m,«=3.33s"'): (a) on r-z plane at /=l and 4; (b) on r-0 plane at/C=l and 11

Velocity vector distributions in paddle mixer (Z>=0.2 m, «=3.33 s *): (a) on r-z plane at /=l and 4; (b) on r-d plane at =11 and 21

36 Chapter 1 . Flow patterns

Velocity vector distributions in anchor mixer (Z)=0.2 m, «=0.83 s *): (a) on r-z plane a t / = l , 5 and 9; (b) on r-0 plane at/C=l, 11 and 20

Notation hi blade length bw blade width d impeller diameter ds shaft diameter D vessel diameter h impeller height (off-bottom clearance) H liquid height / mesh number in Q direction K mesh number in z direction 0) rotational speed

1.1 SingI* phase 37

Jaworski, Z., Nienow, A. W, Koutsakos, E., Dyster, K. and Bujalski, W, Trans. Instn. Chem. Engrs., 69, P^t A, 313 (1991) An LDA Study of Turbulent Flow in a Baffled Vessel Agitated by a Pitched Blade Turbine



Baffle Number: 4 Width: T/10

Impeller Type: 45° pitched bladed turbine Diameter: T/3 Number of impellers: 1 Number of blades on impeller: 6 Projected height of impeller blade: D/5 Off-bottom clearance: 7/4 or T/2

Working fluid Water


Experimental conditions Impeller speed: 101/sec Temperature: 20°C Reynolds number: 24,000

Results

Notation C impeller off-bottom

distance, m H liquid depth in vessel, m R dimension less radial

coordinate T vessel diameter, m V dimensionless mean

velocity V dimensionless r.m.s.

fluctuating velocity Z dimensionless axial

coordinate

Subscripts R radial component RZ dimensionless resultant

for (r-z) Z axial component

Dimensionless velocity profiles for C/H=l/4: (a) VR against Z ; (b) Vz against R.


Dyster, K. N., Koustakos, E., Jaworksi, Z. and Nienow, A. W, Trans. Instn. Chem. Engrs., 71, P ^ A. 11 (1993) An LDA Study of the Radial Discharge Velocities Generated by a Rushton Turbine: Newton Fluids, J?e > 5




Impeller Type: six-bladed Rushton turbine Diameter: T/3 or T/2 Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): D/4 Width of impeller blade (parallel to shaft): D/5 Off-bottom clearance: T/2

Working fluids and their physical properties

^, J Refractive Density Viscosity *" ^ Index (kg/mO (Pasec)

Water Polyethylene glycol Glucose solution Glycerol solution 100% Glycerol

1.333 1.359 1.475 1.457 1.471


Experimental conditions Impeller speed: 50 - 800 rpm

Results

1,000 1.064 1,330 1,260 1,260

1X 10~^ 8.85 X10"^ 105x10^

0.248 1.16

<5: correlating parameter V;/V,ip = 0.454 - 0.128 (r/i?)

Notation D impeller diameter, m N impeller rotational speed, 1/sec Superscripts r radius of measurement point, m ' root mean square value R impeller radius, m — time average value T tank diameter, m Vr radial component of fluid velocity, m/sec Vtip impeller tip speed, TTND, m/sec

1.1 Single phase 39

Mishra, V R and Joshi, J. B., TVans. Instn. Chem. Engrs., 71, ftirt A. 563 (1993) Flow Generated by a Disk Turbine; Part III: Effect of Impeller Diameter, Impeller Location and Comparison with Other Radial Flow Turbines



Baffle Number: 4 Width: r/10

Impeller Type: the standard disc turbine (DT), a straight blade turbine (SBT), a curved blade turbine

(CBT), a modified disc turbine (MDT), and a Brumagin impeller (BT)

0/5

Y J 0 / « -

l^o/*-J

(•) DISC TURBINE ( O T )

f atmn \

— llOnim —

- IT-TLI^

•-S2mm •«{

Mrnm-A 1*31

gyeVATIpN

-1

EMO VIEW

(b)

PERSPECTIVE VIEW

MODIFIED DISC TURBINE (MPT)

( 0 BRUMAGIN IMPELLER

r« tt.Siniii

(d) CURVED BLADE TURBINE ICBT)

<«> STRAIGHT BLADE TURBINE (SBT)

Various designs of radial flow impellers.


Impeller design details

Impeller Name

DT125 DT DT250 MDT Brumagin CBT SET

figure No. 2a 2a 2a 2b 2c 2d 2e

Impeller diameter

mm 125 167 250 167 167 167 167

i.d. mm 16 16 16 16 16 16 16

Hub details o.d. mm 25 25 25 25 36 25 25

height mm 26 26 26 25 28 25 50

Blade width mm 32 42 62.5 52 35 -

71

Blade height mm 24 34 50 38 34 34 34

Blade thickness

mm 2.0 2.0 2.0 1.5 3.0 2.5 2.0

Off-bottom clearance: DT HI2, H/3, and H/A, all other impellers H/2 Working fluid

Water Flow measurement technique

Laser-Doppler anemometry Results

UO ISO ISO 210 RADIAL 01 STANCE,r(mmI

(a) (b)

Radial velocity at the impeller centerline.

Notation H liquid height, m r radial coordinate, m T vessel diameter, m U mean radial velocity, m/sec Vt impeller tip velocity, m/sec Z axial coordinate, m

1.1 Single phase 41

Mishra, V R and Joshi, J. B., Trans. Instn. Chem. Engrs., 72, Part A. 657 (1994) Flow Generated by a Disc Turbine: Part IV: Multiple Impellers


Liquid contained Height: 1.57

Baffle Number: 4 Width: 0.1 T

Impeller Type: a standard disc turbine (DT) and a pitched blade downflow turbine (PTD) Diameter: DT 100 nun; PTD 100 mm Number of impellers: 2

Configurations of impeller combinations.

IC (xn)

0.05 0.1 0.1 0.1 0.15 0.225

C (m)

0.2 0.1 0.15 0.2 0.15 0.112

Name of the

DT-DT

DDl DD2 DD3 DD4 DD5 DD6

configuration

DT-PTD

DPI DP2 DPS DP4 DP5 DP6

Working fluid Water


Experimental conditions Impeller speed: 5 rps Impeller Reynolds number: 6.25 x 10

Power number, flow number, hydraulic efficiency of multiple disc turbine impellers.

Clearance between the two

impellers /C, mm

50 100 100 100 150 225

Clearance from the bottom

C mm

200 100 150 200 150 112.5

Overall power

number Np

7.77 7.77 7.77 7.77 9.95 9.95

1

Upper impeller

0.61 0.60

Flow number

Lower impe-Uer

0.60 0.65

Total

0.92 0.55 0.84 0.78 1.21 1.25

Pumping

effectiveness

11.9 7.0

10.9 10.1 12.2 12.6

Hydraulic efficiency

Mean

19.4 10.7 19.1 19.9 27.0 33.5

Turb ulent

17.8 14.3 17.2 13.4 15.6 19.4

Total

37.3 25.1 36.3 33.4 42.6 52.9


Power number, flow number, hydraulic efficienqr of multiple (disc turbine-pitched blade turbine) impellers.

Clearance between the two

impellers /C, mm

50 100 100 100 150 225

Clearance from the bottom

C mm

200 100 150 200 150 112

Overall

power number

Np

6.53 6.76 6.75 6.98 7.23 7.21

]

Upper impe

ller

0.83 0.86 0.87 0.86 0.82 0.78

low number

Lower impeller

0.96 0.76 0.79 0.73 0.74 0.70

Total

1.79 1.62 1.66 1.59 1.56 1.48

Pump

ing effectiveness

27.43 23.89 24.58 22.73 21.65 20.53

Hydraulic efficiency

Mean

35.1 40.7 33.9 34.2 30.5 24.6

Turb ulent

16.9 23.6 19.9 18.1 17.06 17.8

Total

52.0 64.3 53.8 52.3 47.5 42.4

Results

'//

1 it 11 mi 1 1

\ l l i f / > u i

\\\

. . . . ; • ^Z-^"-^* i . l^C^r*

lf\\ 111 !T \ / ifttt11 111 itji i \ \

n 111 M f

\\\\ * 1

• / l l

< • •

rut 11111

n !i j iM t i I [1

m i M 11\>»

1111 /11*" . . l \ l ^ > - -

iv^ •"• r n r n . r,,.. I . X t < » A \ t ,

' / I I / j i i « / »

i—i-iMlLi '*— yi 11 I T ( I / 1 / ^ 1 / I I f j / M l r .

. / I

•M • M

..J .rl

^ H§iulr

M r I VI M »

\ f 1 1 INNVW

U i i J i / / ' '

(b) 10 W> W (I)

Flow pattern (vector plots) generated by disc turbine-disc turbine (DT-DT) combination.

No.

A B C D E F

C,m

0.2 0.1 0.15 0.2 0.15 0.112

IC,m

0.05 0.1 0.1 0.1 0.15 0.225

Nomenclature

DDl DD2 DD3 DD4 DD5 DD6

1.1 Single phase 43

/ / U t M M I

\ l t i l 1 H "

fTT/TliiiJ

lY|U''"

l / l l i / / / /

nwwvv

v\\

• l l i ^ / / i

% //

I M l / / / " " • ; ,

I f f / j / / / / , . M

n i i / j / / / i . . j

1 M l 111 /111 m .

1 l-'-^

, ^ . . N \ \ \

| | l \ lliw •'

rrrAi) if,.,'l\ innnii

1 Mj \ / u n M M.

Flow pattern (vector plots) generated by disc turbine-pitched blade downflow turbine (DT-PTD) combination.

No.

1 2 3 4 5 6

C,m

0.2 0.1 0.15 0.2 0.15 0.112

/Cm 0.05 0.1 0.1 0.1 0.15 0.225

Nomenclature

DPI DP2 DP3 DP4 DP5 DP6

Notation C clearance of the bottom impeller, m or mm D impeller diameter, m H height of liquid from bottom, m or mm IC clearance between the centers of the two impellers, m or mm N impeller speed, 1/sec Np power number, P/N^D^ P impeller power consumption, W T vessel diameter, m w blade width of PTD, m p liquid density, kg/m^


Moore, L. R T, Cossor, G. and Baker, M. R., Chem. Eng. Sa., 50,2467 (1995) Velocity Distributions in a Stirred Tank Containing a Yield Stress Fluid



Impeller Type: (1) 45° pitched blade with six-blades

(2) a six-bladed standard Rushton disc turbme Diameter: (1)49 mm (2) 50 mm Number of impellers: (1) 1 (2) 1 Number of blades on impeller: (1) 6 (2) 6 Length of impeller blade (perpendicular to shaft): (1) - (2) 12.5 nmi Width of impeller blade (parallel to shaft): (1) 6.8 nun (2) 10.0 mm Thickness of impeller blade: (1) 1.5 mm (2) 1.5 mm

Working fluid and its physical properties an aquenous solution of 0.17 wt% of a carboxy-vinyl polymer

Model Yield stress Ty

Herschel-Bulkley Power law

18.9 Pas 4.6 12.1

0.46 0.29


Results

Radial distribution of radial velocity for the pitched-blade turbine: (D)z*=0.41; (O)z*=0.24; (+)2:*=0.0; (•)z*=-0.24; (•)z*=-0.41.

1.1 Single phase 45

Radial distribution of axial velocity for the pitched-blade turbine: (n)z*=0.41; (O)2:*=0.24; (+)z*=0.0; (•)z*=-0.24; (•)z*=-0.41.

Radial distribution of tangential velocity for the pitched-blade turbine: (n)z*=0.41; (O)z*=0.24; (+)z*=0.0; (•)z*=-0.24; (•)z*=-0.41.

Notation D impeller diameter, m r radial coordinate r* dimension less radial coordinate, r/ru dimensionless r\ impeller tip radius, m T tank diameter, m z* dimensionless axial coordinate

46 Chapter 1. Flow patt«ms

Mavros, P. Xuereb, C. and Bertrand, J., Trans. Instn. Chem. Erie's., 74, Part A, 658 (1996) Determination of 3-D Flow Fields in Agitated Vessels by Laser-Doppler Velocimetry: Effect of Impeller TVpe and Liquid Viscosity on Liquid Flow Patterns

Experimental apparatus Vessel Type: dish-bottomed Diameter: T Height HiH^T

Baffle Number: 4 Width: T/IO

Impeller Type: (1) a standard Rushton turbine (RU) (2) a three-blade Lightnin A310

(3) a MixelTT agitator

c 5 ^ (b)

(a) ^ ^

The Mixel TT agitator; (a) plane view; (b) front view. D=95 mm; blade height 24 mm

Diameter, D: (1), (2), (3)Z)/r=0.5 Off-bottom clearance: T/3

Working fluid and its physical properties 1% (w/w) of carboxymethyl cellulose (CMC) T [mPa]=41.2 f'^'^


1.1 Single phase

Results

I / / ' ' * \ \ \ »

I I 1 1 • • I » • '

U I I M I ''

•7TTH4T^ • / / / / / / ,. . / / M l I -

(a)

v/v;^^=o.4o

\\ i * I '

;;iiiiu . \N>^s;^

(b)

47

(c)

* * I • t V • \\\

* * \ \ \ \

/ / / M / .;

(d)

^^=f

(e)

A\ ^

(t)

i l

Pseudo-2D maps of composite axial and radial velocities, (a-^c) plain water flow patterns; (d~f) flow patterns in 1% CMC solution, (a, d) Rushton turbine; (b, e) Mbcel TT; (c, f) Lightnin A310

48 Chapter 1 . Flow patterns

0.20

0.15

0.10

f S. 0.05

0.00

•0.05 .n in

RU

I I I !

• ' ' 1

fldgeof impalle

1 1. . 1 L,

r

— • — h • Ofh^+S

— O - h - C - S

\ (•) "

1 1 1 1 • 1 •

I

0.20

0.15

0.10

0.05

0.00

>0.05

.n in

1 1 ' I ' • ' i ' ' > •

NRU

•dgeof impalier

} , 1 . . . . . . . I «

- - 0 — h . C - 5

(b) i

20 40 60 r(nim]

80 100

Axial velocity measurements for the Rushton turbine 5 mm above and beneath the agitator blades, (a) water; (b) 1% CMC solution

0.60

0.40

1. 0.20

0.00

-0.20

-0.40

1 ' ' ' 1 ' ' • 1 '

F y » ^

U 1 • t 1 1 i III 1 • * 1 1

' ' 1 ' ' • i ' • ' 1

—•—LA.h-C-5 W — O — N L A . h - C - 5 p

1 . 1 1 I 1 1 • 1 • 1

20 40 60 r|mmj

80 100

Axial velocity profiles 5 mm below the agitators; (a) Mixel TT; (b) Lightnin A310. TT, LA: water; NTT, NLA: 1% CMC solution

95

90

85

80

75

70

65

60

55

' I ' ' • 1 ••• 1 • - I • ' " T ^

-NLA -NTT

100

(a) Radial velocity profiles off the edge (Ar=9.5 nun) of the impellers; (b) axial velocity profiles 5 mm above the agitator blades

Notation C impeller off-bottom clearance, m D impeller diameter, m hb agitator blade height, m T tank diameter, m V fluid velocity, m/sec Y shear rate, Hz

Subscripts r radial tip tip

1.1 Single phase 49

Rutherford, K., Lee, K. C, Mahmoudi, S. M. S. and Yianneskis. M.^AIChE Journal, 42,332 (1996) Hydrodynamic Characteristics of Dual Rushton Impeller Stirred Vessels

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 294 mm (2) 100 mm

Liquid contained Height: (1)294 mm (2) 100 mm


Impeller Type: Rushton impeller Diameter: T/3 Number of impellers: 2 Number of blades on impeller: 6 Impeller clearance and separation: 01=0.257 and C2=0.50T; 01=0.337 and €2=0.337;

01=0.157 and C2=0.50r Working fluid

Distilled water Flow measurement technique

Flow visualization and Laser-Doppler anemometry Experimental conditions

Impeller rotational speed: 250 rpm (Vi =1.28 m/sec) in vessel (1) 2,165 rpm (Vi,>=3.77 m/sec) in vessel (2)

Results

w ^ . \ , • / . • I

111 ' » V * * J ' ' / ' ' / " ^ f

•^ S . ' <

? l l

VHP

Parallel flow 6 =0** r-z plane 360° ensemble-averaged mean velocity vectors: (CI=0.257, C2=0.507).

Merging flow 0 =0° r-z plane 360* ensemble-averaged mean velocity vectors: (CI =0.337, C2=0.337).


/ *

\ »

^1

^ /

\ \ « \ I \

n u!

VHP

Diverging flow B =0** r-z plane 360** ensemble-ave ^ged mean velocity vectors: (C1=0.15T, 02=0.507).

Notation CI off-bottom clearance of the lower impeller C2 separation between the two impellers C3 submergence of the upper impeller below the top of the liquid column height T vessel diameter Yap impeller tip speed

1.1 Single phase 51

Jaworski, Z., Nienow, A. W. and Dyster, K. N., Can. /. ofChem. Eng., 74,3 (1996) An LDA Study of the Turbulent Flow Field in a Baffled Vessel Agitated by an Axial, Down-Pumping Hydrofoil Impeller




Impeller Type: (1) Chemineer HE3 impeller (CHE3) (2) Prochem Maxflo T impeller (PMT)

Diameter: (1) 0.102 m (2) 0.078 m Number of impellers: (1) 1 (2) 1 Number of blades on impeller: (1) 3 (2) 6 Off-bottom clearance: (1) 0.056 m (2) 0.100 m

Working fluid Distilled water


Experimental conditions Reynolds number: (1)4.77x10* (2)2.44x10*

52

Results

Chapter 1 . Flow patterns

Mean axial velocity profiles for Chemineer HE3 impeller.

Mean axial velocity profiles for Prochem Maxflo T impeller.

N

•0.2 0.0 0.2 V

Mean radial velocity profiles for Chemineer HE3 impeller.

N

R Rg R3 R Rg Rg

-0.2 0.0 0.2 w ^R

Mean radial velocity profiles for Prochem Maxflo T impeller.

1.1 SingI* phase 53

•;; ;>C:--''

N

Vector plot of mean velocity vectors in the R-Z plane for CHE3.

Vector plot of mean velocity vectors in the R-Z plane for PMT.

•jMfcJ>Jil»5MML-J 0.2 r 0.0 ^

N

>

y?9W W M . f ? 999

^2

2..

Fluctuating velocity profiles for CHE3. Fluctuating velocity profiles for PMT.


Notation D impeller diameter, m H liquid height in tank, m N impeller rotational speed, 1/sec r radial coordinate, m R dimensionless radial coordinate, r/T, dimensionless T tank diameter, m d mean velocity, m/sec V' rms fluctuating velocity, m/sec V dimensionless mean velocity, v/nDN, dimensionless V dimensionless rms fluctuating velocity, v'/nDN, dimensionless z axial coordinate, m Z dimensionless axial coordinate, z/H

Indices R radial component T tangential component Z axial component

1.1 SingI* phase 55

Hockey, R. M. and Nouri, J. M., Chem. Eng. Sd., 51,4405 (1996) Turbulent Flow in a Baffled Vessel Stirred by a 60° Pitched Blade Impeller




Impeller Type: 60° pitched blade impeller Diameter: 98 mm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 49.0 mm Projected width of impeller blade (parallel to shaft): 18.5 mm Off-bottom clearance: 98 mm

Working fluids water and two mixtures of water and maltose syrup


Experimental conditions Reynolds number (/?e=Z)^Wv)=48,000

Results

\i i 111111

::^. & ^

I • T" 0.0 1.0 2.0 3.0

Mean flow velocities for Reynolds and power numbers of 48,000 and 2.2, respectively, in Q O"* plane: (a) axial and radial velocity vector; (b) tangential velocity profiles.


Notation D impeller diameter, m H liquid height in the tank,

m N impeller rotational

speed, 1/sec r radial distance from the

center of the tank R impeller tip radius, m Vt impeller tip velocity,

itND, m/sec z axial distance from the

bottom of the tank V fluid kinematic viscosity,

mVsec

0.0 1.0 ^ 2.0 r/R

" 1 3.0

Radial and tangential mean velocity vector mr-d plane for Reynolds and power numbers of 48,000 and 2.2, respectively, at different axial positions: (si)z=0,27H: (b)z=0.17^; ic)z=0.068H.

1.1 Singte phase 57

Harvey, A. D., Wood, S. R and Leng, D. E., Chem. Eng. Sci., 52,1479 (1997) Experimental and Computational Study of Multiple Impeller Flows

Experimental apparatus Vessel Type: ellipsoidal-bottomed Height: 55.88 cm

Baffle Number: 4 Width: 3.157 cm Thickness: 0.635 cm

Impeller Type: 45° pitched-blade impeller Number of impellers: 4 Number of blades on impeller: 4

liquid level

4H 'Shaft

Impeller 4(14)

] impeller 3 (I J

2(y

baffle

1 r/R,

a) 2^2=3.58

b)z/Ra«353

c)z/R,=:2.89

d)2/R,»2.55

e) z/Rj= 2.21

f)2/Rj«1.87

g)z/R2-1.53

h)z/Rj«1.19

Impeller dimensions and positioning for

T „ _ Blade X-section Diameter ^P^"^' axu;)(cm) (cm)

1 0.318x1.75 9.207 2 0.318x4.13 22.860 3 0.238x2.54 17.780 4 0.318x2.54 12.383

easel

Height (cm)

5.73 18.82 30.73 42.48

Schematic of multiple impeller configuration


Working fluid and its physical properties 85% (vol/vol) com syrup (viscosity = 928 cP; density = 1,000 kg/m^)



Results

computations experiments

CASE1

|a)2/Rag3.58

b)2ma»3.23

C)zm,«2.89

d)2m,«2.5S

e)2/R,«2.21

]f)^^- 1.87

g)2ma«1.S3

h)z/Rgs1.19

/ / / / / " •

//////^"

Comparison of computed (left-handside) and experimental (right-handside) velocity fields for case 1

1.1 Singl* phase 59

Case 1 velocity profiles for axial stations a-h

Notation / thickness of blade, cm w width of blade, cm


Tanguy, R A„ Thibault, E, La Fuente, E. B-De., Espinosa-Solares, T. and Tecante, A., Chem. Eng. Sci., 52,1733, (1997) Mixing Performance Induced by Coaxial Flat Blade-Helical Ribbon Impellers Rotating at Different Speeds

Experimental apparatus Vessel and impeller geometry

Mixer dimensions

Working fluids and their physical properties Aqueous Solutions of CMC, Gellan, and Xanthan

n (shear thinning index) = 0.26 -- 0.64 consistency index = 2.95 — 21.55 Pas" density = 1,020 kg/m^

Circulation in the vicinity of the Rushton turbine

1.1 Singl* phas«

Computational Results

61

(a) Dispersion pattern induced by the dual impeller mixer. (b) Dispersion pattern induced by the helical ribbon only

? E

1 1 ^

0.04

0.03

0.02

0.01

0.00

-0.01

-0.02

(a)

t I

-0.03 -0.12 -0.08 •0.04 0.00 0.04 0.08

Position (m) 0.12

0.04

0.03

0.02 f

0.01

0.00

-0.01 (9

< -0.02

-0.03

lb)

•0.12 -0.08 -0.04 0.00 0.04 0.08 0.12

Position (m)

(a) Axial velocity profiles at «=1. (b) Axial velocity profiles at w=0.33. (black symbols = dual impeller- white symbols = helical ribbon only).


Mavros, P., Naude, L, Xuereb, C. and Bertrand. J., Trans. Instn. Chem. Engrs., 75, P ^ A, 763 (1997) Laser Doppler Velocimetry in Agitated Vessels: Effect of Continuous Liquid Stream on Flow Patterns

Experimental apparatus Vessel Type: dish-bottomed vessel with a radius of curvature of 190 nun Diameter: 190 mm



Impeller Type: (1) a standard Rushton turbine (2) a Mixel TT

Picture of the Mixel TT agitator

Diameter: 95 nwn Number of impeUers: 1 Number of blades on impeller: (1) 6 (2) 3 Off-bottom clearance: (1) 63 mm (2) 63 nun


Inflow and out flow of water Water flow rate: 6.41 i/min Location of inflow: in the mid-plane between two adjacent balQes, 43 mm away from

the agitator shaft and with its tip 153 nun from the vessel bottom Location of outflow: bottom of the vessel


Experimental conditions Impeller rotational speed: 3 Hz

1.1 Single phas«

Results

63

E

N

-RU -RUCCE") -RU(-CD-)

0 0.2 0.4 0.6 Radial velocity U/U^ [-]

0.8

I

95

90

85

80

75

70

55

' I ' ' ' ' I ' ' • • I ' ' ' ' I

-0.2 -0.15 -0.1 -0.05 0

Radial velocity U^/UH 0.05

2

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

2 « 87 mm H

Rushton turbine

-RU -RUrCE") -RUrCO")

Rushton turbine -RU -RUfCE-) -RU("CD-)

-r 0

1" 0.5

I . I 1.S

[. ' ' ' 1 ' • ' 1 • • '

F iV^ positive \ /

ra MixeITT "

m7////Aiim!i^/A. .

- T — 1 — 1 - 1 1—r - T - i

2 « 92 mm H

—o—TT |j —*—TTrCE-)B —•~7TrCD")R

.1 1. . . 1 L • J

MIxeITT

20 40 60 Vessel radius [mm]

20 40 60 Vessel radius [mm]

Rushton turbine Mixcl TT

Effect of incoming liquid stream on dimensionless mean radial and axial velocities around the impellers.


95

90

85

80

75

70

65

60

55

•-f . 1 - t 1 f , . r-| f t-T r-f-^-

t L*~-.Sv^^^ n ^^^tR:*-~.^_

* T . , «-i T x- j -r-r- .

— 0 ~ RU f C n —A—RU

n ^ ^ • • > ^ J ^ ^ ~ - - — - _ J 0 ^ ^ * > ^ ^ • — — ^ T n ^^"-'^^ '. 1, , a kl nD ^ ^ ^ - ^ H W T • J H 1 X d W J_ / 3 M JS -.-# 1 n .^"^""^^ . ^ , - ^ H H ^ — " • ^ ^ -1

n ^D-*"^^ 1 H ^ - ' 3 K1 .^^^\^ A 0 A - ' D ^ 1

0.1 0.2 0.3 0.4 0.5 0.6

Tangential velocity V A^ [-]

180 150 120 90 60 30

Tangential flow angle 6 ("]

95

90

85

80

75

70

65

6 0

55

E E,

-s I

90 1

85 p 80 1

. 0

1 —Q—rr J 1 —A—TTrCE")j

I • I I I I I I • I I I I I f 1 1

-rrccE-)

I . . . . I . . ^ 1 . I • • . . 1 I . . • . . I . . . « . I . . . • . T

0.02 0.04 0.06 0.08

Tangential velocity V / V [-]

Rushton turbine

0.1 180 150 120 90 60 30

Tangential flow angle 8 [*]

Mixel TT

Effect of incoming liquid stream on the tangential flow around the impellers.

WK,>=0.40

I / / ' * " \ w*

\ I I I ' ^ \ r""

il n * » I * , t

U I I " i

^'^W

s^

^yL>

..nil ^ ^

. / / M l 1 ..)

Feeding-tube plane

90°-rotalcd plane

Batch (no flow)

Composite U„ flow pattern; Rushton turbine, N=3 Hz, QL=6.41 min

1.1 Single phase 65

V/VHP=-OAO

Feeding-tube plane

90°-n)tated plane

Batch (no flow)

Composite U„ flow pattern; Mixel TT agitator, N=3 Hz, QL=SAI min *.

Notation N impeller rotational speed, Hz QL water flow rate, ^/min U instantaneous velocity value, m/sec n mean velocity value, m/sec Vtip impeller tip speed, m/sec

Indices r radial 2 axial q tangential


Schafer, M., Yianneskis, M., Wachter, R and Durst, F.,AIChE Journal, 44, 1233 (1998) Trailing Vortices around a 45° Pitched-Blade Impeller




Impeller Type: 45° pitched-blade impeller Diameter: 50 mm Number of impellers: 1 Number of blades on impeller: 4 Projected width of impeller blade: 10 mm Off-bottom clearance: 50 mm

Working fluid and its physical properties Silicone oil (density = 1,039 kg/m ; dynamic viscosity = 0.0159 Pasec)


Experimental conditions Impeller speed: 2,672 rev/min

Results

Angle-resolved mean velocity vectors in the vicinity of the impeller blade in seven ^ planes: (a) 0=0^; (b) 0=2''; (c) 0=8«; (d) 0=30^

1.1 SingI* phase 67

0.5 v^

0.26 0.20 0.00 td)

Angle-resolved mean velocity vectors near the blade in four planes inclined at 45** to the horizontal plane.

Each of these planes intersects the followmg ^ plane at midblade: (a) 0=80'* (-lO**); (b) 0=0**; (c) 0=4*»; and (d) 0=15^

68 Chapter 1 . Flow patt«ms

0.4

0.3 H

0.2

0.1 H

z/T

r/T

Jpeno^ôo^ôo^^ô^^^^^^^^

1 1 r 0 20 40 60 80 100 120

Blade angle [°]

(a)

3.00-n ,

If 2.50 J

2.O0J

I.50J

i.ooJ

0.50 J

0 00-i 0

i i ^ ^ ^ ^ t ' M i l l i-rn J

50 100 15

Blade angle [°]

(b)

(a) Variation of the nonnalized coordinates rIT, z/T of the vortex axis with blade angle 0; (b) variation of the vortex radius nonnalized with distance from the blade along the vortex axis {r*/d') with blade angle 0; (c) isosurface of vorticity at the edge of the trailing vortex behind an impeller blade.

Notation d' distance from the blade along the vortex axis, m D impeller diameter, m N impeller rotational speed, 1/min r radial coordinate: distance from the axis of the vessel, m r* trailing vortex radius, m T vessel diameter, m VHP impeller tip speed, nND/60, m / s e c z axial coordinate, m 0 the blade; 0 = 0 ° is the vertical plane through the middle of the leading blade

69

1.2 Multi phase 1.2.1 Solid-liquid systems

Gosman, A. D., Lekakou, C, Politis, S., Issa, R. I. and Looney, M. K.,AIChE

Journal, 38,1946 (1992) Multidimensional Modeling of Turbulent IWo-phase Flows in Stirred Vessels

Experimental apparatus Vessel T)rpe: flat-bottomed Diameter: 0.294 m


Baffle Width: 0.0294 m

Impeller Type: disc turbine Diameter: 0.098 m Number of impellers: 1 Off-bottom clearance: 0.098 m

Working fluid, solid and its physical properties Fluid: water Solid: glass particles;

density = 2,950 kg/cm ; mean diameter = 232.5 pm

Computational conditions Impeller speed: 300 rpm Solid concentration: 0.02%

Results

I / / '

• * • • • • • • i i i i i i i t « \ \ \ \ \ i t I I I

I I ' ' • : • « I f I I I I I I I t t t \ \ t I I t I

i

I M ' ' I * « t I I I I I I I 1111 n u M i

1/ / ' '•• ^ » M I I I I 11 M n 11 I I 11

M t l I I I M M t 11 I I i i I

1/ / ' . ' : • ' M I I I I I M I I I I I I M I I

i I t I n u l l I I 11 / I •:• ' I / I I I 1 ' i ' / / / / I \ \ - i ' / / / / /

( \ \ ^t- ^ / / / I \ l ^ - -1' - -+

I M 1 M I 1 I I I 1 n i I I I

i a a a , j

I II 1 I II

/ '^^^\ \ \ \ \ \ \ ' ' • * M \ \ \ \ W

I \ *:• • M I I I 1 1 WW l \ \ - i - ' / / / / / I M I W I \ \ \ -;- - X / / / / / / M I I I

\ \ \ N ^ | - . ^ ^ x / / / / / / / n 11II I I I \ \ \ - ^ - J ^^y^^^y /// / f / ; / I M M % \ > . ^ - ; , , • • - ^ ^ ^ ^ ^ ^ > » • • • • / / / f t / I I I

Velocity vectors @ 6=0°; scale: -* =0.82 m/s.

70 Chapter 1. Flow p«tt«ms

Velocity vectors @ jc=0.908ft scale: -> =0.15 m/s.

Velocity vectors @ x=Q.3H; scale: -> =0.63 m/s.

Notation /f Height of mixing vessel

1.2 Multiphase


71

0.2S'

Cro

ats-

0.10-

0.0S-

0.00-

o

>^ O _-.a<i

O

O

.0.2 0.0 0.2 0.4 0.0 0.0 1.0

Mean velocity comparisons: (a) above the impeller @ Jf=0.1203 m (axial); (b) below the impeller @ jc=0.0757 m (axial); (c) impeller stream @/?=0.0515m (radial).

o Nouri (1992). -o- predicted solid phase, — predicted liquid phase.

Nouri, J. M. and Whitelaw, J. H., Int. J. MuUiphaseflow, 18,21 (1992).

rms velocity comparisons: (a) above the impeller @ x=0.1203 m (axial); (b) below the impeller @ jc=0.0757 m (axial); (c) impeller stream @/?=0.0515m (radial).

o Nouri (1992). -a- predicted solid phase, — predicted liquid phase.


Pettersson, M. and Rasmuson, A. C.,AIChE Journal, 44,513 (1998) Hydrodynamics of Suspensions Agitated by Pitched-Blade Turbine


Liquid contained Volume of liquid in vessel: 7 i

Baffle Number: 4 Width: 22 mm Clearance of baffle from wall: 7 nmi Clearance of baffle from bottom: 8 mm

Impeller Type: 45° pitched four-bladed turbine (downwards pumping) Diameter: 82 nun Number of mipellers: 1 Number of blades on impeller: 4 Length of impeller blade (perpendicular to shaft): 33 mm Projected height of impeller blade: 12 mm Off-bottom clearance: 70 mm

Working fluid, solids and their physical properties Liquid: deionized water Solid: (1) seed particles: spherical metallic coated glass particles (density = 2.6 g/cm ; number

mean size = 4 m) (2) process particles: glass beads (density = 2.42 g/cm ; mean size = 321 ± 9.6 m)

Flow measurement technique Three-dimensional phase-Doppler anemometry

Experimental conditions Impeller speed: 450,525, and 600 rpm Seed particles: 0.10 g; process particles: 0.06% by volume

Results

Normalized 3-D fluid mean velocity, N = 450 rpm.

1.2 Multiphase 73

80 100 0 (mm]

r 20 40 60 80 100

ndUl distance (mm] Normalized rms fluctuating velocities at A = - 1 0 mm. N = 450 rpm.

Normalized turbulent kinetic energy. N = 450 rpm.

3-D intensity of turbulence, N = 450 rpm.


40 80 radial distance [mmj

0.00H

- o - h=-30 mm -1^- h=-10mm| -A- hslOrom •« - h=30 mm

0 40 80 radial distance [mm]

radial distance (mm] radial distance [mm]


^ 0.08

" i 0.06^

§ 0.04

0.02

i " 0.00 J -fci^i »Hi-- r


Normalized Reynolds stresses. N = 450 rpm; = 85°,

Notation Di N Q

Tu U'i

u U'i'U'j

impeller diameter, m impeller speed, 1/sec turbulent kinetic enei:gy, mVsec 3-D intensity of turbulence, % normalized fluctuating velocity, m/sec 3-D mean velocity, m/sec Reynolds stress, mVsec tangential component

1.2 MuKiphas« 75

1.2.2 Gas-liquid systems

Ogawa, K., Yoshikawa, S. and Shiode, H., Kagaku Kougaku Ronbunshu, 18, 495 (1992) Flow Characteristics of Discharge Flow Region in a Stirred Vessel with Aeration




Impeller Type: six flat-blade turbine Diameter: 104 mm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 26 mm Width of impeller blade (parallel to shaft): 20.8 mm Off-bottom clearance: 104 mm

Sparger Location: directly below the impeller 58 mm from vessel bottom Direction of flow: downwards

Working fluids and their physical properties Liquid:

Liquid Kinematic viscosity (mVs)

ion-exchanged water 1.03 x 10"^ 40 wt% glycerol aqueous solution 4.30 x 10~ 60 wt% glycerol aqueous solution 4.30 x 10~® 0.5 wt% polyacrylamide aqueous solution (pseudoplastic viscosity = 0.132 Ns7m ;

integer M = 0.647) Gas: air

Flow measurement technique Electrode reaction velocimetry

Experimental conditions

NiX/s) 0(^/min)

4 7 14

5 14 6 14

Test liquid

water, 40%G., 60%G., PAA water, 40%G., 60%G., PAA water, 40%G.,60%G., PAA water, 40%G., 60%G., PAA

76

Results

Chapter 1. Flow patterns

no aeration

PA A

aeration N=As-\0=lAI/min .,,

Contour line map of velocity for PPA aq.

r/D, l-l

0 0.5 r/0. l-l

Velocity distribution for water

1.2 MultiphM* 77

1.

Z1.2 o" Nl.O

0 ^

^ h

Oll/mtn)

Nn/&) wQler

U

4

• 5 0

6 o

"T] l o

0.5 r/D, (-1

1.0

Relationship between axial position and radial position at where velocity takes maximum value for water

Notation Di impeller diameter, m N impeller rotational speed, 1/sec Q air flow rate, i/min r radial position, m u velocity, m/sec Ut tip velocity of impeller, m/sec Z axial position

78 Chapter 1. Plow patt«ms

Gosman, A. D., Lekakou, C, Politis. S., Issa, R. I. and Looney, M. K.,AIChE Journal, 38,1946 (1992) Multidimensional Modeling of Turbulent TWo-phase Flows in Stirred Vessels



Baffle Width: 0.18 m

Impeller Type: disc turbine Diameter: 0.915 m Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 0.41 m

Sparger Air was injected from a 2.5 cm disc located on the vessel axis, 0.2 m from the base.

Working fluids Liquid: water Gas: air

Computational conditions Impeller speed: 70 rpm Air rate: 1,102 ^/min

wall

Radial profiles of axial velocity at different axial stations @ =17.5**.

1.2 Multiphase 79

Gas phase profiles @ ^=15**; (a) jc=1.52 m; (b) Jif=1.04 m.

D Revill and Irvine (1987), — predictions.

Gas phase profiles @ ^=15°; (c)ji:=0.41m;(d)x=0.12m.

• Revill and Irvine (1987), — predictions.

Revill, B. K. and Irvine, K., ICI pec, private communication.(1987).

Notation X, r, 6 qrlindrical coordinate


Manikowski, M., Bodemeier, S., Liibbert, A., Bujalski, W. and Nienow, A. W, Can. J. ofChem. Eng., 72,769 (1994) Measurement of Gas and Liquid Flows in Stirred Tank Reactors with Multiple Agitators

Experimental apparatus Vessel Type: flat-bottomed Diameter: 440 mm Height: S r Volume: 200 £

Number: 4 Width: 44 mm Clearance of bafQe from wall: 4.4 mm

Impeller Type: (1) Rushton turbine (2) Rushton turbine Diameter: (1) T/3 (2) 0.45 T Impeller setup: three Rushton turbines turbine (1) x 3

two Lightnin impellers and one Rushton turbine impeller (3) x 2 + turbine (2) x 1 Location of impellers:

(3) Lightnin A-315 impeller (3) 0.43 r

|_ 7S2 p.' .

i 1 4 »

[i P D

1 i r' 1 Vl52j ,

r 1012

D

D

1 1320 1 m

r

.'•'l

«-o 1 r

J v^~

Schematic view of the stirred tank, dimensions in mm. On the left hand side of the impeller shaft, the gas sampling probe for gas transit tune measurements is shown. It can be moved parallel to the shaft On the right hand side, the arm is shown on which the probes of the ultrasound measuring device are mounted. The arm by which the probes can be swept between the reactor wall and the shaft is fixed to a steel tube attached to one of the bafQes, as shown on the right hand side of the figure.

Sparger design Sparger position: fixed to the reactor bottom Holes: holes are arranged on a circle of 120 mm diameter

1.2 MuttiphaM 81

Working fluids and their physical properties Liquid: aqueous solutions of CMC

Rheological properties of CMC solutions

Concentration (% w/v) K (Pas") 0.8 1.2

0.086 0.12

«J

8J

RJ

v\\\\\\\J

A

iiwuV:' \\\\\\\\

\\\\\\}

8 j

,.//

J

«J

K\\\\\\\ \\\\\\\M

\\\\\\\\>^

100 200 0 100 200

Radius [mm]

0.83 0.82

Gas: air Bubble velocity distribution measurement

Ultrasound Doppler technique Experimental conditions

Aeration rate: 4.0 mVhr (0.33 wm) Results

5 rev/s 6.7 rev/s 8.3 rev/s

Rj

8 j

SJ

KWWwi

i f v[cm/sj

— r 200

The patterns of the axial-radial components of the mean bubble velocities at 8.3,6.7, and 5 rev/s in a 0.2 % w/v CMC solution aerated at 4.0 mVh.

Notation K consistency index, Pa(sec)'' n Flow behaviour index, dimensionless T tank diameter, m V mean bubble velocity, m/s y shear rate, 1/sec r shear stress. Pa

32 Chapter 1. Plowpattams

Morud, K. E. and Hjertager, B. H., Chem. Eng. Scu, 51,233 (1996) LDA Measurements and CFD Modelling of Gas-Liquid Flow in a Stirred Vessel

Experimental apparatus Vessel Type: dish-bottomed Diameter: 0.222 m

Liquid contained Height: 0.222 m Volume of hquid in vessel: 7.5 i

Baffle Number: 4 Width: O.ID Clearance of baffle from wall: 0.05Z)

Impeller Type: six-bladed Rushton turbine Diameter: D/3 Number of impellers: 1 Number of blades on impeller: 6 Diameter of impeller disc: 0.243Z) Length of impeller blade (perpendicular to shaft): 0.09Z) Width of impeller blade (paraDel to shaft): 0.09Z) Off-bottom clearance: 0.47Z)

Sparger Height: 0.108Z) Diameter: 0.108Z) Location: below the center hne of the impeller shaft Distance between the top of the sparger and the bottom of the vessel: D/5

Working fluids Fluid: distilled water containing 4 g NaCl/^ Gas: air


Experimental conditions Impeller rotational speed (ppm): 360,400,540 and 720 Gas flow rate (WM): 0.09,0.49,0.75,1 and 1.33

1.2 Multiphase

Results

83

(a)

- I — • — I — ' — r 0.0 0.2 0.4 0.6 0.8 1.0

Measured radial gas velocity at the impeller height for different gas flow rates (a) Q=0.09 wm, (b) ©=0.49 wm. (c) Q=1.00 wm, (d) Q=1.33 wm.

g.e-

0.4-

2 0.2-D

0.0-

0

(c)

...

':

h«0.47 D

1.00 W M

—4—720 RPM - e - 5 4 0 R P M — « ^ 400 RPM - B - 3 6 0 RPM

...' y^.-.

, r,r'"

L-t-''-'-.

r : , - ^

'.-i'l-' :• ' 1 • 1 ' 1 ' 1 • .0 02 0.4 0.6 0.6 1 .0

Measured axial gas velocity at the impeller height for different gas flow rates (a) Q=0.49 wm, (b) Q=0.75 wm, (c) ©=1.00 wm, (d) ©=1.33 wm.

84

-L- 0.2 H

h=0.72D

1.00 W M

-540RPM - 360 RPM

- I ' 1 ' 1 ' '' I 0.0 0.2 0.4 0.6 O.B 1.0

(a) r'H (b) rM-1

Measured tangential gas velocity at 1 wm (a) at the impeller level {h=0A7D), (b) above the impeller (h=0.72D).

H

1 Uog

T7

- Q Ho

(a) t Gas (b) (c)

Gas flow rate Q=1.0 wm, (a) Vessel configuration, (b) Predicted gas pattern, (c) predicted gas fraction contours.

Notation D vessel diameter, m h distance from vessel bottom, m Ho initial liquid level, m 0 gas flow rate, W M r radial coordinate, m R vessel radius U axial velocity, m/sec V radial velocity, m/sec W tangential velocity, m/sec Wiip impeller tip velocity, m/sec U* U/WHP; F*= V/Wtip; W*= W/W^p; r*=r/R

85

Chapter 2. Mixing time

2.1 Single piiase

Peters, D. C. and Smith, J. M., Can. J. ofChem. Eng., 47,268 (1969) Mixing in Anchor Agitated Vessels

Experimental apparatus Vessel Type: flat-bottomed Diameter: 6,9 and 12 in

Impeller Type: anchor Number of impeller: 1 Width of impeller blade: 1 in and 1.5 in

Working fluid Polyacryl amide solution

Measurement technique Use of iodine-thiosulfate reaction

Results

I2S CLEARANCE 2S'CLEARANCE so'CLEARANCE

40 40 fO SPEED IN REVS/MIN. -

too

Mixing times for iodine-thiosulphate reaction (clearing). 1 % poly (acrylamide), 12-in. tank, 1-in. wide blade. *the blade-to-wall clearance.

86 Chapter 2. Mixing time

Carreau, P. J., Patterson, I. and Yap, C. Y., Can.]. ofChem. Eng., 54,135 (1976) Mixing of ^scoelastic Fluids with Helical-Ribbon Agitators I — Mixing Time and Flow Patterns

Experimental apparatus Vessel Type: (1) (2) flat-bottomed Diameter: (1) 6 (2) 10 in Height:(l)6 (2) 10 in

Impeller

Impeller

I II III IV V VI VII

d (in.)

5V8 5V8 5V8 4V8 5V8 8% 8%

h (in.)

5% 5 3/8

5V8 5% 5V8 9V32 9V32

ds (in.)

V4 V4 V4 V4 V4 % %

b (in.)

V,6 V,6 V,6 7,6 Vl6 V,6 —

Nt

2 2 2 2 1 2 2

D/d

1.11 1.11 1.11 1.37 1.11 1.11 1.11

l/d

4.48 3.00 4.12 4.00 4.39 4.44 4.69

w/d

0.0970 0.0970 0.195 0.121 0.0970 0.0990 0.0724

p/d

0.719 1.048 0.707 0.848 0.695 0.690 0.710

N.B. The blade of the impeller VII is made of circular tubing, all the others are made of flat ribbon. d - diameter of impeller h — height of impeller d, = diameter of shaft b = blade thickness Nh = number of blade D — inside tank diameter / = overall length of blade u) - blade width p = pitch

.ds

2.1 Single phase 87

Working fluids and their physical properties Glycerol, 2% aqueous solution of sodium carboxyl methyl cellulose (CMC), and 1% aqueous

solution of polyarylamide (Dow Chemical Separan AP-30)

Properties of fluids

p, g/cm^ r]o, poises 9o, g/cm

S R

tu sec. A, sec*

Glycerol

1.25 5.68

— — — -—

Fluid

2% CMC

1.0 100.0 106.0

0.243 0.702 1.26 1.06

1% Separan

1.0 9.0 xlO^ 9.88x10^

0.392 0.796

299.0 428.0

NOTES 1) M data taken at 25X. 2) - 2 5 is the slope of log rj vs. log y at large / . 3) (2-2/?) is the slope of log - (TU -T22) vs. log y at large y. 4) Parameters rj*,, Oo* and ti were obtained by curve fitting the rheological

data to the model. 5) The values of A (elastic time constant) were estimated firom:

(Zi2a)-a. = 2'"

,.(Zi2a)-l]

Here a is a parameter associated with the behaviour of the dynamic viscosity and taken to be equal to 1/(1-25): X is the elastic characteristic time (largest "relaxation time") and Z ( ) is the Riemann zeta function.

Measurement technique Decoloration method: use of the reaction between iodine and thiosulfate in the presence of a

starch solution. Results

• Q

^ • • 0 0

Impeller 1 11 III IV V VI vu

4X10 Influence of impeller geometry on mixing time.

88 Chapter 2. Mixing tini*

3X10 N, RPM

Influence of fluid properties on mixing time.

Notation tm r

- (T11-T22)

p

mixing time, see effective rate of deformation, 1/sec zero shear viscosity, poise primary normal stress difference, dynes/cm^ density, g/cm^

2.1 Singl« phase 89

Brennan, D. J. and Lehrer, I. H., lyans. Instn., Chem. Engrs., 54,139, (1976) Impeller Mixing in Vessels Experimental Studies on the Influence of Some Parameters and Formulation of a General Mixing Time Equation

Experimental apparatus Vessel

Type Diameter (mm) Height (straight section of

cylindrical vessel) (mm) Height (dish-section) (mm) Operating capacity (m ) BafQe width (nrni) Coil diameter (mm)

b: bafQed, fb: flat-bottomed, he: with helical coil

Impeller

Type Diameter (nun) Number of impellers Number of blades

d/D w/d

b-fb 420 610

— 58.2x10-3

39 —

u: unbaffled dp: dish-bottomed

b-db 420 495

102 58.2x10-3

39 —

cp: with cylindrical probe

flat blade disk turbine 63.5,76.0,100.0 and 102.0

land 2 6

u-db-hc 420 505

102 58.2x10-3

— 280

u-db-cp 420 505

102 58.2x10-3

— —

flat blade turbme

land 2 6

0.15,0.18 and 0.24 0.125 and 0.20

Working fluids and their physical properties Newtonian fluids of low viscosity

Measurement technique Decoloration of methyl red indicator with neutralization of NaOH with HCl

Experimental conditions and results Baffled vessels (1) Variable, impeller speed: 72<N<. 1440 rpm

d/D=0,24; H/D=l and 1.1; w/d=0.l25 and 0.2 Impeller speed had only a minor effect on the group NO for lO*<Re^3x 10 NOocFr''-^

(2) Variable, impeller position: 0.24 h/D < 0.73 in flat-bottomed vessel; 0.35 < h/D < 0.65 in dish-bottomed vessel /f/Z)=landl.l

Mixing time 9 was a minimum at h/D - 0.5 Dependence of 6 on h/D was more marked for the dish-bottomed vessel. Similar dependence of 0 on h/D was observed for d/D=Q.24 with u;/Z)=0.125, d/D=0.24 with u;/Z)=0.20 and rf/Z)=0.15 with w/D=0.l25

(3) Variable, impeller blade width: w/D-0.125 and 0.20 d/D=0M;H/D=l2Xidhl

The effect of w/d on ^ was dependent on impeller speed 7 , impeller position h, and vessel geometry

(4) Variable, position of second identical impeller: 2 ^ (hz/d) ^ 5 hi/d=l;d/D=0,lS;H/D=hl

90 Chapter 2. Mixing tim«

Mixing time was reduced by approximately 30% when using dual impellers instead of a single impeller. The position of the additional impeller had negligible effect on G, The investigation was limited to the dish-bottomed vessel

Unbaffled vessel (1) Variable, impeller speed: 157 <N< 1,950 rpm

d/Z)=0.15,0.18, and 0.24; u;/(i=0.125; d/D=02i; w/d=020; H/D=l.l Mixing time 0 decreased with increase of N\mtilN=Ncrit, where 0was a minimum. At N>Nmh 0 increased with further increase of TV

(2) Variable. impeUer position: 0.24 < h/D < 0.66 rf/Z)=0.24; u;/rf=0.125;^/Z)=l.ll

With iV at a single speed <Ncrn the impeller position had negligible effect on 6. (3) Variable, impeller blade width: u;/^=0.125 and 0.20

d/D=024;H/D=l.ll For all TV values investigated, the reduction of 6 achieved by the wider blade over that by the narrower blade was small.

(4) Presence of internal fittings The effects of either a single probe or a heUcal coil as internals in the unbaffled vessel were to retard vortex formation and improve mixing.

Notation d impeller diameter D vessel internal diameter Fr Froude number, N Hig g acceleration due to gravity h vertical clearance between base of vessel at vessel axis and lower horizontal face of

impeller blade H height of liquid surface above vessel base at vessel axis (liquid at rest) N impeller rotational speed Nfrit critical impeller speed in unbaffled vessel at which air entrainment commences Re impeller Reynolds number, Nd ^p/fi w impeller blade width 6 mixing time H viscosity of fluid p density of fluid

2.1 Singl* phase 91

Khang, S. J. and Levenspiel, 0., Chem. Eng. Sci., 31,569 (1976) New Scale-up and Design Method for Stirrer Agitated Batch Mixing Vessels

Experimental apparatus

System

Vessel Type Diameter (m) Height (m)

Baffle Number

Impeller Type Diameter (m) Number of impellers Number of blades

on impeller

d:i:w Pitch/Diameter Off-bottom clearance

(1)

flat-bottomed 0.559 0.559

4

turbine propeller 0.127,0.244 0.114,0.254

1 1 6 3

20:5 : 4

0.280

(2)


4

turbine 0.366,0.488

1 6

1.5/1 0.610

propeller 0.114,0.254

1 3

Working fluids Water and 70% aqueous solution of glycerin


Re>10^

Measurement technique Conductivity measurement

Results For turbines

\2J3

ropeUers pn d

For propeUers

^Pgc pn'd'

= 0.9

Notation d stirrer diameter, m

tank diameter, m Newton's-law conversion factor amplitude decay rate constant, 1/sec length of impeller blade (perpendicular to shaft) stirrer rotational speed, 1/sec

D gr K i

P mixing power requirement, W Re stirrer Reynolds number, nd^p/n,

dimensionless w width of impeller blade (parallel to shaft),

m /i viscosity, g/msec p density, kg/m^

92 Chapter 2. Mixing tiin*

Shiue, S. J. and Wong, C. W, Can. J. ofChem. Eng., 62,602 (1984) Studies on Homogenization Efficiency of Various Agitators in Liquid Blending



Agitator

Agitator

6-Fiat blade turbine

6-Curved blade turbine 4-Curved blade open style turlrine 4-Pitched Wade turbine 4-Pitched Wade turbine with a

draught tube 2-Pitched blade turbine 2-Pitched blade turbine with a

draught tube VEGYTERVpropeUer

D/T

0.325 0.362 0.450 0.325 0.325 0.325 0.325

0.325 0.325

0.325 0.325

LID

0.25 0.241 0.222 0.25 0.231 0.423 0.346

0.346 0.346

0.346 0.50

W/D

0.20 0.207 0.194 0.20 0.269 0.154 0.231

0.231 0.231

0.231 0.231

DalD

0.667 0.690 0.667 0.667 0.769

— —

— —

— —

d

-— — — —

45'> 45**

45** 45°

45** 25**

C/HL

0.5 0.5 0.5 0.325 0.5 0.5 0.5

0.5 0.5

0.5 0.5

I ^—^-^ I I ^— r- I Six-flat blade turbine Sbc-curved blade turbine 4-Curved blade open

style turbine

«c:^^5:o 3-Wade VEGYTERV propeller 4 & 2-pitched blade turbine

Various types of agitators.

2.1 93

Working fluids and their physical properties Tap water, glycerin solutions, and com syrup solutions

Physicochemical properties of liquids

Liquid

Water Glycerin 45 volume % Glycerin 60 volume % Glycerin 75 volume % Com symp 45 volume % Com symp 60 volume % Com symp 75 volume %

Viscosity (Ns/m^xlO^)

0.894 4.75 9.90

31.52 14.56 61.70

408.74

Density (kg/m^)

997.1 1,122.8 1,158.1 1,197.2 1,185.4 1,249.5 1,312.8

Results

-I 1—I—r-

• W e F

pigcerln. g ^

pm syrup

mw%

1 6-Curved| 4-Curved

•ot iU^^^?j

10^ 2 4 6 8 10 4 6 8 10 ^

Re

4 6 8 10=

Homogenization number as a function of Reynolds number: (1) 6-curved blade tiurbine, (2) 4K:urved blade open-style turbine (J)/T=0325, C/HL=0.5).


10-

n i—i—I r r T I 1 1 1 I I I r t ! • • n r r i T

Wafer

Glycerine

Com syrup

^Vbl % eoN iyo 7S^W% « V b l % 60\^l % 75Vbl%

-A— V a A T

• 0 1

Data of Havaset al."'''^' ' — D/T

— 0/T

= 0.254, = 0.382.

C /HL =

C / H L :

0.5

0.5 1

^jjSZjTSZSaj^—^—AAA A A A A ^

1 , t > I I li I

10^2 I 6 8 1 ? 2 4 6 8 1 ? 2 Z 6 8 10 2

Homogenization number as a function of Reynolds numberS-blade VEGYTERV propeller (Z)/r=0.325, C/HL=0.5).

Ho 10

10

• I 1 I » » I I !•'

r V^ter

Glycerine

Gxn syrup

A5Vbl% 60Vbl% 75Vbl*/o SW5? mw% T S J E *

T"" 4-Pitched

• • • • m (D A

2 2-Pirched

a <!> A V e A 0

— 5 — 4-Pitched »Ofauq^li]

A a o o V

• •

4 1 J-Pitched 1

• A B 1 O 1 • 1 A 1 B 1

• B K ^ c»^o^^B6v<37 \; ,n Op n ^

I . . . .Dafa Of Hyas et al.t^'^fl >6-Pitched blade TUrbfie D/T = 0.333 C/HL= 0.5 | . — • ' > • • • • . . ^ - . - . ^ - . . - . - ^ . . . u ^ . c

1?2 4 6 8 1 ? 2 4 6 8 1 0 ' 4 6 8 lO-*

Re

Homogenization number as a function of Reynolds numben(l) 4-pitched blade turbine, (2) 2-pitched blade turbine, (3) 4-pitched blade turbine with a draught tube, (4) 2-pitched blade turbine with a draught tube (D/r=0.325,C//fi.=0.5).

2.1 SingI* phas« 95

Notation C distance between the impeller and the bottom of the tank, m D impeller diameter, m Dd impeller disk diameter, m HL liquid height, m Ho homogenization number, Ntm, dimensionless L length of impeller blade, m N impeller speed, 1/sec Re Reynolds number, ND^p/fi, dimensionless tm mixing time, sec T tank diameter, m W width of impeller blade, m 0 impeller blade angle, degree /I impeller viscosity, Nsec/m^ p impeller density, kg/m^

96 Chapter 2. Mixing t im*

Sano, Y. and Usui, H.,/. Chem. Eng. Japan, 18,47 (1985) Interrelations among Mixing Time Power Number and Discharge Flow Rate Number in Baffled Mixing Vessels

Experimental apparatus Vessel Type: (1) (2) flat-bottomed Diameter (1)0.2 (2) 0.4 m

Liquid contained Height: (1)0.2 (2) 0.4 m

Baffle Number: (1) (2) 4 Width: (1)0.02 (2) 0.04 m

Impeller

Type d/D b/D np

paddle 0.3,0.4,0.5,0.6,0.7

0.05,0.10.0.15,0.20,0.30 2,4,6

turbine 0.4,0.5,0.6,0.7

0.1,0.15,0.2,0.3,0.4 2,4,6,8

i Working fluid Tap water

Experimental conditions 0.3 < d/D < 0.7 0.05 < b/D < 0.3 2 < w> < 8 Re>5x 10

Measurement technique Measurement of electrical conductivity

Results For paddles

neM= 2.1 (d/D)-'-^ ib/D)-^'^ nf^''

For turbines

nftv= 3.8(rf/Z))-^«° (b/D)-"^' ni^'*'

Notation a impeller length, m b impeller width, m c thickness of impeller disk, m d impeller diameter, m D vessel diameter, m n impeller rotational speed, 1/sec np number of impeller blades Re impeller Reynolds number, d n/v, dimensionless 6M mixing time, sec V kinematic viscosity of liquid, mVsec p liquid density, kg/m^

1 J 11 1 '

1 ., d

»- a - ^

ch-

- • 1

1

1

Paddle Turbine (a: c: d = 5 : 2: 20)

2.1 SingI* plMis« 97

Takahashi, K., Yokota, T. and Konno, H.,/. Chem. Eng. Japan, 21,63 (1988) Mixing of Pseudoplastic Liquid in a Vessel Equipped with a Variety of HeUcal Ribbon Impellers

Experimental apparatus Vessel and impeller geometries Vessel type: flat-bottomed Impeller type: helical ribbon

X

Bn

d D

ds

' "'"" "7^

t

: V)

1 ?

z—i

:

Geometrical variables for helical-impellers

Geometry No. d (mm) c/D s/D w/D

DHl DH2 DH3 DH4 DH5 DH6 DH7

95.9 88.5 82.0 91.0 90.3 90.4 91.9

0.0208 0.0574 0.0900 0.0450 0.0482 0.0482 0.0405

0.926 0.909 0.912 0.621 0.455 0.930 0.921

0.100 0.100 0.100 0.100 0.100 0.152 0.200

D=H=100 mm, «^=2, rf,/Z)=0.0938

General configuration of a helical ribbon impeller


Liquid n(-) X(Pas")

3wt%HEC 4wt%HEC 5wt%HEC Com symp

0.768-0.832 0.718-'0.761 0.686-0.735

1

0.724-1.56 2.76-4.60 7.06-14.1 0.550-3.33

Results 0.405^rf/D^ 0.574, 0.455 <5/Z)< 0.930, 0.100<t(;/Z)^ 0.200 and 0.688 <n <0.832

rotational speed of impeller, 1/sec circulation flow rate, mVsec apparent Reynolds number, d^Nplpia, dimensionless impeller pitch, m mixing time, sec blade width, m apparent viscosity, Pa-sec density, kg/m^

Notation A c d ds D h H K n

a function of geometrical variables clearance between blades and wall, m diameter of impeller, m diameter of shaft, m diameter of vessel, m height of impeller, m height of vessel, m consistency index, Pa(secy flow behavior index, dimensionless

N Qi Rea

s tm W

^ P

98 Chapter 2. Mixing tima

Saito, E and Kamiwano, M.J. Chem. Eng. Japan, 22,491 (1989) An Extended Technique for Predicting the Mixing Times of High-Viscosity Liquid in a Mixer—Mixing Systems with Molecular Diffusion of Solute—

Experimental apparatus Vessel Type: (1) flat-bottomed helical screw/draft tube mixer

(2) flat-bottomed helical ribbon-impeller mixer Impeller

(1) Screw impeller mixer (2) Helical ribbon impeller mixer

(1) Screw impeller mixer with draft tube

D(mm)

100 (Do) 150 200

D'(mm) (/(mm)

68 103 137

67 100 133

H(xnm

150 225 300

) H' (mm)

100 150 200

/t(nun)

117 175 233

(2) Helical ribbon impeller mixer

D(mm)

75 (Do) 100 150

d(mm)

64 86

131

^(mm)

80 108 163

^(mm)

70 94

142

u;(mm)

9 12 18

Working fluids and their physical properties Fluids: com syrup and PVA aqueous solutions (viscosities = 0.35-1.5 Pasec at 291K) Solutes: KCl and fluorescein sodium (C2oH2oNa205)

2.1 Single phase

Results

99

n [s-^] Variation of/« with n for helical screw/draft tube mixers (PVA aque. solu.-C2oHioNa205)

Notation Do inner diameter of reference vessel, mm n rotational speed of impeller, 1/sec tm mixing time, sec im arithmetric mean of mixing time, sec

Variation of tm with n for helical ribbon impeller mixers (a) PVA aque. solu.-C2oHioNa205 (b) Com syrup-KCl

100 Chapter 2. Mixing tini*

Saito, E, Aral, K. and Kamiwano, M.J. Chem. Eng. Japan, 23,222 (1990) An Extended Technique for Predicting the Mixing Times of High-Viscosity Liquid in a Mixer—Mixing Systems with Molecular Diffusion and Reaction of Solutes-

Experimental apparatus Vessel and mixer T3rpe: (1) flat-bottomed helical screw/draft tube mixer (d/D=0£7)

(2) flat-bottomed helical ribbon-impeller mixer (d/D=0.S6) Diameter: 75,100,150, and 200 mm

Vessel and impeller geometries

(1) Screwimpellermixer (2) Helicalribonimpellermixer

(1) Screw impeller mixer with draft tube

D(mm)

75 (Do) 100 150 200

D'(mm) d(mm)

51 68 103 137

50 67 100 133

H(mm)

113 150 225 300

^'(mm)

75 100 150 200

h(mm)

88 117 175 233

(2) Helical ribbon impeller mixer

D(mm)

75 (Do) 100 150 200

^(mm)

64 86 131 172

H(mm)

80 108 163 216

h(mm)

70 94 142 188

w{mm)

9 12 18 24

2.1 Singl«phas« 101

Working fluids and their physical properties Com syrups: viscosities = 0,6—1.6 Pa-sec at 291K

Measurement technique Use of chemical reactions

I2 + NaaSzOa -^ Nal + Na2S406 I2 + NaaHPO* - Nal +NaHP04

Results

10

10

•5

10"'

10'

loo

[

<B)

U =Fn p^ztzfc ^ t i u t

m [vrvjN

i 1 h

i m — Colculoled Vfllu

H i Me [T

Hill L teUtllL 1ft i m ^ m i n 1 11 ^^ YvUII

|L HJI mL fflt^ IP

asured Value

Ceyj 0

m c eTf

Dlmmllj

75 100 150 200 Ip

1111

ft 1

i t j I ti

10" 1 N [S'h

10'

Variation of mixing time with rotational speed of impeller for h and Na2S203 reaction system: (A), helical-screw/draft tube mixers, Uquid; //=0.3 Pas;.(B), helical ribbon-impeller mixers, liquid; ;i=0.5 Pa s

Notation d impeller diameter, m D imier diameter of vessel, m Do imier diameter of reference vessel, m N rotational speed of impeller, 1/sec Re Reynolds number, pNdVfi,

dimensionless tm mixing time, sec ^ viscosity, Pasec p density, kg/w?

10^

J 10

10-

(A)

y

(B)

^

tfcS T<N

^

^

— Colculoted Volue I Measured Value

m

key

3

• €

1 0

DInvnl

75 100 j 150 200 l-H

»b

10" 1 N (S-

10^

Variation of mixing time with rotational speed of impeller for liquid of/i=0.5 Pas in helical ribbon-impeller mixers: (A) I2 + 2Na2S203 -^ 2NaI + Na2S406; (B) I2 + 2Na2HP04 ~^ 2NaI +NaHP04

10

10

5

reo

1 ^ [^ & [dK

, ^ in

M C 2 C

1

U-L 1 (J

ction system corn syrup

Na2S203

N02HPO4

fusion system corn syrup

•HioNa205

1 lllll

DImml

75 1 15 0 € a 1 t

0 1200 0

1 Q Olmml

150

A • ' •

' Lsfe^ yJAA-\ "\ \ \

I ' l l • MM 1 i^M

J j i l Jr^ A .^^

^^

nil

i TT ~'

"^^ir^i>~QD-«^"'^ n (f (|( HHiii

1 i l l

i i IIII

\ 11 1 III i l l !

—UU

10° 10' 10== Re 1-1

Variation of (A/if,) with Re for different mixing systems

102 Chapter 2. Mixing tiiiM

Carreau, P. J., P&ris., J. and Gu6rin, P., Can. J. ofChem. Eng., 70,1071 (1992) Mixing of Newtonian and Non-Newtonian Liquids: Screw Agitator and Draft Coil System.

Experimental apparatus Vessel and impeller geometries

Path 1

Path 2

Path 3

Sketch of the mixing system.

System geometry (All dimensions in meters)

1. Vessel: Z)=0.254,/f=0.262(Cl), 0.255(C2), 0.261(C3) 2. Agitator d=0.150, A=0.220,/>=0.147, w=0.067, rf„=0.0159, Cba=0 012

3. Coils

Name Material dc

CI Cr plated Cu 0.1827 C2 Steel 0.1763 C3 Copper 0.1887

he

0.205 0.2075 0.2175

du dti

0.0127(1/2") 0.0095 0.00635(3/4") 0.0043 0.00476(3/16") 0.0032

Cbc

0.0275 0.0285 0.0175

ec

0.0060 0.0064 0.0065

tic

10.5 16.5 19.5

Characteristic parameters: D/d=l.e9, p/d=OM, A/rf=1.47, w/d=0A5, rf„/rf=0.106, Cba/d=OM,



Properties of experimental liquids

Substance

Glycerol

Vitrae oil HV32 Mixture HV320

Com syrup CMC

Xanthan

Polyacrylamide

Cone. (mass %)

89.0 91.5 93.5 95.0 97.5

100. *

100. « •

1.0 2.0 0.75 1.0 1.5

600mg/L 0.2 1.0

iu(Pas) or m (Pas")

0.14 0.213 0.275 0.408 0.598 0.055 0.200 0.785 2.48 0.564 9.5 6.27 6.5 8.62 0.136 0.521 5.04

n (-) 1.0

1

\w

0.748 0.631 0.122 0.196 0.183 0.871 0.734 0.521

P (kg/m^)

1,232. 1,235. 1,240. 1,246. 1,255.

856. 873. 885.

1,383. 996. 996. 995.

i 1,195.

1

k (W/mK)

— 0.320 0.315 0.310

— 0.145

i 0.323 0.588 0.575 0.610

^ 0.356

1

Cp

g/kg-K) —

2,515 2,480 2,451

— 1,901

1 2,358 4,177

1

1 T 2,902 _J_ Pa s, p=995.4 kg/m^ ife =0.610 W/mK,

*Adjusted for desired viscosity. **Com syrup slightly diluted to avoid crystallization. Properties of distilled water used for solutions: //=9 x 10" Cp=417J/kgK.

Results (1) Mixing time

(Nt„U/(NL)N = 1+3.76 Wi"'*^

0m<Wi<0.5

Ntn. = 62.4 - 35.3 [1 - exp (-0.0196i?e)]

Wi = Ni/2r]q

(2) Power consumption iy^/a=i200i?^; ' ( i+354.8m'- ' ' )

where Ci is given by :

a = {0.124 + 0.265 [1 - exp (-0.008367?^^)]} (1 - 0.811 Wi""^^)

Notation Cp specific heat at constant pressure, J/kg*K d agitator diameter, m k thermal conductivity, W/mK ks Metzner-Otto constant, dimensionless m power law parameter, Pasec" n power-law index, dimensionless N rotational speed, 1/sec Np power number, dimensionless Ni primary normal stress differences. Pa Re Reynolds number, d^Np/fX, dimensionless Rcg generalized Reynolds number,

pN^'^^dVinks*"'^, dimensionless

Wi

1

p

mixing time, sec Weissenbeig number, Nil2r]qy dimensionless shear rate, 1/sec viscosity of non-Newtonian liquids, Pasec viscosity of Newtonian liquids, Pasec liquid density, kg/m^

Subscripts N Newtonian nN non-Newtonian



Raghav Rao, K. S. M. S. and Joshi, J. B., Chem. Eng.J., 39, 111 (1988) Liquid-Phase Mixing and Power Consumption in Mechanically

Agitated Solid-Liquid Contactors

Experimental apparatus Vessel Type: (1) (2) flat-bottomed Diameter: (1) 0.57 (2) 1.0 m



Impeller

Type Diameter (m)

Vertical blade height (m) Horizontal blade length (m) Angle of pitch (degree) Blade thickness (m) Disk thickness (m) Number of impellers Number of blades on impeller Off-bottom clearance

DT 0.19

D/5 D/i —

3x10-' 4x10-3

1 6

PTD 0.1425,0.19,0.25,0.33

0.03,0.04,0.063,0.07 0.045,0.075,0.10,0.14

45,45,45,45 3x10-'

— 1 6

r/6, r/4, r /3 , r /2

PTU 0.19

0.04 0.075

45 3x10-'

— 1 6

DT: disc turbine PTD: pitched blade turbine downflow PTU: pitched blade turbine upflow

Working fluid, and solid and its physical properties Liquid: tap water Solid: quartz particles

shape: granular average particle size: 100-2,000 m density: 2,520 kg/m' terminal settling velocity in water: 34—165 mm/sec

Experimental conditions ImpeUer speed: 2—13.3 rps Solid loading 0-40 wt%

Results For PTD

0.19 J0 .11 (Ar0)as=cr"d," JI0L32

2.2 Multi phas« ^Q5

Notation C impeller clearance from bottom, m dp average particle size, ^m D impeller diameter, m N impeller rotation speed, 1/sec Ncs critical impeller speed for solid suspension (solid-liquid system), 1/sec T tank diameter, m X solid loading, wt% 9 mixing time, sec (AT^cs dimensionless mixing time at critical suspension


Kraume, M., Chem. Eng. TechnoL, 15,313 (1992) Mixing Times in Stirred Suspensions

Experimental apparatus Vessel Type: dish-bottomed Diameter: (1) 0.1 (2) 0.33 (3) 1.0 m

Liquid contained Height:(l) 0.1 (2) 0.33 (3) 1.0 m

Baffle Number: (l)'-'(3) 4 Width: (1) 0.01 (2) 0.033 (3) 0.1 m Immersed depth: (1)~(3) 0.8 D

Impeller Type: (a) disk turbine (b) propeller (c) pitched blade turbine Diameter: rf/Z)=0.19~0.6 Number of impellers: 1 Off-bottom clearance: h/D=0,l7

Working fluids, solids and their physical properties Liquid: water and polyvinyl pyrrolidone solutions (viscosities = 12 and 50 mPasec ) Solid: three kinds of glass beads (mean diameters = 0.09,0.37 and 1.5 mm)

Experimental conditions Impeller speed: 100-1,200 rpm Solid concentration: 1.6—16 %

Results T 332)

-JgDws

Notation d agitator diameter, m D vessel diameter, m g gravitational acceleration, m/sec^ h st irrer clearance, m TM. 90% mixing time for 90% slurry height criterion, sec Ws settling velocity of single particle, m/ sec

2.2 Multi phas« ^07


Einsele, A. and Finn, R. K., Ind. Eng. Chem. Process Des. Dev., 19,600, (1980) Influence of Gas Flow Rates and Gas Holdup on Blending Efficiency in Stirred Tanks


Tank diameter (m) Liquid volume {i) htlT

Baffle Number WBIT

Impeller Type Number of impellers Number of blades on impeller Speed (1/sec)

Air sparger Type Number of holes Hole diameter (nmi) sIT Aeration rate (mVsec)

small vessel

0.285 20.0 1.05

4 0.09

six-blade disk turbine 1 6

3.33-15.00

ring 12 0.4 0.20

0.0-0.5

large vessel

0.756 350.0 1.01

4 0.10

six-blade disk turbine 1 6

2.50-7.50

ring 13 3.0 0.18

0.0-1.52

Working fluids and their physical properties Liquids: see table

Physicochemical properties of aqueous phases (25°C)

viscosity" surface tension, liquid/solution Pas 10^ (N/m) x 10

water glycerol (70 wt%) glucose (50 wt%) glucose (70 wt%) Natrosol250H(0.5wt%) Natrosol250H(1.0wt%) Cellosize QP300 (1.0 wt%) Cellosize QP300 (2.1 wt%) Cellosize QP300 (2.6 wt%)

"The rpm in parenthesis refer to the Brookfield LVT measurement with spindle no.L

Gas: air

0.80 70.0 7.0

11.0 185.0 (12 rpm)' 240.0 (12 rpm)' 30.0 (60 rpm)"

310.0 (12 rpm)' 610.0 ( 6 rpm)'

72.0 63.1 70.0 71.2 65.2 64.0 67.0 65.0 64.0


Results

F o r 0 . 8 X 10-3 < / / < 0.61 P a s e c ^^^j 0 = o.O~O.16

(1) the small vessel

r « / r . = l + 13.O(jur-^(0)

(2) the large vessel

r . / r « = 1 + 7.5 Ox)°-2 (0)

Notation hi deal liquid height above tank bottom, m s gas sparger diameter, m T tank internal diameter, m Ta blending time under aerated conditions, sec T„ blending time under non-aerated conditions, sec WB baffle width /J. viscosity, P a s e c 0 gas holdup volume fraction

2.2 MuHi phase 109

Joshi, J. B., Pindit, A. B. and Sharma, M. M., Chem. Eng. Sa., 37,813 (1982) Review Article Number 7 Mechanically Agitated Gas—Liquid Reactors

Ne = 20Al H + 1

' ' ' ' '^ N'D' ^''''

Results Use of results obtained by Van der Molen et al (1) and Hughmark (2) for flat blade turbine

\D) [D)[NV) [gwv^

(1) Van der Molen, K. and Van Mannen, H. R. E., Chem. Eng, Sci., 33,1161 (1978) (2) Hughmark, G., Ind, Eng. Chem. Process Des. Dev., 19,638 (1980)

Notation D diameter of the impeller, m g acceleration due to gravity, ml sec? H height of clear hquid, m N impeller speed, r / s Qg volumetric gas flow rate, mVsec T diameter of vessel, m V volume of liquid, m^ W impeller blade width, m 6 mixing time, sec

110 Chapter 2. Mixing tiiiMi

Pandit, A. B. and Joshi, J. B., Chem. Eng. Scu, 38,1189 (1983) Mixing in Mechanically Agitated Gas—Liquid Contactors^ Bubble Columns and Modified Bubble Columns

Experimental apparatus Vessel, impeller, and sparger geometries

Vessel diameter

r(m)

0.305

1.00

Impeller details

T ,_ Diameter ^ ^ Z)(m)

i)Sixbladed 0.103 disk turbine

*ii) Propeller 0.101

*iii) Pitched 0.101 blade turbine 5 blades

i)Sixbladed 0.34 disk turbine

ii) Curved blade 0.34

iii) Pitched blade 0.34 turbine

Li/D

0.25

0.25

W/D

0.2

0.2

Hi/H

0.33 and 0.50

^/

0.33

Sparger type

Single point and 5 point hole dia = 2.5 mm

Sieve plate sparger 98 holes, hole dia = 2.5 mm

^Upward and downward flow patterns were studied.


Experimental conditions Impeller speed: 3—25 rps Superficial gas velocity: 0—25 mm/sec

Results For six bladed disk turbine

(yolec) = 0.865 (BI

NO = THAI aH + T D) [D)(NV) [gWV'"

Notation a D g H

Hi Li N

a = l, when impeller is centrally located diameter of the impeller, m acceleration due to gravity, m/sec^ hquid height in mechanically agitated column. m height of impeller from the tank bottom, m length of impeller bhde, m impeller speed, 1/sec

Ner

QG

T V Vc W EG

e

critical impeller speed for gas-phase dispersion, 1/sec volumetric gas flow rate, mVsec tank diameter, m total volume of liquid, m gas superficial velocity, m/sec width of impeller bhde, m fractional gas hold-up time, sec

2.2 Multiphase 111

Abrardi, V, Rovero, G., Baldi, G., Sicardi, S. and Conti, R., Trans. Instn. Chem. Engrs., 68, P&rt A, 516 (1990) Hydrodynamics of a Gas-Liquid Reactor Stirred with a Mtdti-Impeller System

Experimental apparatus Vessel and impellers

Vessel Type Diameter (cm)

Liquid contained Height (m)

Baffle Number Width (m)

Impeller Type

Diameter (m) Number of impellers Positions of impellers

Distance between bottom and the first impeller

Distance between 1st impeller and the second impeller

flat-bottomed 0.39

0.39

4 0.04

6DT, 4MFD, 4MFU

T/3 1

T/3

—

flat-bottomed 0.39

0.65

4 0.04

6DT-6DT,6DT-4MFD, 6DT.4MFU

T/3 2

T/3

2T/3

6DT: six-blade disk turbine 4MFD: pitched blade mixed flow turbine, pumping downward 4MFU: pitched blade mixed flow turbine, pumping upward

Sparger Number of holes: 8 ID of hole: 2 nmi Location: beneath the stirrer

Working fluids Liquids: water Gas: air

Experimental conditions Gas flow rate: 5 x 10-*~2 x 10" mVsec Stirrer speed: 150-800 rpm

112

Results

Chapter 2. Mixing time

Mixing time vs UN as a function of QG for the 6DT-4MFD system-A: 7.67 lO"'' mVs; D: 1.0710-^ mVs; 0:210"^ mVs; — : Qc = 0.

(S)

40

30

20 K/

K

/ /

5^^ t i l l

0 .1 .2 .3 .4 .5 1/N(»)

Mixing time vs 1/iVas a function of QG for the 6DT-4MFU system- • ( ): QG = 0; A: 7.67 lO-" mVs; D: 1.6710" mVs; 0:210"^ mVs

N ( S )

Mixing time in ungassed systems-A: 6DT-6DT; • : 6DT-4MFD • : 6DT-4MFU; : 6DT single impeller.

Notation N stirrer velocity, 1/sec IM mixing time, sec T tank diameter, m

2.2 MultiplMiM 113

Satoh, K., Menju, T, Mochizuki, M. and Shono, A., Kagaku Kogaku Ronbunshu, 21,137 (1995) Mixing Times of Liquids in Gas-Liquid Contactors with Mechanical Agitation

Experimental apparatus Vessel Type: flat-bottomed Diameter: 29 cm

Liquid contained Height: 29 cm under migassed conditions

Baffle Number: 4 Width: 2.9 cm

Impeller

Type Diameter (cm) Number of impellers Number of blades on impeller Off-bottom clearance

6DT 8,10,13.5,15

1 6

H/5

6MDT-1 10 1 6

H/5

DT: disc turbine

6MDT-2 10 1 6

H/5

B^^3I>F£) ^

Sparger ^^^ Type: 20 hole nozzle Nozzle diameter: 8 mm Nozzle height: 26 nmi Hole diameter: 1 nmi Location: directly below the impeller

Working fluids Liquid: tap water Gas: air

Experimental conditions Volumetric gas velocity: 0—1.3 dmVsec Impeller speed: 0-15 1/sec Temperature: 20°C Pressure: 1.01 atm

6MDT-1 6MDT-2


Results

iien.^{{iieaf-^r\{iie,)y

=Ka/pDY\Pc.f'

K = iiC.{0.230(4/7r)}'^' = 0249Ka

K„.=(KJ0,mKa)H4/7c){N^/Np)(d/D)\D/Hf

= imxlO\K,/Ka)\Ni/Np)(d/D)\D/H)' Notation

d diameter of impeller, m D diameter of vessel, m H liquid depth in vessel without aeration, m K proportional coefficient Ka Proportional coefficient Kg Proportional coefficient Np power number, dimensionless Nqd discharge flow number, dimensionless Pp agitation power input per unit volume of liquid without aeration, w/w? Pap aeration power input per unit volume of liquid, w/m^ Pcp effective power input per unit volume of liquid, w/m^ 77 coefficient da mixing time under aeration without mechanical agitation, sec Og mixing time under mechanical agitation without aeration, sec 6m mixing time under mechanical agitation with aeration, sec Km coefficient p density of fluid, kg/m^

2.2 Multi phase 125

Nienow, A. W, Trans. Instn. Chem. Engrs., 74, P&rt A, 417 (1996) Gas-Liquid Mixing Studies: A Comparison of Rushton Turbines with Some Modem Impellers

Results Based on the studies at BHR"

or

0»=5.9r ' ' (er) 'S/S/:; \ - i /3 (fl with T^H

*Ruszkowski, S., 1994, A rational method for measuring blending performance and comparison of different impeller types, in Proc 8th Europ Mixing Conf, (IChemE, Rugby), 283-291. Grenville, R. K., Ruszkowski, S. and Garred, £., 1995, Blending of miscible liquids in the turbulent and transitional regimes, 15th NAMFMixifig Conference, Banff, Canada,

Notation D impeller diameter H liquid height N impeller speed Po power input under gassed conditions T vessel diameter £T mean energy dissipation rate 6m mixing time

117

Chapter 3. Power draw and consumption

3.1 Single phase

Rushton, J. H., Costich, E. W and Everett, H. J., Chem. Eng. Progress, 46,395 (1950) Power Characteristics of Mixing Impellers Part 1 Rushton, J. H., Costich, E. W. and Everett, H. J., Chem. Eng. Progress, 46,467 (1950) Power Characteristics of Mixing Impellers Part 2

Experimental apparatus Vessel Type: flat-bottomed

Baffle Number: 4

Impeller Type: propeller, flat-blade turbine, curved blade turbine, shrouded curved blade

turbine with stator ring, and arrowhead turbine

Flat Blade Turbine Arrowhead Turbine


Fluid

water kerosene-carbon tetrachloride mixtures

lubricating oil Unseed oils corn-syrup solutions

Viscosity (cP)

about 1

5-600 5-600

800-20,000 15-43,000

Density (lb/ft3)

59.7-90 •

• •

Curved Blade Turbine

Shrouded Curved Blade Turbine with Stator Ring

^ .

10

s

c

1.0

03

VALUES OF ( — nioraLLnu, NO MFFL

KLOW 1 ^ OF 300 , es

WITH lAFFLESt FOR ALL N ^ } •

1 1 1 1 n i l 1 9 1

*F

g 1

• • M. • • IN. • m I I m. • T/O • 3.0 • 4 IN. • 4 M. • IN IS m. • T/D • 3.3 • I t IH • ll.aiN. • IN 34 M. • T/O • 4.3 • 4 W. • • M. • M 13 m. • T/D • 3.3 • 4 M. • 3 IN. • IN 13 IN. • MFFLES Okl T

f «

• ^

^ 5 ^ ;

t

•*-!

a

. — _ 1

a fl

..<

...

I0> »" w*

REYNOLDS NUMBER Np, . P^ /?

Reynolds Number Correlation for Propellers.

I

I r i

f

t 111 » o a.

100

90

10

s

t

t 1 i

7

^ 1

IN. DMMETCR ( FLAT ( L * D t TUIWINC ANK OIAHETCR I t IN. VRUNE • IN. •MVC KTrOM lOUID DEPTH I t IN.

VE 1 MFFLEt EACH 4 % TANK DMMETEII t • • 10 » • 3 • • . I T * - i t - M l U 4 NO lAFFLEI f ' "V* "nT l ^

I B

i ^'iu^

t 9

"* S 1 • « ^ » > i ^ - i

"

I s t ft

" • •

p ; '

I

«• »• REYNOLDS NUMBER

»' D ' N /

•O t

fS^ 11:

^1-

^ 5''^§|:^'^

ggg'l'S S'i-'9 g'-c S 3 CO

SB. » ^ 1

If 'IP

1 s.

O P

§'i 1 1 « 1 3 re n •1

1 ?• s

Reynolds Number Correlation for a Flat Blade Turbine.

120 Chapter 3. Power draw and consumption

Metzner, A. B. and Otto, R. E.,AIChE Journal, 3,3 (1957) Agitation of Non-Newtonian Fluid

Experimental apparatus Vessel Type: flat-bottomed Diameter: 6-22 in

Baffle Number: 4 or 0 Width: 0.1 T

Impeller Type: six-flat bladed turbine Diameter: 2—8 in T/D ratio: laminar region 1.3—3.7

transition region 2.0—5.5 Number of impellers: 1 Number of blades on impeller: 6

Working fluids and their physical properties Sodium carboxymethyl cellulose (CMC), Carbopol 934 and a suspension of Attasol

Apparent viscosity = 7—180 poises Experimental conditions

Power input: 0.5-176 hp/1,000 gal Rotational speed: 95—1,190 rpm Reynolds number: 2.0-270

Results

Notation D gc

N P fia

P

impeller diameter, ft conversion foctor, Ibm'ft/Wf'sed^ rotational speed, 1/sec power, ft'lbf/sec apparent viscosity, Ibnt/ft density, Ibm/f^

1 1 1

'—r-1

i l _ M

A t.e % CMC

O ATTJ

» CMC k C M M L

* t \

U

i l l 1 i i i 1 I I I 1

I I I 1 III 1 III 1

1^ '

' ! iSi- 1 1 i 1 "^Q^iij^

I I I , j > i r i III iV

•* !^ f^vi

l/,*" / A'U

A! M

i T i 1

ii

• i "

M l 1

i jSBSf^BT-l F ' Power-number-Reynolds-number curve for non-Newtonian fluids; all points in the crowded regions were not shown.


Metzner, A. B., Feehs, R. H., Ramos. H. L, Otto, R. E. and Tuthill, J. D., AIChE Journal 7,3 (1961) Agitation of Viscous Newtonian and Non-Newtonian Fluids

Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.5-1.83 ft

Baffle Number: 4 or 0 Width: 0.1 T

Impeller Type: flat bladed turbine Diameter: 0.167-0.67 ft TID ratio: laminar region 1.3—5.5

transition region 2.0—5.5 Number of impellers: 1

Working fluids and their physical properties CMC, Attasol, Carobopol, Permagel and Pliovic

Flow-behavior index 0.2—1.5 Apparent viscosity 1—180 poises

Experimental conditions Power input: 0.4-176 hp/1,000 gal Impeller speed: 1.58—29 rev/sec Reynolds number: 2-1,760 Apparent viscosity: 1—180 poises

122

Results


1000

REYNOLDS NUMBER. D^Up/p,

Symbol

o V D • A A O V <2>

Fluid

CMC Attasol Carbopol Carbopol Carbopol Carbopol Permagel Permagel Pliovic

n

0.34 0.38 0.26

0.20--0.26 0.30-0.54 0.18-0.29

0.16 0.21 1.5

Power number-Reynolds number correlation for non-Newtonian fluids: single, flat bladed turbine.

Notation D impeller diameter, ft gr dimensional conversion factor 32.2 ftlbM/sec^lbF n flow behavior index of a non-Newtonian fluid, dimensionless N rotational speed of impeller, 1/sec P power consumption, ft/6f/sec T tank diameter, ft /I viscosity, IbM/secft, //«is sometimes used to emphasize that the viscosity (or apparent

viscosity of a non-Newtonian fluid is a function of shear rate) p density, Ibm/ft^

3.1 Singl* pluis« 123

Metzner, A. B., Feehs, R. H., Ramos. H. L, Otto, R. E. and Tuthill, J. D., AIChE Journal 7,3 (1961) Agitation of Viscous Newtonian and Non-Newtonian Fluids

1. Two flat-bladed turbines (1) Ranges of variables covered

Variable

T D T/D n M N NRe Power dissipation

(ft.) (ft.)

(poises) (rev./sec.)

(hp./l,000gal.)

Newtonian data

0.469-1.166 0.33'-1.00 1.023-3.50 1.0 1.48-184 0.03-16.8 0.10-480 0.04-230

Non-Nertonian data

0.469-1.166 0.33-1.00 1.023-3.50 0.14-0.72 2.41-200 0.08-17.3 0.146-620 0.06-175

Baffles, used as indicated on the figuers, were of a width equal to 1/10 T,

(2) Results

1.0 10 100

REYNOLDS NUMBER, O^N/» /M

SYMBOLS, T / O RATIOS 1

h^^< 1 1.000 1 0.666 1 0.500 1 0.333

Lt66

1.166 O

1.75 O ^

2.33 ^ A

3.50 > •

0.786

i.iS O

1.57 ° B

2.36 0^

0.698

L048 •

1.39 <J

2.10 ^ T

0.662

1.023 •

0.496 1

1.41 <

• • A « ^ BAFFLED TANK O a O O V A O < UNBAFFLED TANK

Power number-Reynolds number correlation for Newtonian fluids: two flat-bladed turbines: Curve A'Ax\ T/D > 1.25, baffled tanks, A-i42: T/D > 1.25, unbaffled. Curve B: T/D = 1.16-1.18, C: T/D = 1.02-1.05. Curves B and C join curves i4-i4i andi4-i42 as the Reynolds numbers increase.

124 Chapter 3. Pow«r draw and consumption

p»V.« ' : • nil! • • i i-4-r \U l | 11 ••vV 1 iS^llllI l l |>

Jill NCWTONI

ruiios cm

i'JU .A..

% . M

" T ^ g ^ ^ ^ f 1 i 11 1 nil III

• vn(\

} '

1

J_ 1 1

=7TJ1

1 ( 1 1 11 1

jjl j III

1 1 11 1 1 III

J»JJ

is^¥@i 1 1 ^ 1 1 J^

II

1 j i i 1 1 j 1 i .•

• • ' ' J a»i lllll

jVBwweK?' oj 1 1 li

lllll REYNOLDS NUMBER., D ' N ^ / M

Power number-Reynolds number correlation for non-Newtonians-two flat-blade turbine impellers. See the above table for legend.

2. Fan turbines (1) Ranges of variables covered

« < 1 w = l n>l

T D T/D n

N NRe Power dissipation (hp./l,000 gal.) No. of independent measurements

(ft.) (ft.)

(poises) (rev./sec.)

0.67-0.98 0.33-0.67 1.33-3.0 0.21-0.26 0.5-3.2 2.8-26 6.6-160 8.7-160 46

0.67-0.98 0.33-0.50 1.33-3.0 1.00 1.9-11 1.5-15 1.1-43 7.5-98 35

0.67-0.98 0.33-0.67 1.33-3.0 1.0-1.42 1.9-3.2 1.7-16 7.9-33 5.9-130 49

(2) Results

I

.NEWTONIAN (

j U

I T

:URVE -y

V 11 IPI oA rswj I ii&« nrSter lu^Sfe lit

SYMBOL n T / D • 0.21-0.26 3.0 • 0.21-0.26 2.0 A 0.21-0.26 1.5 V 0.21-0.26 1.33 o 1.0 - 1.42 3.0 O 1.0-1.42 2.0 a 1.0 - 1.42 1.5 V i.O - 1.42 1.33

ID

wm 9 F :i'

^ n • •

300 I 10 100

REYNOLDS NUMBER, O^Hp/^iQ

Power number-Reynolds number correlation for a six-bladed fan turbine.

3.1 Singl* phas« 125

3. Marine propellers (1) Ranges of variables covered

B ^ ^

R J 3 ^

f i l l /

1/

SECTION A-A SECTION B-B

Description of shaft position II used with the marine propellers.

Curve T/D Shaft position

A 0.417 2.2'-4.8 I ,n B 0.417* 2.2-'4.8 I , n C 1.00 1.9--2.0 II D 1.00 1.9-2.0 I E Newtonians II

Power number-Reynolds number correlation for square-pitch propellers (n < 1.0). Asterisks denote upward displacement of fluid.

(2) Results

too

lO

CL

10

bj 1.0

o

o.t

11 i tn 1 1 1 M rS

1 ^ 1111 III *

1 • 1 { j j 1 { • .

1 I Mill

MP= j

IllJil J

1 j 1 1

1

1 1 2 ^ j j 1

11°^ im 1 I f f m—H-H-fnV 1 ' " 1\ ^ ! !

S

) j 1 1 « 1

1

lllll

7m5—^

^ ^ j

Jjlj I n

III ^>fc,l III!

f— j 1 i ( t j !|

1.0 10 100 1,000

REYNOLDS NUMBER, D ^ N / y ^

10.000

126 Chapter 3. Power d m w and consumpticm

4. Double-pitch propellers (1) Ranges of variables covered

Curve TID Shaft position

A B C

1.4-3.0 1.4-3.0

Newtonians

II I n

Power number-Reynolds number correlation for double-pitch propellers {n < 1.0).

(2) Results 100

-.< r-x<

10

Ui

m 3 Z

O

0.2

SI

h L

j 1

1 j

^ -Uokc--I I n *!S I I I i Oo«u: Ilii '

* i l l iS^LL ?ji Jtor:-

» ^ 1 •' ! -

• 1 i l l ,1 ^

1 1

1 1 1

4L^ jt^ni Q

11II

nil

1 i 11 iffl

1.0 10 100 1,000

REYNOLDS NUMBER, D^Hp/ft

10,000

Notation D impeller diameter, ft ge dimensional conversion factor, 32.2 MbAi/sec^lbF n flow behavior index of a non-Newtonian fluid, dimensionless N rotational speed of impeUer, 1/sec Niie Reynolds number, D Np/fi or D Np/fia, dimensionless P power consumption, ftlbF/sec T tank diameter, ft ^ viscosity, IbM/secft ^a apparent viscosity, /ftv/secft p density, Ibju/f^

3.1 Single phase 127

Godleski, E. S. and Smith, J. C.AIChE Journal, 8,617 (1962) Power Requirements and Blend Times in the Agitation of Pseudo-plastic Fluids


Vessel Type

Diameter (in) Liquid contained

Height (in) Baffle

Number Width (in) Clearance of baffle from wall (in)

Impeller Type

Diameter (in) Number of impellers Number of blades on impeller

5.7

5.7

4or0 0.57 1/4

flat-bottomed

11.4

11.4

4or0 1.14 1/4

17.3

17.3

4or0 1.73 1/4

standard six-flat blade turbine

2 1 6

4 1 6

6 1 6

Working fluids and their physical properties Pseudoplastic fluids: Natrosol 250 H (high molecular weight solutions of cellulose)

viscosity of 2% solution: 25,000 centipoises apparent viscosity: 1—100 poises n': 0.28 -1.0

Results

[ota D

Mc

N

n'

P ^

P

tion impeller diameter, ft conversion factor, ft'lbM/sec^'lbf rotational speed. 1/sec flow-behavior index, dimensionless power, ft/^/r/sec apparent viscosity. IbM/ft'Sec fluid density, /fev/ft

REYNOLDS NUMBER. 0 ' N / / / ( ,

Power number-Reynolds number correlation for pseudoplasitic fluids.

128 Chapter 3. Powar draw and consumption

Bates, R. L., Fondy, E L. and Corpstein, R. R., Ind. Eng. Chem. Process Des. and Dev., 2,310 (1963) An Examination of Some Geometric Parameters of Impeller Power

Experimental apparatus Vessel and impeller geometries Vessel diameters. 6,10,12,15, and 24 inches Turbine diameters. 3,4,5,6,7,8, and 10 inches Turbine styles. Flat six-blade disk style; flat, cun ed, and 45° pitched six-blade open style;

four-blade open styles with blade angles 25 to 90° 0.062 to 0.37 0.25 to 0.50 1 through 12 7 to 15%

UbUfb/T range. 0.1 to 1 Working fluids and their physical properties

water and com syrup (Newtonian fluids) viscosity range 1-120,000 cP


Results 500

w/D range. Z)/r range. fib range. Wb/T range.

Power number-Reynolds number correlation in Newtonian fluids various turbine impeller designs.

3.1 SingI* phase 229

otat D gc fib

N Np NRe

P T w Wh

1^ p

ion impeller diameter gravitational constant number of baffles impeller speed, 1/min power number Reynolds number power tank diameter impeller blade width baffle width viscosity liquid density


Beckner, J. L. and Smith, J. M., Trans. Instn. Chem. Engrs., 44, T224 (1966) Anchor-Agitated Systems: Power Input with Newtonian and Pseudo-Plastic Fluids

Experimental apparatus Vessel and impeller geometries Vessel type: flat-bottomed Vessel diameter: 22.9 cm Impeller type: flat-bladed anchor and pitch-bladed anchor

Rotation

••Ub

lin-H

n

\^

± " ] " AA i t

Pitched-bladed anchor. Aims of anchor are pitched at 45 .


Anchors (flat bladed)

No. Z)(cm) h (cm) width (cm) C/DT

1 2 3 4 5

21.71 20.44 19.48 18.04 15.65

15.0 15.0 15.0 15.0 15.0

2.50 2.50 2.50 2.50 2.50

0.0264 0.0542 0.0751 0.1067 0.1584

Anchors (pitch bladed)

Width (cm)

No.

Al A2 A3 A4 A5

Z>(cm)

22.11 20.84 19.33 17.98 16.63

h(cm)

15.0 15.0 15.0 15.0 15.0

Along blade

3.22 3.22 3.22 3.22 3.22

Projected

2.38 2.38 2.38 2.38 2.38

C/DT

0.0177 0.0454 0.0784 0.1078 0.1372


Newtonian systems

Code No. Liquid Viscosity (P) Density (g/cw?)

1

10 4

11 5 2 7

Lubricating oil (British Petroleum, Llandarcy)

Silicone liquid* Dilute golden syrup

(Martineau's) Silicone liquid* Silicone liquid* Concentrated golden syrup Silicone liquid*

6.8'-10.4

31.0-36.0 49.0-^56.0

55.0-61.0 173.0-183.0 385.0-707.0 501.0-618.0

0.886

0.98 1.364

0.98 0.967 1.374 0.967

Non-Newtonian systems

Code No. Liquid k (g cm~ s"" ) Density (g/cnr)

6 14 15 8

12 9

13

10% aqueous CMC** 9.46% aqueous CMC** 7.16% aqueous CMC** 200/100,000 C.S. sihcone* Concentrated PBD*** Polymerised linseed oil Diluted PBD***

0.266-0.338 0.469

0.572-0.611 0.676-0.759

0.702 0.726

0.747-0.766

1,763 567

100-115 943-2,293

1,900-2,475 1,117-1,986

934

1.043 L053 1.055 0.967 0.8 0.982 0.804

* Midland Silicones Ltd.: MS 200. ** Carcoxymethyl cellulose.

*** Polybutradiene dissolved in ethylbenzene. Dilution was with methyl-cyclohexane. (International Synthetic Rubber Co. Ltd.)


Results

P f c T g J N^"D'P ] N^D^P{DT) [* [a (!-«)]"•'J

a = 37-120[|-]

Notation a C D DT k n N P r p T

geometric parameter clearance diameter of impeller diameter of tank constant in T=ky" exponent for power-law fluid rotational speed of impeller power input shear rate density shear stress

3.1 Single ph«s« 133

Bourne. J. R. and Butier, H., Trans. Instn. Chem. Engrs., 47, T263 (1969) Power Consumption of Helical Ribbon Impellers in Viscous Liquids.

Experimental apparatus Vessel and agitator geometries

Summary of Principal Dimensions

Impeller number

1 2 3 4 5

Nagata^ Rl R2 R3 R3'

Gray2 Lightnin^ Hoogendoom and

den Hartog"*

dim)

10.303 11.030 11.142 11.370 34.34

3.7 3.7 7.5

11.2 8.5

14 ft

9.1

dID

0.889 0.952 0.962 0.981 0.954

0.94 0.94 0.95 0.95 0.95

—

0.96

h/D

1.06 1.06 1.06 1.06 1.06

0.9 0.9 0.95 0.95 0.89 2.2

0.9

W/D

0.108 0.108 0.108 0.108 0.104

0.11 0.11 0.10 0.10 0.06 0.09

0.087

S/D

0.345 0.345 0.345 0.345 0.345

0.7 1.05 0.95 0.95 0.68 0.56

0.58

Zo/D

1.22 1.22 1.22 1.22 1.22

1.0 1.0 1.0 1.0 1.1 —

1.5

1 Nagara, S. et al„ Chem. Eng, Oapan), 1957,21,278 2 Gray, J. B., Chem. Eng. Progr., 1963,59,55 3 Viscons Mixing Bulletin B531 4 Hoogendoom, C. J. et al., Chem. Eng. Sci., 1967,22,1689

Principal dimensions of tank and helical ribbon.


Results

__ i£_ nil''*'-I)

n

Notation d outside diameter of ribbon D inside diameter of tank h height of ribbon k hid K consistency factor in the power law / Did n exponent in the power law N rotational speed of ribbon P power consumption Po dimensionless power number, PIpN ^d , dimensionless Re dimensionless Reynold number, pd W "7/iC, dimensionless p density of liquid


Novlk, V and Rieger, E, Trans. Instn. Chem. Engrs., 47, T335 (1969) Homogenization with Helical Screw Agitators


\v

{Lff-fitf

o „

17

Mt>/O-0.1

Vessel Type Inner diameter (mm)

Screw Diameter of screw (nmi) Pitch (mm)

Liquid contained Height (mm)

flat-bottomed 100

60 60

100

flat-bottomed 150

94 94

150

Working fluids and their physical properties Water, glycerol and aqueous solutions of com symp and glycerol

Viscosities of those Uquids = 1—10* cP Results

Results from screw agitator with draught tube.


10' W A/'^—REYNOLDS NUMBER

Results from screw agitator in bafQed vessel.

A ( r , ~ REVNOLOS NUMBER

Results from screw agitator without baffles.

Notation d ou te r d iameter of helical sc rew D inside d iameter of tank Dt inside d iameter of draught tube e offeet of agitator shaft from cen te r of vesse l H he ight of liquid N speed of agitator Np power number , P/pN ^d^, dimensionless P power consumption of agitator s pitch of sc rew Wb width of baffle fi viscosity of liquid p densi ty of liquid 0 mixing t ime

3.1 Siiigl«phas« 137

Nagata, S., Nishikawa, M., Tada, H., Hirabayashi, H. and Gotoh, S.J. Chem. Eng. Japan, 3,237 (1970) Power Consumption of Mixing Impellers in Bingham Plastic Liquids

Experimental apparatus Vessel Type: (1) (2) (3) flat-bottomed Diameter: (1) 20 (2) 30 (3) 40 cm

Impeller

Type d/D hID IID

pitch

Ribbon 0.95 0.1 0.95 1.0

Anchor 0.5-0.95

0.1 0.5-0.95

—

Turbine 0.5 0.1 0.125 —

Paddle 0.3 -0.95 0.05-0.12

— —

a) Ribbon

s c) Turbine d) Paddle

Working fluids and solids Dispersoids: CaCOa, MgCOs, kaolin, and Ti02 Dispersion media: city water, glycerin water solutions, machine oil and salad oil

Results

Np = {PN + KHe')Re-' -^aNy + I

Ribbon Anchor 6-Blade turbine 6-Blade turbine with baffles

Determined coefficients

a

6.13 4.80 3.44 3.44

PN

320 200 70 70

/

0.2 0.29 — 5.5

K

15 30 10 10

h

1/3 1/3 1/3 1/3


6 t^r^2 6 fi |03 2 A 6 6 ^Q4

Np-Re" correlation for ribbon mixer.

10*

50 TOO 500 1000

iV>-/?^"correlation for 6 blade turbine.

5000


Notation b blade width of impeller, cm d diameter of impeller, cm D diameter of mixing vessel, cm h constant, dimensionless He Hedstrom number, Ny{He"fy dimensionless / turbulent power number, dimensionless K proportionality constant / length of anchor arm, height of ribbon, or blade length of impeller, cm n impeller speed, 1/sec Np power number, d ^np/r}, dimensionless Ny yield stress power number, ty/pn^d , dimensionless Re" Reynolds number, d ^nplt], dimensionless a proportionality constant, dimensionless PN proportionality constant, dimensionless r] plastic viscosity, g / c m s e c p density, g/cm^ Ty yield stress for Bingham plastic fluids, g/cmsec^


Hall, K. R. and Godfrey, J. C, Trans. Instn. Chem. Engrs., 48, T201 (1970) Power Consumption by Helical Ribbon Impellers


Diagram of impeller and tank dimensions. Impellers B (10 inch diam.) and A (IV2 inch diam.).

»c^:22iHr^i*.,

Impellers C, B, and D.


Impeller dimensions

Impeller

A B C D E

D

1.65 11.3 11.3 11.3 22.0

dID

0.898 0.912 0.912 0.902 0.91

pid 0.517 0.495 1.00 1.00 1.0

h/d

1.01 0.942 0.996 1.01 1.0

eld

0.0575 0.0485 0.0485 0.0539 0.05

wid

0.135 0.0971 0.0971 0.0981 0.1

NR

1 1 2 1 2

For these impellers H=W2 D. D: inch.

Working fluids and their physical properties Newtonian fluids: aqueous solutions of com syrup (viscosities = 60—460 poise) non-Newtonian fluids: a commercial hydroxypropyl methyl cellulose at various

concentrations in water Results

Po=^e6Re:\p/dr''^(NR){h/d){w/dfHc/dr''

fotaf* c d D gc h H N NR

p p Po Rea T w ^ P

tion clearance between impeUer ribbon and vessel wall impeller diameter diameter of mixing vessel gravitational conversion factor impeller height fluid height impeller speed, 1/sec number of impeller ribbon pitch of impeller ribbon power consumption at impeller shaft {=27tNT) power number, Pgc/N^d^p, dimensionless apparent Reynolds number, d^Np/^, dimensionless torque at impeUer shaft ribbon width apparent viscosity density


Foft, L, Vale§ova, H. and Kudraa, V, Collect. Czech. Chem. Commun., 36,164 (1971) Studies on Mixing. XXVII. Liquid Circulation in a System with Axial Mixer and Radial Baffles

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 190 (2) 290 mm

Liquid contained Height: (1)190 (2) 290 mm

Baffle Number: 4 Width: 0.1 D

Impeller Type: (1) propeller

(2) paddle mixer with three inclined blades (3) paddle mixer with six inclined blades

Number of impellers: (1)~(3) 1 Number of blades on impeller: (l)'-'(2) 3 (3) 6

D (nmi)

Propeller

290 290 290 190 190 190

290 290 290 290 190 190 190

d h2 (mm) (mm)

Rotational speed of mixer (rpm)

{s=d) and paddle mixer with three inclined blades (a=24°)

96.6 145.0 72.5 96.6 58.0 72.5 58.0 58.0 58.0 95.0 58.0 58.0

450-^1,000 800-1,800

1,000-2,000 900-1,600 900-1,600 900-1,600

Paddle mixer with six inclined blades (a=45°)

96.6 145.0 72.5 72.5 58.0 72.5 46.6 72.5 58.0 95.0 46.0 58.0 46.0 46.0

300- 600 600-1,300 900-1,800

1,000-2,000 500-1,000 500-1,000 500-1,000


(a)

Mixer (b)

(a) Three-blade paddle mixer with inclined blades, a=24*', A=0.2 d. (b) Six-blade paddle mixer with inclined blades, a=45*', /»=0.2 d.


Werking fluids

Distilled water Distilled water Aqueous glycerol Aqueous glycerol Aqueous glycerol

P(kg/m') 900

1,000 1,084 1,143 1,161

r7(cP) 0.5 1.0 3.0 9.2

14.42

Results

for i?^> 1.0x10^

Mixer type B f PropeUer(5=(/) 0.592 -0.146 0.026 Three-blade paddle (a=24°) 0.387 0.130 0.060 Six-blade paddle (a=45°) 1.014 -0.212 0.166

Notation d mixer diameter, m D vessel diameter, m hz distance of the mixer rotor above the vessel

bottom, m Kp pumping capacity, dimensionless n rotational speed of the mixer, 1/sec

np Re

% ri P

number of impeller blades Reynolds number, nd^p/rf, dimensionless volumetric flow rate, mVsec dynamic viscosity of fluid, kg/msec liquid density, kg/m^


Nienow, A. W. and Miles, D., Ind. Eng. Chem. Process. Des. Dev., 10,41 (1971) Impeller Power Numbers in Closed Vessels


System

Vessel Type Diameter (in) Height (in)

Baffle Number Width (in)

(1)

flat-bottomed 6,12 6,12

4 0.1 r

1

(2)

flat-bottomed 6,12 6,12

4 0.1 r

Impeller

Type D/T C/Z DwID DJD x/Dw w/D Number of impellers Number of blades

(a): six-blade disk turbine

(a) 1/4-3/4 1/6-3/4

1/5 1/4

0.05-0.44 -1 6

(b): four-blade 45** pitched turbine (c): 2-blade flat paddle

Working fluid water

Experimental conditions Impeller speed

System (1): 40-2,400 rpm System (2): 20-1,000 rpm

Temperature: 25°C

(b) 1/4-3/4 1/6-3/4

— -—

1/4 1 4

(c) 1/4-3/4 1/6-3/4

1/4 -— -1 2

3.1 Single phase

Results

145

Power numbers for 2 x 10* < Nue < 10

Identification, run no.

1 2 3 4 5 6 7

8 9

10 11 12

13 14 15 16 17

r,in.

6 6 6 6 6

12 12

6 6 6

12 12

6 6 6

12 12

D/T

V4 Va 72 72 V4 74 72

74 72 V4 74 72

74 72 VA 74 72

Air/water interface

no no no yes no no no

no no no no no

no no no no no

V6(A)

Impeller clearance, C/Z

V4(B)

6-Blade Disk Turbine

3.6 4.4 4.6 4.2 4.3

3.8 4.7 4.9 4.8 5.0 5.5 5.5

2-Blade Flat Paddles

2.7 2.6 2.5

4-Blade, 45**

1.9 1.6 2.3

2.8 3.1 2.7 2.8 3.0

VaCC)

3.9 4.9 5.3 5.0 5.3

2.9 3.3 2.9

-Pitch Turbine

1.8 1.4 2.2 1.7 1.4

1.7 1.4 1.9

V2(D)

4.1 5.0 5.6

Aerated 5.6 5.9 5.8

3.0 3.4 3.0 3.3 3.5

1.9 1.6 2.3 1.8 1.7

VaCE)

3.9 4.8 5.0

Aerated 5.0

2.8 3.2 2.8

1.9 1.6 2.1

ViiF)

3.7 4.7 4.6

Aerated 4.8

2.7 3.0 2.7

1.8 1.5 2.0

x/D„

0.44 0.33 0.22 0.22 0.14 0.10 0.05

Notation C impeller clearance above the tank bottom, L D hnpeller diameter, L DL length of turbine blade, L Dw width of turbine blade or paddle blade, L N impeller speed, 1/T Np power number, P/pN^D^, dimensionless Nxe Rejmolds number, M) Vv, dimensionless P impeller power, MLVr^ T tank diameter, L w 45°-pitched turbine blade width, L X disk thickness, L Z liquid height, L V fluid kinematic viscosity, L^IT p fluid density, M/D


Nagata, S., Nishikawa, M., Tada, H. and Gotoh, S.J. Chem. Eng. Japan, 4,72 (1971) Power Consumption of Mixing Impellers in Pseudoplastic Liquids


Impeller

Type d/D b/D IID

pitch

Ribbon 0.95 0.1 0.95 1.0

Anchor 0.5-^0.95

0.1 0.5-0.95

—

Turbine 0.5 0.1 0.125 —

Paddle 0.3 --0.95 0.05'-'0.12

-—

a a) Ribbon


c) Turbine d) Paddle

Flow properties at high shear rate*

Liquid

Aqueous CMC LVNO. 1 Aqueous CMC WS-C Aqueous CMC HESS Aqueous PVAl Aqueous PVAc

Weight (%)

0.3-0.5-1.0-10-30-

-6.2 -4.5 -4.5 -15 -35

m

1.00-0.72-0.668-

0.71-0.72-

'0.270 -0.432 -0.436 -0.57 -0.64

i

0.01-13.1' 11.4-62-71-

k

-690 -22.5 -259 '340 '220

•Aqueous CMC WS-C and HESS show the power-law behavior from the low shear rate range (8-100 sec"') to the high shear range (200-1,000 sec"*). However, the others d not obey the power-law

do

3.1 S ing I * phase

Results

iCOO

147

ICC

'

-I

hv 1 *"^

Oj

"ojl^

fo ['o

!

! i

A-iiiC-.n.:- C^!C .^V'li»t:Ot-

Avjj.JCu> PVAl Sc. j i . i f . -n'

[ r\'»\ IQU;

.

i i 1

0.1 10 100 iOOO 10000 1X000

iV -i?g'correlation for pseudoplastic liquids (Ribbon d/D=0.95).

103

r^ 50

"

10

^ ^ t o < l

\e • o X

+ A V

< Q

0

• [ •

Mite n o l i used Ncwionians 3.48% CMC sol. 3.26^; CMC scl. 2.84%CMC sol. 2.51% CMC sol. 2.40% CMC sol. 2.51?; CMC sol. 1.83% CMC sol-1.67 %CNK: sol 1.50 "aCMi: sol. 1.67% CMC sol. l.50?i:CMCsol.

K i t iv r 1 nc uf>d s""t'

no n o J

r)f.)

no no 1 no no i no no 1

4Ba(f le j . 4B' l t l ) f . : .

^ i ^ ^ ^ ^o]

1 10 50 100 500 I L W

iV;>-i?e'correlation for pseudoplastic liquids (6-blades turbine d/D=0.5).

148 Chaiitttr 3. Pow«r draw and consumption

!00

50

10

'

k M I

• ^

^

-d/h 0.533 0.667

0.833

0.950

CMC HESS

1.0%

0 o

1.5%

V +

•

2^%^\

• 1 ^ X {

o 1

* p ; 0.5 5 10

Re' ^ d^nf/fd^ 50 100 500

iV -/?« correlation for pseudoplastic liquids (2-blades paddle).

Notation h blade width of impeller, cm d diameter of impeller, cm D diameter of mixing vessel, cm gc gravitational conversion factor, kgm/kgf sec^ k fluid consistency index, dynesec^/cm^ / length of anchor arm, height of ribbon, or blade length of impeller, cm m exponent in power-law rheological equation, dimensionless n impeller speed, 1/sec iVp power number, dimensionless Re Reynolds number, dhipl\i, dimensionless Re* Reynolds number, d^npliXof dimensionless ju viscosity of Newtonian fluid, poise /!« apparent viscosity, poise p density, g/cm^


Chavan, V V and Ulbrecht, J., Chem. Eng. /., 3,308 (1972) Power Correlation for Helical Ribbon Impellers in Inelastic Non-Newtonian Fluids

Use of published data Geometrical variables No.

G.l G.2 G.3 G.4 G.5 G.6 G.7 G,S G.9 G.IO G.ll G.12 G.13 G.14 G.15 G.16 G.17

Reference

Bourne and Butler Bourne and Butler Bourne and Butler Gray2 Hall and Godfery Hall and Godfery Hall and Godfery Hall and Godfery Hall and Godfery Hoogendom and den Hartog Johnson^ Nagata et al.^ Nagata et al.^ Nagata et al.^ Reher and Bohm^ Ullrich and Schreiber* Zlokamik®

rf(cm)

26.17 28.02 87.22 21.59 4.20

28.70 28.70 28.70 55.88 23.11 10.16 9.40 9.40

19.05 21.00 8.6

18.57

t/d

1.12 1.05 1.05 1.05 1.11 1.10 1.10 1.11 1.10 1.04 1.10 1.06 1.06 1.05 1.19 1.08 1.02

l/d

1.19 1.11 1.11 0.941 1.01 0.942 0.996 1.01 1.0 0.94 0.966 0.95 0.95 1.00 0.952 1.03 1.00

w/d

0.12 0.11 0.11 0.118 0.135 0.0971 0.0971 0.0981 0.1 0.091 0.104 0.12 0.12 0.105 0.114 0.0875 0.099

s/d

0.386 0.362 0.362 0.753 0.517 0.495 1.00 1.00 1.00 0.61 0.773 0.74 1.11 1.00 1.28 1.25 0.499

hid

1.37 1.28 1.28 1.15 1.14 1.12 1.12 1.13 1.12 1.56 —

1.06 1.06 1.05 1.19 —

1.02

NR

2 2 2 2 1 1 2 1 2 2 2 2 2 2 2 2 2

1. J. R. Bourne and H. Butler, Trans, Inst. Chenu Engrs, 47 (1969) T263. 2. J. B. Gray, Chem, Eng. Progr,, 59 (1963) 55. 3. K. R. HaU and J. C. Godfrey, Trans. Inst. Chem. Entrs, 48 (1970) T201. 4. C. J. Hoogendom and A. P. den Hartog, Chem. Eng. Sci., 22 (1967) 1689. 5. R. T. Johnson,Ind. Eng. Chem., 6 (1967) 340. 6. S. Nagata, M. Yanagimoto and T. Yokoyama, Mem. Fac. Eng. Kyoto University, 18 (1956) 444. 7. E. Reher and R. Bohm, Chem. Technik., 3 (1970) 136. 8. H. Ullrich and H. Schreiber, Chemie-Ingr.-Techn., 39 (1967) 516. 9. M. Zlokamik, Chemie-Ingr.-Techn., 39 (1967) 539.

Results

PO = E\ d

4n nW^'-l)

^Re'

where Re = d^N^-""p / k and £ = 2.49

de t 2 (w/d) d d

• ^

\t/d)-[1-2 (u>/d)]\ (t/d)-l


Notation a A d de E h k I n N NR

P Po Re s t w X P

Ald^ surface area of the ribbon impeller impeller diameter equivalent diameter constant height of the hquid colunm consistency index in the power law equation impeller length flow behavior index in the power law equation rotational speed of the impeller number of impeller ribbons power consumption power number, P/d^N^p Reynolds number, d^N^~*^p/k impeller pitch vessel diameter impeller width t/de density

3.1 Single phas* 151

Chavan, V V and Ulbrecht, J., Ind. Eng. Chem. Process Des. Dev., 12,472 (1973)

Power Correlation for Close-Clearance Helical Impellers in Non-Newtonian Liquids

Use of published data Impeller type Helical screw impellers with draught tube Helical ribbon impellers Combined ribbon-screw impellers

Geometrical variables for the impellers

Helical screw impeller with a draught tube.

1 J

1 \ ' 1 i

i

IS

I

T

A single-bladed helical ribbon impeller and combined ribbon-screw impeller.


No.

Geometrical Variables for Helical Screw Impellers with Draught Tube

diem) t/d h/d l/d s/d w/d c/d dr/d Irld Crid

G.l G.2 G.3 G.4 G.5 G.6 G.7

30.5 20.35 20.35 20.35 19.05 14.00 12.70

1.50 2.25 2.25 2.25 2.40 3.28 3.60

1.94 2.70 2.70 2.70 3.10 4.24 4.65

1.50 2.25 2.25 2.25 2.40 3.24 2.%

0.96 0.50 1.00 1.00 0.80 0.93 0.79

0.42 0.39 0.39 0.39 0.42 0.39 0.38

0.104 0.156 0.156 0.156 0.167 0.228 0.250

1.16 1.05 1.05 1.74 1.12 1.53 1.14

1.83 2.54 2.54 2.54 2.93 4.01 4.40

0.104 0.156 0.156 0.156 0.167 0.228 0.250

No.

Geometrical Variables from Literature for Helical Screw Impellers with Draught Tube

Ref. rf(cm) t/d h/d l/d s/d w/d c/d dr/d Ud cjd

G.l G.2 G.3 G.4 G.5 G.6 G.7 G8 G.9

Chavan,e/fl/.(1972) Chavan.«/a/.(1972) Chavan,^fl/.(1972) Chavan,«/a/.(1972) Chavan,g/fl/.(1972) Chavan,€â/.(1972) Nagata,«/a/.(1957) Nagata,«/a/.(1957) Nagata,«/a/.(1957)

20.35 2035 19.05 2035 20.35 19.05 4.50 6.50 6.28

2.25 2.25 2.40 1.50 1.50 1.60 2.22 1.54 1.59

2.63 2.63 2.80 1.75 1.75 1.83 2.22 1.54 1.59

2.31 2.31 2.47 1.56 1.56 1.67 2.0 1.30 1.42

0.5 1.0 0.8 0.5 1.0 0.8 0.67 1.38 0.72

0.39 0.39 0.42 0.39 0.39 0.42

0.31 0.31 0.33 0.19 0.19 0.20 0.11 0.07 0.075

1.13 1.13 1.2 1.03 1.13 1.2 1.15 1.11 1.08

2.25 2.25 2.4 1.50 1.50 1.60 1.55 1.23 1.26

0.19 0.19 0.2 0.13 0.13 0.14 0.25 0.16 0.16

Geometrical Variables from Literature for Helical Ribbon Impellers

No. Ref. d{cm) t/d h/d l/d s/d w/d NR

G.l G.2 G.3 G.4 G.5 G.6 G.7 G8 G.9 G.IO G i l G.12 G.13 G.14 G.15 G.16

Nagata,£/a/.(1972) Nagata,e^fl/.(1972) Nagata,€^<i/.(1972) Nagata,e/fl/.(1970) Nagata,£â/.(1970) Nagata,«rfl/.(1970) Naffit&,etal.il970) Nagata,e/a/.(1970) Nagata,€â/.(1970) Nagata,«/a/.(1970) Nagata,6^tf/.(1970) Miiller(1972) Kappel and Seibring (1970) Kappel and Seibring (1970) Kappel and Seibring (1970) Novak (1972)

19 19 19 19 19 19 19 19

6 6 6 9.6

1.05 1.05 1.05 1.068 1.068 1.068 1.05 1.079 1.105 1.158 1.579 1.08 1.05 1.05 1.02 1.05

1 1 1

1.8 1.25 1.25 1.25

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

•1.0 1.0 1.0 1.2 0.98 0.98 0.98 1.0

1 1 0.5 0.75 1.0 1.25 1.25 1.25 1.25 1.25 1.25 1.24 0.39 0.62 1.05 1.0

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.09 0.1 0.1 0.1 0.1

2 1 1 2 2 2 2 2 2 2 2 1 2 2 2 2

Geometrical Variables for for a Combined Ribbon-Screw Impeller

No. Ref. di (cm) t/dx h/di l/di s\/d\ w\/di dz/dz wz/dz sz/di NR

G.l G.2 G.3 G.4 G.5 G.6 G.7

This woric ^ Nagata,eâ/.(1972) Nagata,eâ/.(1972) Nagata,efa/.(1972) Nagata,efa/.(1972) Nagata,efa/.(1972) Burgbacher (1969)

15 1.03 1.05 1.05 1.05 1.05 1.05 1.05

1.30 1.05 1.05 1.05 1.05 1.05 0.76

1.15 1.0 1.0 1.0 1.0 1.0 0.36

0.57 1.0 1.0 1.0 1.0 0.5 0.72

0.12 0.1 0.1 0.1 0.1 0.1 0.14

0.286 0.42 0.42 0.525 0.525 0.35 0.72

0.4

033

1.0 2 2 1.5 1 1.5 0.72

1 2 1 2 2 1 1

3.1 153

References Butgbacher, G., University of Stuttgart, Department of Mechanical Process Techniques, Study

No. 27 (1969) Chavan, V. V., Ulbrecht, J., Chenu Eng. /., 3,308 (1972) Nagata, S., Yanagimoto, T., Yokoyama, T., Kagaku Kogaku, 21278 (1957) Nagata, S., Nishikawa, M., Tada, H., Hirabayashi, H., Gotoh, S.,/. Chem, Eng. Japan, 3,237 (1970) Nagata, S., Nishikawa, M., Katsube, T., Takaishi, K., Int. Chem, Eng., 12,172 (1972) Kappel, M., Seibring, H., Verfahrenstechnik, 4,470 (1970) MuUer, W., DECHEMA (J)eut. Thes. Chem, Apparatewesen)M(mogr., 66,247 (1971) Novak, v., C. Sc. Theses, Distributed by Statni Technicka Knihovna CSR, Narodni Knihovna,

Praha 1, Klementinum, Czechoslovakia, 1970 Results

For inehstic shear-thinning liquids agitated by the screws with a draught tube

PoRe = 2.bna r^i,. 4n nir'-l)

where

^ = l--2(w/d) a a

._ Ut/d)-l-2(iv/d)\ ""l it/d)-l I

For ribbon and combined ribbon-screw impellers

/ \ ( ^ « / \0^7/ \-0.046/ x-0.036

Notation dimensionless surface area clearance between the impeller and the bottom of the vessel clearance between the draught tube and the bottom of the vessel clearance between the draught tube and the top of the vessel impeller diameter equivalent diameter draught tube diameter height of the liquid column consistency index in power law length of the impeller flight length of the draught tube flow index rotational speed of the impeller number of ribbons power consumed power number, P/pN^d^

Re Reynolds number, d^N^~**p/k s pitch of the impeller

vessel diameter width of the impeller blade density parameter in power corrections viscosity

a c Cr

Cr

d de dr h k I Ir n N NR p Po

t w p k


Rieger, E and Nov^, V, Trans. Instn, Chem. Engrs., 51,105 (1973) Power Consumption of Agitators in HigWy Viscous Non-Newtonian Liquids.

Experimental apparatus Vessel and impeller geometries Helical screw agitators

1 1

^

^ 1

1 — 3 ^ ^

>i * M I

(a) (b) (0 (d) (e)

System

d(mm) s/d d/D Dt/d c/D

Helical ribbons

System

rf(mm) s/d d/D w/d

Screw agitator with a draught tube

Figure (a)

Anchor-type agitators

System

^(mm) w/d d/D hr/d

60 and 94 1.0 0.61 1.1

Figure (c)

96 and 141 1.0 0.95 0.1

Anchor Figure (d)

90 and 133 0.133 0.9 0.89

Screw agitator in the off-centered position

Figure (b)

60 and 94 1.0 0.61

0.02

Pitched blade anchor Figure (e)

133 0.89 0.9 0.89

3.1 SingI* phas* 255

Working fluids and their physical properties aqueous solutions of CMC aqueous solution of polyacrylamide mixtures of CMC solutions with com syrup and starch solutions

n=0.31-^0.97 if=0.5-60 kg/mCsec)"-^

Results

P( > = 0.7;r^fi^^

U J "hr/d {D/df

ReT [(Z)/rf)'^''-0.75r Notation

c d D Dt hr H k K n N P Po Ren s w y

clearance between the agitator and vessel wall agitator diameter vessel diameter draught tube diameter agitator length height of hquid level in the vessel coefficient in equation ya=kN consistency index flow behaviour index speed of impeller power power number Reynolds number, Nd^p/KikN)*"-' pitch of the agitator width of the agitator blade shear rate

156 Chapter 3. Pow«r draw and ccmsumption

Chavan, V V and Ulbrecht, J., Trans. Instn, Chem. Engrs., 51,349 (1973) Power Correlation for Off-Centered Helical Screw Impellers in Highly Viscous Newtonian and Non-Newtonian Liquids

Experimental apparatus Vessel and impeller geometries Vessel type: flat-bottomed Vessel diameter: 45.6 cm

No.

Off-centered helical screw impeller

Geometrical variables for helical screw impellers with draught tube

diem) t/d h/d l/d s/d w/d eld eld

G.1.1 Q.\2 G.1.3 G.1.4 G.1.5 G.1.6 G.1.7 G.1.8

29.2 20.35 20.35 29.2 20.35 20.35 20.35 20.35

1.56 2.25 2.25 1.56 2.25 2.25 2.25 2.25

2.02 2.70 2.70 2.02 2.70 2.70 2.70 2.70

1.62 2.25 2.25 1.62 2.25 2.25 2.25 2.25

0.54 0.5 1.0 0.54 0.5 0.5 1.0 1.0

0.45 0.39 039 0.45 039 039 039 039

0.109 0.156 0.156 0.109 0.156 0.156 0.156 0.156

0 0 0 0.173 0.25 0.50 0.25 0.50

Working fluids Aqueous solutions of com symp, Natrosol, CMC and PAA


Results

Po

1.9 1+

(«-i)

Notation dimensionless surface area of the impeller clearance between the impeller and the bottom of the vessel diameter of the impeller offset of the centre of the impeller from the center of the vessel height of the liquid column consistency index in power law liquids length of the impeller flow behaviour index in power law model rotational speed of the impeller power consumed power number, P/pN^d^^ dimensionless

Re' Reynolds number, d W^'^p/^* dimensionless s impeller pitch t vessel diameter w width of the impeller blade p density

a c d e h k I n N P Po


Sawinsky, J., Havas. G. and De^, A., Chem. Eng. Sci., 31,507 (1976) Power Requirement of Anchor and Helical Ribbon Impellers for the Case of Agitating Newtonian and Pseudo-plastic Liquids

Experimental apparatus Vessel and impeller geometries The values of the coefficients and the exponent of equation (1)

d/D lid bid sId Re C a L

Anchor impeller

0.5 ~ 0.98 0.5 - 1.5

0.07 - 0.16 -

<30 17

0.45 2/ + (/

Helical-ribbon impeller

0.84 - 0.% 0.8 ~ 2.36

0.084 - 0.12 0.36 - 1.28

<100 19

0.45 Z'Ki^idnlsf

The values of the coefficients of equations (2) and (3)

Anchor impeller Helical-ribbon impeller

dID 0.8 -lid 0.9 bid 0.1 -sId m 0.3 - 0.8 j 1.4 B 7,6 dID-33

esults

N ^A.dW'K

^ - K T I Am =j'<l>'A

^ =exp[(m-l)-5]

T =/ ry '"

-0.95 --1.1 -0.13

0.8 -1.0 1.0

7.6<//Z)-5

(1)

(2)

(3)

0.84 ~ 0.96 0.8 ~ 1.1

0.084 ~ 0.12 0.36 ~ 1.28 0.3 -1.0

1.0 4.2(i/Z)-0.5

3.1 Siiigl«plMis« 259

Notation a b C d D e i K I L m n N Re s z f ^ P T

constant width of impeller blade, m coefficient diameter of impeller, m diameter of vessel, m clearance between vessel wall and impeller edge, m constant consistence factor height of impeller, m length of impeller edge, m viscosity index speed of agitator, 1/sec power consumption of impeller, kgmVsec^ Reynolds number, d^np/fi, dimensionless pitch of helical ribbon, m number of impeUer ribbons shear rate, 1/sec viscosity, kg/msec density, kg/m^ shearing stress, kg/msec^

IQQ Chapter 3. Pow«r draw and consumption

Matsumura, M., Masunaga, H., Haraya, K. and Kobayashi, J.,/. Ferment. TechnoL, 56,128(1978) Effect of Gas Entrainment on the Power Requirement and Gas Holdup in an Aerated Stirred Tank




Impeller Type: six-blade turbine Diameter: 0.487 Dr Number of impeUers: 1 Number of blades on impeller: 6 Off-bottom clearance: DT/3

Working fluids and their physical properties Liquid: water, ethyl alcohol, benzyl alcohol, ethylene glycol, and sucrose solution

viscosity: 0.8—30 cp surface tension: 22—71 dynes/cm densities: 0.8-1.3 g/ao?

Results

Nfr ^ 0.45 Npo = 5.3

NFr > 0.45 Npo = 3.80 M v -

Notation Di impeller diameter, m DT tank diameter, m g gravitational acceleration, m/sec^ N rotational speed of impeller, 1/sec NF^ Froude number, N'^Dilg, dimensionless Npo power number in ungassed liquid, PogdpN^D?, dimensionless Po power consumed in agitation of ungassed liquid, kgm/sec p density of liquid, kg/m^


Patterson, W. L, Carreau, R J. and Yap, C. Y.^AIChE Journal, 25,508 (1979) Mixing with Helical Ribbon Agitators. Part II Newtonian Fluids


Sketch of helical ribbon agitator system.

Impeller characteristics

Geometry

A B C D E F G H

Impeller

I

n m IV V VI

vm VI

d (mm)

0.130 0.130 0.130 0.105 0.130 0.222 0.219 0.222

D (mm)

0.145 0.145 0.145 0.145 0.145 0.248 0.248 0.291

h (mm)

0.137 0.137 0.137 0.137 0.137 0.234 0.238 0.234

ds (mm)

6.35 6.35 635 6.35 6.35 9.53 9.53 9.53

fib

2 2 2 2 1 2 2 2

Did

1.11 1.11 1.11 1.37 1.11 1.11 1.12 1.30

lid

4.48 3.00 4.12 4.00 4.39 4.44 4.75 4.44

wid

0.097 0.097 0.195 0.121 0.097 0.099 0.072 0.099

Pid

0.719 1.048 0.707 0.848 0.695 0.690 0.724 0.690



Fluid P(kg/m^) A/(Ns/m2)

100% glycerol 100% glycerol 100% glycerol Silicone oil Vitrea oil

1,254 1,254 1,259 1,100

869

0.568 0.708 0.800 0.137 0.193

Results

'^' "d'Np

siny + 1.8cosy]

{jm (1)

This equation can be simplified on the following grounds: 1. For commonly used helical ribbon agitators, w/d = 0.1, and yf=^ 15 deg. Therefore, we set

(u;/(/)0i6 ~ 0.69, sin v = 0.258, and cos y/^ 0.965. 2. Within the range of the experimental conditions, ReS'^ varies from 1.52 to 2.17. Hence, we

take Re^^ = 1.82 as an average value. Equation (1) then reduces to

Np=24nt d'Np

Na93 m (2)

Notation d diameter of impeller, m ds diameter of impeller shaft, mm D diameter of vessel, m h height of impeller, m H height of liquid in vessel, m / length of impeller blade, m fib number of blades N rotational speed of impeller, 1/sec Np power number, P/pN ^d , dimensionless p impeller pitch P power consumed, W Re Reynolds number for mixing systems, d Nplji, dimensionless w blade width, m /x fluid viscosity, Nsec/m^ p fluid density, kg/m^ \lf blade inclination angle, degree

3.1 SingI* phas* 163

Yap, C. Y, Patterson, W. I. and Carreau, R J., AIChE Journal, 25,516 (1979) Mixing with Helical Ribbon Agitators Part III Non-Newtonian Fluids


Impeller characteristics

Sketch of helical ribbon agitator system.

Geometry

A B C D E F G H

Impeller

I

n m IV V VI

vm VI

d (mm)

0.130 0.130 0.130 0.105 0.130 0.222 0.219 0.222

D (mm)

0.145 0.145 0.145 0.145 0.145 0.248 0.248 0.291

h (mm)

0.137 0.137 0.137 0.137 0.137 0.234 0.238 0.234

ds (mm)

6.35 6.35 6.35 6.35 6.35 9.53 9.53 9.53

ftb

2 2 2 2 1 2 2 2

D/d

1.11 1.11 1.11 1.37 1.11 1.11 1.12 1.30

l/d

4.48 3.00 4.12 4.00 4.39 4.44 4.75 4.44

w/d

0.097 0.097 0.195 0.121 0.097 0.099 0.072 0.099

p/d

0.719 1.048 0.707 0.848 0.695 0.690 0.724 0.690



Fluid

100% glycerol 100% glycerol Vitrea oil 1.0% Natrosol 250-HR 1.5% Natrosol 1.5% CMC-7H 2.0%CMC-7H 0.8%SeparanAP-30 1.0%SeparanAP-30 1.5% Separan** AP-30

P(kg/m3)

1,254 1,249

869 1,000 1,000 1,000 1,000 1,000 1,000 1,000

^ (Ns/m^)

0.568 0.800 0.193 1.07

24.0 2.5

10.0 340

1,100 1,200

S -~ —

0.235 0.381 0.175 0.244 0.382 0.392 0.417

^i(s)

-~ — 0.233 1.30 0.437 1.26 99.3 298 145

A*(s)

— — — --0.12 0.052 0.59 0.70 0.60

*The characteristic elastic time constant was calculated from Theological data at a shear rate equal to 10 s~* through the relation ^ = TU - Tzz/tn y.

**Aged polymer powder.

Results -1

Notation d diameter of impeller, m ds diameter of impeller shaft, mm D diameter of vessel, m h height of impeller, m H height of liquid in vessel, m / length of impeller blade, m Hb n u m b e r of blades N rotational speed of impeller, 1/sec Np power number, P/pN^d^, dimensionless p impeller pitch P p o w e r consumed, W Reg generahzed Reynolds number, d Wp/n^, dimensionless 5 fluid rheologicd parameter, dimensionless 1 fluid characteristic time, sec

w blade width, m 7 shear rate, 1/sec r]e effective viscosity, Nsec /m^ /x fluid viscosity,Nsec/m^ p fluid density, kg/m? Ti2 shear stress, N/m^ Til - T22 primary normal stress difference, N/m^

3.1 Singl«plMis« 165

Blasinski, H. and Rzyski, E., Chem. Eng. /., 19,157 (1980) Power Requirements of Helical Ribbon Mixers

Use of published data Vessel and impeller geometries

Vessel type: flat-bottomed Impeller type: helical ribbon

Schema of the helical ribbon mixer.

Xl

1 ^ 1/ - b

J. ^ 1 f 0

1

1

I

\

Ref. K eld Hid pid hid hid 1 1 2 3 3 3 4 4 6 7 S 9

10 11 12 13 2 2 2 5 5 5 5 5 5 5 5

130 130 250 300 416 257 336 248 420 235 590 310 237

1,000 760 296 230 130 207 215 210 205 218 198 234 194 174

0.095 0.055 0.048 0.03 0.01 0.05 0.026 0.032 0.029 0.036 0.021 0.052 0.0375 0.01 0.026 0.026 0.057 0.054 0.048 0.017 0.035 0.055 0.035 0.035 0.035 0.035 0.035

1.19 1.11 1.12 1.06 1.02 1.10 1.052 1.064 1.412 1.072 1.008 1.103 1.64 1.02 1.28 1.158 1.136 1.13 1.12 1.034 1.071 1.111 1.071 1.071 1.071 1.071 1.071

1.28 1.1

0.745 0.753 0.57 0.61 0.772 1.25 0.5 0.362 1 0.517 1 0.495 0.431 0.446 0.446 0.446 0.446 0.357 0.596 0.892

1 1 0.996 1 1 1 1 0.96 0.941 1.036 0.915 0.966 1.03 1 1.11 1 1.01 1.01 0.942 0.862 0.893 0.926 0.893 0.893 0.893 0.893 0.893

0.114 0.103 0.0971 0.1 0.1 0.1 0.105 0.117 0.118 0.167 0.0905 0.1035 0.0875 0.1 0.11 0.1 0.135 0.0981 0.0971 0.103 0.107 0.111 0.142 0.071 0.107 0.107 0.107

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

IQQ Chapter 3. Pow«r draw and consumption

Results

For i?^ < 100 4 = 0.01 ~ 0.095, ^ = 1.02 ~ 1.64, 4 = 0-357 ~ 1.28, a d d

- = 0.862--1.11, - = 0.071-0.167, « = lor2 d d

X - O ^ / \0 .45/ \-0.63/r \1 .01/ \0.14

e Poi?^ = 3 4 . l | -

References 1. E. 0. Reher and R.B6hm, Chem. Tech., 22 (1970) 230. 2. K. R. HaU and J. C. Godfrey, Trans. Inst. Chem., 48 (1970) 201. 3. A. Mersmann, W. D. Einenkal and M. KSppel, Chem. Ing. Tech., 47 (1975) 953. 4. S. Nagata, Mixing, Kodansha, Tokyo, and Wiley, New York, 1975. 5. H. Blasiiiski, and Cz. Kuncewicz,Inz. Chem., 8 (1978) 807. 6. J. B. Gray, Chem. Eng. Prog., 59 (1963) 55. 7. M. D. Gluz and I. S. Pavlushenko, Zh. Pnkl Khim., 40 (1967) 1485. 8. C. J. Hoogedoom and A. P. den Hartog, Chem. Eng. Sci, 22 (1967) 1689. 9. R. T. Jounson, Ind. Eng. Chem. Proc. Des. Dev., 6 (1967) 340.

10. H. Ullrich and H. Schreiber, Chem. Ing. Tech., 39 (1967) 218. 11. M. Zlokamik, Chem. Ing. Tech., 39 (1%7) 539. 12. J. R. Bourne and H. Butler, Trans. Inst. Chem. Eng., 47 (1969) 263. 1.3 V. Nov^ and F. Rieger, Chem. Eng. J., 9 (1975) 63.

Notation b width of ribbon blade, m D tank diameter, m d impeller diameter, m e clearance between impeller and tank wall, m H height of liquid level above tank bottom, m h height of impeller, m i number of helixes in impeller K Po Re, dimensionless N rotational velocity of impeller, 1/sec P mixing power input, W Po power number, P/N ^d p, dimensionless p pitch of heUcal impeller, m Re Reynolds number, Nd pl ry, dimensionless 77 viscosity of liquid, Pasec p density, kg/m^


Bertrand, J. Couderc, J. R and Angelino, H., Chem. Eng. Sci, 35,2157 (1980) Power Consumption, Pumping Capacity and Turbulence Intensity in Baffled Stirred Tanks; Comparison Between Several Turbines


Liquid contained Height: 0.40 m Volume of liquid in vessel: 50.3 £


Impeller Type System 1 Si

System 2 S2 System 3 S3 System 4,5 S4, S5 System 6 Se

Geometries

six flat blade disk turbine (Figure 1) six flat blade disk turbine (Figure 1) an impeller shown in Figure 2 an impeller shown in Figure 2 an impeller shown in Figure 3

H-T«400mm

h«-|-«2CX)rrwn

w«'jt«40mm

C^'-j-O'lOOmm

!„•-*-•27 mm

L«-?-»33mm

Figure 1


•4^S Sj system

S) system

S,ond £^ systems

^133

Figure 2

Off-bottom clearance: Si

r/2 S2

0.37 S3

r/2 S4

r/2 Ss

r/2

Working fluid water

Experimental conditions and results Systems S, S,

5^"^^,^^ u. 14,700-67,800 Reynolds number *'»»'w u«,c»w

Power number NP 5.1

Non-dimensional - ^Q pumping coefficient NQ

Notation D agitator diameter, m Dc agitator disk diameter, m h agitator level in the tank, m H water level in the tank, m Ip width of the blades, m Ig height of the blades, m

14,700-67,800

N agitator rotational speed, 1/sec Np power number, P/p7^^^Z)

dimensionless NQ pumping coefficient, Q/ND^^

dimensionless

4.9

1.61

14.700-67,800 14.700-67,800 10,100-46,400

P Q Re

T w A P e

4.2 3.4 9.2

1.11 0.65 131

power input, kgmVsec^ piunping capacity, mVsec Reynolds number, ND^p/fi, dimensionless tank diameter, m baffle width, m viscosity, kg/msec density, kg/w? flow angle, degree


Takahashi, K., Aral, K. and Saito, S.J. Chem. Eng. Japan, 13,147 (1980) Power Correlation for Anchor and Helical Ribbon Impellers in Highly Viscous Liquids


Impeller

Type Diameter (cm) Height (cm) w/D dJD

anchor 11.52-12.67

11.50 0.102 0.094

helical ribbon 10.28-12.00

12.50 0.102 0.094

^

g4

d D

^ ^

w

1 J

1 1

•i

1

!

1 1

LJ

L»h/sineB

Geometrical configurations of anchor and helical ribbon impellers.

Cjeometrical variables of anchor and helical ribbon impellers

Geometry

Anchor impellers

HeUcal ribbon impellers

No.

ACl AC2 AC3 AC4 AC5

DHl DH2 DH3 DH4 DH5

d

11.52 12.16 12.48 12.54 12.67

12.00 11.24 10.28 11.29 11.38

c/D

0.0500 0.0250 0.0125 0.0100 0.0050

0.031 0.061 0.098 0.059 0.055

D/s

1.02 1.02 1.02 1.54 2.05

L

39.72 37.46 34.63 54.65 72.59

270 Chapter 3 . Power draw and consumption

Working fluids and their physical properties Aqueous solutions of com syrup

viscosities: lO-^-SOO poise Results

F o r anchor impellers

NpRe^ }^^I^ k.f{D/c) 21n{4 + 8c/f(;)-l d ^

where /(Z)/c) = l+0.00735(Z)/c)°-*^

For anchor and helical ribbon impellers

2hi(4+8c/M;)-l d where

sin^fl=s/-J(;r(/)^ + 5

Notation c clearance between impeller and vesse l wall, cm d impeller diameter, cm ds shaft diameter, cm D vesse l diameter, cm gr gravitational constant, gcm/Gsec^ h he ight of blade, cm H height of vessel , cm L length of blade, h/sin GB, cm Hp number of blades N rotational speed of the impeller, 1/sec Np power number, PgclpN^d^, dimensionless P power consumption, Gem/sec Re Reynolds number, d^Np/^f dimensionless s impeller pitch, cm w blade width, cm GB blade angle, rad jix viscosity, g/cmsec p density, g/cm^

3.1 Singl« phas» 271

Gray, D. J., Treybal, R. E. and Baraett, S. M., AIChE Journal, 28,195 (1982) Mixing of Single and Two Phase Systems: Power Consumption of Impellers



Impeller Type: six flat-blade disc turbine Diameter: 0.0906 Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: C/D=^ 0.5,1.167 and 1.5

Working fluid Water

Results

7V = 5.17(C/Z))°-2 for C/D<hl

Np=^ 5.17 for C/Z)> 1.1

Notation C impeller height off the tank bottom, m D impeller diameter, m gc gravitational constant, kgm/kgf sec Po mechanical agitation power in ungassed Uquid, W N impeller rotational speed, 1/sec Np power number, Pagc/pN^D^, dimensionless p liquid density, kg/m^


Takase, H., Unno, H. and Akehata, T, Kagaku Kogaku Ronbunshu, 8,560 (1982) Power Consumption of Surface Aerator in a Square Tank


System

Vessel Type

Length and width (m) Water depth (m)

Impeller Type

Diameter of disk (m)

di ilbiWd

Number of impellers Number of bladed Off-top clearance (m)

(1) (2)

flat-bottomed square tank

0.2 0.075-0.2

disk with

0.03,0.06

1 6

0,0.01,0.02

0.3 0.075-0.3

(3)

0.5 0.075-0.5

six blades underneath the disk

0.03,0.06,0.12

20:7:2

1 6

0,0.01,0.02

0.06,0.12

1 6

0,0.01,0.02



System (1) di(m) Impeller speed (rps)



0.03 5.00-41.7

0.03 5.00-41.7

0.06 1.67-16.7

0.06 1.67-16.7

0.06 1.67-16.7

0.12 0.83-6.67

0.12 0.83-6.67

3.1

Results Below t h e critical Reynolds n u m b e r

173

H/W<03S

Np=32 H] xr ,^-0.77|lo«io(*7IK)+a7f~

- Npr^lO

H/W ^0.3S

AT AT ,^-0.77|logio(rf.7iy)+0.7f^

Above t h e critical Reynolds n u m b e r

H/W^03S

Np = 0.88 (Re/Recr''\di/Wy''''

H/W<03S

Np = 0.17 (Re/Recr'\di/Wy'\H/Wf'

Notation di impeller diameter, m gr gravitational conversion, kgm/kgfsec^ H water depth, m Hso initial impeller submergence, m lb blade length, m n rotational speed of impeller, 1 / sec Np power number, Pgc/p « W , dimensionless Npnax max imum value of iVp P power, kgfm/sec Re Reynolds number, pndiVi^, dimensionless RBC Reynolds number at Hso=0 Wb blade width, m W tank width, m /x viscosity of water, kg/msec p density of water, kg/m^


Sano, Y. and Usui, H.,/. Chem. Eng. Japan, 18,47 (1985) Interrelations among Mixing Time, Power Number and Discharge Flow Rate Number in Baffled Mixing Vessels

Experimental apparatus Vessel Type: (1) (2) flat-bottomed Diameter: (1)0.2 (2) 0.4 m



Impeller

Type d/D b/D

tip

paddle 0.3,0.4,0.5,0.6,0.7

0.05,0.10.0.15,0.20,0.30 2,4,6

turbine 0.4,0.5,0.6,0.7

0.1,0.15,0.2,0.3,0.4 2,4,6,8

t Ibd

Paddle (a: c: b = 5: 2:20)

Turbine


Experimental conditions 0.3 < d/D < 0.7 0.05 < b/D < 0.3 2<np<S Re>5x 10

Results For paddles

Np=73(d/Dr For turbines

Np=3.6{d/D)-

Notation

Hb/DtW

Hb/Df^np"

a impeller length, m b impeller width, m c length of impeller disk inserted into

blade, m d impeller diameter, m D vessel diameter, m n impeller rotational speed, 1/sec

Np P Re

number of impeller blades power number, P/pvPd^y dimensionless mixing power consumption, W impeller Reynolds number, d^n/v, dimensionless kinematic viscosity of liquid, mVsec Uquid density, kg/m^

3.1 SingI* plias» 175

Bertrand, J. and Couderc, J. R, Chem. Eng. Res. Des., 63,259 (1985) Evaluation of the Power Consumption in Agitation of Viscous Newtonian or Pseudoplastic Liquids by Two-bladed, Anchor or Gate Agitators

Experimental apparatus Vessel Type: flat-bottomed Height: T Volume: 200 £

Agitator geometries

Agitator

Two-bladed impeller

Anchor

Gate-agitator

^Experimentally studied.

D/T 0.336

*0.508 0.656 0.828 D/T 0.730

*0.779 0.828 0.926 D/T 0.631

*0.656 0.730 0.828

Geometries studied

(I>A/T

0.0417

<I>A/T

0.0417

il>A/T

0.0417

Dimensions

H/T

1

H/T

1

H/T

1

W/T

0.0737

DYO/T

0.165 0.189 0.263 0.361

Dvo/T 0.312 0.337 0.410 0.509

DY/T

0.484 0.509 0.582 0.681

1 1

D

W\ 1 ^ 1

th_| I—^ 1 H 1

g a J wi 1 T J

Two-bladed impeller Anchor Gate-agitator

276 Chaptor 3. Power draw and consumption

Working fluids Newtonian fluid: a viscous oil Pseudoplastic fluid: a carbopol solution

Results Newtonian fluid

(1) Two-bladed impeller 0.08 <Re<45 D/T = 0.508

NpRe = 175 Re> I NpRe increases with Re

(2) Anchor 0.26 <Re<20

NpRe = 149 (3) Gate-agitator

0.1 <Re<20 NpRe = 169

Pseudoplastic fluid (1) Two-bladed impeller

for an Ostwald de Waele fluid 0.1 <Re<lO andn> 0.7

for a Carreau fluid Re < 0.4 and 0.4 < « < 1

NpRe = 175 (73r-' (2) Anchor

for a Carreau fluid NpRe = 149 (16)"-

(3) Gate-agitator for an Ostwald de Waele fluid

NpRe = 169 (12 jy-' Notation

D agitator diameter, m m consistency index, kg/m(sec)"~^ n flow behaviour index N rotational speed, 1/sec Np power number, P/pN^D^, dimensionless P power consumption, kgmVsec^ Re Reynolds number, dimensionless

for Newtonian fluids, pNDVr] for Ostwald de Waele fluids, pN'^^'D'^lm for Carreau fluids, pNDVr]o

T tank diameter, m T] viscosity, kg/msec rjo viscosity, kg/msec p fluid density, kg/m^


Shamlou, R A. and Edwards, M. E, Chem. Eng. Set., 40,1773 (1985) Power Consumption of Helical Ribbon Mixers in Viscous Newtonian and Non-Newtonian Fluids


Type: dish-bottomed Impeller type: helical ribbon

Details of impellers used

No.

1 2 3 4 5 6 7 8 9

10

T

400 400 400 400 400 400 150 150 150 150

D

352 352 352 352 352 370 135 135 130 113

w

34 34 34 34 34 36 13 14 13 12

All measurements are in mm.

Working fluids Newtonian Uquids: water,

P

352 352 352 176 190 185 135 75

133 60

P/D

1 1 1 0.5 0.5 0.5 1 0.56 1.02 0.531

w/D

0.097 0.097 0.097 0.097 0.097 0.097 0.097 0.104 0.100 0.106

c/D

0.0682 0.0682 0.0682 0.0263 0.0263 0.0405 0.0556 0.0556 0.0769 0.1637

tib

1 2

h/D HIT

1.0 1.1 1.0 1.1 1.0 1.1 1.0 1.1 1.0 1.1 1.0 1.1 1.02 1.1 1.08 1.1 1.02 1.1 1.02 1.1

silicone oils, lubricating oils, glycerol and various concentrations of sugar solutions

Non-Newtonian liquids: aqueous solutions of carboxymethyl cellulose and various grades of chocolate

Results

fc=34-144(C/Z))

U^ksN

PoRe^Kp=\bO\^ \^)

nb / \ / \0.67

\P\\n \ l J W

For Non-Newtonian Uquids // can be replaced by IXA-

UlaLlUIl c clearance between impeller tip and P

vessel wall, m Po D impeller diameter, m Re h impeller height, m T H liquid height, m w ks impeller shear rate constant YA I length of impeller blade, m // N impeller rotational speed, 1/sec fiA fib number of impeller blades p p impeller pitch

power input, W power number, P/pN^D^, dimensionless Reynolds number, pNDV^, dimensionless tank diameter, m impeller width, m average shear rate, 1/sec Newtonian viscosity, kg/msec average apparent viscosity, kg/msec Uquid density, kg/cm^

178 Chapter 3. Power dmw and consumption

Sestak. J., Zitny, R. and HouSka, M.MChE Journal, 32,155 (1986) Anchor-Agitated Systems: Power Input Correlation for Pseudoplastic and Thixotropic Fluids in Equilibrium

Vessel and agitator geometries

H/D<1

d/D«a9

K/d»at2

h/d*Q89|

^ifti 0d

#0

rr 2

[3

#d«3&6mm

#d«90 mm

4d»13Smm

#0>4Z8mm

#0*100 mm

#D«1S0 mm I

Dimensions of the anchor impellers (one pair of side arms).

Working fluids, their physical properties and results Po = C{n)/Re„


Summary of experimental results

Fluids

Newtonian: Silicone oil Mineral oil Sugar syrup

Pseudoplastic: Kaolin in water (50% w/w)

Polyox WSR in water (1% w/w) Wallpaper gum (CMC* in water)

PAA** in water (10% w/w)

CMC in water (3.8% w/w)

PAA in water (6% w/w)

CMC in water (8% w/w)

CMC in water (3.6% w/w)

Thixotropic (equilibrium values): Neoponite No. 1 Neoponite No. 2

Wallpaper paint

Laponite in ¥^ter (5% w/w)

K, Pas"

0.259 0.9256 2.612 2.531

129.98 129.14 130.32 130.15

0.794 4.973 7.64

67.50 80.04

1.2 1.305

15.05 12.2 13.53 12.25 11.64 11.637 1.07

46.7 35.9

12.6

300

n

1.0 1.0 1.0 1.0

0.158 0.0782 0.1215 0.1288 0.62 0.74 0.61 0.816 0.53 0.874 0.810 0.744 0.9595 0.854 0.66 0.70 0.732 0.905

0.484 0.497

0.249

0.022

A kgm"

840 900

1,362 1,362

1,424 1,424 1,424 1,424 1.002 1,015 1,015 1,110 1,110 1,014 1,014 1,016 1,016 1,016 1,024 1,024 1,024 1,013

1,929 1,927

1,439

1,021

T, X

19.9 20.2 24.0 24.3

24-32 24-32 24-32 24-32 20.1 20 20 20 20 20.1 20.1 20.1 20.1 20.1 20:2 20.2 20.2 20.1

21 21

21

21

No. of Av. C(«) Experiments

213.710.7 210.411.0 194.712.5 191.812.9

16.9210.4 15.0610.22 16.4610.22 17.5210.30 62.812.7

99.7211.53 64.7311.37 %.8312.14 43.4211.14

133.9912.15 124.7011.81 80.9611.68 193.311.96

120.7511.53 62.7511.03 73.5311.77 86.4911.30

136.8214.60

44.011.1 39.211.1 39.913.5 23.511.0 19.910.7 21.710.6 8.510.5 5.410.5 5.810.4

Total

4 14 14 12

12 8

13 12 4

10 5

11 9

13 6

10 7

10 6 7

12 19

11 10 10 11 11 9 9 9 7

305

d, mm

38.6 38.6 90

135

135 38.6 38.6 90 38.6 38.6 38.6 38.6 38.6 90 90 90 90

135 90 90

135 135

38.6 90

135 38.6 90

135 38.6 90

135

*Carboxymethyl cellulose. **Polyacrylamide.

Notation C (n) dimensionless function of geometry and n d agitator diameter, m K constant, Pa(sec)" n flow behavior index, r=K'y'*f dimensionless N rotational speed, 1/sec P power input, W Po power number, P/(p -N 'd% dimensionless Ren Reynolds number for power law fluid, N^'^d^plK, dimensionless p fluid density, kg/m^ T shear stress. Pa


Hirose, T. and Murakami, Y.J. Chem. Eng. Japan, 19,568 (1986) IWo-Dimensional Viscous Flow Model for Power Consumption in Close-Clearance Agitators

Results Use of published data

NpRe= ^ -— TTT—In T " ;r - 4 dsma/Hfib fibO

s

V

<<2 ^

^ I <

1 ' 1 H

r^\

L-^ s. 1 r

*—

H

k.

Nomenclature for agitator geometry.

VESSEL WALL

Two-dimensional flow model.

Ota b d H n fib

Np P Re

tion width of blade, m diameter of impeller, m height of impeller, m speed of rotation, 1/sec number of blades power number, Plpn^d^, dimensionless power consumption, W Reynolds number, pndV^, dimensionless

5 a Pi

s fi p

pitch of blade, m inclination angle of blade, rad correction factor 0.9 (paddle) and 0.7 (others) clearance between blade tip and wall, m viscosity, Pasec density of liquid, kg/m^


Papastefanos, N. and Stamatoudis, M., Chem. Eng. Res. Des., 67,169 (1989) Effect of Vessel and Impeller Geometry on Impeller Power Number in Closed Vessels for Reynolds Numbers between 40 and 65,000.


System

Vessel Type square One size length (cm) Diameter (cm) Height (cm)

Baffle Number Width (cm)

mpeller

Type Diameter (cm) Number of impellers Number of blades on impeller Length of impeller blade

(perpendicular to shaft) Width of impeller blade

(parallel to shaft) Disk diameter (cm) Thickness of disk (mm) Thickness of blade (mm)

(1)

flat-bottomed 28.4 —

28.4

4or0 2.8

W 15.0

1 6

D/A

D/5

9.5 2.5 1.2

(2)

cylindrical flat-bottomed

( b ) ~ 14.7

1 6 —

D/5

— — 1.2

— 28.4 28.4

4or0 2.8

(c) 14.9

1 6 —

Z>/5

— — 1.2

(a): flat vertical six-blade disk style, (b): flat vertical six-blade open style, (c): 45° pitched six-blade open style

UP

€2 #

(A) (B)

Schematic diagram or (A) a six-Uade disk style impeller and of (B) a six-Uade open style.


Working fluids and their physical properties Com syrup solutions

Viscosity: 7x 10" -4Pasec Experimental conditions

Reynolds number: 40 — 6.5 x 10* Results

1

r I t I 111 „

"^T^

' ' « • « I • I I I 1 1 I I M I I _ji I. I I i n

NR.« pND*

Plot of InNp versus InNae for a flat vertical six-blade disk style impeller. (® Baffled square vessel, ® Baffled cylindrical vessel, ® Unbaffled square vessel)

Plot of InNp versus inNR, for a flat vertical six-blade open style impeller. (® Baffled cylindrical vessel, ® Baffled square vessel, ® Unbaffled square vessel)

3.1 Siiigl«phas« 183

Plot of hiNp versus InNR, for a 45** pitched six-Wade open style impeller. (® Baffled square vessel, ® Baffled cylindrical vessel, (D Unbaffled square vessel)

^ .

Plot of hiNp versus ITINR, for baffled cylindrical vessels. ((D Flat vertical six-blade open style impeller, © Rat vertical six-blade disk style impeller, (3) 45** pitched six-blade open style impeller)

184 Cha|il«r 3. Powar draw and consumption

. 1 '

-J I I I M111 I I I > m 1,1 _J I I I I HI I I I I l i l t 10*

Re H

Plot of InNp versus InNRe for baffled square vessels. (® Flat vertical six-blade disk style impeller, ® Flat vertical six-blade open style impeller, (D 45** pitched six-blade open style impeller)

'-' \2li

" AAA

7— * ^ A

1 t » I 1 1 1

^ s " ^ AA^

u I i I I tt I

Hot of lni\ ^ versus InNRe for unbaffled square vessels. (® Flat vertical six-Wade open style impeller, ® Flat vertical six-blade disk style impeller, (D 45** pitched six-Wade open style impeller)


fotat D D, DL

Dw gr N Np NR,

P X

^ P

ion impeller diameter, m disk diameter, m length of impeller blade, m width of impeller blade, m gravitational conversion factor, kgm/kgfsec^ impeller rotational speed, 1/sec powder number, PgdpN^D^, dimensionless Reynolds number, pND^I^i, dimensionless impeller power, W disk thickness, m viscosity, Pasec fluid density, kg/m^


Carreau, E J., P^s, J. and Guerin, R, Can. /. ofChem. Eng., 70,1071 (1992) Mixing of Newtonian and Non-Newtonian Liquids: Screw Agitator and Draft Coil System.


Pathi

Path 2

Path 3

Sketch of the mixing system.

System geometry (all dimensions in metres)

1. Vessel: Z)=0.254, if=0.262(C1), 0.255(C2X 0.261(C3) 2. Agitator: £/=0.150, A=0.220, j>=0.147, M;=0.067. rf«=0.0159. cta= =0.012

3. Coils

Name Material dc

CI Cr plated Cu 0.1827 C2 Steel 0.1763 C3 Copper 0.1887

he

0.205 0.2075 0.2175

du

0.0127(1/2") 0.00635(3/4") 0.00476(3/16")

du

0.0095 0.0043 0.0032

Cbr

0.0275 0.0285 0.0175

ec

0.0060 0.0064 0.0065

He

10.5 16.5 19.5

Characteristic parameters: D/d=1.69,p/d=0M, h/d=lA7, w/d=0A5, do/d==0.106, Cba/d==OM,



Properties of experimental liquids

Substance

Glycerol

Vitrae oil HV32 Mixture HV320

Com syrup CMC

Xanthan

Polyacrylamide

Cone. (mass %)

89.0 91.5 93.5 95.0 97.5

100. *

100. 9|C3|C

1.0 2.0 0.75 1.0 1.5

600mg/L 0.2 1.0

M(Pas) or m (Pas")

0.14 0.213 0.275 0.408 0.598 0.055 0.200 0.785 2.48 0.564 9.5 6.27 6.5 8.62 0.136 0.521 5.04

n ( - ) 1.0

\J 0.748 0.631 0.122 0.196 0.183 0.871 0.734 0.521

P (kg/m^)

1,232. 1,235. 1,240. 1,246. 1,255.

856. 873. 885.

1,383. 996. 996. 995.

\ 1,195.

\

k (W/mK)

— 0.320 0.315 0.310

— 0.145

\ 0.323 0.588 0.575 0.610

\ 0.356

i

Cp g/kg-K)

— 2,515 2,480 2,451

— 1,901

1 2,358 4,177

1 2,902

\ •Adjusted for desired viscosity.

**Com syrup slightly diluted to avoid crystallization. Properties of distilled water used for solutions: //=9 x lO"'' Pas, p=995.4 kg/m^ ife=0.610 W/mK, c^=417J/kgK.

Results

NpICi = 1200/?«/* (1 + 354.8 Wi^"^)

where Ci is given by:

a = {0.124 + 0.265 [1 - exp (-0.00836/?€^)]}(1 - 0.811 Wi""'^^)

Notation Cp specific heat at constant pressure, J/kgK d agitator diameter, m k thermal conductivity, W/mK ks Metzner-Otto constant, dimensionless m power law parameter, Pasec" n power law index, dimensionless N rotational speed, 1/sec Np power number, dimensionless Ni primary normal stress differences. Pa Reg generalized Reynolds number, pN^'*dVmki*'~^, dimensionless Wi Weissenberg number. Nil 2 rj g, dimensionless g shear rate, 1/sec 7] viscosity of non-Newtonian liquids, Pasec ^ viscosity of Newtonian liquids, Pasec p liquid density, kg/m^


Carreau, R J., Chhabra, R. R and Cheng,]., AIChEJournal, 39,1421 (1993) Effect of Rheological Properties on Power Consumption with Helical Ribbon Agitators.


Geometrical characteristics of agitators

Geometry d(m) D/d hid p/d void

HRl HR2 HR3 HR4 HR5 HR6

0.263 0.263 0.263 0.360 0.360 0.360

1.11 1.11 1.11 1.11 1.11 1.11

1.05 1.05 1.05 1.03 1.03 1.03

0.695 0.850 0.695 0.686 1.030 0.686

0.097 0.133 0.133 0.083 0.133 0.133

H h

• W i«

d

D Sketch of helical ribbon agitator system.

Working fluids and their physical properties Rheological parameters of the fluids

Fluids

Dilute com syrup #1 Dilute com syrup #2 Dilute glycerol #1 Dilute glycerol #2 2.5% XTN 0.5%XTN(gly./H2O) 1.8% XTN 0.8% XTN 0.5% XTN 3% CMC 1%CMC 0.4% CMC (gly./HzO) 0.1%CMC(gly./H2O) 0.7% gellan (com symp) 800 ppm PAA (com symp) 0.35% PIB (PB+Kerosene)

n (-)

1 1 1 1 0.183 0.199 0.200 0.240 0.250 0.299 0.409 0.530 0.701 0.910 0.940 1

m (Pas*)

12.0 4.16 0.470 0.067

22.4 4.13

11.8 2.31 1.84

9.75 1.20 0.750

10.5 8.19

U (s)

7.83 0.110

no (Pas)

469 1.57

n^ (Pas)

0.19

»' (-)

0.782

0.740 1.12

1.67 2.00

vfi (Pas")

7.85

18.0 0.140

0.150 1.29

P (kg/m")

1,440 1,360 1,140 1.100 1,080 1,200 1,080 1,050 1,030 1,060 1,040 1,200 1,200 1,300 1,350 1,100

3.1 Single phase

Results

189

10^

2;

g z u

o a.

10* V

10'

10 k-

10

I 1 1 1 1

r ^v

r )|k

1 ' ' "

• 3%CMC O IX CMC A 2.6X x m • 0.0X XTN V 0.7X gdUaa

Nvwtoaiui HRa

mm»

4

1 r "L- 1

^ " " " ^ 1 il 4 il 1 1 J

10~* 10"^ 10° lO' 10* 10' 10*

Generalized Reynolds Number, Re

Power data for the shear thinning inelastic fluids.

g

0)

3

o a.

Generalized Reynolds Number, Re

Power data for the viscoelastic fluids.

^9Q Chapter 3. Power draw and consumption

Notation d agitator diameter, m D vessel diameter, m h impeller height, m H height of liquid in the vessel , m Kp proportionality constant of the power number, Np=KpT]e/(d^Np) m power law parameter, P a ( s e c ) " m' parameter, PaCsec)" n power law index n! parameter N impeller rotational speed, 1/sec Np power number, P/d^N^p, dimensionless p impeller bitch, m P power, W Reg generalized Reynolds number, d^Np/rje, dimensionless h Cross model parameter, sec w impeller width, m Ye effective shear rate , 1/sec T]e effective viscosity, ?]«=m | ye | " ' S P a s e c Tjs solvent viscosity, P a s e c r]o zero-shear viscosity. Pa-sec p liquid density, kg/w?


Kamei, N., Hiraoka, S., Kato, Y., Tada, Y., Shida, H., Lee, Y-S., Yamaguchi, T. and Koh, S.-T, Kagaku Kogaku Ronbunshu, 21,41 (1995) Power Correlation for Paddle Impellers in Spherical and Cylindrical Agitated Vessels


System

Vessel Type Diameter (mm)

Baffle Impeller

Type

Diameter (mm) Width of blade (mm) Number of blades on

Number of impellers

impeller

(1)

spherical 163,190

no

paddle

1

57, 76,95 19,28,38,76

2,4,6,8

(2)

flat-bottomed 130,145,170

no

paddle

1

Working fluids Ion-exchanged water, glycerin solution and com syrup

Results For cylindrical vessels

Rec ={ Kr]\a(D/d)

f

C, = [{1.96 (y< '6 / f f )" ' } - ' ' +(0.25)-'-']-*"-'

m = [{Q.nOiynfblDf'^y''^ +(0.333)-'-']-'''•'

Cir = 23.8 (d/Dr'^ib/DT'^irn^'b/H)-"*

/-=7.56xlO-^(rf/D)C,°'

192 Cha|it«r 3. Pow«r draw and consumptioii

^ 2HD/d) p -

7 = '

[D/d)-(d/D)

171110.157+inpHD/d)}'-''']

n'p^Hl-(d/D)'}

r]\xi{Dld)

^ (PD/df

1/3

For spherical vessels

(4VY" Z)= ± 1 . =0.874A

Notation b height of impeller blade, m d impeller diameter, m D diameter for qrlindrical vessel, Da diameter for spherical vessel, m H liquid height, m Up nmnber of impeller blades N rotational speed, 1/sec Np power number, P/pN^d^, dimensionless P power consumption, W Red impeller Reynolds number, Nd^p/fi, dimensionless V volume of spherical vessel, m fi viscosity, Pasec p density. kg/m^


Mochizuki, M., Takei, N., Satoh, K. and Akehata, T, Kagaku Kogaku Ronbunshu, 21,628 (1995) Power Required for Upper and Lower Impellers in Turbulent Mixing Vessels with Dual Impellers


Liquid contained Height: 300 or 600 mm


Impeller Type: flat blade disk turbine (D)

downward pumping-45° pitched blade turbine (Pd) upward pumping-45° pitched blade turbine (Pu)

Diameter: 100,125 and 150 nun Number of impeller: 1 or 2 Number of blades on impeller: 6 Blade width: d/5

hi D-D h2/dT>0,S others /i2/rfr>l/3


Results

Power numbers for dual impellers with 0.1 m diameter (O: D-D, A: Pd-Pd, D: Pu-Pu, A: Pd-Pu, • : Pu-Pd, ©: D-Pd, O: Pu-D, • : D-Pu, V: Pd-D).


1 | — I — I — I — r -

Q.

2 0.5

2

Relative power required for upper and both stage in dual impellers, Np, u/Np,t (O: D-D, A: Pd-Pd, D: Pu-Pu, A: Pd-Pu, • : Pu-Pd, ©: D-Pd, O: Pu-D, • : D-Pu, V: Pd-D).

1 1 1 \ r

I 1 L_J I I I L

10

JL

d

Effect of impeller diameters on power (O: d = 10 cm, A: rf = 12.5 cm, D: </= 15 cm).

D-Pddual

Pd-Pd dual

0.5

Notation d diameter of impeller, mm or m dr diameter of vessel, mm hi bottom clearance of impeller, m hz impeller spacing, nmi hs distance between the upper impeller and water surface, nmi n rotational speed of impeller, 1/min Np power number, P/pn^d^, dimensionless P agitation power input, W p liquid density, kg/w?

Subscripts t total (dual impellers) U upper impeller

h?/dT H


Brito-DE la Fuente, E., Choplin, L. and Tanguy R A., lyans. Instn. Chem. Engrs., 45, P^t A, 75 (1997) Mixing with Helical Ribbon Impellers: Effect of High Shear Thinning Behavior and Impeller Geometry


Liquid contained Height of liquid/height of impeller: 1.14

Impeller Type: helical ribbon screw impeller

Helical ribbon screw impeller (all dimensions are in m).

Geometrical ratios of impellers used'.

Impeller Type

HRS-IA HRS-2A HRS-IB HRS-2B HR-IB HRS-1.5

D/d" 1.135 1.135 1.135 1.135 1.135 1.135

hid w/d

0.108 0.108 0.162 0.162 0.162 0.135

s/d

1.0 0.5 1.0 0.5 1.0 0.7

Ws/W

1.25 1.25 1.17 1.17 -

1.20

Ss

0.370 0.185 0.370 0.185

-0.247

' All dimensions in m. ** The mixing vessels diameter, Z)=0.210 m.


Working fluids, their physical properties and experimental conditions

Rheological properties of the fluids.

Fluid Power law model parameters ' Range

PB96%-KER4%(NEW1) w = 1.0; w = 33.67 0=25 PB91%-KER9%(NEW2) « = 1.0; w = 6.69 0=25 GLY 90% - H2O 10% (NEW 3) « = 1.0; m = 0.17 9 = 22.5 CMC 3% (VEl) n = 0.359 12 < 0 < 30

w = 113.8-1.7200 l<y<60 XTN 0.5% (PSTl) n = 0.0916 + 3.0 x 10- 0 20 < 0 < 26

m = 5.0817 - 5.42 x 10- 0 1 < 7 < 100 XTN 3% (PST2) n = 0.1377; m = 21.34 20 < 0 25; 0.1 < y < 500 CMC 0.5% (PST3) n = 0.904 - 8.29 x 10- 0 20 < 0 < 30

m = 0.738 -1.74 x 10- 0 100 < 7 < 100 CMC 1.5% (PST4) n = 0.372 + 1.28 x 10- 0 20 < 0 < 30

m = 11.3-0.1770 l<y<10 CMC 1.5% (PST5) n = 0.6044; m = 14.8765 8 < 0 < 10; 0.1 < 7 10 Gellan fermentation broth (PST6) n = 0.19; w = 9.7 0 = 30; 0.1 < 7 < 100

* The power law model: ti^my"'^. ^ 0 in **€; 7 in s"*; m in Pas". PB=polybutene; KER=kerosene; GLY=glycerol CMC=carboxy methylcellulose; XTN=xanthan.

Results

Np=173ARe-^

D

•0.72 / >v0.l4

w

Np=- , ,

197


Raghav Rao, K. S. M. S. and Joshi, J. B., Chem. Eng./., 39, 111 (1988) Liquid-Phase Mixing and Power Consumption in Mechanically Agitated Solid-Liquid Contactors




Impeller

Type Diameter (m) Vertical blade height (m) Horizontal blade length (m) Angle of pitch (degree) Blade thickness (m) Disk thickness (m) Number of impellers Number of blades on impeller Off-bottom clearance

DT 0.19 D/b D/4

— 3x10- ' 4x10-3

1 6

PTD 0.1425,0.19,0.25,0.33 0.03,0.04,0.063,0.07 0.045,0.075,0.10,0.14

45,45,45,45 3 X10-3

— 1 6

r/6, r/4, r/3, r/2

PTU 0.19 0.04 0.075 45

3x10-3 -1 6

DT: disc turbine PTD: pitched blade turbine downflow PTU: pitched blade turbine upflow

Working fluids, solids and their physical properties Liquid: tap water Solid: quartz particles

shape: granular average particle size: 100—2,000 ^m density: 2,520 kg/m' terminal settling velocity in water: 34-165 mm/sec

Experimental conditions Impeller speed: 2—13.3 rps Solid loading: 0-40 wt%


Results (1) Effect of impeller design

the power required for suspension by menus of a PTD impeller is much lower than with PTU and DT impeller

(2) Effect of loading PTD,DT NpsL ocX'-'' PTU NpsLocX'''''

(3) Effect of particle size PTD, PTU NpsLocdp'"* DT iNfeiocrf/oe

(4) Effect of impeller diameter

(5) Effect of tank diameter

Notation dp average particle size, m D impeller diameter, m Ncs critical impeller speed for sohd suspension (soUd-liquid system), 1/sec NpsL power for solid-liquid system, dimensionless iPm)cs power consumption per unit mass at Ncs (soHd-liquid system), W/kg T tank diameter, m X solid loading, wt%

3.2 Multiphas* 199


Oyama, Y. and Endoh, K., Kagaku Kogaku, 19,2 (1955) Power Characteristics of Gas-Liquid Contacting Mixers

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 16.5 (2) 20 (3) 27.4 cm

Liquid contained Height: (1) 16.5 (2) 20 (3) 27.4 cm

Baffle Number: (l)-'(3) 4 Width: (1)~(3)Z)//10

Impeller Type: paddle, vaned disk, and flat blade turbine Geometry:

—i- Paddle A/A = 1/3 P /A = l/4

Vaned disk A/A = 1/3 Pr./A-1/3.05 A/A = 1/3.38

Flat blade turbine A/A = 1/3 W A = 1/3.94 A/A = 1/3.22 A/A = 1/1.30

Experimental impellers.

Off bottom clearance: A/3 Sparger Type: a single nozzle Diameter of nozzle: 1.5 and 6 mm


Experimental conditions Air rate: maximum 600 cc/sec Temperature: 19°C

Chapter 3. Pow«r draw and consumption

A: r u t bUd iartHnc(N;«8)

6 Vdfieddtsk (Ni-8)

C- Vo/ieddisft (Ni«6)

0- Varied disk** (Ni«l6)

(Ni«4) p: Paddle

4 6 d 10

Power characteristics of gas-liquid contacting mixers.

12 J4

Notation A impeller diameter, cm

tank diameter, cm impeller rotational speed, 1/sec QalnD?, dimensionless number of impeUers power consumption under aeration, kgf/msec power consumption without aeration, kgf/msec volumetric rate of air, cc/sec impeUer width, cm

A n NA Ni P. Po Qa Wi

3.2 Multiphas* 201

Bruijn, W, van't Riet, R. and Smith, J. M., Trans. Instn. Chem. Engrs., 52,88 (1974) Power Consumption with Aerated Rushton Turbines

Experimental apparatus Vessel Type: flat-bottomed Dimension: 50 cm x 50 cm

Baffle Number: 4

Impeller Type: a standard Rushton Diameter: 7£ cm Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 25 cm

Sparger Type and diameter

Type

open type ring sparger ring sparger ring sparger

Diameter (10" m)

0.5 2.3 5.0 7.4

Working fluids Liquid:

Liquid

Water Water Water Kerosene

Addition

12.5 weight % NaCl 0.83 vol % Teepol

CT(N/mxlO-3)

73 76 28 26

Gas: air


Results (1) the influence of surface tension and dissolved ionic solutes

1

z 8 o« Ui

§ a.

S06 < Ui 1 1

5?

r|—

" •

1 1

1

1

$ K

r

A

1 •

L

A

! * • K

,

A

• • — » i :

»

H

J

0 001 0O2 a09 0//V0'—OiMENSONLESS GAS MFLOW RATE

Symbol Fluid # distilled water V 12-5 weight %NaCl X 0* 83 volume % Tccpol A kerosene

Square vessel, D « / / = 14s-*

Power consumption curves with different fluids.

004

Ko 5-5 5-3 5-4 5-4

7-6 cm

Re 81,000 81,000 81,000 49,400

(2) the influence of the number of blades

0 OOS 0^0 O'lS 0//V0'-OIMENSIONLESS GAS INFLOW RATE

Symbol Number of blades Ko A 6 5-6 O 9 8-6 X 12 1 0 0 • 18 120

Square vessel, i> = 7-6cm N^ 12s-* Fluid: distilled water Re = 69,300

Power curves for stirrers with different number blades.

3.2 Mumphas* 203

(3) the influence of the gas spargers

i

uj 0 oc

I

02]

« t

• • « % • • . • i « « « - ^

0« t <H)2 003 0-04 Q/A^O' —CNMENSiONLESS GAS INFLOW RATE

Symbol Sparger diameter X 0' 5 cm O + •

2-3 cm 5*0 cm 7*4 cm

Square vessel, Z) = ?• 6 cm N^ 10s-* Fluid: distilled water Re « 57,800 Ko « 5-4

Power curves for different gas spargers.

Notation D stirrer diameter, m

power number, Po/pN^D^, dimensionless stirrer speed, 1/sec gassed power consumption, Nm/sec ungassed power consumption, Nm/sec gas flow rate, mVsec Reynolds number, pNDVr], dimensionless liquid viscosity, Nsec/m^ density, kg/m^ surface tension, N/m

N Pi Po Q Re r] P a


Loiseau, B., Midoux, N. and CharpentierJ.-CAIChE Journal, 23,931 (1977) Some Hydrodynamics and Power Input Data in Mechanically Agitated Gas-Liquid Contactors

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 22 cm (2) -Volume: 8.9 (2) 5.5^

Liquid contained Dispersion height: (1) 22 cm (2) T


Impeller Type: a six flat-blade Rushton disk turbine Diameter: T/3 Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: T/3

Sparger Type: (1) an open tube (diameter 0.8 cm)

(2) a perforated ring (diameter 6 cm; thirty holes; diameter of hole 0.1 cm) (3) a porous ring (diameter 6 cm)

Location: beneath the turbine Working fluids and their physical properties

Liquid:

Type of liquid

Pure hquids

Nonfoaming solutions

Foaming solutions

Liquid

Water Glycol

Water + lauric Alcohol (1.7 p.p.m) Ethanol (95% by volume) Water + sugar (60 wt %)

Water + HCl (5N) + CuCl (0.9 M) Aqueous sodium Sulfite sodium (0.2 M) Acetic acid + propionaldehyde (2 M) Water + sugar (36 wt %) Aqueous sodium* Sulfite solution (0.8 M)

P,10^ kg/m^

1.0 1.11

1.0

0.803 1.278

1.145 1.028

1.024 1.158 1.085

M. 10-^ Pas

1.0 19.75

1.0

1.50 48.50

1.25 L12

1.22 5.40 1.50

cj, 10-3 N/m

72.0 48.1

23.0

23.9 53.5

44.4 61.0

28.0 54.0 56.1

Gas: air

3.2 Multiphase 205


Type of liquid

Pure liquids


Foaming solutions

Liquid

Water Glycol

Water + lauric Alcohol (1.7 p.p.m) Ethanol (95% by volume) Water + sugar (60 wt %)

Water+ HCl(5N) + CuCl (0.9 M)

Aqueous sodium Sulfite sodium (0.2 M) Acetic acid + propionaldehyde

(2M) Water + sugar (36 wt %) Aqueous sodium* Sulfite solution (0.8 M)

Np

3.80 ±0.15 Variable with

Re 3.72 ±0.11


Re 3.38 ±0.08

3.68 ±0.11

3.28 ±0.13

3.15 ±0.11 4.56 ±0.11 3.63 ±0.12

Us,

10-2 m/s

0.07-2.12 0.07-0.62

0.07-0.62

0.07-0.62 0.07-0.62

0.64-4.7

0.27-2.12

0.27-2.12

0.07-0.62 0.07-8.5

rev/min

340-1,650 350-1,400

440-1,500

380-1,600 400-1,400

480-1,720

340-1,625

350-1,500

400-1,650 300-3,000

*iV^=4.56 for r=0.19 m, Vi:=5.5 x 10"^ ml 7V^=3.63 for 7=0.22 m, V)r =8.9 x IQ- m\

Results

Pa=C PoND^ Q.0J56

G

= CM"

For nonforming systems Pa = 0.83Af°-

For forming systems ft = 0.69M°-^

or if M<2xl0^

if M>2xl0^ P . = 1.88M°-3i i Notation

C constant D agitator diameter, m n exponent N rotational speed of impeller, 1/min Np power number . PaIpN^D^, dimensionless Pa aerated power input by mechanical agitation, W PQ unaerated power input by mechanical agitation, W QG volumetric flow ra te of gas , mVsec T tank diameter, m Us superficial gas velocity based on the cross section of the tank, m / s e c VL liquid volume, m^ H liquid viscosity, P a s e c p liquid density, kg/m^ G liquid surface tension, N / m


Matsumura, M., Masunaga, H., Haraya, K. and Kobayashi, J.,/. Ferment. TechnoL, 56, US (1978) Effect of Gas Entrainment on the Power Requirement and Gas Holdup in an Aerated Stirred Tank




Impeller Type: six-blade turbine Diameter: 0.487 Z)T Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: DT/3

Sparger Type: a single nozzle Location: underneath the impeller

Working fluids and their physical properties Gas: air Liquid: water, ethyl alcohol, benzyl alcohol, ethylene, glycol and sucrose solution

viscosity: 0.8-30 cP surface tension: 22^^71 dynes/cm densities: 0.8—1.3 g/cm^

Experimental conditions Impeller speed: 7.08—16.5 rps Superficial velocity of sparged gas: 5 x 10"*—1 x 10" m/sec

Results

1_ (l-r?)'

^ = 1.913xlO-^ iVx)-'-'(7\ i..f (7\r,K./ (7\r .r f ^ l

3x10'^ <NA <9xl0-\ 7xlO^<NRe<2xlO^

BxlO^ <Nwe <lxlO*, 6x10'^ KNFT <3

3.2 Multi phas« 207

Notation Di impeller diameter, m DT tank diameter, m / volumetric flow rate of entrained gas, i/min gr gravitational conversion factor, kg-m/kgf sec^ N rotational speed of impeller, 1/sec NA Aeration number, VslNDi, dimensionless NA modified aeration number, VTINDU dimensionless Npr Froude number, N^Di/go dimensionless N^ power number in gassed liquid, PggdpN^D^, dimensionless NRe Reynolds number, ND?pl\i, dimensionless Nwt Weber number, N^D?pla, dimensionless Pg power consumed in agitation of gassed liquid, kgf m/sec 0 volumetric flow rate of gas sparged from the tank bottom, ^/min Vs total gas volume dispersed in tank, ^ VT overall superficial gas velocity, calculated firom the sum of Q and/, m/sec p density of liquid, kg/m^ a surface tension of liquid, g/sec^

20g Chapter 3. Power draw and consumption

Gray, D. J., Treybal, R. E. and Barnett, S. M.,AIChE Journal, 28,195 (1982) Mixing of Single and Two Phase Systems: Power Consumption of impellers


Liquid contained Height: 0.5 m Volume of liquid in vessel: 0.232 m


Impeller Type: six flat-blade turbine Diameter: 0.1524 m Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 0.0762 and 0.178 m


Results

-^^^^^ = 0.75 NW^PL

g'TC {VG/^GYN'D^

with use of data taken by Bimbinet (1) and Hassan and Robinson (2) (1) Bimbinet, J. J., Air-Liquid Contacting in Mixing Vessels, Holdup and Flooding, M. S. Thesis,

Dept. of Chem. Engr., Purdue Univ., Lafayette, IN (1959) (2) Hassan, I. T. M. and Robinson, C. W.,AIChE Journal, 23,48 (1977)

Notation C impeller height off the tank bottom, m D impeller diameter, m g local gravitational acceleration, m/sec^ gc gravitational constant, kgm/kgf sec^ N impeller rotational speed, 1/sec PT total power input in gas-Uquid dispersion, W T tank diameter, m VG superficial gas velocity, m/sec 0G volume fraction holdup PL mass density of Uquid, kg/w?


Lu, W.-M. and Ju, S.-J., Chem. Eng. Set., 44,333 (1989) Cavity Configuration, Flooding and Pumping Capacity of Disc-Type Turbines in Aerated Stirred Tanks




Impeller

Type Diameter (m) Number of impellers Number of blades on impeller Length of impeller blade (perpendicular to shaft) Width of impeller blade (parallel to shaft) Off-bottom clearance

A 0.072,0.096,0.142

1 6

D/4 D/5 T/3

B 0.096

1 4

Z)/4 D/b T/3

C 0.096

1 8

D/4 D/b T/3

A: standard 6-flat-blade disc-type turbine B: 4-flat-blade turbine C: 8-flat-blade turbine

Sparger Type: a perforated ring Diameter of ring: 0.08 m O.D. of ring tube: 0.00635 m Holes: 2 mm holes drilled every 2 cm Location: 3.5 cm below the impeller


Experimental conditions The operating conditions for impeller pumping capacity measurements under aeration

D (cm)

7.2

9.6

fib

6

6

N (rev min~*)

550 650 800 800 650 800 275 400 500 500

Q Wmin)

10.6 10.6 10.6 21.3 21.3 31.8 10.6 10.6 10.6 21.3

D (cm)

9.6

14.2

9.6

fib

6

6

4

N (rev min"*)

400 500 155 185 230 230 185 230 350 450

Q (i/Tmn)

21.3 31.8 10.6 10.6 10.6 21.3 21.3 31.8 10.6 10.6

D (cm)

9.6

9.6

fib

4

8

N (rev min"

550 550 450 550 225 325 400 400 325 400

Q ') (^/min)

10.6 21.3 21.3 31.8 10.6 10.6 10.6 21.3 21.3 31.8


Results Xa412 / _ \131

OL =1.25x10 ' ""

--(Clf) (4.07+ 1.21«6-0.147M*)

where 4=0.072 for the highest limit of impeller flooding andi4=0.064 for the lowest limit of gas dispersion.

Notation D impeller diameter, m g gravitational acceleration, m/sec^ nh number of blades on impeller N impeller speed, 1/min NF flooded impeller rotational speed, 1/sec Fg impeller power consumption under aeration, W 0 air flow rate, mVsec QL impeller pumping capacity, mVsec T tank diameter y clear liquid volume, m^

3.2 MuttiphaM 211

Hudcova, V, Machon, V and Nienow, A. W, Biotch. andBioeng., 34,617 (1989) Gas-Liquid Dispersion with Dual Rushton Turbine Impellers


Liquid contained Height:/f/r= lor 2


Impeller Type: 6-blade Rushton disc turbine Diameter: Z)/r= 1/3 Number of impellers: 1 or 2 Number of blades on impeller: 6 Distance between two impellers when two impellers are employed: AC; 0.2Z)~3.0Z) Off-bottom clearance: T/3

Sparger Type: a ring sparger Diameter: 0.1 m Number of holes: 16 Diameter of each le: 0.002 m


Results

T T 1^ 1^

10

0-8

0-6

04

0-2

V Upper impeller {PqlP)n,2 ^ Lokrer impeller {PqlP)n,\ O Both Impellers

1vvm(for H=T); H=2T; AC/D»1

J - _L J - J i I L 002 004 006 008 0-10 0-12 OH 0-16 0-18 0-20 0*22

Fir, (a)


1 0

0-8

0-6

0-4

0-2

^ , ^ 1

^ Upper impetler [PilPh.i A Lover impeller (P,/P)„, i O Both impellers

h vvm ( for H=T); Hs2T; AC/D«1

J - -L. -L. 002 0-04 006 008 010 0-12 0-14

Flo

(b)

Pg/P versus Be at AC/D = 1 at constant aeration rate; (a) Qc = 2.3 x 10" mVs; (b) QG = 1.15 x 10"^ mVs.

10

08

06

04

-J

— 1 1 —

. , !.— . .1

~ r

X

a

J L

^ ^ / ° N«325s* ' a 02 O 05 y 10 A 15 X 30

p *

0 S o S O g V V 7 7 ° ^ — • A A A A A A

Single impeller

1 1 - — - L 1 J 1 1

H

0 02 0 04 0 06 0 08 010 012 OK 016 016 0 20 0 22

(Pg/P)2 versus Flc, N = 3.25 s" \

*Eq. (JPg/P)2 = 0.5m/P)i + 1 -SG}

3.2 Multiphase 213

n 1 1 1 1 \ 1 1 1 r AC/0 = 10 N«2-5s"^

OX

02K

•A—

(<JG)F.„-2

. A , „-... A -

A ^

— 7 — 7 — 7 ^

A

7 . ..7 A—A

" V 'V

V Upper impeller (Pg/P)n=2

A Lower impeller (Pg/P)n=i

I I i I I J I { L 0 0 0 2 OOA 0 0 6 008 010 012 OR 016 018 0-20

Pg/P versus Flc for the individual impellers, AC/D = 1.0.

Nota t ion AC distance between two impellers, m

impeller diameter, m gas flow number, QG/ND^, dimensionless liquid height, m stirrer speed, 1/sec minimum speed to prevent flooding, 1/sec power drawn number ungassed conditions, W power drawn under gassed conditions, W gas flow rate, mVsec vessel diameter, m gas holdup

D FIG

H N NF

P P. QG T EG

Subscripts 1,2 a single or two impellers, respectively « = 1, n = 2 the lower and upper impeller, respectively F at the flooding-loading transition


Abrardi, V, Rovero, G., Baldi, G., Sicardi, S. and Conti, R., lyans. Instn. Chem. Engrs., 68, Part A, 516 (1990) Hydrodynamics of a Gas-Liquid Reactor Stirred with a Multi-Impeller System

Experimental apparatus Vessels and Impellers




Impeller Type

Diameter (m) Number of impellers Positions of impellers

Distance between bottom and the first impeller

Distance between 1st impeller and the second impeller

flat-bottomed 0.39

0.39

4 0.04

6DT,4MFD,4MFU

T/3 1

r/3

—

flat-bottomed 0.39

0.65

4 0.04

6DT-6DT, 6DT-4MFD, 6DT.4MFU

r/3 2

r/3

21/3

6DT: six-blade disk turbine 4MFD: pitched blade mixed flow turbine, pumping downward 4MFU: pitched blade mixed flow turbine, ptunping upward

Sparger Number of holes: 8 ID of hole: 2 nun Location: beneath the stirrer

Working fluids Liquids: water Gas: air

Experimental conditions Gas flow rate: 5 x 10-*-2 x 10"' mVsec Stirrer speed: 150—800 rpm

3.2 MultiphaM

Results

215

Power number vs N for the 6DT-6DT system. See a table attacned for symbols.

Symbol •

• D A

o •

QG

mVs 0

5.0010" 7.6710-" 1.0710-' 1.5310-' 2.0010-'

wm

0.386 0.593 0.825 1.185 1.546

/ = bottom impeller in flooding conditions.

Po, A j l A J A ^ A A

200 - 1 1 T"

600 N (rpn)

Power number vs N for the 6DT-4MFD system. See a table attached for symbols.

7

6 -

5 -

4 -

3-

2-

\ ^ - . ^ . . -ffv 'Sn D-fl'i fiuja-n-'?-/^V^^4-S5!tS^

1 1 1 1 1 1 1 1

200 400 600

H(rp«)

Power number vs N for the 6DT-4MFU system. See a table attacned for symbols.

Notation D stirrer diameter, m

stirrer velocity, 1/sec or 1/min power, W power number under gassed conditions, P/N^D^, dimensionless gas flow rate, mVsec tank diameter, m

N P POG

QG

T


Smith, J. M. and Katsanevakis, A. N., Thzns. Instn. Chem. Engrs., 71, Part A, 145 (1993) Impeller Power Demand in Mechanically Agitated Boiling Systems


Impeller

Type Diameter (mm) Number of impellers Number of blades on impeller

Length, width, and thickness of blade and disk

A 240,180,130

1 6

B 180 1 6

225,200,165 1 6

shown in a figure attached

A: Rushton turbine B: Hollow blade impeller (blade concave-convex turbine) C: 45° pitched blade impeUer

nm -H0.25 OU-

02D

36 t= 1

1 022D

_n 6 Blade Rushton

D ^ 240. 180 and 130 mm 6 Blade PB turbine

D s 225. 200 and 165 mm

A -HO.25

0.20 ^ ^ R-O.UD

D s 180 mm 6 Blade Concave-Convex turbine

Working fluid Boiling water

3.2 Multiphase 217

Results 5UILS / \0.4

(/?PZ)) = ^ = constantffi. A { vf J

Notation g acceleration due to gravity, m/sec^ PB power consumption in boiling system, W Pu ungassed power demand of impeller, W RPD relative power demand S impeller submergence below free liquid surface, m Vi tip speed of impeller, m / s e c


Mochizuki, M., Takei, N., Satoh, K., Akehata, T. and Miyauchi, T, Kagaku Kogaku Ronbunshu, 19, 560 (1993) Power Required for Upper and Lower Impellers in Gas-Liquid Stirred Vessels with a Dual Turbine


Liquid contained Height: 300 or 600 mm


Impeller

Type Diameter (mm) Impeller width (mm)

/i2(mm) hi (mm)

(1)

100 20

5-30 75

(2)

flat six-blade disk turbine 125 25

5'-30 75

(3)

150 30

5-30 75


Experimental conditions Air flow rate: 8.3 x 10-^-7.5 x 10* mVsec (20°C, 1 atm)

Results

Power requirements for dual turbines with a large impeller spacing.

N A 1-1

3.2 MuKi plias« 219

10

cT

0-5

Power requirements for dual turbines with a small impeller spacing.

d » 10 ca

n « 400 rp»

-L

O Dual iapcller : Both A (h ,/d «0.5) : Upper D : Lower

Sinjle iapellcr

I I -L J-0 &05 0-10

N A I-I

(Single impeller: liquid height = 300 mm; flat six-blade disk turbine (d = 100 mm)) Notation

d impeller diameter, mm hi bottom clearance of lower impeller, mm hz impeller spacing, mm n rotational speed of impeller, 1/sec NA gas flow number, Qg/nd^, dimensionless P agitation power input, W Qg gas flow rate, mVsec

Subscripts 0 unaerated g aerated


Bakker, A. and Van den Akker, H. E. A., lyans. Instn. Chem. Engrs., 72, P ^ A, 573 (1994) Gas-Liquid Contacting with Axial Flow Impellers



Baffle Number: 4 Width: 0.077 T Clearance of baffle from wall: 0.023 T

Impeller

Type A 315 SR(%) 90 Rt.i(%) 77 Hb 4 Dim) 0.178 Blade width (m) -

Off-bottom clearance (m)

CD - ^bAb p _ flbAb, *JI\ — ~~~'~" J\b, 1 — —————

ED' E(D'-4 4

Leeuwrik 160 80 6

0.168 —

0.75 Z) or Z)

1

dL)

PBT 60 45 6

0.176 0.2 Z>

PBT: down wards pumping pitched blade turbine, 6 blades at 45° blad Sparger

Type

a pipe sparger (PS) a small ring sparger (SRS) a large ring sparger (LRS) a quadruple pipe sparger (QPS)

dsim)

-0.4 Z> 0.75 Z)

—

Working fluids and their physical properties liquid: distilled water

glycerol solutions (1) viscosity = 36 mPasec density = 1,190 kg/m^ (2) viscosity = 80 mPasec density = 1,220 kg/m^

Gas: air

221

N » 4 H t

.J I I I I t .

Power curves for the PBT at constant impeller speed.

Pg/p. o Vtg • OJOOS m/i

- ^ Vag • 0.011 m/t

A3^ • U r o * Mno 8p«ro«r

mJ. t.. 1 . I I I t

Power curves for the A315 at constant impeller speed. Power curves for the A315 at constant superficial gas velocity Q^rge ring sparger).

e v«o-aoo$m/« « VsQ • oxm M/s • Vsg . QLOW m/a

• Laro«Mno tparftr

. Pc/V| {iH/m"9)

100

0 • • ' ' ' • • • • ' • • • •

.1 v«a ("•/•)

Power curves for the PBT at constant superficial The minimum power consumption necessary to gas velocity. prevent direct loading.

16


h

[ J9^^^^

fn^:* ^

r

I 0 4Hi •

I • 7 Nz

[• • 4 HI -

I « 7Hx

1—1 1 1 1

SRS

1 >

' *»^«,^

N ^

t 1 , 1 , . A

' » » •

» 7"^r^ \

A318 • Cn* • 0.4

1 1 1 1 1 1 1 1 1 1

J

.7

J

A

A

H A315 • LAS • 8/0 - 0.1 - Vtg • 0.01 m/t

• M mPas ^ • 10 fflPM

y - >'''*'''^^"**>^_ ^^y*^

*^^/^ • "5^ \ y

• • • ' • ' • 1 t 1 l _ _

>v,»

J — 1 — 1 t —

.00

Power curves for the A315 with a small ring sparger Power curves for the A315 at three liquid viscosities, and a pipe spaiger at constant impeller speed.

,Po^u L r y -11 n

L \

Y o 4 Hx • S/O • 0.7

\ • 7Hi I «4Hl • t /D«OJ k • 7Hx L L i—J-J„ l - . - l . . *._L- i—X

•—o ..v-o-- «'—« * 1 - T T

• ^ — . - i

A31S . C/T - 0.4

OiMlMnf 8paro«r

,^L_t., i 1 1 1 i 1 1 1

Vsg - 0.00$ ml% Vag - OJOIO m/t Vtg « OJm m/t

P«T - M mPa* • U r o * Mifl Spwo^

.1 L.

J4 .1

Power curves for the A315, amall ring, sparger, two impeller to sparger separation distances, constant impeller speed.

Notation Ab area of one impeller blade Ah, 1 projected area of one impeller blade C impeller to bottom clearance dkub impeller hub diameter dt sparger diameter D impeller swept diameter Fig gas flow number Ub number of impeller blades N impeller rotational speed P power consumption Po impeller power number 5 impeller-spaiger separation T vessel diameter % superficial gas velocity Wi liquid v o l u m e

Subscripts g gas under gassed conditions u ungassed conditions

.02 .04 M J l

Power curves for the PBT at 80 mPa s.

.1

3.2 Mutti phas« 223

Smith, J. M. and Tarry, K., Trans. Instn. Chem. Engrs., 72, P&rt A, 739 (1994) Impeller Power Demand in Boiling Solutions


Impeller Type: Rushton impeller Diameter: 0.18 m Number of impellers: 1 Number of blades on impeller: 6 Submergence: 0.3 m

Working fluids 5 and 10 wt% NaCl solutions

Results

A.„.76ter BJ [vf )

Notation g acceleration due to gravity, m/sec^ PB power under boiling conditions, W Pu power under ungassed conditions, W S impeller submergence, m Vi impeller blade tip velocity, m/sec

224 Chapter 3. Pow«r draw and eonsumptloii

Cheng, J. and Carreau, R J., Chem. Eng. Sd., 49,1965 (1994) Aerated Mixing of Viscoelastic fluids with Helical Ribbon Impellers

Experimental apparatus Vessel and impeller geometries Type: flat-bottomed Dimensions: D/d=hll

w/d=0,133 p/d=0.695 /j/J=1.05


Rheological properties of test fluids

Test fluids

Glycerol 2.5% xanthan (H2O) 0.5%xanthan(H2O) 3%CMC(H20) 1%CMC(H20) 0.5% xanthan (glycerol/H2O) 800 ppm PAA (com syrup) 0.5% PIB (FB+kerosene)

n (-) 1 0.183 0.250 0.299 0.409 0.199 0.94 1

m (Pas")

0470 22.4

1.84

4.13 1.03 8.19

h (s)

7.83 0.110

lo (Pas)

469 1.57

ris (Pas)

0.19

n' (-)

0.782 1.67 2.00

in' (Pas")

7.85 0.15 1.29

Notes: n, w, parameters in the power law model: 7;=my"; /i, rjo, parameters in Cross model: 77=770/1+(fiy)*~''; 77,, parameter in the expression: 77=mx"+77,;«', m', parameters in the expression: Ni-m'/y"',

Gas: air Results

Np = P/d^N^p

Laminar flow regime, 0.28 ^ Rea ^ 70 (0.028 <.Na<. 0.87,0.0044 ^ Wi < 0.060):

Np = 1030i?e.-°-^Wfl «»* (1 + 724 Fr«2.i5)

Transition flow regime, 70 <. Rea <> 2600 (0.0087 <,Na^ 0.63,0.013 Wi <, 0.96):

Np = 40.3i?««-°-^iVfl«-^(l + 3.79 F f«-*«0

Notation d impeller diameter, m D vessel inner diameter, m h height of liquid in vessel, m ks effective syear rate constant N impeller rotational speed, 1/sec Na aeration number, Q/Nd^, dimensionless Np power number, P/d^N^p, dimensionless p impeller pitch, m P power, W 0 flow rate, mVsec Rea aerated Reynolds number calculated from aerated deformation rate, % t\ Cross model parameter, sec Vg gas superficial velocity, m / s e c w impeller width, m

3.2 MuKi phm99 225

Wi Weissenberg number, \if\Nlr]a, d imensionless Ya aerated e£fective deformation rate eq (1), 1 / s e c Yb additional deformation rate due to bubble passing, eq (2), 1 / s e c Ye effective shear rate due to mechanical agitation, eq (3), 1 / s ec T]a aerated effective viscosity, Pasec r]s solvent viscosity, Pasec p hquid density, kg/m^ V i primary normal s tress difference coefficient, Pasec^

Ya = W^e (1) 76 = 15001; (2)

Ye^ksN (3)


Linek, V, Moucha, T. and Sinkule, J., Chem. Eng. Sci., 51,3203 (1996) Gas-Liquid Mass Transfer in Vessels Stirred with Multiple Impellers-I. Gas-Liquid Mass Transfer Characteristics in Individual Stages


Liquid contained Height: (1) IT(2)2T(3)3T (4) 4 T Volume of liquid in vessel: (1) 0.00517 (2) 0.00517 x 2 (3) 0.00517 x 3 (4) 0.00517 x 4 m


Impeller Type: a standard Rushton turbine Diameter 7/3 Number of impeUers: (1) 1 (2) 2 (3) 3 (4) 4 Number of blades on impeller: (1)~(4) 6 Length and width of impeller blade: D:L:w:b = 20:5: A: 15 Positions of impellers:

Distance between bottom and first impeller: D Distance between first and second impeller: T Distance between second and third impeller: T Distance between third and forth impeller T

Sparger Location: underneath the first impeller

Working fluids Liquid: distilled water and 0.5 M Na2S04 solution Gas: air, nitrogen and pure oxygen

Experimental conditions Superficial gas velocity: 2.12,4.24 and 8.48 nun/sec Agitator speed: 5.5—18.8 1/sec Temperature: 20°C

Results For water

(«iW = 0.0377 7V^^Sr°- ^ (e2-^4)agit = 0.104 N^'^Vs-''^

For0.5MNa2SO4 (ei)agit = 0.177 N^Vs-'''^ fe~4W = 0.090 i\r3-oit;,-«-359

Notation b D {^dagit

L N T Vs

w

diameter of agitator disk, m diameter of agitator, m power input by agitator per unit volume of liquid in length of blade, m agitator speed, 1/sec diameter of vessel, m superficial gas velocity, m/sec width of blade, m

\ stage i ,W/m3

3.2 Multi phase 227

Mochizuki, M., Takei, N., Sato, T, Tada, H., Sato, K. and Akehata, T, Kagaku Kogaku Ronbunshu, 23,342 (1997) Power Required for Upper Impeller in Gas-Liquid Vessels Agitated by Dual Turbines with Various Designs




Impeller

Type Diameter (m) Impeller width (m)

hzim)

hiim)

(1)

0.100 (S) 0.02

0.05-0.30

0.075

flat

(2)

six-blade disk turbine 0.125 (M)

0.025

0.05-0.30

0.075

(3)

0.15 (L) 0.030

0.05-0.30

0.075


Experimental conditions Air flow rate: 8.3 x 10-^-7.5 x 10"* mVsec (20°C, 1 atm) Rotational speed of impeller: 150—500 1/min

Results

tl-'-'"' g JK^T)

4 7 = 0.55 dr—d


I (a)

L Type 1 hj-dOcm n«500min'' d-IOcm J I—I i i _ j I i 1-

L Type II ha-Scm n-350min-' d«10an j I I I I 1 * 1 I 1 1 1—I—I U.

E ^ ^ • o4 «. _•.

Dual impeller ^ Upper Lower

"" Single impeller ]

Type lit h2-25cm n-300mln-' d»15cm H -J I I L—J ' « « « ' I I I

5 10 NAXIO* H

Type I, II and HI of {Pg/Po)-NA curves for dual disk turbins.

0.5 h \ \S:nY \ y.L A

" S,M:n

S:I M,L:DI

S.M: I Lin

\ ^

0.5

IWdrH

Map of Type I, II and III of (P /Po)~^k curves for dual disk turbins (A^^^O.ll). S, rf = 0.10 m; M, rf = 0.125 m;L,rf = 0.15 m.

Type I: a region where the power reduction (1 - (Pg/Po)) (PR) of the lower impeller is ahnost equal to that of the single impeller and the PR of the upper impeller is always less than that of the lower impeller under the same experimental conditions and the PR of the upper impeller is always less than that of the lower impeller. Tjrpe II: a region where the above-shown relationship between the PR of the lower impeller and the upper impeller is reversed by increasing the gas flow rate. Type III: a region where the PR of the upper impeller is almost equal to that of the lower impeller.

Notation d dr Fr g hi

fe n NA

P Q.

impeller diameter, m vessel diameter, m Froude number, n^d/g, dimensionless acceleration of gravity, m/sec^ bottom clearance of lower impeller, m impeller spacing, m rotational speed of impeller, 1/sec gas flow number, Qglnd^, dimensionless agitation power input, W gas flow rate, mVsec

Subscripts 0 g U

unaerated aerated upper impeller

3.2 MuKiphaM 229

Birch, D. and Ahmed, N., Ttans. Instn. Chem. Engrs., 75, P ^ A, 487 (1997) The Influence of Sparger Design and Location of Gas Dispersion in Stirred Vessels



Baffle Number: 4

Impeller Type: (1) FDT (Rushton turbine)

(2) PDD (downward pumping 45° six bladed pitched blade disc turbine (3) PDU (upward pumping 45° six bladed pitched blade disc turbine

FDT

Z) = 0.200m w = D/4 q = D/5 r = 3w/5 a = 45°

PDT

Details of the impeller geometry.

Off-bottom clearance: (1) (2) 0.2 m

230

Sparger

h

Chapt«r 3. Pow«r draw and consumption

Q_ O o A

r-'nr

u 9 <? ie o !•»

RiHtla Rinfla RintSa RiHx3l Rmt4a Foint

A,

m • o •

RingJb 1 Rint2b RiniSh Rinjt4l Rint4b

Ring Spai]gers Ringl -» Rmg4

i s : • T I ' T

-LZ)

*?i:if±r:a .} ) )

point Spuger

T I -Sr"

S £1 h-135 H

200 290 400

T = 600 H Schematic of the sparger size and location with respect to the impeller position. Impeller diameter is 200 mm. (Note: the nomenclature a, b, I in italics refer to positions above, below and level to the impeller plane, respectively).

Results

(a) Aerated power conswnption and (b) the gas holdup as a function of the flow number for spaiging arrangements placed below the impeller with the Rushton impeller (FDT), at a stirrer speed of 6.1 s"^

(a) Aerated power consumption and (b) the gas holdup as a function of the flow number for sparging arrangements placed level with the impeller for the Rushton impeller (FDT), at a stirrer speed of 6.1 s'K

3.2 MultiphaM 231

M J*

i: s '

4

A'

1 «*«»

Jtf^\

1 \—

*

. y < ^ ^

1 1—

• o«o PIHMS « | S ^ N.6 . IA

^T^*!]!------*

— 1 — 1 — 1 — ^

b

1

0 Om OM 006 OM a i &12 014 OM o i l

Flow Bmber, Q/ND*

(a) Aerated power consumption and (b) the gas holdup as a function of the flow number for sparging arrangements placed below the impeller with the pitched blade disc impeller pumping upward (PDU), at a stirrer speed of 6.1 s"*. The dotted lines indicate the point of the flooding transition.

OM 01 a n 014 01* o i i

How MMMber. Q ^ N D '

^ N-6.IA MW3« 0 1 Wnim 0

«kg<« o fate t

(a) Aerated power consumption and (b) the gas holdup as a function of the flow number for sparging arrangements placed above the impeller with the pitched blade disc impeller pumping upward (PDU), at a stirrer speed of 6.1 s~*. The dotted lines indicate the point of the flooding transition.

vS? roms

(a) Aerated power consumption and (b) the gas holdup as a function of the flow number for spaiging arrangements placed below the impeller with the pitched blade disc impeller pumping downward (FDD), at a stirrer speed of 6.1 s~^ The dotted lines indicate the point of the flooding transition.

(a) Aerated power consumption and (b) the gas holdup as a function of the flow number for spaiging arrangements placed above the impeller with the pitched blade disc impeller pumping downward (FDD), at a stirrer speed of 6.1 s"*. The dotted lines indicate the point of the flooding transition.


Notation D impeller diameter, m N impeller speed, 1/sec Pg power draw, gassed liquid, W Pu power draw, ungassed liquid, W Q volumetric gas flow rate, mVsec e gas holdup

3.2 Multiphase 233

3.2.3 Solid-liquid-gas systems

Koloini, T, Plazl, I. and Zumer, M., Chem. Eng. Res. Des., 67,526 (1989) Power Consumption, Gas Hold-up and Interfacial Area in Aerated Non-Newtonian Suspensions in Stirred Tanks of Square Cross-Section

Experimental apparatus Vessel geometries and experimental conditions Type: flat-bottomed vessel of square cross-section

variable

side length suspension depth stirrer type

stirrer diameter clearance from bottom suspension volume sparger type sparger location VG m/sec N 1/min P/V W/m^ PL kg/m^ j]ef mPasec T °C

SQT-0.3

0.3 m 0.33 m standard six blade Rushton 0.1m 0.11m 0.03 m tube underneath of stirrer 0.0058-'0.027 200-800 30-1,600 1,050-1,230 3-100 20 or 30

SQT-0.7

0.7 m 0.82 m

0.267 m 0.21m 0.4 m' tube underneath of stirrer 0.02-0.08 100-500 30-2,250 1,050-1,160 1.9-12 20 or 30

Working fluids, solids and their physical properties Fluids: Suspensions of CaCOa and Ca(0H)2

Rheological properties of CaCOa and Ca(0H)2 suspensions at 20°C

Cone. (wt. %)

CaCOs 10 15 25

Ca(0H)2 5

10 15 20

/ir(Pas«)

0.025 0.14 2.1

0.0035 0.037 0.33 1.1

n(-)

0.6 0.45 0.22

0.87 0.54 0.28 0.23

Gass: air+COa for SQT-0.3 and flue gas for SQT-0.7


Results Power consumption

ForSQT-0.3

P = 1.5 PSND^' /^0.56

0 ^

Notation D impeller diameter, m K fluid constancy index, Pasec" n fluid behavior index N stirrer speed, 1/sec P stirrer power input in gassed suspension, W PQ stirrer power input in ungassed suspension, W QG gas flow rate, mVsec VG superficial gas velocity, m/sec V suspension volume, m 77 effective viscosity, Pasec PL suspen sion density, kg/m^

3.2 Multiphas* 235

Satoh, K., Shimada, H. and Yoshino, Z., Kagaku Kogaku Ronbunshu, 17,937 (1991) Power Requirements of Gas-Liquid Contactors with Mechanical Agitation

Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.1,0.21,0.29 and 0.40 m

Liquid contained Height: D under ungassed conditions

Baffle Number: 4 Width: 0.1 Z)

Impeller

Diameter of Wide of Length of Angle of Number of Sign. impeller blades blades blades blades

dim) b/di-) l/d{-) (degree) ( - ) Type

Flat Blade Disk Turbine

Modified Disk Turbine-1


Pitched Blade Disk Turbine

Pitched Blade Turbine

6DT

6MDT-1

6MDT-2

6PBDT

6PBT

0.08 0.10 0.12 0.15

0.08 0.10 0.15

0.08 0.10 0.12 0.15

0.10

0.08 0.10 0.15

1/5

V2/5

1/4

1/4

(>f2+l)/10

V2/5

1/5

1/4

1/4

1/2

90

+45 -45

+45 -90

45

45

6

6

6

6

Off-bottom clearance: H/b Sparger Type: 20 hole nozzle Nozzle diameter: 8 mm Nozzle height: 26 mm Hole diameter: 1 mm Location: directly below the impeller

Working fluids, solids and their physical properties Liquid: tap water Solid: glass spheres density = 2.52 g/cm ; average particle diameter = 70 fim

kaohn density = 2.55 g/cm ; average particle diameter = 5 pm Gas: air

236

Results


—-"(ir(fm Values of a and p for various impellers

Impeller

axlO-^OV/m^) P (-)

6DT

8.38 1.33

6MDT.1

9.90 1.19

6 MDT-2

radial down

8.38 7.30 1.26

• 6PBDT

4.50 1.32

6PBT

3.40

r^ = K {Pav)c

K = 3.0 for all impellers

Notation h width of impeller blade, m

diameter of impeller, m diameter of vessel, m diameter of standard vessel, m Froude number for agitation, N^d/g, dimensionless acceleration of gravity, m/sec^ liquid depth in vessel without aeration, m length of impeller blade, m rotation speed of impeller, 1/sec aeration power input per unit volume of liquid, W/m^ agitation power input to gassed liquid per unit volume of liquid, W/m^ density of suspension, kg/m^ density of water, kg/m^

d D Do Fr g H I N

PaV

P

Subscript c values at the critical point

3.2 Multiphas« 237

Satoh, K. and Shimada, H., Kagaku Kogaku Ronbunshu, 19,557 (1993) Power of Impeller Required for Complete Off-bottom Suspension of Solid Particles under Gassing Conditions




Impeller

Type Sign. Diameter oi

impeller d{m)

0.08 0.10 0.12 0.15

0.08 0.10 0.12 0.15

0.08 0.10 0.12 0.15

• Wide of blades

b/d{-)

V2/5

(V2"+1)/5

^2/5

Length of blades l/d(-)

1/4

1/4

1/4

Angle of blades

(degree)

+ 45 -45

+ 45 -90

45

Number of blades d(-)

6

6

6

Modified Disk Turbine-1 6 MDT-1

Modified Disk Turbine-1 6 MDT-2

Pitched Blade Disk Turbine 6 PBDT

I > ^=^ Q- F€^ ^2r^^^ 6M0T-1 6MOr-2 6 PBDT

Off bottom clearance: HIb Sparger Type: 20 hole nozzle Nozzle diameter: 8 mm Nozzle height: 26 nun Hole diameter: 1 nun Location: directly below the impeller

Working fluids, solids and their physical properties Liquid: tap water SoUd: glass spheres (density = 2.52 g/cm ; average particle diameter = 72.3,116.9,203.5 and

480.3 \m) Gas: air

238

Results

{Rv)c=a(Frr\^ DJ [Doj [pw

Values of a and P for various impellers

Impeller

axlO-^OV/m^)

P(-)

6MDT-1

9.90

1.19

6MDT-2

radial down

8.38 7.30

1.26

APRTlT OrDU I

4.50

1.32

rav (Pav)c

K = 3.0 for all impellers

Notation b width of impeller blade, m d diameter of impeller, m D diameter of vessels, m Do diameter of standard vessel, m Fr Froude number for agitation, N^d/g, dimensionless g acceleration of gravity, m/sec^ H liquid depth in vessel without aeration, m / length of impeller blade, m N rotation speed of impeller, 1/sec Pav aeration power input per unit volume of hquid, W/m^ Pgv agitation power input to gassed liquid per unit volume of liquid, W/m^ T tank diameter, m p density of suspension, kg/m^ pw density of water, kg/m^

Subscript c values at the critical point

239

Chapter 4. Heat transfer

4.1 Single phase

Mizushina, T, Ito, R., Murakami, Y. and Kiri, M., Kagaku Kogaku, 30,719 (1966) Experimental Study of the Heat Transfer of Newtonian Fluid to the Wall of Agitated Vessel


Liquid Height: 38.0 cm


Impeller

Type

Diameter (cm) Width (cm) Arm height (cm) Angle of blade (°) Off-bottom clearance (cm)

anchor

18,25 —

25,28 90 2

paddle

18 3.0 — 90

6,26

propeller

18 3.0 — 45

6,17

Working fluids Newtonian fluids

Experimental conditions Re number:

Anchor: 2.13 x 10^ ~ 1.18 x 10 Paddle: 1.35 x 10^ - 5.48 x 10* Propeller: 9.82 x 10^ ~ 9.17 x 10*

Results For wall-side heat transfer coefficient

X felW • \ l / 3 / x0.15 r f

0.63 ^sin^n^

H

• = 0.46 UN

V

240 Chapter 4. H«at tninster

For power consumption

m 5 0.14 / X 0.1 / j \^^^

\ l / 3 / . \0.15 f f , . \\ ii^ * ^ ( « , r 1-0.211 0 . 6 3 - ^ ^ ^ H ^ " '

2 r - - V " = 0.551 £ ^ ^

Notation ft impeller width, cm Cp specific heat of liquid, cal/g°C D vessel diameter, cm H height of heat transfer surface, cm hj heat transfer coefficient on the inside wall of agitated vessel, cal/cm^sec°C L impeller diameter, cm N impeller speed, 1/sec Npf power number in fiilly bafiled condition, dimensionless tip number of impeller blades Pgc power consumption of impeller, dynecm/sec w anchor arm width, cm Q angle oi blades to the horizontal plane, degree A thermal conductivity of liquid, cal/seccm°C \i viscosity of liquid, g/cmsec V kinematic viscosity of liquid, cmVsec p density of liquid, g/cm^

Subscripts b bulk temperature w wall temperature


Mizushina, T, Ito, R., Murakami, Y. and Tanaka, S., Kagaku Kogaku, 30,819 (1966) Experimental Study of the Heat Transfer of Non-Newtonian Fluids to the Wall of Agitated Vessel

Experimental apparatus Vessel Type: dish-bottomed Diameter: 296 mm Height: 380 mm


Impeller Type: (1)~(4) anchor Diameter: (1) 250 (2) 180 (3) 250 (4) 250 mm Number of impellers: 1 Number of blades on impeller: (1)^(4) 2 Height of anchor arm (paraUel to shaft): (1) 280 (2) 280 (3) 220 (4) 280 mm Width of anchor arm (perpendicular to shaft): (1) 25 (2) 35 (3) 25 (4) 35 mm Off-bottom clearance: (1)~(4) 40 mm

Working fluids and their physical properties For pseudoplastic fluids

- h . l f f i= 1 |8 •^.~ 185

145 1 ..>

is,

Unit mm

mm 250 - -

—-rt • H H

35

\ fc LJl •


Fluid in jacket: water Fluid in tank: aqueous solutions of CMC and polyethylene-toluene solution

Solution n 0.5% CMC-water solution 2.0% CMC-water solution 2.5% CMC-water solution 3.0% CMC-water solution 3.5% CMC-water solution 4.0% CMC-water solution 25% polystyrene-toluene solution

1.0 0.65-0.82 0.59-0.67 0.57-0.65 0.51-0.58 0.44-0.55 0.85-0.95

For plastic fluids Fluid in Fluid in

Sample

S-2 S-3 S-4 S-5 S-6 S-7

jacket: water tank: cement slurry

Concentration

(wt%)

54.0 49.4 55.3 56.8 50.4 48.1

(Vol%)

28.1 25.5 29.8 31.0 26.0 24.5

So

(dyne/cm^)

25.1 10.6 36.6 53.1 13.03 7.24

A

(kcal/mhr°C)

0.721 0.704 0.733 0.741 0.705 0.707

Cp

(kcal/kg°C)

0.56 0.61 0.57 0.56 0.61 0.62

P

(g/cm^)

1.56 1.47 1.57 1.60 1.51 1.47

Results For the pseudoplastic fluids

M = o . 4 £ ^ A 1 /x« A J t//o

//« and //o are obtained from

T = To

l fl + 7 -r+^l-r

'VNp^

For the plastic fluids

Nu\^ Vb J

Pr 1/3

1 +

""•fel ±L 1/3

rib

OARe'

l+4MxlO^He0.lPr'"Re 1/3 r,^-6/6


Notation a constant, 1/sec Cp specific heat of liquid, c a l / g ° C D v e s s e l diameter, cm He Hedstrom number, L^Sop/rjbf dimensionless hj heat transfer coefficient based on the inside waD of agitated vessel, cal/cm^sec°C h* heat transfer coefficient between stagnant layer and agitated liquid, cal/cm^sec'^C / thickness of stagnant layer, cm L impeller diameter, cm -A impeller speed, 1/sec Nu Nusselt number, hjD/k, dimensionless Nu* Nusselt number, /j'D/A, dimensionless Re Reynolds number, DNp/^ib, dimensionless Pr Prandtl number, Cp blK dimensionless SQ yield value, dyne/cm^ 7] plastic viscosity, g/cmsec A thermal conductivity of fluid, cal/seccm°C fi viscosity of fluid, g/cmsec p density of fluid, g/cm^ T shear stress, dyne/cm^

Subscripts b bulk temperature w wall temperature

244 Chapter 4. Heat transfer

Mizushina, T, Ito, R., Murakami, Y. and Kiri, Y, Kagaku Kogaku, 30,827 (1966) Experimental Study of the Heat Transfer to the Cooling Coil in an Agitated Vessel


Liquid contained Height: 38.0 cm


Impeller For Newtonian fluids

Type

Diameter (cm) Width (cm) Arm height (cm) Arm width (cm) Number of blades Angle of blade (°) Off-bottom clearance (cm)

paddle

5,10,12,13,18 2.6,3

— —

2,4 45,90

4,10,17,26,27

anchor

12,18 — 18 1.7 2 90 10

turbine

12,18 2.6,3.6

— — 4 90

4,10,17

For Non-Newtonian fluids

Type

Diameter (cm) Impeller width (cm) Arm height (cm) Arm width (cm) Number of blades Angle of blade (°) Off-bottom clearance (cm)

anchor

12,18,18.3 — 18 1.5 2 90 10

turbine

18 3.6 — — 4 90 10


Cooling coil For Newtonian and non-Newtonian fluids

HcID Dr/D dcID dgID dJD

0.777, 1.03 0.76

0.0405,0.0541 0.0467,0.0487

0.135

coil

A B

dc

1.2 1.6

d, 1.37 1.44

Dc

22.5

He

23.0 30.5

cooling area based on the outside dia.

0.281 (m ) 0.414 (m )

(A) (B)

246 Chapter 4. H«at transfer

Working fluids Newtonian fluid: water, water-glycerin solution and caster oil Non-Newtonian fluid: carboxy methyl cellulose and cementrock slurry

Results For Newtonian fluids

^''^'^23Re'^'Pr'^(^^'^^^

3 x l 0 ^ > / ? e > 1 0 l when

0.15 ^ >^1.7^ >^0.14

He ^0.32,

Hr "'^^ ' = 0.32

For non-Newtonian fluids / N0.15 ^ N1.7X X0.14

A y He J \^^ J v^O

a-e'""-) p^^_c,m,a-e-"^r'N"-'

fl = 1.42x10"'

10S/?r>0.2, 1>«>0.53. when f ^ l > 0 . 3 2 , f ^ l = 0.32

Notation a constant, 1/sec b impeller width or anchor arm height, cm Cp specific hea t of liquid, c a l / g ° C dc cooling pipe diameter shown in figure, cm Dc cooling coil d iameter shown in figure, cm he h e a t t ransfer coefficient based on outs ide wall of cooling coil, cal/cm^sec-°C He he ight of cooling coil shown in figure, cm L impel ler d iameter , cm m cons tan t of power law equation, dynesec" /cm^ n cons tan t of power law equation, d imensionless Up n u m b e r of blade N impeller speed, 1/sec Re Reynolds number, L^Np/^b, dimensionless Re** modified Reynolds number, dimensionless Pr Prandtl number, Cp^blK dimensionless Pr* modified Prandtl number, dimensionless w anchor arm width, cm 0 angle of blade to the horizontal plane, degree A thermal conductivity of liquid, cal/seccm°C /z viscosity of liquid, g/cmsec p density of hquid, g/cm^ 0(n) function of n

Subscripts h value evaluated at buld temperature c value evaluated at coil temperature


Coyle, C. K., Hirschland, H. E., Michel., B. J. and Oldshue, J. Y., Can. J. of Chem. Eng., 48,275 (1970) Heat Transfer to Jackets with Close Clearance Impellers in Viscous Materials


Vessel Diameter (m)

Helical ribbon impeller Diameter (in) Pitch (based on the impeller diameter) Off-bottom clearance (in)

Liquid level

14

13 0.5 1/2 14

30

29 0.5 1/2 30

Cooling device Type: jacket Cooling liquid: water

Working fluids and thir physical properties Organic materials with pseudoplastic characteristics Thermal conductivity: 0.08-0.09 Btu/hrT/ftVft

Results 14-in. dia. tank, 13-in. diameter helical impeller

N rpm

7 10 18 20 25 50

Viscosity at shear rate 5 sec:\ 100°F

100,000 2,000

100,000 2,000

30,000 30,000

30-in. dia. tank, 29-in. <

N rpm

6 6

12 18 18 49

Notation

Viscosity at shear rate

5 secrS 100°F

30,000 100,000 30,000 30,000

100,000 100,000

Viscosity Power law

exponent, n

0.2 0.8 0.2 0.8 1.0 1.0

iiameter helical impeller

Viscosity Power law

exponent, n

0.8 0.2 0.8 0.8 0.2 0.2

h heat transfer coefficient, Btu/hr^F/ft^

h

Btu/hr * F/sq.ft

3.7 4.5 4.2 3.6 4.0 5.0

h

Btu/hr °F/sq.ft

4.6 4.0 5.5 5.7 4.5 2.0

248 Chapter 4. H«at tninsfor

Nagata, S., Nishikawa, M., Takimoto, T, Kida, E and Kayama, T., Kagaku Kogaku, 35,924 (1971) Jacket Side Heat Transfer Coefficient in Mixing Vessel

Experimental apparatus Vessel Type: (1) dish-bottomed (2) flat-bottomed

Baffle Number: unbailed or 4 Width: Z)/10

Impeller type and geometries Impeller

turbine for vessel (1) paddle

turbine for vessel (3)

d(cm)

7.5,10,15,20 4.2,6.8,8.2,10,10.3 11,12.2,15,18.5 10,15,20

bicm)

1,1.5,2,3,4,6 1,1.5,2,3,6,4.2 6.8,11 2,3,4,6

/(cm)

1.875,2.5,3.75,5

rf»=lcm

np

2,4,6,8,16 16,6,4,3,2

6

9

90°, 60°, 45° 90°, 60°, 45°, 30°

90°


turbine pitched paddle

Fluid in jacket: steam Fluid in vessel: tap water, glycerin and CMC solution Physical properties at 20°C

water glycerin CMC solution

P (kg/m^)

1,000 1,200 1,000

essel (2) Fluid in jacket: steam Fluid in vessel: tap water

Cp

(kcal/kg. 'C)

1.0 0.70 1.0

k

(kcal/mhrX)

0.512 0.25 0.512

M (poise)

0.01 10.0

0.03-7

4.1 Singl« phas« 249

Results Without baffles Re > 100 and 2<Fr< 2,000

(hjD/k) = a {d'np/fir\Cp^i/kf\nJtir'''' (d/Dy'^'inpr' v0.15

J^Ci/m] (smdf^(H/D)'

without coils a = 0.51 with coils a = 0.54

With baffles i?^ >100

(hjD/k) = lAO(d'np/^)''\Cp^/kf\fiJ^y'''*

/ \0.45 / \0.2

Notation b width of impeller blade, cm c impeller height, cm Cp specific heat of fluid, kcal/kg°C d impeller diameter, cm dn diameter of coohng water spout, cm D vessel diameter, cm hj heat transfer coefficient on the inside wall of agitated vessel, kcal/m^hr°C H hquid height in mixing vessel, cm i number of impellers

k thermal conductivity of fluid, kca l /mhr°C n impeller rotational speed, 1/sec Hp number of impeller blades 6 angle of impeller blade, degree /z viscosity of bulk fluid, k g / m h r ^«, viscosity of liquid at wall temperature, k g / m h r p density of fluid, kg/w?

250 Chapter 4. H«at trainsffar

Nagata, S., Nishikawa, M. and Takimoto, T, Kagaku Kogaku, 35,1028 (1971) Heat Transfer to Helical Coils Immersed in Mixing Vessel

Experimental apparatus Vessel Type: dished-bottomed Diameter: 30 cm


Baffle Number: unbaffled or 4 Width: Z)/10

Impeller Experiment I

Type: turbine Number of impeUers: 1 Geometries: d/D = 0.33

h/D = 0.03'-'0.2 np = 2-16 C//f= 0.13-0.6 sin0 = 0.5-1

Experiment H Type: six blade turbine (^=90°)

d/D

0.5 0.33

b/D

0.1 0.067

CdH

0.5 0.5-0.625

C2lH

0.125-0.48 0.125-0.48

Cooling coil

No.

1 2 3 4 5

Z)r (mm)

225 225 225 210 240

dgixam)

10 15 20 15 15

Lf (mm)

230 230 230 230 230

ft (mm)

80 80 80 80 80

Working fluids and their physical properties Fluid in coil: water Fluid in tank: tap water, glycerin and CMC solution Physical properties at 20* 0

water glycerin CMC solution

P (kg/m )

1,000 1,200 1,000

Cp

(kcal/kg°C)

1.0 0.70 1.0

k

(kcal/mhr-^C)

0.512 0.25 0.512

A' (poise)

0.01 10.0

0.03-7

4k1 Singi« phas* 251

Results (1) Impellers are pkiced inside of cooling coils

(2) Impellers are placed outside of cooling coils (without baffles)

(3) Impellers are placed outside of cooling coils (without baffles)

Nuc=2mRe'^Pr'^^Vis-''\d/Dr'^{ib/Df\npr [j^dliH] (smGfHH/Dy'^

Notation b impeller width, cm C impeller height, cm Cp specific heat of fluid, kcal/kg-°C d impeller diameter, cm dco outside diameter of coil tube, cm dg clearance between individual turn of coohng coil, mm D vessel diameter, cm Dc coil loop diameter, cm ha, heat transfer coefficient at outer surface of cooling coil, kcal/m^hr°C H liquid height in mixing vessel, cm He lowest coil level, nmi i number of impellers

k thermal conductivity, kcal/mhr*'C Lc overall hight of cooling coil, nrni n impeller speed, 1/sec ftp number of impeller blades Nuc Nusselt number (coil side), heoD/k, dimensionless Re agitation Reynolds number, d^np/fi, dimensionless Pr Prandtl number Cp ji/k, dimensionless Vis viscosity index, ^w/^, dimensionless 0 angle of impeller blade, degree p hquid density, kg/m^ ^ viscosity of bulk hquid, poise fiw viscosity of liquid at wall temperature, poise

252 Chapter 4. H«at transter

Edney, H. G. S. and Edwards, M. E, Trans. Instn. Chem. Engrs., 54,160 (1976) Heat Transfer to Non-Newtonian and Aerated Fluids in Stirred Tanks

Experimental apparatus Vessel Type: flat-bottomed Diameter 1.22 m Height: 1.22 m



Impeller Type: six-flat-bladed disc turbine Diameter: 0.305 m Number of impellers: 1 Number of blades on impeller: 6 Width of impeller blade (parallel to shaft): 0.061 m

Cooler Mean helix diameter: (1) 0.559 (2) 0.762 (3) 0.955 m Coil internal diameter: 0.041 m Coil external diameter: 0.047 m

Working fluids Fluid in cooling coil: water Fluid in tank:

non-Newtonian fluids: various dilute solutions of sodium carboxymethyl cellulose and polyacryl amide

Experimental conditions 4.01 X 102 <i?gi< 9.2x10' 4.34 <Pri< 1.9 X10^ 6.5 X10"* <IXA< 0.283 Nsec/m^

Results

iVM = 0.036i?erW-^' r 'v - 0 3 7 5 r -i 0 2

Dc\ f//J [DT\ \Â.\

Notation Cp specific heat of agitated liquid dc outside diameter of coil tubing D impeUer diameter Dc mean helix diameter DT tank diameter he process side heat transfer coefficient for

coil k thermal conductivity of process liquid N rotational speed of im] [)eller

Nu Rei

Pri

MA tÂu,

Nusselt number, hcddk, dimensionless modified Reynolds number, pNDÎÂf dimensionless modified Prandtl number /i^ Cplk, dimensionless average apparent viscosity average apparent viscosity at mean temperature of heat transfer surface


Sano, Y., Usui, H., Nishimura, T. and Saito, E., Kagaku Kogaku Ronbunshu, 4, 159 (1978) Correlation of Heat Transfer CoefiBcient at the Wall of Mixing Vessel

Experimental apparatus Vessel and cooling coil geometries

System (1) (2)

Vessel Type Diameter (cm) Height (cm)

Baffle Number

Liquid contained Height (cm)

Cooling coil Outside diameter of tube (nmi) Diameter of coil (cm)

flat-bottomed 10 10

4-'12

10

6 6

flat-bottomed 19 20

4--12

19

12 12

Impeller

System (2) (1)

Type d/D b/D tip

e IB/D

paddle paddle 0.33,0.4,0.5,0.6,0.7,0.8,0.9 0.33,0.4,0.5

0.1,0.2,0.5 0.1,0.2,0.5 2,6 2

30^ 60°, 90° 90°

turbine 0.5 0.1 6

90° 0.12

A h I l|l \^ C ^

^

paddle pitched paddle

Impeller

turbine

Working fluids and their physical properties Liquids: water and aqueous solutions of glycerin (viscosity = 0.55—8.5 cP)

Experimental conditions Rotational speed of impeller 110—550 rpm Temperature of bulk liquid 25-40°C Difference of temperature between bulk liquid and wall 5~20°C Reynolds number 900-70,000 Prandtl number 5-70


Results

hD = 0.512 eD

.a227

Pr \052 x > 0.08

l/3\d_] [ ^

Notation b impeUer width, cm Cp beat capacity of liquid, kcal/g°C d impeUer diameter, cm D vessel diameter, cm h heat transfer coefficient, kcal/cm^hr°C IB blade length of turbine type, cm tip number of impeller blades P power dissipated in mixing vessel, kgcmVsec^ Pr Prandtl number, C /x/A, dimensionless V liquid volume in vessel, cm^ e energy dissipation per unit mass, P/pv, cmVsec? 6 angle of impeller blade, degree A thermal conductivity, kcal/cmhr°C ^ viscosity of bulk liquid, g/cmsec V kinematic viscosity of liquid, cmVsec p density of liquid, g/am?

4.1 Single ph«s« 255

De Maerteleire, E., Chem. Eng. ScL, 33,1107 (1978) Heat Transfer to a Helical Cooling Coil in Mechanically Agitated Gas-Liquid Dispersions

Experimental apparatus Geometrical characteristics of experimental equipment

1. Heat transfer vessel — flat bottomed cylindrical glass jar wall thickness: 0.001 m height: 0.250 m diameter: 0.180 m liquid height in the vessel: 0.204 m depth gas distributor below hquid surface: 0.200 m depth impeller below hquid surface: 0.195 m.

2. Baffles — four baffles made of stainless steel thickness: 0.001 m width: 0.018 m placed 0.001 m jfrom the vessel waU at right angles.

3. Impeller — four bladed paddle impeller diameter: 0.100 m blade dimensions:

thickness: 0.001 m width: 0.020 m length: 0.035 m blade angle: 45 deg.

4. Coil — helical cooling coil made of pure red copper height: 0.115 m number of turns: 5 clearance between two turns: 0.013 m outside diameter of coil tubing: 0.012 m inside diameter of coil tubing: 0.008 m inside diameter of hehx: 0.100 m.

Working fluids Liquid: distilled water, distilled water + a surface active agent, isopropyl alcohol, ethylene glycol

and two mineral oils. Experimental conditions

Range of variables covered

Impeller speed: 100 ~ 800 rpm Nusselt number 167 ~ 1,553 Reynolds number: 167 ~ 245,000 Prandtl number: 2.91 - 1,262 Viscosity ratio: 0.194 - 0.904

Results


Notation Cp specific heat of agitated liquid, kcal/kg°C Dr impeller diameter, m DT vessel diameter, m hu external coil heat transfer coefficient, kcal/secm^°C k thermal conductivity of process liquid, kca l / secm°C N rotational speed of impeller, 1/sec or rpm Nu Nusselt number, huDT/k, dimensionless Re Reynolds number, Dr^ yN/pt,, dimensionless Fr Prandtl number, Cp^ilk, dimensionless Vi viscosity ratio, ji/^wy dimensionless ^ dynamic viscosity of process liquid, kg/msec ^w dynamic viscosity of process liquid at temperature of coil surface, kg/msec 7 fluid density, kg/m^


Bourne, J. R., Buerli, M. and Regenass, W, Chem. Eng. Sd., 36,347 (1981) Heat Transfer and Power Measurements in Stirred Tanks Using Heat Flow Calorimetry

Experimental apparatus Bench-scale experiments Vessel

Diameter: 0.114 m Internal heat transfer surface: 0.04216 m

hnpeller

Type turbine anchor Diameter (mm) 38 109.1

d/D 0.33 0.957 h7d s/d

Pfaudler type 67

a59

gate 54

0.47 L73 0.15

Full-scale experiments Vessel

Type dish-bottomed Working capacity (m ) 2.5 Wall heat transfer surface (m ) 6.93 Diameter (m) 1.59

Impeller Type anchor

Diameter (m) 1.52 d/D 0.957 h'/d s/d

dish-bottomed 5.4

14.4 1.95

gate 0.89 0.46 L79 0.16

' t 2.5 m steel tank with anchor impeller. 5.4 m glass-lined tank with gate impeller.


Working fluids Bench-scale experiments

Fluid in jacket: low viscosity silicone oil Fluid in tank: toluene, isopropanol, ethylene glycol and glycerin

Full-scale experiments Fluid in jacket: water Fluid in tank: ethylene glycol

Results (1) Turbine

Nu=^QA2Re^^Pr^'^ for i?« = 8-46,000

(2) Anchor

Nu^hQRe^'^Pr^^^Vi^'^' for Re<.10

Nu = 0.29 /?^°-^^ Pr^'^ Ft°- ^ for Re = 70'-600,000

(3) Pfaudler

Nu = Q27Re^''Pr^'^ for i?g = 9-^55,000

(4) Gate

Mt< = 0.55/?e°®/V^/'W°" for i?« = 12'-300,000

Notation Cp heat capacity at constant pressure, J/kgK d diameter of impeller, m D diameter of tank, m h fihn heat transfer coefficient, W/m^K h height of impeller,m k thermal conductivity of fluid in tank, W/mK N impeller rotational speed, 1/sec Nu Nusselt number, hD/k, dimensionless Pr Prandtl number, /i Cplk, dimensionless Re Reynolds number, Nd V/M, dimensionless 5 width of anchor and gate blade, m Vi viscosity ratio, n/iiw, dimensionless ^ fluid viscosity, kg/msec ^w fluid viscosity at wall, kg/msec p density of fluid, kg/m^

4.1 Single phsM 259

Sano, Y., Usui, H. and Saito, E., Kagaku Kogaku Ronbunshu, 7,253 (1981) The Correlation of Heat Transfer Coefficient at Outside Surface of Helical Coil with Agitation Power

Use of existing data Vessel diameter: up to 1.22 m Re = 10^-2 X10^ {edcMv^ = 10*~10^^) (/r./Z) = 0.063-0.018 HID=:l

/ ^ \ 0.205 X \0t2>' v0.1x x - 0 3

¥-«-^(^J [% [^ (t) ' •*'' -Data used are shown below

Oldshue, J. Y. and A. T. Gretton: Chenu Eng, Progr., 50,615 (1954) Nagata, S., M. Nishikawa and T. Takimoto: Kagaku Kogaku, 35,1028 (1971) Edney, H. G. S., M. F. Edwards and V. C. Marshall: Trans, Instn, Chem, Engrs,, 51,4 (1973) Sano, Y., H. Usui and E. Saito: Kagaku Kogaku Ronbunshu, 7,253 (1981)

Notation b impeller width, m Cp specific heat, J/kgK d impeller diameter, m dco outside diameter of coli tube, m D vessel diameter, m H liquid height in mixing vessel, m hco heat transfer coefficient at outer surface of coil, W/m^K n rotational speed of impeller, 1/sec P power dissipated in mixing vessel, kgmVsec^ Pr Prandtl number, Q/z/A, dimensionless Re Reynolds number, d^n/v, dimensionless V hquid volume in a vessel, m^ Vis viscosity index, w//^, dimensionless e energy dissipation per unit mass of hquid, P/pV, mVsec^ A thermal conductivity of hquid, W/mK jLL viscosity of bulk hquid, kg/msec fiw viscosity of liquid at outside of coil wall, kg/msec V kinematic viscosity of hquid, mVsec p density of liquid, g/cm^


Sano, Y., Usui, H. and Saito, E., Kagaku Kogaku Ronbunshu, 7,253 (1981) The Correlation of Heat Transfer Coefficient at Outside Surface of Helical Coil with Agitation Power

Experimental apparatus Vessel and cooling coil geometries

System (1) (2)


Baffle Number Width

Cooling coil Outside diameter of tube (mm) Diameter of coil (cm) Pitch (mm)

flat-bottomed 10

4-8 0.05-0.13Z)

6 6

12

flat-bottomed 19

4- 8 0.0b-0.13D

12 12 24

Impeller

Type d/D bID Hp

e Off-bottom clearance

paddle 0.33-0.5 0.1-0.5

2,6 90° H/2

turbine 0.5 0.1 6

90* H/2

pitched paddle 0.5

0.1-0.2 6

30°, 60°, 90° H/2

paddle pitched paddle

Impellers

It d J

turb ine

Working fluids water and aqueous solutions of glycerin


Results

5.5 < /V < 96, 10' < (Erfi / v') < 10'°, 900<i?«<7xl0*, 0.33<(///)<0.5, 0.1<ft/Z)<0.5

i2*L = o.755l^l W i - l [4--(fm Notation

b impeller width, m Cp heat capacity of liquid, J / k g K d impeller diameter, m dco outside diameter of coli tube, m D vessel diameter, m hro heat transfer coefficient at outer surface of coil, W/m^K H liquid height in mixing vessel, m IB blade length of turbine type, m n rotational speed of impeller, 1/sec tip number of impeller blades P power dissipated in mixing vessel, kgmVsec^ Pr Prandtl number, Cp^/X, dimensionless Re Re3molds number, d^n/v, dimensionless V hquid volume in a vessel, cm^ Vis viscosity index, fiw/K dimensionless e energy dissipation per unit mass, P/pV, mVsec 0 angle of impeller blade, degree A thermal conductivity of liquid, W/mhrK /i viscosity of bulk liquid, kg/msec V kinematic viscosity of hquid, mVsec p density of liquid, kg/m^


Kuriyama, M., Ohta, M., Yanagawa, K., Aral, K. and Saito, S.,/. Chem. Eng. Japan, 14,323 (1981) Heat Transfer and Temperature Distributions in an Agitated Tank Equipped with Helical Ribbon Impeller


D=L = 100 (mm) p= 90 (mm) w/D = 0.1 (-) c/D= 0.019 (-)

0.057 0.08A

Working fluids and their physical properties Aqueous solutions of com symp viscosity = 1.4 kg/msec at 30°C

heat capacity = 2.2 x 10^ J/kg°C themial conductivity = 0.36 J/msec*

Results

Nu = OM RePr (^j^r

Notation clearance between blade tip and tank wall, m specific heat, J/kg-®C outside diameter of impeller, m inside diameter of tank, m heat transfer coefficient, J/m^sec**C height of vessel, m rotational speed of impeller, 1/sec Nusselt number, hD/X, dimensionless height of helical ribbon impeller, m Prandtl number, /x Cp/X, dimensionless Reynolds number, d^np/in, dimensionless width of heUcal ribbon impeller, m

/i viscosity at bulk temperature, kg/msec ^iw viscosity at wall temperature, kg/msec A themial conductivity of fluid, J/secm**C p density of fluid, kg/m^

c Cp d D h L n Nu P Pr Re w


Kuriyama, M., Aral, K. and Saito, S.J. Chem. Eng. Japan, 16,489 (1983) Mechanism of Heat Transfer to Pseudoplastic Fluids in an Agitated Tank with Helical Ribbon Impeller


0=L = l60(mm) ps 144 {mm) w/D = 0.1 (-) d,^0=QI (-) c/0s0.02A(-)

0.068 (-) 0.076 (-)

luid)

^Torque meter

lip ring

L.—-Variable speed motor

Designs of agitated tank and impeller.

Top view of bottom plate

Working fluids 3% and 5% solutions of carboxymethyl cellulose (CMC) at 40°C

Cone (wt%) m K(N.s'"/m2)

0.7 0.5

3 30

Results

Nu ( 2 ^'^

F = U+

£1=0.46 £2=4

w = 0.5-1.0


Notation c clearance between blade tip and tank wall, m Cp specific heat, J /kg°C d outside diameter of impeller, m D inside diameter of tank, m h heat transfer coefficient, J /m^sec°C K fluid consistency coefficient, Nsec"/m^ m flow behavior index n rotational speed of impeller, 1/sec Nu Nusselt number, hDl\ dimensionless p pitch of helical ribbon impeller, m Pr Prandtl number, \iCplK dimensionless Re Reynolds number, d^np/^y dimensionless £b £2 adjustable parameters jU viscosity at bulk temperature, k g / m s e c jUr viscosity correction factor, dimensionless ^w viscosity at wall temperature, k g / m s e c A thermal conductivity of fluid, J / s e c m ° C p density of fluid, kg/m^


Shamlou, R A. and Edwards, M. E, Chem. Eng. Sd., 41,1957 (1986) Heat Transfer to Viscous Newtonian and Non-Newtonian Fluids for Helical Ribbon Mixers


Type Diameter (mm)

Impelle r Type: helical ribbon Dimensions:

No.

1 2 3 4 5 6 7 8 9

10

T

400 400 400 400 400 400 150 150 150 150

D

352 352 352 352 352 370 135 135 130 113

flat-bottomed 400

w

34 34 34 34 34 36 13 14 13 12

P 352 352 352 176 190 185 135 75

133 60

slightly dished-based 150

p/D w/D

1 0.097 1 0.097 1 0.097 0.5 0.097 0.5 0.097 0.5 0.097 1 0.097 0.56 0.104 1.02 0.100 0.531 0.106

cID

0.0682 0.0682 0.0682 0.0263 0.0263 0.0405 0.0556 0.0556 0.0769 0.1637

« 6

1 2 1 1 1 1 2 1 1 1

hID HIT

1.0 1.1 1.0 1.1 1.0 1.1 1.0 1.1 1.0 1.1 1.0 1.1 1.02 1.1 1.08 1.1 1.02 1.1 1.02 1.1

All measurements are in nrni.


Thermal and physical properties of experimental fluids

Fluid used

Chocolate 7% CMC 3% CMC 1.5% CMC Glycerol

Lub. oil Silicone oil

Sugar sol. 3% Carbopol 8% Biozam R

Density (kg/m^)

1,280 1,060 1,000 1,000 1,250

see Fig. 3 see

Fig. 3 1,483 1,000 1,000

Specific heat (kJ/kg-K)

4.6at46°C 4.2 4.2 4.2 2.35at43^C

2.18at40°C

1.51at50X 2.5at50°C 4.2 4.2

Thermal conductivity (W/mK)

0.2118 at 46°C 0.595 at 45°C 0.600 at 45X 0.595 at 45°C 0.250 at 46°C

0.150 at 45°C

0.159 at 60°C 0.375 at 50°C 0.52at45X 0.600 at 48°C


10*

lo'r-n—r

8

.^ 8 M

> 10»

— \ — ! — I — r Un« Fluid

J \ I I I \ I L

10*

(Temp. 24*C)

10* S

1

I > ^

Fig. 2 Shear stress-shear rate for typical non-Newtonian fluid used in this work.

10' g 970

>960 | -

950 h

10» 0 10 20 30 40 50 60 70 80 90

Temperatur* (*C)

Fig. 1 Viscosity of Newtonian fluids used in this work.


10-^ < Re < 10^

4xlO^</V<10®

4xlO"^<7t<1.0

0.0263 <c/Z)< 0.1637

0.5<p/D<1.0

«t = l,2

940

\ I I r

Silicone oil 880

870

860

10 20 30 40 50 60 70 Temperature CO

850

Fig. 3 Density variation with temperature for silicone oil andlub. oil used in this work.

i.au i...O: H = 1.0

Results In the range Re

Nu 1 /Vl/3^jl/5 6

<1.0

ip/D)(c/Df Re'

In the range lO<Re< 10^

Nu

Pr^'^Vi^ • = 0.45i?^^

4.1 Singto phas« 267

Notation c clearance between impeller tip and vessel wall, m Cp specific heat capacity of fluid, J /kgK D impeller diameter, m h impeller height, m H liquid height, m k fluid thermal conductivity, W/mK N impeller rotational speed, 1/sec fib number of impeller blades Nu Nusselt number, hjT/ky dimensionless P power input, W Pr Prandtl number, Cpfi/k, dimensionless p impeller pitch, m T tank diameter, m Vi viscosity ratio, /i/^«r, dimensionless w impeUer width, m Re Reynolds number, pND Vfi or pND Vpu* dimensionless y shear rate, 1/sec // Newtonian viscosity, kg /msec /44 average apparent viscosity, kg /msec ^w viscosity at wall temperature, kg /msec p liquid density, kg/w? T shear stress, dyne/cm^


Aksan (Sizgek), D., Borak, E and Onsan, Z. I., Can. J. ofChem. Eng.y 65,1013 (1987) Heat Transfer CoefiBcients in Coiled Stirred-Tank Systems

Experimental apparatus System (1) single tank (2) two-tanks-in-series

Vessel Type: flat-bottomed Diameter: 0.20 m Height: 0.24 m


Impeller Type: flat-blade turbine Diameter: 0.08 m Number of impellers: 1 Number of blades on impeller: 6 Width of anchor arm (perpendicular to shaft): 0.02 m Off-bottom clearance: 0.06 m

Heating coil Tjrpe: helical coil Coil diameter: 0.16 m Coil-tube diameter: 4.35 mm ID Coil spacing: 6.35 mm

Working fltiids Fluid in heating coil: hot water Fluid in tank: cold water

Experimental conditions Impeller speed: 200,380,450 and 500 rpm /?^=19,000-77,000

Results

HI = 0.023{H/DH)(cH t/kf iDHVHPk /jutf-'ifn,/fi^f' [1+3.5 (DH /DC)]

HO = 1.40 (k/DT)(NDi p . /fitf'\c„tit /kf^(tit /fi.f'*

Notation Ch specific heat, hot water, J/kg°C Cw specific heat, cold water, J/kg°C DT, DA* Dcf DH tank, agitator, coil, coil tube diameter, respectively, m HI individual heat transfer coefficient, inside coil, W/m^**C HO individual heat transfer coefficient, agitated side, W/m^°C k thermal conductivity of water, W/m°C N agitator speed, 1/sec or 1/min VH velocity of hot stream, m/sec ph density of hot water, kg/m^ pw density of cold water, kg/w? p,b viscosity at bulk temperature, kg/msec liu, viscosity at wall temperature, kg/msec

4.1 Singl«phas« 269

Frobese, D.-H. and Bohnet, M., Chem. Eng. TechnoL, 12,324 (1989) Heat Transfer to Liquids and Suspensions in Agitated Narrow Vessels


double jacket

-baffle

cooling coil

0 s 908 mm Dj s Z20 mm Lj s 890 mm H/Os 3 d /0= 0.3-0.52 h,/D= 0.5 a,/0= 1 b/0 s 0.1 3 propeller mixer

\ 1 -— - ^

section A - A

Diagrammatic representation of the agitated vessel used in the tests.

Working fluids and their physical properties Fluid in jacket: saturated steam Fluid in tank: water and aqueous Drivanil solution

Properties of pure Drivanil density: 1,074 kg/m^ viscosity: 18,000 mPasec thermal conductivity: 0.175 W/mK specific heat: 2.08 KJ/kg- 'K

Experimental conditions Temperature of tank liquid: 50~80°C Viscosity of tank liquid: 0.355—73 mPasec

Results Re > 10* Nu = 0.5i?e2/3pj^i/3(yy/^^)ai4

pitch of propeller blade 30*

Geometrical data of employed propeller mixers.

270 Chapter 4. Heat transffar

Notation Cp specific heat capacity of liquid, J/kgK d impeller diameter, m D vessel diameter, m n impeller speed, 1/sec Nu Nusselt number, aZ)/A, dimensionless Pr Prandtl number, Cp t] /A, dimensionless Re Reynolds number, nd p/ T], dimensionless a heat transfer coefficient, W/m^K T] viscosity of liquid, Pasec T] „ viscosity of liquid at wall temperature, Pasec A thermal conductivity of liquid, W/mK p liquid density, kg/w?

4.1 Singl* phas« 271

Wang, K. and Yu, S., Chem Eng. Sci., 44,33 (1989) Heat Transfer and Power Consumption of Non-Newtonian Fluids in Agitated Vessels

Experimental apparatus Vessel, cooling coil and agitator geometries

Schematic diagram of cooling-tube configuration

Inner helical coils External helical coils

I I

Vertical tubes

272

Type

Flat blade disc turbines

Pfaudler impellers

Genmetrical configuration of impellers

Form

d:dt:b:dr = l:l/4:l/5:2/5

c::i^^ . 1

Chapter 4. H«at tninster

Scale

d = 0.092 b = 0.0184 tip = 3,6 «« = 2,3

d = 0.092 b = 0.0184 fip = 3, «« = 2,3

MIG impellers

50

d/2'^d||^»

0=15^

(/ = 0.089,0.115,0.1035 Hp = 2, w« = 3,5 ^ = 30°

d:di:wi:w2 = l: 0.347:0.216: 0.173

Plate paddles rf = 0.075,0.085,0.107 ftp = 2, w« = 1 b = 0.049

Semi-elliptical impeller

d / 2 d = 0.142 ^ = 0.142 tip = 2, w« = 1 0=45°

Anchors 15

K=m=a

d = 0.181,0.194,0.2125 b = 0.169 tip = 2 «« = 1

4.1 Single phaM 273

Working fluids and their physical properties Aqueous solutions of CMC (less than 4%)

n = 0.49-0.92 iir= 0 .02-12 P a ( s e c r

Results Jacket:

M = 0.4561 ^

Cooling tube:

M (I] (Zbsmd] (D

H \H

-1.63

k

f ^ \ 2 / » / \ l / 3 / \<

Notation b width of a single blade, m Cp specific heat, W/kgK d impeller diameter, m dr outside diameter of cooling tube, m D vessel diameter, m he fihn coefficient from fluid to cooling tubes, W/m^K hj fihn coefficient firom fluid to jacket, W/m^K E liquid height, m k thermal conductivity, W/mK K consistency index at bulk temperature, Pa(sec)" n flow behavior index «« number of impeller on the axis np number of blades of an impeller E power per unit mass, W/kg B inclined angle of blade, degree lia apparent viscosity of non-Newtonian fluid, Pasec Va kinematic viscosity, Va-liJpy mVsec p density, kg/m^


Kizil9e5, E A. Onsan, Z. I. and Borak, E, Can. J. ofChem. Eng., 68,1057 (1990) Heat Transfer Coefficients in Finned-Coil Stirred-Tank Systems



Impeller Type: flat-blade turbine Diameter: 0.08 m Number of impellers: 1 Number of blades on impeller: 6 Width of anchor arm (parallel to shaft): 0.02 m Off-bottom clearance: 0.06 m

Heating coil Type: helical coil with disc-type fins Coil diameter: 0.16 m Coil-tube diameter: 4.35 nmi ID Coil spacing: 5.0,7.0 and 11.0 nmi

Working fluids Fluid in heating coil: hot water Fluid in tank: cold water

Experimental conditions Re = 20,000-110,000 Rcc = 3,600-14,000

Results Steady-state experiments with variable agitator speed

(W = 20.0 cmVs, M = 20.0 cmVs; to = 22.4''C, Ti = 69.0'»C)

hs

(mm)

11.0 (A/= 0.0438 m )

7.0 04/ = 0.0761 m )

5.0 (A/= 0.0932 m )

/ , \ *„= 0.001881^^ J

N

(rpm)

125 200 300 400 500 125 200 300 400 500 125 200 300 400 500

tx Ti

(°C) C O

43.0 48.8 44.2 48.3 44.8 47.7 44.8 47.0 45.3 47.4 43.7 49.1 44.2 48.0 44.5 47.4 44.8 47.3 44.8 46.7 43.5 48.3 44.1 47.5 44.8 47.4 44.8 47.1 45.6 45.6

f KTT^2 >°-"V ^o•^/ \^^* NDlp„

. A/* ;

IC^tib

[~) ML] M

A4f

(m^) 0.0816 0.0781 0.0751 0.0733 0.0720 0.1002 0.0941 0.0886 0.0854 0.0831 0.1093 0.1023 0.0950 0.0910 0.0864

X X0J07

h. I*/J

/roO>are)

(W/m

3.541 4,726 6,131 7,336 8,406 3,545 4,717 6,109 7,345 8,362 3,540 4,771 6,122 7,337 8,415

/to (fimied)

'• O 2,640 3,869 5,456 6,916 8,277 2,420 3,529 4,963 6,328 7,508 2,258 3,293 4,648 5,903 7,072


Notation A^, Af effective and fin areas, m^ Cu, specific heat of cold water, J/kg°C DAf DH agitator and coiltube diameter, m hf fin thickness, mm ho heat transfer coefficient, agitated side, W/m^°C hs fin space, nmi k thermal conductivity of water, W/m°C M cold water flow rate, mVsec N agitator speed, 1/min or 1/sec /o, h inlet and exit cold water temperature, °C Ti, Tz inlet and exit hot water temperature, **C W hot water flow rate, mVsec Ate, //«, viscosity at bulk and wall temperature, kg/msec pw density of cold water, kg/m^


Carreau, R J., P ^ s , J. and Guerin, E, Can. J. ofChem. Eng., 72,966 (1994) Heat Transfer to Newtonian and Non-Newtonian Liquids in a Screw Agitator and Draft Coil System

Experimental apparatus Vessel and agitator geometries (all dimensions in m) Vessel diameter/): C1~C3=0.254

Liquid height in the vessel H: Cl=0.262, C2=0.255,C3=0.261in

Agitator diameter d: C1~C3=0.150, A=0.220, />=0.147, «;=0.067, A=0.0159, Cte=0.012 m

Coil Name Material

CI Cr plated Cu C2 Steel C3 Copper

dc he du

0.1827 0.205 0.0127 0.1763 0.2075 0.00635 0.1887 0.2175 0.00476

dii Cbc

0.0095 0.0275 0.0043 0.0285 0.0032 0.0175

Cc

0.0060 0.0064 0.0065

n.

10.5 16.5 19.5

Working fluids and their physical properties Fluid in vessel:

Substance ( Cone. // (mass %) n

mass %) or m (mass %) (—) (kg/m^) (W/mK) Cp

a/kg-K)

Vitreaoil HV32 Mixture HV320

Com syrup CMC

Xanthan

Polyacrylamide

100 *

100 «* 1.0 2.0 0.75 1.0 1.5

600nig/L 0.2 1.0

^Adjusted for desired viscosity.

0.055 0.200 0.785 2.48 0.564 9.5 6.27 6.5 8.62 0.136 0.521 5.04

**Qom syrup slightly diluted to avoid crystallisation.

1.0

1 i • 0.748 0.631 0.122 0.196 0.183 0.871 0.734 0.521

Properties of distilled water used for solutions: ;i=9x 10" Pas, p =

Fluid in coil: water

856. 873. 885.

1,383. 996. 996. 995.

\ 1,195.

i 995.4 kg/m^* =

0.145

1 0.323 0.588 0.575 0.610

1 0.356

1 = 0.610 W/mK, c

1,901

1 2,358 4,177

7 2,902

1 = 417J/kgK


Experimental conditions Agitation speed = 0.67—3 rps Reg = 3 - 1 , 3 0 0 Prg = 500-30 ,000

Results (A °* ^

M* = 0.387/?^f"/V;^' —

R e g = ^

^ ' = k

Notation Cp heat capacity, J / k g K d agitator diameter, m die outside diameter of the coil tube, m he liquid-side heat-transfer coefficient, W/m^K k thermal conductivity of hquid, W / m K ks the Metzner-Otto constant m consistency index of the power law, P a s e c n power low index, dimensionless lis number of coil loops N rate of rotation of the agitator, 1/sec Prg generalized Prandtl number, dimensionless Reg generalized Reynolds number, dimensionless /J, viscosity of Newtonian fluid, P a s e c 77 effective viscosity, P a s e c p liquid density, kg/w?


4 .2 Multi phase 4.2.1 Solid-liquid systems

Mizushina, T, Ito, R., Koda, S., Kabashima, A., Hiraoka, S. and Nakamura, T., /. Chem. Eng. Japan, 10,160 (1977) Heat Transfer under Solidification of Liquid on Agitated Vessel Wall

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 16 (2) 7 cm Height: (1)16 (2) 7 cm

Liquid contained Height: (1)16 (2) 7 cm

Impeller Type: (1) (2) anchor Diameter: (1) 15.2 (2) 6.2 cm Height: (1)15.2 (2) 6.1 cm Number of impellers: (1) (2) 1

Working fluids, solids and their physical properties Liquids: lauric acid, capric acid, and water Solids: lauric acid and capric acid

Thermal conductivity (kcal/mhr'^C)

Specific heat (kcal/kg°C)

Viscosity (g/cmsec)

Density (g/cm^)

Melting point CC)

Lauric add

0.140

0.38 (solid) 0.515

0.0688 (50°C) 0.0537

(60°C) 0.8744

(41.5°C) 0.8707

(50,25°C) 43.20

Capric acid

0.121

0.32 (solid) 0.440

0.0434 (50°C) 0.0288

(70X) 0.8884

(35.05^0 0.8773

(50,17°C) 31.00

Water

0.533 (40^0 0.548 (50) —

0.999

0.00656 (40°C) 0.00549 (50°C) 0.9922 (40X) 0.9981 (50X) 0.0

4^2 MuttiphaM 279

Results

(hiDL

A = V^ UW 1/3 >r x0.14

I — DL=D'2S

V = 0.15 iPPildf {T]iPDL/d)ln(DL/d)} 1/3

r7 = l+exp -o(a_:

--(f)(fl] Notation

c specific heat, cal/g°C d impeller diameter, cm D vessel diameter, cm DL apparent vessel diameter, cm hi convective heat transfer coefficient, cal/cm^sec°C N rotational speed, 1/sec P correction feictor S solid layer thickness, cm 7] correction factor, dimensionless A thermal conductivity of liquid, cal/seccm-°C // viscosity at bulk temperature, g/cmsec ^w viscosity at wall temperature, g/cmsec p density of Uquid, g/cm^ y/ correction constant, dimensionless


Kung, D. M. and Harriott, R, Ind. Eng. Chem. Res., 26,1654 (1987) Heat Transfer to Concentrated Suspensions in Agitated Systems

Experimental apparatus Vessel Type: flat-bottomed vessel with slightly sloped bottom Diameter: 15 in Height: 18 in


Baffle Number: 4 Width: 2 in Clearance of baffle from wall: 1/8 in

Impeller

Type six flat bladed

turbine 45° pitched

blade turbine

Diameter (in) 4 Number of impellers 1 Number of blades on 6

impeller Off-bottom clearance (in) 4

4 1

marine-t5rpe propeller

3.8 1

Cooler and heater Jacket heat transfer area: 2.19 ft^ Hehcal cooling coil:

diameter: 7.5 in diameter of tubing: V2 in heat transfer area: 2.16 ft

Working fluid, solids and their physical properties Liquid: water Sohd: polystyrene beads and quartz sand

3p [xm

polystyrene beads RH1911 190 ROMAXL.195 680

quartz sand Agsco Nolo 45

kp J/(msK)

0.084 0.084

L73

c J/(kgK)

1.340 1,340

710

P kg/m'

1,050 1,050

2,650

Experimental conditions Impeller speed: 300—540 rpm Volume fraction of dispersed phase: 0~40%

4.2 MuKiphas* 281

Results

Turbine hdhc^ = 1 -1.25 ^

Propeller hr/hc'' = 1 -1.03 0r

Pitched turbine hdhc^ = 1 -1.15 ^

There is only a small if any effect of particle size in the range 200-700 \ym. Notation

c_ heat capacity, J/kgK dp average diameter of particles, m he film coefficient outside of coil h? film coefficient with no solids kp thermal conductivity of particle, J/msecK p fluid density, kg/m^ ^ volume fraction dispersed phase

282 Chapter 4. H»at transfer

Frobes, D.-H. and Bohnet, M., Chem. Eng. TechnoL, 12,324 (1989) Heat Transfer to Liquids and Suspensions in Agitated Narrow Vessels


pitch of propeller blade 30"

Diagrammatic representation of the agitated vessel used in the tests.

Geometrical data of employed propeller mixers.

Working fluids, solids and their physical properties Fluid in jacket: saturated steam Fluid in tank: water and aqueous Drivanil solution

Properties of pure Drivanil density: 1,074 kg/m^ viscosity: 18,000 mPasec thermal conductivity: 0.175 W/mK specific heat: 2.08 KJ/kgK

Solid: ghss spheres mean particle diameter: 4 50=68—294 ^m density: 2,480 kg/w? thennal conductivity: 1.16 W/mK specific heat capacity: 750 kJ/kg-K

Experimental conditions Temperature of tank liquid: 50—80°C Viscosity of tank liquid: 0.355—73 mPasec

Results

Nu = 0.5 Re^'^Pr' ^2Cr+0.lj

4.2 Multi phas» 283

Notation Cp specific heat capacity of liquid, J /kgK Cr actual solid volume concentration, mVw? d impeller diameter, m dp5o mean particle size, m D vessel diameter, m n impeller speed, 1/sec Nu Nussel number, (,aD)IK dimensionless Pr Prandtl number, {Cp TJ) /A, dimensionless Re Reynolds number, (nd^p)/77, dimensionless a heat transfer coefficient, W/m^K ri viscosity of liquid. Pa-sec T]w viscosity of liquid at wall temperature, Pasec A thermal conductivity of liquid, W/mK p liquid density, kg/w?

284 Chapter 4. Haat transfer


Rao, K. B. and Murti, R S., Ind. Eng. Chem. Process Des. Dev., 12,190 (1973)

Heat Transfer in Mechanically Agitated Gas-Liquid Systems


Heat transfer vessel Vessel diameter, m (D) Shape of base Material of construction Liquid height, m (ffi) Heat transfer area, m (AJ)

Turbine impeller Diameter, m (L) Number of blades (tib) Blade length, m (/) Blade width, m (w) Turbine position. Hi

from bottom of the tank Coil

Material of construction Outside diameter of coil tube, m (do) Mean diameter of coil helix, m (dc) Pitch, m (p) Number of terns («) Heat transfer area, m (Ac)

Sparger geometry (discharge downward) Ring diameter, m Hole diameter, mm Pitch, mm Number of holes

(1) 0.70

dished S.S. 304

0.89 2.40

0.233 6 0.059 0.047 0.233

copper 0.016 0.51 0.054

15 V2 1.26

0.233 3 9

60

(2) 0.226

dished S.S. 304

0.226 0.204

0.075 6 0.019 0.015 0.075

S.S. 304 0.0127 0.20 0.025

10 0.26

0.075 3 9

20

Working fluids and their physical properties Liquid: water, transformer oil and Clavus oil

Equations for physical properties of oils (Temperature range 30~90°C)

Ofls Heat capacity, Cp,

kgcal/kg°C Thermal conductivity, k,

kgcal/hrm^^^C/m Viscosity, /f,

kg/hrm Density, p,

kg/m^

Transformer oil (Shell Diala oil B) C, = 0.001 n+0.414 * = -0.000067 Tt+O.!! fi = 68.2-0.61 T* p = -0.63 r*+929

Clavus 33 oil (SheU clavus 33 oil) C, = 0.001 r»+0.408 k = -0.000059 n+0.11 /i = 136.1-1.197* p = -0.72 r«+947

Gas: air

4.2 Muiti ph«s« 285


Impeller speed, rpm Air rate, m/sec Warer rate, kg/hr Nusselt number, NNH Reynolds number, N^ Prandtl number, Npr Viscosity ratio, ju«,/ Viscosity tatio, fir/fi Froude number, Npr

40-500 0.002'-0.083

273-1,090 700-5,000

1x103-5x10* 2-266

0.18-0.98 1.02-1.50

0.008-0.53

Results For jacket

hiR = 1.35 iN;,)'^(N^)'^(N^)-^'\N^r"' k

For coil

^ = 0.87 (N;.f'*(Nf,f'"(N^)-^\NF.)-^'' k

Notation Cp hea t capacity of wa te r per unit mass , kcal/kg*°C D inside diameter of vessel, m e constant in modified Reynolds number g acceleration due to gravity, m/hr^ hj film coefficient of heat transfer, inside vessel wall to liquid kcal/hrm^°C he film coefficient of heat transfer, vessel liquid to coil wall, kcal/hrm^°C k thermal conductivity of agitated liquid at the bulk temperature, kcalm/hrm^°C L impeller diameter, m N agitator speed, 1/min Npr Froude number, N ^L/g, dimensionless Npt Prandtl number, Cpfi/k, dimensionless NRe modified Reynolds number, {Lp/fiKLN-^eVsX dimensionless Npis viscosity ratio number jU»/^ or //^///, dimensionless Tb bulk hquid tempera ture , "*€ Vs superficial gas velocity based on empty cross-sectional area, m / h r IJ, viscosity of agitated liquid at bulk tempera ture , k g / m ^ viscosity of agitated liquid at coil wall, k g / m h r ^w viscosity of agitated liquid at vessel wall, k g / m h r p densi ty of hquid at bulk temperature , kg/m^

286 Chapter 4. H«at tnmster

Nagata, S., Nishikawa, M., Itaya, M. and Ashiwake, K., Kagaku Kogaku Ronbunshu, 1,460 (1975) Study of Heat Transfer for Aerated Mixing Vessel and Aerated Tower

Experimental apparatus Vessel Type: dish-bottomed Diameter: 30 cm


Baffle Number: 4 Width: 3 cm

Impeller

standard six-flat blade Type turbine

Diameter (cm) 15 Number of impellers 1 Number of blades on impeller 6 Off-bottom clearance (cm) 10

three-blade propeller

14 1 3

10

Cooling coil Cooling coil dimensions (3/4" copper tube)

Loopdia. (mm)

1 225 2 225 3 225 4 210 5 240

Gap between tube (mm)

10 15 20 15 15

Ovexall height of coil (nun)

230 230 230 230 230

Lowest coil level (mm)

80 80 80 80 80

Surfstcearea (m*)

0.300 0.266 0.231 0.249 0.276

Sparger Type: a ring with 12 holes Diameter of spargen 10 cm Diameter of hole: 2 mm Direction of air flow: down ward Location: 4.3 cm from the bottom of vessel

Working fluids and their physical properties Liquid: water and non-Newtonian fluids Gas: air

Properties of materials used (60**C)

Materials (kg/m^) /ior/4, (cP)

Cp Otcal/kg*>C) (kcal/mhrX)

Water Glycerin sol. CMC sol. Air

983 1,200-1,230

983 1.07

0.469 32-95

6.9-840 0.096

1.00 0.56-0.725

1.00 0.25

0.563 0.25-0.254

0.563 0.022

4.2 MuKiphaM 287

Results For jacket

x{npf^aCi/iH)^(sme)'^(H/D)-^^

For coil

X inpf^'a Ci/iHf'Hsmef^iH/D)-^

Re'^{{P,+Pa)gJpd'NpY"d'p/^ Notation

h width of impeller blade, cm C height of impeller from bottom, cm Cp specific heat, kcal/kg**C d impeller diameter, cm D vessel diameter, cm gc acceleration due to gravity, m/hr^ he heat transfer coefficient for coil side, kcal/m^hr-^C hj heat transfer coefficient for jacket side, kcal/m^hr-^C H height of hquid level, cm i number of impellers k thermal conductivity, kcal/mhr°C n impeller speed, 1/sec tip number of impeller blades Np power number, Pgdp n^d , dimensionless Nuc Nusselt number for coil side, hcD/k, dimensionless Nuj Nusselt number for jacket side, hjD/ky dimensionless Pa power by aeration, kgm/sec Pg agitational power with aeration, kgm/sec Pr Prandtl number, Cp^/k, dimensionless Vis viscosity correction term, A //x, dimensionless 6 angle of impeller blade,degree ^ viscosity of hquid, g/cmsec li„ viscosity of hquid at wall temperature, g/cmsec p liquid density, kg/m^


Edney, H. G. S. and Edwards, M. E, TYans. Instn. Chem. Engrs., 54,160 (1976) Heat Transfer to Non-Newtonian and Aerated Fluids in Stirred Tanks




Impeller Tjrpe: six-flat bladed disc turbine Diameter: 0.356 m Number of impellers: 1 Number of blade on impeller: 6 Width of impeller blade (parallel to shaft): 0.061 m

Cooler Mean helix diameter: (1) 0.559 (2) 0.762 (3) 0.965 m Coil internal diameter: 0.041 m Coil external diameter: 0.047 m

Sparger Type: a T-shaped pipe Length: 0.35 m Location: 0.05 m beneath the turbine

Working fluids Fluid in cooling coil: water Fluid in tank:

non-Newtonian fluids: various dilute solutions of aqueous polymer solutions of sodium carboxymethyl cellulose and polyacrylamide

Gas: air

4.2 Multi phase 289

Results

Fluid

Water 7B = 307.9 K

Water TB = 308.1 K

Polyacrylamide rB = 308.1 K

Polyacrylamide TB = 308.1 K

N rev s"*

L95

2.55

2.01

3.18

Q. SCFH

0 500 800

1,000 1,300 1,600 2,000 2,500 3,000

0 500 800

1,000 1,300 1,600 2,000 2,500

0 500 750

1,000 1,500 2,000 2,500

0 500 750

1,000 1,500 2,000 2,500 3,000

hr Wm- K-

2,852.3 3,304.5 2,670.9 2,833.8 2,838.6 2,751.9 2,773.9 3,078.4 2,975.2 3,339.5 3,829.4 4,138.5 3,472.5 3,497.9 3,626.0 3,504.1 3,385.9 1,009.0 1,152.8 1,184.2 1,245.3 1,230.0 1,230.0 1,230.0

1,790.4 1,823.5 1,797.3 1,777.7 1,726.8 1,717.0 1,679.0 1,669.9

Notation he process side heat transfer coefficient N rotational speed of impeller Qg volumetric gas flow rate TB bulk fluid temperature


Steiff, A. and Weinspach, P-M., Ger. Chem. Eng., 1,150 (1978) Heat Transfer in Stirred and Non-Stirred Gas-Liquid Reactors

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 0.19 (2) 0.45 (3) 0.7 m Height:^//) = 1,2, and 3

Impeller Type: six-blade impeller Number of impeUers: 1 Number of blades on impeller: 6

Working fluids and their physical properties Liquid: three different fluids viscosity = 0.65 x 10"^ ~ 88 x 10"^ Pasec;

surface tension=0.02 ~ 0.07 N/m Gas: air


0.5 <. Rec ^16,000 A<.PrF< 825

1.6 X I Q - ^ ^ F T G < 4 X 1 0 - 2 l^H/D^3

0<Re„^2,2xlO-^

Results For wall-aerated liquid

\l/3" 5^ = 0.054 iRecFrGPrF)'

-{0.79+0.186x10'^ Rem)

For coil-aerated liquid

5^ = 0.137

where 5/ s

[ReGFrcPrFJ

Nu

x(Ren-^imr^\3f^ 7lF J

-(0.73+0.164xl0"®^«») r \-0.42

x(i?e. + 1.000r' fcl

DR

Notation a thermal diffusivity, mVsec c specific heat capacity at constant

pressure, J/kgK D reactor diameter, m DR impeller diameter, m g gravitational acceleration, m/sec^ H dispersion height, m n stirring speed, 1/sec VGO superficial gas velocity, m/sec a heat trans fer coefficient, W/m^ K 7] viscosity. Pa sec A thermal conductivity, W/mK p density, kg/cm^

Dimensionless group

A F T]F T]F

P T F ^ T]FCF

XF FrG =

VGO

gDR

Subscripts F Uquid G gas m mean value W waU


De Maerteleire, E., Chem. Eng. Scu, 33,1107 (1978) Heat Transfer to a Helical Cooling Coil in Mechanically Agitated Gas-Liquid Dispersions


1. Heat transfer vessel — flat bottomed cylindrical glass jar wall thickness: 0.001 m height: 0.250 m diameter: 0.180 m hquid height in the vessel: 0.204 m depth gas distributor below hquid surface: 0.200 m depth impeller below hquid surface: 0.195 m.

2. Baffles — four baffles made of stainless steel thickness: 0.001 m width: 0.018 m placed 0.001 m from the vessel wall at right angles.

3. Impeller — four bladed paddle impeller diameter: 0.100 m blade dimensions:

thickness: 0.001 m width: 0.020 m length: 0.035 m blade angle: 45 deg.

4. Coil — hehcal coohng coil made of pure red copper height: 0.115 m number of turns: 5 clearance between two turns: 0.013 m outside diameter of coil tubing: 0.012 m inside diameter of coil tubing: 0.008 m inside diameter of helix: 0.100 m.

5. Gass sparger — circular and made of porous sintered glass diameter: 0.030 m thickness: 0.004 m.

Working fluids Liquid: distilled water, distilled water + a surface active agent, isopropyl alcohol,

ethylene glycol, two mineral oils and non-Newtonian fluid Gas: air

Experimental conditions Range of variables covered

Impeller speed: 100 ~ 873 rpm Gas rate Vsi 0.1976 ~ 1.5814 m/sec Nusselt number: 182 ~ 1,555 Reynolds number: 169 ~ 261,000 Prandtl number: 2.97 ~ 1,270 Viscosity ratio: 0.243 ~ 0.904 Weber number: 35 ~ 6,263 Froude number: 0.027 - 2.009


Results

Nu = 0.318 {Rer'\M'^\Vir''(Wef'^{Frr X 0.079

AO.627 / ix,\0.342 / T / ; \ 0 . 1 3 9 /f7/^\0.053 / E!M\-0.156 I

{DrN

Notation C specific heat of agitated liquid, kcal/kg-'^C Dr impeller diameter, m DT vessel diameter, m Fr Froude number, N^Drlg, dimensionless g acceleration force, m/sec^ hu external coil heat transfer coefficient, kcal/m^sec°C k thermal conductivity of process liquid, kcal/msec°C N rotational speed of impeller, 1/sec or 1/min Nu Nusselt number, huDrlk, dimensionless Pr Prandtl number Cp fx/k, dimensionless Re Reynolds number, Dr^ yNI\iy dimensionless Vs superficial gas velocity, m / s e c Vg volumetr ic flow rate of gas , m V s e c Yi viscosity ratio, /XZ/AC-, dimensionless We Weber number, D^N^-y/a, dimensionless 7 fluid density, kg/m^ /i dynamic viscosity of process liquid, kg/msec ^ dynamic viscosity of process liquid at temperature of coil surface, kg/msec G surface tension of process liquid, kg/sec^

4.2 Multi plMis« 293

Nishikawa, M., Kunioka, S., Fujieda, S. and Hashimoto, K., Kagaku Kogaku Ronbunshu, 8, 494 (1982) Heat Transfer to Non-Newtonian Liquid in Aerated Mixing Vessel

Experimental apparatus Vessel Type: dish-bottomed Diameter: 30 cm



Impeller Type: six-blade turbine Diameter: 15 cm Number of impellers: 1 Number of blade on impeller: 6 Off-bottom clearance: T/4

Sparger Diameter of sparger ring: 10 cm Number of holes: 12 Diameter of hole: 2 mm Direction of gas flow: downward

Working fluids and rheological properties Liquid: aqueous solutions of CMC

weight, % (agitation controlling region) (bubbling controlling region)

CMC 1 0.53 0.051-0.062 poise 0.051-0.063 poise CMC 2 0.88 0.11-0.14 0.11-0.15 CMC 3 1.41 0.20-0.26 0.19-0.29 CMC 4 2.21 0.52-1.00 0.48-L15

Gas: air Results

h = {{PJf)h,-¥Paha}l{{P,/f)'^Pa} P,=Nppn^d^/gc Pa=u,pHnD\glgc)/A

For jackets /y = 10 For coils /c=2.5


Notation d impeller diameter, cm D vessel diameter / weighting function g gravitational acceleration, cm/sec^ gc gravitational acceleration factor, kgm/kgsec^ h heat transfer coefficient, kcal/m^h°C ha heat transfer coefficient under aeration, kcal/m^h-°C H height of hquid level, cm n impeller speed, 1/sec Np power number , Pggr/p n^d , dimensionless Pa aeration power, kgm/h Pg agitation power, kgm/h Ug superficial gas velocity, m / h ^a apparent viscosity of non-Newtonian, g / c m s e c p hquid density, g / c m

4.2 Multiphas* 295

Kurpiers, R, Steiff, A. and Weinspach, R-M., Ger. Chem. Eng., 8,48 (1985) Heat Transfer in Stirred Multiphase Reactors

Experimental apparatus Vessel Type: dish-bottomed Diameter: 0.45 m Height: 1.35 Z)

Impeller Type: six-bladed disc turbine Diameter: Z)/3 Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 0.50 d

Working fluids and their physical properties Liquids: water, ethylene glycol, diethylene glycol, and glycerol

liquid

water

ethylene glycol diethylene glycol glycerol

40°C 20°C 50X 50°C 80°C 70°C 62X

r\L (mPas)

0.651 1.000 6.83 9.74

31.5 48.2 70.9

PTL

4.30 6.94

65.7 114 289 434 630

Gas: air Experimental conditions

Agitator speed: 0—720 rpm Superficial gas velocity: 0—0.13 m/sec

Results

Nuw=K

Notation

^m NeRel + GaRec -41) Ho-e

Cp specific heat, J/kgK d stirrer diameter, m D vessel diameter, m e bottom clearance of aeration ring, m Ffn Froude number, n^d/g, dimensionless g gravitational acceleration, m/sec^ Ga Galileo number, gD^/Vf dimensionless hw mean wall heat transfer coefficient, W/m^K Ho height of non-aerated liquid, m K constant n stirring speed, 1/sec Ne Newton number, P/pn^d^, dimensionless Nuw Nusselt number, hwD/k, dimensionless P power input of agitator, W PTL Prandtl number, r\CplK dimensionless

Ne^'^Frn '<tl Ren

RBG

VGO

V T] T]w A V

« p

Reynolds number, ndVv, dimensionless gas Reynolds number, VGOD/V, dimensionless superficial gas velocity, m/sec volume of non-aerated liquid, m viscosity. Pa-sec viscosity at waU, Pasec thermal conductivity, W/mK kinematic viscosity, mVsec constant density, kg/cm^

Subscript L liquid

296 Chapter 4. H«at tninsfor

Xu, G. J., Li, Y. M., Hou, Z. Z., Feng, L. E and Wang, K., Can. J. ofChem. Eng., 75,299 (1997) Gas-liquid Dispersion and Mixing Characteristics and Heat Transfer in a Stirred Vessel

Experimental apparatus Vessel Type: dished-bottomed Diameter: 0.386 m

Liquid contained Height: 1.5/)

Baffle Number: baffled

Impeller

•^i-

• $ •

Rushton turbine (RT)

Flat blade paddle (FBP)

45° pitched blade disc turWne (PBDT)

-4 45** pitched blade

paddle (PBP) Concave blade disc

turbine (CBDT) Conical turbine

(CT)

HMHM

Brumagin impeller (BI)

4.2 MuKiphas* 297

Dimensions of the impellers used

Impeller type*

Rushton turbine Flat blade paddle 45° pitched blade disc turbine 45° pitched blade paddle Concave blade disc turbine Conical turbine Brumagin impeller

*Blade number of each impeller is i

Notation

RT FBP PBDT PBP CBDT CT BI

Dimensions of the impellers

b b b b b b b:

:/:flfz,:(/ = 0.2:0.25:0.751:l :d = 02:l :l:dD:d = 0.2S:0.25:0.751:l : d = 0.28 :1 :/:(/z,:(/ = 0.2:0.25:0.75:l :(/z,:rf = 0 . 4 : l : l \l:d = 0.27:0.22:1, blade angled by 45°

6. Flow patterns of PBDT and PBP are upfolw.

Dual impeller combinations used

Impeller combination type*

Two 45° pitched blade disc turbines Two Rushton turbines Concave blade disc turbine (upper) Conical turbine (lower) 45° pitched blade disc turbine Conical turbine Conical turbine 45° pitched blade disc turbine 45° pitched blade disc turbine Concave blade disc turbine 45° pitched blade disc turbine Rushton turbine

in the experiment

Notation

2PBDT 2RT

CBDT+CT

PBDT+CT

CT+PBDT

PBDT+CBDT

PBDT+RT

*Blade number of each impeller is 6. Flow patterns of 45° pitched blade disc turbine is up flow.

Diameter: 0.40 Z) Number of impellers: 2 Clearance between the two impellers: 0.60 D Height of the lower impeller from the bottom: 0.40 D

Sparger Type: perforated ring Diameter of ring: 0.25 D Diameter of hole: 2 mm Distance between holes: 1.5 cm Location: D/6 below the impeller

Cooling device Jacket


Experimental conditions Air flow rate: up to 0.02 m/sec Impeller rotational speed: 2—81/sec Temperature: 50**C

Results

Nu^RmPr'^Vis'''

in which Hz =^ReN+S(NQ'-TFr')ReG


Parameter estimates of the correlations

Impeller type

2PBDT 2RT CBDT+CT FBDT+CT CT+PBDT PBDT+CBDT PBDT+RT

S

0.68 8.90 1.11 2.41 14.2 17.0 0.66

T

6.22x10^ 1.94x10* 1.59x10" 1.88 X 10« 2.23 X10^ 7.54 xlO^ 8.45 X10^

R

0.700 0.006 0.734 0.189 0.099 0.816 0.105

s

0.236 0.266 0.203 0.272 0.269 0.187 0.284

t

2.73 1.58 2.98 1.96 1.35 1.93 2.33

r

1.85 1.43 1.68 0.71 5.05 1.44 5.22

Notation Cp specific heat of process hquid, J / k g K d impeller diameter, m D vesse l diameter, m Fr Froude number, N Mig, dimensionless g gravitational constant, m/sec^ hw fluid/wall heat transfer coefficient, W/m^K k thermal conductivity of process liquid, W / m K N impeller speed, 1 /sec NQ aeration number, QclNd^y dimensionless Nu Nusselt number, KDIk, dimensionless Pr Prandtl number Cp î/k, dimensionless QG gas flow rate, mVsec r constant R constant RBG aeration Reynolds number, VsDp/^, dimensionless Res stirring Reynolds number, d^Nplî, dimensionless 5 constant 5 constant Vs superficial gas velocity, m / s e c Vis d imensionless viscosity ratio, ^/fXw, d imensionless H dynamic viscosity of process fluid, k g / m s e c îw dynamic viscosity of process fluid at temperature of waU surface, k g / m s e c p density, kg/m^

4.2 Multiphase 299


Steiff, A. and Weinspach, R-M., Ger. Chem. Eng., 5,342 (1982) Fluid Dynamics, Heat and Mass Transfer in Agitated Aerated Slurry Reactors

Experimental apparatus Vessel Type: dish-bottomed

Baffle Number: 4

Impeller Stage: single-and two-stage Off-bottom clearance:

single stage: Hn/d = 0.5 two stage: /fc/rf = 0.5 and 2.58

Working fluids and solid Solid: glass beads Liquid: water Gas: air

Results 6000

I ^ ^ T E 5000

•5 i.000

2000

1000

O!

r 1 : L Woter t gloss beods L Vft, « Ocm/s ^ f dp « 71 ^n» j d ^

[• y 1 ^f^/n

1 ^ . t S< State of complete \ sus pension

• I • • ! • . . • 1

ir

L-^

i

Symbol

o

O

• 1 1,1 i,..<

n ^\

1 "Pys 0

0 025 0 050

ioioo , . . , 1 ^ ...1

I i

100 200 300 100 500 600 700 800 100 200 300 t M 500 600 700 800

6000

5000

1000

3000

2000

1000

ol

Air / woter i gloss beods

vg. t 0 35 cm/s

dp * 7 l> jm .

i ^ C)

. ^ s ^

i^r Symbol •^vs

0 0 025 0 050 0 100

100 200 30C 100 500 600 700 800

Stirring speed n M/min]

6000

5000

1000

3000

2000

1000

0

1 ; 1

Air/ woter/ gloss beods voe « 2 5 cm/s

A dp « 7 l i jm ^ ^ 1

• X"

^ •

^ JVW^'"'^""

y

/ • / /

.1 . 1 i . . .

•

• 0)

(

^ ^ ^ _ 1 . . - .

, Symbol

X

o o

. . f . . J

1 *v$ 0

0 025 0 100

100 200 300 100 500 600 700 800

Stirring speed n M/min]

Comparison of heat transfer in stirred single-phase and multiphase systems.


Notation d stirrer diameter, m dp particle diameter, \\m HR stirrer clearance, m n stirrer speed, 1/sec Vco superficial gas velocity, m/sec <bvs solid volimie fraction

4.2 M u l t l p h a s * 301

Kurpiers, E, Steiff, A. and Weinspach, R-M., Ger. Chem. Eng., 8,48 (1985) Heat Transfer in Stirred Multiphase Reactors

Experimental apparatus Vessel Type: dish-bottomed Diameter: 0.45 m Height: 1.35 Z)

Impeller Type: six-bladed disc turbine Diameter: Z)/3 Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 0.50 d

Working fluids, solid and their physical properties Liquids: water, ethylene glycol, diethylene glycol and glycerol

liquid

water

ethylene glycol

diethylene glycol

glycerol

40°C 20°C

50°C

50*^0

80°C 70°C 62°C

r]L (mPas)

0.651 1.000

6.83

9.74

31.5 48.2 70.9

PTL

4.30 6.94

65.7

114

289 434 630

Solid: glass beads solid density = 2,460 kg/m ; particle mean diameter = 10—1,800 im; soUd concentration = 0—0.10 volume fraction

Gas: air Results ^'

w

S X

5h

1 Symbol

- • —

— o —

— --A

^

d^/pm]

0 IS 71

300 430 724

1800 J

HfOtinQ, T|.*40lC

I 0x1 oio 0/ds

0.45m 3

Air-l>qu>d-9los« b»ods

VQ,s0.3Scm/s

*9vs'0.10 Ps*2460kg/m>

hifluence of particle size on heat transfer io' in the stirred three-phase system. 10* 10'

Agitator sp««d n

302 Chapter 4. Haat transfer

o X

W

i

3

n = UOU min .-1

nof complefe suspended

3 D/d= 3 *^vs=0.10 lO 'h «>^ H«/d=0.5 Ps=2U0 kg/m^

0 IS 71 300 U30

nu 1800

10-' 2 5 t)-' 2 m/s 5 X)*

Superficiol gas velocity VQ

Influence of particle size and of superficial velocity on heat transfer coefficients hw.

ungossed

fotat Cp d dp

D hw HR

n PTL TL

VGO

ri A Ps (Pvs

ion specific heat, J/kgK stirrer diameter, m particle diameter, ^m vessel diameter, m mean wall heat transfer coefficient, W/m^K bottom clearance of mixer, m stirring speed, 1/sec Prandtl number, rjCp/X, dimensionless liquid temperature, °C superficial gas velocity, m/sec viscosity, Pasec thermal conductivity, W/mK density of solid, kg/m^ volume fraction of solid

Subscript L liquid

4*2 Multi phas« 303

Kurpiers, E, Steiff, A. and Weinspach, E-M., Ger. Chem. Eng., 9,190 (1986) Reactor Wall/Fluid Heat Transfer in a Stirred Single- or Multi-phase Reactor Using Single or Two-stage Disk Stirrers

Experimental apparatus Vessel Type: dish-bottomed Diameter: 0.45 m Non-gassed filling height: 1.35 D Volume: 0.091 m

Baffle Number: 4 Width: 0.1 Z) Immersion depth of baffle in the non-gassed state: 0.45 m

Impeller Type: six-blade disc turbine Diameter: D/3 Number of impellers: (1) 1 (2) 2 Number of blades on impeller: 6 Ground clearance of lower stirrer (m): (1), (2) 0.5 d Ground clearance of upper stirrer (m):(2) rf~1.35 d

Sparger Bottom clearance (m): 0.083 D

Working fluids, solids and their physical properties Liquids: water, ethylene glycol, diethylene glycol and glycerol

liquid

water

ethylene glycol

diethylene glycol

glycerol

40°C 20°C

50°C

50*»C

80°C 70X 62*»C

T]L (mPas)

0.651 1.000

6.83

9.74

31.5 48.2 70.9

PTL

4.30 6.94

65.7

114

289 434 630

Solid: glass beads solid density = 2,460 kg/m^; particle mean diameter = 15—1,800 im; sohd concentration = 0—0.10 volume fraction


Agitator speed: 0—720 rpm Superficial gas velocity: 0—13.3 cm/sec Solid concentration: 0—0.10 volume firaction

304 Chapter 4. H«at transfar

Results For the single phase "fluid" system, the two-phase "gas-liquid" and "solid-hquid" systems, as well as the three phase "gas-solid-liquid" system, the following heat-transfer relationship is given:

V T 0.238

NU Wm = 0.1 11.581 f NemReL + GomReGm xM Tlw )

2Qb<.Nuwm

4.2<Prn.

^6,809

<632

0.033 < (7]/r]jv)m ^3.021

2.69x10'<Gfl« < 2.16x10''

IM^Ne^ < 10.17

6.51x10^ <Renm < 4.05x10'

0.021 ^Fr„ < 2.150

0^i?ec«. ^7.067x10*

Notation Cp d D Frn g Ga hw n Ne Nuw P PTL Ren Rec VGO

V ri

A V

p

specific heat, J/kgK stirrer diameter, m vessel diameter, m Froude number, n^d/g, dimensionless gravitational acceleration, m/sec^ Galileo number, gDVv, dimensionless mean wall heat transfer coefficient, W/m^K stirring speed, 1/sec Newton number, P/pn^d^, dimensionless Nusselt number, ftwDIK dimensionless power input of agitator, W Prandtl number, r\Cplk, dimensionless Reynolds number, n^Vv, dimensionless gas Reynolds number, VGOD/V, dimensionless superficial gas velocity, m/sec volume of non-aerated liquid, m^ viscosity, Pasec viscosity at wall, Pasec thermal conductivity, W/mK kinematic viscosity, mVsec density, kg/cm^

Subscript L liquid m average value of homogeneous suspension

305

Chapter 5. Mass Transfer

5.1 Solid-liquid systems

MUler, D. N., Ind. Eng. Chem. Process Des. Dev., 10,365 (1971) Scale-up of Agitated Vessels. Mass Transfer from Suspended SoluteParticles

Experimental apparatus Vessel and impeller geometries and dimensions Vessel type: dish-bottomed Impeller type: flat paddle Number of paddles: 4

Nommal vessel size, gal ~

A B C D E F G H I J K

Numbers of bafQes

1

6 8V4 12 4 V4 Vaz Vs V, V2 V.6 'A 4

10 Dimensions, in.

12 17 V2 24 8

Vk V16 % % 1 'A 1 4

100

27 39 Vs

54 18

3 % */64

1 'V16 1 % 2V4 V32 2V4 4

Working fluid and solid Liquid: water Solid: benzoic acid


Nominal vessel size, gal 1 10 100 ImpeUer speed (rpm) 170-490 103-290 25-168

Impeller power input 0.05—19 hp/10^ gal Results

ife = 0.0267Z)/Z)p(2 + 1.107Vi;'7\ri/')(«'r''

Notation D molecular dififiisivity, cmVsec Dp particle diameter, cm g acceleration of gravity, cm/sec^ k mass transfer rate constant, cm/sec «' impeller speed, 1/sec NR^P particle Reynolds number, Dpujv,

dimensionless

Nsc P Us

V

P

0.06Arod ^f"*^ 0.06Arod

SIDE VIEW

Schmidt number, v/Z), dimensionless agitator power input, hp slip velocity, cm/sec kinematic viscosity, cmVsec fluid density, g/cm^

306 Chapter 5. Mass transffar

Levins, D. M. and Glastonbury, J. R., lyans. Instn. Chem. Engrs., 50,132 (1972) Particle-Liquid Hydrodynamics and Mass Transfer in a Stirred Vessel Part. II - Mass Transfer

Experimental apparatus Vessel Type: flat-bottomed Diameter, liquid height, and impeller diameter:

System

DT (mm) H (mm) Ds (mm)

Baffle Number: (1)-

(1) 250 216 63

(5)3 Width:(l)~(5)0.1Z)r

Impeller

Type

Number of impellers Number of blades on impeller

A (nun) Ds/W Po

(2)

250 216 75

Flat blade turbine

."sfc 1 6

8 2.24

(3)

250 216 100

(4)

126 120 63

Curved blade

turbine

?^ 1 6

8 2.10

(5)

126 120 75

45'' pitched blade turbine

*

1 6

63,75,100 9.4, as, &25

1.18,1.25,1.20

Marine propeller

(square pitch)

^

1 3

0.41

5.1 Solid-liquid systems 307

Working fluids, solids and their physical properties Liquid: see table Solid: see table

System

Solid Density Particle Viscosity Diffusivity Density Dofference Diameter v A x 10'

pt (kg/m ) Ap(kg/m^ ^ (micron) (centistokes) (mVs) Sc » v/D,

A. Catron exchange resins in aqueous bases

B. Anion exchange resins in (i) aqueous ackis (ii) sucrose-water-HCl

C. Spherical copper powder in (i)IrKIsolutron (ii) IrKI-sucrose solutron

D. Spherical iron powder (i) Ck>pper coated in I2-KI

solution (ii) In IrKI-sucrose solutron

£. Spherical aluminum powder copper coated in IrKI solutron

F. Ammonium nitrate in ethanol G. Stearic acid in ethanol H.Nsq[>hthalene in methanol

i;280

1.100 1,170-1,190

8,480 8,480

7,120 7 3 0

2350 1,490

800 1,020

280

100 30-50

7,130 6,930-7,060

5,770 5,730-5360

1,500 700 10

230

114-637

30.8-593 96.1-593

46.1-78.3 61.2

72.9-98.2 89.1

45.6-79.2 1,613-1,953

890 1,490

0.89

0.89 1.72-2.89

0.60 3.85-17.3

0.60 3.85-17.3

0.60 1.42 1.42 0.71

2.13-2.85

1.49-3.34 1.32-1.98

1.27 0.0485-0.216

1.27 0.0485-0216

1.27 0541 0.65 1.95

313-418

267-597 868-2,190

473 1.78x10^-3.57x10=*

473 1.78xl0*~337xl0'

473 2.630 2.190

364

Results

kdp _

Dr = 2+0.47

^^V^ Dr)

When a significant density difference exists, an equation similar to those proposed for forced convection mass transfer is recommended:

\ l / 2 / xO.38

Notation dp Ds DT Dr H k N P Po V

e V

PL

particle diameter stirrer diameter tank diameter diffusivity liquid height mass transfer coefficient stirrer speed power power number, PIN^D^ pu dimensionless resultant relative velocity energy dissipation rate/unit mass kinematic viscosity of fluid liquid density

3og Chaptor 9. Mass transfer

Kuboi, R., Komasawa, I., Otake, T. and Iwasa, M., Chem. Eng. Scu, 29,659 (1974) Fluid and Particle Motion in Turbulent Dispersion—III Particle-Liquid Hydrodynamics and Mass-Transfer in Turbulent Dispersion




Impeller Type: six flat-bladed turbine Diameter: 52 mm Number of impellers: 1 Number of blades on impeller: 6 Width of impeller blade (parallel to shaft): 10 mm Off-bottom clearance: 35 mm

Working fluid, solid and their physical properties Liquid: 0.01 N NaOH solution Solid: ion-exchange resin (DAIA-ION SKIB) particles

density = 1.20 g/cm^ diameter = 0.0246,0.0480 and 0.0940 cm Experimental conditions

Stirrer speed: 380-3,600 rpm Average energy dissipation rate: 5.8 x 10^—4.9 x 10^ cmVsec^ Temperature: 20 ± 0.5°C Hold-up of particles ^ 0.01

Results S*=2+0.49(/?^Sc)^/2

Notation dp particle diameter, cm 0 diffusivity, cmVsec k mass-transfer coefficient at a fixed value of £, cm/sec Rep particle Reynolds number based on relative velocity, dp «7v, dimensionless Sc Schmidt number, v /0 , dimensionless Sh Sherwood number, kdp/0, dimensionless u' relative velocity, '^{pf-VpY, cm/sec V turbulence component velocity, cm/sec £ energy dissipation rate per unit mass, cmVse(? V kinematic viscosity of fluid, cmVsec

Subscripts P particle / fluid

5.1 SolifMlquid systems 309

Sano, Y., Yamaguchi, N. and Adachi, T.J. Chem. Eng. Japariy 7,255 (1974) Mass Transfer CoefiFicients for Suspended Particles in Agitated Vessels and Bubble Colunms


Vessel No Type Diameter (cm) Height (cm)


Impeller Type Diameter (cm) Number of impellers Number of blades Length of impeller blade (cm) Width of impeller blade (cm) Off-bottom clearance

V-1

17.5 17.5

4 0.1 r

turbine 0.2877

1 6

0.3Z) 0.2Z) 0.337

V-2

9.5 9.5

4 0.157

paddle 0.337

1 2

0.5Z) 0.2Z> 0.337

V-3.1 flat-bottomed

20 20

4 0.157

paddle 0.337

1 2

0.5Z) 0.2Z) 0.337

V-3.2

20 20

unbaffled -

paddle 0.337

1 2

0.5Z) 0.2Z) 0.337

V-4

40 40

4 0.157

paddle 0.337

1 2

0.5 Z) 0.2Z> 0.337

Working fluids, solids and their physical properties System Continuous phase Dispersed phase

2 X10-3 N/^HCl solution water water water

ion exchange resin benzoic acid

KMn04 j3-naphthol

Solid dp

Properties of solid particle (20X)

Cs PP 0 Sc (g/cc) (g/cc) (cmVsec) ( - ) Apparatus

n (r.p.m.)

wt.% of solid

Ion ex. resin — (Natype)

60 -833

1.40

Benzoic acid 107 66 0.49 2.9x10-' 1.31 - 2 3 5 0 -1,080 -0.58

KMn04 107 79 0.44 6.25x10"^ 2.70 -780 -333 -0.57

/3-naphthol 1,530 520 0.34 0.60x10"' 1.22 - 2 3 5 0 -1,140 -0.40

Z)H*=8.5x10-' Z)N.*=1.19X10-5

0.78x10-*

1.59x10-''

0.71x10-*

217

1,280

628

1,410

V-2,V-3.1, V-3.2, V-4, T-l ,T-2 V-1,T-1

V-1,T-1

V-3.1,T-1

240-1,600

240-1,600

400-1,600

700-1,200

0.05 -0.1

0.06

0.15

6x10-

Experimental conditions Temperature: 20°C

310 Chapter 5. Mass transfer

Measurement techniques

System Technique

1 Conductivity measurement 2 Conductivity measurement 3 Conductivity measurement 4 UV spetrophotometry

Results

Sh = [2+0A(ed} /vy^* 'Sc^^^]'(l>c

Notation Cs saturated concentration, g/cm^ dp specific surfoce diameter, ^m or cm dp screen diameter, ^m D impeDer diameter, cm 0 diffusion coefficient, cm/sec k mass transfer coefficient, cm/sec n impeller speed, 1/sec Sc Schmidt number, v/0, dimensionless Sk Sherwood number, kdp/0, dimensionless T vessel diameter, cm £ rate of flow energy supply per unit mass of fluid, cmVsec^ V kinematic viscosity, cmVsec pp density of solid, g/cm^ ^ Carman's surface factor

5.1 Solid-liquid systMAS 311

Boon-Long, S., Laguerie, C. and Couderc, J. E, Chem. Eng. Sd., 33,813 (1978) Mass Transfer from Suspended Solids to a Liquid in Agitated Vessels

Experimental apparatus Vessel Type: flat-bottomed Diameter: 9.0-63.4 cm

Liquid contained Height: T


Impeller Type: six-bladed disc turbine Diameter, turbine diameter, blade length and blade width:

Vessels and stirrers dimensions

T (cm) 63.4 40.0 29.0 19.0 9.0

Da (cm) 21.0 13.3 9.7 6.3 3.0

S (cm) 15.8 10.0 7.3 4.7 2.3

L (cm) 5.3 3.3 2.4 1.6 0.8

W (cm) 4.3 2.7 1.9 1.3 0.6

np

6 6 6 6 6

Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: T/2

Working fluid and solid Liquid: water SoUd: benzoic acid

Results

10,000 <Re< 30,000, 110,000 < Ga < 1,000,000, 21< U < 2,900 30 < TId < 215 , 300 <Sc< 2,000

Notation d Da D, g Ga k L MT np N Re

S

particle diameter stirrer diameter diffusivity gravitational constant =(PV^V(M') mass transfer coefficient stirrer blade length total mass of particle number of stirrer blades stirrer speed Reynolds number (referred to the particle). dT(on/ii, dimensionless turbine diameter

Sc Sh

T U

V W Wc

i" P Ps CD

Schmidt number, ^,/pDv, dimensionless Sherwood number (referred to the particle), kdlDp, dimensionless vessel diameter solid concentration or quantity group, Mrlpd^, dimensionless vessel volume stirrer balde width baffle width viscosity of liquid density of liquid density of acid particles stirrer angular velocity, 2 nN

312 Chapter 5. Mass transfor

Conti, R. and Sicardi, S., Chem. Eng. Commun., 14,91 (1982) Mass Transfer from Freely-Suspended Particles in Stirred Tanks

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 128 (2) 190 (3) 228 mm

Baffle Number 4

Impeller Type: (a) 4 flat blade impeller (b) 6 flat blade turbine Number of impellers: 1 Number of blades on impeller: (a) 4 (b) 6 Diameter and off-bottom clearance:

T .10^ (m)

128 128 190 190 190 190 190 190 190 190 190 190 190 190 190 190 190 190 228 228 228 228 228

190

190 190 190 190

D T

0.36 0.56 0.24 0.38 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.30 0.38 0.24 0.24 0.24 0.24 0.25 0.19 0.25 0.32 0.25

0.33

0.33 0.33 0.33 0.33

C T

0.33 0.33 0.33 0.33 0.17 0.22 0.33 0.50 0.17 0.22 0.33 0.50 0.33 0.33 0.17 0.22 0.33 0.50 0.33 0.33 0.33 0.33 0.33

0.33

0.15 0.20 0.33 0.50

Dp .10^ (m)

3.6 3.6 1.1 1.1 2.4 2.4 2.4 2.4 3.6 3.6 3.6 3.6 3.6 3.6 6.1 6.1 6.1 6.1 2.4 3.6 3.6 3.6 6.1

3.6

0.92 0.92 0.92 0.92

benzoic add

cylindrical particles

ion exch. resins

4flat blades

impeller

6flat blades tutbine

5.1 Solid-liquid systoms

Working fluids and solids

313

System

Liquid water Solid benzoic acid cylindrical particles

NaOH solution ion exchange resins

Notation Dp particle specific diameter, m Sc Schmidt number, dimensionless Sh Sherwood number, dimensionless ^ power consumption per unit of mass mVsec^ V kinematic viscosity, mVsec

314 Chapter 5. Mass transter

Lai, R, Kumar, S., Upadhyay, S. N. and Upadhya, Y. D., Ind. Eng. Chem. Res., 27,1246 (1988) Solid-Liquid Mass Transfer in Agitated Newtonian and Non-Newtonian Fluids


Baffle Number: baffled and unbaffled Width: Z)//20

Agitator Geometries

agitator

basic paddle disk turbine

plane turbine propeller"

diameter

6.0 4.0 6.0 8.0

10.0 12.0 6.0

4.3,10.0

no.

2 4

2.4 2,3.4,6

4 4 4 4

length (cm)

3.0 1.0

3.0,1.5 2.0 2.5 3.0 3.0

2.15,5.0

blades

width (cm)

2.0 0.8

2.0,1.2 1.6,2.0,2.5.3.0

1.6 2.0 2.0

0.5,1.0

thickness (cm)

0.50 0.25

0.5,0.25 0.25 0.25 0.25 0.50 0.10

"Stainless steel twisted blades; the rest are all of Perspex.

Working fluids, solids and their physical properties Fluids:

parameter

fluid

n

Newtonian

fluids

ethylene glycol, water, 60% aq. propylene glycol

1.0

non-Newtonian

1.0%, 2.0%, and 3.0% aq. CMC sohi.

0.68'-0.933

Solids: benzoic acid particles

shape

peUet

sphere

hp (cm)

0.4266 0.4383 0.2211 0.2505 0.1607

dp (cm)

1.2154 0.8606 0.8956 0.5541 0.5824 2.0080 1.6740 1.2130

Dp (cm)

1.1211 0.8643 0.7736 0.5442 0.5129 2.0080 1.6740 1.2130

p, (g/cm^)

1.3281 1.2508 1.2506 1.2524 1.2501 1.2124 1.1748 1.1122

5.1 Solid-Hquid systems 315


rro Sc A (cm) Ds (cm) Dp (cm)

rpm

16.8-36.0 624--10^ 14.5'-25.0''(B,UB) 4.0-'12.0(DT,PT,BP,PR) 0.5129'-1.1211 (P) 1.213-'2.008 (S) l'-2,850

18.8--34.2 10^-10^ 18.0-21.0 (B,UB) 4-12.0 (DT, PT, BP) 0.5129-1.1211 (P) 1.213-2.008 (S) 27-2,580

" P=pellet, S=sphere, B=baffled, UB=unbaffled, DT=disk turbine, PT=plane turbine, BP=basic paddle, PR=propeller.

Results

5/i^=2.0+0.02i?g,2/35î/3 j^g^ < 8.5x 10^ ^ KcDp

Shp=^2.0-\-2.02Res'^^Sc'^^ Res > 8.5x 10^ "

Shp=2.0+0mSRef^^^Sc'^^ Ref < 10^ ^^' " ^ (or ^l)

Shp=2,0-^3.9SRei''^^Sc^^^ Re!>W ^„ JcNDsDpp êp=— —

^(OTfia)

Shp=2.0-^0A74Re;^^^Sc'^^ l<Rei< 800 Shp=2,0+7,525Rei'^*Sc^^^ Re'p > 800 ^^^ - nY^Df^û (or Ua)

Notation dp particle diameter, cm DM diffusivity, mVsec Dp equivalent particle diameter, m or cm A agitator diameter, m Dt vessel diameter, m hp thickness of pellet, m HL height of liquid from bottom of the vessel, m Kc mass-transfer coefficient, m/sec n flow behavior index, dimensionless N rotational speed of agitator, 1/sec Re'p modified particle Reynolds number, Dp^^^D^'^Np/D?'^H^^^^ (or /xj), dimensionless Rep particle Reynolds number, itNDiDppI^ (or ^*a\ dimensionless 5c Schmidt number, /x (or fxDpDM, dimensionless Shp particle Sherwood number, KcDplDn, dimensionless p density of fluid, kg/m^ p, density of soHd, g/cm^ or kg/m^ [i viscosity, Pasec /x^ apparent viscosity for non-Newtonian fluids, Pasec

316 Chapter 5. Mass transffsr

Asai, S., Konishi, Y. and Sasaki, Y.J. Chem. Eng. Japan, 21,107 (1988) Mass Transfer between Fine Particles and Liquids in Agitated Vessels

Experimental apparatus Vessel Type: flat-bottomed Diameter: 13.2 and 9.0 cm

Baffle Number: 4 Width: r/lO

Impeller Type: six-flat-blade turbine Diameter: T/2 Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): T/4 Width of impeller blade (parallel to shaft): T/5 Off-bottom clearance: T/3

Working fluids solids and their physical properties

Run No.

1 2 3 4 5 6 7 8 9

10

11 12

Systems

Dilute suspension Cation exchanger-10"^ kmol/m^ NaOH sol. Anion exchanger-10"* kmol/m^ HCl sol. Anion exchanger-10"^ kmol/m^ H2SO4 sol. Anion exchange-10~^ kmol/m^ oxalic add sol. Anion exchanger-10"^ kmol/m^ picric acid sol. Anion exchanger-(10"^ kmol/m^ HCl + 32 wt% sucrose) sol. Copper-5 x 10" kmol/m^ Iodine sol. Copper-(5x 10" kmol/m^ Iodine + 32 wt% sucrose) sol.* Lead sul£eite-water Lead su]£ate-44 wt% glycerin sol.

Dense suspension Anion exdianger-lO"^ kmol/m^ HCl sol. Anion exchanger-(10"^ kmol/m^ HCl + 32 wt% sucrose) sol.

hulicle diameter

d

(m) 23-842 27,202 27,202 27,202 27,202 27,202 31-966 5-102

23 20

43,57 43,57

Particle density

P (kg/m^

1,190,1,290 1,110 1,110 1,110 1,110 1,140 8,190 8,190 6,200 6,200

1,110 1,140

Kinematic viscosity vxlO^ (m7s)

8.96 8.96 8.96 8.96 8.96

27.0 6.49

32.2 8.96

30.1

8.96 27.0

Diffusivity

DxlO^ (mVs)

2.13 3.33 2.60 1.92 1.49 1.15 1.68 0.340 0.994 0.267

3.33 1.15

•Containing 3.0 kmol/m^ KI and 5x 10" kmol/m^ H2SO4 Physical properties at 25°C

Experimental conditions Stirring speed: 2.2—251/sec Temperature: 25°C

Results S/r=[2 -*+ {OMie^^^d^^Vv) 0.58 Sc^^^V^Y^^''

where 0.0229 < e^^^d^^Vv < 495, 269 <Sc< II3OO

Notation d particle diameter, m D hquid-phase difiiisivity, mVsec k mass transfer coefficient, m/sec Sc Schmidt number, v/D, dimensionless Sh Sherwood number (referred to the particle), kd/Dy

dimensionless

T vessel diameter, m e energy dissipation rate per unit

mass of Uquid, mVsec V kinematic viscosity, mVsec

5.1 Solid-liquid systems 317

Armenante, E M. and Kirwan D. J., Chem. Eng. Scu, 44,2781 (1989) Mass Transfer to Microparticles in Agitated Systems

Working fluids solids and their physical properties

System

71% glycerol solution + NaOH + ion exchangers



Water + NaOH + ion exchangers

NaNOa solution + AgNOs + ion exchangers

Number of experimental

points 23 14 55 28 23 24 28 17 27

6 10 6

6 8 2

4 11 15

24

Mean particle diameter

(urn) 6 9

18 45 58 84

146 345 424

6 18 58

6 18 58

6 18 58

9

Solution properties at 25°C

Viscosity Diffusivity Ocgm-'s-'xlO^cp)) (m^s-'xlO^

19.5 0.13

8.8 0.25

3.1 0.53

0.89 2.1

0.89 1.6

Sc (xlO-^)

1.3

0.31

0.053

0.0042

0.0055

Results 5;j=2+0.52i?«°-^2 5 1/3

Notation d particle diameter, m or ^m

di^sion coefficient, mVsec mass transfer coefficient, m/sec turbulent Reynolds number, e^'^d^^^a, dimensionless Schmidt number, a/Dj dimensionless Sherwood number, kd/Dj dimensionless power input per unit mass of fluid, mVsec^ kinematic viscosity, mVsec

D k Re Sc Sh e a

318 Chapter 5. Mass transfar

Jadhav, S. V and Ptogarkar, V G.,Ind. Eng. Chem. Res., 30,2496 (1991) Particle-Liquid Mass Transfer in Mechanically Agitated Contactors


System (1)

Vessel Type flat-bottomed Diameter, m 0.15

Impeller Type DT(4,6bla(ied)

PTU(4,6bladed)

Diameter, m 0.05 Off-bottom clearance T/3

(2)

flat-bottomed 0.30

DT(4bladed) PTU(4bladed) PTU(6bladed)

0.1,0.19 T/6,T/4,T/3

(3)

flat-bottomed 0.57

DT(4bladed) PTU(4bladed) PTU(6bladed)

0.19 T/3

DT: disk turbine PTU: upflow pitched-blade turbine

Working fluids and solid Liquid:

solution

water 0.1% CMC 0.2% CMC

density, viscosity, diffiisivity, kg/m^ kg/(ms) x 10 mVs x 10

1,000 8 1,004 19.2 1,004 37.4

1.0 0.94 0.9

Sc

800 1,966 3,996

Solid: benzoic acid


Vessel diameter, i

0.15 0.30 0.57

particle diameter m m X10®

550'-l,100 550-1,100 550-1,100

Sc

800 800-4,000

800

N/Ns

0.8-2.5 0.4-2.3

0.65-1.45

Results ksL=h72 X10"^ (N/Nsf''^ (5c)-<^

Notation D diffiisivity of solute in the liquid, mVsec ksL solid-liquid mass-transfer coefficient, m/sec N speed of agitation, 1/sec Ns critical suspension speed of the particles, 1/sec Sc Schmidt number, /pD, dimensionless T tank diameter, m fi viscosity of the hquid, kg/msec p density of the liquid, kg/w?

5.2 Liquid-liquid systems 319

5.2 Liquid-liquid systems

Feraandes, J. B. and Sharma, M. M., Chem. Eng. Sci., 22,1267 (1967)

Effective Interfacial Area in Agitated Liquid-Liquid Contactors


Type: flat-bottomed Diameter, height, and volume of liquid contained:

Vessel

Diameter (cm) Height (cm) Height of liquid (cm) Volume of liquid (0

T-10

10.2 13.0 13.0 0.8

T-15

14.7 14.0 14.0 2.5

T-17

16.5 25.0 25.0 2.8

T-30

29.3 30.0 30.0 20.0

T-40

40.0 45.0 45.0 50.0

T~56

56.0 65.0 65.0

150.0

T-86

86.0 120.0 120.0 500.0

Impeller

(a) B^IPB 1^ - 0=0250 ° b«a20D

c» 0-700

(g)

(b) n\n ja fl»0-25D

(0

(d)

o\

a« 0-250

(e)

Type of agitators used: (a) six-bladed straight tiirbine;.(b) four-bladed straight paddle; (c) four-bladed 45*" inclined paddle; (d) four-bladed cutved paddle; (e) six-bladed straight paddle; (f) six-bladed curved paddle; (g) three-bladed propeller.


(i) Six-bladed turbine impellers T-10:Z)/r=0.33;0.43 T-15:D/T=0M;0A T-17:Z)/r=0^; 0.35; 0.55 T-30: P/r=0.19; 0.33; 0.37; 0.4; 0.47; 0.62 T-40:Z)/r=0.33 T-56:/)/r=0.33 T-86:Z>/r=0.33

(ii) (a) Four-bladed straight paddle impellers T-10: D/r=0.33; 0.4 T-17:2)/r=0.32;0.36 T-30:Z)/r=0.34 T-A0:D/T=0.34 T-56:Z)/r=0.32 T-86:Z)/r=0.33

(b) Four-bladed 45° inclined paddle impellers T-30:Z)/r=0.33

(c) Four-bladed curbed paddle impellers T-30:/)/r=0.33

(iii) (a) Six-bladed straight paddle impellers T-30:Z)/r=0.33

Qy) Six-bladed curbed paddle impellers T-30:Z)/r=0.33

(iv) Three-bladed propeller impellers T-17:/)/r=0.42 T-30:Z)/r=0.33 T-40:Z)/r=0.34 T-56:Z)/r=0.33 T-86:Z>/r=0.33

Working fluids solids and their physical properties Continuous phase: see table Dispersed phase: see table

Run No.

1 2 3 4 5

6

7

8 9

10

System

Dispersed phase

«-hexyl formate «-butyl trichloroacetate

2-ethyl hexyl formate

Isobomyl formate 2MNaOH

4MNaOH

6MNaOH

«-hexyl formate n-hexyl formate n-hexy] formate

Continuous phase

2MNaOH 2MNaOH

2MNaOH

2MNaOH 2-ethyl hexyl

2-ethyl hexyl

2-ethyl hexyl formate

2MNaOH 4MNaOH 6MNaOH

Density

Dispersed phase

(g/cm^)

0.851 1.254 0.872

1.00 1.082

1.160

1.215

0.851 0.851 0.851

Continuous phase

(g/cm^)

1.082 1.082

1.082

1.082 0.872

0.872

0.872

1.082 1.160 1.215

Viscosity

Dispersed phase

(cP)

1.49 0.96

1.14

8.30 1.307

2.267

3.37

1.49 1.49 1.49

Continuous phase

lie (cP)

1.307 1.307 1.307

1.307 1.14

1.14

1.14

1.307 2.267 3.37

Interfacial Tension

a (dyn/cm)

10.0

7.5 1.5 8.5 1.5

2.0

2.5

---

Results For turbine agitator with a vessel diameter of up to 40 cm and for paddle and propeller agitators

for all sizes of the tanks

aocnDT'^'<l>

For a turbine agitator in vessels above 40 cm diameter

floe WZ)0

Notation a specific interfacial area, anVcm^ D diameter of the impeller, cm n number of revolutions of agitator per minute, 1/min T tank diameter, cm <l> volume fraction of dispersed phase


Eckert, R. E., McLaughlin, C. M. and Rushton, J. K.AIChE Journal, 31,1811 (1985) Liquid-Liquid Interfacial Areas Formed by Turbine Impellers in Baffled^ Cylindrical Mixing Tanks


System



Impeller Type Diameter (P/T) Nmnber of impellers Nmnber of blades Off-bottom clearance (m)

(1)

flat-bottomed 14.2

4 1.42

A 1/3 1 6

H/3

(2)

flat-bottomed 29.5

4 2.95

A 5/12

1 6

H/3

(3)

flat-bottomed 43.9

4 4.39

A 1/2 1 6

H/3

A: a standard six-blade turbine

Working fluids and their physical properties Design I

Continuous phase: water Dispersed phase: organic Uquids (see Table 1)

Design II Continuous phase: water and with addition of various amounts of com syrup Dispersed phase: organic hquids (see Table 2)

Table 1

Liquid

ii-Octanol Oleic acid Nitrobenzene Xylene Kerosene n-Heptane Paraffin oil

cr dynes/cm (10-

201:*

8.5 15.6 25.66 37.77

— — —

^N/cm)

25t:**

8.6 14.3 24.4 37.4 39.0 41.6 52.5

20t:

8.95 —

1.98 0.65

— 0.416

—

^ mPa •s

251:

7.13 28.7

1.86 0.602 1.32 0.445

129.0

Pd g/cm^

20t:

0.827 0.854 1.205 0.861

— 0.684

—

25X:

0.825 0.890 1.20 0.860 0.796 0.714 0.874

* 20*0 values from Lange, Handbook of Chemistry, *• 2510 is the approximate temperature at which data were determined and runs conducted.


Table 2

a at

Liquid |if=1.87 dynes/cm*

Kerosene Xylene M-Heptane

35.1 37.4 45.5

//f=4.0 dynes/cm

34.9 36.7 44.6

* Dynes/cm=10~ N/cm.

xperimental conditions

Variable Minimum Maximum Units

a 0 T D/T N G

^d

Pd ^c

Pc p P/V Nnc Nwe U

2.17 0.005 14.2 0.34 1.33 8.6 0.445 0.714 0.874 0.996 8,100 1.32 7,200 137 80

19.40 0.08 43.9 0.54 11.67 52.5 129.0 1.20 4.05 1.140 428,300 17.42 114,700 1,528 207

cmVcm^ (dimensionless) cm (dimensionless) 1/sec dynes/cm (10" N/cm) mPasec g/cw? mPasec g/cm^ gcm/s g/cm^sec (dimensionless) (dimensionless) cm/sec

>/°'pr-'-^(P/V)°°'w°'' Results

fl=O.O3640°-^(T''Prf-°-^/j where a =5.78-1.02 In (cr).

Notation a interfecial area, cmVcm? D diameter of impeller, cm H liquid height, cm N impeller speed, 1/sec P power exerted on fluids by impeller, g cm/sec (1,31 x 10" hp) P/V power per unit volume, g/cm^sec (0.499 hp/1,000 gal) T mixing tank diameter, cm u impeller tip speed di\aded by 100, cm/sec /z viscosity, mP^sec p density, g/cm^ a interfacial tension, dyne/cm (10"^ N/cm) 0 volume fraction of dispersed phase

Subscripts c continuous phase d dispersed phase


Skelland, A. H. R and Xien, Hu, Ind. Eng. Chem. Res., 29,415 (1990) Dispersed-Phase Mass Transfer in Agitated Liquid-Liquid Systems




Impeller Type: six-flat-blade turbine Diameter: (1) 0.0667 (2) 0.0762 (3) 0.1016 m Number of impellers: 1 Number of blades on impeller: 6

Working fluids Solvents: Continuous phase: deionized water

Dispersed phase: diisobutyl ketone, two mixtures of chlorobenzene, and water-mineral oil (60% and 70% by volume oil)

Solutes: Succinic acid and acetic acid

Physical and transport properties at 24°C

1.

2.

3.

system

DBK-succinic acid-water

40% chlorobenzene, 60% mineral oil-acetic acid-water

30% chlorobenzene, 70% mineral oil-acetic acid-water

N/m

0.02030

0.02749

0.02581

kg/m^

997.3

997.3

997.3

kg/m^

810.0

945.0

919.1

Ns/m^

0.00091

0.00091

0.00091

Ns/m^

0.00103

0.0047

0.0088

s/m^

1.377

0.4063

0.2845

m

6.289

45.000

35.000

Experimental conditions Temperature: 24±0.2*'C Volume fraction of dispersed phase: 0.0141—0.0909 Impeller speed: 3.167-12.00 rps

Results

fc ,-6x .-0.0204 r^2

[(D/tF.95-to)]

pM=(l>Pd+(l-<l>)pt

= 5.0 (10-*) 0 dfNpM

IHM

0 , .0.

flM


Notation dr impeller diameter, m D molecular diffusivity, mVsec kd dispersed phase individual mass-transfer coefficient, sec m equilibrium distribution ratio of component A, continuous phase/dispersed phase tp time at which the mass-transfer process is finished, sec tp, 95 time at which 95% of the possible mass transfer has occurred, sec T vessel diameter, m // viscosity, Nsec/m^ p, Ap density and density difference between two phases, respectively, kg/w? G interfacial tension, N/m 0 volume fraction of dispersed phase



Skelland, A. H. R and Moeti, L. T, Ind. Eng. Chem. Res., 29,2258 (1990) Mechanism of Continuous-Phase Mass Transfer in Agitated Liquid-Liquid Systems



Baffle Number: 4 Length: 0.2300 m Width: 0.0190 m Thickness: 0.0031 m

Impeller Type: six-flat-blade turbine Diameter: 0.1000 m Number of impellers: 1 Number of blades on impeller: 6

Working fluids and their physical properties Solvents: Continuous phase: deionized water

Dispersed phase: chlorobenzene, o-xylene, and benzaldehyde Solutes: nonanoic acid, heptanoic acid, and benzoic acid

Dynamic viscosities of liquids

temp, 'C

5 12 19 26 33 40 47 54 61 70

chlorobenzene

0.00095 0.00092 0.00087 0.00073 0.00072 0.00066 0.00063 0.00059 0.00056 0.00048

dynamic viscosity, Ns/m^

o-xylene

0.00094 0.00085 0.00073 0.00071 0.00059 0.00053 0.00050 0.00047 0.00042 0.00039

benzaldehyde

0.00214 0.00185 0.00161 0.00142 0.00131 0.00119 0.00107 0.00098 0.00090 0.00081

water

0.00152 0.00124 0.00103 0.00087 0.00075 0.00065 0.00058 0.00051 0.00046 0.00040


Interfacial tensions of liquids with water

interfacial tension, N/m

temp, °C

5 12 19 26 33 40 47 54 61 70

chlorobenzene

0.0345 0.0343 0.0340 0.0338 0.0334 0.0325 0.0315 0.0289 0.0274 0.0268

o-xylene

0.0348 0.0342 0.0339 0.0335 0.0331 0.0318 0.0306 0.0278 0.0263 0.0259

benzaldehyde

0.0164 0.0160 0.0159 0.0152 0.0148 0.0142 0.0137 0.0128 0.0116 0.0108

Densities of liquids

densities, kg/w?

temp, T

5 12 19 26 33 40 47 54 61 70

chlorobenzene

1,091 1,091 1,088 1,083 1,083 1,082 1,082 1,079 1,078 1,077

(?-xylene

858 858 857 856 796 786 786 778 778 778

benzaldehyde

1,049 1,049 1,049 1,026 1,026 1,025 1,025 1,023 1,021 1,021

water

1,000 1,000

998 998 995 992 990 986 983 978

Di^sivities of solutes in water

WDr, mVs

temp, C

5 12 19 26 33 40 47 54 61 70

nonanoic acid

4.20 4.80 5.80 6.80 8.00 9.40

11.00 12.40 14.00 16.20

heptanoic acid

5.20 5.80 7.10 8.10 9.50

11.10 12.80 14.30 16.20 18.50

benzoic acid

8.30 9.40

11.70 13.60 16.10 18.80 22.10 24.90 28.30 32.70

Results

M . = 1.237 X10^ f-ii-1 i^!^


Notation di impeller diameter, m dp particle or drop diameter, m Dr molecular diffiisivity of solute in the continuous phase, mVsec g acceleration due to gravity, m/sec^ kc individual mass-transfer coefficient for the continuous phase, m/sec N impeller speed, 1/sec T vessel diameter, m /x viscosity, Nsec/m^ p density, kg/w? a interfacial tension, N/m ^ volume fraction of dispersed phase, dimensionless


328 Chapter 5. Mass translsr

Hiraoka, S., Tada, Y., Suzuki, H., Mori, H., Aragaki, T. and Yamada, I.,/. Chem. Eng. Japan, 23,468 (1990) Correlation of Mass Transfer Volumetric Coefficient with Power Input in Stirred Liquid-Liquid Dispersions

Experimental apparatus Vessel Type: (l)-(3) flat-bottomed Diameter: (1) 10 (2) 14 (3) 17 cm

Baffle Number: 4

Impeller Experiment I Experiment II

Vessel Type flat-bottomed Diameter (cm) 10,14,17

Impeller Type blade paddle Diameter (cm) 5.0 7.0 8.5 Width (cm) 1.0 1.4 1.7 Number of impellers 1 Number of blades on impeller 6

flat-bottomed 14,17

blade paddle 7.0 7.0 1.4 0.91,1.75,2.33,3.5 1 1

2-8 6


Experiment I Experiment II

Continuous phase Dispersed phase

NaOH aq. solution Mixture of n-amyl acetate and toluene Mixture of «-hexyl acetate and toluene (0,10,30,50 vol% of toluene)

NaOH aq. solution «-hexyl acetate

Physical properties and reaction rate constant of esters at 30°C

axl03(N/m)

Z)>iXlOi° Z)A° fc 0 Ester (mVs) (mol/^) (^/mols) (pure)

n-amyl acetate 8.75 0.0135 0.113 15.31 w-hexyl acetate 8.13 0.0039 0.097 14.77

10 30

15.98 18.49 15.69 18.30

50 (vol% toluene)

21.69 21.59

Experimental conditions Stirrer speed: 150'-550 rpm Temperattire: 30°C 0o: 0.0018-0.0081 0/0o: 1-0.0015


Results

d,= 0.261 (CT'"/p<"/Vr)

.=[X4/Irfi \ i / i ^

J Notation

^ impeller width, m d impeller diameter, m dp droplet diameter, m Sp characteristic droplet diameter, m D vessel diameter, m DA diffusivity, mVsec H liquid depth, m ki reaction rate constant, ^/molsec kia mass transfer volumetric coefficient, 1/sec P power input, W Pv power input per unit volume, P/{nD ^HIA), W/m^ Pvi power input per unit volume swept out by impeller, P/(jcd b/4\ W/m^ Sc Schmidt number, v/D>i, dimensionless V kinematic viscosity, mVsec p density, kg/m^ o" interfacial tension, N/m 0 volume fraction of droplet

Subscript 0 initial value


Hiraoka, S., Kamei, N., Kato, Y, Tada, Y, Asai, K., Hibino, S. and Yamaguchi, T, /. Chem. Eng. Japan, 26,227 (1993) Mass Transfer Volumetric Coefficient and Droplet Diameter in Liquid-Liquid Dispersions Stirred with a Paddle Impeller with Wire Gauze

Experimental apparatus Vessel Type: (1) (2) flat-bottomed Diameter: (1) 14 (2) 17 cm with wire gauze

Baffle Number: 4

Impeller

Type I II III wire-gauze paddle paddle wire-gauze paddle

Number of impellers 1 1 1 Number of blades on impeller 6 6 6

Mesh size of gauze: 5 and 10

Typel

Wire-gauze impellers (unit: mm)

Working fluids Continuous phase: aqueous solution of NaOH Dispersed phase: n-hexyl acetate

Residts

*,« = 0.45 « ^ M l S c -

and

where

dp=d3z= 0.261 (CT* / p'^m*)

I\r==P/(aD^H/4)

I\n=Pli.nd'blA)

5.2 Liquid-liquid systems 3 3 X

Notation b impeller width, m d impeller diameter, m dsz Sauter mean diameter, m dp droplet diameter, m Jp characteristic droplet diameter, m D vessel diameter, m DA diffiisivity, mVsec H hquid depth, m kia mass transfer volumetric coefficient, 1/sec P power input, W Pv power input per unit volume, P/(KD^H/4), W/m^ Pvi power input per unit volume swept out by impeller, P/iTud^b/i), W/m^ Sc Schmidt number, v/Z)>t, dimensionless V kinematic viscosity, mVsec p density, kg/w? a interfacial tension, N/m 0 volume fraction of droplet


5.3 Gas-liquid systems

Calderbank, R H., T¥ans. Instn. ofChem. Eng., 36,443 (1958) Physical Rate Processes in Industrial Fermentation Part I: The Interfacial Area in Gas-Liquid Contacting with Mechanical Agitation

Experimental apparatus Vessel Type: (1) (2) flat-bottomed Diameter: (1)20 (2) 7 V4 in

Liquid contained Height:(l)20(2)7V4in Volume of liquid in vessel: (1) 100 (2) 5 ^

Baffle Number: (1) (2) 4 Width: (1) (2)7/10

Impeller Type: six-bladed turbine Diameter: (1) (2) 1/3 T Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): (1) 1.67 in Width of impeller blade (parallel to shaft): (2) 1.33 in Off-bottom clearance (1) 6.67 in

Sparger Number of holes: (1) many (2) one Hole diameter: (1) 1/8 in (2) 1/8 in Location (1) (2) the center of the tank bottom

Working fluids and their physical properties Liquid: ten different liquids; water, ethyl alcohol, methyl alcohol, isopropyl alcohol,

»-butyl alcohol, ethylene glycol, carbon tetrachloride, ethyl acetate, nitrobenzene and toluene

a = 73.5-21.7 dynes/cm Pc = 0.79-1.6 gm/cc ^ = 0.5—28.0 centipoise


Re > 10*

7, = 0.01-0.06 ft./sec

P/t; = 0.01-0.20 hp/ft

Temperature = 15 ± 0.1*»C

5.3 Gas-liquid s y s t e m s 333

Results For

N 0.3

/?g«^|i5^ < 20,000

flo = 1.44 0.4 ^ 0 ^

a' .as {VslVif'

For \03

/ ?e« | i5^ > 20,000

log„2:3£ = i . 9 5 x l O - i ? . - f M f

Notation a gas-liquid interfacial area per unit volume of dispersion, 1/cm OQ gas-liquid interfacial area per unit volume of dispersion for low impeller

Reynolds numbers , 1/cm D gas bubble diameter, cm Di impeller diameter, cm N impeller speed, 1/min P power dissipated by impeller, in aerated liquid or liquid-liquid dispersion, hp Re impeller Reynolds number , DfNpdlicy dimensionless T tank diameter, in V, superficial gas velocity, f t / sec 7/ tenninal gas-bubble velocity in free r ise, f t / sec V volume of liquid, ft^ pc continuous phase density, g / cc a interfacial tension, dynes / cm iXc continuous phase viscosity, cp


Westeiterp, K. R., van Dierendonck, L. L. and de Kraa, J. A., Chem. Eng. Set., 18,157(1963) Interfacial Areas in Agitated Gas-Liquid Contactors

Experimental apparatus Vessel Type: (1) flat-bottomed (b) dish-bottomec

Vessel

Diameter (m) Height (m) Height of impeller (m) Liquid height (m) Volume of liquid (0

Impeller

T14

0.140 0.40 0.07 0.140 2.2

T15

0.152 0.35 0.075 0.152 2.7

T19

0.191 0.40 0.095 0.191 5.5

T60

0.60 1.10 0.030 0.60 170

T90

0.90 1.10 0.45 0.90 570

Turbine impellers in T14:Z>/r = 0.52; 0.68 T15:Z)/r = 0.47; 0.62 T19: D/T = 0.2; 0.3; 0.4; 0.5; 0.6; 0.7 T60: D/T = 0.2; 0.3; 0.4; 0.6; 0.7 T90: D/T = 0A7

Four-bladed paddle impellers in T15:Z)/r = 0.57 T19: D/T = 0.3; 0.4; 0.5; 0.6; 0.7 T60: D/T = 0.2; 0.3; 0.6

Two-bladed paddle impellers in T19:Z)/r = 0.5;0.7

Propellor impellers in T19:Z)/r = 0.4;0.6;0.7

~r C

JL

C=a25D

B: Four-bladed paddle impeller C: Two-bladed paddle impeller

Sparger Type: a ring with small holes

a^0.25D i b^0.20D f A=a70/)

A: Turbine impeller

- C •

C=0.2SD

D: Propeller impeller

5.3 Gas-liquid systems 335

Working fluids Liquid: NaaSOs solution Gas: air

Experimental conditions: Temperature: 30 ± r C Impeller speed: 1.67-601/sec Superficial gas velocity (based on empty cross-section of vessel) 10~ < t;, < 35 x 10" m/sec

Results

3.8^Z)<42cm

HS<(^leHe = (7.5 ± 1.2) x 10" (w - no)D<(pTM

Notation c concentration in liquid phase , kmol/m^ D d iameter of t he impeller, m 0 diffusion coefficient in t h e liquid phase , mVsec

H height of Uquid above tank bottom, m He pi/RTcif distribution coefficient (i: location in liquid phase at boundary between gas and

hquid) k first-order react ion velocity constant, 1/sec n number of revolut ions of agitator per second, 1/sec fiQ minimum n u m b e r of revolutions of agitator per second, 1/sec p partial pressure, N/m^ R gas constant, J/kmol K 5 specific inter facial area, mVm^ T tank diameter , m T t empera ture , °C or K Vs linear gas velocity based on empty cross-section of vessel, m / s e c e volume fraction of liquid in t he dispersion p density, kg/m^ a surface tension, kg/sec^

336 Chaptsr 5. Mass transfsr

Lee, J. C. and Meyrick, D. L., Trans. Instn. Chem. Engrs., 48, T37 (1970) Gas-Liquid Interfacial Areas in Salt Solutions in an Agitated Tank



Baffle Number: 4 Width: 1.2 in

Impeller Type: six-bladed disk turbine Diameter: 4 in Disk radius: 1V2 in Number of impeDers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 15/16 in Width of impeller blade (parallel to shaft): 3/4 in

Sparger Diameter of orifice: 1/16 in Location of orifice: at the center of the vessel base

Working fluids and their physical properties Liquid: aqueous solution of sodium chloride (concentration = 0.05—0.50 g mol/i)

aqueous solution of sodium sulphate (concentration = 0.005—0.25 g mol/i) Gas: air

Experimental conditions Temperature: 18 *0 Impeller speed: 300—600 rpm


Results

337

60

< 30h

Spe^d (rev/min) NaCI Na2S04 300 / A 400 0 • 500 V T 600 D •

"-Inttrfacial areas at suptrficlal gas veiocity 0-012 ft/sec

600

0-05 I ' ' ' i • ' 'I

&70 020 0-30 0 ^ &50 CONCENTRATION OF No CI (g mol«/J)

> I I i

005 0075 0-10 0-15 020 025 CONCENTRATION 0 ? NSjSO^ (g mole / l )

6-0

50

^^-0

< 30

5 20

NaCI Spttd (rev/min) 300 400 500 600 D •

—Interfacial areas at superficial gas velocity 0-02 ft/sec

NajSO^ •

T

020 030 0^0 060 CONCENTRATION OF No CI (g mole/ I )

JL JL a06 0075 010 0-75

CONCENTRATION Or NCj SO^ (g mole /O 020 025


60L

50 h

Speed (rev/min) 300 400 500 600

NaCI A O V D

Na.SO.

—Interfocial ortas at suptrftcial gas velocity 0-03 ft/stc

40

20

. MO .1000 J I , 1 » ,

aiO &20 &30 0 ^ 050 CONCENTRATION 0^ Na CI (g mo le /0

2000 L - .

3000 • I

J L - L 005 {K)75 aiO

CONCENTRATION OF NOjSO^ (g mole/I) 0-15 020 025


Mehta, V D. and Sharma, M. M., Chem. Eng. Sci., 26,461 (1971) Mass Transfer in Mechanically Agitated Gas-Liquid Contactors

Experimental apparatus Vessel and impeller geometries Vessel type: flat-bottomed Detail of the vessels and the agitators used in this investigation

Height of the agitator

Tank from the Tank capacity Agitator base of Speed of Liquid

diameter, litres, for diameter, D/T the vessel, B/T agitator height, H/T No. r(cm) H/T=l Diem) range J9(cm) range (rev/min) ^(cm) range

1

2

3

4

12.5

20.0

40.0

70.0

1.50

6.30

50.0

280

4.0, 5.8

5.8, 7.0, 9.0,

10.0, 10.4*

17.0 18.0**

28.0 33.0

0.33 to

0.465

0.29 to

0.52

0.425 and

0.45

0.40 0.47

4.25

5.6, 6.4, 8.0 &

10.0

10.0 14.0 & 16.3

25.0

0.34

0.28 to

0.50

0.25 to

0.405

0.36

2 8 0 -1,900

750 -1,900

4 4 0 -1,140

2 5 0 -490

12.5

14.0 20.0 30.0

30.0 to

50.0

70.0

1.0

0.70 to

1.50

0.75 to

1.25

1.0

*Agitator was of the following types: (i) 5-bladed axial flow turbine; (ii) 6-curved bladed turbine; (iii) 4-curved bladed turbine and (iv) 6-straight bladed disk turbine

**Agitator was of the following types: ( i ) 6-straight-bladed disk tutbine; (ii) 6-curved-bladed turbine; (iii) 6-curved-bladed turbine; (iii) 6-straight-blade(d pumping turbine; (iv) 6-bladed axial flow turbine.

Baffle Number: 4 Width: 0.1 T Length: T


Working fluids, their physical properties and experimental conditions

H/T-\, B/T^O.M; Mode of gas dispersion: sparged contacting

No.

1

2

3

4

5 6

7

8

9

Solute gas

O2

O2

O2

O2

CO2 CO2

CO2

O2

O2

Absorbent

5.0M-HC1+ 0.92M-CuCl 2.30M-HC1+ 0.322 M-CuCl 0.92Af-HCl+ 3.0M-NaCl+ 0.27M-CuCI 2 .5M-Ha+ 3.2M-CUCI2+ 0.675 Af-CuCl 2.47M-NaOH 1.42JI/.NaOH+ 0.5M-Na2SO4 0.62M-NaOH+ 1.03f-Na2SO4 0.61M-NaOH+ 1.0JVf-Na2SO4+ 0.05J»f-Na2S2O4 0.20M-NaOH+ 1.0M-Na2SO4+ 0.198 M-Na2S204

Kineties of the reaction order with respect to

Solute

1

1

1

1

1 1

1

0

0

Reactant

2

2

2

2

1 1

1

1

2

V. 4.0

4.0

4.0

4.0

7.65 7.25

7.25

7.25

6.85

T

20

20

20

20

12.5 12.5

12.5

12.5

12.5

D/T

0.35

0.35

0.35

0.35

0.465 0.465

0.465

0.465

0.465

Viscosity of the

solution (cP)

1.08

1.06

1.12

2.51

1.51 1.37

1.44

1.37

1.32

Ionic strength

5.92

2.62

4.19

12.74

2.80 3.42

3.62

3.75

3.80

Speed of the

agitator (rev/min)

1,440

1,440

1,440

1,440

1,500 1,440

1,440

1,440

1,480

a (cm'^)

6.90

6.30

6.70

11.70

4.68 3.48

3.25

3.67

3.90

Results aocND/yff D/T = 0.4'-0.5

Notation a effective interfacial area based on unit clear liquid volume, cmVcm^ B height of the agitator from the base of the vessel, cm D diameter of the agitator, cm H height of clear liquid, cm N speed of the agitator, 1/min T diameter of vessel, cm Vg superficial gas velocity, cm/sec


Prasher, B. D. and Wills, G. B., Ind. Eng. Chem. Process Des. Dev., 12,351 (1973) Mass Transfer in an Agitated Vessel

Experimental apparatus Vessel Type: flat-bottomed Diameter: 11.5 in

Liquid contained Height: 11.5 in


Impeller Type: a flat six-bladed radial flow impeller Diameter: T/S Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): r /4 Width of impeller blade (parallel to shaft): T/b Off-bottom clearance 7/3

Sparger Orifice diameter: 1/8 in Location: at the bottom of the tank

Working fluids and their physical properties Liquid: distilled water and 0.085 M strength caustic solution Gas: CO2

Experimental conditions Agitation speed: 150—350 rpm Gas superficial velocity: 0.29—1.2 cm/sec

Results ki = 0,b92DA^'\£/vf'^

Notation DA molecular diffiisivity of solute gas, cmVsec ki liquid side mass transfer coefficient in non-reacting case, cm/sec T tank diameter, cm e energy of dissipation by turbulence per unit mass, cmVsec V kinematic viscosity, cmVsec


Robinson, C. W. and Wilke, C. R., Biotec. andBioeng., 15, 755 (1973) Oxygen Absorption in Stirred Tanks: A Correlation for Ionic Strength Effects

Experimental apparatus Vessel Tjrpe: flat-bottomed Diameter: 6 in Height: 1ft

Liquid contained Volume of liquid in vessel: 2.5 £


Impeller Type: six-blade turbine impeller Diameter: 2 in Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 2 in

Sparger Orifice diameter: 1/8 in Location: directly under the impeller axial center line

Vt orking fluids and their physical properties Liquid:

Physicochemical properties of experimental solutions

Ionic strength,

Fr. g-ion/liter

Density, PL (30''C),

g/cm^

Interfadal Viscosity, tension.

|i">C CT-c cP dynes/cm pH

H (atm-cmV

g-mol) xlO-'

|x lO^ eq. (2)

Distilled Water 0.00

0.22 3/KCl 0.220

0.135 M KCl+KOH - K2CO3 0.221" Medium A-l"" 0.136 0.1253f Na2S04 -0.004MCuSO4 0.391

0.250 MNa2S04 - 0.004 M CUSO4 0.766 0.375J»fNa2SO4 -0.004 JlfCuS04 1.141 0.500 MNa2S04 - 0.004 M CUSO4 1.516

0.500 Jif NazSOa - 0.004 M CUSO4 1.516 0.11 MNa2S04+KOH - K2CO3 0.418' 0.10 MKCl 0.100

0.9957 0.894925 71.925 0.80130

1.012 O.8OI30 72.730

1.003 1.014 1.032 1.045 1.067 1.059

1.003

0.801230

0.84130

0.99423O

1.0982S

I.O3I30

72.430 71.730 72.230 72.930

72.630

6.45

7.93

5.45

5.50

8.94

7.35

8.345

8.796 8.760 8.570 9.300

10.38 11.68 12.88 12.88* 9.646 8.547

3.51

3.49 (3.49) 3.41 3.46 3.45

3.08 2.96

(3.46)

a Average of all runs. b Composition: 1.6 g K2HPO4,0.48 g MgS04-7H20; 4.6 g NH4CI, 0.02 g NaCl; 0.03 g Hgh per liter distiUed water. c Assumed equal to value in 0.500 M Na2S04 - 0.004 M CUSOA d Champagnet et al.: French Patent 1,387,842 (1963).

Gas: O2,02+N2, or air


Experimental conditions Impeller rotational speed: 400—2,200 rpm Power input: 31.6-17,950 w/m^ Gas rate: 0.00375-0.0150 ft/sec Temperature: 30°C

Results

e = X{PG/VL)\vsr^ (1)

^^{pLf^{DLf"/G''\nLf" (2)

A = 18.9-28.7 rV(0.276 + r°) (3)

r*> = rr, o<rr<o.40 n = 0.40, rr>0.40 !0*

E )0'

Generalized correlation for sparing soluble gas stirred-tank overall volumetric mass transfer coefBcients.

M -T—I—I ( I n n r—r

o Woter a Medium A-1 A O.I25M N02 SO4 - 0.004 M Cu SO4 V 0.22M KCI • 0.50M N02 SO3 -

0.004M Cu SQi T O.I35M KCI + KOH-KgCOj AO.IIM N02S04-^

T—I 1 1 I If

10' 102 10* [f^/VifCft-lbj/mln-ft*)"

10*

Notation Ci DL

H kia

k'la PG Vs

VL

Zi TT

r° e

A

PL G

the concentration of an ionic species, g-mole/cm^ liquid-phase diffiisivity, cmVsec Henry's law coefficient, atm cmVg-mole overall mass transfer coefficient based on liquid-phase concentration difference driving force for absorption without reaction, 1/sec effective overall volumetric mass transfer coefficient for absorption with reaction, 1/sec impeller power input to gassed hquid, ft-lbf/min gas superficial velocity based on empty tank cross-sectional area, ft/sec volume of gas-free liquid, cm^ the charge on an ionic species ionic strength defined by V2 2Z,^C„ g-mole/cm^ ionic strength, g-mole/cm^ /fifl or fefl/0,1/sec absorption fector for mass transfer with chemical reaction kLa/kLa{=2A), dimensionless proportionality constant defined by Eqn (3), g^^ cm®* ^ sec°^ liquid viscosity, g/cm sec physical property factor defined by Eqn (2), g"°*° cm°-^^ sec ** liquid density, g/cm^ inteifacial tension, dyne/cm


Bossier, J. A., Farritor, R. E., Hughmark, G. A. and Kao, J. T. E, AIChE Journal, 19,1065 (1973) Gas-Liquid Interfacial Area Determination for a Turbine Agitated Reactor

Experimental apparatus Vessel Type: flat-bottomed Diameter: 4 in



Impeller Type: six flat blade turbine Diameter: 2 in Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 4/3 in

Working fluids, their physical properties, experimental conditions and results

Table 1. Unbroken interface without reaction

System Temperature, °C rev./min. ki.cm/s

Tetradecane + alkyl, N2 Tetradecane -1- alkyl, N2 Tetradecane -1- alkyl, N2 Tetradecane, O2 Nujol,N2 NuioI,N2

50 50 50 23 50 10

100 200 290 100 300 500

0.0085 0.017 0.0235 0.0125 0.0097 0.0043

Table 2. Cio Aluminum alkyl oxidation rate

System Temperature, **C k, liters/g mol-s

^-xylene 23 1.4x10* Tetradecane 50 5.5 x 10* Tetradecane 23 1.9 x 10* Tetradecane 10 6,400 Nujol 23 3,890

5.3 Gas-iiquid systems 345

Tables. Interfacialarea

System

^-xylene-02 Tetradecane-02 Nujol-Oz AqNaOH-C02

Liquid phase

^-xylene Nujol 17VNa2S04 Water

rev./min.

850 850 850 900

Table 4. Oxygen

kia, 1/s

0.85 0.0115 0.173 0.145

JDoxlO^ cmVs

4.8 3.3 1.2 1.8

I absorption data

kit cm/s

0.094 0.0077 0.075

Viscosity, cP

1.2 3.6

71 1.05

a cmVcm^

9.0 10.8 2.33 2.3

vID

313 69,000

580

Notation a interfacial area per unit volume of liquid D molecular diffiisivity Do diffiisivity of oxygen k kinetic rate constant ki liquid phase mass transfer coefficient V kinematic viscosity


Robinson, C. W. and Wilke, C. R.,AIChE Journal, 20,285 (1974) Simultaneous Measurement of Interfacial Area and Mass Transfer Coefficients for a Well-Mixed Gas Dispersion in Aqueous Electroljiie Solutions

Experimental apparatus Vessel Type: flat-bottomed Diameter: 6 in Height: 1ft

Liquid contained Volume of liquid in vessel: 2.5 i


Impeller Type: six-blade turbine impeller Diameter: 2 in Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 2 in

Sparger Orifice diameter: 1/8 in Location: directly under the impeller axial center line

Working fluids Liquid: KOH-K2CO3 solution and Na2S04+KOH-K2CO3 solution Gas:N2+C02

Experimental conditions Temperature 30 ± 0.3°C

Results

Interfacial Area, Liquid-Phase Oxygen Mass Transfer, Gas Holdup, and Average Bubble Diameter in KOH-KaCOs

N rev/s

13.33 15.00 16.67 18.33 20.00 21.67 23.33 26.67 28.33 33.33

P/V W/m'

780 1,030 1.355 1,920 2,480 3,260 4,240 6,740 7,930

12,630

OH-mol/m^ xlO-3

0.0827 0.0862 0.0758 0.0828 0.0798 0.0650 0.0830 0.0189 0.0136 0.0211

Concentration COf FT

mol/m^ mol/m^ X10-^ X 10-^

0.0057 0.0063 0.0071 0.0036 0.0061 0.0091 0.0042 0.0241 0.0267 0.0257

0.0998 0.1051 0.0971 0.0936 0.0981 0.0923 0.0956 0.0912 0.0937 0.0982

Avg. 0.0965

Exit gas CO2 y3.2

0.02230 0.00988 0.00586 0.00472 0.00399 0.00350 0.00250 0.00439 0.00478 0.00219

Specific area

118 310 523 607 834

1,050 1,650 1,900 1,680 3,210

m/s X 10

0.0443 0.0271 0.0180 0.0148 0.0200 0.0156 0.0105 0.0133 0.0150 0.0098

Gas holdup,

HG

0.0453 0.0573 0.0693 0.0800 0.0990 0.107 0.116 0.140 0.144 0.181

Bubble avg.

diam, db mxlO^

0.231 0.111 0.0796 0.0791 0.0690 0.0422 0.0422 0.0441 0.0514 0.0340


Concurrent Oxygen Desorption, Carbon Dioxide Absorption-With-Reaction: Comparison of Steady State and Unsteady State/Pseudo Steady State Methods with KOH-K2CO3

N rev/s

15.00 16.67 21.67 26.67

kua (s (a)

0.0717 0.0907 0.167 0.248

-') (b)

0.0820 0.0944 0.164 0.253

a (m~ (a)

314 475

1,160 1,810

') (b)

310 523

1,050 1,900

ku (m/s X10 ) (a) (b)

0.0228 0.0271 0.0191 0.0180 0.0144 0.0156 0.0137 0.0133

(a) Continuous flow steady state method. (b) Unsteady state O2 desorption, pseudo steady state CO2 absorption-with-reaction.

Interfacial Area, Liquid>Phase Oxygen Mass Transfer Coefficient, Gas Holdup and Average Bubble Diameter in Na2S04 + KOH-K2CO3 (avg. Fr = 0.418)

N rev/s

11.67 15.00 16.67 20.00 21.67 23.33 25.00 28.33 31.67 35.00

P/V W/m^

331 875

1,135 2,160 2,690 3,470 4,120 6,120 8,075

10,840

Specific area (a).

138 185 304 749 891

1,310 2,150 2,080 2,740 3,750

ku m/s X 10

0.0259 0.0483 0.0318 0.0212 0.0183 0.0164 0.0119 0.0126 0.0138 0.0101

Gas holdup HG

0.0240 0.0427 0.0534 0.0853 0.0906 0.104 0.112 0.128 0.147 0.171

Bubble avg. diam., (db) mxlO'

0.104 0.138 0.105 0.0684 0.0611 0.0476 0.0313 0.0369 0.0322 0.0274

Notation a C dt HG

ku kua

n N P V

z r

gas-liquid interfacial area per unit liquid volume, 1/m concentration of dissolved gas, mol/m^ gas bubble average diameter (Xnid?llLnid?), m or mm fractional gas holdup, volume of dispersed gas per volume of gas-liquid dispersion, dimensioniess liquid-phase mass transfer coefficient of oxygen in non-reactive system, m/sec overall volumetric mass transfer coefficient of oxygen based on liquid-phase concentration difference driving force for absorption without reaction, 1/sec integer impeller rotational speed, 1/sec agitation power input to gassed Uquid, W/m^ volume of gas-free liquid, m reaction stoichiometric coefficient, dimensioniess ionic strength, r=l /2 l^jZ^Cj, mol/^


Miller, D. K.AIChE Journal, 20,445 (1974) Scale-Up of Agitated Vessels Gas-Liquid Mass Transfer


System

Vessel Type Diameter Height Liquid height Volume (m )

BafQe Number Width Thickness Off-bottom clearance

Impeller Type

Diameter Number of impellers Number of blades on

impellers Blade width

(parallel to shaft) Thickness of blade Impeller-sparger

clearance Sparger

Type Diameter of ring Hole size Number of holes Hole spacing Orientation

(1)

dish-bottomed 0.1524 0.305 0.1460 0.00252

4 0.0127 0.001588 0.00952

0.1016 1 4

0.01905

0.000794 0.00952

ring 0.00889

0.001588 0.00318 40 10

0.00698 0.0279 down up

(2)

dish-bottomed 0.305 0.610 0.292 0.0252

4 0.0254 0.00318 0.01905

four-bladed flat paddle

0.001588 80

0.00696 up

0.203 1 4

0.0381

0.001588 0.01905

ring 0.1778 0.00318

20 0.0279

up

0.00635 10

0.0559 up

(3)

dish-bottomed 0.686 1.372 0.657 0.252

4 0.0572 0.00714 0.0429

0.457 1 4

0.0857

0.00357 0.0429

ring 0.406

0.00318 0.00635 50 25

0.0260 0.0516 up down

Unit: m

Working fluids Liquid: aqueous solution saturated with CO 2 Gas: air

Results For stripping of CO 2 from the aqueous solution with air (1) Mean bubble size

/)flv=4.15 (pjvrpf"

0°-' +0.0009

(l>Ug

{U,+Ugj Ut-^Ug )

5.3 Gas-liquM systems 349

(2) Interfacial area

\Peivrpr a = lM ,a6 Ut+Ug

(3) Mass transfer coefficient

^1.376 kl=6S3Dm

Notation a interfacial area per unit aerated volume, 1/m DBM mean bubble diameter, m ki mass transfer rate constant, m/sec ki reduced mass transfer rate constant Pe effective power input, W Ug actual superficial gas velocity, m/sec Ut bubble terminal velocity of rise, m/ sec V deal liquid volume, m^ /// liquid viscosity, Nsec /m^ PI liquid density, kg/w? G surface tension, N / m 0 fraction gas holdup


Perez, J. E and Sandall, 0. CAIChE Journal 20, 770 (1974) Gas Absorption by Non-Newtonian Fluids in Agitated Vessels




Impeller Type: six flat-blade disk turbine Diameter: 5.08 cm Number of impeUers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 1.27 cm Width of impeller blade (parallel to shaft): 1.02 cm Off-bottom clearance: 5.08 cm

Sparger Type: a tube Diameter: 4.0 nun ID Location: 3.18 cm below impeller

Working fluids and their physical properties Gas: CO2 Liquid: Carbopol solutions

Physical properties

Surface tension against carbon

dioxide Diffusion coef. Henry's constant (nmiHg cc/g-mole) @23°C @25°C X10"^

Liquid dynes/cm cmVsxlO^ 24X 30^C 35°C

Water 0.25% Carbopol 0.75% Carbopol 1.00% Carbopol

69.94 65.08 64.44 63.43

1.98 2.09 1.74 1.58

2.171 2.222 2.816 3.407

2.522 2.639 3.337 4.096

2.843 2.943 3.732 4.751


Rheological properties

Liquid 0.25% Carbopol

0.75% Carbopol

1.00% Carbopol

Temperature, X 24 30 35

24 30 35

24 30 35

Flow behavior index, n

0.916 0.916 0.916

0.773 0.773 0.773

0.594 0.594 0.594

Consistency index, /i:(g/cms2-«)

0.0428 0.0379 0.0355

0.507 0.483 0.469

5.29 4.83 4.12

Experimental conditions Impeller speed: 200'-500 rpm Superficial gas velocity: 0.162—0.466 m/sec

Results

^ ^ = 2 1 . 2 ^ ^ ^ ^ " pD) {a) U'

Notation a effective interfacial area per unit volume, 1/cm d impeller diameter, cm D d i^s ion coelffident, cmVsec kc mass transfer coefficient, cm/sec N impeller speed, 1/sec Ys superficial gas velocity through sparger tube, cm/sec ja average shear rate, 1/sec /x« effective viscosity, g /cmsec lig gas viscosity, g /cmsec p liquid density, g/cm^ a surface tension, dynes/cm T shear stress, djmes/cm^


Yagi, H. and Yoshida, E, Ind. Eng. Chem. ProcessDes. Dm, 14,488 (1975) Gas Absorption by Newtonian and Non-Newtonian Fluids in Sparged Agitated Vessels

Experimental apparatus Vessel Diameter: 25 cm



Impeller Type: standard six-blade turbine Diameter: 10 cm Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 10 cm

Sparger Type: a 5 nun single nozzle Location: 5 cm below the impeller

Working fluids and their physical properties Liquid see tables

Physical properties of Newtonian hquids (30°C, cgs units)

Glycerol-water

Millet-jelly-water

CMC

PANa

1

Wt%

0.4 1.0 1.33 2.0

0.01 0.05 0.1

P

1.009 1.054 1.134

1.036 1.080 1.211 1.285

Physical properties of

*»C

30 30 30 30

20 20 20

P

0.998 1.000 1.001 1.003

0.998 0.998 0.999

a

71.0 69.5 66.6

72.9 75.0 82.3 87.7

DLXW

2.28 1.49 0.53

1.9 1.3 0.39 0.13

/

0.009 0.015 0.051

0.013 0.021 0.133 0.702

non-Newtonian liquids (cgs units)

G

7L2 68.4 67.7 67.4

72.8 64.5 64.4

DLX 10^ K

2.3 2.28 2.28 2.28

2.0 2.0 1.9

0.117 1.21 3.87

13.2

0.129 1.79 5.20

n

0.95 0.82 0.74 0.66

0.78 0.53 0.42

A

0.0017 0.03 0.129 1.56

0.18 2.3 8.3

Gas: nitrogen


Experimental conditions Temperature: 30°C Impeller speed: 5—9 rps Superficial gas velocity: 0.2—8 cm/sec

Results For oxygen desorption with nitrogen from two Newtonian fluids

<vs

g mm:\ For oxygen desorption with nitrogen from non-Newtonian fluids

- = 0.060 kLod''

Dl

fNp] He J

1.5 / „ x0.19

g

^tefmlf)-—• r Notation

d impeller diameter, cm DL liquid phase diffusivity, cmVsec g gravitational constant, cm/sec^ kia volumetric liquid phase mass transfer coefficient, 1/sec K fluid consistency index, g/cmsec n fluid behavior index, dimensionless N rotational speed of impeller, 1/sec Vs superficial gas velocity, cm/sec A characteristic material time, sec jU liquid viscosity, g/cmsec p liquid density, g/cm^ G surface tension, g/sec^


Ranade, V R. and Ulbrecht, J. UAIChE Journal, 24,796 (1978) Influence of Polymer Additives on the Gas-Liquid Mass Transfer in Stirred Tanks

Experimental apparatus Vessel Diameter: 0.3 m



Impeller Type: standard six-blade turbine Diameter: (1) 0.08 (2) 0.1 (3) 0.14 m Number of impellers: 1 Number of blades on impeller: 6

Sparger Type: a single nozzle Internal diameter: 0.004 m Location: 0.05 m under the center of the turbine

Working fluids and their physical properties Liquid: a solution of sodium carbonate and bicarbonate Gas: CO 2 and air Additives: sodium carboxymethyl cellulose (CMC) and polyacrylamide Separan AP-30 (PAA)

Rheological properties of aqueous solutions of CMC and PAA

Concentration, ppm n KxlO^ b i4xlO^ CMC PAA - Ns^m-^ - Ns^m'

100

200

1,200

100 0.975 2.33 0.975 70 1.00 2.85

200 0.80 5.45 0.92 85 0.92 58.0

LOOO 055 L27 077 750

Properties of the CMC and PAA solutions in the carbonate buffer

Concentration, ppm Viscosity, ^ 10^ Density Surface tension CMC PAA Ns«m-2 kgm'^ Nm"

100 — 200 —

1,200 —

0

,— 100 — 200

— 1,000

0

Experimental conditions Gas flow rate: 20-- 85 ^/min

1.48 1.44 1.57 1.52 5.27 5.31 1.10

1,050 1,010 1,000 1,001 1,000 1,000 1,060

O0677 0.0680 O0673 0.0677 0.0676 0.0680 O0681

9.3 Oas-liquid systMiis 355

Results

Ni=Ar"

nf"

^ £ £ 1 ^ = 2 . 5 x 1 0 - h ^ i ^ U l (UIOOZ).)—

^i I / J U-'J Notation

a interfacial area per unit volume of dispersion, 1/m A material parameter of liquid, N(s ecf/w? b material parameter of liquid, dimensionless D tank diameter, m De modified Deborah number, NX, dimensionless DL molecular diffusion coefficient of gas in the Uquid, mVsec ki true liquid side mass transfer coefficient, m/sec K constant, dimensionless n material parameter of liquid, dimensionless N impeller speed, 1/sec N\ normal stress difference, N/m^ 5i2 shear stress N/m^ y shear rate, 1/sec A characteristic fluid time, sec /I viscosity, Nsec/m^ liw viscosity of water, Nsec/m^ p liquid density, g/cm^

356 Cha|it«r 5. Mass tninsffsr

Figueiredo, M. M. L and Calderbank, R H., Chem. Eng. Sci, 34,1333 (1979) The Scale-Up of Aerated Mixing Vessels for Specified Oxygen Dissolution Rates



Baffle Number: 4

Impeller Type: flat bladed turbine Diameter: 0.27 m Number of impellers: 1 Length of impeller blade (perpendicular to shaft): 0.06 m Width of impeller blade (parallel to shaft): 0.06 m

Sparger Type: open-ended tube Location: below the impeller


Experimental conditions Power consumption: 0.41 x 10^-4.8 x 10 w/m^ Impeller rotational speed: 4.16-8.331/sec Superficial gas velocity: 6.34,8.87, and 12.7 x 10" m/sec

Results Interfacial area 0^=593 (P/VL)'''^ (7,)°-^

Bubble size rf«H=3.5 x 10" m

Mass transfer product ife/:fl7 /7=1 x lO-HP)^'"^ (Vsf'^

Notation Od gas-liquid interfacial area, m^ dsm Sauter mean bubble diameter, m kia mass transfer product, 1/sec P impeller power dissipation, watt VL volume of hquid, m Vs superficial gas velocity, m/sec T tank diameter, m

5.3 Gas-Hquid systems 357

Meister, D., Post, T, Dunn, I. J. and Bourne, J. R., Chem. Eng. Set., 34,1367 (1979) Design and Characterization of a Multistage^ Mechanically Stirred Column Absorber

Experimental apparatus Vessel Type: flat-bottomed Diameter: 150 mm Height: 200 mm/stage Number of stages: 9

Baffle Number: 4 Width: 15 mm Height: 180 mm Clearance of baffle from wall: 5 mm

Impeller Type: six-bladed turbine Diameter: 60 mm Number of impellers: 1 or 2/stage Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 12 mm Width of impeller blade (parallel to shaft): 12 nmi Positions of impellers

Distance between bottom and the first impeller: 0.2 ft Distance between the first and the second impeller: 0.47 Hs

Worldng fluids Liquid: an aqueous solution of sulfite Gas: air

Experimental conditions ImpeUer speed: 6.7-20.0 1/sec Superficial gas velocity: 4.7—28.8 mm/sec

Results For two impellers

.0.707

For one impeller \ 0.801

^Lfl=104.9 r ' ^^'-^ {C" Notation

H, stage height, nrni Kia oxygen transfer coefficient based on total volume, 1/hr P total power consumption aerated, W P/V power consumption per unit volume, Wi Use superficial gas velocity, mm/sec


Van't Reit, K., Ind. Eng. Chem. Process Des. Dev., 18,357 (1979) Review of Measuring Methods and Results in Nonviscous Gas-Liquid Mass Transfer in Stirred Vessels

Use of existing date reported by (1) Calderbank, P. H., Trans, Instn. Chem, Eng„ 36,443 (1958). (2) Valentin, F. H. H., Preen, B. V., Chem. Ing Tech,, 34,194 (1962). (3) Van't Riet, K., Thesis, University of Technology, Delft, (1975). (4) Robinson, C. W., Wilke, C. R„AIChEJ„ 20,285 (1974). (5) Hassan, I. T. M., Robinson, C. W.,Biotechnol, Bioeng,, 19,661 (1977). (6) Smith, J. M., Van't Riet, K., Middleton, J. C, 2nd European Conference on Mixing, Cambridge,

England, Paper F4,1977. Results

For ion-free water

ifeiA = 2.6X10"'I-^j vf (1/sec)

2<F<2,600/

500 <P/K< 10,000 (W/m')

For water with ions

/j/:i4 = 2.0xlO"M~| vs" (1/sec)

2<F<4,400/

500 < P / 7 < 10.000 (W/m')

Notation A specific contact area, mVm ki mass transfer coefficient in the Uquid phase, m/sec P stirrer power consumption, W V fluid volume, m vs gas superficial velocity, m/sec

5.3 Gas-liquid s y s t e m s 359

Farritor, R. E. and Hughmark, G. A., Chem. Eng. Commun., 4,143 (1980) Interfacial Area and Mass Transfer with Gas-Liquid Systems in Turbine-Agitated Vessels

Experimental apparatus Vessel Type: flat-bottomed Diameter: 4 in


Impeller Type: six flat blade turbine Diameter: 2 in Number of impellers: 1 Number of blades on impeller: 6

Working fluids, experimental conditions and results (1) Interfacial area data

System

^-xylene + alkyl, O2 tetradecane + alkyl, O2 Nujol + alkyl, O2

N.rps

14.2 14.2 20

v„ cm/sec P/7, watts/m^ «, cm"

6.1 1,810 9.5 5.4 1,750 8.3 5.9 5,750 3.6

(2) Mass transfer data

System

^-xylene + alkyl, O2 tetradecane + alkyl, O2

kif cm/s

0.11 0.077

V, cmVs 0 X10 , cmVs

0.015 4.8 0.058 3.3

Notation a interfacial area pe r unit volume of liquid 0 diffusivity ki liquid phase mass transfer coefficient N impeller speed P power input to gassed liquid V liquid volume Vs superficial gas velocity V kinematic viscosity


Hughmark, G. A., Ind. Eng. Chem. Process Des. Dev., 19,638 (1980) Power Requirements and Interfacial Area in Gas-Liquid Turbine Agitated Systems

1. Power requirements

Reference

Vessel geometry Impeller

Vessel diameter to vessel (m) diameter ratio

Physical properties of liquid Gas rate

Bimbinet (1959) 0.305,0.457 0.333-0.50 max liquid viscosity=90 cP Michel and Miller (1962) 0.165,0.305 0.25-0.46

Pharamond, Houston, and Roques (1975)

0.29,0.48,1.0 0.333

density=0.87~0.6 g/mt viscosity=0.8~28 cP surface tension=25~72 dyn/cm viscosity=0.9~3.0 cP surface tension=55~72 dyn/cm

0.2—1.8 vol of gas per liquid volume/minute

(wm)

Pg/P = 0.10 iQINV)-^" iN^DVgDiV^'^)-^'^

2. Gas holdup

(1)

Vessel geometry

Vessel diameter Reference

Kawecki, Reith, van Heuven, and Beck (1967)

Brown and Craddock (1969) Rushton and Bimbinet (1968) Parritor and Hughmark (1980)

(m)

0.191 0.22 0.304 0.10

ImpeUer to vessel

diameter ratio

0.40 0.345-0.573

0.54 0.50

Liquid

water water water

^-xylene and tetradecane systems

Gas rate

1.2—3.6 vol of gas per hquid volume/minute

(wm)

0 = 0.74 {Q/NV)^'^{N^DVgDiV^^^y'^{J)pN^DVoV^'Y^^

3. Bubble diameter analysis

(2)

Reference

Vessel geometry Vessel diameter Impeller to vessel

(m) diameter ratio System

Brown and Craddock (1969) Lee and Meyrick (1970)

0.22 0.304

0.345-0.573 0.333

air-water air-water

Dp^gplG = 5.5 {ip^'ViN^DVgDiV^'^iPglP)^'^) */2} (3)

4. Interfacial area By combining eqns (1), (2), and (3)

a=l,3S(gp/ay^HQ/NV)'^m^DVgDiV^^^)'^(PpN^DVaV^^y'''' (4)

Bimbinet, J. J., M. S. Thesis, Purdue University, Lafayette, Ind., 1959. Brown, D. E., Craddock, J., Paper presented at the Symposium on Mixing, Institute of Chemical

Engineers, Leeds, Sept., 1969. Calderbank, P. H., Trans. Instn, Chem, Eng., 37,443 (1958). Calderbank, P. H., Trans. Instn, Chem. Eng., 38,173 (1959).

5.3 Gas-liquid systems 35][

Farritor, R. E., Hughmark, G. A., Chem, Eng. Commum,, 4,143 (1980). Kawecki, W., Reith, T., van Heuven, L. W., Beck, W. J., Chem, Eng. 5d., 22,1519 (1967). Lee, J. C , Meyrick, D. L., Trans. Instn. Chem. Eng., 48, T37 (1970). Michel, B. J., MiUer, S. A.MChEJ., 8,262 (1962). Pharamond, J. C, Roustan, M., Roques, H., Chem. Eng. Set., 30,907 (1975). Rushton, J. H., Bimbinet, J. J., Can. J. Chem. Eng. 46,16 (1968).

Notation a interfacial area D impeller diameter A impeller blade width Dp bubble diameter g acceleration of gravity ki mass transfer coefficient N impeller speed P power input to ungassed liquid Pg power input to gassed hquid Q gas rate V liquid volume e energy dissipation p liquid density (7 surface tension 0 gas holdup


Hassan, I. T. M. and Robinson C. W, Can. J. ofChem. Eng., 58,198 (1980) Mass Transfer Coefficients in Mechanically Agitated Gas-Aqueous Electrolyte Dispersions

Experimental apparatus Vessel Diameter: 0.1524 m Height: 0.3048 m

Liquid contained Volume of liquid in vessel: 2.65 dm

Baffle Number: 4

Impeller Type: six-flat blade turbine impeller Diameter: 0.0508 m Number of impellers: 1 Number of blades on impeller: 6

Working fluids Liquid: oxygen-saturated Na2S04 + KOH, KCl -H KOH, and K2SO4 + KOH electrolyte solutions Gas: air

Experimental conditions P^/F: 440-10* W/cm^ Superficial gas velocity: 0.37-1.11 cm/sec Impeller speed: 12.2—31.7 rev/sec n 0.1-1.2 kmol/m^ Temperature: 30°C

Results (1) ki increases with increasing Tand is independent of Pg/V for P^/F<2,000. (2) kL decreases with increasing Pg/V for Pg/V>2,000 and is independent of t;,. (3) kia is dependent on all three variables Pg/V, v,, and F.

Notation a mass transfer effective interfacial area/unit liquid volume, 1/m ki liquid-phase oxygen transfer coefficient, m/sec kia overall volumetric oxygen transfer coeflScient, 1/sec Pg mechanical agitation power input to dispersion, W Vs gas superficial velocity, m/sec V fluid volume, m r ionic strength, kmol/m^


Sridhar, T. and Potter, 0. E., Chem. Eng. Sci, 35,683 (1980) Interfacial Areas in Gas-Liquid Stirred Vessels

Experimental apparatus Vessel Diameter: 13 cm Height: 26 cm Volume: 1.70 X10-3 m



Impeller Type: flat blade turbine Diameter: 4.5 cm Number of impellers: 1 Number of blades on impeller: 6 Width of impeller blade (parallel to shaft): 0.8 cm Off-bottom clearance: 4.2 cm

Sparger Type: a single-hole nozzle-type sparger Diameter: 0.6 cm Number of nozzles: 1

Working fluids and their physical properties Liquid: cyclohexane

viscosity: 0.20x 10-^-0.93x 10"^Nsec/m^ density: 0.64 x 10^-0.78 x 10 kg/m^ surface tension: 10.30 x 10-^-24.60 x lO'^ N/m

Gas: nitrogen density: 1.18-17.90 kg/m'

Experimental conditions Temperature: 24~150°C Pressure: 1—10 atm Superficial gas velocity: 1 x 10" —5 x 10" m/sec Stirrer speed: 8—301/sec Power input: 0.376-2.6 kW/m^

Results Interfacial areas in gas-liquid stirred vessels can increase as much as 75% as compared to those

obtained under similar operating conditions but at atmospheric pressure.

a = 1.44 [(P, IVf-'p'^la'-'] {V, lYsf^Er /P,Hp, I Paf''

Notation a mean interfacial area per unit volume of Vs rise velocity of a single bubble, m/sec

dispersion, 1/m p liquid density at system conditions, ET total power input, W kg/m^ Pg power input through agitator to gas hquid pa density of air at operation conditions,

dispersion, W kg/m^ V volume of hquid, m pg gas density, kg/m^ Vg superficial gas velocity, m/sec a surface tension, N/m


Sridhar, T. and Potter, 0. E., Ind, Eng. Chem. Fundam., 19,21 (1980) Gas Holdup and Bubble Diameters in Pressurized Gas-Liquid Stirred Vessels

Experimental apparatus Vessel Diameter: 13 cm Height: 26 cm



Impeller Type: flat blade turbine Diameter: 4.5 cm Number of impellers: 1 Number of blades on impeller: 6 Width of impeller blade (parallel to shaft): 0.8 cm Off-bottom clearance: 4.2 cm

Sparger Type: a single-hole nozzle-type sparger Diameter: 0.6 cm Number of nozzles: 1

Working fluids and their physical properties Liquid: cyclohexane Gas: air

Experimental conditions Superficial gas velocity: up to 0.032 m/sec Impeller speed: 17.5—24.21/sec Pressure: atmospheric—1.034 MN/m^

Results

fl = 1.44 (PJVf'p' P^= 0.706 Po'ndf

Of Notation

a interfacial ar^a per unit volume of dispersion, 1/m ET total energy input, W Pg mechanical agitation power input in gas-liquid dispersion, W Po mechanical agitation power input in ungassed liquid, W Qg volumetric gas flow rate, mVsec V volume of liquid in reactor, m^ Vg superficial gas velocity, m/sec V, terminal velocity of bubble in firee rise, m/sec Pa density of air at operation temperature, kg/w? Pg gas density at system conditions, kg/w? p liquid density at system conditions, kg/m^ a surface tension, N /m

5.3 Gas-liquid systmns 365

Nishikawa, M., Nakamura, M., Yagi, H. and Hashimoto, K.J. Chem. Eng. Japan, 14,219 (1981) Gas Absorption in Aerated Mixing Vessels

Experimental apparatus Vessel, impeller, and sparger geometries

Vessel diameter Liquid depth Liquid volume Impeller diameter Disc diameter Number of blades Blade angle Blade width Impeller level Number of baffles BafQe width Sparger arm length Sparger inlet pipe Holes in sparger Spacing of holes Hole diameter Sparger level

D H V d d. tip

e b

c flB b„ Ls Lp Hh S d,

a

(cm) (cm) (cm^) (cm) (cm) (-) (-) (cm) (cm) (-) (cm) (cm) (cm)

(-) (cm) (cm) (cm)

Dimensions of experimental apparatus Paddle

15 15

2,650 7.5

4 45**

1.5 3.75 4 1.5 3 3

21 0.5 0.1 1.5

30 30

21,200 12,15

3.8,5.6 4,6

90** 2,2.4,3

7.5 4 3 6 5

21 1 0.1 3

15 15

2,650 5,7.5 7.5 6

90' 1,1.5

3.75 4 1.5 3 3

21 0.5 0.1 1.5

Turbine

20 20

6,280 10 11.3 6

90' 2 5 4 2 4 4

21 0.7 0.1 2

30 30

21,200 15 22.5 6

90' 3 7.5 4 3 6 5

21 1 0.1 3

60 60

170,000 30 22.5 6

90' 6

15 4 6

12 10 21 2 0.15 5

Working fluids and their physical properties Liquid: distilled water Gas: air and nitrogen

Experimental conditions Impeller speed: 0—16.67 rps Temperature: 30°C Superficial gas velocity: 0.085~1.13 m/sec Power number:

Paddle: 2.62 and 3.08 Turbine: 3.70,5.45 and 5.50

Results For the agitation-controlling condition

turbine: ha = 3,92x10-^PjJ^P^ paddle: ha = 5.69 x lO^Pi^'/jJ-^ . Par=U,g. P^=Npn'd'/V

Notation d impeller diameter, cm g gravitational acceleration, cmVsec kia capacity coefficient based on plug flow type mixing, 1/sec n impeller speed, 1/sec Np power number , dimensionless Par aeration power p e r unit mass of liquid in aerated mixing vessel , cmVsec^ Pgr agitation power pe r unit mass of liquid in aerated mixing vessel , cmVsec^ Ug superficial gas velocity, c m / s e c V liquid volume, cm^

366 Chapter 5. Mass transfsr

Nishikawa, M., Nakamura, M. and Hashimoto, K.,/. Chem. Eng. Japan, 14,227 (1981) Gas Absorption in Aerated Mixing Vessels with Non-Newtonian Liquid

Experimental apparatus Vessel and impeller geometry: see Nishikawa, M., Nakamura, M., Yagi, H. and Hashimoto, K.,/. Chem, Etig,, Japan, 14,219 (1981)

Working fluids and rheological properties Gas: air Liquid:

Water 30% MiUet Jelly 60% MiUet Jelly 0.5% CMC solution 1% CMC solution 2% CMC solution 4% CMC solution 6% CMC solution

pig/cm^)

0.995 1.13 1.29 1.00 1.01 1.03 1.05 1.07

Physical properties of liquids a(g/cm^

71.0 71.0 71.0 71.0 68.4 67.4 66.0 64.3

DLX 10-^(cmVsec)

2.6 1.2 0.182 2.60 2.34 2.28 2.11 1.92

^(g/cmsec)

8.0x10-^ 2.54x10-2

0.419 0.073 0.215

non-Newton non-Newton non-Newton

m{-)

1.0 1.0 1.0 1.0 1.0 0.87 0.77 0.59

k (g/sec^-)

8.0x10"^ 2.54x10-2

0.419 0.073 0.215 1.31

10.8 185.5

Results

X ((Aia).«. /af^(dn' /gf^\nd/u,r''

X (Z)/(f)-"-*7\r^{l+2 (A«r}-°-'' + 0.112 {P«, / (P^ INp -h Par)} (uj^^

X ((Ha)a/pDLr(gD'p/Gf''(gDy/(fia)ar'

x{i+o.isaujdarf''r' Notation

d impeller diameter, cm dap Sauter mean bubble diameter, cm D vessel diameter, cm DL liquid-phase diffusivity, cmVsec g gravitational acceleration, cm/sec^ k fluid consistency index, g/sec "*" kia volumetric liquid-phase mass transfer

coefficient, 1/sec m flow behavior index n impeller speed, 1/sec Np power number, dimensionless Par aeration power per unit mass of liquid, cmVsec Pgr agitation power per unit mass of liquid,

cmVsec

Ub average ascending velocities of gas bubbles, cm/sec

Ug superficial gas velocity c m / s e c X characteristic material time, 1/sec // liquid viscosity, g/cmsec ^a apparent viscosity, g/cmsec p liquid density g/cm^ G surface tension, g/cm^

Subscripts a aerated tower condition g agitation controlling condition


Chandrasekharan, K. and Calderbank, R H., Chem. Eng. ScL, 36,819 (1981) Further Observations on the Scale-up of Aerated Mixing Vessels


Liquid contained Height: 1.22 m Volume of liquid in vessel: 1.43 m'

Impeller Type: flat blade type Diameter: 0.27 m Number of impellers: 1 Length of impeller blade (perpendicular to shaft): 0.06 m Width of impeller blade (parallel to shaft): 0.06 m



Run Code

VsXlO^m/sec Approx./f**% Ns rpm (kLa)wMxlO^

1/sec HwM % (kLa)pFXlO'

1/sec HPF % /yVLwatt/m'

10

3.5 3.05

105

1.33

1.22

1.18

1.22 94

11

3.5 2.91

168

2.17

1.98

1.86

2.87 475

19

18 73

201

4.70

2.92

4.28

3J20 694

20

18 8.6

266

8.23

6.08

6.40

5.98 1,596

12

3.5 3.18

197

2.82

2.52

2.27

3.40 766

13

7.1 5.19

139

2.44

2.08

2.17

2.08 187

14

7.1 5.19

181

3.20

2.11

2.76

2.08 454

15

7.1 4.67

224

4.10

2.02

3.53

2.78 881

16

11.0 6.29

158

3.23

2.52

2.90

2.51 245

17

11.0 6.68

189

3.81

2.67

3.37

2.67 448

18

11.0 6.68

233

5.25

3.84

4.42

4.76 881

Results

Model Parameter value

kLa = E/DM' {PIVOHQMr^

kia = E/DM^ {PIVLYiVs)^^-"

E = 0.0248, A = 0.551

A = 0.524, B = 0.780, E = 0.0262

xi = 0.0287 Av^'°'^^''^-^'"^ X2 = 0.563, Xz = 0.631

A = 0.573, B = 0.481, E = 0.752, E = 0.0135

Notation DM diameter of column, m

gas hold-up mass transfer product, 1/sec stirring speed, 1/min power consumed, W total gas flow rate, mVsec

H

Ns P QM

VL total volume of liquid, m Vs superficial gas velocity, m/sec

subscripts PF plug flow gas WM well-mixed gas


Judat, H., Ger. Chem. Eng., 5,357 (1982) Gas/Liquid Mass Transfer in Stirred Vessels-A Critical Review

Use of existing data (see table)

Geometrical parameters of the evaluated studies.

Reference

Linek, Mauthoferov^ MoSnerov (1970) Robinso,Wilke(1973) Moser. Edlinger, Moser (1975) Vafopulos, Sztatescny, Moser (1975) Uhl, Winter, Heimark (1976)*

Smith, van't Riet, Middleton (1977)

Pollard (1978) Hecker(1979) Lopes de Figueiredo, Calderbank (1979)**

Zlokamik (1975) Judat(1976) Mateme (1979)

Dim)

0.290 0.152 0.440 0.440

12.192 12.192 12.192 12.192 0.610 0.610 1.830 1.830 1.810 0.400 0.915

0.400 0.395 0.180

^(m)

0.290 0.152 0.440 0.440 6.096 6.096 6.096 6.096 0.610 0.610 1.630 1.630 1.810 0.400 0.915

0.400 0.395 0.180

VFJm')

0.0182 0.0025 0.0625 0.0669

906 906 906 906

0.180 0.180 4.4 4.4 4.63 0.0505 0.600

0.047 0.048 0.0046

dim)

0.100 0.051 0.147 0.147 3.099 1.905 1.829 1.676 0.305 0.203 0.914 0.670 0.600 0.133 0.274

0.090 0.079 0.054

Did 2.9 3.0 3.0 3.0 3.934 6.4 6.666 7.274 2.0 3.0 2.0 2.731 3.0 3.0 3.346

4.444 4.975 3.333

bid

1 1 1 1 0.344 0.560 0.583 0.637 0.833

0.946

1.115

HID

1 1 1 1 0.5 0.5 0.5 0.5 1 1 0.891 0.891 1 1 1

1 1 1

•Turbine stirrer with 4 blades, **turbine stirrer with square blades 0.06 m.

Linek, V., Mayrhoferov , J., MoSnerovd, J., Chem, Eng, Sci., 25 (1970) pp.1033-1045. Robinson, C. W., Wilke, C. R., BiotechnoL Bioeng, 15 (1973) pp.755-782. Moser, A., Edlinger, V., Moser, F., Verfahrenstechnik (Mainz), 9 (1975) Nr. 11, pp.553-565. Vafopulos, L, Sztatescny, K., Moser, F., Chem,-Ifig,'Tech,, 47 (1975) Nr. 16, p.681. Uhl, V. W., Winter, R. L, Heimark, E. UAIChESymp. Ser,, 73 (1977) pp.33-41. Smith, J. M., van't Riet, K., Middleton, J. C, Proceedings of the Second European Conference on

Mixing, Cambridge, 1977, F 4-51/F 4-66. Pollard, G. J., Proceeding of the International Symposium on Mixing, Mons, 1978, C 4-1/C 4-16. Hocker, H., Thesis, Univ. Dortmund, 1979. Lopes de Figueiredo, M. M., Calderbank, P. H., Chem, Eng., Sci„ 34 (1979) pp.1333-1338. Zlokamik, M., Chem. -Ing.-Tech., 47 (1975) Nr. 7, pp.281-281. Judat, H., Thesis, Univ, Dortmund, 1976. Mateme, W., Diplomarbeit, Univ. Dortmund, 1979.

(kia)* = 9.8 X 10-'(P/K)*°-^/ (5"^' + 0.81 X10-°''^^)

Notation a interfacial area per unit volume, mVm b bottom clearance by the impeller, m D vessel diameter, m d impeller diameter, m g gravitational acceleration, m/sec^ H liquid height, m


ki liquid-side mass transfer coefficient, m/sec kia volumetric mass transfer coefficient, 1/sec P impeller power input, W q volumetric gas flow rate, mVsec V volume of liquid, m^ V kinematic viscosity of liquid, mVsec p density of liquid, kg/m^

B^iqlD ) (v^) '^'^ dimensionless superficial gas velocity Did diameter ratio HID dimensionless liquid height hid dimensionless bottom clearance by the impeller {kio)* s kia iy/g^y^ dimensionless volumetric mass transfer coefficient (P/V)* s {PIV)I[p (v *) ^ ] impeUer power input per unit volume


Chapman, C. M., Gibilaro, L. G. and Nienow, A. W, Chem. Eng. Sci., 37,891 (1982) A Dynamic Response Technique for the Estimation of Gas-Liquid Mass Transfer Coefficients in a Stirred Vessel




Impeller Type: standard six-blade Rushton Diameter: 0.28 m Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): D/4 Width of impeller blade (parallel to shaft): D/5 Off-bottom clearance: 0.14 m

Sparger Tjrpe: three-hole nozzle Location: in a central bearing on the vessel base

Working fluids, their physical properties Liquid: de-ionized water Gas: air

Experimental conditions Maximum impeller speed: 61/sec Gas flow rate: 0.575 x lO'^ and 2.298 x lO'^ mVsec

Results

gas rate mVs X10^

2.298 2.298 0.575 0.575

impeller speed 1/s

3.8 3.1 2.8 3.0

Notation D impeller diameter, m kid mass transfer coefficient, 1/sec

gas holdup m X10'

11.3 10.8 3.5 3.9

Vs

0.107 0.077 0.055 0.062


Albal, R. S., Shah, Y. T and Schump6, A., Chem. Eng.J., 27,61 (1983) Mass Transfer in Multiphase Agitated Contactors


System

Vessel Type Diameter (cm) Height (cm) Volume (£)


Baffle Number Width (cm) Height (cm)

Impeller Type

Diameter (cm) Number of impellers Number of blades on impeller Position (cm) distance between bottom and 1st (cm] distance between 1st and 2nd (cm) distance between 3rd and top (cm)

Conventional arrangement


2

10.2

4 1.28 22.6

six-blade 45°

4.6 1 6

3.4 — —

Unconventional arrangement


2

—

4 1.28 22.6

pitched turbine

5.7 3 6

3.4 5.7 5.7

I' At 'I ^4T **~57-

10.2

Conventional Arrangement Unconventional Arrangement

Agitated vessel with conventional and unconventional arrangements (all dimensions in centimeters).


Working fluids and experimental conditions

Liquid system System arrangement Range of parameters

Oa-water conventional unconventional

02-glycerin solutions unconventional

O2-CMC solutions unconventional

100-400 rpm 400-1,000 rpm

liquid level 13.5-17.5 cm

600-1,000 rpm viscosity 7 x 10"^-0.11 Pasec

800-1,000 rpm concentration 0.2—lwt%

Results

0 = 1.41x10"

{p0 ( Jl T D^npT'hn^D

^ J

Notation a interfacial area per unit liquid, 1/m D impeller diameter, m 0 difiiisivity of gas in solution, mVsec ki liquid side mass transfer coefficient, m/sec n stirring speed, 1/sec jS viscosity of solution, Pasec p density, Vag/rc? a surface tension, kg/sec^

5.3 G«s-lii|uid systems 373

Kara, M., Sung, S., Klinzing, G. E. and Chiang, S. H., Fuel, 62,1492 (1983) Hydrogen Mass Transfer in Liquid Hydrocarbons at Elevated Temperatures and Pressures

Experimental apparatus Vessel Type: dish-bottomed Diameter: 76 mm Volume: 1 dm^

Liquid contained Liquid height/vessel diameter: 1.0—1.84

Baffle Width: 8 mm

Impeller Type: six flat-bladed turbine Diameter: 32 mm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 6.4 mm Width of impeller blade (i»rallel to shaft): 10.3 mm

Working fluids Liquid: tetralin and hydrogenated SRC H liquid Gas: H2

Experimental conditions Temperature: 606-684 K Total pressure: 7.0-13.5 MPa Impeller speed: 50—4001/min

Results kia = 3.43 X W\P/Vf\H / DTT^^

Notation a specific interfacial area, 1/m DT vessel diameter, m H liquid height, m ki liquid side mass transfer coefficient, m/sec P impeller power consumption, W V liquid volume, m


Deimling, A., Karandikar, B. M., Shah, Y. T. and Carr, N. L., Chem. Eng. /., 29,127 (1984) Solubility and Mass Transfer of CO and H2 in Fischer-Tropsh Liquids and Slurries

Experimental apparatus Vessel Type: flat-bottomed autoclave Diameter: 0.101 m Height: 0.267 m

Liquid contained Height: 0.136 m Volume of liquid in vessel: 1.1 x 10" m

Impeller Type: inclined blade Diameter: (1) 0.057 (2) 0.057 (3) 0.057 m Number of impellers: 3 (two: in liquid phase; one in gas phase) Off-bottom clearance: (1) 0.034 (2) 0.091 m from the bottom of the vessel (liquid phase) (3) 0.057

m from the top of the vessel (gas phase) Sparger The gas is entrained into the liquid by the two stirrers

Working fluids and their physical properties Liquid: Fischer-Tropsch liquids Gas: CO2, H2

Properties of the liquids used in this investigation

Solvent

PT light FT medium FT heavy*

Carbon number range

Ce-C, C12 — C21

^€22

Average molecular

weight

(kg kmol"*)

113.9 201.2 368.5

Surfece tension at 297 K

(mNm-^)

23 26

Density (kg m~ ) at the following temperatures

298 K

723.0 776.2 820.3

373 K

713.5 749.7 778.3

423 K

681.6 733.1 745.0

473K 523K

715.7 702.0 705.0 680.0

' Melting point 353 K at atmospheric pressure.

Experimental conditions Temperature: 373-523 K Pressure: 1—4 MPa Stirrer speed: 800-1,1001/min


Results

375

0 10

-1 10

•2i 'L 4-10

F-T LIGHT F-T MEDIUM

1^-.

-1 10 h

4-10

F-7 HEAVY

5-0

CO

-^r^l^c"

(a) 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4

P j [MPa]

10

-1 10

-2 J 4-10

-1 10 <r

-2 4-10

F-T LIGHT

1 .^ ^ -o

- C - * T

F - T MEDIUM F-T HEAVY n

^

CO

^-^ 2 .

J H ,

(b) 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 5

^2 !•***•)

Volumetric mass transfer coefficient kia for CO and H2 in various fractions of an FT liquid as a function or pressure at different temperatures (0 ,523 K; A, 473 K; 0 ,425 K; D, 373 K) and two stirrer speeds: (a) 1,000 rev min"*; (b) 800 rev min"*.


1000

r-T MEDIUM.

1 • / /

CO

1

1000

[MPa]

Inter Eicial area a for CO and H2 absorption in the FT medium fraction as a function of pressure a:two different temperatures and stirrer speeds: • , 523 K, 1,000 rev min"*; • , 373 K, 1,000 rev min'^ 0 ,523 K, 800 rev min-*; D , 373 K, 800 rev min'^

Mass transfer coefficient ki for CO and H2 as a function temperature: , correlation of Calderbank and Moo-Young [15] for ki for large bubbles (curves 1) and small bubbles (curves 2); -B-, data of the persent work.

10

-1 — 10

• -21 -J 4-10

F-7 LI3H7 F-T MEDIUM F-T HEAVY

^"^ti-^

- o — 0 - .

CO

1?

-2 4-10^

^ .^'

. ^ J H^

100 200 100 200 T [ -Cl

100 200 300

Volumetric mass transfer coefficient kia for CO and H2 in various fractions of FT liquids as a function of temperature at different pressures (stirrer speed, 800 rev min" ): O, about 4.6 MPa; D, about 3.4 MPa; A, about 12 MPa; O, about 1.0 MPa.

5.3 Gas-liquki systems 377

10

-1 10

4 1 0

10 h

•2 4.10

4

j F-T LIGHT j F-T MEDIUM} F-7 HEAVY

1 > ; i I*

1 t '•

1 r _

! 1 /I T ^ 1 1 1 ' ' 1

J' i <* Oo T ^ 1

• ' T M . "1 ' . 1

102 10^ 4-10^ io-> 4-io3r s irpmj

lo3^

Volumetric mass transfer coefGcient kia for CO and H2 in various fractions of an FT liquid vs. stirrer speed (temperature T, 373 K): O, about 4.6 MPa; D, about 3.4 MPa; A, about 2.2 MPa; O, about 1.0 MPa.

Notation a interfacial area (related to liquid volume VL), mVm kid volumetric mass transfer coefficient, 1/sec P pressure, MPa s stirrer speed, 1/min T temperature, K or °C

Subscript 2 equilibrium state after absorption


JureCiC, R., Berovid, M., Steiner, W. and Koloini, T, Can. J. ofChem. Eng., 62, 334 (1984) Mass Transfer in Aerated Fermentation Broths in a Stirred Tank Reactor


Vessel Type Diameter (m) Volume (m )

Liquid contained Volume of liquid in vessel (m )

Baffle Number Width (m) Clearance of baffle from wall (m)

Impeller Type

Diameter (m) Number of impellers Number of blades on impellers Positions of impellers

hi(m) fc(m) hsim) h,{m)

Sparger Type Location

Pilot

dish-bottomed 0.41 0.125

0.1

4 0.04 -

curved blade disc turbine with four blades

0.22 2 4

0.12 0.40 0.34

-

a ring type —

Industrial

dish-bottomed 3.3 80

67.5

4 0.33 0.07

flat blade disc turbine with six blades

LI 4 6

1.2 2.1 2.1 2.1

a ring type 1.2 m from the bottom


L

I D-

L J —

)

V 1

-c

l_

1 1

u

1 1 1

1 - 1 < ^

1 "^ I JC" 1 f

Pilot plant fermentor Industrial fermentor

E: the position of oxygen electrode Working fluids and their physical properties

Liquid: a fermentation broth iir= 13.9X10-3Pa(secr „ = 0.678 for x-^KiyY


N QglVxW vcxlO^ (ms-i)

PJV (Wm-^)

77^x103 (Pas)

Pilot plant fermentor

Industrial fermentor

4.17-6.67 7.2-14.6 1.7-5.5 1,800-8,100 3.76-4.38

1.17-1.83 8.0-33.4 17.0-39.0 450-2,100 5.17-6.59

'PMcalculated as single impeller power input (Miller, 1974) for each region separately. Vis liquid volume per impeller. Miller, D. N., AIChE Journal, 3,445 (1974)

Results

ha

(QS) Sc-

' a


Notation DL liquid phase diffiisivity, mVsec kio volumetric liquid phase mass transfer coefficient, 1/sec K fluid consistency index, Pa(sec)" n flow behavior index N impeller speed, 1/sec Pm power input of single turbine, W Qg gas flow rate, mVsec Sc Schmidt number, r\lpDu dimensionless VG superficial gas velocity, m/sec V liquid volume per impeller, m^ 7 shear rate, 1/sec J] liquid viscosity, Pasec 7]^ effective Uquid viscosity, Pasec V kinematic viscosity, mVsec p liquid density, kg/m^ c liquid surface tension of broth, N /m Gw surface tension of water, N/m T shear stress, Pa


Ledakowicz, S., Nettelhoff. H. and Deckwer, W.-D., Ind. Eng. Chem. Fundam., 23,510 (1984) Gas-Liquid Mass Transfer Data in a Stirred Autoclave Reactor

Experimental apparatus Vessel Type: dish-bottomed Diameter: 80 mm Volume: 1 E

Impeller Type: turbine Diameter: 48 mm Number of impellers: 1

Sparger Location: beneath the center of the impeller

Working fluids Liquid: Fischer-Tropsch slurry Gas: H2, N2, CO and CO2

Experimental conditions Pressure: up to 6 MPa Temperature: 180-280°C

Results

fis > 700 rpm

Notation a specific interfacial area (referred to

liquid volume), 1/cm ki liquid side mass transfer coefficient,

cm/sec fis stirrer speed, 1/min pi liquid phase partial pressure, Pa T temperature, **C VL liquid volume, cm^

12s

100

50

25

V^.SSOcm^

T « 200 -C

400 ris. rpm 1200

Dependency of volumetric mass transfer coefficients (liLa) on stirrer speed.

382 Chapter 5. Mass tninsffar

Albal, R. S., Shah, Y. T, Carr, N. L. and Bell, A. T, Chem. Eng. Sci, 39,905 (1984) Mass Transfer Coefficients and Solubilities for Hydrogen and Carbon Monoxide under Fischer-Tropsch Conditions

Working fluids and their physical properties Liquid: Fischer-Tropsch liquid

Density of the liquid

Temp. (K) Density (kg/w?)

348 423 523

778.5 727.6 682.9

Gas: H2 and CO Experimental conditions

Stirrer speed: 800 and 1,000 rpm Temperature: 348,423, and 523 K Pressure: 1.2-3.2 MPa

Results

xo«

s

2

0-1

s

z

- X

• 4-

1 1 1 1

1000 rpa, 423 K for CO

1000 rpi. 3 a X for CO 000 rpa, 423 K for Hj

100 rpB. 34« K for Nj

A

0

1 1

-

] '•' A • 4. 1

• * i l l ! 1 1 1 1

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4 0

Pressure (MPa) 300 350 400 450 500 SSO 600

Temperature ("K)

kid vs pressure for w?a-CO and wax-Ha systems. kia vs temperature for wax-H2 and wax-CO systems. Legend: A, 1,000 rpm for CO; -f, 800 rpm for CO;

X, 1,000 ipm for H2; 0,800 rpm for H2.

Notation kia volumetric liquid-side mass transfer coefficient, 1/sec

5.3 Gas-llquld systems 383

Onken, U., Sick, R. and Weiland, R, Chem.Eng. Set., 40,1990 (1985) Determination of Gas-Liquid Mass Transfer by Oxidation of Hydrazine

Experimental apparatus Vessel Volume: (1)6 (2) 100^

Liquid contained Volume of liquid in vessel: (1) 4.5 (2) 60 £

Working fluids Liquid: aqueous solution of hydrazine Gas: oxygen


Catalyst systems investigated in respect to application as homogeneous catalysts

Catalyst system

Cobalt trisulphophthalocyanine

Copper tetrasulphophthalocyanine

CUSO4/NH3

NiS04/NH3

C0SO4/NH3

CuS04/alkanolamines

"Levoxin" (Bayer AG)

1,4-Naphthoquinone, 2-Sulphonic acid

Cau

pH: T:

Can'

pH: T:

CCal

CNI:

pH: T:

CCol

CCul

pH: T:

pH: T:

CaU

pH: T:

Reaction conditions

lO-^-lO-'kmol/m" 11.8--12.8 20~35*'C

lO-'-^-lO-^kmol/m' 12.0-12.8 20-'35**C

10''~10-'kmol/m'

10-'~10-^kmol/m^ 10.5-11 25*»C

10-^-10-2 kmol/m'

lO-'-lO-^kmol/m^ 10.5-12 25*'C l~3ccu

7.7-13.2 25°C

10-^-10-2 kmol/m' 6-12 25*'C

Suitable for the detennination

oiPia

+

+

+

(+)

-

—

Remarks

synthesized and delivered by Bayer AG

CAS-No. 147-14-8

high NHs-concentration

no advantage in comparison to CUSO4/NH3

precipitation

coalescence inhibition, ligands: monoethanolamine, diethanolami-ne, N, iV^bis-(2-hydroxypropyl)-ethanol amine

levoxin = hydrazinehydrate + activator, activity not constant

activity not constant

384

Results

Chapter 5. Mass transfor

a4 a6 0.0 1.0 Suptrficiol gos vtlodfy w ,. (em/s)

Comparison of chemically and physically determined jSia-values.

6 0.2 0.4 0.6 aa 1.0 suptrficial gat velocity,M^Q (cm/tl

0.2 0.4 0.6 0.6 1.0

Suptrficiol gos vtiocity Ws lcm/sl

Reproducibility of ^/.a-values by hydrazine oxidation. Comparison of coalescence inhibiting additives.

Notation WsG superficial gas velocity, cm/sec Pia volumetric mass transfer coefficient, 1/sec

5.3 Gas-liquid systems 3 5

Ruchti, G., Dunn, I. J., Bourne, J. R. and von Stockar, U., Chem. Eng. /., 30,29 (1985) Practical Guidelines for the Determination of Oxygen Transfer Coefficients (kia) with the Sulfite Oxidation Method

Experimental apparatus Vessel Type: dished-bottomed Diameter: 0.34 m Volume: 0.05 m



Impeller Type: turbine Diameter: 0.113 m Number of impellers: 1

Working fluids Liquid: aqueous Na2S03 solution containing cobalt ion catalyst Gas: air

Results For sulfite oxidation

N(s-')

5.0 8.3

10.0 1L7 14.2 16.7

kias (s'O

0.025 0.13 0.23 0.36 0.46 0.72

kiOD (S" )

0.058 0.11 0.16 0.30 0.39 0.44

Notation kia volumetric oxygen transfer coefficient based on VL, 1/sec N stirring speed, 1/min VL volume of liquid phase, m

Subscripts D dynamic electrode method 5 sulfite method


Gibilaro, L. G., Davies, S. N., Cooke, M., Lynch, R M. and Middleton, J. C, Chem. Eng. Sci., 40,1811 (1985) Initial Response Analysis of Mass Transfer in a Gas Sparged Stirred Vessel

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 0.305 (2) 0.61 m

Liquid contained Height: (1)0.305 (2) 0.61m

Impeller Type: (1) (2) standard six-blade Rushton Diameter: (1) (2) TI2 Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade perpendicular to shaft): Z)/4 Width of impeller blade parallel to shaft): D/b Off-bottom clearance: 7/4


Experimental conditions Specific power input: 0.4—7 kW/m^ Superficial gas velocity: 5 x 10~^~25 x 10" m/sec

Results

kLa = 0A9{P/VLy'\vsf''^

Notation D kia P T Vs VL

impeller diameter, m mass transfer coefficient, 1/sec power, kW tank diameter, m superficial gas velocity, m/sec volume of liquid, m


Karandikar, B. M., Morsi, B. I., Shah, Y. T. and Carr, N. L, Chem. Eng. /., 33,157 (1986) Effect of Water on the Solubility and Mass Transfer Coefficients of CO and H2 in a Fisher-Tropsch Liquid



Impeller Tjrpe: six flat-bladed turbine Diameter: 0.0635 m Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 0.0667 m

Working fluids Liquid: a medium fraction (C11-C12) of Fisher-Tropsch liquid Gas: CO and H2

Experimental conditions Temperature: 423-498 K Pressure: 1—4 MPa

Results

^

0.01

O 700 rym t^ teoo i>ni 13 » 0 0 rym

0*EW STMBOL : I

Effect of total mean pressure on kia for CO inFTandFTS.

id

J

0.1";

0.01:

finni-

::::::;::;™::;.::~-:nr::™;:;-:™;r:::;::::;:™:::~;;-:™r:::::::::;;

_ "' " —^ "* "TII]'--'^ **"

^,^„,-—!--;,• TT 2 1 : ^.txr-A

j:z^B ^^^J^^^tT"""^ _ -^^"^""'^^ i ^ J A— 0 1

_....„ „.».-K; ~-.A - - k

^ J^'

WW SYWtOL: n pAUKsni toLtm ^SJ^—\

;3:z.z:i.Uj::jips>r"—":""""n'r::r|

\/^

T —

V

0 TOOtym

A 1000 t y n

0 ttOOrpM

~~._

Effect of total mean pressure on kua for H2 inFTandFTS.


1 -

ot-

N , : 1000 rpm ^ n Symbols : CO [>ork Symbols: K?

1 ' -''t-4 — — , - < - ,0'

^nc* — T ' :•' 1

• *•' \ -': i

J ^ r ^ : 9.9 MTk

100 150 200 250

T [ C ]

Effect of temperature on kia for CO and Hz in FTS.

0}

\-

0.1-

i

0.01-

0.001-

: ; v ^ . - i _ i . . ; . i .

-j— -4—-r-f-T-rt-r.

1 \ \ \ \ /i\

1-:r-jrL-r::

444414. i • i i/9'

• y • /'•/'• o^' / hr/^^- '• '• ••

A T/\ i 1 iTi /" i//f M i ni J(\ mill

E5E5^ •~4-V^^*' ' . " • ; , ' , ,-, l , , . i , , : , r , - , j -

|..->.4-4-4.4.i..u.

... _ . ;....:...;.,i..j.iJ

4.—j-~4...4..4~j..n

: : : : : : : : 1 ... rrttrnl o o «z9i IM H

D 4Mr M M j

EEEll-:4„J:.:i4:±i:iJ

i 1 i

i i j

-'SYMBOLS OPEN:FT

DARKrns

4-ffl

1 1 » i » » 1 1 1

P > L [KVm3]

Effect of specific power input on kia for CO in FT and FTS.

Effect of specific power input on kta for H2 in FT and FTS.

Notation kiM mass transfer coefficient, 1/sec P * power input in agitation, kW T temperature, °C or K Pm mean pressure, MPa VL liquid volume, m^ FT Fischer-Tropsch liquid FTS Fischer-Tropsch liquid saturated with water

5.3 Gas-liquid systams 339

Chaudhari, R. V, Gholap, R. V, Emig, G. and Hofinann, H., Can. J. ofChem. £n^., 65, 744 (1987) Gas-Liquid Mass Transfer in "Dead-End" Autoclave Reactors


System

Vessel Capacity, (m ) Diameter, flfr, (m) Effective volume of reactor

(in the presence of internals), (m ) Liquid contained

Volume, (m ) Height, fe, (m) Vg/Vi range

Impeller Type

Diameter, A, (m) di/dr range hi range*, (m) hi/h2 range"

Sparger Height from bottom*, .(m)

(1)

0.6x10-3 5.8x10-2

5.40x10-*

1.5xl0-*-4xl0-* 5.6x10-2-^15.2x10-

0.35-2.6

2.1x10-2-3.9x10-^ 0.36-^0.67

1.4x10-2-8x10-2 0.25'-'0.85

0.3x10-2

(2)

2x10-3 10x10-2

17.60x10-'*

8x10-* 2 9.8x10-2

1.2

four-bladed propeller ^ 7x10-2

0.7 4.9x10-2

0.5

0.5x10-2

(3)

5 X10-3 15x10-2

42.45x10-*

15x10-* 9.6x10-2

1.83

10.5x10-2 0.7

3.1 X10-2 0.32

0.5x10-2

* For single stirrer only •Sparger was kept fixed for mode B operation

Working fluids and their physical properties (1) Dynamic physical absorption

(a) Liquid: water Gas: acetylene 0)) Liquid: ethanol Gas: air

(2) Oxidation of sodium sulfite Liquid: an aqueous solution of sodium sulfite (0.6 kmol/m^) Gas: oxygen

(3) Catalytic hydrogenation of styrene Liquid: styrene Gas: hydrogen

Physical properties of the system components used in this work at experimental conditions

Components

Hydrogen Oxygen Acetylene Ethanol Water Sulfite solution (0.6 kmol/m^)

Density kg/m3

0.089 1.42

610 790

1,000 1,050

Viscosity poise

8.8 X10-5 2.1 X10-* 9.5 X10-5 1.1 X10-2 8.9x10-3

9x10-3

Surface tension. (N/m)xl0-3

— -—

22.2 72 74.5



System (1) (2) (3)

Agitation Speed (Hz) 5-15 5.5-13.5 5.5-15.5

Mode A: the gas was introduced in the gas phase without a dip-tube Mode B: the gas was introduced throu^ a dip-tube in the liquid

Results For mode B operation

- . \l-88 / . \2.16 / . \1.16

[V,) [drj [h) Ar>8.33Hz, d,/dT>0,5, VJVL>X and /ii/fe>3

Notation a gas-liquid interfacial area per unit volume of reactor, mVm^ di impeller diameter, m dr tank diameter, m h\ height of the first impeller firom the bottom, m hi height of the liquid, m ki liquid fihn mass transfer coefficient, m/sec N speed of agitation, Hz Vg volume of the gas in the reactor, m^ VL volume of the liquid in the reactor, m^

5.3 Gas-liquid systMns 392

Karandikar, B. M., Morsi, B. I., Shah, Y. T. and Carr, N. L, Can. J. ofChem. Eng., 65,973 (1987) Effect of Water on the Solubilities and Mass Transfer Coefficients of Gases in a Heavy Fraction of Fischer-Tropsch Products


Baffle Number 4 Width: 0.0127 m

Impeller Type: six flat-bladed turbine Diameter: 0.0635 m Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 0.0667 m

Working fluids Liquid: a heavy fraction of Fischer-Tropsch Hquid Gas:CO,H2,CH4andC02

Experimental conditions Temperature: 423-498 K Impeller speed: 700-1,000 1/min Mean total pressure: 0.7—4.5 MPa

Results

kia for CO and H2 in F-T hquid fractions with and without dissolved water at 423 K

kia.s'^

Gas

CO

H2

Stirrer speed (rev/min)

1,000

1,200

1,000

1,200

Mean pressure (MPa)

1.1 2.2 3.3

1.1 2.2 3.3

1.1 2.2 3.3

1.1 2.2 3.3

Medium F-T

0.0435 0.0500 0.0625

0.100 0.130 0.180

0.185 0.215 0.300

0.380 0.440 0.550

Medium F-TS

0.0520 0.0700 0.100

0.120 0.170 0.220

0.079 0.100 0.150

0.250 0.330 0.380

Heavy F-T

0.058 0.096 0.160

0.160 0.220 0.290

0.240 0.350 0.500

0.400 0.640 0.780

Heavy F-TS

0.066 0.110 0.190

0.130 0.210 0.330

0.130 0.230 0.340

0.210 0.380 0.730

F-T Fischer-Tropsch liquid F-TS Fischer-Tropsch hquid saturated with water


For CO and H2

kia = 0.1607 -^— exp (0.108P«) - 0.046 11000 J

For CO2 and H2

kia = 0.0171 - i — exp (0.38P«) + 0.00525 l ioooj

Notation kia mass transfer coefficient, 1/sec N stirrer speed, 1/min Pm mean total pressure, MPa

5.3 Gas-liquM systems 393

Ogut, A. and Hatch, R. T, Can. J. ofChem. Eng., 66, 79 (1988) Oxygen Transfer into Newtonian and Non-Newtonian Fluids in Mechanically Agitated Vessels


System

Vessel Type Diameter (m) Volume (m )

Liquid contained Heighten//))

Baffle Number Width (Bw/D)

Impeller Type

Diameter (m) Number of impellers Number of blades on impellers Width of impeller blade

(parallel to shaftXB/rf) Off-bottom clearance {d/He)

Sparger Type Diameter of orifice (m)

(1)


0.87

4 0.13

0.762 1 6

0.14

1.09

single orifice 0.16 X10-2

(2)


0.85

4 0.14

six-blade paddle

0.10 1 6

0.125

1.00

single orifice 0.16x10-2

(3)


1.0

4 0.15

0.177 1 6

0.14

1.10

single orifice 0.95x10-2


(1) Newtonian; aqueous solution of sodium sulfite (2) non-Newtonian; modified sodium polyacrylate (MSPA) was added to the Newtonian fluid

Physical properties of non-Newtonian Liquid (25°C)

MSPA Cone. (kgm-3)

10 20 30 40

n ( - )

0.89 0.78 0.72 0.68

K (Pas")

a (Nm- )

P (kgm-')

3.26 10.40 20.50 33.20

0.0573 0.0555 0.0538 0.0538

1.079 1.079 1.079 1.079

Gas: air



System

Agitation speed (1/sec) Air flow rate (mVsec) Temperature (°C)

Results For Newtonian fluids

(1)

5-12.33 (3.33'-20)xl0-5

25

(2)

5-11.67 (3.33-20) X 10-5

25

(3)

1.82-3.75 (0.83-3.3) X10-'

25

For non-Newtonian fluids

Notation B impeller width, m Bw baffle width, m d impeller diameter, m D tank diameter, m H liquid height, m HB impeller height above base, m kia volumetric oxygen transfer coefficient, 1/sec K fluid consistency index, Pasec" Vs superficial gas velocity, m/sec n flow behavior index, dimensionless N rotational impeller speed, 1/sec jUa apparent viscosity, Pasec p liquid density, kg/m' G surface tension, N/m


Oyevaar, M., Zijl, A. and Westerterp, R., Chem. Eng. Technol, 11,1 (1988) Interfacial Areas and Gas Hold-ups at Elevated Pressures in a Mechanically Agitated Gas-Liquid Reactor

Experimental apparatus Vessel Type: flat-bottomed Diameter: 8.8 cm



Impeller Type: standard six-blade disc turbine Diameter: 0.4 T Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 0.33 T

Working fluids and their physical properties Liquid: DEA (diethanol amine)

Data for the DEA-water system at 298 K.

m kij,(ci,EA,LyDco2 = 9.3835x 10" [DEA]" ' -2.6101 xlO""

w = 0.791-0.044 [DEA]'

PL = 0.9958 +1.555 x 10" [DEA] -1.1410 x 10'" [DEA]'

HL = exp (-0.1135 + 2.5718 x 10"' [DEA]+4.6937 x 10"' [DEA]')

[DEA] in mol/kg and [DEA]' in mol/i.

Gas: mixtures of CO2 and N2 Experimental conditions

Temperature: 298 K Flow rate of N2: 0-9 m N/hr Flow rate of CO2: 0-0.3 m N/hr

396

Results

150Ch

1200 a Vm i 900-1

600-

300H

a

O ti. L2m • N • l«.7 tpt

• • •

o o o

Chapter 5. Mass transffar

O

024 0^8 0-72 ^ P

""^ MPa

a96 12

TOO-.

600-1 - 5 . Vm I 500-j

40oJ

30CH

20a

Interfacial area vs reactor pressure at f;^=1.00cin/s(CSTR).

O «| • too GM/S

• Vg . 1^0 CM/l

A »i • 2.00 cm/s

l« • o

04 as 1-2

MPa

t O

1-6 —r

20

Interfadal area vs reactor pressure at i\^=16.7rps(CSTR).

Notation a interfadal area, 1/m r bulk concentra t ion, mol/w? Dco2 diffiisivity of CO2, mVsec kn,p r o t e cons tant for reaction of o rde r («, p), w? ^+""^VmoP^''"^^sec m distribution coefficient Ci-mCg N stirring speed, 1/sec P pressure, MPa T tank diameter, m Vg superficial gas velocity, m/sec or cm/sec PL liquid density, kg/m^ / I I liquid viscosity,Nsec/m^


Kawase, Y. and Moo-Young, M., Chem. Eng. Res. Des., 66,284 (1988) Voltimetric Mass Transfer Coefficients in Aerated Stirred Tank Reactors with Newtonian and Non-Newtonian Media

Results Use of existing data

iljLfl = 0.675 V ^ i -(K/p) ,1/2(1+11)^3/5

For Newtonian fluids 0.0008 Pas ^^<. 0.0702 Pas 0.15 m ^ A < 1.22m

For Non-Newtonian fluids 0.59<n<0.95 0.00355 Pa s" ^K^ 10.8 Pa s" 0 .15m<A<0.6m

! 0 '

-r 10

!C r^U

Roomsor. one WiUe (1973) 0 woier Ptrtz ond Sondoll (I97'i) • woter

Wong ond Shinon 11966) T woier riguereoo ond CalderDonK (1979) • woier

ChondreseRhoron and Colaeroonk<l98l} O Water Hosson ond Robinson (1977^3 A woier

/ Ntshtkowc etal. (I9BI) / • Woter -

/ V 0.5% CMC (xi« 73x10"^ Po-$)

Yogi ond Yoshido (1975) O Jelly lfi»l.3 xlO'^Pos) O Jelly i^«l23x 10** Po-$) £i. Jelly (u«702xI0'*?»$)

-50%

10' n-2 10-

^»^L°'coic. ls"'l

Comparison of volumetric mass transfer coefficient data for Newtonian fluids with the proposed correlation.

Figueredo, M. and Calderbank, P. H., 1979, Chem Eng Sci, 34:1333. Nishikawa, M., Nakamura, M., Yagi, H. and Hashimoto, K., 1981,/. Chem Eng Japan, 14:219. Perez J. F. and SandaU. 0. C, 1974, AIChEJ, 20:770. Yagi, H. and Yoshida, F., 1975, Ind Eng Chem Process Des Dev, 14:489. Robinson, C. W. and Wilke, C. R., 1973, Biotech Bioeng, 15:755


Hassan, I. T. M. and Robinson, C. W., 1977, Biotech Bioeng, 19:661. Chandrasekharan, K. and Calderbank, P. H., 1981, Chem Eng Sci, 36:819. Wong, C. W. and Shiuan, J. H., 1986, Chem Eng Commun, 43:133.

Comparison of volumetric mass transfer coefficient data for non-Newtonian fluids with the proposed correlation.

Perez, J. F. and Sandall, 0. C, 1974, AIChEl 20: 770. Yagi, H. and Yoshida, F., 1975, Ind Eng Chem Process Des Dev, 14: 489. Ranade, V. R. and Ulbrecht, J. J., 197S,AIChEl 24:796.

Notation a specific surface area, 1/m De reactor diameter, m 0 difiusivity, mVsec K consistency index in a power-law model, Pasec" ki liquid-phase mass transfer coefficient, m/sec n flow index in a power-law model, dimensionless U^ superficial gas velocity, m/sec Ut terminal velocity of bubble in firee rise, m/sec r energy dissipation rate per unit mass, W/kg ^a viscosity of continuous phase, Pasec /!«, viscosity of water, Pasec p density, kg/w? a surface tension, N/m

5.3 Gas-liquid systMns 399

Stenberg, 0. and Andersson, B., Chem Eng. Sci, 43, 719 (1988) Gas-Liquid Mass Transfer in Agitated Vessels-I. Evaluation of the Gas-Liquid Mass Transfer Coefficient from Transient-Response Measurements Stenberg, 0. and Andersson, B., Chem Eng. Sci, 43, 725 (1988) Gas-Liquid Mass Transfer in Agitated Vessels—IL Modeling of Gas-Liquid Mass Transfer


System

Vessel Type

Diameter (m) Height (m)

Liquid height (m) Volume of liquid in vessel (m ) Baffle

Number Width (m)

Impeller Type

(1)

1.56 2.35 1.56 3.0

3 0.16

Diameter 0.521 Number of impellers 1 Number of blades on impellers 6 Blade height (m) 0.104 Blade width (m) 0.13 Off-bottom clearance 0.52

Sparger Location below the impell

(2)

ahnost flat-bottomed

0.95 1.37 0.95 0.6

3 0.091

standard six-blade flat turbine

(3)

0.54 0.80 0.54 0.12

3 0.054

0.305 0.178 1 1 6 6

0.061 0.036 0.076 0.045 0.32 0.18

er below the impeller below the impeller



System (hquid volume, m )

Impeller speed (1/min) Pc/Vmrn') V^102(m/sec) ND (m/sec)

0.12

50-1,650'

2.1' 1.34-

130 -9,100 -8.3 -2.44

0.60 3.00

100-370 450'-820 115'-3,760 45- 660 0.73-4.0 0.26-2.0 0.51-1.87 0.43-l.lc J

Temperature: 25°C


Results Model (1) kLa=Pi eddB

Model (2) kia^Pi F,/(l+40.9V;)(PG/V)* -2VrfB

Values of fix and P2

Volume m

0.12 0.60 3.00 AU

Model (1) Pi

0.29510.010 0.38310.006 0.25310.010 0.34510.008

Model (2) ^ 1

0.28610.089 0.41510.008 0.34010.012 0.34810.011

Notation a ds D ki N PG Vs V PuP2 EG

gas-liquid interfacial area per unit volume of dispersion, 1/m bubble diameter, m agitator diameter, m liquid side mass transfer coefGcient, m/sec impeller speed, 1/sec power input by impeller, W gas superficial velocity, m/sec volume of dispersion, m constant volume fraction of dispersed gas hold-up

5.3 Gas-liqulcl systems 40^

Ridgway, D., Sharma, R. N. and Hanley, T. R., Chem. Eng. Sd., 44,2935 (1989) Determination of Mass Transfer Coefficients in Agitated Gas-Liquid Reactors by Instantaneous Reaction




Impeller Type: six-blade disk turbine Diameter: 0.10 m Number of impellers: 1 Number of blades on impeller: 6

Working fluids Liquid: a solution of indigo disulfonate Gas: oxygen with up to 4 wt% ozone

Experimental conditions Impeller speed: 81/sec Superficial gas velocity: 3.2 x 10" m/sec

Results Use of an instantaneous reaction between ozone and indigo disulfonate

kia = 0.048 1/sec

Notation kia volumetric mass transfer coefficient, 1/sec


Satoh, K. Shimada, H. and Yoshino, Z., Kagaku Kogaku Ronbunshu, 15,733 (1989) Gas Absorption Efficiency of Gas-Liquid Contactors with Mechanical Agitation




Impeller

6DT 6M0T-1 6MDT-2 6PB0T 6PBT

Types of impeller (Direction of rotation: from right side to left side)

Dimensions of impeUers

Impeller




Pitched Blade Disk Turbine


Sign.

6DT

6MDT-1

6MDT-2

6PBDT

6PBT

Diameter of impeller

dim)

0.08 0.10 0.12 0.15

0.08 0.10 0.15

0.08 0.10 0.12 0.15

0.10

0.08 0.10 0.15

Wide of blades b/d(-)

1/5

V2/5

(V2+l)/10

V2/5

1/5


1/4

1/4

1/4 .

1/4

1/2

Angle of blades

(degree)

90

+45 -45

+45 -90

45

45

Number of blades

(-)

6

6

6

6

6

Off-bottom clearance: H/5


Sparger Type: 20-hole nozzle Nozzle diameter: 8 mm Nozzle height: 26 mm Hole diameter: 1 mm Location: directly below the impeller


Experimental conditions Temperature 20 *0

Results

kia = hSxlO-^{Pav{^PaV+P^)}'^

^ = 1/3.0

Notation b width of impeller blade, m d diameter of impeller, m H liquid depth in vessel without aeration, m kia overall volumetric mass transfer coefficient based on liquid phase, 1/sec / length of impeller blade, m Pav aeration power input per unit volume of liquid, W/m^ Pgv agitation power input to gassed liquid per unit volume of liquid, W/m^ ^ power input correction


Arrua, L A., McCoy, B. J. and Smith, J. M., AIChE Journal, 36,1768 (1990)

Gas-Liquid Mass Transfer in Stirred Tanks


Baffle Number: 8 Width: 0.7 cm Clearance of baffle from wall:

Impeller Type: flat-bladed impeller Diameter: 5.0 cm Number of impellers: 1 Width of impeller blade(parallel to shaft): 1.0 cm

Sparger Type: single nozzle Diameter of nozzle: 0.3 cm Location: 1.0 cm directly below the

impeller Working fluids

Liquid: an aqueous solution of NazCOs Gas: He

Results *. For desorption of CO2 by He V)

o O

s a

en CO CD

2

Notation GB gas-Uquid interfacial are per unit

volume of liquid, 1/cm ki liquid side mass transfer

coefficient, cm/sec

100 200 400 600 800 1.000

Mass transfer coefficient vs. stirrer speed.


Miller, S. A., Ekstrom, A. and Foster, N. R.,/. Chem. Eng. Data, 35,125 (1990) Solubility and Mass-Transfer Coefficients for Hydrogen and Carbon Monoxide in n-Octacosane

Experimental apparatus Vessel Type: dish-bottomed Diameter: 46 mm Height: 180 mm

Impeller Type: six-blade impeller Diameter: 31.7 mm Number of impellers: 1 Number of blades on impeller: 6

Working fluids Liquid: Fischer-Tropsch slurry Gas: H2 and CO

Experimental conditions and results

Sunmiary of mass-transfer coefficients for hydrogen and carbon monoxide at various stirrer speeds and initial pressures''

gas

H2 H2 H2 H2 H2 H2 CO CO CO CO CO CO CO

stirrer, rpm

250 750

1,250 1,250 1,250 1,750

250 750

1,000 1,250 1,250 1,250 1,750

temp, K

525 525 526 526 528 526 526 525 525 526 526 528 525

ha, S-'

0.02 0.09 0.97 0.93 0.94 1.28 0.04 0.09 0.41 0.83 0.95 1.08 1.50

ft, MPa

2.19 2.19 1.52 2.13 3.05 2.20 2.21 2.21 2.18 1.15 2.08 3.20 2.18

P^, MPa

2.03 2.01 1.40 1.95 2.80 2.02 2.05 2.00 1.98 1.04 1.88 2.90 1.98

CL, mol/^

0.081 0.091 0.063 0.091 0.129 0.088 0.081 0.106 0.101 0.053 0.101 0.151 0.101

' The equilibrium pressures and concentrations of material dissolved in the liquid phase are also given.

The effect of stirrer speed on the mass-transfer coefficients was found to be significant between 250 and 1,750 rpm.

Notation CL hquid-phase concentration, mol/£ kio mass-transfer coefficient, 1/sec P pressure, MPa

Subscripts 0 time=0 eg equilibrium


Panja, N. C. and Rao, D. E, lyans. Instn. Chem. Engrs., 69, P ^ A, 302 (1991)

Experimental Studies on ki/t in a Mechanically Agitated Contactor

from Transient Electrical Conductivity Response Data


System

Vessel Diameter (m)


Impeller Type

Diameter (m) Number of impellers Number of blades on impellers Off-bottom clearance

(1) (2) (3)

0.164 0.295 0.41

4 4 4 0.0164 0.0295 0.041

6-flat blade disk mounted turbine

0.074 0.15 0.15 1 1 1 6 6 6

r / 3 r / 3 T/3

Working fluids Liquid: distilled water Gas: CO2

Experimental conditions Rotational speed of impeller:

System

Rotational speed of impeller (rpm)

(1) (2)

200-600 150-300

(3)

150-300

Results For 70 < (Pg/V) < 2,000 watt/m^ and 1.3 x 10" < V, < 7.0 x 10" m/sec kLa=4,193 X10-2 (p^/v)0.495 - 0.75

Notation kia liquid side volumetric mass transfer coefficient, 1/sec Pg power required for rotating the impeller with gas sparging, W T vessel diameter, m V liquid contacting volume in stirred vessel, m Vs superficial gas velocity, m/sec

5.3 Gas-liquifl systems 407

Oyevaar, M. H., Bos, R. and Westerterp, K. R., Chem. Eng. 5a., 46,1217 (1991) Interfacial Areas and Gas Hold-Ups in Gas-Liquid Contactors at Elevated Pressures firom 0.1 to 8.0 MPa



Impeller Type: (1) (2) a six-bladed disc turbine Diameter: (1) A/Z>=0.4 (2) A/Z)=0.5 Number of impellers: (1) (2) 1 Number of blades on impeller: (1) (2) 6

Sparger Type: a single tube Diameter of tube: 3 or 8 mm Location: located centrally below the impeller


Liquid: aqueous diethanol amine Gas: N2 and N2-CO2 mixtures (containing ca 1

V0l%0fC02) Experimental conditions

Pressure: up to 8.0 MPa Superficial gas velocity: 1,5, and 10 cm/sec Impeller speed: 8.3,16.7, and 25.0 rps

Results Up to 1.2 MPa

600

400

200

iO A B

• 0yrvava»KI9M)d,«3fiini A OytvMrctd(l9H)rofDttspUK O ptCKIM MiOjr

nz :JU.

0.0 0.4 O.t .2 1.6 j ;

"MPa

2.0

Comparison between the inteitadal area of the present study at VG=1.0 cm/s and N=16.7 rps with those of Oyevaar et oL (1988): Di/D=OA and di= 3mm.

lAn

lUUU

100

600

400

200

0

800

600

400

200

0

800

600

400

200

.1 V^» 1.0 GBI

» - • • — ^ • _ » — — •

II 1 i^ii i 1 -J* ' *

1 v^« 3.000^

—•——•

—. - ^ * •

am iiLi 1 1 tmkm * * |vc-5.0c«fk|

. •-• •^^

• t . 1 • 1

N-23.0 rps 1

N-16.7ip«

N - 8 J rps

N»25.0fps

N» 16.7 rps

—^. _i . j N»2S.0rpf 1

N-16.7 rps

N«83rps

* 1 .

0,0 0.4 0.8 U 1.6 2.0 P

biteifacial area vs reactor pressure, A7/>=0.4 and d,=3 mm.

408

Upto8.0MPa

aooo

Chapter 5. Mass transter

2000 1/to

1000

v-»a.Oaa^ c ^ K«25J0ipf

\ N-I6.7rps

/ / . N-t.3ips

0 2 4 6 I 10 12

P

Intertacial area vs reactor pressure at t/c=3.0 cm/s: Di/D^OA and flf,= 3mm.

l/m

ISOO

1200

900

600

300

0

1200

900

eoo

300

0

1200 r

900

600

300

0

, N - 16.7 rpi

N • S.3 rps

v_«3.0cm^ G .,N«25.0rps

. / , N • 16.7 rps

t~* • • . N . S.3 rps

v^-S.Ocm^ ^ N « 23.0 rps

^. N « 16.7 fps

^. N « 8.3 ips

0 2 4 6 8 10 12 T MP*"""*

Interfadal area vs reactor pressure: A/Z>=0.5 and rf,=8 m m .

1000

I 800 h

400h

200

0

800

600 I-

400

0

800

600

400h

200

0

'l.Ocm^

^^ . N-25.0 rps

^«N-16.7n» . •N-8.3 ips

wtmJ» v-«3.0c«^

^^N-23.0fps

_ , N • 16.7 tf%

2001 . . . , ^ , N . 8.3 ips

I 1 i iL

v.»S.0cm%

^ N-25.0fps

L ^ ^ ^ — i * ^ * ^ ^ N • 16.7 rpi

L t - ^ ^ * . N - 8 3 r p s

10 12

P "MP?-

Interfacial area vs reactor pressure: Di/D=OA and </,=8 mm.

(1) The increase in the interfacial area with increasing reactor perssure is larger for higher superficial gas velocities.

(2) The increase in the interfacial area with increasing reactor pressure becomes considerably smaller for the gas inlet di=S nmi.

(3) The relative increase in the interfacial area dp/aatm with increasing reactor pressure is the same for agitation rates above and below the critical agitation rate No.

(4) The relative increase in the inter&cial area dp/aatm with increasing reactor pressure is the same for both impellers of defferent diameter A.


Notation a specific interfacial area, mVm^ dispersion di gas inlet diameter, m D vessel diameter, m Di impeller diameter, m N agitation rate, 1/sec No critical agitation rate, 1/sec P pressure, Pa V superficial velocity based on the empty cross-sectional area of the vessel, m/sec

Subscript G gas

4X0 Chapter 5. Mass transfsr

Chang, M.-Y. and Morsi. B. I., Chem. Eng. Set., 46,2639 (1991) Mass Transfer Characteristics of Gases in Aqueous and Organic Liquids at Elevated Pressures and Temperatures in Agitated Reactors

Experimental apparatus Vessel Type: dish-bottomed Diameter: T Volume: 3.954 X 10-3 m

Liquid contained Volume of liquid in vessel: 2.5 x lO'^ m

Baffle Number: 4 Width: 0.1 T Height: 0.229 m

Impeller Type: six flat-blade turbine Diameter: A Number of impellers: 1 Number of blades on impeller: 6

Working fluids Liquid: ;i-hexane and water Gas: Nz and CH4

Experimental conditions Temperature: 328-378 K Pressure: 1—50 bar Mixing speed: 13.3-20.0 Hz (800-1,200 rpm)

Results Sh = 2.39 X10-" Eu^^ We""^ Sc^ Re*"^

which is valid for the following ranges: 560 <Eu< 10,960 760 <We< 7,410 14 < Sc < 128

102,400 <Re< 282,600 Notation

Di impeller diameter, m DA diffiisivity coefficient, mVsec Eu modified Euler number, PmlipijD^N^),

dimensionless ki liquid-side mass transfer coefficient, m/sec kia volumetric liquid-side mass transfer coefficient,

1/sec N mixing speed, Hz or 1/sec Pi initial pressure, bar PF final equilibrium pressure, bar Pm gas mean pressure, (Pi,/ + P\,F)I2, bar Re Reynolds number,NpiDi'l\iL, dimensionless Sc Schmidt number, PLLKPLDA dimensionless Sh Sherwood number, {kLa)D?IDA, dimensionless

T We

P ^ a

vessel diameter, m Weber number, piN^D^/a, dimensionless density, kg/m^ viscosity, kg/msec suiface tension, N/m

Subscripts F G L 1

final state gas phase liquid phase component 1

5.3 Gas-liquid systems 4X1

Chang, M.-Y., Eiras, J. G. and Morsi. B. I., Chem. Eng. Process., 29,49 (1991) Mass Transfer Characteristics of Gases in n-Hexane at Elevated Pressures and Temperatures in Agitated Reactors

Experimental apparatus Vessel Type: gas-inducing type autoclave Volume: 3.954 X10-3 m

Liquid contained Volume of liquid in vessel: 2.5 x 10" m

Baffle Number: 4 Width: 0.1 T Height: 0.229 m

Impeller Type: six flat-blade turbine Number of impellers: 1 Number of blades on impeller: 6

Sparger Diameter of holes: 0.0015 m Location: the end of the impeller shaft

Working fluids Liquid: »-hexane Gas:H2,N2andCH4

Experimental conditions Pressure: 1—50 bar Temperature: 328-378 K Mixing speed: 800-1,200 rpm

Results

( z.fl)cH4 < (kiahz < (kLa)n2 Dimensional analysis was employed to obtain a correlation for the kia values in terms of different

variables such as AP, N, pu o, and DA- The analysis led to the following correlation:

Sh = 6.67 X 10^ £w-i° We^"" Sc""' Re'^^

which is valid in the ranges

177 <Eu< 2,232 1,913 <We< 7,239

8.6 <Sc< 28.5 146,000 <i?f< 290,000


10"

10

10"

10"

] • Hydrogen

j £ Nitrogen

] • Methane

1 : J c

y'/y'* 1 -''// i y'y •'' \'/ ,•*

7^ +30% y/y

,p\'''

i 30%

10 10" 10 ' 10 '

KLS (exp), 1/s

Comparison of experimental and predicted kia values for Hz, Nz, and CH4 in n-hexane.

Notation volumetric gas-liquid interfadal are, 1/m diffiisivity coefficient, mVsec impeller diameter, m liquid-side mass transfer coefficient, m/sec volumetric liquid-side mass transfer coefficient, 1/sec mixing speed, 1/min tank diameter, m pressure drop during gas absorption, bar viscosity, kg/msec density, kg/m^ surface tension, kg/sec^ Euler number, AP/(pxi),W^), dimensionless Reynolds number, NPLD?I^L, dimensionless Schmidt number, ^I(PLDA\ dimensionless Sherwood number, ihLa)D?IDAf dimensionless Weber number, piN^D^Ia, dimensionless

a DA Di ki kia N T AP

P a Eu Re Sc Sh We

Subscript G gas phase L liquid phase

5.3 Gas-liquid systems 4^3

Linek, V, Sinkule, J. and Benes, P., Chem. Eng. Sci, 47,3885 (1992) Critical Assessment of The Dynamic Double-Response Method for Measuring ha : Experimental Elimination of Dispersion Effects


Liquid contained Height: 0.29 m Volume of liquid in vessel: 0.0182 m^

Baffle Number 4 Width: 0.029 m

Impeller Type: six-blade turbine Diameter: T/3 Number of impellers: 1 Number of blades on impeUer: 6 Off-bottom clearance: 0.1 m

Working fluids Liquid: distilled water, an aqueous solution of 0.5 M Na2S04, and an aqueous solution

of 0.5 M Na2S04 with an addition of 1 wt% CMC (carbomethyl cellulose) Gas: air

Experimental conditions Impeller speed: 4.17—17.51/sec Superficial gas velocity: 2.12—4.24 mm/sec Temperature: 20°C

Results For water:

For 0.5 M Na2S04 solution:

kLa = 3,11 xlO-U^'^vJ"-^

For l%wt CMC in 0.5 M Na2S04 solution:

ife/:fl = 3.95 X 10-* ^ 1 " «;,«•*

Notation e power dissipated in unit volume of hquid phase, W/m^ kia specific mass transfer coefficient, 1/sec T tank diameter, m Vs superficial gas velocity, m/sec

414 Chaptor 5. Mass tninsfsr

Nocentini, M., Fajner, G., Pasquali, G. and Megelli, E, Ind. Eng.Chem. Res., 32,19 (1993) Gas-Liquid Mass Transfer and Holdup in Vessels Stirred with Multiple Rushton Turbines: Water and Water-Glycerol Solutions

Experimental apparatus Vessel Type: flat-bottomed Diameter: 23.2 cm Height: 105 cm


Baffle Numben4 Width: 2.32 cm

Impeller Type: six-bladed Rushton turbine Diameter: 7.73 cm Number of impeUers: 4 Number of blades on impeller: 6 Length and width of impeller blade:

D:L:W:d^20:5:4:l5 Positions of impellers

Distance between bottom and the first impeller: 11.5 cm Distance between the first and the second impeller: 23 cm Distance between the second and the third impeller 23 cm Distance between the third and the forth impeller: 23 cm

Sparger Type: a ring-type sparger Location: below the bottom turbine


Liquid

Distilled water Aqueous solutions of glycerol

45wt% 65wt% 75wt% 83wt%

Viscosity (mPa-s)

0.9

3.7 14 29 62

Gas: water-saturated air

Experimental conditions Temperature: room temperature Air flow rate: 0.1—0.7 wm

5.3 Gas-liquid systems 4^5

Results For air-water system

fefl = 1.5x10 [Tj ' For aerated aqueous glycerol solutions

Notation a surface area per unit volume of dispersion, 1/m Ci constant d disk diameter, m D turbine diameter, m ki mass-transfer coefficient (liquid side), m/sec L blade length, m Pg gassed power consumption, W Us superficial gas velocity, m/sec V volume of the hquid in the vessel, m W blade width, m /z dynamic viscosity of t h e liquid. Fa-sec ju«», 20 reference viscosity (water at 20°C), Pasec


Linek, V, Benes, R, Sinkule, J. and Moucha, T, Chetn. Eng. Sd., 48,1593 (1993) Non-Ideal Pressure Step Method for kia Measurement



Impeller Type: six-blade Rushton turbine Diameter: T/3 Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 0.1 m

Working fluids Liquid: distilled water and an aqueous solution of 0.5 M Na2S04 Gas: oxygen and air

Experimental conditions Gas velocity: for oxygen absorption: 2.12 x 10" m/sec

for air absorption: 4.24 x 10" m/sec Results

For water:

jfeifl = 3.84 X10-3 ^^"t;, *

For 0.5 M Na2S04 solution:

kLa = 3.11 xlOW^Vs'''

Notation a interfadal area per unit volume of liquids, 1/m e power dissipated in unit volume of the liquid phase, W/m^ ki liquid-side mass transfer coefficient of oxygen, m/sec T vessel diameter, m Vs superficial gas velocity, m/sec


Baird, M. H. I., Rao, N. V R. and Shen, Z. J., Can J. ofChem. Eng., 71,195 (1993) Oxygen Absorption in a Baffled Tank Agitated by Delta Paddle Impeller

Experimental apparatus Vessel Type: flat-bottomed Diameter: 30 cm Height: 30 cm Volume: 27 i

Impeller Type: paddle impeller Diameter: 20 cm Number of impellers: 1

\ 58 A^3B*

(b)

(0

(d)

-^ 17 Impeller geometries, with dimensions shown in mm. Side views except for (b). (a) Standard geometry, 20 cm diameter; (b) Swept forward (plan view); (c) Serrated upper edge; (d) Distributor tube added.

Off-bottom clearance: 7.5 cm


Sparger Type: single-hole nozzle Diameter of hole: 6 mm Location: 1 cm beneath the center of the impeller

Working fluids and their physical properties Liquid: water

Physical properties of liquid used (20°C)

Dendity, kg/m^ Viscosity, mPasec Suiface tension, mN/m

Gas: air Results

Water

997 1.00

72.0

Mineral oil

875 10.85 32.9

kpa = 0.0060 (P/F)°-^ (7c)°-'*

Notation a specific interfacial area, 1/sec kp mass transfer coefficient, m/sec P power dissipation, W V liquid volume, m' VG superficial gas velocity, m/sec


Tecante, A. and Choplin, L., Can. J. ofChem. Eng., 71,859 (1993) Gas-Liquid Mass Transfer in Non-Newtonian Fluids in a Tank Stirred with a Helical Ribbon Screw Impeller

Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.210 m Working volume: 8 £

Impeller Type: helical ribbon screw (HRS) Diameter: 185 nmi Number of impellers: 1 Gap between the HRS and the gas sparger: 5 nrni Gap between the HRS and the vessel bottom: 20 mm Dimensions and geometric ratios of the HRS impeller:

Impeller dimensions (mm)

d

185

H

185

w

20

^s

25

s

92.5

Geometric ratios

D/d

1.14

w/d

0.11

d/s

2

Wg/W

J2B_\

Working fluids and their physical properties Gas: air Liquid: aqueous solutions of polyacryl amide (PAA), sodium carboxymethyl cellulose

(CMC) and xanthan (XTN)


Liquid rheological properties at 25''C

Fluid'

XTNl XTN2 XTN3 XTN5 PAAl PAA5 CMCl CMC 2 CMC 3 CMC 5

Cone, (kg/w?)

1 2 3 5 1 5 1 2 3 5

/^CPas")

75.6 416.1

1,059.3 3,116.0

149.1 591.9 23.8 46.7 70.6

190.0

n

0.56 0.39 0.34 0.19 0.54 0.53 0.87 0.88 0.88 0.84

'XTN solutions contained 1 kg/m^ of NaCl to stabilize their viscosity. All solutions contained 100 mg/L of sodium azide to prevent microbial contamination and were stored at 4* 0.

Experimental conditions Air flow rate: 0.133,0.208, and 0.258 ^/sec Agitation speed: 100,150,200,250, and 300 rpm Temperature: 25 ± 0.5°C

Results For PAA solutions

KLO = 0.00410 (A/l^J°-2i ^ 031 ^ -0.40

For CMC solutions

Kia = 0.00342 (P^/V^)"-'" w/-^ TI^"'""

For XTN solutions

KLO = 0.00125 (Pg/VL)'''^' uj"-^ 77«- *3

Notation K consistency index, Pa(secy KLO volumetric oxygen mass transfer coefficient, 1/sec n flow behavior index Pg p o w e r input under aeration, W Ug superficial gas velocity, m/sec VL Liquid volume, m^ T]a apparent viscosity Pasec


Stegeman, D., Ket, R J., Kolk, H. A., Bolk, J. W, Knop, R A. and Westerterp, K. R., Ind. Eng. Chem. Res., 34,59 (1995) Interfacial Area and Gas Holdup in an Agitated Gas-Liquid Reactor under Pressure

Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.156 m Height: 0.312 m Volume: 4.7 i



Impeller Type: a standard six-blade disk turbine Diameter: 0.052 m Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): di/b Width of impeller blade (parallel to shaft): di/4 Off-bottom clearance 0.052 m

Sparger Type: a simple tube Diameter of hole: 6 or 10 nmi Location: centrally below the impeller

Working fluids and their physical properties Liquid: see table

Physical properties of the used liquid phases

liquid mixture

DEA concn (mol L'O viscosity (Pa s) density (kg m~ )

DEA: diethanolamine

DEA/water

1.5 1.45x10-3

1,017

DEA/water/40% ETG

1.25 4.0x10-3

1,065

DEA/water/60% ETG

1.3 8.4x10-3

1,088

Gas: a mixture of CO2 and N2 (3 vol% of CO2 in 99.9% pure N2) Experimental conditions

Temperature: 298 K Pressure: up to 6.6 MPa

422

Results (1) Influence of the agitation rate on the interfacial area

Chapter 5. Mass tninsfar

N(s-') 8.3

12.5 15 16.7 18.3 20.8 25

flCmVm^)

100 107 185 240 290 370 500

(2) Influence of the pressure on the interfacial area

600

400

200

n

. •

...m

• . . .

• • ^

k^ ^

«

'A

•

20.8 12.5

1

•••••••

•

...•

4

•

" W

N [1/sl 18.3 ~ T ^ 10.0 - K -

1

•

•

A

•

18.7 8.3

L — _

£/««

- •

I

D.Olin/s

- 15.0

•

•

'A""\

•

0 2 4 6 P [MPa]

Interfacial area vs system pressure for f«c=0.01 m/s at several agitation rates, for 771=1.4 mPas.

600

400

POO

n

-"£'•£' m

_•

M—

20.8 12.5

• ...«

,..•. • A

•

. ^ - i c

-•••

L .

N 11/8) 18.3 - A —

• 10 - H -

•

•

. j g L

J

18.7 8 ^

•

•. • •

Pi

1

< / « -

' •

D.02nn/t

- 16

1 —

•

•A—

• •

•« M •

0 2 4 6

Interbdal area vs system pressure for UG=0.02 m/s at several agitation rates, for i}2,=1.4 mPas.


These figures show a decrease of the interfacial area at low pressures and an increase at higher pressures. The decrease is more pronounced at lower gas velocities and high agitation rates.

Notation a specific interfacial area, mVm^ di impeller diameter, m N impeUer rotational speed, 1/sec P absolute pressure in the reactor. Pa UG superficial gas velocity based on the empty cross-sectional area of the vessel, m/sec r]L kinematic viscosity of Uquid, Pasec


Moucha, T, Linek, V and Sinkule, J., Tyans. Instn. Chem. Engrs., 73, Part A, 286 (1995) Measurement of kija in Multiple-Impeller Vessels with Significant Axial Dispersion in Both Phases


Liquid contained Height: 0.76 m Volume of liquid in vessel: 20.8 £


Impeller Type: Rushton turbine Diameter: 0.063 m Number of impellers: 4 Number of blades on impeller 6 Length and width of impeller: d: z: w: b = 20:5:4: IS Positions of impellers

Distance between bottom and the first impeller: d Distance between the first and the second impeller: D Distance between the second and the third impeller: D Distance between the third and the forth impeller: D

Working fluids Liquid: distilled water and 0.5 M aqueous solution of Na2S04 Gas: air, nitrogen and pure oxygen

Experimental conditions Superficial velocity: 2.12,4.24, and 8.48 mm/sec Impeller frequency: 5.5—18.83 1/sec

Results

For water €1=0.0377 N^^'v:''^'^

M l = 0.0146 rf"'t;?-^ ^2-4= 0.104 iV^^'t;;^ fefl2~4= 0.0177 ^2^ t;?""

For0.5MNa2SO4

ei= 0.0177 7V^

fofli= 5.79x10"

- 0 ^ 7 Vs

4^1^^,0.439

^2-4= 0.090 TV^ 't;;'-^

Notation b diameter of impeller disk, m d impeller diameter, m D vessel diameter, m ei specific power dissipated in bottom

stage, W/m^ 2-4 specific power dissipated in upper

stages, W/m^

kiai

w

Vs

z

volumetric oxygen transfer coefficient in bottom stage, 1/sec average volumetric oxygen transfer coefficient in upper stage, 1/sec impeller width, m superficial gas velocity, m/sec impeller length, m


Linek, V, Moucha, T. and Sinkule, J., Chem. Eng. Sci., 51,3203 (1996) Gas-Liquid Mass Transfer in Vessels Stirred with Multiple Impellers-I. Gas-Liquid Mass Transfer Characteristics in Individual Stages


Liquid contained Height: (1) IT (2) 2T (3) 37 (4) 47 Volume of liquid in vessel: (1) 0.00517 (2) 0.00517 x 2 (3) 0.00517 x 3 (4) 0.00517 x 4 m'


Impeller Type: a standard Rushton turbine Diameter: 7/3 Number of impellers: (1) 1 (2) 2 (3) 3 (4) 4 Number of blades on impeller: (1)~(4) 6 Length and width of impeller blade: Z):L:M;:ft=20:5:4:15 Positions of impellers:

Distance between bottom and first impeller: D Distance between first and second impeller: 7 Distance between second and third impeller: 7 Distance between third and forth impeller: 7


Working fluids Liquid: distilled water and 0.5 M Na2S04 solution Gas: air, nitrogen and pure oxygen

Experimental conditions Superficial gas velocity: 2.12, 4.24 and 8.48 mm/sec Agitator speed: 5.5—18.8 1/sec Temperature: 20X

Measurement technique Dynamic pressure method

Results For water For 0.5 M Na2S04

ife Ji =6.46x10-' rf-^'^i^*^ fefli = 1.29xl0-*rf-^t;f '

ifeLfl2~4 =8.61x10-' el^v"^ ife fl2-4 =5.25xlO-'^]~'It^f'^ {e{)a^ = 0.0377 N'-'^i;:'^ («,)^ = 0.177 N^vS^^'

( 2 4 W = 0.104 N^^v:'"^ ( 2-4 W = 0.090 N^^'v:"^ ei=(ei)agii-^VsPLg


Notation b d iameter of impeller disc, m D d iameter of agitator, m ei total power input per unit volume of liquid in stage i, W/m^ (edagii power input by agitator pe r unit volume of liquid in s tage /, W/m^ kiOi volumetric mass transfer coefficient per unit volume of liquid in stage i, 1/sec L length of impeller blade, m N agitator speed, 1/sec T d iameter of vessel , m Vs superficial gas velocity, m / s e c w width of impeller blade, m Pi liquid density, kg/w?


Barigou, M. and Greaves, M., lyans. Instn, Chem. En^s., 74, Part A, 397 (1996) Gas Holdup and Interfacial Area Distributions in a Mechanically Agitated Gas-Liquid Contactor



Baffle Number: 4

Impeller Type: standard Rushton turbine Diameter: 0.333 m Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 0.25 m

Working fluids and their physical properties Liquid: deionized water

(density = 999 kg/m ; viscosity = 1.00 mPasec; surface tension = 70.99 m-N/m) Gas: air

Experimental conditions Air flow rate: 0.00164,0.00438 and 0.00687 mVsec Impeller speed: 100—385 rpm


Restdts

\a3o a = 186f|-l C/r

Notation a total interfacial area, 1/m N impeller speed, 1/sec Pg gasses power input, W Q gas flow rate, mVsec ^5 superficial gas velocity, m/sec


5.4 Solid-liquid-gas systems

Joosten, G. E. H., Schilder, J. G. M. and Janssen, J. J., Chem. Eng. Sci., 32,563 (1977) The Influence of Suspended Solid Material on the Gas-Liquid Mass Transfer in Stirred Gas-Liquid Contactors



Number: 4 Width: 1.25 cm

Impeller Tjrpe: a standard Rushton turbine Diameter: Z?/3 Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: D/3

Sparger Type: three small orifices in the bottom of the vessel

Working fluids and solids Liquid: kerosine SoUd: polypropylene, sugar and glass beads Gas: He and N2

Results

VvT

\0^

' SUPERFCIAL GftS VELOCmr • LZ.tan/s ' D4.5 an/$ • OB.O cm/$ . - R E F - v ^ . /6

2-5 on/i Go ^ 0

oqS/ ^ t/ t^

I t ! 1 ' l ! J L — L - l • ' • ' > .

10-^ TOTAL PJi/SR ?tR UNIT VOUJ^kW/fr^

REF Dierendock, L. L. van, Thesis, Enchede (1970) The values of ki/i in clear liquid as a function of the total power input in the

5.4 Solid-liquM-gas systems 429

L G;.iSS 3£OS 3£^m k GLASS BEADS SS^m Z SI/3AR 74-C5iim • =>Xr»RCPYLENE 53-105 Anrj O POLYPROPYLENE 250/xm

0.04

0.02!

oa

STIRRING POWER = 15 kW/m^ SUPERFICIAL GAS VELOCITY =Z5 cm/s

10 20 30 40 SOLIDS CONCENTRATION .•/•v

The volumetric mass-transfer coefficient as a function of the volume fraction of solids in the slurry.

D SUGAR 74-105 ;xm t GLASS BEADS 53 AND 88 ^ ^ o POLYPROPYLENE 53-105 AND 250 ;im

0.4 r

0 2

0.1

OXK

QOZh

0.0I»- J L-L 1 2 4 6 8 10 20 40 60

RELATIVE VISCOSITY

The volumetric mass-transfer coefficient as a function of the relative viscosity of the slurry.

Notation a gas-liquid interlacial area per unit volume of liquid+solid, 1/m D diameter of vessel, m kh liquid-side mass transfer coefficient, m/sec


Chandrasekaran, K. and Sharma, M. M., Chem. Eng. Sd., 32,669 (1977) Absorption of Oxygen in Aqueous Solutions of Sodium Sulfide in the Presence of Activated Carbon as Catalyst


Baffle Number: 4

Impeller Type: six bladed turbine Diameter: 6 cm Number of impellers: 1 Number of blades on impeller: 6

Working fluids, solid and their physical properties Liquid: aqueous solutions of sodium sulfide Solid: activated carbon average particle size well below 100 fim Gas: oxygen

Experimental conditions Temperature: 70 *0 Agitation speed: 800-2,0001/min Concentration of activated carbon: 0.07—2.0 % w/w Concentration of sodium sulfide: 0.03—0.17 moMi

Results (1) The rate of absorption of oxygen in 0.15 M NaaS solution containing 0.07 and 0.20 % w/w of

activated carbon was found to increase with an increase in the speed of agitation. (2) The value oikua increases significantly in the presence of small amounts of fine activated

carbon particles.

5.4 Solid-liquid-gas systems 432

Uchida, S., Moriguchi, H., Maejima, H., Koide, K. and Kageyama, S., Can. J. ofChem. Eng., 56,690 (1978) Absorption of Sulfur Dioxide into Limestone Slurry in a Stirred Tank Reactor


Liquid contained Volume of liquid in vessel: 1,500 cm^

Baffle Number: 8 Width :10 mm

Impeller Type: eight-blade impeller Diameter: 70 mm Number of impellers: 2 Number of blades on impeller: 8

Working fluids solid experimental conditions and results Gas:C02andS02 Liquid: water and NaOH solution Solid: limestone Mass transfer characteristics of stirred tank reactor at 20°C (1) A values for C02-NaOH solution

n (rpm) 91 150

A (cm ) 145 160

241

180

391

245

(2) ki values for O2-H2O and CO2-H2O

n (rpm) 91 150

O2-H2O 1.42 2.20 CO2-H2O 1.32 1.85

241

3.10 2.60

391

6.50 5.40

(3) kc values for SO2-O.67 mol/£ NaOH solution

n (rpm) 91 150

kc 2.25 2.30

241

3.00

391

3.90

Notation A gas-liquid interfacial area, cm^ kc gas film mass transfer coefficient, ^mol/m^secPa ki liquid film mass transfer coefficient without chemical reaction, m/sec n impeller speed, 1/min


Miyachi, M., Iguchi, A., Uchida, S. and Koide, K., Can. J. Chem. Eng., 59,640 (1981) Effect of Solid Particles in Liquid-Phase on Liquid-Side Mass Transfer Coefficient



Impeller Type: eight-blade impeller Diameter: 70 mm Number of impellers: 2 Number of blades on impeller: 8

Working fluids and their physical properties Liquid: water Solid: CaCOs dp=h20-l0 im Gas: oxygen

Experimental conditions Impeller speed in gas phase: 13.3 1/sec Impeller speed in Uquid phase: 2.551/sec Temperature: 293 K Slurry (water and CaCOs): 0.2-10 wt%

Results The values of volumetric mass transfer coefficient, ha, initially decrease and increase with

increasing slurry concentration The values ofkia are about 2.2 x 10"* 1/sec

5.4 Solid-llquid-gas systems 433

Deimling, A., Karandikar, B. M., Shah, Y. T. and Can, N. L, Chem. Eng.J.y 29, 127 (1984) Solubility and Mass Transfer of CO and H2 in Fischer-Tropsh Liquids and Slurries

Experimental apparatus Vessel Type: flat-bottomed autoclave Diameter: 0.101 m Height: 0.267 m


Impeller Type: inclined blade type Diameter: (a) 0.057 (b) 0.057 (c) 0.057 m Number of impellers: 3 Off-bottom clearance: (a) 0.034 (b) 0.091 (c) 0.057 m (off-top clearance)

Sparger The gas is entrained into the hquid by two stirrers (a) and (b)

Workkig fluids solids and their physical properties Liquid: Fischer-Tropsch liquids Gas: CO2 and H2 Solid: glass beads (size=125~177 \xm; p =2,600 kg/m^)

Properties of the liquids used is this investigation

Solvent

FTHght FT medium FT heavy"

Carbon number range

Ce-Cii

C12-C21

^C22

Average molecular

weight (kg kmol"*)

113.9 201.2 367.5

Surface tension at 298 K (mNm *)

23 26 -

Density (kg m "

298 K

723.0 776.2 820.3

373 K

713.5 749.7 778.3

^ at the following temperatures

423 K

681.6 733.1 745.0

473 K 523 K

-715.7 702.0 705.0 680.0

'Melting point, 353 K at atmospheric perssiure.

Experimental conditions Temperature 373-523 K Pressure: 1—4 MPa Stirrer speed: 800-1,1001/min

434

Results

Chapter 5. Mass transffar

0 10

10

r - T HEAVY

A""^ f^

- » 1 • -

o / \ f

. / •

F-T HEAVY

| \ o \ o \

| \ o \ °N

I \ 1 0 1 2 3 4 5 0

Pj (MPa) 20 40

Solids Concn (wlX)

(a) (b)

0 1 2 3 4 5 0 20 40 Pj [MPa] Solids Concn [ w t x ]

(a) (b)

CO

Volumetric mass transfer coefficient kia for CO and H2 in the FT heavy fraction as a function of (a) pressure (0 ,0 wt.% solids; • , 7.5 wt.% solids; <•, 15.0 wt.% solids; • , 30.0 wt% solids) and (b) solids concentration (O, about 1.0 MPa; A, about 2.2 MPa; D, about 3.4 MPa) (stirrer speed, 800 rev min"*).

Volumetric mass transfer coefficient kia for CO and H2 in the FT heavy fraction as a function of (a) pressure (0 ,0 wt.% solids; • , 7.5 wt.% solids; <>, 15.0 wt.% solids; • , 30.0 wt.% solids) and (b) solids concentration (O, about 1.0 MPa; A , about 2.2 MPa; D, about 3.4 MPa) (stirrer speed, 1,000 rev min"*).

Notation kia volumetric mass transfer coefficient, 1/sec Pi pressure at equilibrium state after absorption, MPa

5 ^ Solid-liquid-fias systems 435

Marrone, G. M. and Kirwan, D. J., AIChE Journal, 32,523 (1986) Mass Transfer to Suspended Particles in Gas-Liquid Agitated Systems



Impeller Type: six-blade disk turbine Diameter: 6.4 cm Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 6.4 cm

Working fluids and solids Liquid: aqueous NaOH solution Solid: ion exchange resins Gas: N2

Results

5/j = 2 + 0.36i? /''Sc /3

Rep^dp'^'e'^Vv 2.0

o

1.0

.8

1 0 P rrm «0

0 0.35 < Pg / P j s 0.7

• O<P0/PjSO.3S

1 # p /P«.« 1 ft • ^Q^^J

y nr

III 5

m

^ * ^ O^^B

^ t

' 1

1 1 .3 .4 .5.6.7.8^10 2X> 4.0 8X> 8J0

R8p«(€dp*y^' / i .

Correlation of solid-liquid mass transfer in gassed, agitated vessels.

Notation dp particle diameter, m PG power input to fluid from gas, W PT total power input to fluid from gas, W Sc Schmidt number, dimensionless Sh Sherwood number, dimensionless e power dissipated per unit mass of liquid, mVsec^ V kinematic viscosity of liquid, mVsec


Bartos, T. M. and Satterfield, C. K.AIChE Journal, 32,773 (1986) Effects of Finely Divided Solids on Mass Transfer between a Gas and an Organic Liquid

Experimental apparatus Vessel Type: dish-bottomed autoclave Diameter: 7.6 cm


Impeller Type: (1) propeller (2) six-bladed turbine Diameter: (1) 3.8 (2) 3.2 cm Number of impellers: 2 Number of blades on impeller: (1) 3, (2) 6

Sparger Gas was spaiged into the vessel via an inlet tube mounted flush to the bottom (0.10 cm ID)

Working fluids, solids and their physical properties For the measurement of interfecial area

Gas: CO2+N2 Solid: polypropylene, glass, barium glass, coated glass and fillite (glassy alumina-sihca fly ash) Liquid: solution of 90% toluene and 10% isopropanol (the solution contains cyclohexylamine)

For the measurement of mass transfer coefficient Gas: Desorption of helium by nitrogen Solid: the same as above Liquid: the same as above

Physical properties of solids

Particle Composition

Polypropylene Polytetralluoroethylene Soda-lime silica glass

Barium titanate glass

Soda-lime silica glass Silicone-coated soda-lime silica

glass Glassy alumina-silica fly ash

(fillite)

Supplier

Polysdences Polysciences Potters bidustries

Potters Industries

Ferro Corp. Ferro Corp.

Fillite, Inc.

Designation

6,068,4,342 1,344 P-004, P-006, P-007, P-008 H-002,H-003, H-005, H-008 MS-M MS-ML-W

200/7

Shape

granular flat spherical

spherical

spherical spherical

spherical

Density g/mL

1.0 2.0 2.5

4.5

2.5 2.5

0.7

Size Range micron

30-180 350-550 30-220

30-220

30-180 30-120

30-180

Experimental conditions Gas flow rate: 35 m^ (STP)/sec (%=0.75 cm/sec) Liquid plus slurry volume: 400 m^ Stirring speed: 350—1,750 rpm Particle concentration: 0.7—4.5 g/m^

5.4 Solid-liquid-gas systoms 437

Results

0 200 400 600 800 1000 1200 STIRRING SPEED, RPM

Inteifacial area, a, varies lineariy with stirring speed at low values ofR; no solids present. Calculated value of a depends upon assumed gas RTD.

'm 0.20

"1 I I 1 i I I I r

J I I L 0 200 400 600 BOO 1000 1200 1400 1600 1800

STIRRING SPEED. RPM

Overall mass transfer coefficient varies linearly with stirring speed; no solids present

160

1 4 0

S

< UJ c 120 <

1 0 0

-,

r - • \

•

- •

-

J

— 1 —

•

• ^ •

1

— P

t

L

1 1

f pelypropyltnt

• g lo t t

• QlOtt

# borium glott

A coattd 9I0M

• f i l l i t t

• •

L A

T gm/ml

i.O

2 .5

2 . 5

4 .5

2 . 5

O.T

L

6,fim

100 -J

70

140 4

8 0

100 -J

180

•J A

0.40

OJO

M-^20

0.10

"T

A

-

•

J -

1

•

^ ^ . A

I

T

^^

1 r 1

m f i l i i iC

T 9lott

• PTFE

• pelrpropyifnc

**"^»w,^N" 1250 rpm

T

• * ^ 4 I N « 7 5 0 r p m

•

i 1 1

I " 1

im/ml d,/*w>

0 . 7 2 0 0 J

2.5 6 0

2.0 150 J

1.0 150 1

H

J

• ~]

t 1 5 10 15 20 25

SOLIDS CONCENTRATION, VOL. %

Inter&cial area decreases with increased solids concentration; 950 rpm, /?=0 (PFR) assumption.

5 iO 15 20 25 30

SOLIDS CONCENTRATION. VOL. %

35

Overall mass transfer coefficient is dependent upon particle composition at high volume fractions of solids.


2.0 h

1.8

O O O

1.2

n 1

L

• -

• IT [A * "•

T

h

L. • f i l i i l t

' A f i l i i t c

T Oiott

1

•

T

p,qmfm

oT" 0.7

2.5

• poly prepy lent 1.0

J \ 1

•

T

•

d.^m

leo 6 0

6 0

ISO

J

"1

T

-J

—r

•

• •

•

L.

H

J

—

• ^

—1

"1

_J

J

0 5 10 15 20 25

SOLIDS CONCENTRATION , VOL. %

ki is independent of solids loading; 950 rpm.

Notation a measured interfacial area per volume of slurry, mVm^ of (solid + liquid) b particle diameter, [im ki liquid phase mass transfer coefficient, ml sec kia overall mass transfer coefficient, 1/sec R recycle ratio = flow of recycle/flow of fresh feed p particle density, gimi

5.4 Solid-liquM-gas systems 439

Alper, E. and Ozturk, S., Chem. Eng. Commun., 46,147 (1986) Effect of Fine Solid Particles on Gas-Liquid Mass Transfer Rate in a Slurry Reactor


Type: flat-bottomed Diameter: 75 mm

Baffle Number: 4

Stirrer

Type Diameter (mm) Number of stirrers Number of blades on stirrers Off-bottom clearance (mm)

Gas-side stirrer

four flat blade 30 1 4

83

Liquid-side stirrer

four flat blade 70 1 4

32

four flat blade 30 1 4 8

Working fluids and solids Liquid: 0.8 M Na2S03 solution Gas: oxygen Solid: activated carbon and Avicel cellulose

Experimental conditions Temperature: 278-308 K Stirrer speed: 80—160 rpm

Results

0.2 0.3 Oi,

Activottd corbon V. w /w

Oxygen absorption into sodium sulphite solutions containing finely powdered activated carbon: Effect of solid loading on {kUki).

120 rpm

0.8M Na 2 50,-pur* 0 ,

pH.7.3 l C o * ' ) « 0

T = 288 K

0.1 0.2 0.3 0.4

Aviccll cellulose V* w /w

Oxygen absorption into sodium sulphite solutions containing finely powdered Avicell cellulose: Effect of solid loading on {kJkL).


20 M

6 16 to S

•^ 0

120 rpm I * OS M Na2S0, - pur* 0 , pH.7.3 |Co**)«0 O pur* solutior> A AcC « 0.2 v. w / w

1-

3.0

2.5 "i 24

2.0 ^ 20

u»^ 16 9 K • w 12 jt

• * ' B

296 x e T. K

Effect of temperature on {kJkL).

Ts29eK 0.8 M No, SO, -pur* 0 , pH.7.3 (Co- ]s0 O clear solution A AcC . 0.2 •/. w/w

- ^ - 2.6

2.0

100 120 UO 160

N rom

Effect of stirring speed on {kJkL^.

Notation ki liquid side mass transfer coefficient for slurry, m/sec ki!^ liquid side mass transfer coefficient for clear solution, m/sec N stirring speed, 1/min


Oguz, H., Brehm, A. and Deckwer, W.-D., Chem. Eng. Scu, 42,1815 (1987) Gas/Liquid Mass Transfer in Sparged Agitated Slurries

Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.145 m Volume: 4 dm^



Impeller Type: four flat-blade impeller Diameter: T/2 Number of impellers: 1 Number of blades on impeller: 4 Length of impeller blade (perpendicular to shaft): T/2 Width of impeller blade (parallel to shaft): D/5 Off-bottom clearance: 0.3 T

Sparger Type: a ring type Number of holes: 12 Diameter of hole: 0.5 nmi Location: bottom of the vessel

Working fluids, solids and their physical properties Slurry:

Particle systems studied at 25°C

Slurry system Sea sand/H20

Kieselguhr/HzO

AI2O3/H2O

Fe203/H20

Ti02/H20

ZnO/HzO

Diameter (Jirn)

<80

<50

<32

<0.5

<0.5

< 1

Density (lO^kgm^)

2.59

2.07

3.2

4.38

3.61

4.72

Volume fraction 0

0.075 0.100

0.025 0.050 0.075 0.100

0.050 0.075 0.100

0.025 0.050 0.075 0.100

0.025 0.050

0.010 0.025

Viscosity parameters

0.979 1.371 0.833 4.232

0.979 1.372 0.852 4.556 0.798 8.905 0.835 16.785

0.936 1.897 0.922 2.461 0.926 3.051

0.899 2.530 0.835 5.402 0.530 64.5 0.443 181.9

0.659 20.06 0.403 310.6

0.732 7.00 0.665 20.94

Gas: air

442 Chapter 5. IMass transter

Experimental conditions Temperature: 25°C Gas flow rate: 50-250 i/hr Stirring speed: 500—800 rpm Particle concentration: up to 10% by vol

Results

kLa = 6.6x10" / \ -0 .39 / ^ \0.75

?ia5 G

1.38 ^ ^ « / A ^ L < 21.3

0.05 ^ O c < 0.25 m'/h

0.78<Pr/F5/<6.3kW/m'

Notation D impeller diameter, m kia liquid side mass transfer coefficient referred to gas free slurry volume (VL+VS), 1/sec PT total power input in aerated stirred slurry, W T tank diameter, m QG volumetric gas flow rate, mVh V volume, m^ /z dynamic viscosity, mPa sec

Subscripts L liquid S solid SI slurry

5.4 SolifMiquid-gas systems 443

Mills, D. B., Bar, R. and Kirwan, D. ].,AIChE Journal, 33,1542 (1987) Effect of Solids on Oxygen Transfer in Agitated Three-Phase Systems

Experimental apparatus Vessel Type: dish-bottomed Diameter: 28.8 cm

Liquid contained Ungassed height: 28.8 cm

Baffle Number: 4 Clearance of baffle from wall: 2 mm

Impeller Type: a six-blade flat disk turbine Diameter: 0.34 Dr Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 0.25 Di Width of impeller blade (parallel to shaft): 0.20 Di Off-bottom clearance: 0.30 Dr

Sparger Type: a ring sparger whose diameter is 9Di/lO Location: approximately halfway between the impeller and the bottom Holes: 11 equally spaced 1.02 mm diameter holes in the underside

Working fluids, solids and their physical properties Liquid: aqueous NaCl solution (NaCl concentration: 0,0.1,0.25, and 0.5 M) Solid: soda-lime glass beads (particle density = 2.46 g/cm ; mean diameter = 66 [un;

size range = 44—88 M,m; hardness 6 Mohs) Gas: air

Experimental conditions Temperature: 25 ± 1.5°C Solid concentration: 0,10, 20,30 and 40% v/v Superficial gas velocity: 0.36,0.65 and 1.13 cm/sec Stirring speed: 600,650, 700, 750 and 800 rpm

Results

Af/:fl = (0.10-0.00180) [y)

Notation DI impeller diameter, m DT tank diameter, m kia volumetric oxygen mass transfer coefficient in a slurry, 1/sec PT total power, kW/m^ V volume of condensed phases, Uquid and solid, m Vs superficial gas velocity, cm/sec 0 volume concentration of solids, % v/v

444 Cha|it«r 5. Mass transfer

Kojima, H., Uchida, Y., Ohsawa, T. and Iguchi, A.,/. Chem. Eng. Japan, 20, 104 (1987) Volumetric Liquid-Phase Mass Transfer Coefficient in Gas-Sparged Three-Phase Stirred Vessel



Impeller Type: six-blade flat disk turbine Diameter: 40,60,80, and 120 mm Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 60 mm

Working fluids, solids and their physical properties Gas: 100% CO2 Liquid: tap water Solid: glass beads 0.15-0.18 nmi, p^=2,390 kg/w?

Amberlite 0 .84-1.0 mm, pp= 1,270 kg/m^ polypropylene beads 2.7—4.0 mm, p/=867 kg/w?

Experimental conditions Gas flow rate: 2.69 x 10"^ - 2.22 x 10"* mVsec Liquid flow rate: 2.30 x 10'^ - 6.20 x 10'^ mVsec Temperature: 9.2 ± 30.2°C Impeller speed: 2.08—10.11/sec Volume fraction of solid particles: 0—0.26

Results e > 0.24 kia/a-e'p) = 0.19 e°-^ vc^'^ e < 0.24 ha/a-e'p) = 0.12 e®- ^ VG""'*^

Notation kia liquid-side volumetric mass transfer coefficient, 1/sec T tank diameter,m VG superficial gas velocity, m/sec e specific energy dissipation rate, J / k g s e c e'p volume fi:action of solid particles pp density of solid particles, kg/m^

5.4 Solid-fiquid-gas systems 445

Asai, S., Konishi, Y. and Kajiwara, T.,/. Chem. Eng. Japan, 22,96 (1989) Effect of Sparged Gas on Mass Transfer between Fine Particles and Liquids in an Agitated Vessel

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 13.2 (2) 9.0 cm

Baffle Number: (1)4 (2) 4 Width: (1)1.32 (2) 0.90 cm

Impeller Type: (1) (2) six flat blade turbine Diameter: (1) (2) T/2 Number of impellers: (1) (2) 1 Number of blades on impeller: (1) (2) 6 Length of impeller blade (perpendicular to shaft): (1) (2) T/4 Width of impeller blade (parallel to shaft): (1) (2) T/5 Off-bottom clearance: (1) (2) T/3

Sparger Type: single nozzle Diameter: 0.1,0.2, and 0.3 cm i.d. Location: at the center of the vessel bottom

Working fluids, solids and their physical properties

System (1) (2)

Liquid Solid particle size (\im)

Gas

10-3 kmol/m^ NaOH solution cation exchange resin

23.0 air

10-3 kmol/m^ HCl solution anion exchange resin

64.8 and 456 air

Experimental conditions Impeller rotational speed: 1.67—6.671/sec Air flow rate: 16.1 x 10-^ ~ 235 x 10" mVsec Temperature: 25°C

Results Sh = [25*+{0.61(£^/3^*/Vv)°-^5c^/3j5^]i/5.8

£ = Er = BM-^SG

SG = UGgPs/pL - UGg

Notation d particle diameter, m D liquid-phase diffiisivity, mVsec k mass transfer coefficient, m/sec g acceleration of gravity, m/sec^ Sc Schmidt number, v/D, dimensionless Sh Sherwood number, kd/D, dimensionless T vessel diameter, m UG superficial gas velocity, m/sec e eneigy dissipation rate per unit mass of liquid,

mVsec

£c

£M

ET

pL Ps

energy dissipation due to gas sparging, mVsec energy dissipation due to mechanical agitation, mVsec? total eneigy dissipation rate, mVsec kinematic viscosity of liquid, mVsec liquid density, kg/m^ slurry density, kg/w?


Koloini, T, Plazl, I. and 2umer, M., Chem. Eng. Res. Des., 67,526 (1989) Power Consumption^ Gas Hold-up and Interfacial Area in Aerated Non-Newtonian Suspensions in Stirred Tanks of Square Cross-Section

Experimental apparatus Vessel geometries and experimental conditions Type: flat-bottomed vessel of square cross-section Side length: (1)0.3 (2) 0.7 m

variable


stirrer diameter clearance from bottom suspension volume sparger type sparger location VG m/sec N 1/min P/V W/m^ PL kg/w? 7]^ mPasec T ""C

SQT-0.3

0.3 m 0.33 m standard six blade Rushton 0.1m 0.11m 0.03 m tube underneath of stirrer 0.0058-0.027 200-800 30-1,600 1,050-1,230 3-100 20 or 30

SQT-0.7

0.7 m 0.82 m standard six blade Rushton 0.267 m 0.21m 0.4 m' tube underneath of stirrer 0.02-0.08 100-500 30-2,250 1,050-1,160 1.9-12 20 or 30

Working fluids, solids and their physical properties Fluids: Suspensions of CaCOa and Ca(0H)2

Rheological properties of CaCOa and Ca(0H)2 suspensions at 20°C Cone. (wt. %)

CaCOs 10 15 25

Ca(0H)2 5

10 15 20

iTCPas")

0.025 0.14 2.1

0.0035 0.037 0.33 1.1

« ( - )

0.6 0.45 0.22

0.87 0.54 0.28 0.23

Gases: air+C02 for SQT-0.3 and flue gas for SQT-0.7 Results

Interfacial area for SQT-0.3

a = 1.55(P/V)0-** piO-2 ^-0.6 gO ^ 0.48 ^ -0.185

for SQT-0.7 a = 4.86(P/V)°-3 p / 2 ^-0.6 ^05 ^Lie ^ -0.42


Notation a interfacial area, 1/m N stirrer speed, 1/sec P stirrer power input in gassed suspension, W V suspension volume, m VG superficial gas velocity m/sec £ gas hold-up % effective viscosity, Pasec PL suspension density, kg/m^ c surface tension, kg/sec


Dietrich, E., Mathieu, C, Delmas, H. and Jenck, J., Chem. Eng. Sci., 47,3597 (1992) Raney-Nickel Catalyzed Hydrogenations: Gas-Liquid Mass Transfer in Gas-Induced Stirred Slurry Reactors

Experimental apparatus Vessel, impeller, and sparger geometries Characteristics of the main reactor

Tank capacity Tank diameter Stirrer diameter d/r Sparger height from bottom Volume of liquid

v,/v, VllVr Liquid height stirrer position Vessel material Impeller material

Gas inducers

Wr T d

hi Vi

H hilH

Q&

0.510-3 m' 710-2 m 3.2 10-2 m 0.45 1.210-3 m 0.25 to 0.3810-3 m 0.32 to 1 0.76 to 0.5 6.5 to 9.9 10-2 m 0.12 to 0.18 stainless steel stainless steel

ni hr

Stirrer A Stirrer B

Working fluids and solids Liquid: distilled water, ethanol, a mixture obtained by hydrogenation of adiponitrile Sohd: pyrophoric and non-pyrophoric Raney nickel particles Gas: H2

5.4

Results

Solid-liquid-gas systems 449

2.4 .

z\ T^ 1.6-

-^ 1-2 -

^ O.B.

. ; ' / • 2.2X Nl KOK PYR. y^

y m D% Ni

^ \ ^ 2 .3% Ni PYR ^

u \t » ze M ^ 3e

ROTATIOK SPEED (rps) • JBO • ^ E2&>)G FYS. A ISZD-K NOX PTK.

Pyrophoric or non-pyrophoric Raney nickel effects on Ki a in water.

5 ,Mt-

CD

lA

1.2

0.8

CJ

0.<

02

C

7«2DC>i»arw

KM e S OM OIK S C!I2 eh4 SOLE) COKCSKTPJOTON (KftAc)

Non-pyrophoric Raney nickel effects on Kia in hydrogenation mixture.

thi

U "

U 1

I ;

OJ-

0.6-

" O.^r

02] 0]

T »

/

/ - : •

t'-

1

\

\

• l«aDC f«UiTi -r T»«)Cli«lfrfii ,

# T«20Cy«Shi A T«aXKs2k«l

' '".X 1 •^•<r -x

- ^ ^ " ^ - c ^

' ••fc - • " H —.—,—• ~?' -r-*

) 0.02 0.M 0.06 OJM 0.1 0.12 0.14

SOLD) CONCEHTRATION (Kg/Kg)

Pyrophoric Raney nickel effects on Kia in hydrogenation mixture.

i • 4 • ii i io

Power Consumption (Kff/nf) • iL B / T = 0 ^ Ta20-C • i^ E/7*0JB7 T-aO-C

• B: H/I-O.W T«20-C A B: EA*0-S3 T«BD-C

Kia vs power consumption for two gas-inducers.

a =1.5-2 when ^ < 4kW/m^ i3 =0.6- 0.8 when ^ > 4 kW/m^

Notation Kia volumetric mass transfer coefficient, 1/sec ^ power consumption, kWw?


Kushalkar, K. B. and Ptogarkar, V G.,Ind. Eng. Chem. Res., 33,1817 (1994) Particle-Liquid Mass Transfer in Three-Phase Mechanically Agitated Contactors

Experimental apparatus Vessel Type: (1) flat-bottomed (2) flat-bottomed Diameter: (1) 0.3 (2) 0.57 m


Impeller

type

A B C D E F G

diameter (m)

0.10 0.15 0.19 0.10 0.19 0.10 0.19

no. of blades

4 4 4 4 4 4 4

blade width (m)

0.02 0.03 0.038 0.02 0.057 0.02 0.057

blade thickness (m)

0.0019 0.0019 0.0028 0.0019 0.0028 0.0019 0.0028

hub diameter (m)

0.05 0.05 0.05 0.05 0.05 0.05 0.05

no. of impellers

A disk turbine DTI B disk turbine DT2 C disk turbine DT3 D pitched blade turbine (downflow) PTDl E pitched blade turbine (downflow) PTD2 F pitched blade turbine (upflow) PTUl G pitched blade turbine (upflow) PTU2

Sparger Ring diameter: 0.085 m Orifice diameter: 0.002 m No. of orifices: 6

Working fluids, solid and their physical properties Liquid: water and aqueous solution (Newtonian) of (carboxymethyl) cellulose (CMC) Solid: benzoic acid particles Gas: air System: dissolution of benzoic acid particles in water and aqueous solutions of CMC

(A) Physical properties of the systems used

system

density, kg/m^ viscosity, kg/ms difliisivity, 10^ mVs solubility, kmol/m^ Schmidt number, Sc

water

1,000 0.0008 1.0 0.0342 800

0.1% CMC

1,004 0.00192 0.94 0.035 1,966

0.2% CMC

1,004 0.00374 0.94 0.035 3,996

5.4 Solid-Hquid-gas systems 452

(B) Particle characteristics

av. screen diameter, dp, nm

surface area, mVkg shape factor, ^ sphericity, \if mean particle diameter

W^0/V^), ^m

550

16.65 0.5 0.67 410

655

13.98 0.5 0.67 490

856

10.70 0.5 0.67 639

1,100

8.33 0.5 0.67 820

Experimental conditions Particle loading: 0.5 wt% Superficial gas velocity: 0.015-0.03 m/sec

Results For benzoic acid-water-air system

Xl.05

fei = 2 . 7 9 x 1 0 " ' I - ^

For benzoic acid-CMC solution-air system

feL=1.19xlO-'f-^l {Sc)-^''' . J Notation

Dm diffusivity, mVsec ksL particle-liquid mass-transfer coefficient, m/sec N rotational speed of the impeller, 1/sec Nag critical impeller speed for suspension of solid particle in aerated liquid, 1/sec Sc Schmidt number, pilpDm, dimensionless p density of liquid, kg/m^ /i viscosity of liquid, Pasec

452 Chapter 5. Mass tninsfsr

Kushalkar, K. B. and Pangarkar, V G., Ind. Eng. Chem. Res., 34,2485 (1995) Particle-Liquid Mass Transfer in Three-Phase Mechanically Agitated Contactors: Power Law Fluids


Type Diameter (m) Number of impellers Number of blades on impellers Blade width (m) Blade thickness (m)

DTI 0.1 1 4

0.02 0.0019

PTDl 0.1 1 4

0.02 0.0019

PTUl 0.1 1 4

0.02 0.0019

DTI: disc tuibine PTDl:pitched blade turbine (down flow) PTUlipitched blade turbine (up flow)

Sparger Type: a ring type Diameter: the diameter of the ring sparger/the diameter of the impeller=0.8

Working fluids, solid and their physical properties Gas: air Liquid: aqueous solution of carboxymethyl cellulose

Physical properties of non-Newtonian fluids used

cone of density, K, diffusivity, solubihty, CMC,wt% kg/m^ Pas'* n lO'^mVs kmol/m' 0.25 1,000 0.0058 0.985 0.95 0.0348 1.00 1,030 0.0440 0.750 0.82 0.0406 1.50 1,040 0.1350 0.633 0.75 0.0452

Solid: benzoic acid

Particle characteristics

av. screen diameter, dp, 10"® m

surface area, mVkg shape factor, 0 sphericity, y/ mean particle diameter

(dp(lf/yf\lO-^m

550

16.65 0.5 0.67

410

655

13.98 0.5 0.67

490

856

10.70 0.5 0.67

639

1,100

8.33 0.5 0.67

820

5.4 Soliil-liquid-9«s systems 453

Measured physical properties of non-Newtonian fluids in MAC

cone, of CMC, wt% density, kg/m^ K, Pas" n

A. Liquid saturated with benzoic acid (unaerated) 0.25 1,000 0.0038 0.985 1.00 1,030 0.0875 0.750 1.50 1,040 0.1750 0.657

B. Liquid saturated with benzoic acid (aerated) 0.25 1,000 0.004 0.985 1.00 1,030 0.009 0.973 L50 1 040 0015 0.965

MAC: mechanically agitated contactor Experimental conditions

Particle loading: 0.5 wt% Superficial gas velocity: 0.015—0.03 m/sec

Results

ksL=h72xlO-\N/Ns)'''HSc)-^^

Notation dp average screen size of particle, m Dm diffusivity, m^sec K power law consistency index, Pasec" ksL particle Hquid mass transfer, coefficient, m/sec n flow index N rotational speed of the impeller, 1/sec Ns critical impeller speed for suspension of solid particle in aerated Uquid, 1/sec Sc Schmidt number, /z/pZ>«,dimensionless // viscosity of liquid, Pasec fia apparent viscosity for non-Newtonian Uquid, Pasec p density of liquid, kg/w?


Kawase, Y., Araki, T, Shimizu, K. and Miura, H., Can. J. ofChem. Eng., 75, 1159 (1997) Gas-Liquid Mass Transfer in Three-Phase Stirred Tank Reactors: Newtonian and Non-Newtonian Fluids




Impeller

Type Diameter (m) Number of impellers Number of blades on impellers Blade width (m) Blade thickness (m) Off-bottom clearance (m)

DTI

six-bladed disk turbine 0.096

1 6

0.020 0.025 0.066

DT2

six-bladed disk turbine 0.066

1 6

0.0135 0.017 0.066

Sparger Type: a ring type Diameter of ring: DT/3 Number of holes: 20 Diameter of hole: 1 nmi Location: DT/Q above the tank bottom

Working fluids, solids and their physical properties Gas: air Liquid: tap water and aqueous solutions of carboxymethyl cellulose (CMC)

Physical properties of hquids at actual test conditions

density A(kg/m3)

water 999 CMCl(0.15wt%) 1,001 CMC2(0.5wt%) 1,001

flow index consistency index « ( - ) iiC(Pas")

1 0.00095 0.863 0.038 0.697 0.079

surfoce tension (T(N/m)

0.0712 0.0665 0.0691

Sohd: cylindrical particles

density (kg/w?)

particle A 1,030 particle B 1,200

diameter (m)

0.002 0.002

length (m)

0.003 0.004

5.4 Solicl-liquid-gas systems 455

Experimental conditions Temperature: room temperature Gas rate: 5-10 i(STP)/min (0.8-1.6 wm (volair/voMiquidmin)) Solid concentration: 5,10 and 15 vol%

Results \ 7r3/5 (9+4«)/10(l+«) f rr ^'"^ f TT \^'^

C' = 0.675

P/=p,^5' + P/(l-05)

- >vl/2(l+«) 3/5

(u Y f"" V

K = K- i+8.2O(0;r 1 - 2.478 0; +18.456 m" - 20.32 (0.'f

(1)

(2)

(3)

g

0.001

0.01 f

0.00 i 0.01

ifeiflCEXPER.) [s-*]

Solid loading led to higher mass transfer rates in non-Newtonian system, Comparison between predicted values and experimental data for kia in CMC

Notation C constant e D diffusivity, mVsec DT reactor diameter, m /Xc K^ consistency index, P a s e c " K consistency index of slurry defined by fLu>

Equation (3), Pasec" pi kia volumetric liquid-phase mass transfer pi

coefficient, 1/sec p, n flow index a Ug superficial gas velocity, m/sec 0i Ut terminal velocity of bubble in firee rise m/sec

energy dissipation rate per unit mass, W/kg apparent viscosity of slurry in stirred tank, Pasec viscosity of water slurry, Pasec hquid density, kg/m^ apparent density of slurry, kg/m^ solid density, kg/m^ surfoce tension, N/m solid concentration in slurry


5.5 Mass transfer to free surface

Kataoka, H. and Miyauchi, T, Kagaku Kougaku, 36,888 (1972) Effect of Physical Properties and of Turbulence on the Rate Coefficient of Mass Transfer at the Free Surface of Agitated Vessels in Turbulent Region

Experimental apparatus Vessel Type: (1) (2) flat-bottomed Diameter (1) 23.7 (2) 15.1 cm

Liquid contained Height: (1)23.7 (2) 15.1 cm

Baffle Number: (1) (2) 4 Width: (1)2.37 (2) 1.51 cm

Impeller Type: (1) (2) six flat-bladed turbine Diameter: (1)8 (2) 5 cm Number of impellers: (1) (2) 1 Number of blades on impeller:(l) (2) 6 Off-bottom clearance: (1) (2) 7/3

Working fluids, their physical properties and experimental conditions Liquid: distilled water, ethyl alcohol, benzene and toluene Gas:C02,02,H2andHe

Experimental conditions and physical properties of samples used

DT

(cm) /

CO C*

(mol/0 PL

(g/cm^) HxW

(g/cmsec) Z)ixlO= (cmVsec)

o (dyne/cm) liquid

29.5-32.1 (8.80 -8.46) xlCT^ 0.858-0.855 5.23 -5.06 0.595-0.621 27.4-27.1 CO2 Toluene

15.1

23.7

18.4-21.6 19.4-20.9 18.7-21.8

19.5-22.8 19.9-23.8 19.3-21.4 18.6-20.5 18.8-23.1 18.9-21.3 21.6-25.8

(4.12 -3.76)xl0-2 (4.00 -3.85) X10-2 0.108-0.103

(1.40 -1.32)xia-2 (8.14 -7.93) X10-* 0.120-0.115 0.108-0.105

(3.57 -3.62) X10- (4.06 -3.80) X10-2 (3.96 -3.86)xl0-*

0.999-0.998 0.998 0.879-0.878

0.998 0.998-0.997 0.805-0.804 0.88 -0.878 0.806-0.81 0.999-0.998 0.998-0.997

1.89 -1.86 1.02 -0.985 0.66 -0.63

1.02 -0.938 1.01 -0.918 1.42 -1.40 0.66 -0.638 1.51 -1.42 1.03 -0.976 0.964-0.880

1.73 1.78 4.0

2.25 4.18 2.92 3.99 4.84 1.75 5.75

-1.89 -1.85 -4.23

-2.46 -4.64 -2.99 -4.13 -5.21 -1.84 -6.43

72.3-72.4 72.7-72.4 29.1-28.7

72.7-72 J2 72.6-72.0 23.0-23.5 29.1-28.8 22.7-23.5 72.8-72.3 72.3-71.8

CO2 CO2 CO2

O2 H2 CO2 CO2 H2 CO2 He

Distilled water Distilled water Benzene

Distilled water Distilled water 92 wt% Ethanol Benzene 92 wt% Ethanol Distilled water Distilled water

Resildts For the distilled water

DL = 0.04

( o J {PLDL

5.5 Mass transfer to ffraa surfoca 457

For the organic solvents

DL PLDL

1/2/ 2^3 V/2

Notation C* equilibrium concentration of gas in liquid, mol/i Di impeller diameter, cm DL dilftision coefficient of gas in liquid, cmVsec ki liquid-film gas transfer coefficient, cm/sec n number of revolution, 1/sec // viscosity of liquid, g/cmsec PL density of liquid, g/cm^ G surface tension of liquid, dyne/cm


Teramoto, M., Tai, S., Nishii, K. and Teranishi, H., Chem. Eng.J., 8,223 (1974) Effects of Pressure on Liquid-Phase Mass Transfer Coefficients

Experimental apparatus Vessel Diameter: 5.6 cm


Impeller Tjrpe: (1) turbine-type with sbc flat blades (2) propeller-type with three twisted blades Diameter: (1) 26 (2) 33 mm Number of impellers: (1) (2) 1 Number of blades on impeller: (1) 6 (2) 3 Off-bottom clearance: (1) {2)HL/2

Working fluids Liquid: water, -xylene and ethanol Gas: He, H2, Ar, CO2 and N2

Experimental conditions Pressure: 2--'100 atm

Results For absorption of He, H2, Ar, CO2 and N2 with water and absorption of He and N2 with ethanol ki

was independent of pressure. For absorption of He with -xylene ki decreased with increasing pressure at pressures higher

than 70 atm. Notation

HL liquid height, cm ki hquid-phase mass transfer coefficient, cm/sec

5.5 Mass transffsr to fwmm surfoc« 459

Farritor, R. E. and Hughmark, G. A., AIChE Journal, 20,1027 (1974) Mass Transfer to the Free Interface in a Stirred Vessel

Experimental apparatus Vessel Type: flat-bottomed Diameter: 100 cm Volume: 0.76 m (200 gal)

Impeller Type: six-blade impeller Diameter: 50 cm Number of impellers: 1 Number of blades on impeUer: 6


Experimental conditions Temperature: 21.5°C Impeller speed: 43 rpm

Results Use of data taken in this study along with existing data ((1)~(3)).

k^0.0256 \'!J^' Nsr

(1) Bossier, J. A., R. E. Farritor, G. A. Hughmark, and J. T. F. Kao, "Gas-Liquid Interfecial Area Determination for a Turbine Agitated Reactor," AIChEJ., 19,1065 (1973).

(2) (joodridge, F. and I. D. Rodd, "Mechanism of Interfacial Resistance in Gas Absorption," Ind. Efig, Chem. Fundamentals, 4,49 (1965).

(3) Kozinski, A. A. and C. J. King, "The Influence of Diffusivity on Liquid Phase Mass Transfer to the Free Interface in a Stirred Vessel," ibid,, 12,109 (1966).

Notation D impeller diameter De diffiisivity g acceleration due to gravity k mass transfer coefficient Np power number, Pg/n^D^p, dimensionless Nsc Schmidt number, v/A, dimensionless n impeller speed P power input V vessel Uquid volume V kinematic viscosity p density


Matsumura, M., Masunaga, H. and Kobayashi, J.,/, Ferment Technoly 55,388 (1977) A Correlation for Flow Rate of Gas Entrained from Free Liquid Surface of Aerated Stirred Tank



Baffle Number: 3 Width: 25 mm Height:/fe/Z)r= 1.36

Impeller

System

Type

Number of impellers Number of blades on impellers DJDT Wi/Di bIDi HJIDT

(1)

1 6

0.400 0.220 0.254 0.333

(2) (3)

six flat-bladed turbine


Physical properties of liquids used in

t Materials CO

Water 30 Ethylene glycol 30 Benzyl alcohol 20 Ethyl alcohol 12

P (g/cm^)

0.996 1.11 1.04 0.795

1 6

0.487 0.205 0.254 0.333

this work.

^ (cP)

0.80 12.5 6.10 1.39

1 6

0.609 0.214 0.254 0.333

a (dyne/cm)

7.12 44.8 34.5 22.4

Experimental conditions Impeller rotational speed: 5.08—16.5 rps

5.5 Mass transfer to ffra« surface 461

Results (1) Effect ofi\r,V, and A

7 / ^y-22 ^5.2 •^13.0

a-rif (2) Effect of liquid physical properties

^6.4

: im3xlO-'\NAr'^(NEef\Nwe)'^(NF,f"' ''

3xl0~^ <NA <9xl0-\ 7x10^ <NRe <2xl0^

SxlO^ <Nwe <lxlO\ 6xlO-^<NFr<3

Notation b impeller blade length, cm Di impeller diameter, cm DT tank internal diameter, cm / volumetric flow rate of entrained gas, i/min F volumetric flow rate of nitrogen gas, ^/min g gravitational acceleration, cm/sec^ HB baflle height, cm Hi impeller height from tank bottom, cm N impeller rotational speed, 1/sec NA Aeration number, VJNDu dimensionless NFT Froude number, N^Dilg, dimensionless NRe Reynolds number, ND?plpiy dimensionless Nwe Weber number, N^Di^p/a, dimensionless Vs total gas volume dispersed in tank, i Wi impeller width, cm r? //(F+/) pi liquid viscosity, g / c m s e c p liquid density, g/cm^ a surface tension of hquid, g/sec^


Hozawa, M., Yokohata, H., Imaishi, N. and Fujinawa, K., Kagaku Kogaku Ronbunshu, 7,138 (1981) Effect of Surface Tension on Liquid Phase Mass Transfer Coefficient at a Turbulent Free Surface


Liquid contained Height: 97 mm Volume of liquid in vessel: 800 cm^


Impeller Type: rod stirrer Diameter: 70 mm Number of impellers: 1

Working fluids and their physical properties Liquid: see table Gas: desorption of oxygen by nitrogen

Properties of liquids (at 25°C)

Solvent p(kg/m^) M(Pas) cT(N/m) Z)(mVs)

Methanol Carbon tetrachloride Benzene Nitrobenzene Water

0.7865 x l O ' 1.5843x10^ 0.8736 xlO^ 1.1983 xlO^ 0.9970 xlO^

0.553x10-3 0.903x10-2 0.602x10-3 1.840x10-3 0.894 X 10-3

21.9x10-3 26.0x10-3 28.2x10-3 43.2x10-3 72.0x10-3

4.44 X 10-^ 4.33x10-' 4 .62x10-' 1.90x10-' 2 .23x10-'

Experimental conditions Temperature: 25**C Agitator speed: 120,167,200 and 240 rpm

Results Sh = const. Sd"^ Re''\alaw)''

6 = -1.05w-°*^

Notation D diffusivity, mVsec /x viscosity, Pasec di impeller diameter, m v kinematic viscosity, mVsec ki liquid phase mass transfer coefficient, m/sec p density, kg/cm^ n Number of revolution, 1/sec a surface tension, N/m Re Reynolds number, d?nlv, dimensionless Cw surface tension of pure water, N/m Sc Schmidt number, v/Z), dimensionless Sh Sherwood number, kidi/D, dimensionless

5.5 Mass tmnsfsr to frs# surffacs 463

Takase, H., Unno, H. and Akehata, T, Kagaku Kogaku Ronbunshu, 9,25 (1983) Oxygen Transfer in Sinface Aeration Tank with Square Cross Section


System

Vessel Type

Length and width (m) Water depth (m)

Impeller Type

Diameter of disk (m)

di :h:wb

Number of impellers Number of bladed Off-top clearance (m)

(1)

0.2 0.075-0.2

(2)

flat-bottomed square tank

0.3 0.075-0.3

(3)

0.5 0.075-0.5

disk with six blades underneath the disk

0.03,0.06

1 6

0,0.01,0.02

0.03,0.06,0.12

20: 7 : 2

1 6

: 0,0.01,0.02

0.06,0.12

1 6

0,0.01,0.02




System (2) A(m) Impeller speed (rps)

System (3) A(m) Impeller speed (rps)

0.03 5.00-41.7

0.03 5.00-41.7

0.06 1.67-16.7

0.06 1.67-16.7

0.06 1.67-16.7

0.12 0.83-6.67

0.12 0.83-6.67

Temperature: 15~24*'C

^ ^ Chapter 5. Mass transffar

Results Below the critical rotational speed of impeller

| ^ = 1 . 7 x l O - ' ( « d , ) - ' 4 : ^ (1-2.2 Hs^U ioH'«.o<*/"''H"

Above the critical rotational speed of impeller

W) [Hs + Wb

Notation d, impeller diameter , m Hs substantial impeller submergence at ;f > n^ m Hso initial impeller submergence , m h blade length, m M oxygen transfer ra te , kg- Oz/sec n rotational speed of impeller, 1 /sec He critical rotational speed of impeller, 1/sec P power, kgfm/sec Ro equivalent diameter of square tank, m Wb blade width, m W tank width, m

5.5 Mass transisr to frae surface 465

Veljkovic, V B., Bicok, K. M. and Simonovic, D. M., Can. J, ofChem. Eng., 69, 916 (1991) Mechanism, Onset and Intensity of Surface Aeration in Geometrically-Similar, Sparged, Agitated Vessels


System

Vessel Diameter (m)

Liquid height (m) Baffle

Number Width (m)

Impeller Type Diameter (m) Number of impellers Number of blades on impeller Length/vessel diameter Width/vessel diameter Off-bottom clearance (m)

Sparger Type Distance between impeller and nozzle tip (m)

(1)

0.2 0.2

4 0.02

A 0.067

1 6

0.25 0.2

0.067

B 0.02

(2)

0.3 0.3

4 0.03

A 0.10

1 6

0.25 0.2 0.10

B 0.03

(3)

0.45 0.45

4 0.045

A 0.15

1 6

0.25 0.2 0.15

B 0.045

(4)

0.675 0.675

4 0.0675

A 0.225

1 6

0.25 0.2

0.225

B 0.0675

A: six-flat-blade turbine B: a single nozzle

Working fluids Liquid: distilled water Gas: air

Results (1) Onset of gas entrainment under unsparged conditions

NsD = 0.732

(2) Onset of gas entrainment under sparged conditions

ReliWesT'-'^'iNasr''''' = 104.1 for 0.001 <UB< 0.004 m / sec

(3) Intensity o f surface aeration

when Pr <PpfSA a,A=3.59xlO-'*w/''

when Pp>Pr, SA

a s A = 5 . 7 1 x l O " V r / W f i


(4) Intensity of gas entrainment

a,=2.76xlO-*'P."M^'^ for 0.001 <.UB<> 0.004 m / sec

(5) Intensity of gas absorption at free surface

UA = 5.71xlO"*ftM^^ -2.76x10"^ ft^^M^^-^

Notation D impeller diameter, m Nus aeration number, NSAD/UB, dimensionless N, entrained below the free surface under unsparged conditions, 1/sec NsA characteristic impeller speed required for surface aeration to intensity under sparged

conditions, 1/sec Ns* characteristic impeller speed required for gas entrainment to occur under sparged

conditions, 1/sec Pr specific power input under sparged conditions, W/m^ Pp, SA specific power input required for surface aeration to intensity under sparged conditions,

W/m' RBS Reynolds number, PLNS*DV^L, dimensionless UB superficial sparged velocity, m/sec WBS Weber number, pLiNsyDVpi, dimensionless aA surface absorption intensity a, surface entrainment intensity asA surface aeration intensity jLiL liquid viscosity, Pasec PL liquid density, kg/m^

5.5 Mass transfer to ffraa surffaca 467

Mizan, T. L, Li, J., Morsi, B. L, Chang, M.-Y., Maier, E. and Singh, C. P. R, Chem. Eng. Sd., 49,821 (1994) Solubilities and Mass Transfer Coefficients of Gases in Liquid Propylene in a Surface-Aeration Agitated Reactor


Baffle Number: 2 Volume: 4 i

Impeller Type: Rushton-type six flat-blade impeller Number of impellers: 1 Number of blades on impeller: 6

Working fluids and their physical properties Liquid: liquid propylene Gas: hydrogen and ethylene

Diffusivity of hydrogen and ethylene in liquid propylene

Component

Hydrogen Ethylene

Diflusivity,Z)xl0^m2s-^)

297 K 313 K 333 K

35.6 45.5 64.8 17.0 21.6 30.8

Experimental conditions Pressure: 11—55 bar Temperature: 297-333 K Mixing speed: 13.3-20.0 Hz

Results Sh = 55,2We-'^Re'^Fr''''

741 <FF^< 31,060 198,000 </?^< 445,100 0.922 </V< 2.073

Notation D diffusivity of gas in Uquid, mVsec Di impeller diameter, m

Froude number, DiNVg, dimensionless gravitational acceleration, m/sec^ volumetric liquid-side mass transfer coefficient, 1/sec mixing speed, 1/sec Reynolds number, NpiDiVfiLf dimensionless

Fr g

N Re

Sh Sherwood number, kiaD^/D, dimensionless

We Weber number, PLN^D?IG, dimensionless

liL hquid viscosity, kg/msec pL Liquid density, kg/m^ a surface tension, kg/sec^

468 Chapter 5. Mass tnnisfsr

Tekie, Z., Li, J., Morsi, B. I. and Chang, M.-Y., Chem. Eng. 5d., 52,1541 (1997) Gas-Liquid Mass Transfer in Cyclohexane Oxidation Process Using Gas-Inducing and Surface-Aeration Agitated Reactors

Experimental apparatus Vessel Type: dished-bottomed Diameter: 0.127 m Volume: 3.86x10- 111^

Liquid contained Volume of liquid in vessel: 2.5 x 10" m


Impeller Type: six flat-blade turbine Diameter: 0.0635 m Number of impellers: 1 Number of blades on impeller: 6

Shaft (gas sparger) Diameters: 0.01 m Number of gas-sparging holes: 2 holes in liquid phase; 2 holes in gas phase Diameter of hole: 1.5 x 10" m

Working fluids Liquid: qrclohexane Gas: nitrogen and oxygen

Experimental conditions Pressure: 1- 40 bar Temperature: 380-480 K Mixing speed: 13.3-20 Hz

Results For gas-inducing and surface-aeration reactors

2,100 <W «< 13,300, l<F r<3 5/> = 4.51 X10'W^ -**-"'Fr 'd+1.867 X10'£j

O

£g

otat DA Di Fr g kia

N Sh We

=3.8s.:o-(i^J" f \ -0 .74^ \ a 8 2 x xl.97

ifl] \2£\ \£A ,//LJ \PL) \C,]

No = 11.6 Hz and ao= 0.025 N/m

ion diffusivity, mVsec impeller diameter, m Froude number, DiNVg, dimensionless gravitational acceleration, m/sec^ volumetric liquid-side mass transfer coefficient. 1/sec mixing speed, Hz (1/sec) Sherwood number, kioD/^/DAf dimensionless Weber number, PLN^D?I{ 7, dimensionless

^g

A* P o

gas holdup viscosity, kg/msec density, kg/m' surface tension, N/m

Subscripts G L

gas liquid

469

Chapter 6. Scale-up rules

6.1 Single phase

Rieger. E and Novdk, V, Chem. Eng. ScL, 27,39 (1972) Scale-Up Method for Power Consumption of Agitators in the Creeping Flow Regime.

Experimental apparatus Vessel and agitator geometry

Screw diameter: 60 mm and 94 mm

i

il

r

r

^

'^

^

Pi ^ ill • i 1 1

1 i Di = l.ld

D = l.6d

i

in

i-H

II

- 5

\

in

11

J

i 1 i

j i i !

Screw agitator with a draught tube.

Working fluid Pseudoplastic fluid: 4% CMC solution in water

Scale-up rule f X 2/(2-«)

Notation d diameter of agitator M flow index of power-law fluid N speed of agitator

Subscript M standard condition

470 Chapter 6. Scai«-up rates

Khang, S. J. and Levenspiel, 0., Chem. Eng. Sci., 31,569 (1976) New Scale-up and Design Method for Stirrer Agitated Batch Mixing Vessels

Experimental apparatus System


Baffle Number

Impeller Type Diameter (m) Number of impellers Number of blades Pitch/Diameter Off-bottom clearance (m)

(1)


4

three-blade marine type 0.114,0.254

1 3

1.5/1 0.280

(2)


4

three-blade marine type 0.114,0.254

1 3

1.5/1 0.610


Experimental conditions i?^>10*

Scale-up rule

(n/K) (d/Df=1.5 Pge/(pn^d')=0,9

Notation d stirrer diameter, m D tank diameter, m gc Newton's-law conversion factor K amplitude decay rate constant, 1/sec n stirrer rotational speed, 1/sec P mixing power requirement, W Re stirrer Reynolds number, nd p ///, dimensionless fj, viscosity, g/m sec p density, kg/w?

6.1 Single phase 47I

Khang, S. J. and Levenspiel, 0., Chem. Eng. Sci., 31, 569 (1976) New Scale-up and Design Method for Stirrer Agitated Batch Mixing Vessels



Baffle Number

Impeller Type Diameter (m) Number of impellers Number of blades Diameter/Blade length

/Blade height Off-bottom clearance (m)

(1)


4

standard disk type 0.127,0.244

1 6

20/5/4

0.280

(2)


4

standard disk type 0.366,0.488

1 6

20/5/4

0.610


Experimental conditions Re>lO'

Scale-up rule

(n/K) (d/Df^=Pgc/(pn'd')^0,5

Notation d stirrer diameter, m D tank diameter, m gc Newton's-law conversion factor K amplitude decay rate constant, 1/sec n stirrer rotational speed, 1/sec P mixing power requirement, W Re stirrer Reynolds number, nd p ///, dimensionless jj. viscosity, g/m sec p density, kg/in?

472 Chapter 6. Scal«-up rates

Van der Molen, K. and Van Maanen, H. R. E., Chem. Eng. 5a., 33,1161 (1978) Laser-Doppler Measurements of the Turbulent Flow in Stirred Vessels to Establish Scaling Rules

Experimental apparatus and experimental conditions

System

Vessel

(1)

Type flat-bottomed Diameter (m) Height (m)


Impeller

0.12 0.12

4 O.IZ)

Type a standard six-blade Rushton turbine

Diameter (m) Number of impellers Number of blades Diameter of disc (m) Thickness of disc (mm) Length of impeller blade (m)

(perpendicular to shaft) Width of impeller blade (m)

(parallel to shaft) Off-bottom clearance (m)

Experimental conditions Impeller speed (Hz) Reynolds number (J^(2rof/v)

D/3 1 6

Z)/4 1.5,0.5 D/12

D/15

D/2

5.0 8x10^

(2)


4 OlD

a standard six-blade Rushton turbine

D/3 1 6

Z)/4 1.0

D/12

D/15

D/2

2.8 2.6x10*

(3)


4 0,1D

a standard six-blade Rushton turbine

D/3 1 6

Z)/4 3.0

D/12

D/15

D/2

1.3 1.2x10^

Working fluid Water

Scale-up rule Assumption: iV Z) = constant or iV oc2)~2/3

Mean velocity ^NDocD^'^ Periodic component ocD^'^ Turbulent intensity oc/)i/6 Energy in the smaller eddies ocD~^'^

Notation D vessel diameter, m N impeller speed, 1/sec fo impeller radius, m V kinematic viscosity, mVsec


McManamey, W. J., TYans. Instn. Chem. Engs., 58,271 (1980) A Circulation Model for Batch Mixing in Agitated, BafQed Vessels

Experimental apparatus Impeller Type: turbine and propeller Location of impeller:

turbine: 0.2-0.6/f propeller: 0.5-0.86 fT

Scale-up rule For radial flow impellers

KocNPo(d/T)^

For axial flow impellers

l/KocHi(2H^T)N-'d-^ (down flow)

l/Koc HiiH-Hi){2H^T)N-'d-^ (up flow)

Notation d impeller diameter, m H height of the liquid surface above the base of vessel, with the liquid at rest, m H\ height of the impeller above the base of vessel, m K amplitude decay rate constant (mixing rate constant), 1/sec N impeller speed, 1/sec P power input to impeller, W Po power number, Pip N^d , dimensionless T vessel diameter, m p density, kg/m^


Bowen, R. L, Chem. Eng. March, 195, (1985) Agitation Intensity: Key to Scaling Up Flow-Sensitive Liquid Systems

Experimental apparatus Liquid contained Height: Z/r=0.5'-'2 Volume of liquid in vessel: 102-106 gallons

Impeller Type: turbine and propeller Diameter: 6-100 in Z)/r=0.2-0.7

Operating conditions Bulk fluid velocity: 2~60 ft/min Impeller speed: 10—700 rpm

Scale up rule Tank turnover rate and agitation intensity

O/K=10.8M/F^(Z/7^2/3

ImpeUer tip speed and agitation intensity

ND=l.SnNj/NQ(D/Tf

Torque/unit volume

r A. A^

lotati D gc N Ni Np No NRe

P Q Q Q/V T TQ

V

z p

on impeller diameter, ft gravitational constant impeller speed, 1/min agitation intensity number, t;*/(6 ft/min), 1/3 to 10, dimensionless power number, Pgc/pN^D^=2nTQgc/pN^D^, dimensionless Impeller discharge coefficient, qlND^, dimensionless Reynolds number, pNOV^, dimensionless prime-mover power fluid flow produced by impeller, ft /min fluid flow in tank, gpm tank tumovers/min tank diameter, ft impeller shaft torque tank volume, gal or gal/turnover liquid height in tank, ft density, lb/ft?

6.1 Siiigl«ph«s« 475

Bujalski, W, Nienow, A. W, Chatwin, S. and Cooke, M., Chem. Eng. Sci.y 42, 317 (1987) The Dependency on Scale of Power Numbers of Rushton Disc Turbines

Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.22-1.83 m Height: = r

Baffle Number: 4 Width: 7710

Impeller Type: Rushton disc turbine Diameter: 0.25-0.697 Number of impellers: 1 Number of blade on impeller: 6 Diameter of disc: 3/4Z) Disk thickness Oci/D): 0.0122-0.0341 Length of impeller blade (perpendicular to shaft): Z)/4 Width of impeller blade (parallel to shaft): D/5 Off-bottom clearance: H/3

Working fluid Water


i?«=2xl0*-30xl0*

Scale-up rule

with a constant Xi/D and D«« T PoocZ)0195r°0^28^ 2) .258

or iVocZ)-°-75

Notation D impeller diameter, m H liquid height in vessel, m N impeller rotational speed, 1/sec P power input from impeller into the Uquid, W Po power number, P/PL N^D^, dimensionless Po mean peak power number corrected for blade width, dimensionless Re Reynolds number, NDVv, dimensionless T vessel diameter, m Xi disk thickness, m PL liquid density, kg/m^ V kinematic viscosity, mVsec

476 Chapter 6. Scal«-up nil«s

Costes, J. and Couderc, J. R, Chem. Eng. Sci., 43,2751 (1988) Study by Laser Doppler Anemometry of the Turbulent Flow Induced by a Rushton Turbine in a Stirred Tank: Influence of the Size of the Units-L Mean Flow and Turbulence


System

Vessel Type Diameter (m) Height (m) Liquid volume (i)

BafQe Number Width (m)

Impeller Type Diameter (m) Number of impellers Number of blades on impeller Length of impeller blade (m)



(1)


70

4 0.044

Rushton turbine 0.148

1 6

0.0370

0.0296

0.222

(2)

flat-bottomed 0.630 0.630 200

4 0.063

Rushton turbine 0.210

1 6

0.0525

0.0420

0.315

Working fluid Water

Experimental conditions i?«=27,000-85,000

Scale-up rule Noe/Nop^ZJ

NQC=QC/ND^

NQP=QP/ND^

Qp= 7c(D-^2s)fVrdz

Notation D agitator diameter, m

agitator rotational speed, 1/sec circulation flow number pumping coefficient circulation flow, mVsec pumping capacity, mVsec distance between the measure point and the blade, m time-smoothed radial velocity, m/sec axial position, m

N Nor NOP

Qc Qp s Vr z


Obot, N. T, Chem Eng. Progress, 47, July (1993) Design Mixing Processes Using the Frictional Law of Corresponding States

Scale-up rule Use of the frictional low of corresponding states: Two mixer flow fields are similar if the critical Reynolds numbers and the critical power numbers are equal for both fields.

Examples (1) Reference conditions

Impeller type: marine-type propeller Baffles: no baffles ^=2.6 Rec=l6.2 7?««=61,000 Z)=0.5m r=1.4m p=l,000kg/m^ Ai=10"^kg/ms

Scale-up conditions impeller type: marine-type propeller Z)=0.5m, r=1.4m p=l,100kg/m^ )U=0.021 kg/ms

(2) Reference conditions Impeller type: marine-type propeller Baffles: no baffles ^=2.6 i?«r=16.2 i?««=61,000 Z)=0.5m r=L4m p=l,000kg/m3 //=10-3kg/ms

Scale-up conditions impeller type: six flat-blade turbine Baffles: with baffles Z)=0.46m p= 1,100kg/m^ ^=0.021 kg/ms

(3) Reference conditions Impeller type: marine-type propeller Baffles: no baffles ^=2.6 7?«r=16.2 Re„,=6h000 J9=0.5m 7= 1.4m p= 1,000kg/m^ /i=10"3kg/ms

Scale-up conditions impeller type: six flat blade turbine Z)=1.4m p=l,100kg/m3 iU=0.021 kg/ms

Notation D Re Ren, T 1^ P 0 *-

impeller diameter, m Reynolds number similarity parameter tank diameter, m viscosity, kg/msec density, kg/m^ power number reduced power number

Subscripts a c Cfl

arbitrary conditions critical value

z critical value for arbitrary conditions c, r critical value for reference conditions

478 Chapter 6. Scale-up rulas

Ogawa, K. and Kuroda, C, AIChE Symposium Series, No. 305,91,95 (1995) A New Scale-up Rule and Evaluation of Traditional Rules from a Viewpoint of Energy Spectrum Function

Experimental apparatus Vessel Diameten 5^50 cm

Impeller Type: turbine Diameter: D/3 Off-bottom clearance D/3

Working fluids Water and aqueous solutions of glycerin

Experimental conditions Impeller speed: 100^400 rpm

Scale-up rale Use of energy spectrum function (1) If the scale-up ratio is less than 27 in volume, the turbulent kinetic energy = constant (2) If the scale-up ration is more than 27 in volume

(a)MVZ) ^ =constant when the higher wave number range plays significant role for the mixing

(b)MV/)=constant when the lower wave number range plays significant role for the mixing

Notation D vessel diameter, m u^ turbulent kinetic energy, mVsec

479

6.2 Multi phase

6.2.1 Solid-liquid systems

Zwietering, T, N., Chem. Eng. Sci., 8,244 (1958) Suspending of Solid Particles in Liquid by Agitators

Experimental apparatus System (1) (2) (3) (4) (5) (6)

Vessel Type Diameter (m) volume (0



A 0.154 2.9

0.154

4 0.0154

B 0.192 5.5

0.192

4 0.0192

A 0.24 11

0.24

4 0.024

B 0.29 19

0.29

4 0.029

A 0.45 70

0.45

4 0.045

A 0.60 170

0.60

4 0.060

A: flat-bottomed B: flat, dished (radius=vessel diameter), and conical bottom (120")

Stirrer types and dimensions

Type of stirrer Diameter (m)

Paddles, Z>/W Paddles, Z)/PF Flat blade turbines Vaned disks Propellers

0.06, 0.08, 0.112, 0.16 0.06, 0.08, 0.16, 0.224 0.06, 0.08, 0.12, 0.16, 0.06, 0.08, 0.10, 0.12, 0.05, 0.07, 0.115

0.20 0.16, 0.20

f •M -0- >

Paddle stirrer D/W=2

\ w \ M -D- »

0-2 Dl a

0-25 O/V""^

Paddle stirrer Six blade turbme D/W=4

Vaned disk

Five types of stirrers used in the experiments.

e3 ' d^ - 0 •

Propeller


Working fluids, solids and their physical properties Liquid:

Liquid Density (kg/m ) 77(cP) v(mVsec) X10^

Water Acetone Carbon tetrachloride Potassium carbonate

solution Oil

1,000 790

1,600 1,440

840

1.0 0.31 1.0 5.0

9.3

1.0 0.39 0.65 3.5

ILl

Solid:

Solid Density (kg/m^) Particle size (ji)

Sand Sodium chloride

2,600 2,160

125-150, 250-350, 710-850 125-150, 150-250, 250-350

Experimental conditions Solid concentration=0.5—20 wt%

Scale-up rule Assumption: geometrical similarity, equal liquid and solid properties, and equal particle sizes For complete suspension of solid particles «Z)®- =constant

Notation D stirrer diameter, m n stirrer speed, 1/sec P power input to the stirrer for complete suspension of solid, Nm/sec V volume of liquid, m W width of paddle, m /i viscosity of liquid, cP V kinematic viscosity of liquid, mVsec

6.2 Multiphase 481

Miller, D. N., Ind. Eng. Chem. Process Des. Develop., 10,365, (1971) Scale-up of Agitated Vessels Mass Transfer from Suspended Solute Particles

Experimental apparatus Vessel and impeller geometries and dimensions Vessel type: dish-bottomed Impeller type: flat paddle Number of paddles: 4

Nominal vessel size, gal

1 10 100

Dimensions, in.

A B C D E F G H I J

Numbers of baffles

6 8V4 12 4 % V32

V, V, V2 V16 4

12 17 V2 24 8

V/2 Vie % V4 1 % 4

27 39%

54 18

3'/. '/64

l " / l 6

l " / l 6 2V4 V32 4

Working fluid, solid and its physical properties Liquid: water Solid: benzoic acid in 5/32-in. cylindrical pellets

Experimental conditions Nominal vessel size, gal

Impeller speed (rpm) 1

170-490 10

103^-290 100

25-168

Impeller power input 0.05—19 hp/10^ gal

Scale-up rule For forced convection 7Vsh =constant

Nst.,=2'\-l.lONsty^Ns}'' Ui=^{4Dpg(f>p-p)/3pCDy^' «,/w/=0.000644(«')'-^

For free convection iVish =constant

For radical diffusion iVsb^=constant Nst,=2(PJDHNjuy'Ns}^' DJD=3,0S(P/VT'^

0.06Arod 0.06A rod

SIDE VIEW

432 Chapter 6. Scale-up rules

Notation CD drag coefficient d impeller diameter, cm D molecular diffusivity, cmVsec De effective diffiisivity, cmVsec Dp particle diameter, cm g acceleration of gravity, cm/sec^ k mass transfer rate constant, cm/sec n' impeller speed, 1/sec NGT Grashof number, Dp^gAp/v^p, dimensionless NRC particle Reynolds number, DpUs/v, dimensionless Nsc Schmidt number, v/D, dimensionless Nsh impeller Sherwood number, kd/D, dimensionless Nshp particle Sherwood number, kDp/D, dimensionless P agitator power input, hp Us slip velocity, m/sec ui terminal settling velocity of solid, cm/sec V volume, 10^ gal V kinematic viscosity, cmVsec Ap bulk and interface solution density difference, g/cm^ p fluid density, g/cm^ PP particle density, g/cm^

6.2 Multl phas* 433

Okamoto, Y., Nishikawa, M. and Hashimoto, K., Kagaku Kogaku Ronbunshu, 5,410 (1979) Eneigy Dissipation Rate Distribution in Mixing Vessels and Its Effects on Liquid-Liquid Dispersion and Solid-Liquid Mass Transfer


Liquid contained Height: (1) 15 (2) 30 (3) 60 cm

Baffle Number: 4 or 0 Width: (1) 1.5 (2) 3.0 (3) 6.0 cm

Impeller Type: six-bladed disk turbine Diameter: 0.5 Z> Number of impeUers: 1 Number of blades on impellers: 6 Length of impeller blade (perpendicular to shaft): 0.25 d Width of impeller blade (parallel to shaft): 0.2 (f Off-bottom clearance: (1) 7.5 (2) 15 (3) 30 cm

Working fluid Use of data taken by Harriott and Levins

Harriot, P., AIChE Journal, 8,93 (1962) Levins, D. M. and Glastonbury, J. R., Chem. Eng. Set., 27,537 (1972)

Scale-up rule \a2o • \a22

pr(d^ pV) [D

Notation d impeUer diameter, cm D vessel diameter, cm k solid-liquid mass transfer coefficient, cm/sec P power consumption, gcmVsec^ V volume of vessel, cm^ p density, g/aa?

484 Chapter 6. Scal«-up rutos

Chapman, C. M., Nienow, A. W, Cooke, M. and Middleton, J. C, Chem. Eng. Res. Des., 61, 71 (1983) Particle-Gas-Liquid Mixing in Stirred Vessels Part I: Particle-Liquid Mixing

Experimental apparatus Vessels employed in this study

Diameter, rCm) Liquid height, H (m) Volume, VL (m^) BafQe width (%) Spaiger

Temperature control Material fo

construction

Geometry Viewing

Type/Tank

(a)T56 Disk

turbine

Angled blade disc turbine

Mixed flow impeller pumping up

Mixed flow impeller pumiHng down

Mixed flow impeller pumping down

Marine propeller (b) Other tanks

T29

T30 T91

Tl83

T29 (UCL)

0.29 0.29 0.0192

10 Pipe point

source

Water jacket Perspex and glass

T30 (ICD

0.30 0.30 0.0212

10 Pipe point

source

None Perspex

Cylindrical with flat Through sides and

Impellers used (a) in Tse

No. of Notation blades

DT

ADT

4MFU

4MFD

6MFD

AFD

DT 4MFD 4MFD DT DT

4MFD DT

4MFD

6

6

4

4

6

3

6 4 4 6 6

4 6

4

Diameters, Dim)

0.14 0.187 0.28 0.28

0.28

0.14 0.28 0.14

0.29

0.145 0.145 0.072 0.15 0.457

0.457 0.902

0.794

Tse (UCL)

0.56 0.56 0.138

10 Three point

T9,

qci) 0.91 0.91 0.592

10

Tl83 qci) 1.83 1.68 4.41 10

t Pipe point Pipe point bottom bearing source

source Water jacket None

Perspex

t base oase

source

None Perspex Polypropylene

: (b) in other vessels

Vertical height of blade (m)

D/5 D/5 D/5

0.039

D/S

D/5 D/5 D/5

Not constant

D/5 0.029 0.015 D/5 D/5

0.0984 0.175

0.165

Horizontal length of blade (m)

D/4 D/4 D/4 D/4

a 120

a050 ai2o ao50

D/4 ao55 a025 D/4 D/4

a 159 D/4

a349

with Perspex windows

fc, \ri. *^ Via wuiuuws

in side and base

Disc and blade

thickness (mm)

3.2 3.2 3.2 2.5

3.2

3.2 3.2 3.2

3.2 3.2 1.6 2.0

4.8 disc 6.35 blade

6.35^ 6.35 disc 9.5 blade

9.5

Angle/pitch ofUade

— —

45**

45**

45** 45** 45**

1.5/)

— 45'* 45**

—

45''

45**

^The central horizontal portion of each Uade was double this thickness

6.2 MuKi phase 485

Working fluids, solids and their physical properties Liquid: de-ionized water and tap water Solid:

Particles employed in this study

Particles Shape

Suiface to volume mean

Size range diameter (jim) (\im) (kgm- )

Polystyrene Diakon Dowex ion exchange resin Anthracite

Glass powder

Soda glass ballotini Sand

Lead glass ballotini

Spherical Spherical Spherical

Flat and irregular (sphericity#0.4to0.5)

Granular (sphericity #0.7)

Spherical Granular

(sphericity #0.9) Spherical

250--355 420 ~ 710 500 ~ 1,000

500--600

250-^355

180 - 250

300 ~ 710

8 0 - 1 0 5 4 4 0 - 5 3 0 850 - 1,000

2,500 ~ 2,800

302 583

—

309

206

470

—

1,050 1,200 1,250

1,400

2,200

2,480

2,650

2,900 2,900 2,900 2,900

Scale-Up rule NjsocT^-''

cNjs^D^

Notation D Njs

impeller diameter, m impeUer speed at which solids do not spend more than 1 to 2 seconds on the bottom when observed, 1/sec

T vessel diameter, m £T mean energy dissipation rate, W/kg (£r)/5 mean energy dissipation rate at the speed at which solids do not spend more than 1 to 2

seconds on the bottom when observed, W/kg


Momonaga, M., Hibi, F. and Yazawa, H., Kagaku Kogaku RonbunshUy 10,192 (1984) Agitation Effect on Size Distribution in the Crystallization of Phenoxy Acetic Acid Compounds.


System

Vessel Type Diameter (mm) Depth (mm)

Baffle Number

Impeller Type Diameter (mm) Number of impellers

(1)

dish-bottomed 130 150

4

Pfaudler 72,78,86,90,92

1

(2)

dish-bottomed 600 —

4

Pfaudler 420,500

1

Working fluids and solid Liquids: an acetone solution of phenoxy acetic acid and water Solid: phenoxy acetic acid (the solid is crystalhzed in water by adding water to the acetone solution of phenoxy acetic acid).

Experimental conditions Temperature: 5°C Impeller speed (rpm):

System (1): 200-600 System (2): 80-106

Scale-up rule

DPI" ' = constant

Notation d impeller diameter, mm D vessel diameter, mm Dp representative particle diameter, ^im g gravity acceleration, m/sec^ N rotational speed of impeller, 1/min Np power number, P/piN^d^ P power consumption of agitation, kgm/sec Z power consumption ratio of agitation, dimensionless PI density of liquid, kg/w? Ps density of sohd, kg/m^

6.2 MultiphaM 487

Buurman. C, Resoort, G. and Plaschkes, A., Chem. Eng. Sci., 41,2865 (1986) Scaling-up Rules for Solids Suspension in Stirred Vessels




Baffle Number Width (m) Clearance of baffle from wall (cm)

ImpeUer Type

Diameter (m) Number of impellers Niunber of blades Width of impeller blade (m)


(1)

dish-bottomed 4.26 10

4.26

4 0.426

1

45° downward-pumping axial turbine

0.47 1 4

1/4D

1/37

(2)

dish-bottomed 0.48

Working fluid, solid and its physical properties Liquid: tap water Solid: sand

density=2,590 kg/w?; average size (d32)=157 \im Experimental conditions:

Suspension height: 4.3 m Stirred speed: 2-^141/sec Maximum sohd concentration: 15 vol%

Scale-up rule For complete solid suspension

Notation D impeUer diameter, m He stirrer speed for complete suspension, 1/sec T vessel diameter, m

488 Chapter 6. Scal«-up rules

Molerus, 0. and Latzel, W, Chem. Eng. Sa., 42,1423 (1987) Suspension of Solid Particles in Agitated Vessels-I. Archimedes Numbers < 40


System

Vessel Type Diameter (m)

Liquid contained Height (^/Z»

Baffle Number

Impeller Type Diameter (D,/Z» Number of impellers Number of blades on impeller Off-bottom clearance (ft/A)

(1)

dish-bottomed 0.19

1

4

marine propeller 0.315

1 3 1

(2)

dish-bottomed 0.45

1

4


1 3 1

(3)

dish-bottomed 0.45

1

4


1 3 1

Working fluid, solids, and their physical properties Liquid: tap water and water-ethylene glycol mixtures SoUd:

Solid material Density (kg/m^) Mean particle diameter (jim)

Steel beads Glass beads

7,639 - 7,841 2,480 -- 2,496

170 - 1,937 34-654

Experimental conditions: Volume concentrations of solid particles = 0.5—30%

Scale up rule

For ^r<40 U = ^ ^ ^ ^ = ^ PF

ODocD'^^

Notation Ar Archimedes number, dimensionless

diameter of particles, m diameter of vessel, m diameter of stirrer, m gravitational acceleration, m/sec liquid height, m stirrer height above bottom, m kinematic viscosity, mVsec fluid density, kg/m^ soHd density, kg/m^ angular velocity, 1/sec

dp D Ds g H

ft V pF Ps

6.2 MuttiphaM 489

Molerus, 0. and Latzel, W, Chem. Eng. Set., 42,1431 (1987) Suspension of Solid Particles in Agitated Vessels-II. Archimedes Numbers > 40, Reliable Prediction of Minimum Stirrer Angular Velocities


System


Liquid contained Height (ff/Z))

Baffle Number

Impeller Type Diameter (JDs/D) Number of impellers Number of blades on i impeller

(1)

flat-bottomed 0.19

1

4


1 3

Workiiig fltiid, solids and their physical properties Liquid: tap water SoUd:

Solid material

Glass ballotini

Spherical iron particles

(2)

flat-bottomed 1.5

1

4

marine propeller I D.315

1 3

Density (kg/m^) P ^ d e size dp (^m)

2,500

7,800

200 514 650

522 900

1,900

Experimental conditions Volume concentrations of solid particles = 0.5-^30%

Scale up rule

For Ar>40 V PF )

Notation Ar Archimedes number, dimensionless C proportionality factor dp diameter of particles, m D diameter of vessel, m A diameter of stirrer, m g gravitational acceleration, m/sec

H liquid height, m V kinematic viscosity, mVsec PF fluid density, kg/m^ ps solid densi^, kg/m^ (o angular velocity, 1/sec

490 Chapter 6. Scale-up rulas

Mak, A. T. C. and Ruszkowski, S. W, IChemE. Symposium Series, No. 121, 379 (1990) Scaling-up of Solids Distribution in Stirred Vessels



Liquid contained Height Volume of liquid in vessel (m ) Off bottom clearance Off-wall clearance


Impeller Type

Diameter (m) Number of impellers Number of blades Off-bottom clearance (m)

(1)

dish-bottomed 0.61

T 0.165 T/5 T/60

4 7/12

downwards pumping 45° 4-bladed pitched

blade turbine 0.31

1 4

r/4

(2)

dish-bottomed 1.83

T 4.5 T/5 T/eo

4 7/12

downwards pumping 45° 4-bladed pitched

blade turbine 0.93

1 4

r/4

Working fluid, solid and its physical properties Liquid: water Solid: BIS Chelford (particle size=150-210 |iim)

Experimental conditions ImpeUer speed: 20 ~ 100 rpm Solid concentration: up to 30 wt%

Scale-up rule Pr=constant

Notation P„ power input per unit volume T vessel diameter, m

6.2 Multiphase 491

Ditl, E and Nauman, E. B.^AIChE Journal, 38,959 (1992) Off-bottom Suspension of Thin Sheets


System

Vessel Type Diameter (mm)

Liquid contained Height (mm)

Baffle Number Width (mm)

Impeller Type

Diameter (mm) Number of impellers Number of blades

Off-bottom clearance (C/D)

(1)

flat-bottomed 295

295

4 29.5

(2)

flat-bottomed 440

440

4 44.0

(a) 45^ pitched four-bladed turbine (b) LightninA310 (c) Flat six-blade turbine

77Z) = 3((a)102,(b)96,(c)97) 1

(a)4,(c)6

7yZ) = 3((a),0))152.4) 1

(a)4,(c)6

(a) 1/3,2/3,1, (b) 1/3,2/3,1, (c) 1/3,2/3

Working fluid, solids and their physical properties Liquid: a Newton fluid Solid: (a) thin and flat PVC and Al sheets: thickness 0.5,0.8, and 2.5 mm

(b) thin and curved PET sheets: thickness 0.8 mm Experimental conditions

Solid concentration: PVC: 0,0.1 and 0.5 wt% PET: up to 15 wt% Scale-up rule

Single particle or nonagglomerating systems thick particles i\r,r°'^=constant thin particles i\^^r°^=constant

Multiple particle or agglomerating system thick particles iV^r°-^=constant

Notation C off-bottom clearance of impeller, m D impeller diameter, m Ng impeller speed required for particle suspension, 1/sec or 1/min T tank diameter, m

492 Chapter 6. Seal«-up rates

Petela, R., Fueh 72,511 (1993) A Design Method for Scale-up of Selective Agglomeration Plant for Upgrading Coal with respect to Sulfur and Mineral Matter Content


Parameter

Total slurry flow rate, m (kg s"*) Diameter of impeller, d (mm) Rotation speed of impeller, n (rev min~ ) hmer diameter of tank, D (mm) Height of liquid level in tank, H (mm) Height of impeller wing, h (mm) Cieometric ratios: d/D^a

D/H^f h/H^g

Number of tank,/; Number of impeller wings, i Residence time in tank, T (min) Real residence time in the zone of greatest

velocity gradient, t (ms) Total power, P(kW) Specific energy consumption, E (kW kg"*)

Laboratory

0.0226 45

2,100 110 138 12 0.409 0.797 0.087 1 4 1

0.33

0.04 1.8

1

30 525 180

1,483 2,696

796 0354 0.550 0.295 5

16 13.4

0.33

158 5.3

Plant

2

30 158 600 445 809 379

0354 0.550 0.469 7

24 0.51

033

31.7 1.06

3

30 105 900 297 539 265

0354 0.550 0.492

10 24 0.21

033

21.1 0.70

Working fluid and solid Liquid: water Solid: coal powder

Experimental conditions w=180-2,100rpm

Scale-up rule Shear rate (nd)= constant Residence time (ihk/m)=constant

Notation d impeller diameter, m h height of impeller, m i number of impeller wings k number of tanks m mass flow rate of slurry, kg/sec n rotational speed of impeller, 1/sec

6.2 Multiphase 493

6.2.2 Liquid-liquid systems

Skelland, A. H. R and Seksaria, R., Ind. Eng. Chem. Process Des. Dev., 17,56 (1978) Minimum Impeller Speeds for Liquid-Liquid Dispersion in Baffled Vessels

Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.2135 m Height: 0.2500 m Volume: 0.01 m^


Baffle Number: 4 Width: 0.0190 m Thickness: 0.0025 m Length: 0.2300 m Length of baffle inmiersed in the liquid from air-liquid interfece: 0.1930 m

Impeller Type: (1) propellers (three-bladed, square-pitched downward thrusting)

(2) 45° six pitched turbines (projected width D/S; downward-thrusting) (3) six flat-blade turbines (blade width D/S) (4) six curved-blade turbines (blade width D/S)

Diameter: (1) 0.1,0.075,0.06 m (2) 0.1,0.075,0.062 m (3) 0.106,0.078,0.065 m (4) 0.102,0.076,0.063 m

Number of impellers: 1 Off-bottom clearance: i/ /4, H/2,3H/4

Working fluids and their physical properties Continuous phase: water Dispersed phase: see table

Fluid properties at 25*0

Fluid Density, Dynamic viscosity, kg/m^ Ns/m2

Interlacial tension with water,

N/m

5-cSt Dow Commg 200 Fluid 10-cSt Dow Coming 200 Fluid 15-cSt Dow Coming 200 Fluid Benzaldehude Ethyl acetate Water

920 940 948.3

1,041 894

1,000

0.0046 0.0094 0.0143 0.0014 0.00046 0.0010

0.0425 0.0435 0.0437 0.0145 0.00627

—

Experimental conditions Volume fraction of organic liquid: 0.50 Temperature: 25V

494 Chapter 6. Scal«-up nilas

Scale-up rtile (a) Constant TID

ML. N2'

1.1

(b) Variable T/D

P •— < V

3n5 N^D i 1 J.-1.3

Values of 3tfi-1.7

Set no. 3fli-1.7

Propeller

Pitched-blade turbine

Flat-blade turbine

Curved-blade turbine

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16

-0.85184 -0.03935 -0.52013

1.06951 1.45360 0.75631 3.07030 0.92113 3.17422

* 0.94297

« 2.68732

4c

0.70168 -0.07970

*Asterisks indicate insufficient data.

Notation a\ constant D impeller diameter, m H liquid height, m N minimum rotational speed of impeller for complete liquid-liquid P power input to the system, W T tank diameter, m fx dynamic viscosity, Nsec/m^ p density, kg/m^ a interfacial tension, N/m

6.2 IMultiphaM 495

Skelland, A. H. R and Lee, J. M., AIChE Journal 27,99 (1981) Drop Size and Continuous Phase Mass Transfer in Agitated Vessels




Baffle Number Width (m) Length (m) Thickness (m) Length of baffle immersed in the

liquid from air-liquid interface ImpeUer

Type Diameter (m) Number of impellers Number of blades

(1)


0.210

4 0.019 0.230 0.0031 0.193

six flat-blade turbine 0.078

1 6

(2)


0.246

4 0.019 0.290 0.0031 0.229

six flat-blade turbine 0.106

1 6

Working fluids Continuous phase and dispersed phase: see Table 1 and 2

Table 1 Five systems studied.

System Dispersed Phase Continuous Phase Solute

1 2 cSt Dow Coming^ 200 Fluid 2 2 cSt Dow Coming^ 200 Fluid 3 2 cSt Dow Coming^ 200 Fluid 4 Ethyl acetate 5 Benzaldehyde

Water* Water*+20% sucrose** Water*+30% sucrose **

Water Water

Heptanoic add Heptanoic acid Heptanoic acid Heptanoic acid Heptanoic acid

* Double-distilled water ^ Clear dimethyl siloxane "" Colonial pure cane sugar

Table 2 Physical and transport properties at 23*0

System

1 2 3 4 5

a N/m 0.039 0.032 0.033 0.006 0.015

Pc kg/m^

1,000 1,087 1,131 1,000 1,000

pd kg/m^

873 873 873 894

1,041

^c

N-s/m'

0.0010 0.0018 0.0029 0.0010 0.0010

A^rf N-s/m^

0.0019 0.0019 0.0019 0.00046 0.0014

0rXlO*o

mVs 6.01 5.66 4.02 6.01 6.01

496 Chapter 6. Scal«-up nil«s

Experimental conditions Volume fraction of dispersed phase: 0.03^0.09 Impeller speed: 3^8 rps

Scale-up rule

N2

0.651 di2

dh

U58

PilVoh ^Pi PzlVoh Pz 71 =(fl

Notation di impeller diameter, m N impeller speed, 1/sec P power dissipated by impeller, Nm/sec T vessel diameter, m

6.2 Multl phase 497

Eckert, R. E., McLaughlin, C. M. and Rushton, J. U.,AIChE Journal, 31,1181 (1985) Liquid-Liquid Interfacial Areas Formed by Turbine Impellers in Baffled, Cylindrical Mixing Tanks

Experimental apparatus System (1) (2) (3)



Impeller Type Diameter (J) IT) Number of impellers Number of blades Off-bottom clearance (m)

A: a standard six-blade turbine

Working fluids and their physical properties Design 1

Continuous phase: water Dispersed phase: organic liquids (see table)

Design 2 Continuous phase: water and com syrup Dispersed phase: the same as those used in Design 1

Organic liquids used, design I (Continuous phase: water)

a dynes/cm jUr pd (10-5N/cm) mPa-s g/cm3

Liquid

w-Octanol Oleic acid Nitrobenzene Xylene Kerosene w-Heptane Paraffin oil

201C*

8.5 15.6 25.66 37.77

— — —

251C**

8.6 14.3 24.4 37.4 39.0 41.6 52.5

20t:

8.95 —

1.98 0.65

— 0.416

—

25t:

7.13 28.7

1.86 0.602 1.32 0.445

129.0

201C

0.827 0.854 1.205 0.861

— 0.684

—

251C

0.825 0.890 1.20 0.860 0.796 0.714 0.874

flat-bottomed 14.2

4 0.142

A 1/3 1 6

H/3

flat-bottomed 29.5

4 0.295

A 5/12

1 6

H/3

flat-bottomed 43.9

4 0.439

A 1/2 1 6

H/3

* 20^ values from Lange, Handbook of Chemistry. '* 25*0 is the approximate temperature at which data were determined and runs conducted.


Experimental levels, Design II

Levels

Variable

0 a* l^r T D/T N

Units

(dimensionless) dynes/cm (10"^ N/cm) mPas cm (dimensionless) s-i

* Varies slightiy with //r

Low

0.01 35.1 0.874

14.2 1/3 Ni

Middle

0.02 37.4

1.87 29.5 5/12 N2

High

0.04 45.5

4.00 43.9 1/2 Ns

Interfacial tensions for organic liquids used, Design II

Liquid

Kerosene Xylene w-Heptane

* Dynes/cm=

/Xf=1.87 dynes/cm*

=10-'N/cm.

Experimental conditions:

Variable

a 0 T D/T N a l^d pd Mr Pc P P/V NRC

Nwe U

35.1 37.4 45.5

a

/Xf =4.0 dynes/cm

34.9 36.7 44.6

Range of variables studied

Minimum

2.17 0.005 14.2 0.34 1.33 8.6 0.445 0.714 0.874 0.996 8,100 1.32 7,200 137 80

Maximum

19.40 0.08 43.9 0.54 11.67 52.5 129.0 1.20 4.05 1.140 428,300 17.42 114,700 1,528 207

Units

cmVcm^ (dimensionless) cm (dimensionless) s-i dynes/cm (10~^ N/cm) mPas g/cm^ mPas g/cm^ gcm/s g/cm^s (dimensionless) (dimensionless) cm/s

Scale-up rule rUlnl-23T-0.18

\ U 1

2L D2] (TZ

A 71

6.2 Multi phas* ^99

Notation a interfacial area per unit volume dispersion, cmVcm^ D impeller diameter, cm N impeller speed, 1/sec NRe impeller Reynolds number, D W pdiie, dimensionless Nwe Weber number, D^N^ pdlOy dimensionless P power exerted on fluids by impeller, gem/sec (1.31 x 10"^ hp) P/V power per unit volume, g/cm^ sec (0.499 hp/l,0(X) gal) T mixing tank diameter, cm U impeller tip speed, cm/sec u impeller tip speed divided by 100, cm/sec V volume of the mixing tank, cm^ /i viscosity, mPasec p density, g/cm^ G interfacial tension, dyne/cm (10"^ N/cm) 0 volume fraction of dispersed phase


500 Chapter 6. Scale-up nilas

Skelland, A. H. P. and Ramsay, G. G., Ind. Eng. Chem. Res., 26,77 (1987) Minimum Agitator Speeds for Complete Liquid-Liquid Dispersion

Experimental apparatus Vessel and agitator dimensions

internal diameter liquid height in of vessel, m

0.216 0.241 0.241 0.241 0.292

vessel, m

0.216 0.121 0.241 0.362 0.292

bafQe width. m

0.019 0.019 0.019 0.019 0.025

impeller diameter, m

0.102, 0.076, 0.102, 0.076, 0.102, 0.076, 0.102, 0.076, 0.102, 0.076

0.065 0.065 0.065 0.065

square pitch, downthrusting propeller (three blades)

downthrusting pitched-blade turbine (six blades)

flat-blade turbine (six blades)

curved-blade turbine (six blades)

disk turbine (six blades)

set

1 2 3 4

5 6 7 8

9 10 11 12 18 19

13 14 15 16

17

HIT

1/2 3/2

1

impeller location

Hl^ 3H/4: H/2

H/4,3H/4

H/4 3ff/4 H/2

H/A,3H/4

H/4 3H/4 H/2

H/4,3H/4 H/2 H/2

H/4 3H/4 H/2

H/4,3H/4

H/2

a

0.67 0.95 0.79 1.33

1.44 1.17 1.97 1.27

2.02 *

1.38 *

1.24 1.70

1.86 •

1.20 0.94

1.70

^Asterisks indicate insufficient data due to splashing

6 ^ MuHiphsM

Axial flow impellers used r rvvxV-J

501

cifeo

(a) Pitched blade turbine (b) Marine-type propeller

Radial flow impellers used

\j

(c) flat-blade turbine (d) curved-blade turbine (e) disk turbine

Working fluids and their physical properties Continuous phase: deionized water Dispersed phase: see table

Fluid properties at 23 "C

fluid

ethyl acetate benzaldehyde chlorobenzene carbon tetrachloride water

density, kg/m^

894 1,041 1,106 1,590

997

dynamic viscosity, N-s/m^

0.00046 0.0014 0.0010 0.0010 0.0009

interfacial tension with water, N/m

0.00627 0.0145 0.0352 0.045

Experimental conditions Temperature: 23*0

Scale-up rule With assumption that constant physical properties and constant volume fraction of dispersed phase

(1) Full geometric similarity (2) Variable T/D

N„,

Notation D impeller diameter, m

liquid height im vessel, m minimum rotational speed of impeller for complete liquid-liquid dispersion in agitated, baffled vessels without regard to uniformity, 1/sec

T tank diameter, m a constant (the values of are shovm in a table attached)

H

502 Chapter 6. Scal«-up nilas

Okufi, S., Perez de Ortiz, E. S. and Sawistowski, H., Can. J, ofChem. Eng., 68,400 (1990) Scale-up of Liquid-Liquid Dispersions in Stirred Tanks


System




Impeller Type

Diameter (cm) Number of impellers Number of blades Length of impeller blade (cm)

(perpendicular to shaft) Width of impeller blade (cm)

(parallel to shaft) Impeller blade thickness (mm) Off-bottom clearance

(1)

flat-bottomed 11

11

4 LI

six-blade disk turbine

T/3 1 6

Z)/4

D/5

0.79 D

(2)

flat-bottomed 22

22

4 2.2


T/3 1 6

D/i

D/S

1.59 D

(3)

flat-bottomed 44

44

4 4.4


T/3 1 6

Z)/4

D/5

3.18 D

Working fluids Continuous phase: water Dispersed phase: (a) w-heptane

(b) n-heptane containing different concentrations of di-(2-ethylhexyl) phosphoric add in an aqueous solution of sodium sulphate

Experimental conditions Impeller speed: 317^1,000 rpm Dispersed phase volume fraction: 0.1-^0.4

Scale-up rule

ayoc impeller tip speed

Notation av interfacial area per unit volume, 1/cm D impeller diameter, cm T vessel diameter, cm

6.2 Multi phas« 5Q3

Smit, L, IChemE. Symposium Series, No. 136,309 (1994) An Alternative Scale Procedure for Stirred Vessels



Impeller Diameter (m) Impeller speed (rpm)

(1)

dish-bottomed 0.45

0.065 1,470

(2)

dish-bottomed 2.7

0.95 100

Working fluids Continuous phase: a liquid Dispersed phase: a liquid

Scale-up rule Coalescence in Uquid-liquid dispersion

3

D\ p ]ocT^ /r-H--OOilStailt

Di/D2=iTi/T2f"

/r-t^oonstant

Ni/N2=(Ti/T2r'''

Notation D impeller diameter, m P mixing power, W T vessel diameter, T tc hquid circulation time V liquid volume, m^

504 Chapter 6. Scal«-up rulas


Figueiredo, M. M. L. and Calderbank, R H., Chem. Eng. Scu, 34,1333 (1979) The Scale-up of Aerated Mixing Vessels for Specified Oxygen Dissolution Rates


System

Vessel Type Volume (m ) Diameter (m) Height (m)

Impeller Type Diameter (m) Number of impellers Length of impeller blade (m)


(parallel to shaft)

(1)

flat-bottomed 0.043 0.38 0.38

flat-bladed turbine

(2)

flat-bottomed 0.60 0.91 0.91

flat-bladed turbine 0.27

1 0.06

0.06


Experimental conditions For system (2)

Power consumption: 0.41 x 10^-4.8 x 10 W/m^ Impeller rotational speed: 4.16^8.33 1/sec Superficial gas velocity: 6.34,8.87 and 12.710"^ m/sec

Scale-up rule

kLoc(p/VLr^a/v,f^ Notation

ki liquid side mass transfer coefficient, m/sec P agitator power dissipation, W VL volume of liquid, m

6.2 Muttiphas* 505

Nishikawa, M., Nakamura, M., Yagi, H. and Hashimoto, K.,/. Chem. Eng. Japan, 14,219 (1981) Gas Absorption in Aerated Mixing Vessels


Dimensions of experimental apparatus

Vessel diameter Liquid depth Liquid volume Impeller diameter Disc diameter Number of blades Blade angle Blade width Impeller level Number of baffles Baffle width Spaiger arm length Sparger inlet pipe Holes in sparger Spacing of holes Hole diameter Sparger level

D{cm) H(cm) Vicm^) d(cm)

dd (cm)

%(-) e{-) b{cm) C(cm)

« B ( - ) hwicm) Ls (cm) Lp (cm)

«*(-) 5 (cm)

dk (cm) C,(cm)

Paddle

15 15

2,650 7.5

4 45^

1.5 3.75 4 1.5 3 3

21 0.5 0.1 1.5

30 30

21,200 12, 15

3.8, 5.6 4, 6

90** 2, 2.4, 3

7.5 4 3 6 5

21 1 0.1 3

15 15

2,650 5, 7.5

7.5 6

90* 1, 1.5

3.75 4 1.5 3 3

21 0.5 0.1 1.5

Turbine

20 20

6,280 10 11.3 6

90** 2 5 4 2 4 4

21 0.7 0.1 2

30 30

21,200 15 22.5 6

90** 3 7.5 4 3 6 5

21 1 0.1 3

60 60

170,000 30 22.5 6

90** 6

15 4 6

12 10 21 2 0.15 5

Working fluids Liquid: distilled water Gas: air and nitrogen

Experimental conditions Impeller speed: 0-16.671/sec Temperature: 301: Superficial gas velocity: 0.085-^1.13 m/sec Power number

Paddle 2.62,3.08 Turbine 3.70,5.45,5.50

Scale-up rule For effective scale-up

W2/Wi={l--(Po^/Bn)2Ku,2/H2)/{l-(Poui/Pia)l}(u,l/Hi)

Notation H liquid height in vessel with no aeration, cm P partial pressure of absorbed gas, atom Ug superficial gas velocity, cm/sec w gas component absorbed per unit volume of liquid

Subscripts 1 smaller tank 2 larger tank

506 Chapter 6. Scate-up nilas

Satoh, K. Shimada, H. and Yoshino, Z., Kagaku Kogaku Ronbunshu, 15,733 (1989) Gas Absorption Efficiency of Gas-Liquid Contactors with Mechanical Agitation




Impeller

6DT 6MDT-1 6MDr-2 6PBDT 6PBT

Types of impeller (Direction of rotation: from right side to left side)

Dimensions of impellers

Impeller Sign.

Diameter of impeller

dim)

0.08 0.10 0.12 0.15

0.08 0.10 0.15

0.08 0.10 0.12 0.15

0.10

0.08 0.10 0.15

Wide of blades b/di-)

1/5

V2/5

(>/2+l)/10

>/2/5

1/5


1/4

1/4

1/4

1/4

1/2

Angle of blades

(degree)

90

+45 - 4 5

+45 - 9 0

45

45

Number of blades

(-)

6

6

6

6

6




Pitched Blade DiskTutbine


6DT

6MDT-1

6MDT-2

6PBDT

6PBT

Off-bottom clearance: H/5



Experimental conditions Temperature: 20*C

Scale-up rule

Notation D diameter of vessel, m d diameter of impeller, m H liquid depth in vessel without aeration, m kia overall volumetric mass transfer coefficient based on liquid phase, 1/sec Pav aeration power input per unit volume of liquid, W/m^ Pev effective power input per unit volume of liquid, W/m^ Pgv agitation power input to gassed liquid per unit volume of liquid, W/m^ y constant ^ power input correction

508 Chapter 6. Scal«-up rules

Schluter, V and Deckwer, W.-D., Chem. Eng. Sci., 47,2357 (1992) Gas/Liquid Mass Transfer in Stirred Vessels


Vessel Volume (m )

Liquid Height (/i/D)

Impeller Type Diameter W/D)

RT IT

Number of impellers RT IT

(1)

0.072

2.1

RTorIT

0.4 0.7

3 4

(2)

0.3

2.1

RTorIT

0.4 0.7

3 4

(3)

1.5

2.1

RTorIT

0.4 0.7

3 4

(4)

3

1.3

RT

0.34

3

RT: Rushton turbine IT: Intermig impeller

Working system Biological test system (cultivations of the strictly aerobic yeast was carried out under oxygen limited conditions)

Experimental conditions 0.5^P/Vi: 16kW/m'

0.0038 <, qclVi ^ 0.027 1/sec

Scale-up rule

For Rushton turbine: haocP^-^ (qc/Vif^

For Intermig turbine: haocP^-^^ (qG/Vif'^

Notation D reactor diameter, m d stirrer diameter, m h liquid height, m kia volume referred mass transfer coefficient, 1/sec P power input, kW qc gassing rate, mVsec VL liquid volume, m

6.2 MuKiphas* 509


Chapman, C. M., Nienow, A. W, Cooke, M. and Middleton, J. C, Chem. Eng. Res. Des., 61,167(1983) Particle-Gas-Liquid Mixing in Stirred Vessels Part III: Three Phase Mixing

Experimental apparatus Vessels employed in this study

T29(UCL) TaoCICI) TseCUCL) TsiaCI) Ti83aCI)

Diameter, T (m) Liquid height, ^(m) Volume, Vkdn*) Baffle width (%) Sparger

Geometry Viewing

0.29 0.29 0.0192

10 Pipe point

source

Temperature control Water jacket Material fo Perspex

construction and glass

0.30 0.30 0.0212

10 Pipe point

source

None Perspex

Cylindrical with flat base Through sides and base

0.56 0.56 0.138

10 Three point

)ottom bearing soiurce

Water jacket Perspex

0.91 0.91 0.592

10 Pipe point

source

None Perspex

1.83 1.68 4.41 10

Pipe point source

None Polypropylene wifli Perspex

windows

ase in side and base

Impellers used (a) in T56: (b) in other vessels

Type/Tank Notation

Vertical Horizontal No. of Diameters, height of length of blades Dim) blade (m) blade (m)

Disc and blade

thickness Angle/pitch (mm) of blade

(a)T56 Disk

turbine

Angled blade disc turbine

Mixed flow impeller

pumpmg up Mixed flow mipeller

pumping down Mixed flow impeller

pmnping down Marine propeller

a>) Other tanks T29

T30 T91

Tl83

DT

ADT

4MFU

4MFD

6MFD

AFD

DT 4MFD 4MFD DT DT

4MFD DT

4MFD

6

6

4

4

6

3

6 4 4 6 6

4 6

4

0.14 0.187 0.28 0.28

0.28

0.14 0.28 0.14

0.29

0.145 0.145 0.072 0.15 0.457

0.457 0.902

0.794

D/5 D/5 D/5 0039

D/5

D/5 D/5 D/5

Not constant

D/5 0029 0015 D/5 D/5

00984 0175

0165

D/4 D/4 D/4 D/4

0.120

0.050 0.120 O050

D/4 O055 0.025 D/4 D/4

0.159 D/4

0349

3.2 3.2 3.2 2.5

3.2

3.2 3.2 3.2

3.2 3.2 1.6 2.0

4.8 disc 6.35 Made

6.35^ 6.35 disc 9.5 blade

9.5

— —

45*

45°

45** 45'' 45''

1.5D

— 45° 45° —

45°

45°

^The central horizontal portion of each blade was double this thickness

5X0 Chapter 6. Scala-up rulas

Working fluids, solids and their physical properties Liquid: water Gas: air SoUd:

Particles employed in this study

Particles Polystyrene Diakon Dowex ion exchange resin Anthracite

Glass powder

Soda glass ballotini Sand

Lead glass ballotini

Shape Spherical Spherical Spherical

Flat and irregular (sphericity =% 0.4 to 0.5)

Granular (sphericity % 0.7)

Spherical Granular

(sphericity #0.9) Spherical

Size range (jim)

250-355 420 - 710 500-1.000 t oo -^ 600 \I\r\f \J\nJ

250 - 355

180-250 300 - 710

80-105 440 - 530 850 - 1,000

2,500 - 2,800

Surface to volume mean

diameter (|im)

302 583 —

309

206 470

— — — —

Density (kgm- )

1,050 1,200 1,250 1,400

2,200

2,480 2,650

2,900 2,900 2,900 2,900

Experimental conditions ImpeUer rotational speed: 2 ^ 6 rps Gas flow rate: 0~1.()0 w m

Scale-up rule ANjs=Njsg-Njs = 0.940^

Notation Njs agitation speed required to just completely suspend all the particles under ungassed

conditions, 1/sec Njsg agitation speed required to just completely suspend all the particles under gassed

conditions, 1/sec Qg gas flow rate, wm

6.2 MuKiphaM 511

Frijlink, J. J., Bakker, A. and Smith, J. M., Chem. Eng. ScL, 45,1703 (1990)

Suspension of Solid Particles with Gassed Impellers




Baffle Number Width (m) Ofif-wall clearance

Impeller Type

Diameter (m) Number of impellers Number of blades Width of impeller blade (m)


a)

dish-bottomed 0.44

0.44

4 0.1 r

0.01 r

see the impeller

0.47 1

4 or 6 r/4

(2)

flat-bottomed 1.20

1.20

4 0.17 0.017

types shown below (six-bladed impeller only)

0.47 1 6

varied over a wide range (0.177,0.257, and 0.47)

Impeller type for system (1) D6F standard disc turbine with six flat blades D6C standard disc turbine with six flat blades, R=D/5 (see a figure attached) D6CC standard disc turbine with six flat blades, R=D/10 9076 open turbine with six flat blades, radial pumping 60°46(4) open turbine, downwards mode with six (four) ilat blades 45**>L6(4) blade angle to the horizontal 60°, 45°, 30°, respectively, pumping downwards 60°T6(4) blade angle to the horizontal 60°, 45°, 30°, respectively, pumping upwards

R: radius of curved blade

convex direction of rotation

concave direction' of rotation

The disc turbine with curved blades. All experiments with this impeller were conducted with the concave blade faces forward.


Working fluids^ solids and their physical properties Liquid: water Gas: air Solid: glass bends and sand (size distributions = narrow around 0.12 mm; density = 2,500 kg/m^)

Scale-up rule Constant Qg (gas flow rate, wm)

Disc turbines ej^=Pj^/V-D-^^ Inclined blade impellers

upward pumping ejsg=^Pj3glV^D^'^ downward pumping ejsg^Pjsg/V-^D^-^

Notation D impeller diameter Ppg power required to have just suspended solids under gassing V volume of vessel £j^ power input per unit volume to have just suspended solids under gassing

513

Chapter 7. Other subjects related to multi-phase systems

7.1 Flooding

Warmoeskerken, M. M. C. G. and Smith, J. M., Chem. Eng. Scu, 40,2063 (1985) Flooding of Disc Turbines in Gas-Liquid Dispersions: A New Description of the Phenomenon


System



Impeller Type

Diameter (m) Number of impellers Number of blades Off-bottom clearance (m)

(1)

flat-bottomed 0.44

4 0.044

six-blade Rushton turbine 0.176

1 6

0.176

(2)

flat-bottomed 0.64

4 0.064

six-blade Rushton turbine 0.256

1 6

0.256

(3)

flat-bottomed 1.20

4 0.120

six-blade Rushton turbine

0.48 1 6

0.48

Sparger: a ring sparger mounted below the stirrer Working fluids

Liquid: water Gas: air

Experimental conditions Fr=0.01-0.32

Results At the onset of flooding Fl= 1.2 Fr

Notation D impeller diameter, m Fl gas flow number, Qg/ND^, dimensionless Fr Froude number, N^D/g, dimensionless g gravitational constant, m/sec^ N stirrer speed, 1/sec Qg gas flow rate, mVsec

514 Chapter 7. Other subjects related to multi-phase systems

Tanaka, M. and Izumi, T, Chem. Eng. Res. Des., 65,195 (1987) Gas Entrainment in Stirred-Tank Reactors

Experimental apparatus Vessel and impeller geometry Vessel type: flat-bottomed Vessel and impeller dimensions:

Tank diameter (m): Z)r=0.12,0.15,0.2 Dimensionless liquid depth: HL-0.67'^1A2 Dimensionless impeller height: H=02^0.75 Dimensionless impeller diameter:

A/Z)r=0.32,0.36,0.42 and 0.50 Dimensionless width of baffle plate: B=0.1 Length of draught tube (m): hd=0,14 Diameter of draught tube (m): 0.08 Number of full-length baffles: 0,2 and 4 Number of half-length baffles: 2 Impeller diameter (m): 0.05

Impeller type: I Six-bladed Rushton turbine II Pitched-blade turbine with four blades at 45° from

the vertical; downwards thrusting III Pitched-blade turbine with four blades at 45° from

the vertical; upwards thrusting IV Three-bladed propeller; downwards thrusting V Three-bladed propeller upwards thrusting

short / bafte

draug/ht \y/ tube

'^ P-

DT (cm)

Schematic diagram of experimental apparatus.

Impeller I Impeller II Impeller III Impeller IV Impeller V

-&- —r~ —?— W W n T ^ 18 18

Details of impellers, (unit: nmi)

Working fluids Liquid: water, water and dodecyl-ether (surfactant) Gas: air

7.1 Flooding 515

Experimental conditions Values of dimensionless power number (fiilly turbulent region).

Impeller type Without bafOe Half length

With baffle Full length

Two baffles

14.4 10.6 10.8 10.4 10.8

Four baffles

14.8 10.6 10.8 10.4 10.8

I II m IV V

10.8 10.4 10.8 10.2 10.8

13.8 10.4 10.8 10.2 10.8

Results For fully baffled conditions

g IroJ {DT [Dr}[ h, j

For each of the number and lengths of baffle plates

p,_Nfd,^jh,-h: g [ K

di/Dr = 0.42, h,_IDj.=l.A2 and yly^ = l.Q

(1)

(2)

Values of coefficients in equation (1).

Impeller

I II in IV V

0.023 0.084 0.080 0.078 0.046

0.88 1.44 1.72 1.22 1.34

0.60 1.06 1.24 0.72 0.78

Values of coefficients in equation (2).

Number of Baffles

Impeller Type

m IV 4

2

0

Half-length-

A d A d A d A

0.36 0.60 0.24 0.40 0.17 0.30 0.20 0.32

1.31 1.06 0.86 0.86 0.51 0.70 0.62 0.72

1.27 1.24 0.93 1.16 0.44 0.60 0.51 0.76

1.19 0.72 0.80 0.60 0.44 0.24 0.54 0.36

0.67 0.78 0.56 0.68 0.44 0.60 0.51 0.64

5X6 Chapter 7. Oth«r subjecto r»lat«il to multi-phase systems

Notation A, A coefficients in equations (1) and (2) a' coefficient in equation (2) Cy d coefficients in equation (1) B d imensionless width of baffie plate, WblDr DT tank diameter, m di impeller diameter, m F, F' Froude number, Nldilg, dimensionless g acceleration due to gravity, cm/sec^ hd diameter of drought tube, m hi distance of impeller from base of reactor, m HL liquid depth, m H d imensionless distance of impeller from free surface, {ni- hi)/hi HL d imensionless liquid depth, hi/Dr Ne impeller speed for o n s e t of gas entrainment, 1 / s e c Wb width of baffle plate, m Y surface tension of solution, N/m /o surface tension of pure water, N/m

7.1 Flooding 5^7

Hudcova, V, Nienow, A. W, Haozhung, W. and Houxing, L, Chem. Eng. Sci., 42,375 (1987) On the Effect of Liquid Height on the Flooding/Loading Transition


Geometries investigated to see effect of liquid height

Ref.

Nienow «/fl/. (1985) Nienow «/fl/. (1985) Nienow g/fl/. (1985) This work This work

T

0.44 0.44 0.44 0.56 0.56

HIT

1.0 1.0

0.6-1.36 1-2

2

sIT

0.025-0.25 0.025 0.025 0.025

0.025-0.75

CIT

0.4 0.25 and 0.4 0.25 and 0.4

0.25 0.25-1.0

DIT

0.4 0.4 0.4 0.33 0.33

Set

1 2 3 4 5

Nienow, A. W. and Allsford, K. V., 1985, The effect of sparger type on gas dispersion by Rushton turbines Multistream 1985,1. Chem Engng Symp Sen, No 94, pp. 3.1-3.5.

Results The flooding-loading transition occurs at values OINF and Of, which satisiy the equation given by

{FlG)F=mD/T)^FrF

The liquid height changes have no effect on the flooding-loading transition. Notation

C impeller clearance from tank bottom, m D stirrer diameter, m FIG gas flow number, QG/ND^, dimensionless Fr Froude number, N ^D/g, dimensionless H liquid height in the vessel, m g gravitational constant, m/sec^ N stirrer speed, 1/sec QG gas flow rate, mVsec 5 sparger-impeller separation, m T vessel-diameter, m

Subscript F flooding-loading transition

518 Chapter 7. Othar subj«cto ralatad to multi-phasa systems

Wong, C. W, Wang, J. R and Huang, S. T, Can J. ofChem. Eng., 65,412 (1987) Investigations of Fluid Dynamics in Mechanically Stirred Aerated Slurry Reactors


Liquid contained Ungassed height: 0.29 m


Impeller Type: (1) A-310 propeDer (3-AP) (2) two types of 4-blade 45° pitch turbine (4-PT)

(3) two types of 6-blade Rushton disc turbines (6-DT)

f====^ D , -

6-flat blade

disc turbine

l - D i - !

.D i -

4-blade

45**pitch turbine A-310 propeller

Di 5 ' Di 4 Di 5

Types of impellers

Diameter: DT/3 OTDT/2 Number of impellers: 1 Number of blades on impeller: (1), (2) 4, (3) 6 Off-bottom clearance: DT/3 OTDT/4

Working fluids, solids and their physical properties Solid: see Table 1 Liquid: see Table 2 Gas: air

7.1 Flooding 519

Table 1 Properties of particles used in this investigation

Material Tyler screen

mesh No. Particle mean diameter

dp i\im) Density

P.(kg/m3) Shape

River sand

Glass bead

Glass powder

Aluminum powder

Cadmium powder

Corundum powder

2 0 - 3 5 3 5 - 4 5 60-100

1 2 - 1 6 2 0 - 3 5 60-100

2 0 - 3 5 60-100

60-100

60-100

60-100

675 425 200

1,200 675 200

675 200

200

200

200

2,755 2,755 2,755

2,514 2,514 2,514

2,514 2,514

2,700

8,642

3,130

Irregular

Spherical

Irregular

Irregular

Irregular

Irregular

Table 2 Physical properties of test fluids (251:)

Liquid Surface tension (N/mxlO-3)

Viscosity (kg/msec x 10 )

Density (kg/m )

Water 0.5 wt. %

NaCl solution 20wt. %

Glucose solution

Results Flooding characteristics

- ^ = 0.48(iV|A/^)

72.7

66.7

60.0

0.982

0.983

1.581

998.2

1,004.6

1,075.1

NFD]

Notat ion dp particle diameter, ^m Di stirrer diameter, m DT vessel diameter, m g gravitational constant, m/sec^ L length of the blade of stirrer, m NF critical stirrer speed before flooding, 1/min QG gas flow rate, w m W width of the blade of stirrer, m Ps solid density, kg/m^

520 Chapter 7. Oth«r subjecto ralated to multi-phase systems

Lu, W.-M. and Ju, S.-J., Chem. Eng. Scu, 44,333 (1989) Cavity Configuration, Flooding and Pumping Capacity of Disc-Type Turbines in Aerated Stirred Tanks




Impeller Type: (1) a standard 6-flat-blade disc-type turbine (2) 4 flat-blade disc-type turbine

(3) 8 flat-blade dis-type turbine Diameter: (1) 7.2, (2), (3) 9.6 cm Number of impellers: (1) 1 (2) 1 (3) 1 Number of blades on impeller: (1) 6 (2) 4 (3) 8 Length of impeller blade (perpendicular to shaft): (1) Z)/4, (2) Z)/4, (3) D/4 Width of impeller blade (parallel to shaft): (1) Z>/5, (2) Z)/5, (3) D/5 Off-bottom clearance: (1) T/3, (2) 7/3, (3) T/3

Sparger Type: a perforated ring of 8 cm diameter made of 0.635 cm o.d. steel tube Holes: 2 nun holes drilled every 2 cm



The operating conditions for impeller pumping capacity measurements under aeration

D (cm)

7.2

9.6

Tib

6

6

N (rev min"')

550 650 800 800 650 800 275 400 500 500

Q ii/min)

10.6 10.6 10.6 21.3 21.3 31.8

10.6 10.6

10.6

21.3

D (cm)

9.6

14.2

9.6

m 6

6

4

N (rev min"0

400 500 155 185 230 230 185 230 350 450

Q (^/min)

21.3 31.8 10.6 10.6

10.6 21.3 21.3

31.8

10.6 10.6

D (cm)

9.6

9.6

fib

4

8

N (rev min"^)

550 550 450 550 225 325 400 400 325 400

Q (j?/min)

10.6 21.3 21.3 31.8 10.6 10.6 10.6 21.3

21.3

31.8

Results

where A=0.072 for the highest limit of impeller flooding and A=0.064 for the lowest limit of gas dispersion. The flooding correlation is in close agreement with the newest published data.

7.1 Flooding 52i

Notation D impeller diameter, m g gravitational acceleration, m/sec^ N impeller speed, 1/min NF flooded impeller rotational speed, 1/sec fib number of blades Pg impeller power consumption under aeration, watts Q air flow rate, mVsec T vessel diameter, m V liquid volume, m


Hudcova, V, Machon, V and Nienow, A. W, Biotch. andBioeng., 34,617 (1989)

Gas-Liquid Dispersion with Dual Rushton Turbine Impellers


Liquid contained Height: / T = lor 2


Impeller Type: 6-blade Rushton disc turbine Diameter: Z)/r= 1/3 Number of impellers: 1 or 2 Number of blades on impeller: 6 Distance between two impellers when two impellers are employed: AC; 0.2Z)~3.0Z) Off-bottom clearance: T/3

Sparger Type: a ring sparger Diameter: 0.1 m Number of holes: 16 Diameter of each hole: 0.002 m


Results 50

10

The minimum speed to prevent flooding, Nff for two aeration rates as a function oif impeller spacing. 0

• Lower impeller

« -—— Upper impeller

I— O Q_=115Kl0"'m^s'' ' G

-^ Single impeller

^ - v " ^

10 AC/O

2 0 3 0

Touching is shown in (b) (AC = 0,2D)

7.1 Flooding 523

UP

Flow patterns as a function of impeller spacing.

Notation AC distance between two impellers, m D impeller diameter, m H liquid height, m NF minimum speed to prevent flooding, 1/sec QG gas flow rate, mVsec T vessel diameter, m

524 Chapter 7. Othar subj«cto nilat«d to multi-phasa systems

Machofl, V, Foft, I., AntoSova, E., §panihel, B. and Kudma, V, Collect. Czech. Chem. Commun., 56,636 (1991) Gas flooding of an Inclined Blade Impeller




Impeller Type: a six plane blade impeller with its blades inchned at the angle of a=45° Diameter: 0.096 m Number of impellers: 1 Number of blades on impeller: 6 Width of impeller blade: 0.0193 m Off-bottom clearance: 0.1 m

Sparger Type: a ring type Ring diameter: 0.067 m Hole diameten 0.002 m Location: 0.01 m under the impeller

Working fltiids Liquid: water Gas: air

Experimental conditions Temperature: 2(fC Impeller speed: 4—101/sec Gas flow rate: 0.167 x 10"* -3.5 x 10"* mVsec

Results «r=41.68 7/2

Notation fic impeller critical frequency of revolutions characterizing impeUer loading/floodmg transition,

1/sec Vg gas (air) flow rate, mVsec

7.1 Ftooding 525

Takahashi, K. and Nienow, A. W.,/. Chem. Eng. Japan, 25,432 (1992) Effect of Gas Density on Power Consumption in Aerated Vessel Agitated by a Rushton Turbine



Baffle Nmnben4 Width: 0.029 m

Impeller Type: Rushton turbine Diameter: 7/3 Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: T/A

Working fluids Liquid: deionized water and water saturated with CO2 Gas: He, air, and CO2

Experimental conditions Impeller speed: 3.33 and 5.00 1/sec

Results Nienow et al}^

{FlG)F=30(D/TfHFr)F (1)

Bujalski2>

(flG)F=imD/T)'^'(Fr)F (2)

(FlG)F=l33(;c2/D)-'''''(D/T)''^(Fr)F (3)

where (FIG)F and (FrV are the gas flow number and the Froude number at the flooding-loading transition, respectively. Gassed power and the flooding-loading transition are independent of gas density.

Gas flow number at flooding-loading transition

N

3.33 5.00

He-D*

0.0664 0.103

Experimental

System Air-D* Air-S**

0.0553 0.111 0.107

CO2-S**

0.0587 0.108

Eq.(l)

0.0703 0.158

Calculated

Eq.(2)

0.0544 0.122

Eq.(3)

0.0450 0.101

D*: Deionized water. S**: Water saturated with CO2.

1) Nienow, A. W., M. M. C. G. Warmoeskerken, J. M. Smith and M. Konno: Proc. 5" Eur. Conf. on Mixing, BHRA, Cranfield, 143 (1985).

2) Bujalski, W.: PhD Thesis, University of Birmingham (1986).

526 Chapter 7. OtiMr subjeeto r»lat«il to multi-phase systems

Notation D impeller diameter, m FIG gas flow number, QG/NL^, dimensionless Fr Froude number , N^D/g, dimensionless g gravitational constant, m/sec^ N impeller speed, 1/sec QG gas flow ra te , mVsec T vessel-diameter, m X2 blade thickness, m

527

7.2 Hold-up 7.2.1 Liquid-liquid systems

Weinstein, B. and Treybal, R. E.^AIChE Journal, 19,304 (1973) Liquid-Liquid Contacting in Unbaffled, Agitated Vessels

Experimental apparatus Vessel Type: (1) (2) flat-bottomed Diameter: (1) 0.245 (2) 0.382 m Height: (1) 0.245 (2) 0.382 m

Liquid contained Height: (1) 0.245 (2) 0.372 m

Impeller Type: (1) (2) six flat-blade turbine Diameter: (1) 0.0762 and 0.127 (2) 0.127 m Number of impellers: (1) (2) 1 Number of blades on impeller: (1) (2) 6 Length of impeller blade (perpendicular to shaft): (1) (2) D/A Width of impeller blade (parallel to shaft): (1) (2) D/5 Oft-bottom clearance: (1) (2) H/3

Working fluids and their physical properties Continuous phase and dispersed phase:

System properties at 25°C

Saturated liquid solvent/solute

Density, kg/m^=(g/cm^)

(1,000)

Viscosity Ns/m2=

centip/1,000

Interfacial tension, N/m=

(dynes/cm)/l,000

Cyclohexanone/water Water/cyclohexanone Octanol/water Water/octanol Methylamyl acetate/water Water/methylamyl acetate Isopropyl benzene/water Water/isopropyl benzene

946 996 831 996 857 997 856 996

0.002015 0.001146 0.00743 0.000902 0.000863 0.000892 0.000722 0.000896

0.00376

0.0102

0.0166

0.0360

Experimental conditions Impeller

Impeller speed, Vessel diam., m revys

SmaU(l) 0.0762^ 5.0-10.33 SmaU(l) 0.127" 2.5-5.33 Large (2) 0.127 4.17-5.33

Flow rate total liquid mVs X10*

0-3.785* 0-3.785 0-3.785

Dispersed-phase fraction of total feed''

0.125-0.833 0.125-0.833 0.125-0.500

Avg. dispersed phase holdup

0.079-0.593 0.090-0.512 0.079-0.496

Avg. drop diam., ^, m X10*

2.32-8.44 2.21-6.74 2.72-6.95

Avg. specific interface area,

a, mVm

991-6.560 1,253-7,255 1,204-6,002

'6gal/min. ** Continuous flow. ''3 in. ''5 in.

Temperature: 24~31°C

528 Chapter 7. Other subjecto related to multi-phase systems

Measurement technique Light-transmittance technique

Results

Circumstance Equation PD<PC \T _ inasaOxr0.247 xr-a427xr-a430xr-a401xra0987

All data ^ " " "^ ^ ^ ^ ^

Both vessels

Small vessel

r" 2 pZ) > pC N.= 10^703^-0.131^-a0752^-a0677â0299â0949

AUdata Notation

D impeller diameter, m gr conversion factor: 1 kgm/Nsec^ or 32.17(lbm)(ft/lbf)sec^ H liquid height in vessel, m NF QoPcOgclp^, dimensionless NG pu^glpcC^g?, dimensionless ^ r PQDUcWa^gc^, dimensionless Nfi p-o/p-Cf dimensionless Np t^plpc dimensionless i% 'ÎXF, dimensionless P power input to impeller, Nm/sec Q flow rate, mVsec T vessel diameter, m V vessel volume, m^ XF volume fraction of dispersed liquid in feed mixture = QDKQC + QD\ dimensionless Ap absolute value of density difference = | pc - pz) |, kg/m^ p viscosity, Ns/m^ or kg/msec p density, kg/m^ G interfacial tension, N/m (j> local dispersed-phase holdup, m^ disp-phase holdup/m^ dispersion ^ vessel-average of 0, mVm^

Subscripts C continuous phase D dispersed phase

7.2 Hold-up 529

Weinstein, B. and Treybal, R. E.^AIChE. Journal, 19,851 (1973) Dispersed Phase Holdup in Baffled Mixing Vessels

Experimental apparatus Vessel Tjrpe: flat-bottomed Diameter: 0.305 m Height: 0.305 m



Impeller Type: six-bladed flat blade turbine Diameter: 0.1525 m Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 0.1017

Working fluids and their physical properties The physical properties at 25°C

Continuous liquid

Water Aqueous CaCb Aqueous CaClz Water

Despersed liquid

Kerosene Kerosene Kerosene Kerosene + isobutanol

Density, kg/m^ (g/cm") (1,000) Cont. Disp.

1,000 809.3 1,343 811.3 1,175 810.5

990 811.1

Viscosity (Ns/m^) X 1,000 = centip. Cont. Disp.

0.905 1.364 4.775 1.326 1.734 1.391 1.140 1.327

Interfadal tension, N/m =

(dynes/cm)/l,000

0.0396 0.0383 0.0368 0.01365

Experimental conditions Flow late: 0.000118-0.000255 mVsec Volume fraction dispersed hquid in feed: 0.250—0.650 Impeller speed: 0-3.83 rps Holdup of dispersed liquid in vessel: 0.017—0.650

Measurement technique Visual inspection

Results

N6 = 10

Notation

.0.117^0.300^-0.178^-0.0741^-0^76^0.136

g gr

NF

NG

N, N, N, P Q V

acceleration of gravity, m/sec^ conversion factor: 1 kgm/Nsec^ QDP?ogclix?, dimensionless VU^glpcC^g?, dimensionless PQD\i?lva^g?, dimensionless \iDliic, dimensionless Ap/pc» dimensionless ^/JCF, dimensionless power input to impeller, Nm/sec flow rate, mVsec vessel volume, m^


XF volume firaction of dispersed liquid in feed mixture = QD/(QC + Oz?), dimensionless Ap absolute value of density difference, pc - pn^ kg/m^ /I viscosity, Nsec/m^ p density, kg/m^ a interfacial tension, N/m ^ vessel-average dispersed-phase holdup, m disp. phase/m^ dispersion


7.2 Hold-up 532


Lee, J. C. and Meyrick, D. L, Trans Instn. Chem. Engrs., 48, T37 (1970) Gas-Liquid Interfacial Areas in Salt Solutions in an Agitated Tank




Impeller Type: six-bladed disk turbine Diameter: 4 in Disk radius: 1/2 in Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 15/16 in Off-bottom clearance: 3/4 in

Sparger Diameter of orifice: 1/16 in Location of orifice: at the center of the vessel base

Working fluids Liquid: aqueous solution of sodium chloride concentration=0.05—0.50 g mol/^

aqueous solution of sodium sulphate concentration=0.05—0.25 g mol/f Gas: air

Experimental conditions Temperatiure: 18°C Impeller speed: 300—600 rpm

532

Results


Speed (rev/min) NaCl 300 A 400 O 500 V 600 D

Na2S04

c,(rfy/dc)»e 200 «00 MO 3000

010 020 aiO 040 »S0 CONCENTDATION Of Na CI (g moi*/ l)

OOS 0075 010 OlS O20 0-2S CONCENTRATION OF N a j S O ^ C g m o l * / ! }

Fractional gas hold-up at superficial gas velocity 0.03 ft/sec

Speed (rev/min) NaCl Na2S04 300 A A

CpCdV/dcj'O 200 (OO 000 1000 1 , 1 I ' ' '

2000 3000

0-10 020 O30 040 O50 CONCENTRATION OF Na CI (g mo(«/l)

» I L. 005 075 OW 015 O20 025

CONCENTRATION OF Na2S04(g mote/I)


7.2 Hold-up 533

Speed (rev/min) NaCl Na2S04 300 A A 400 O • 500 V • 600 D •

rA ^ A A A

C.CdY/dc)** 200

OK) 020 &30 040 050 CONCENTRATION OF No CI (g m o t t / l )

04$ O075 010 01S a20 02S CONCENTRATION Of NOjSO^ (g mol«/0


534 Chapter 7. Otlwir subjacto rolated to multi-phasa systems

Miller, D. N., AIChE Journal 20,445 (1974) Scale-Up of Agitated Vessels Gas-Liquid Mass Transfer


System

Vessel Type Diameter Height Liquid height Volume (m )

Baffle Niunber Width Thickness Off-bottom clearance

Impeller Type



(parallel to shaft) Thickness of blade Off-bottom clearance

Sparger Type Diameter of ring Hole size Number of holes Hole spacing Orientation

(1)

dish-bottomed 0.1524 0.305 0.1460 0.00252

4 0.0127 0.001588 0.00952

0.1016 1 4

0.01905

0.000794 0.00952

ring 0.0889

0.001588 0.00318 40 10

0.00698 0.0279 down up

(2)

dish-bottomed 0.305 0.610 0.292 0.0252

4 0.0254 0.00318 0.01905


0.001588 80

0.00696 up

0.203 1 4

0.0381

0.001588 0.01905

ring 0.1778 0.00318

20 0.0279

up

0.00635 10

0.0559 up

(3)

dish-bottomed 0.686 1.372 0.657 0.252

4 0.0572 0.00714 0.0429

0.457 1 4

0.0857

0.00357 0.0429

ring 0.406

0.00318 0.00635 50 25

0.0260 0.0516 up down

Units: m

Working fluids Liquid: aqueous solution of CO 2 Gas: air

7.2 Hold-up 535

Results For stripping of CO2 from the aqueous solution with air Gas holdup

\0.5 / . . __ \ / \0.5 <t>Ug

^U,+U^ -f-0.000216 ((pjvrp^

[u,+u^

a = lM

Notation a interfacial area per unit aerated volume, 1/m Pe effective power input, W Ug actual superficial gas velocity, m/sec ui bubble terminal velocity of rise, m/sec V clear liquid volume, m^ PI liquid density, kg/m^ a surface tension, N/m <l> fraction gas holdup

536 Chapter 7. Otli«r subjects ralated to multi-phasa systems

Hassan, I. T. M. and Robinson, C. W, AIChE. Journal, 23,48 (1977) Stirred-Tank Mechanical Power Requirement and Gas Holdup in Aerated Aqueous Phases


System


Liquid contained Height (m) Volume (m )

Baffle Number Width

(1)

flat-bottomed 0.152

0.152 2.65x10-3

4 0.10 r

(2)

flat-bottomed 0.291

0.291 19.0x10-3

4 0.103 T

Impeller

Type six flat-blade turbine NB D/T WilD Li/D TilD HilD

6 1/3 0.20 0.25

0.03125 1.0

six-blade paddle 6

1/3 0.20 1.0

0.03125 1.0

four-blade paddle 4

2/3 0.188

1.0 0.020

1.0


Physical properties at 25°C

Liquid/solution Density kg/m^

Viscosity (Ns/m2)xl03

Surface tension (N/m)xl03

Water Propionic add (9.8 wt %) Methyl acetate (2.29 wt %) Ethylene glycol (8 wt %) Ethylene glycol (20 wt %) Glycerol (40 wt%) Sodium sulfate (0.4 kg mole/m^)

1,000 1,000 1,000 1,008 1,021 1,104 1,057

0.80 1.0 1.0 1.27 1.72 3.00 0.856

72.0 44.0 58.2 55.0 47.4 64.9 73.6

Gas: air

7.2 Hold-up 537

Sparger

System Type Number of spargers Orifice diameter (m) Hs/D UT

(1) single-hole orifice

2 0.00317

0.50 0.275

(2) single-hole orifice

2 0.00595

0.50 0.275

Experimental conditions Aeration rate System (1) 0.063'-1.235 x 10"^ mVsec

System (2) 0.333'-1.47 x lO'^ mVsec

Impeller type N(s-^) PglV

(W/m^) N(s-^) P,IV

(W/m^)

Six-blade turbine Six-blade paddle Four-blade paddle

5-35 5-35

1.7-11.7

30-16,200 30-19,000 55-12,000

3.3-16.7 3.3-13.3 0.83-3.3

62-4,750 27-3.470 15-1,120

Results

pL

Po pL

Impeller and aqueous system

Liquid volume m'xlO^ C,

Six-blade turbine Water and aqueous

nonelectrolytes 0.4 kgmole/m^

Na2S04 solution

Six-blade paddle Water and aqueous

nonelectrolytes

Four-blade paddle Water and aqueous

nonelectrolytes

0.113

0.209

0.102

0.316

0.57

0.44

0.65

0.5

2.65 19.00

2.65

2.65 19.00

r 2.« 1 19.1

65 00

0.774 0.82

0.587

0.80 1.20

0.31 0.76

-0.25 -0.25

-0.25

-0.25 -0.25

-0.22 -0.22

Notation C\ proportionality constant, dimensionless Cz proportionality constant, kgsec/m^ D impeller diameter, m HI height of impeller above tank bottom, m Hs height of sparger outlet above tank bottom, m LI length of impeller blade, m Ls distance of sparger firom tank centerline, m m exponent of Weber number, dimensionless

538 Chapter 7. OtiMr subjects r»lat«il to multi-phasa systems

N impeller rotational speed, 1/sec NA aeration number, Q/ND^, dimensionless NB number of impeller blades Nwe impeller Weber number, N^D^pjcr, dimensionless Pg mechanical agitation power in gas-liquid dispersion, W Po mechanical agitation power in ungassed liquid, W Q volumetric gas aparging rate, mVsec T tank internal diameter, m Ti impeller blade thickness, m V liquid volume, m Wi impeller blade width, m z exponent, dimensionless p mass density, kg/m^ a air-liquid surface tension, N/m 0 gas holdup volume fraction, dimensionless

Subscripts D property of gas-liquid dispersion L property of liquid

7.2 Hold-up 539

Loiseau, B., Midoux, N. and Ch2irpentieTj.'C.,AIChE Journal, 23,931 (1977) Some Hydrodjrnamics and Power Input Data in Mechanically Agitated Gas-Liquid Contactors

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 22 cm (2) -Volume: 8.9 (2)5.5^

Liquid contained Dispersion height: (1) 22 cm (2) T


Impeller Type: a six flat-blade Rushton disk turbine Diameter: 7/3 Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: T/3

Sparger Type: (1) an open tube (diameter 0.8 cm)

(2) a perforated ring (diameter 6 cm; thirty holes; diameter of hole 0.1 cm) (3) a porous ring (diameter 6 cm)

Location: beneath the turbine Working fluids and their physical properties

Liquid:

Summary of systems studied

Type of liquid

Pure lequids


Foaming solutions

Liquid

Water Glucol

Water + lauric Alcohol (1.7 p.p.m) Ethanol (95% by volume)




AlO^kg/m^

1.0 L l l

1.0

0.803

1.145

1.028

1.024

1.158 1.085

/i, 10-3 p^.g

1.0 19.75

1.0

1.50

1.25

1.12

1.22

5.40 1.50

a,10-'N/m

72.0 48.1

23.0

23.9

44.4

61.0

28.0

54.0 56.1

Gas: air

540 Chapter 7. OtiMr subjects rslatsd to multi-phass systems


Type of liquid

Pure liquids


Foaming solutions

Liquid

Water Glycol

Water + lauric Alcohol (1.7 p.p.m) Ethamol (95% by volume) Water + sugar (60 wt %)




Np


Re 3.72 ±0.11


Re 3.38 ±0.08

3.68 ±0.11

3.28 ±0.13

3.51 ±0.11 4.56 ±0.11 3.63 ±0.12

M„ 10-2 j^/g

0.07-2.12 0.07-0.62

0.07-0.62

0.07-0.62 0.07-0.62

0.64-4.7

0.27-2.12

0.27-2.12

0.07-0.62 0.07-8.5

Rev/min

340-1,650 350-1,400

440-1,500

380-1,600 400-1,400

480-1,720

340-1,625

350-1,500

400-1,650 300-3,000

*Np = 4.56 for T=0.12 m 7L = 5.5 x IQ- m^ Np = 3.63 for T=0.22 m VL = 8.9 x IQ- m\

Results 0J6^-0J6 ..-0.056 a = 0.011tt,"-*CT

PGQGRT

"" McVihiiPslpo)

{EA+eof

Notation D agitator diameter MG molar mass, kg/mol N rotational speed of impeller, 1/min Np power number, Pa/pN^D^, dimensionless psf po absolute pressure at the sparger and above the liquid, respectively. Pa Pa aerated power input by mechanical agitation, W QG volumetric flow rate of gas, mVsec R gas constant, J /molK T tank diameter, m or temperature, K Ui superficial gas velocity based on the cross section of the tank, m/sec VL volume of liquid in the tank, m^ a gas holdup EA mechanical agitation power in gas-liquid dispersion per unit volume of clear hquid,

eA = Pa/VL,Wm' SD sparged gas isothermal expansion power per unit volume of clear liquid, W/m^ p. hquid viscosity, Pasec p hquid density, kg/m^ a Hquid surface tension, N / m

7.2 Hold-up 541

Matsumura, M., Masunaga, H., Haraya, K. and Kobayashi, J.,/ Ferment. TechnoL, 56,128 (1978) Effect of Gas Entrainment on the Power Requirement and Gas Holdup in an Aerated Stirred Tank




Impeller Type: six-blade turbine Diameter: 0.487 Z)r Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: Z)r/3

Sparger Type: a single nozzle Location: underneath the impeller

Working fluids and their physical properties Gas: air Liquids: water, ethyl alcohol, benzyl alcohol, ethylene glycol and sucrose solution

viscosity: 0.8-30 cP surface tension: 22—71 dynes/cm densities: 0.8—1.3 g/cm^

Experimental conditions Impeller speed: 7.08—16.5 rps Superficial velocity of sparged gas: 5 x 10'^-l x 10" m/sec

Results

<p,=6Mxio-HN^,r\N^,r^(N^r^(N:y'' Notation

Di DT

f

gc N N;

Nfr NRe Nwe

impeller diameter, m tank diameter, m volumetric flow rate of entrained gas, i/min gravitational acceleration, m/sec^ rotational speed of impeller, 1/sec modified aeration number, VT/ND„ dimensionless Froude number, N^Dt/gt dimensionless Reynolds number, ND?p/Gy dimensionless Weber number, N'^D?p/G, dimensionless

0

VT

Vw v^ / P a 0r

volumetric flow rate of gas spaiged from the tank bottom, t/vam overall superficial gas velocity, calculated fi-om the sum of Q and/, m/sec liquid volume of tank, i. total gas volume dispersed in liquid, I viscosity of liquid, kg/msec density of liquid, kg/m^ surface tension of liquid, kg/sec^ gas holdup defined by V^/Vw

542 Chapter 7. Otiwr subj«cto ralat«d to multi-phasa systems

Yung, C. N., Wong, C. W. and Chang, C. L, Can. J. ofChem. Eng., 57,672 (1979) Gas Holdup and Aerated Power Consumption in Mechanically Stirred Tanks

Experimental apparatus Vessel Type: (1) hemispherical-bottomed (2) flat-bottomed Diameter: (1) (2) 0.4 m

Liquid contained Height: (1) (2) 0.4 m

Baffle Number: (1) (2) 4 Width: (1) (2) 0.04 m

Impeller

Type

Diameter (m)

Number of impellers Number of blades on impeller


standard six-blade turbine four-blade paddle

0.09,0.13, and 0.18 m

0.09 - 0.18

Sparger Type: a tube type Diameter of tube: 5/8 in Size of sparger orifice: 0.006 m Location: just below the impeller


Physicochemical properties of aqueous phases

Liquid/solution

Tap water Ethylene glycol 15 volume % Ethylene glycol 30 volume % Acetone 30 volume % Sodiiun chloride 0.2 M Sodium chloride 0.4 M Sodium sulfate 0.03 M Sodium sulfate 0.312 M

Surface tension mN/m

71.97 65.50 60.54 38.29 72.39 72.74 71.98 72.61

Viscosity mNs/m^

0.8 1.25 2.10 1.30 0.88 0.89 0.92 0.93

Density kg/m^

1,000 1,022 1,047

960 1,005 1,014 1,001 1,036


Gas superficial velocity: 0.0971—2.16 cm/sec Impeller speed: 3.33-23.3 rps

7.2 Hold-up 543

Results

For aqueous non - electrolyte solutions

(f> = aN0a*N*f{D/T)lA

For aqueous electrolyte solutions

QocQ^N^D14

Notation D impeller diameter, m N impeller speed, 1/sec Na aeration number, Q/ND3, dimensionless Nwe Weber number, piN2D2/at dimensionless Q gas flow rate, m3/sec T tank diameter, m a dimensionless proportional constant pi density of liquid phase, kg/m3

a surface tension, N/m 0 gas holdup


Figueiredo, M. M. L and Calderbank, P. H., Chem. Eng. ScL, 34,1333 (1979) The Scale-Up of Aerated Mixing Vessels for Specified Oxygen Dissolution Rates



Baffle Number: 4

Impeller Type: flat bladed turbine Diameter: 0.27 m Number of impellers: 1 Length of impeller blade (perpendicular to shaft): 0.06 m Width of impeller blade (parallel to shaft): 0.06 m



Experimental conditions Power consumption: 0.41 x 10 - 4.8 x 10 w/m^ Impeller rotational speed: 4.16^8.331/sec SuperiScial gas velocity: 6.34,887, and 12.7 x 10" m/sec

Results /f=0.34(P/VL)°' (V;)°- ^

Notation H gas holdup (= volume of gas/volume of dispersion) P impeller power dissipation, W VL volume of liquid, m Vs superficial gas velocity, m/sec

7.2 Hold-up 545

Meister, D., Post, T, Dunn, I. J. and Bourne, J. R., Chem. Eng. Set., 34,1367 (1979) Design and Characterization of a Multistage, Mechanically Stirred Column Absorber

Experimental apparatus Vessel Type: flat-bottomed Diameter: 150 mm Height: 200 mm/stage Number of stages: 9

Baffle Number: 4 Width: 15 mm Height: 180 mm Clearance of baffle from wall: 5 mm

Impeller Type: six-bladed turbine Diameter: 60 nmi Number of impellers: 1 or 2/stage Number of blades on impeUer: 6 Length of impeller blade (perpendicular to shaft): 12 nrni Width of impeller blade (paraUel to shaft): 12 nmi Positions of impellers

Distance between bottom and the first impeller: 0.2 Hs Distance between the first and the second impeller: 0.47 Hs

Working fluids Liquid: an aqueous solution of sulfite Gas: air

Experimental conditions ImpeUer speed: 6.7-20.0 1/sec Superficial gas velocity: 4.7—28.8 mm/sec

Results

For two impeUers

e = 1.21x10-^ N^'^US^

For one impeller

e = 3.16x10-^ N^'^U^ Notation

Hs stage height, nmi N impeller speed, 1/sec Use superficial gas velocity, nun/sec e gas holdup

546 Chapter 7. Other subjects r»lat«d to multi-phasa systems

Sridhar, T. and Potter, 0. E., Ind. Eng. Chem. Fundam, 19,21 (1980) Gas Holdup and Bubble Diameters in Pressurized Gas-Liquid Stirred Vessels




Impeller Type: six flat-bladed turbine Diameter: 4.5 cm Number of impellers: 1 Number of blades on impeller: 6 Width of impeller blade (parallel to shaft): 0.8 cm Off-bottom clearance: 4.2 cm

Sparger Type: single-hole nozzle Diameter nozzle: 6 mm Number of nozzles: 1

Working fluids Liquid: cyclohexane Gas: air

Results

-(^I + 0.000216 (fi/vfy-' N O ^

ET

P^= 0.706 P^ndf

Qr Notation

di impeller diameter, m total energy input, W dispersed phase holdup stirrer speed, 1/sec mechanical agitation power input in gas-liquid dispersion, W mechanical agitation power input in ungassed liquid, W volumetric gas flow rate, mVsec volume of liquid in reactor, m terminal velocity of bubble in free rise, m/sec superficial gas velocity, m/sec

Et H n Pi

V v. Vs

pg

liquid density at system conditions, kg/m^ density of air at operating temperature, kg/m^ gas density at system conditions, kg/m^ surface tension, N/m

7.2 Hold-up 547

Chapman, C. M., Nienow, A. W, Cooke, M. and Middleton, J. C, Chem. Eng. /?g5.Z)es.,61,82(1983) Particle-Gas-Liquid Mixing in Stirred Vessels Part II: Gas-Liquid Mixing


Type: flat-bottomed Diameter: 0.56 m



Impeller Type: (1) disc turbine (2) 4MFD (mixed flow impeller pumping down wards) Diameter: (1) 0.28 (2) 0.14 m Number of impellers: (1) (2) 1 Number of blades on impeller: (1) 6 (2) 4 Length of impeller blade (perpendicular to shaft): (1) D/4 (2) 0.050 m Width of impeller blade (parallel to shaft): (1) (2) D/b Off-bottom clearance: T/4, r / 6

Sparger Type: three-point bottom bearing

Working fluids Liquid: deionized water Gas: air

Results

£=1.97 {erf ^HVs?'^

Notation D impeller diameter, m H liquid height at rest, m Hg height of gas-liquid dispersion, m T vessel diameter, m Vs superficial gas velocity m/sec e gas hold-up, (Jig - H)/Hg, dimensionless ET mean energy dissipation rate, W/kg

548 Chapter 7. OtiMr subjects r»lat«d to multi-phasa systems

Oyevaar, M., Zijl, A. and Westerterp, R., Chem. Eng. TechnoL, 11,1 (1988) Interfacial Areas and Gas Hold-ups at Elevated Pressures in a Mechanically Agitated Gas-Liquid Reactor




Impeller Type: standard six-blade disc turbine Diameter: 0.4 T Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 0.33 T

Working fluids and their physical properties Liquid: DBA (diethanol amine)

Data for the DEA-water system at 598 K

^'^KA^mKiyI^co^ = 9-3835x 10"* [DEA]°-^ -2.6101 xlO"'*

m = 0.791-0.044 [DEA]'

p^ = 0.9958 +1.555 x 10"' [DEA] -1.1410 x 10" [DEA]

1/ = exp (-0.1135 + 2.5718 x 10" [DEA] + 4.6937 x 10" [DEA]')

[DEA] in mol/kg and [DEA]' in moML

Gas: mixtures of CO 2 and N2 Experimental conditions

Temperature: 298 K Flow rate of N2:0-9 m^N/hr Flow rate of CO2: 0-0.3 m^N/hr

7.2 Hold-up

Results

549

a35-i

0 2 8

0.21-J

014

O07^

O D

• A

O N • 12.5 rpt

• N • 16.7 ipt

A N • 20.8 ipi

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O N • 29.3 ipt

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D

A

L

• O

- I 1 1 1 1 1 1 1 1 r 0 0-4 0 8 12 16 2 0

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Gas hold-up vs reactor pressure at Vg = 2.00 cm/s in water.

a25-

020 -

g

\ 015-

010-

O05-

u-c

0 o

A A

A

• • °o

O N • N

A N

A N

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1 1 1 —

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g 0-15-

0-10-

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c

Q

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"1 1"' 0 8 ^ P

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A

A

•

O 1 1

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0

A

A

•

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1.6 • 2.C

Gas hold-up vs reactor pressure at Vg = 2.00 cm/s in converted DEA solution.

Gas hold-up vs reactor pressure at Vg = 2.00 crn/s in fresh DEA solution.

550 Chapter 7. Other subjects rslatsd to multi-phase systems

03Oi

. 0-24-

g 1 ai8-

0-12-

ao6-

n-c

o •

A

1 )

• i -

* i

6

1.00

1.00

cm/t (water)

cm/i (DEA)

2.00 cm/s (water)

2.00 cm/s (DEA)

«

P

A

A •

1 1

12

— ^ N Vs

A O •

"le"

A

A O

•

T"

A A

O

•

— 1 1

2A

A

O

•

r 30

Mean gas hole-up vs stirring speed in water and in converted DEA solution.

Notation C bulk concentration, mol/m^ Dco2 diffusivity of CO2, m V s e c k„,p rate constant for reaction of order («, ^), m " "" Vmol *"" * sec m distribution coefficient Ci = w Q N stirring speed, 1/sec P pressure, MPa T tank diameter, m Vg superficial gas velocity, m/sec Eg ga s holdup pL liquid density, kg/m^ fit liquid viscosity, Nsec/m^

7.2 Hold-up 551

Greaves, M. and Barigou, M., IChemE Symposium Series, No. 108,235 (1988) Estimation of Gas Hold-Up and Impeller Power in a Stirred Vessel Reactor




Impeller

Type Diameter (mm) Number of impellers Number of blades Disk diameter (mm) Disk thickness Length of impeller blade

(perpendicular to shaft) (mm) Width of impeller blade (mm) Blade thickness (mm) Off-bottom clearance (mm)

disc turbine 250

1 6

188 3.18 62.50

50.00 3.18 250

disc turbine 333

1 6

250 3.18 83.30

66.60 3.18 250

disc turbine 500

1 6

375 4.76

125.00

100.00 4.76 250

Sparger Type: a single pipe Location: below the impeller disc

Working fluids Liquid: water and a 0.15 M NaCl solution Gas: air

Experimental conditions Air flow rate: 1.64 x 10'^~8.33 x 10" mVsec Impeller speed: 0.67-8.33 rps


552 Chaptw

Results System Air-water

°::"elation - 4 . 0 7 i V - 0 ^ "

"^Sl^Se -3.85 "" ^ ^

Large cavity e = 1.33N^Q'>-** regime

*Vortex regime

Notation D impeller diameter, m N impeller speed, 1/sec 0 gas flow rate, mVsec T vessel diameter, m e gas hold-up fraction

7. OtiMr

(C (C (C

subjects r»iat«cl to n lulthphas*

Air-NaCI solution

e = 2.867\ °- 0°- * / \1.64

7.2 Hold-up 553

Nocentini, M., Fajner, G., Pfeisquali, G. and Megelli, E, Ind. Eng. Chem. Res., 32,19 (1993) Gas-Liquid Mass Transfer and Holdup in Vessels Stirred with Multiple Rushton Turbines: Water and Water-Glycerol Solutions

Experimental apparatus Vessel Type: flat-bottomed Diameter: 23.2 cm Height: 105 cm



Impeller Type: six-bladed Rushton turbine Diameter: 7.73 cm Number of impellers: 4 Number of blades on impeller: 6 Length and width of impeller blade

D:L:W:d = 20:b:A:15 Positions of impellers

Distance between bottom and the first impeller: 11.5 cm Distance between the first and the second impeller: 23 cm Distance between the second and the third impeller: 23 cm Distance between the third and the forth impeller: 23 cm

Sparger Type: a ring-type sparger Location: below the bottom turbine


Liquid

Distilled water Aqueous solutions of glycerol

45wt% 65wt% 7.Swt% 83wt%

Viscosity (mPas)

0.9

3.7 14 29 62

Gas: water-saturated air

Experimental conditions Temperature: room temperature Air flow rate: 0.1—0.7 wm


Results

For air-water system

0.375 2 I -Q 1 j-7-0.62 e G = 8 . 3 5 x l O - ' p ^ U°

For aerated glycerol syatem

eG=C

^ xO.375 ^ >^-l/3 Pg Tjm Ul Vj ' {^w,20

Notation C constant d disk diameter, m D turbine diameter, m L blade length, m Pg gassed power consumption, W Us superficial gas velocity, m/sec V volume of the liquid in the vessel, m^ W blade width, m Cg fii^ctional gas holdup jU dynamic viscosity of the liquid, Pasec jdw. 20 reference viscosity (water at 20°C), Pasec

7.2 Hold-up 555

Rewatkar, V B., Deshpande, A. J., Pandit, A. B. and Joshi, J. B., Can. J. of Chem. Eng., 71,226 (1993) Gas Hold-up Behavior of Mechanically Agitated Gas-Liquid Reactors Using Pitched Blade Downflow Turbines

Experimental apparatus Vessel geometries

Type Diameter (m) Liquid height (m) Number of baffles Baffle width (m) Impeller clearance (m)


4 0.057 r/3


4 0.10 r/3


4 0.15 r/3

Impeller

No. of Blade Hub Horizontal Blade pitch Blade Impeller blades Diameter width 0. D blade length (degree) thickness

ni, D(m) W{m) d„{m) h(m) 0 ife(mm)

PTD PTD PTD PTD PTD PTD PTD PTD PTD PTD PTD

0.19 0.33 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.5 0.75

0.057 0.099 0.038 0.0475 0.057 0.0665 0.076 0.0665 0.057 0.15 0.225

0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.05 0.05

0.07 0.14 0.07 0.07 0.07 0.07 0.07 0.07 0.075 0.225 0.35

45 45 45 45 45 45 45 45 45 45 45

2.8 2.8 2.8 2.8 2.8 2.8 2.8 4.3 2.8 2.8 2.8

PTD: pitched-blade down flow turbine

Sparger

(CKONCCHTRIC RING tSRRilO)

3 2 ^ j ^

(0) PIPE (SPSO)

(E)RlHC(SRr.«.4.)

SRR200

R, • iO R}> (0 R ) * 10

R4 > too

SRRi to l

R | * 0 . 5 R2tlS.O R]* t20 R i * 160 R *20S|

All dimcnsiaocort in mm not to the scolc

Spai:ger design.

556 Chapter 7. OtiMr subjects r»lat«il to multi-phasa systems

Sr. Sparser model

1. SR, 2. SR2 3. SR3 4. SR4B 5. SR7 6. SR9 7. SRio 8. SRi, 9. SR12

10. SR,3 11. SR,4 12. SR15 13. SR,6 14. SRi7 15. SR18 16. SR19 17. SR22 18. SRR2 19. SP, 20. SPz 21. SCi 22. SR05 23. SR05

Sparger type

ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring ring concentric rings pipe pipe conical ring ring

Ring diameter

i.d. (mm)

67 67 67

114 158 245 350 350 350 350 350 350 350 350 350 350 550

o.d. (mm)

95 95 95

152 190 280 400 400 400 400 400 400 400 400 400 400 600 200 200

- Orifice size

(mm)

3 3 3 3 3 6 3 3 3 3 3 3 3 2 6 6 6 2 3.6 3.6 2 3 3

Number of

orifices

6 6 6

12 6

21 42 42 84 84

168 168 189 189 21 21 21 28 14 14 28 21 21

Sparger location (below = +ve above = -ve)

(mm)

100 152 -35 100 100 100 100 390 100 390 100 390 100 390 100 390 390 152 70

152 95

100 390


Experimental conditions Impeller rotational speed: 0.4—10.5 rps Superficial air velocity: 1.5—30 mm/sec

Results

EG = 3 .54^ {Frr\mt^


flow number, Q/ND^, dimensionless Froude number, iV^Z)/ , dimensionless gravitational acceleration, m/sec^ impeller rotational speed gas flow rate, mVsec vessel diameter, m fractional gas fold-up

Fr g N Q T

7.2 Hold-up 557

Bakker, A. and Van den Akker, H. E. A., Trans. Instn. Chem. Engrs., 72, P ^ A, 573 (1994) Gas-Liquid Contacting with Axial Flow Impellers



Baffle Number: 4 Width: 0.077 T Clearance of baffle from wall: 0.023 T

Impeller

Type SR(%) Rt,i{%) fib

Dim) Blade width (m)


4

PBT: down wards pumping pi Jparger

A 315 90 77 4

0.178

«6A.l

Leeuwrik 160 80 6

0.168

0.75 Z) or Z)

PBT 60 4 6

0.176 0.2 Z)

tched blade turbine, 6 blades at 45° blade ai

Type a pipe sparger (PS) a small ring sparger (SRS) a large ring spaiger (LRS) a quadruple pipe sparger (QRS)

dsim)

0.4/) 0.75 Z)

Working fluids and their physical properties Liquid: distilled water

glycerol solutions (1) viscosity = 36 mPasec; density = 1,190 kg/w? (2) viscosity = 80 mPa-sec; density = 1,220 kg/m^

Gas: air

558

Results


Local Holdup for • PBT

I 10 Tlmo (MInutti)

Time dependent local gas holdup with the pitched blade turbine OV = 5 Hz, «v = 0.0067 m/s , 2rlT = 0.7, zlH = 0.6).

Notation Ah a rea of o n e impel ler blade Ah, 1 projected a r ea of one impel ler blade duub impeller hub diameter A sparger diameter D impeller swept diameter H liquid height nb number of impeller blades N impeller rotational speed T vessel diameter Vsg superficial ga s velocity

7.2 Hold-up 559

Linek, V, Moucha, T and Sinkule, J., Chem. Eng. Scu, 51,3203 (1996) Gas-Liquid Mass Transfer in Vessels Stirred with Multiple Impellers-I. Gas-Liquid Mass Transfer Characteristics in Individual Stages


Liquid contained Height: (1) 1T (2) 2 T (3) 3 T (4) 4 T Volume of Uquid in vessel: (1) 0.00517 (2) 0.00517 x 2 (3) 0.00517 x 3 (4) 0.00517 x 4 m'


Impeller Type: a standard Rushton turbine Diameter: T/3 Number of impeUers: (1) 1 (2) 2 (3) 3 (4) 4 Number of blades on impeller: (1)~(4) 6 Length and width of impeller blade: D:L:w:b = 20:5:4:15 Positions of impellers:

Distance between bottom and first impeller: D Distance between first and second impeller: T Distance between second and third impeller: T Distance between third and forth impeller: T


Working fluids Liquid: distilled water and 0.5 M Na2S04 solution Gas: air, nitrogen, and pure oxygen

Experimental conditions Superficial gas velocity: 2.12,4.24 and 8.48 mm/sec Agitator speed: 5.5—18.8 1/sec Temperature: 20°C

Results

For water

€i=0m4e^v^

£2_,=0.285(?J:ft;f-^

(e0^=0m77N''''v;'

(«2-4)^=o.io4i\r^-^t;;

[)379

-0J04

For0.5MNa2SO,

ei=0.0152^f^f;f^

e2.4=0.04566j:fi;f^

(e,)^= 0.117 N'^'v:'-'''

(V4)^=0.090i\r^°^t;;^-^^

ei=(ei)^+v,pa

550 Chapter 7. Other subjects related to multi-phasp systems

Notation b diameter of impeller disk, m D diameter of agitator, m ei total power input per unit vo lume of liquid in stage f, W/m^ (ei)agn power input by agitator per unit vo lume of liquid in stage t, W/m^ L length of impeller blade, m N agitator speed, 1/sec T diameter of vessel, m Vs superficial gas velocity, m/sec w width of impeller blade, m ei gas holdup in stage i PL hquid density, kg/ir?

7.2 Hold-up 561

Barigou, M. and Greaves, M., Trans. Instn, Chem. Engrs., 74, P&rt A, 397 (1996) Gas Holdup and Interfacial Area Distributions in a Mechanically Agitated Gas-Liquid Contactor



Baffle Number: 4

Impeller Type: standard Rushton turbine Diameter: 0.333 m Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 0.25 m

Working fluids and their physical properties Liquid: deionized water

density = 999 kg/m ; viscosity = 1.00 mPasec; surface tension = 70.99 mN/m Gas: air

Experimental conditions Air flow rate: 0.00164,0.00438, and 0.00687 mVsec Impeller speed: 100—385 rpm


Results

Notation N impeller speed, 1/min Q gas flow rate, m^sec

Vertical profiles of radial mean gas holdup; Q = 0.00687 m^s'K - O - ^=180 rpm; -<>- N= 285 rpm; -A-7\^=385 rpm.


Birch, D. and Ahmed, N., Trans. Instn. Chem. Engrs., 75, Part A, 487 (1997) The Influence of Sparger Design and Location of Gas Dispersion in Stirred Vessels



Baffle Number: 4

Impeller Type: (1) FDT (Rushton turbine)

(2) PDD (downward pumping 45° six bladed pitched blade disc turbine) (3) PDU (upward pumping 45° six bladed pitched blade disc turbine)

FDT

D = 0.200 m w = D/4 q = D/5 r = 3w/5 a = 45°

PDT

Details of the impeller geometry.

Off-bottom clearance: (1) (2) 0.2 m

7.2 Hold-up

Sparger

h

Q <> flCH

bC

tt King Spaigers Riagl -^ Ring4

ITT J ) B O , . ^ . .

I ?±xz^^::^::^:=xz) • •

) ) 3 —)

P«>im Spaiger

563

A

Q

k r o [+_

Rintla Ringla Rms3a RiMgSI Rint4a Foint

iL

m • B

•

Rimlh ] Rintib Rini3b Ring4l Rint4b '

T rg

11

T S

h-135 H 200 1 290 ^

— 400 ^ T = 600 H

Schematic of the sparger size and location with respect to the impeller position. Impeller diameter is 200 nmi. (Note: the nomenclature a, b, I in italics refer to positions above, below and level to the impeller plane, respectively).

Results

o n tM OJK ai ai2 ai4 ait an r.<»ND'

(a) Aerated power consumption and (b) the gas holdup as a function of the flow number for sparging arrangements placed below the impeller with the Rushton impeller (FDT), at a stirrer speed of 6.1 s'^

20

It

4

1 MmgM

r 1 »^

y r 1 » -

• 1 *••*•

^

1 1

Ijl|)CHSi*__

^ ^ - -

1 1- 1 »

<" *

1

A« OM ai ai2 1.14

FlofWMnber.<yND'

(a) Aerated power consumption and (b) the gas holdup as a function of the flow number for sparging arrai^ements placed level with the impeller for the Rushton impeller (FDT), at a stirrer speed of 6.1 s"'.


(a) Aerated power consumption and (b) the gas holdup as a function of the flow number for sparging arrangements placed below the impeller with the pitched blade disc impeller pumping upward (PDU), at a stirrer speed of 6.1 s"\ The dotted lines indicate the point of the flooding transition.

0 ilMff<« o

POIMS

(a) Aerated power consumption and (b) the gas holdup as a function of the flow number for sparging arrangements placed above the impeller with the pitched blade disc impeller pumping upward (PDU), at a stirrer speed of 6.1 s'*. The dotted lines indicate the point of the flooding transition.

Notation D impeller diameter, m N impeller speed, 1/sec Pg power draw, gassed liquid, W Pu power draw, ungassed liquid, W Q volumetric gas flow rate, mVsec e gas holdup

7.2 Hold-up 565


Koloini, T, Plazl, I. and Zumer, M., Chem. Eng. Res. Des., 67,526 (1989) Power Consumption, Gas Hold-up and Interfacial Area in Aerated Non-Newtonian Suspensions in Stirred Tanks of Square Cross-Section

Experimental apparatus Vessel geometries and experimental conditions Type: flat-bottomed vessel of square cross-section

variable


stirrer diameter clearance from bottom suspension volume sparger type spaiger location VG m/sec N 1/min P/V W/m^ PL kg/m^ r]tf mPasec T °C

SQT-0.3

0.3 m 0.33 m standard six blade Rushton 0.1m 0.11m 0.03 m tube underneath of stirrer 0.0058-'0.027 200-800 30-1,600 1,050-1,230 3-100 20 or 30

SQT-0.7

0.7 m 0.82 m

0.267 m 0.21m 0.4 m' tube underneath of stirrer 0.02-0.08 100-500 30-2,250 1,050-1,160 1.9-12 20 or 30

Working fluids, solids and their physical properties Fluids: Suspensions of CaCOs and Ca(0H)2

Rheological properties of CaCOs and Ca (0H)2 suspensions at 20°C

Cone. (wt. %)

CaCOa 10 15 25

Ca(0H)2 5

10 15 20

/JTCPas")

0.025 0.14 2.1

0.0035 0.037 0.33 1.1

n ( - )

0.6 0.45 0.22

0.87 0.54 0.28 0.23

Gases: air+C02 for SQT-0.3 and flue gas for SQT-0.7


Results Gas hold up

ForSQT-0.3

e = 0.01211^7 I vl''^:^'^

E = 0.018 QG

ND' 'hj^^D^y-^

ForSQT-0.7

£ = 0.104


fluid constancy index, Pa sec" fluid behavior index stirrer speed, 1/sec stirrer power input in gassed suspension, W gas flow rate, mVsec superficial gas velocity, m/sec suspension volume, m gas hold-up effective viscosity, Pasec viscosity of water, Pasec suspension density, kg/m^ surface tension, kg/sec

K n N P QG

VG

V e ri^

PL

a

7.2 Hold-up 567

Dutta, N. N. and Ptogarkar, V G., Can. J. ofChem. Eng., 73,273 (1995) Critical Impeller Speed for Solid Suspension in Multi-Impeller Three Phase Agitated Contactors


System Vessel

Type Diameter (m) Height (m)


Sparger Type Diameter Tube diameter (mm) Orifice diameter (mm) Distance between orifices (mm)

Location

(1)


4 0.015

a nng sparger 0.8 Z) 12.5

2 10

(2)


4 0.030

a nng sparger 0.8 Z) 25.4

3 20

0.1 r above the bottom

Impeller

Impeller type No of blade

Dia.Z) (m)

Blade width (m)

Blade length (m)

Disc turbine (DT)

Pitched turbine down flow (PTD)

Pitched turbine upflow(PTU)

PTU and PTD: angle of pit

4

6

4

6

0.05 0.10

0.075 0.10 0.05

0.075 0.10 0.05

0.075 0.10

tch=45*'; Blade thickness: 2mm

D/5 D/5 D/5 D/5 D/4

D/4 D/4: D/4

D/4: D/4

D/4 0.03 D/4 0.03 D/4

D/4 0.03 D/4

D/4 D/4

Positions of impellers: Distance between first and second impeller: T Distance between second and third impeller: T Distance between third and forth impeller: T

553 Chapter 7. Oth«r subj«cto r»lat«d to multi-phasa systems

Working fluids, solids and their physical properties Liquid: deionized water Gas: air Solids: sand, ion exchange resin and iron oxide pellet

Particles Employed in the Study

Particle

Sand

Ion exchange resin

Iron oxide pellet

Shape

Irreguler (Sphericity = 0.84)

Spherical

Spherical

Size range (^m)

125- 250 250- 300 550- 600 850-1,000 850-1,000 550- 600 850-1,000 550- 600

Density (kg/m )

2,490 2,470 2,453 2,453 1,180 1,180 3,400 3,500

Experimental conditions Superficial gas velocity: 0—15 m m / s e c Solid loading: 0 . 5 - 1 0 % w/w

Results

.,-3^(1 Fr^^Fl^

Notation D impeller diameter, m Ft flow number, Qg/ND^, dimensionless Fr Froude number, N^D/g, dimensionless g acceleration due to gravity, mVsec N impeller rotational speed, 1/sec Qg volumetric flow ra te gas, mVsec T tank diameter, m Bg fractional gas holdup

569

7.3 Critical agitation speed

7.3.1 Solid-liquid systems

Zwietering, T, N., Chem. Eng. Set., 8,244 (1958) Suspending of Solid Particles in Liquid by Agitators


System (1) (2) (3) (4) (5) (6)

Vessel Type Diameter (m) Volume {0



A 0.154 2.9

0.154

4 0.0154

B 0.192 5.5

0.192

4 0.0192

A 0.24 11

0.24

4 0.024

B 0.29 19

0.29

4 0.029

A 0.45 70

0.45

4 0.045

A 0.60 170

0.60

4 0.060

A: flat-bottomed B: flat, dished (radius=vessel diameter), and conical bottom (120 )

Stirrer

Type of stirrer Dimension (m)

Paddles, Z)/F^=2 Paddles, Z)/Pr=4 Flat blade turbines Vaned disks Propellers

0.06, 0.06, 0.06, 0.06, 0.05,

0.08, 0.08, 0.08, 0.08, 0.07,

0.112, 0.16, 0.12, 0.10, 0.115

0.16 0.224 0.16, 0.12,

0.20 0.16, 0.20


Liquid Density Qcg/m^) n(cP) v(mVsec) X10^

Water Acetone Carbon tetrachloride Potassium carbonate

solution Oil

1,000 790

1,600 1,440

840

1.0 0.31 1.0 5.0

9.3

1.0 0.39 0.65 3.5

ILl

Solid:

Solid Density (kg/m^) Particle size (41)

Sand Sodium chloride

2,600 2,160

125-^150, 250-350, 710^-850 125-^150, 150-250, 250-350

570 Chapter 7. OtiMr subjects related te multi-pliasa systems

Experimental conditions Solid concentration=0.5~20 wt%

Restilts

n^sv^^'x^HgAC/CL) D-^'^B' ,0.45 T\-<iJB5 D O . 1 3

P = B^T\gAO'^x' A'as

^035^^0.15 'D g0.15j)0.

a: constant, a = 1.3 for paddles and (7 = 1.5 for turbines Notation

B weight of the solids in suspension per weight of liquid, % stirrer diameter, m acceleration due to gravity, m/sec^ stirrer speed (for complete suspension), 1/sec power input to the stirrer (for complete suspension of solid), Nm/sec dimensionless parameter, dimensionless vessel diameter, m volume of liquid, m particle size of the solid, m density of the Uquid, kg/m^ density of the sohd, kg/m^

T] viscosity of liquid, cP V kinematic viscosity of hquid, mVsec

D g n P s T V X

a

7.3 Critical agitation spaad 572

Weisman, J. and Efferding, L. E., AIChE Journal 6,419 (1960) Suspension of Slurries by Mechanical Mixers

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 5 % (2) 9 Vs, (3) 11 Vs in

Baffle Number: (1)4 (2) 4 (3) 4 Width: (1)Z)/12, (2)Z)/12, (3)Z)/12

Impeller Type: six-bladed paddle-type Diameter: 2,3 and 4 in Number of impellers: 1 Number of blades on impeller: 6 Width of impeller blade (parallel to shaft): rf/8

Working fluids and solids (a) aqueous slurries of thorium oxide (b) aqueous and nonaqueous slurries of spherical glass beads

Results

^V;w,(Ap)| e^ ) ^ '

Notation a height of lowest impeller above vessel bottom, ft. d impeller diameter, ft. D vessel diameter, ft. g local gravitational acceleration, ft./sec^ gc mass acceleration/force conversion factor, (lb.-massXft.)/(lb.-forceXsec ) Pi minimum mixing power required to suspend solids, ft. Ib.-force/sec Us relative vertical velocity between particle and fluid in turbulent region=1.74{ \g5(Ap)\ /pt) '^,

ft./sec. Vt volume of vessel 1 diam in height, cu. ft. 8 particle diameter, ft. £/ liquid fraction based on vessel volume V), dimensionless Pt density of suspending liquid, Ib.-mass/cu. ft. p, density of sohd, Ib.-mass/cu. ft. Ap=ps -pt, Ib.-mass/cu. ft.

572 Chapter 7. Othar subjects ralatad to multi-plias* systems

Schwartzberg, H. G. and Treybal., R. E., Ind. Eng. Chem. Fundam., 7,1 (1968) Fltiid and Particle Motion in Turbulent Stirred Tanks Fluid Motion Schwartzberg, H. G. and Treybal., R. E., Ind. Eng. Chem. Fundam., 7,6 (1968) Fluid and Particle Motion in Turbulent Stirred Tanks Particle Motion

Experimental apparatus Vessel Type: flat-bottomed Diameter:

Tank

1 2A 2B 3

Tank dimensions

Diameter (Inches)

17.3 11.3 11.3 9.2

Full height (Inches)

18.2 17.0 9.4 9.4

Liquid contained Height: r and 1.5 r


Impeller Type: sbc-bladed turbine Diameter: (1) 4, (2) 6, (3) 9 in Number of impeller: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): D/4 Width of impeller blade (parallel to shaft): D/5 Off-bottom clearance: 0.17 H

Working fluids, solids and their physical properties Liquid: viscosity=1 -- 5 cP Sohd:

Particle properties, settling velocities and velocity magnitude differences

Velocities, inches/sec

IVtide

IRC50, ion exchange resin Lucite diamond tablets

Lucite spheres Nylon square tablets

Marble PVC cubes'

' In 5-cp. sugar solution.

Effective Density, Grams/cc.

1.108 1.175

1.175 1.128

2.85 1.319

Av. Size, Inches

0.0215 0.09x0.10

xO.lO 0.231

0.13x0.13 X 0.085 0.044 0.165

5, agitated settling

0.2 1.5

1.9 1.1

2.1 1.0

Sg, still settling

0.507 2.62

6.75 2.40

4.88 2.85

w, Vr-Dr

0.15 1.7

0.7 1.5

1.9 0.4

S/Sg

0.40 0.57

0.28 0.46

0.43 0.35

No. of Test conditions

5 13

3 4

3 4



/?«,=8,600-175,000

Results \Vr\ =(1.39M)2)/(r2/f 2)1/2+ lY

Notation D impeller diameter H depth of liquid filled in tank N impeller rotational speed Ret impeller reynolds number 5 particle settling velocity in agitated fluid plane speed of particle and fluid Sg particle settling velocity in still fluid T tank diameter Vp average vertical plane speed of particle Up average vertical plane speed of fluid W difference in average vertical plane speed of particle and fluid

574 Chapter 7. Othar subjects ralated to multi-phas* systems

Nienow, A. W, Chem. Eng. Sci., 23,1453 (1968) Suspension of Solid Particles in Turbine Agitated Baffled Vessels


Liquid contained: Height: 14 cm Volume of liquid in vessel: 2,150 cm^

Buffle Number: 4 Width: 1.4 cm

Impeller Type: disk turbine Diameter: (1) 3.64, (2) 4.90, (3) 7.30 cm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): L/4 Width of impeller blade (parallel to shaft): L/5 Off-bottom clearance: H/7,if/6,^/5, i//4, H/3

Working fluids, solids and their physical properties Liquid: water or very dilute electrolyte solution SoUd: soda glass Ballotini and various salts

size and concentrations: see Table 1 and Table 2

Table 1. Ballotini specifications (Ap =1.48 g cm'^

Mean size (^m)

153 195 300 600

Z(%w/w solids)

0.093 0.116, 1.80 0.116, 1.97, 10.0 0.112, 1.87

B.S. mesh range

85 - 120 7 2 - 8 5 4 4 - 6 0 2 2 - 3 0

Table 2. Specification of other solids

Mean size (^m)

2,230 324

9,000 2,230

324 775 195 775

6,300 775

7,000

Solid material

Potassium sulphate (Ap = 1.66 gem-')

Sodium chloride (Ap = L16gcm-3) Anmionium alum (Ap=0.64 gem-') Anmionium chloride (Ap =0.53 gem-') Potassium chloride (Ap =0.99 gem-')

B.S. mesh range

7 - 8 4 4 - 5 2

PeUet(H^«=1.0g) 7 - 8

4 4 - 5 2 1 8 - 2 2 7 2 - 8 5 1 8 - 2 2

PeUet(W^«=0.20g) 1 8 - 2 2

PeUet(W ,«=0.55g)

7.3 Critical agitation sp««d 575

Experimental conditions Liquid temperature: 25 *C

Results

Notation d nominal particle size, cm L impeller diameter, cm Ns suspension velocity, Hz X percentage by weight of solids in the suspension Ap density difference between solid and liquid phase, g/an?

576 Chapter 7. Other subjects r»lat«cl to multi-phasa systems

Narayanan, S., Bhatia, V K., Guha, D. K. and Rao, M. N., Chem. Eng. ScL, 24, 223 (1969) Suspension of Solids by Mechanical Agitation

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 11.4, (2) 14.1 cm

Liquid contained Height: (1) 11.4, (2) 14.1 cm


Impeller Type: eight ilat-blade paddle Diameter: D/T; 0.32,0.4,0.5 Number of impellers: 1 Number of blades on impeller: 8 Off-bottom clearance: T/2

Working fluids, solids and their physical properties Liquid: water Solid: quartz (density=1.14^2.6 g/cm ; particle size=-25+35, -72+85 and -120+150 Mesh)

Experimental conditions Solid concentrations: 2.5~20%

Results Minimum impeller speed for suspension of solids

D/T^QA D/T^O.5

Particle dia.s0.0675 cm 0.02108 cm 0.02108cm

51. B V NT NE F V NT NE F v NT NE F No. (g/8) (cm/sec) (rev/min) (rev/min) (^E/NT) (cm/sec) (rev/min) (rev/min) (NE/NT) (cm/sec) (rev/min) (rev/min) (NE/NT)

1 2 3 4 5 6 7 8

2.5 5.0 7S

10.0 125 15.0 173 20.0

24.2 30.25 36.6 41.5

495

57.0

455 569 689 778

931

1,070

746 799 851 890

995

1,083

1.64 1.404 1.234 1.144

1.07

1.013

20.4 28.0 34.0 39.0

43.45 475 54.7

3835 527.0 639.0 733.0

816.0 893.0

1,028.0

625 684 789 850

915 970

1,050

1.630 1.305 1.235 1.160

1.120 1.085 1.022

20.40 28.00 34.00 39.00 43.45 4750 51.1 54.70

257 353 429 492

5.17 565 609 650

411 480 465 497 498 529 585 596

1.60 1.36 1.084 1.010 0.960 0.936 0.961 0.917

System: Quartz-water

p^=2.63g/cc pL=0.998g/cc <TL=72.6 dynes/cm 7=11.4 cm

NE = IJS2B^ •r- 2T-Z) ^J\^g(pp-PL)

2Dp HsHsL ^PL Pp-^HspL


Notation B % solids concentration (100 Hs)f dimensionless D impeller diameter, cm Dp particle diameter, cm F correction factor, NEINT, dimensionless g acceleration due to gravity, cm/sec^ Hs solids concentration, g of solid/g of liquid HsL net hydrostatic head of slurry, cm of water NE experimentally determined impeller speed, 1/sec NT theoretical impeller speed, 1/sec T tank diameter, cm V pick-up or suspension velocity of the fluid, cm/sec pL liquid density, g/cm^ Ps solid density, g/cm^

578 Chapter 7. Otiwr subj«cto r»lat«il to multi-phasa systems

Joosten, G. E. H., Schilder, J. G. M. and Broere, A. M., Trans. Instn. Chem. Eng., 55,220 (1977) The Suspension of Floating Solids in Stirred Vessels

Experimental apparatus Vessel Type: dish-bottomed Diameter: (1) 0.27, (2) 0.54, (3) 0.8, (4) 1.8 m

Baffle For 0.27 m diameter vessel

Number Width

4 0.1 Z> 2 0.1 or 0.2 Z) 1 0.1--0.35/)

Length: from the top of the liquid to a wetted depth of 0.1 to 1 Z> Type: triangular baffles, baffles placed non-normal to wall, and streamlined bafQes

Impeller Type: 6-bladed inchned-blade paddle 4-bladed inclined-blade paddle

2-bladed inclined-blade paddle 3-bladed marine propeller Number of impellers: 1 Number of blades on impeller: 2^6

Working fluids, solids and their physical properties Liquid: water Solid: small rubber particles and corks the size of corks=13 x 7 mm; the size of rubber particles

=3'-^7and2-^4mm Results

Stirrer types snd sizes used in the 0.27 m diameter vessel dID

0.6 0.6 0.6 0.6

0.6 0.6 0.6 0.44 0.44 0.29 0.29 0.29

0.6

0.6 0.6 0.6 0.38

HID

0.15 0.33 0.11 0.33

0.15 0.11 0.33 0.15 0.33 0.11 0J22 0.33

0.15

0.15 0.33 0.15 0.15

No. of bafQes rfmok

6-bladed inclined-blade paddle 4 4 1 1

0.35 0.38 0.072 0.081

4-bladed indined-blade paddle 4 1 1 1 1 1 1 1

0.41 0.077 0.086 0.34 0.35 1.28 1.28 1.30

2-bladed inclined-blade paddle 1 0.18

3-bladed marine propeller 4 1 1 1

>1.94 0.48 0.48

>2.90

Po

1.9 1.8 1.4 1.3

1.7 1.3 1.2 1.3 1.1 1.5 1.3 1.2

0.8

0.30 0.27 0.29 0.34

Pnun/K(kw/m")

1.32 1.41 0.088 0.097

1.38 0.083 0.090 0.32 0.30 0.48 0.42 0.40

0.20

>2.84 0.27 0.30

>1.3

7.3 Critical agitation sp«iNl 579

--•liK^f; Values of the constant d for the various stirrers (baffle 0.2 x 0.3 D)

6-bladed inclined-blade paddle 3.3 x lO'^ 4-bladed inclined-blade paddle 3.6 x 10"^ 2-bladed inclined-blade paddle 7.4x10-2 3-bladed marine propeller 19.6 x 10 "

For 4-bladed inclined-blade paddle (one baffle 0.2x0.3 D)

Frmui= 3.6x10' ^J x-3.65/ NO.42

0.27 <i )< 1.8 m; 0.1^Ap/pL<0.76; 2^rf^<13nmi; PL = 1,000 kg/m^

Notation d d dp D Fr Fn

0.29 <rf/Z)< 0.60; 0.11 </i/Z)< 0.33 ry = 10-3 Ns/m^;

constant stirrer diameter particle diameter vessel diameter dunensionless Froude number minimum Froude number of solid suspension

h height of stirrer above the bottom P power consumption of stirrer Po dimensionless power number of stirrer p, q constants V volume of vessel contents 7] liquid viscosity PL hquid density Ap density difference between liquid and soUd

580 Chapter 7. Oth«r subjacts r»lat«fi to multi-phase systems

Baldi, G., Conti, R. and Maria, E., Chem. Eng. Sci., 33,21 (1978) Complete Suspension of particles in Mechanically Agitated Vessels

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 12.2, (2) 19.0, (3) 22.9 cm

Liquid contained Height: (1) 12.2, (2) 19.0, (3) 22.9 cm

Baffle Number: (1)4, (2) 4, (3) 4 Width: (1) 0.122, (2) 0.190, (3) 0.229 cm

Impeller Type: eight flat-bladed disc turbine Diameter: (a) 3.2, (b) 4.0, (c) 4.8 cm Number of impellers: 1 Number of blades on impeller: 8 Diameter/Blade length/Blade height=4/l/l Off-bottom clearance: C/Z)=0.5'-1.5


PL (kg/m^) ^L (kg/(msec))

0.645x10-3 1.05x10-3 1.80x10-3 3.17x10-3

Solid: sand particles p,=2,650 kg/cm3; particle size: mono-modal particle class = 50,130,370 and 545 [im; bi-modal particles were made by mixing particles of two of the mono-modal classes

Experimental conditions Concentrations of solids: 2,5,10 and 20 kg/m3

Results

^ //L ( A / y ) Dp 0.125

Notation B solid concentration D stirrer diameter Dp particle diameter g gravity acceleration Nm minimum stirrer velocity JLLL viscosity of the liquid phase pL density of the Uquid phase p, density of the sohd phase Ap=ps-pL

Water (411)) Water (1810) 1 molal MgS04 in water sob 2 molal MgS04 in water sohi

992 998

1,141 1,236

7.3 Critical agitation sp«Ml 581

Musil, L. and Vlk, J., Chem. Eng. ScL, 33,1123 (1978) Suspending Solid Particles in an Agitated Conical-Bottom Tank

Experimental apparatus Vessel Type: vessel fitted with conical bottom with an apex angle p = 120° Diameter: 0.6 m

Impeller Type: impellers with inclined flat blades Diameter: (a) three-blade impeller: (1) 0.20, (2) 0.25, (3) 0.315 m

(b) six-blade impeller: (1) 0.15, (2) 0.175, (3) 0.245 m Number of impellers: (a) 1, (b) 1 Number of blades on impeller: ,^

(a)3,(b)6 Off-bottom clearance:

h=hi+h2=(DHD/2 cotg fi-^hz

Working fluids, solids and their physical properties Liquid: city water or glycerol

solution (25% and 50%) Solid: glass balotini mean diameter

0.7 and 1.1 mm Experimental conditions

Ar =fl3^pAp/)u2=1.7x10^-2.2x10*

Solid volume concentration=0.04 and 0.08

Results The critical impeUer speed was obtained theoretically and experimentally as a function of physical properties of the mixed slurry as well as of several selected geometrical parameters of the mixing device Schematic representation of the

impeller clearance.

Employed axial-type impellers with inclined flat Uades:(a) Three-blade impeUer; ^=0.2rf; a=24*'; (b) Six-blade impeller; b=0,2d; a=45**.

582 Chapter 7. Ofhmr subj«cto ralated to multi-phase systems

600

i 4 0 0

300

200

100

ArxlO-^

O 0.20 m • 3 C V 0.25

• T V A 0.315

A A i\ V 0.25

27.9 7.20 2.27 0.18

27.9 7.20 2.27 0.18

27.9 7.20 2.27 0.18 2.27

0.04

0.08

0.100 /i.m

0.200 0300

Critical impeller speed He as a function of the impeller clearance h for the three-blade impellers.

600

400

200h

o c » T W T V V A A i

d

0.15 m

0.195

0.245

i4rxlO-'

7.20 2.27 0.18

27.9 7.20 2.27 2.27 0.18 7.20 2.27 0.18

?

0.04 0.04 0.04 0.04 0.04 0.04 0.08 0.04 0.04 0.04 0.04

010 ^,fn a2o 030

Critical impeller speed ric as a function of the impeller clearance h for the six-blade impellers.

Notation a nominal particle size, m Ar Archimedes nmnber, dimensionless c mean volume fraction of solids for the whole batch d impeller diameter, m g gravitational acceleration, m/sec^ h impeller clearance, m Ai liquid viscosity, kg/msec p liquid density, kg/w? Ap density difference between solid and liquid, kg/m^

7.3 Critical agitation spMd 583

Chundacek, M. W, Ind. Eng. Chem. Fundam., 25,391 (1986) Relationships between Solids Suspension Criteria, Mechanism of Suspension, Tank Geometry, and Scale-Up Parameters in Stirred Tanks


' ! T 1

t 11

i ii 11

1 1

J! { II

i ! D h .1 • H ii : 1 '—'

i i c !

L . D 1

T = D d = 0 33D b = 0-10D a = 0-02D f = 0 0 2 D c = 0-0630

too-330

« 1

•

cjiu i 1 1

U - 1 r*^

h

!i 1 ti * i

] .--J^—rJ. lb

m IL. JLj

hA fU^i 1 1 tj; 1 1 1 ' ^7 ' i

D

T d b a f

d i

h i

fii hj

c

e

= = = = = = =

= =

D 0-33D OlOD 0 02D 0 02D 0-30D 0-20D 0-70D 0-15D 0 2510 0-50D 0-25D

(1) Geometrical parameters of standard flat-bottom tank (FBT).

(2) Geometrical parameters of cone-and-fillet tank(CFT).

Vessel Diameter: 0.5,1 m

Baffle Number: (1), (2) 4 Width: (1), (2) 0.1 Z) Clearance of baffle from wall: (1), (2) 0.02 D

Impeller Type: (a) three-blade square-pitch propeller (3BSPP) (6IBT(45°))

(b) six-inclined-blade turbine (45°) Number of impellers: (a) 1 or 2, (b) 1 / ^ ^ ^ ° Number of blades on impeller: (a) 3, (b) 6 y /y/\ 7

0-012 d > 0-2 d

Geometric parameters of the six-inclined-blade turbine 6IBT (45**).


Working fluid, solid and their physical properties Liquid: water Solid: silica sand p5=2,650 kg/m^

Experimental conditions Temperature: 25*0 Concentrations of solid: 6.1,12.2 and 24.4% v/v

Results

,-.K.[±ji..rD-[^]

Constants and Regression Coefficients for Various Tank and Impeller Combinations Using Various Suspension Criteria for Determination of Suspension Speed.

tank

FBT

FBT

CFT

CFT

impeller

3BSPP

6IBT (45°)

3BSPP

dualSBSPP

criterion

98%' complete** 0.90 D' 0.95/)"

98% complete 0.90 Z) 0.95 Z)

98% complete 0.90 D 0.95 D

98% complete 0.90 D 0.95 D

K,

13.31 13.78 21.59 21.51

10.48 13.58 15.46 16.24

11.79 11.25 15.61 17.04

8.04 8.52

10.88 13.60

Xi

0.18 0.18 0.06 0.03

0.22 0.22 0.11 0.12

0.15 0.09

-0.07 -0.09

X2

0.56 0.56 0.63 0.62

0.55 0.52 0.58 0.56

0.54 0.46 0.62 0.64

0.44 0.41 0.55 0.60

Xz

-0.86 -0.53 -0.66 -0.62

-0.75 -0.58 -0.75 -0.72

-0.64 -0.68 -0.70 -0.74

-0.69 -0.68 -0.78 -0.75

XA

0.06 0.07 0.04 0.02

0.07 0.08 0.13 0.12

0.06 0.06 0.08 0.08

0.07 0.05 0.06 0.07

• 98 % suspension. ^ Complete off-bottom suspension. ' 0.902) suspension. *• 0.95/) suspension.

Notation £ impeller clearance, m C mean solids concentration, % v/v dm solids median diameter, mm D tank diameter, m Kx constant N impeller speed, 1/sec JCi-4 exponent


Molerus, 0. and Latzel, W, Chem. Eng. Sci., 42,1423 (1987) Suspension of Solid Particles in Agitated Vessels—I. Archimedes Numbers :S 40


System (1) (2) (3)


Liquid contained Heighten//))

Baffle Number

Impeller Type Diameter (D,/Z)) Number of impellers Off-bottom clearance (ft/A)

dish-bottomed 0.19


1 1

dish-bottomed 0.45


1 1

dish-bottomed 1.5


1 1

Working fluids, solids and their physical properties Liquid: tap water and water-ethylene glycol mixtures Solid:

Solid material Density (kg/ir?) Mean particle diameter (\xm)

Steel beads Glass beads

7,639 - 7,841 2,480 -- 2,496

170 - 1,937 34 -- 654

Experimental conditions: Volume concentrations of solid particles = 0.5 ~ 30%

Results Minimum stirrer angular velocities for fluid/solid combination with i4r ^ 40 are predicted as follows:

(i) for a given Ar Eqn (1) yields a Reynolds number Rei and a friction velocity ut (ii) insertion of Ut into Eqn (2) gives ««, (iii) use of Eqn (3) yields angular velocity co

^\l^Ps-Pr =lAr (1) 3 v PF 3

Ref.iif\

M, =0.182— E

K=o.m

(2)

(3)


Notation Ar Archimedes number, dimensionless dp diameter of particles, m D diameter of vessel, m Ds diameter of stirrer, m g gravitational acceleration, ml sec? Ret Reynolds number, dimensionless ut shear stress velocity, m/sec Mc. reference velocity, m/sec V kinematic viscosity, mVsec PF fluid density, kg/m^ ps solid density, kg/m^ (o angular velocity, 1/sec

7.3 Critical agitation sp««d 5g7

Barresi, A. and Baldi, G., Chem. Eng. Set, 42,2949 (1987) Solid Dispersion in an Agitated Vessel

Experimental apparatus Vessel Type: torispherical bottom (dish-bottomed) Diameter: 0.39 m

Liquid contained Height: 1.19 T


Impeller Type: A 310 Lightnin propeller

iS' pitched four-blade turbine 45° pitched six-blade disk turbine Six vertical blade disk turbine

Diameter: T/3 Number of impellers: 1 Off bottom clearance: H/3

Working fluid, solids and their physical properties Liquid: water Solid: gkiss beads

Solid physical properties

Particle diameter pp ut (MJn) (kg/m ) (m/s)

100-177 2,670 1.63x10-2 208-250 2,600 2.81x10-2 417 - 500 2,600 6.21 x lO"'

Experimental conditions Temperature: 20X^ Solid concentrations: 0.50,1.51 and 5.19 kg/100 kg

Results

Notation B solid concentration, kg/100 kg Dp particle diameter, m H height of liquid in vessel, m Njs minimum suspension stirrer velocity, 1/sec T vessel diameter, m Ut terminal settling velocity, m/sec

5g3 Chapter 7. Othar subjects rolatsd to multi-phass systems

Wichterle, K., Chem. Eng. Sd., 43,467 (1988) Conditions for Suspension of Solids in Agitated Vessels

Results Theoretical work

ilmin=2.5 for disc turbines in position H2=D/3

i4mm=3.5 for 45° pitched six-blade turbines in position H2/D=0.2'^0A

Bjs=constant=l0±2

(/=impeller diameter

dp^ particle diameter

dp*'=^dp'pLApg/fi'

Notation D tank diameter g gravitational acceleration H2 impeller clearance Njs impeller speed necessary for just suspension Njf normalized critical imleller speed

N*js--Njsd^pi''D-"Y"\Apgy"' p, liquid viscosity PL liquid density Ap didfference of the solid and Uquid densities

7.3 Critical agitation sp«Mi 589

Raghava Rao, K. S. M. S., Rewatkar, V B. and Joshi, J. B.,AIChEJoumaly 34, 1332 (1988) Critical Impeller Speed for Solid Suspension in Mechanically Agitated Contactors

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 0.3, (2) 0.4, (3) 0.57, (4) 1.0, (5) 1.5 m

Liquid contained Height: (1)^(5)7

Baffle Number: (1)^(5) 4 Width: (l)--(5) 0.1 r

Impeller Type: (a) disk turbine

(b) pitched turbine downflow (c) pitched turbine upflow

Diameter: Z)/r=0.175-0.58

Design details of impellers used

Impeller

Disk turbine (DT)

Pitched turbine, upflow (PTU)

Pitched turbine. downflow (PTD)

No. bkides

6

6

6

Dia. Dim)

0.1900 0.285

0.1900

0.100 0.142 0.190 0.250 0.330

0.375 0.500 0.190 0.190 0.190

0.190 0.190 0.330 0.330

Blade Width W(m)

D/5 D/5

0.057

0.030 0.042 0.057 0.075 0.099

0.113 0.152 0.048 0.076 0.067

-do--do-

0.083 0.117

Blade length /(m)

D/4 DIA

0.075

0.030 0.046 0.075 0.100 0.142

0.165 0.227 0.07 -do--do-

-do--do-

0.142 0.142

Blade thickness ^(m)

2.3x10-3* 2.3x10-3*

2.3x10-3

2.3x10-3 2.3x10-3 2.3x10-3 2.3x10-3 2.3x10-3

0.0023 0.0023 0.0028 0.0028 0.0028

0.0043 0.0064 0.0023 0.0023

*DT disk thickness=3x 10"^ PTU, PTD angle of pitch=45'»

Number of impellers: 1 Number of blades on impeller: (a), (b), (c) 6 Off bottom clearance: 7/6, 7/4,7/3 and 7/2

590 Chapter 7. Otiwr subjects ralatiMl to multi-ph«s« systems

Working fluid, solids and their physical properties Liquid: tap water Solid: quartz particles (particle diameter=100,340,700,850 and 2,000 im; density=2,520 kg/m^)

Experimental conditions Impeller speed: 3.5 ~ 13.3 rpm SoHd concentration: 0 50 wt%

Results For PTD impeller

/ = 3.3

for 100<rf^<2,000, 0<X<50wt.%, 0.175<Z)/r<0.58 and W /Z) = 0.3

Notation df avarage particle size, ^m D impeller diameter, m / constant g gravitational constant, m/sec^ Ncs critical impeller speed for solid suspension, 1/sec T tank diameter, m W blade width, m X solid loading, wt. % 7 kinematic viscosity, mVsec PL density of liquid, kg/m^ ps density of solid, kg/m^ Ap = ps -pL


Thring, R. W. and Edwards, M. E, Ind. Eng. Chem. Res., 29,676 (1990) An Experimental Investigation into the Complete Suspension of Floating Solids in an Agitated Tank



Baffle Number: 4 Width: 12.2 cm Off-bottom clearance: 0 or 0.305 m

Impeller Type:

Types and dimensions of impellers

type of stirrer

(a) turbine: 6-bladed (b) propeller: 3-bladed (c) paddle: 2-bladed

D

0.45 0.38 0.61

dimension, m

A D, W

0.1125 0.225 0.0675

0.0915

Z

0.076

SroEVIEW TOP VIEW

TURBINE

— D

? ^

(b)

PROPELLER

2

(c)

PADDLE

Types of impellers used in the experiments.

592 Chapter 7. OtiMr subjects rolatad to multi-phas* systems

Number of impellers: (a)^(c) 1 Number of blades on impeller: (a) 6, (b) 3, (c) 2 Off bottom clearance: HL/3-2HL/3 (HL: liquid depth)

Working fluid, solid and its physical properties Liquid: water Solid: high-density square-shaped (aspect ratio of unity) white polyethylene tips (size range=1.40

-3.35 mm; density=925 kg/m^) Experimental conditions

Concentrations of solid: 0.75—3.75 w/w Results

(i) There is a small effect of solid concentrations on the agitator speed required for complete suspension,

(ii) Of the three stirrers used, the propeller requires the highest speed, while the paddle requires the least,

(iii) There is a shght influence of the impeller clearance above the tank bottom on the minimum speed required for solid drawdown.

(iv) Baffle configuration does not effect minimum speed required for solid drawdown. However it strongly influences the power input to just attain complete suspension.


Rewatkar, V B. and Joshi, J. B., Ind. Eng. Chem. Res., 30,1784 (1991) Critical Impeller Speed for Solid Suspension in Mechanically Agitated Three-Phase Reactors. 2. Mathematical Model

Results Using published data the following relationships were obtained

NsD

a = 0296ViJ'{T/C)

Vs^.'-aVc NsD

(r/Z)f^Z°-'= 0.1322

0.3<r< 1.5m, 1.7<T/Z><6, C=T/3, 1 ^Vi-<200mm/sec, 0.34<X^50wt.%an(i 3^T/C^6

Notation C impeller clearance from tank bottom, m D impeller diameter, m Ns critical impeller speed for a solid suspension in a solid-liquid system, 1/sec T tank diameter, m Vc liquid circulation velocity in the bulk, m/sec Vs- terminal settling velocity of particle, m/sec X solid loading, wt%

594 Chapter 7. Oth«r subjects ralated to multi-phass systems

Armenante, R M., Huang, Y.-T. and Li, T, Chem. Eng. Sci., 47,2865 (1992) Determination of the Minimum Agitation Speed to Attain the Just Dispersed State in Solid-Liquid and Liquid-Liquid Reactors Provided with Multiple Impellers


Type: flat-bottomed Diameter: (1) 0.292, (2) 0.33 m Height: (1)0.292, (2) 0.33 m

Baffle Number: fully baffled

Impeller Type: (a) disc turbine

(b) flat-blade turbine (c) 45° pitched-blade turbine

Diameter: (a) 0.065, (b) 0.076, (c) 0.102 m Number of impellers: 1,2, or 3 Clearance of the lowest impeller off the tank bottom and the spacing between impellers were

varied Working fluid, solid and its physical properties

Liquid: distilled water Gas: glass beads (the average size=110 ^m)

Experimental conditions Solid concentration: 0.5% by weight

Results (1) The dependence on Z)(C=constant)

NjsocD-^^ for «=1 NjsocD-^-'^ for «=2 NjsocD-^-'^ for «=3

(2) The dependence on D (C//)=constant) NjsOcD-^^' for «=1 7y;>ocZ)-i-7o for n=2

(3) The dependence on 5 (C/Z)=constant)

Notation C clearance of bottom impeller off the tank bottom, m D impeUer diameter, m n number of impeUers mounted on the same shaft Njs minimum agitation speed for complete suspension of solid particles in solid-liquid systems,

1/min 5 distance between impellers, m


Janzon, J. and Theliander, H., Chem. Eng. Sci., 49,3522 (1994) On the Suspension of particles in an Agitated Vessel

Experimental apparatus Vessel Type: dish-bottomed Diameter: 0.58 m Height: (3/4) r

Baffle Number: 4 (bottom mounted baffles)

Impeller Type: pitched-blade Diameter: T/3 Number of impellers: 1 Width of impeller blade (parallel to shaft)/impeller diameter: 1/5 Off-bottom clearance/height of vessel: 0.16

Working fluid, solids and their physical properties Liquid: de-aerated water (density ^=1,040 kg/m ) Solid: spherical glass pearls

The particles used

Average diameter 80% of particles in Density Settling velocity'' dp a size interval ps vp

(|Lim) (|im) (kg/m ) (m/s)

42 137^ 307»

0.5 xlO^^ IxW^

23-63^ 106-184^ 238 ~ 371»

— —

2,806 2,520 2,864 2,563 2,554

0.0074 0.0216 0.0557 0.0805 0.1604

' Measured with a Malvern 2,600c Laser Particle Sizer. ^ According to the manufacturer's specifications. *" Calculated using VB=ybdp, water 20*C.

Experimental conditions water temperature: ^20*0 particle concentration: < 0.022 vol impeller speed: 100 ~ 175 rpm

Results The ratio between the velocity of the hquid at the off-bottom suspension point and the settling velocity of the particles decreases as the particle size increases. Bp (the velocity of particles/the settUng velocity of particles)=2.7'^30.4. This is contrary to the results obtained by K. Wichterle (Chem. Eng. Sci., 43,467 (1988)).

Notation dp particle diameter, m T vessel diameter, m VB hquid velocity, m/sec Vp the settling velocity of the particles, m/sec yb shear rate, 1/sec

596 Chapter 7. OtiMr subjects r»l«t«d to multi-phas« systems

Myers, K. J., Fasano. J. B. and Corpstein. R. R., Can. J. ofChem. Eng., 72, 745 (1994) The Influence of Solid Properties on the Just-Suspended Agitation Requirements of Pitched-Blade and High-Efficiency Impellers



Baffle Number: 4 Width: 0.029 m Clearance of baffle from wall: 7/72 Clearance of baffle from vessel bottom: T/10

Impeller Type: (a) Chemineer HE-3 impeller,

(b) 45° pitched-blade impeller with four blades Diameter: (a) 0.1 m (Z)/r=0.34), (b) 0.1 m (Z)/r=0.34) Number of impellers: (1) 1, (2) 1 Number of blades on impeller: (1), (2) 4 Width of impeller blade (parallel to shaft): (a) -, (b) 0.20 D Distance of turbine or paddle center line (at impeller center) from bottom of vessel: 0.25 T

Working fluids, solids and their physical properties Liquid: tap water or a saturated salt-water solution (p/= 1,180 kg/m?) Solid:

Properties of solids studied and experimental data

Material Shape Density (kg/m^) SizeCnm) Njs(FE)(s-') Njs(ffE){s-')

Resin 1 Resin 2 Resin 3 Resin 4 Acrylic 1 Acrylic 2 Plastic 1 Plastic 2 Plastic 3 Glass 1 Glass 2 Glass 3 Glass 4 Aluminum Sandl Sand 2 Sand3 Sand4 Sands Salt Ceramic

Spheres Spheres Spheres Spheres Rectangular Cylinders Rectangular Cylinders Spheroids Ellipsoid Cylinders Ellipsoid Cylinders Spheres Spheres Spheres Spheres Spheroids Granules Granules Granules Granules Granules Cubes Spheres

1,053 1.097 1,230 1,270 1,028 1,179 1,140 1,320 1,410 2,440 2,520 2,480 2,570 2,660 2,390 2,620 2,910 2,590 2,590 2,140 2,650

780 580 620 680

3,200 3,200 3,150 2,900 2,920

600 3,000

14,500 15,900 3,000

450 600 85

1,450 1.850

350 19,100

2.17 2.33 3.33 3.57 2.20 4.52 4.28 5.80 6.82 9.53

10.3 14.1 14.1 10.9 7.45

10.3 5.13

10.5 10.9 5.20

15.8

3.27 3.73 5.53 5.68 3.35 7.07 6.52 8.83 9.93

14.8 17.5 22.2 21.8 16.8 11.5 14.9 8.45

17.1 16.5 7.91

25.3

7.3 Critical agitation spaad 59^

Results f XO.45

Pi 0.45

02

HE refers to high-efficienqr impeller PB refers to pitched-blade turbine

Notation dp particle diameter or size, ^m D impeller diameter, m Njs just-suspended agitation speed, 1/sec T tank diameter, m PI liquid density, kg/m^ Ps solid density, kg/m^

593 Chaptar 7. Otimr subjacts rslatad to multi-plMis* systems

7.3.2 Liquid-liquid systems

Esch, D. D., D'angelo, E J. and Pike, R. W, Can. J. ofChem. Eng., 49,872 (1971) On Minimum Power Requirements for Emulsification of TWo-Phase, Liquid Systems

Experimental apparatus Vessel Type: flat-bottomed Diameter: 11.4 in


Impeller Type: six-bladed disk turbine Diameter: 4.0 in Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 4.0 in


System Continuous phase Dispersed phase

1 water heptane 2 com syrup heptane 3 water oil 4 com symp oil 5 sulfuric acid heptane

Physical properties of hquids j

Density Liquid (g/mi)

Water (Baton Rouge City) 0.996 Heptane (Matheson, Tech.) 0.679 Com symp solution (Com Products) 1.203 S. A. E. 30 motor oil (Quaker State) 0.875 Sulphuric acid (98%) (Mallinkrodt A. S. C.) 1.840

studied

Surface tension (dynes/cm)

73.0 19.0 56.7 27.0 55.1

Viscosity (cP)

0.861 0.391 9.15

215.0 37.0



System Volume fraction continuous phase Impeller speed (rpm)

348-648 486-804 318-642 456-708

870

1 2 3 4 5

0.323-0.645 0.323-0.645 0.307-0.645 0.403-0.645

0.35

Temperature: 75-80T

Results Critical mixing data

System Continuous phase volume fraction

Critical impeller speed (rps)

Water-heptane

Com syrup solution-heptane

Water-oil

Com syrup solution-oil

0.323 0.403 0.500 0.564 0.645

0.323 0.403 0.500 0.564 0.645

0.307 0.403 0.500 0.564 0.645

0.403 0.500 0.564 0.645

7.78 7.00 5.81 6.35 6.35

11.27 9.60 8.77 8.42 8.00

7.35 5.83 5.53 5.30 4.83

8.98 8.58 7.65 6.97

Sulphuric acid (98%)-heptane (2%) 0.35 13.1

600 Chapter 7. Othar subj«cto ralatad to multi-phase systems

Skelland, A. H. P. and Seksaria, R., Ind. Eng. Chem. Process Des. Dev., 17,56 (1978) Minimum Impeller Speeds for Liquid-Liquid Dispersion in BafQed Vessels

Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.2135 m Height: 0.2500 m Volume: 0.01 m


Baffle Number: 4 Width: 0.0190 m Length of baffle immersed in the liquid from air-liquid interface: 0.1930 m

Impeller

Type

Diameter (m)

Number of impellers Number of blades

on impeller Width of impeller blade

Off-bottom clearance

propeller

0.1,0.075, 0.06

1 3

45° pitched-blade turbine

0.1,0.075, 0.062

1 6

projected width 1/8 of the

impeller diameter

flat-blade turbine

0.106,0.078, 0.065

1 6

1/8 of the impeller diameter

H/i,H/2,3H/4

curved-blade turbine

0.102,0.076, 0.063

1 6


Working fluids and their physical properties Continuous phase: water Dispersed phase:see table

Fluid properties at 25*'C

Fluid

5-cSt Dow Coming 200 Fluid 10-cSt Dow Coming 200 Fluid 15-cSt Dow Coming 200 Fluid Benzaldehyde Ethyl acetate Water

Density, kg/m^

920 940 948.3

1,041 894

1,000

Dynamic viscosity. N-s/m^

0.0046 0.0094 0.0143 0.0014 0.00046 0.0010

Interfadal tension with water, N/m

0.0425 0.0435 0.0437 0.0145 0.00627

—


Experimental conditions Volume fraction of organic liquid: 0.50 Temperature: 25°C

Results

[D'p.g (1)

(2)

Correlations and average deviation between Nap and pred"

Set no.

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

Eq (2) type correlations

Co

0.348148 0.151858 0.293388 0.044722

0.047382 0.063248 0.009150 0.031193

0.009103 *

0.036654 *

0.013292 «

0.048231 0.066748

ao

-1.38272 -1.65355 -1.49329 -2.02317

-2.15120 -1.91877 -2.69010 -1.97371

-2.72474 «

-1.98099 *

-2.56244 *

-1.90056 -1.64010

% av, dev

Propeller 10.71 13.19 11.80 8.53

Pitched-Blade Turbine 10.87 18.21 11.92 9.68

Flat-Blade Turbine 6.93 *

12.88 *

Curved-Blade Turbine 8.51 «

9.54 5.24

Eq (1) type correlations

Ci

15.3244 9.9687

15.3149 5.2413

6.8231 6.2040 2.9873 3.3545

3.1780 « 3.9956 *

3.6108 * 4.7152 4.2933

fli

0.28272 0.55355 0.39329 0.92317

1.05120 0.81877 1.59010 0.87371

1.62474 •

0.88099 •

1.46244 *

0.80056 0.54010

% av, dev

11.24 11.71 12.28 8.19

10.52 18.15 12.94 8.55

6.49 *

11.00 *

7.96 *

8.99 4.28

Overall 10.62 10.17 "Asterisks indicate there were insufficient data to correlate results. Sets 1,5, 9,13: impeller midway in denser phase, H/4. Sets 2,6,10,14: impeller midway in lighter phase, 3H/4. Sets 3, 7,11,15: impeller at organic-water interface, H/2. Sets 4,8,12,16: two impellers, one midway in each phase, H/4,3H/4.

[ota

Co Ci D g H N

T ao A' P Ap

a

tion constant constant constant impeller diameter, m acceleration due to gravity, m/sec^ height of liquid in vessel, m minimum rotational speed of impeller for complete liquid-liquid dispersion in agitated vessels, 1/sec tank diameter, m constant dynamic viscosity, Nsec/m^ density, kg/m^ positive density difference between continuous and disperse phases, kg/m^ interfacial tension, N/m

Subscripts c continuous d dispersed

602 Chapter 7. Otiwr subjects rvlatsd to multi-phass systsms

Skelland, A. H. R and Lee, J. M., Ind. Eng. Chem. Process Des. Dev., 17,473 (1978) Agitator Speeds in Baffled Vessels for Uniform Liquid-Liquid Dispersion

Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.2135 m Height: 0.2500 m Volume: 0.01 m


Number: 4 Width: 0.0190 m Length of baffle immersed in the liquid from air-liquid interface: 0.1930 m

Impeller

Type

Diameter (m)

Number of impellers Number of blades

on impeller Width of impeller blade

Off-bottom clearance

propeller

0.1,0.075, 0.06

1 3

45° pitched-blade turbine

0.1,0.075, 0.062

1 6

projected width 1/8 of the

impeller diameter

flat-blade turbine

0.106,0.078, 0.065

1 6


H/A,H/2.3H/A


0.102,0.076, 0.063

1 6


Working fluids and their physical properties Continuous phase: water Dispersed phase:see table

Fluid properties at 25°C

Fluid

5-cSt Dow Coming 200 Fluid 10-cSt Dow Coming 200 Fluid 15-cSt Dow Coming 200 Fluid Benzaldehyde Ethyl acetate Water

Density, kg/m^

920 940 948.3

1,041 894

1,000

Dynamic viscosity. Ns/m^

0.0046 0.0094 0.0143 0.0014 0.00046 0.0010

Interfacial tension with water, N/m

0.0425 0.0435 0.0437 0.0145 0.00627

—


Experimental conditions Volume fraction of oi ganic liquid: 0.50 Temperature: 25X

Results

g^'^ - \D) [n,) U J [D'p.g

N' = Na+x)

Impeller performance, measured by N', the speed required to produce an Im of 98%, for all impellers at H/2 in all five systems'

D = 0.lm, i ) / r= 0.47

Z) = 0.076 m, J[)/r = 0.36

i> = 0.063 m, D/T = 030

impeller

flat-blade turbine curved-blade turbine pitched-blade turbine propeller


flat-blade turbine curved-blade turbine pitched-blade turbine propeUer

5-cSt S.O.-H2O

2.92 3.40 4.25

10.1

4.58 5.91

10.1 15.5

7.33 8.75

16.8 21.7

10-cSt S.O.-H2O

2.92 3.92 4.41 7.75

4.25 5.58 9.08

13.8

6.25 8.42

15.8 16.8

15-cSt S.O.-H2O

2.58 3.40 4.25 7.00

4.40 5.58 8.75

11.8*

6.25 8.08

15.2 16.8*

B.-H2O

3.00 2.58* 2.92 6.67*

4.25* 4.58* 6.25*

13.2*

6.08* 6.67*

11.1* 16.8*

EA-H2O

3.25* 2.92 3.10* 7.75

4.58* 5.25 5.58*

13.5

6.25* 6.67

10.8* 18.2

average TV 'for all conditions


4.59 5.45 8.56

13.16

* S.O. = silicone oil; B. = benzaldehyde; E.A. = ethyl acetate. * Denotes a nonaqueous continuous phase.

Effect of impeller location, measured by N\ the speed required to produce an /« of 98%. System: 5-cSt S.O.-HzO^

impeller

Z> =

H/4

flat-blade turbine 3.92 curved-blade turbine 4.58 pitched-blade turbine 5.74 propeDer 8.08

0.1m,Z)/r =

H/2

2.92 3.40 3.92

10.1

= 0.47

3H/4

3.58 4.25 4.92 5.91

Z) = 0.063 m,/>/r=

H/4

14.5 14.8 18.2 17.5

H/2

7.33 8.75

16.8 21.7

= 0.30

SH/4 c

c

16.2* 17.2

" S.O. = siUcone oil. * Denotes a nonaqueous continuous phase. '^ Unavailable due to splashing.

Average deviation between N'and N

mipeller m" — > — - — = x w 1 N

0.0667 0.0446 0.0747 0.1421 0.0827

* m = total values in each category; then ^'=7^(1 + jc).

flat-blade turbine curved-blade turbine pitched-blade turbine propeller overall

18 18 19 19 74

504 Chapter 7. Othar subj«cto r»l«t«d to multhphasa systems

Notation Oi constant Ci constant D impeller diameter, m g acceleration due to gravity, m/sec^ H height of liquid in vessel, m Im mixing index, % N minimum rotational speed of impeller for complete liquid-liquid dispersion in agitated

vessels, 1/sec N' minimum rotational speed of impeller for grossly uniform liquid-liquid dispersion in agitated

vessels, corresponding to an Im of 98%, 1/sec T vessel diameter, m X average deviation between N' and N ao constant jU viscosity, Nsec/m^ p density, kg/m^ Ap positive density difference between continuous and disperse phases, kg/m^ a interfacial tension, N/m

Subscripts c continuous d disperse

7.3 Critical agitation spaad g05

Godfrey, J. C, Reeve, R. N., Grilc, V and Kardelj, B., IChemE. Symposium Series, No.89,107 (1984) Minimum Conditions for the Production of Liquid-Liquid Dispersions in Agitated Tanks

Experimental apparatus Vessel Type: square cross-section tank Size: (1) 0.15 m x 0.15 m (2) 0.30 m x 0.30 m

Liquid contained Height: (1) 0.15 m (2) 0.30 m

Baffle No baffle

Impeller

standard six flat- three-blade (square pitch) Type blade disc turbine marine propeller Diameter (m) 0.0495 0.099 0.0495 0.099 Off-bottom clearance (m) 0.0495 0.099 0.0495 0.099

Working fluids and their physical properties Liquid: distilled water Liquid: seven different kinds of organic fluids

Results Minimum Reynolds number for liquid - hquid dispersion

Archimedes number

Reynolds number

Modified Suratman number s« ,=£ i^

Notation D impeller diameter, m Subscripts g acceleration due to gravity, m/sec^ c continuous phase K constant min minimum N impeller speed, 1/sec Ap density difference, kg/m^ 77 viscosity, Pasec a surface or interfacial tension, N/m

606 Chapter 7. OtiMr subjects r«lat«il to multi-phas« systems

Skelland, A. H. R and Ramsay, G. G.,Ind. Eng. Chem. Res., 26,77 (1987) Minimum Agitator Speeds for Complete Liquid-Liquid Dispersion

Experimental apparatus Vessel and agitator dimensions

internal diameter liquid height in of vessel, m vessel,

0.216 0.241 0.241 0.241 0.292

m

0.216 0.121 0.241 0.362 0.292

bafle width, m

0.019 0.019 0.019 0.019 0.025

impeller diameter, m

0.102, 0.076, 0.102, 0.076, 0.102, 0.076, 0.102, 0.076,

0.065 0.065 0.065 0.065

0.102, 0.076

square pitch, downthrusting propeller (three blades)

downthrusting pitched-blade turbine (six blades)

flat-blade turbine (six blades)

curved-blade turbine (six blades)

disk turbine (six blades)

set H/T impeller location

1 ] 2 ] 3 ] 4 ]

5 ] 6 ] 7 ] 8 ]

9 ] 10 ] 11 ] 12 ] 18 1/ 19 3/

13 ] 14 ] 15 ] 16 ]

17 ]

L H/A L 3H/4 I H/2 [ H/i,3H/4

L H/A L 3^/4 L H/2 I H/4,3H/i

[ H/4 L 3H/4 L H/2 [ H/4,3H/4 '2 H/2 '2 H/2

[ H/4 [ 3H/4 L H/2 L H/4,3H/4

L H/2

C

4.38 2.76 4.33 1.46

1.95 1.96 0.84 0.94

0.91 •

0.95 *

0.70 1.10

1.03 *

1.34 1.20

0.53

a

0.67 0.95 0.79 1.33

1.44 1.17 1.97 1.27

2.02 *

1.38 «

1.24 1.70

1.86 *

1.20 0.94

1.70

^Asterisks indicate insufficient data due to splashing

7.3 Critical agitation spMd

Axial flow impellers used

607

(a) Pitched blade turbine (b) Marine-type propeller

Radial flow impellers used

\m n

(c) flat-blade turbine (d) curved-blade turbine (e) disk turbine

Working fluids and their physical properties Continuous phase: deionized water Dispersed phase: see table

Fluid properties at 23*C

fluid

ethyl acetate benzaldehyde chlorobenzene carbon tetrachloride water

density, kg/m^

894 1,041 1,106 1,590

997

dynamic viscosity, N-s/m2

0.00046 0.0014 0.0010 0.0010 0.0009


0.00627 0.0145 0.0352 0.045

Experimental conditions Temperature: 23**C

Results

2 I i I (N,y)^=C'\-^ ^ KNGCNBO)

Values of or and C are shown in a table attached to the section of experimental apparatus.

503 Chapter 7. Otiwr siibj«cto r»lat«d to multi-ph«s« systems

Notation C constant D impeller diameter, m g acceleration due to gravity, m/sec^ H liquid height in vessel, m N rotational speed of impeller, 1/sec NBO Bond number, D'^gt^la, dimensionless Npf Froude number, DN^pmlgl^, dimensionless (NFt)nm minimum Froude number for complete liquid-liquid dispersion, dimensionless Nca Galileo number, D^pMg^p/îyf, dimensionless T tank diameter, m a constant ô îd viscosities of continuous and disperse phases, Nsec/m^

Pc pd densities of continuous and disperse phases, kg/m^ pM = 0Prf + (1 - 0)po kg/m^ Ap =|pr-prf | ,kg/m^ a interfacial tension, N/m 0 volume fraction of disterse phase


Skelland, A. H. R and Moeti, L. T, Ind. Eng. Chem. Res., 28,122 (1989) Effects of Surface Active Agents on Minimum Impeller Speeds for Liquid-Liquid Dispersion in Baffled Vessels



Baffle Number: 4 Width: 0.0190 m Thickness: 0.0030 m Length: 0.2300 m Length of ba£Qe in liquid from air-Uquid interface: 0.1930 m

Impeller

Type

Diameter (m) Number of

impellers Number of blades

on impeller

Off-bottom clearence

square pitch, down thrusting

propeller (a)

0.10 and 0.06 1

3

down thrusting 45^ pitched-blade

turbine (b)

0.10 and 0.062 1

6

flat-blade turbine (c)

0.10 and 0.065 1

6

H/4,H/2,3nd3/4H

curved-blade turbine (d)

0.10 and 0.065 1

6

C=&3 J l rnQjrrn

(a) Propeller (b) Pitched-blade turbine (c) Flat-blade turbine

Mixing impellers used.

(d) Curved-Wade turbine

Working fluids and their physical properties Continuous phase: distilled water Dispersed phase: chlorobenzene or benzaldehyde

610

fluid

chlorobenzene benzaldehyde water

Chapter 7. Oth«r subjects rslatsd to multi-phass systsms

Fluid properties at 23°C

density, kg/ia?

dynamic viscosity, (N.s)/m2

1,107 1,041 998

0.0010 0.0014 0.0010


0.0352 0.0154

Surface active agents: nonionic octylphenoxypolyethoxyethanol anionic dodecyl sodium sulfate cationic dodecyl pyridinium chloride

Experimental conditions Temperature: 23°C Volume fraction of organic liquid: 0.50

Measurement technique Visual observation and conductivity measurement

Results

- - ( ^ J ^°'^ApQ-^Vr<y''>°°' L> pM

pM-<l>pd+(l-0Pc

1-0 A^ + A^j

(1)

(2)

(3)

propeller

pitched blade

curved blade

flat blade

overall nonionic anionic cationic




C

4.165 ±0.317 4.342 4.142 4.017

0.655 ±0.063 0.739 0.606 0.628

0.988 ±0.100 1.033 0.982 0.952

0.847 ±0.085 0.840 0.816 0.888

a

0.791 ±0.071 0.804 0.787 0.782

2.123 ±0.089 2.072 2.182 2.114

1.456 ±0.097 1.494 1.423 1.450

1.502 ±0.096 1.610 1.493 1.403

7.3 Critical agitation sp««d QH

Notation C constant D impeller diameter, m g acceleration due to gravity, m/sec^ H liquid height in the vessel, m Nnm minimum rotational speed of impeller for complete liquid-liquid dispersion in agitated,

baffled vessels, without regard to uniformity, 1/sec T tank diameter, m a constant /Xr, jUd viscosities of continuous and disperse phase, Nsec/m^ jiiM given in eq (3),Nsec/m^ pr, Pd densities of continuous and disperse phases, kg/m^ Ap I pr-prf I, kg/m^ a interfacial tension, N/m 0 volume fraction of disperse phase

612 Chapter 7. Othar subjaete r«lat«il to multi-phas« systems

Skelland, A. H. P. and Kanel, J. S., Ind. Eng. Chem. Res., 29,1300 (1990) Minimum Impeller Speeds for Complete Dispersion of Non-Newtonian Liquid-Liquid Systems in Baffled Vessels

Experimental apparatus Vessel Type: flat-bottomed Diameten 0.2135 m Height: 0.2500 m


Baffle Number: 4 Width: 0.0190 m Thickness: 0.0025 m

Impeller

Type

Diameter (m) Width (m) Off-bottom

clearence (m) Number of

impellers Number of blades

on impeler

flat-blade turbine

0.1014,0.0761 0.0124,0.0091

0.1068

1

6


0.1022,0.0756 0.0125,0.0090

0.1068

1

6

pitch-blade tuibine

0.1013,0.0753 0.0130,0.0095

0.1068

1

6

propeller

0.102,0.076 —

0.1068

1

3

(a) Propeller

Jl rrig

(b) Pitched-blade turbine (c) Flat-Made turbine (d) Curved-blade turbine

Mixing impellers used.

7.3 Critical agitation sp««il 523

Working fluids and their physical properties Continuous phase: distilled water or one of four aqueous solutions of carbopol (non-Newtonian) Dispersed phase: diisobutyl ketone (DBK) (Newtonian)

fluid

water 0.1000 wt% Carbopol 0.1125 wt% Carbopol 0.1250 wt% Carbopol 0.1500 wt% Carbopol DBK

p at 26°C, kg/m^

996.5 996.5 996.3 996.6 996.5 807.6

or with DBK at26X,

N/m

0.021 0.020 0.020 0.020 0.021

consistency at 25°C

K kgs 'Vm

8.90x10-* 5.79x10-2 2.87x10-' 4.19x10-' 1.47 9.47x10-*

n

1.0 0.83 0.67 0.64 0.52 1.0

Results

0^106/\r \T \-0.084

< )

1-0 ( ^d-^tic)

For non-Newtonian fluids viscosity is replaced by Vermeulen et al's viscosity experssion combined with Metzner and Otto's definition of apparent viscosity, /44.

Impeller type C a

flat-blade turbine (6 blades) 0.86 ± 0.30 1.49 ± 0.34 curve-blade turbine (6 blades) 1.15 ± 0.23 1.31 ± 0.21 pitch-blade turbine downthrusting (6 blades) 0.76 ± 0.21 1.96 ± 0.28 square pitch propeller downthrusting (3 blades) 3.41 ± 1.08 1.10 ± 0.34

Notation C constant D impeller diameter, m g acceleration due to gravity, m/sec^ N impeller rotational speed, 1/sec NBO Bond number, D^g^p/a, dimensionless (NFy)iui>* minimum Froude number, DN^pAs/gAp, dimensionless TVmin minimum impeUer speed for complete dispersion, 1/sec Nca Galileo number, D^pMgAp/^j/, dimensionless T tank diameter, m a constant ^A apparent viscosity, kg/msec liir, ^id viscosities of continuous and disperse phases, kg/msec pc, pd densities of continuous and disperse phases, kg/n? pM = 0A/ + (1 - (l>)pc, kg/m^ Ap = |pf-prf|,kg/m^ (7 interfacial tension, N/m 0 volume fraction of disperse phase

514 Chapter 7 . Othar subjacto r»lat«d to multi-phas* systems

Armenante, E M., Huang. Y.-T and Li, T, Chem. Eng. Sd., 47,2865 (1992) Determination of the Minimum Agitation Speed to Attain the Just Dispersed State in Solid-Liquid and Liquid-Liquid Reactors Provided with Multiple Impellers


Baffle Number: fully baffled

Impeller Type: (a) disc turbine (b) flat-blade turbine (c) 45° pitched-blade turbine Diameter: (a) 0.065 (b) 0.076 (c) 0.102 m Number of impellers: 1,2, or 3 Clearance of the lowest impeller off the tank bottom and the spacing between impellers were varied

Working fluids and their physical properties Continuous phase: distilled water Dispersed phase: mineral oil (density=826 kg/m )

Experimental conditions Volumetric fraction of oil: 10%

Results (1) The dependence on D (C/=constant)

disc turbines «/ocZ)-2•03 for« = l

NaiocD-^'^ forn = 2 Ncdo-D-'^ for« = 3

(2) The dependence on Z)(C//Z)=constant) disc turbines

NaiocD-'-^ forM = l NaiOcD-'^ for« = 2 NaiocD-'^' for« = 3

(3) The dependence on S (C/Z)=constant) N..i oc 5° ' for disc turbines Nrd oc S°" for flat-blade turbines Ntd oc S° ' for pitched-blade turbines (pumping up)

Notation Ci distance of top impeller from air-liquid interface, m D impeller diameter, m n number of impellers mounted on the same shaft Nni minimum agitation speed for complete dispersion in liquid-liquid systems, 1/min 5 distance between impellers, m

7.3 Critical agitation spaad g 5


Chapman, C. M., Nienow, A. W, Cooke, M. and Middleton, J. C, Chem. Eng. Res. Des., 61,82(1983) Particle-Gas-Liquid Mixing in Stirred Vessels Part II: Gas-Liquid Mixing


Liquid contained Height: 0.56 m Volume of liquid in vessel: 0.138 m^

ImpeUer Type: disc turbine Diameter: 0.28 m Off-bottom clearance: 0.14 m

Working fluids Liquid: Tap water Gas: air

Results

(/ G)ci>-°''(Fr)cz)°-2 (Z)/r)«-25 = 2.25

or substituting for^ in the Froude number

^cz)Z)70c°-'r°-25=4 where the constant 4 has the units m - s~^^

Notation D impeller diameter, m FIG gas flow number, QG/ND^, dimensionless Fr Froude number, N^D/g, dimensionless g gravitational constant, m/sec^ N impeller speed, 1/sec QG gas flow rate, mVsec or wm T vessel diameter, m

Subscripts CD condition at which impeller just dispersed gas throughout the vessel

616 Chapter 7. Othar subjects rvlatad to multi-phasa systams


Nienow, A. W. Konno, M. and Bujalski, W, Chem. Eng. Res. Des., 64,35 (1986) Studies on Three-Phase Mixing : A Review and Recent Results


Impeller Type: (1) six-blade disc turbine, (2) 6 blade 45° pitch downward turbine, (3) 6 blade 45° pitch

upward turbine Diameter: T/2 Number of impellers: (1), (2), (3) 1 Number of blades on impeller (1), (2), (3) 6 Off-bottom clearance: 7/4

Working fluids, solids and their physical properties Sohd: lead glass ballotini (size=440~530 m) Liquid: water Gas: air

Experimental conditions Solid content: 0.1%

Results Data for water-air-0.1% lead glass ballotini (440-530 im) (7=0.45 m; Z)=T/2; C=r/4)

OK. Disc Turbine

SRS LRS 6 Blade 45° (Down)

SRS LRS 6 Blade 45° (Up) SRS LRS

0.0

0.3

1.0

3.5

Njs (er)js NF (er)F NcD (et)cD NJS, (£T)jSg

NF (er)F NcD (er)cD NJS, (er)jSq

NF (£r)F NcD {et)cD NJS, (ex)jsg

2.9 1.12 0.7 0.014 1.8 0.23 3.4 1.6 1.0 0.032 2.3 0.31 3.9 1.59 1.67 0.12 2.5 0.32 5.1 2.09

2.9 1.12 0.7 0.013 1.8 0.25 3.3 1.5 1.0 0.033 2.2 0.30 3.9 1.72 1.8 0.14 2.5 0.31 5.1 2.08

3.7 0.67 LI 0.02 1.8 0.066 3.5 0.53 1.3 0.035 2.5 0.15 4.7 0.77 1.6 0.091 4.9 0.63 7.3 1.47

3.7 0.68 0.67 0.005 1.7 0.058 3.4 0.47 0.92 0.02 2.5 0.15 4.4 0.70 1.6 0.095 4.6 0.55 6.9 1.40

3.9 0.77 1.3 0.03 2.3 0.16 4.2 0.93 1.6 0.04 2.6 0.23 4.4 0.93 2.1 0.10 2.6 0.21 4.8 0.87

3.9 0.78 0.92 0.011 1.7 0.078 4.1 0.87 LI 0.017 1.8 0.096 4.3 0.87 1.4 0.03 2.2 0.15 4.7 0.84

SRS- small ring sparger, 0.54 D; LRS—largel ring sparger, 0.84 D

7.3 Critical agitation spaad giy

Notation C impeller clearance above the base, m D impeller diameter, m N impeller speed, 1/sec Njsg the agitation speed required to just completely suspend all the particles under gassed

conditions, 1/sec QvG specific gas flow rate, wm T vessel diameter, m BT mean energy dissipation rate, W/kg (Erhsg the mean energy dissipation rate required to just suspend all the particles under gassed

conditions, W/kg

Subscripts g under gasses conditions CD conditions at which impeller just dispersed gas throughout the vessel F conditions at which impeller is flooded JS at the speed at which solids do not spend more than 1 to 2 seconds on the bottom when

observed

618 Chapter 7. Other subjects rslatsd to multi-phass systems

Wong, C. W, Wang, J. P and Huang, S. T, Can J. ofChem. Eng., 65,412 (1987) Investigations of Fluid Dynamics in Mechanically Stirred Aerated Slurry Reactors


Liquid contained Ungassed height: 0.29 m


Impeller Type: (1) A-310 propeller (3-AP) (2) two types of 4-blade 45° pitch turbine (4-PT)

(3) two types of 6-blade Rushton disc turbines (6-DT)

e-flat blade disc turbine

wED ri D

U-Di-J

Di 5' A 4

4-blade 45**pitch turbine

^ ^ Di-

Di 5 Types of impellers

f=^=^^ -Di-

A-310 propeller

Diameter: DT/3 or DT/2 Number of impellers: 1 Number of blades on impeller: (1), (2) 4, (3) 6 Off-bottom clearance: DT/3 OXDTI^

Working fluids, solids and their physical properties Solid: see Table 1 Liquid: see Table 2 Gas: air


Table 1 Properties of particles used in this investigation

Material

River sand

Glass bead

Glass powder

Aluminum powder

Cadmium powder

Corundum powder

Tyler screen mesh No.

2 0 - 3 5 3 5 - 4 5 6 0 - 1 0 0

1 2 - 1 6 2 0 - 3 5 6 0 - 1 0 0

2 0 - 3 5 6 0 - 1 0 0

6 0 - 1 0 0

6 0 - 1 0 0

6 0 - 1 0 0

Particle mean diameter dp (|Lim)

675 425 200

1,200 675 200

675 200

200

200

200

Table 2 Physical properties of test fluids (25 *C)

Liquid

Water 0.5 wt. %

NaCl solution 20wt. %

Glucose solution

Surface tension (N/mxlO-3)

72.7

66.7

60.0

Viscosity (kg/msec x 10 )

0.982

0.983

1.581

Density A(kg/m3)

2,755 2,755 2,755

2,514 2,514 2,514

2,514 2,514

2,700

8,642

3,130

Density (kg/m^)

998.2

1,004.6

1,075.1

Shape

Irregular

Spherical

Irregular

Irregular

Irregular

Irregular

Results Gassed critical stirrer speed for suspension, Nj^^ for 6-DT

NjviocX'''''

Ap°-

Notation Di stirrer diameter, m DT vessel diameter, m dp partide diameter, m L length of the blade of stirrer, m Njs critical stirrer speed for just complete suspension of solids in tiquid-solid system, 1/min Nj^ gassed critical stirrer speed for suspension, 1/min QG gas flow rate, w m IV width of the blade of stirrer, m X solid mass fraction, % Ps solid density, kg/ia? Ap difference between particle and liquid densities, kg/w?

520 Chapter 7. Othar subjects ralated to multi-phasa systams

Rewatkar, V B. and Joshi, J. B., Ind. Eng. Chem. Res., 30,1784 (1991) Critical Impeller Speed for Solid Suspension in Mechanically Agitated Three-Phase Reactors 2. Mathematical Model

Results Using published data the foUowing relationships were obtained (i) For all spargers located 100 mm below the impeller

v;=o.i96M)r-°"FG-°-2«^

(ii) For spargers located away from the impeller, 152 mm in a 0.57-m-i.d. vessel and 390 mm in a 1.5-m-i.d. vessel

V.=0.3471M)^-^r-°-2^Fc-°-^

(iii) For spargers located above the impeller

V . = 0 . 0 5 3 6 M ) 7 G - ° ^

(V^J-aVc) ^x/D)X''VS''* = 0.18 NSGD

where

a = 0.9Vif 0.57 < r < 1.5 m, 1.7 <T/D<6, C = r /3, 20 < 7,« < 200 mm/sec, 0.34 ^ AT 50 wt% and 1.5<l^c<30nmi/sec

Notation C impeller clearance from tank bottom, m D impeller diameter, m N impeUer rotational speed, 1/sec NsG critical impeller speed for a sohd suspension in a gas-Uquid-solid system, 1/sec T tank diameter, m Vr liquid cfrculation velocity in the bulk, m/sec VG superficial gas velocity, m/sec Vsoo terminal setthng velocity of particle, m/sec X solid loading, wt%


Dutta, N. N. and Pangarkar, V G., Can. J. ofChem. Eng., 73,273 (1995) Critical Impeller Speed for Solid Suspension in Multi-Impeller Three Phase Agitated Contactors


System (1) (2)

Vessel Type flat-bottomed flat-bottomed Diameter (m) 0.15 0.30

Baffle Number 4 3 Width (m) 0.015 0.030

Sparger Type a ring sparger a ring sparger Diameter 0.8/) 0.8 Z) Tube diameter (nmi) 12.5 25.4 Orifice diameter (mm) 2 3 Distance between orifices (nmi) 10 20

Location 0.1 r above the bottom

Impeller

Impeller type No of Dia.Z) blade m

Blade width m

Blade length m

Disc turbine (DT)

Pitched turbine down flow (PTD)

Pitched turbine upflow (PTU)

0.05 0.10 0.075 0.10 0.05 0.075 0.10 0.05 0.075 0.10

Z)/5 Z)/5 DIS DI5 Z)/4 Z)/4 Z)/4 Z)/4 Z)/4 Z)/4

Z)/4 0.03 2)/4 0.03 Z)/4 Z>/4 0.03 Z)/4 D/A D/4

PTU and PTD: angle of pitch = 45*'; Blade thickness: 2 mm.

Positions of impellers: Distance between first and second impeller: T Distance between second and third impeUer: T Distance between third and forth impeller: T

622 Chapter 7. Oth«r subjects r»lat«il to multi-phasa systems

Working fluids, solids and their physical properties Liquid: deionized water Gas: air Solid: sand, ion exchange resin and iron oxide pellet

Particles employed in the study

Particle Shape Size range (pm) Density Oag/w?)

Sand

Iron oxide pellet

Irregular (Sphericity 0.84)

Spherical

Spherical

125-250 250-300 550-600 850-1,000 850-1,000 550-600 850-1,000 550-600

2,490 2,470 2,453 2,453 1,180 1,180 3,400 3,500

Experimental conditions Superficial gas velocity: 0—15 mm/sec Solid loading: 0.5-10% w/w

Results Effect of particle size

Nj^ocd'p^

Ni, :<« Effect of sohd loading

Effect of density difference

Ap^ps-pi Effect of impeller diameter

Effect of tank diameter

. 'PO.624

. j«0.65

DT and PTD impellers

PTU impellers

PTD impeller

DT impeller

PTU impeller

PTD impeller

DT impeller

PTU impeller

Notation dp particle diameter, m D impeller diameter, m Nj^ critical impeller speed of solid suspension in the presence of gas, 1/sec T tank diameter, m X solid loading, mass % p density, kg/w?

Subscripts L liquid 5 solid

623

7.4 Size and its distribution of dispersed piiase

7.4.1 Drop size and drop-size distributions

Sprow, E B., Chem. Eng. Sci., 22,435 (1967) Distribution of Drop Sizes Produced in Turbulent Liquid-Liquid Dispersion

Experimental apparatus Vessel Type: flat-bottomed Diameter: 8 V* in Height: 12 in Volume: 2 gal

Baffle Number: 4 Width: 3/4 in

Impeller Type: six flat-blade turbine Diameter: (a) 2 V2 (b) 3 (c) 4 in Number of impellers: (a) (b) (c) 1 Number of blades on impeller: (a) (b) (c) 6 Width of impeller blade (parallel to shaft): W/D=l/S Off-bottom clearance: H/3

Working fluids and their physical properties Continuous phase: 1% NaCl in water Dispersed phase: iso-octane

Properties at 20^C

Liquid Density (g/cm ) Viscosity (cP)

iso-octane 0.692 0.51 1% NaCl in water 1.005 0.99

inter&cial tension=41.8 dynes/cm

Experimental conditions Temperature: 20 ± 0.5 C

Measm-ement technique Coulter counter

Results For ^ < 0.015

rf32=0.0524cy'V'^'^"^^'^''^'

Q24 Chapter 7. Othar subjects rslated to multi-phass systems

Notation d dsz Cljagx

D H n N W Pc 0

drop diameter TLnidiVnidi^ maximum stable size impeller diameter liquid height number of particles impeller speed width of impeUer blade density of continuous phase volume fraction dispersed phase

7.4 5iz« and its distribution off disporsod pliaso 625

Chen, H. T. and Middleman, S.,AIChE Journal, 13,989 (1967) Drop Size Distribution in Agitated Liquid-Liquid Systems

Experimental apparatus Vessel Type: flat-bottomed Diameter: (1) 4 (2) 6 (3) 8 (4) 10 (5) 12 (6) 18 in

Liquid contained Height: (l)~(6)r

Baffle Number: (1)~(6) 4 Width: (1M6) 0.1 r

Impeller Type: six-blade turbine Diameter: (a) 2 (b) 3 (c) 4 (d) 5 (e) 6 in Number of impellers: (a)—(e) 1 Number of blades on impeller: (a)—(e) 6

Working fluids Continuous phase: distilled water Dispersed phase: see table

Physical properties of systems studied^

System

i-Octane Cyclohexane Benzene Chlorobenzene Xylene Toluene Phenetole Anisole Ethyl hexanoate Oleic Acid 10-Undecenoic add Tri-butyl Phosphate Benzyl alcohol Isoamyl alcohol

Density (g/cc) Pc

0.997 0.997 0.997 0.997 0.997 0.997 0.998 0.997 0.997 0.997 0.996 0.997 1.001 0.993

Pd

0.703 0.761 0.873 1.101 0.860 0.867 0.965 0.993 0.871 0.895 0.908 0.979 1.042 0.825

Viscosity (centipoise)

Mr

0.899 0.894 0.896 0.890 0.895 0.896 0.896 0.895 0.901 0.895 0.890 0.894 1.270 0.982

l^d

0.520 0.762 0.607 0.776 0.610 0.550 1.16 1.01 1.23 25.8 10.3 3.91 5.30 3.48

Interracial tension

(dynes/cm) a

48.3 46.2 40.2 37.7 36.1 31.6 39.4 25.8 20.7 15.6 10.4 8.58 4.75 4.80

^ Properties given are mutually saturated phase at 25X.

Experimental conditions Reynolds no. (ATLVv): 1.2 x 10*--10.4 x 10* Weber no. (N^L^p/cr): 70 -2,000 Impeller speed (N): 80-1,000 rpm L/T (L: impeUer diameter): 0.21-0.73 Concentration of dispersed phase (0): 0.001—0.005 Temperature: 25°C

Measurement technique Photography

626 Chapter 7. Other subjects i«lat«d to multf-phaso systems

Results

S32/L = 0.053NwT

Drop-size distribution

MDi/D32) = 1

0.23 V2^ exp -9.2[^-1.06l

Notation A

fAiDiim

L N

Nwe T V

p a 0

D32

0.23 V2FA exp -9.2 &-I diameter of a drop in the i^ size interval, cm Sauter mean diameter, cm area distribution function of drops volume distribution function of drops impeller diameter, cm impeller speed, 1/sec Reynolds number, NL^/v, dimensionless Weber number, VN^pIo, dimensionless vessel diameter, cm kinematic viscosity of continuous phase, cmVsec^ density of continuous phase, g/cc interfacial tension between phases, g/sec^ concentration of dispersed phase


7A Six* and its distributton off disp«rs«d phaso 627

Sprow, F. K.AIChE Journal 13,995 (1967) Drop Size Distributions in Strongly Coalescing Agitated Liquid-Liquid Systems

Experimental apparatus Vessel Type: flat-bottomed Diameter: 8 VA in Height: 8 3/4 in Volume: 2 gal

ImpeDer Type: six flat-blade turbine Diameter: 2 V2 in Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 3 in

Working fluids and their physical properties Continuous phase: 1% sodium chloride in water Dispersed phase: methyl isobutyl ketone

Liquid Density, g/cc Viscosity, centipoise

Methyl isobutyl ketone 1% sodium chloride in water

0.80 1.005

0.59 0.99

Interfacial tension = 9.3 dynes/cm

Experimental conditions Temperature: 20 ± 0.5°C

Measurement technique Coulter counter

Results

c 70 4( u lb m 120 )4s iu m m :n c I Di»p Oiaaelci. HICIM} SOp

Drop size distribution at two sampling points (1,000 revymin, 0 = 0.25).

n I i I I I 11

ANHrt-C

-i I t 1, M M I seo 1000

i.Rni

Effect of impeller speed on average diameter (0 = 0.25).

528 Chapter 7. Oth«r subj«cto r»lat«d to multi-phase systems

Notation A surface area per unit volume d drop diameter

D F

n

V

P a 0

0 3 2 = T

A

impeller diameter force parameter constant number of drops of a particular size total number of drops, impeller speed kinematic viscosity density interfacial tension volume fraction dispersed phase

Subscripts c continuous phase d dispersed phase max maximum stable size min minimum stable size

lA Siz« and its distribution off disporsod pliaso 529

Brown, D. E. and Pitt, K., Chem. Eng. Sci., 27,577 (1972) Drop Size Distribution of Stirred Non-Coalescing Liquid-Liquid System

Experimental apparatus Vessel Type: glass pipe line Diameter: 30 cm Height: 30 cm

Impeller Type: six-bladed disc turbine Diameter: 10 cm Number of impellers: 1 Number of blades on impeller: 6 Width of impeller blade: 2.5 cm

Working fluids Continuous phase: water Dispersed phase: kerosene

Experimental conditions Impeller speed: 250,300,350 and 400 rpm Dispersed phase hold-up value: 0.05,0.10 and 0.20 Temperature: 20 °C


Results Drop-size distribution

Fr 0.20 V^ exp -12.51—-1.07

dsz

d32=0.70d„m

Notation d drop size, cm dsz Sauter mean diameter, cm dnax maximum drop diameter, cm Fp (d/dsz) normahzed volume fraction per cm

530 Chapter 7. OtiMr subj«cte r«lat«d to multi-phas» systems

Mlynek, Y. and Resnick, W.AIChE Journal, 18,122 (1972) Drop Sizes in an Agitated Liquid-Liquid System




Impeller Type: (1) six-blade turbine (2) four-blade turbine Diameter: (1) 10 (2) 9 cm Number of impellers: (1) (2) 1 Number of blades on impeller: (1) 6 (2) 4 Length of impeller blade (perpendicular to shaft): (1) 2.5 (2) - cm Width of impeller blade (parallel to shaft): (1) 2 (2) 0.78 cm Off-bottom clearance: 9.67 cm

Working fltiids and their physical properties Continuous phase: water Dispersed phase: a mixture of carbon tetrachloride and isoocctane (density = 1.055 g/m^;

interfeicial tension = 41 ± 2 dyne/cm) Experimental conditions

Dispersed phase hold up: 0.025—0.34 Impeller speed: 150—500 rpm

Measurement technique Light transmittance measurement

Results Drop size

d32/D = 0.058 We-^'W -h 5.4X)

Coalescence rates

w ^ - 1 ^ ^ 0 ^ ^ 3 - 0 . 9

Notation dsz D N w We X P G

Sauter mean drop diameter impeller diameter impeller speed coalescence rate expressed as ; relative rate of change of diameter Weber number, pN^DVa, dimensionless dispersed phase hold up density interfacial tension

7.4 Siz« and i U ilistributioii of disp«rs«il phmmm 631

Mlynek, Y. and Resnick, W, Can J. ofChem. Eng., 50,134 (1972) On Local Hold-Up and Average Drop Size in a Liquid-Liquid Stirred System




Impeller Type: six-blade turbine Diameter: 10 cm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 2.5 cm Width of impeller blade (i u:allel to shaft): 2 cm Off-bottom clearance: 9.67 cm

Working fluids Continuous phase: water Dispersed phase: carbon tetrachloride

Experimental conditions Average dispersed phase hold-up: 0.1 (volume fraction) Impeller speed: 260,310 and 360 rpm


Results

o - I

< »«H

1 1

V i f V L ^ .

V^t' 1

1 1 1

1 1 1

1

1 1

i 1 L_

•~^-c-~

^^^ -N, N V IMPELLER SPEED \ \

• 260 RPM \ \ A 310 RPM \ \ -360 RPM \

FRACTIONAL HEIGHT IN VESSEL

Fractional holdup as function of height above tank bottom.

.- •* A—

\

WPELLER SPEED

• 260RPM 1310 RPM

, FRACTIONAL HEIGHT M VESSEL

Average drop diameter as function of height above tank bottom.

632 Chapter 7. OtiMr subjects r«lat«d to multi-phasa systams

Weinstein, B. and Treybal, R. E.,AIChE Journal, 19,304 (1973) Liquid-Liquid Contacting in UnbafQed, Agitated Vessels

Experimental apparatus Vessel Type: (1) (2) flat-bottomed Diameter (1) 0.245 (2) 0.382 m Height: (1)0.245 (2) 0.382 m


Impeller Type: (1) (2) six flat-blade turbine Diameter: (1) 0.0762 and 0.127 (2) 0.127 m Number of impeUers: (1) (2) 1 Number of blades on impeller: (1) (2) 6 Length of impeller blade (perpendicular to shaft): (1) (2) D/i Width of impeller blade (paraUel to shaft): (1) (2) D/5 Off-bottom clearance: (1) i2)H/3


System properties at 25°C

Saturated Uquid solvent/solute

Density,

(1,000)

Viscosity N-s/m2=

centipA,000

Interfacial tension, N/m=

(dynes/cm)A,000

Cyclohexanone/water Water/cyclohexanone Octanol/water Water/octanol Methylamyl acetate/water Water/methylamyl acetate Isopropyl benzene/water Water/isopropyl benzene

946 996 831 996 857 997 856 996

0.002015 0.001146 0.00743 0.000902 0.000863 0.000892 0.000722 0.000896

0.00376

0.0102

0.0166

0.0360


Impeller Impeller speed,

Vessel diam., m revys

SmaU(l) 0.0762' 5.0-10.33 Small (1) 0.127^ 2.5-5.33 Large (2) 0.127 4.17-5.33

Flow rate total liquid mVsxlO*

0-3.785' 0-3.785 0-3.785

Dispersed-phase fraction of total feed^

0.125-0.833 0.125-0.833 0.125-0.500

Avg. dispersed phase holdup

0.079-0.593 0.090-0.512 0.079-0.496

Avg. drop diam., ^, m X10*

2.32-8.44 2.21-6.74 2.72-6.95

Avg. specific interface area,

a, mVm*

991-6,560 1,253-7,255 1,204-6,002

'6gal/min. ** Continuous flow. "Sin. *'5in.

Temperature: 24-31 °C

Measurement technique Light-transmittance technique

7Jk SiM and Its distribution off disporsod phaso 633

Results Drop diameters for batch operation

Circumstance Equation

All data

Both vessels

T 3 Small vessel

T 2

i^=yVc^.409gl246j^4^1

— 1/ -0-335 ^0.850 T2J54 W2=yvc" d /

Drop diameters for continuous flow

Circumstance

All data

Both vessels D 1 T 3

Small vessel D 1 T 2

Equation J^^lQ(-2.066-f0.732f) ^ 0.047 ^-^2M (^^^/^^j0.274

//Hr,=10 ^ ' "^2.673?)

52=yVc"^-^^^£°-^^J/-®° d^ = 10 -2-1^2+0.765?) y O.0344 -0.192 (^^^/^^j0.263

ArHv=io - - "'2-«» ^ i^=^V^-O.131g0.730j^2^

J =10<-i- 9 o-"9 > vc^°^ f- -2 ^ (cgc/pcy^ j^jy^_20<-5122+2.133^

S2=yVc^-232g0iJ12j^2.288

Notation

dp D gc H Nwe

L

r e V P CT

0

local specific interfacial area, mVm^ vessel-average oia, mVw? vessel-average of d {dp: diameter of droplet, m) impeller diameter, m conversion factor: 1 kgm/Nsec^ or 32.17(lbm)(ft/lgf) sec^ liquid height in vessel, m Weber number, pcU^dp/agcy dimensionless vessel diameter, m square of root-mean-square turbulent fluctuating velocity over the wave-number range under consideration mVsec^ a dimensional constant rate of energy dissipation/mass of liquid, mVsec^ kinematic viscosity, mVsec^ density, kg/m^ interfacial tension, N/m local dispersed-phase holdup, m^ dispersed-phase holdup/m^ dispersion vessel-average of 0, mVm^


g34 Chapter 7. Othar subj«eto r»lat«d to multi-phas« systems

Coulaloglou, C. A. and Tavlarides, L UAIChE Journal, 22,289 (1976) Drop Size Distributions and Coalescence Frequencies of Liquid-Liquid Dispersions in Flow Vessels

Experimental apparatus Vessel Type: flat-bottomed Diameter: 245 mm Height: 254 mm Volume: 12 i

Baffle Number: 4

Impeller Type: six blade disk turbine Diameter: 100 mm Number of impeUers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): D/4 Width of impeller blade (parallel to shaft): D/5

Working fluids and their physical properties Continuous phase: distilled water Dispersed phase: oil mixture of 63% kerosene and 37 % dichlorobenzene (density = 0.972 g/cm^;

viscosity = 1.30 cP) Interfacial tension: a = 42.82 dyne/cm

Experimental conditions Holdup fraction: 0.025-0.15 Impeller speed: 190-310 rpm Normal residence time of continuous and dispersed feed: 10 min


Results d^/D=OMl (1+4.470) (We)f^-^

Notation di drop diameter dzz Sauter mean diameter, ZnidiVZnidi^ D impeller diameter N impeller speed (We) T tank Weber number, N^D^pJa, dimensiouless Pc density of continuous phase G interfacial tension 0 holdup fraction

7 ^ Siz« and ito distribution off disporsod pliaso 635

Coulaloglou, C. A. and Tavlarides, L. L, Chem. Eng. Sd., 32,1289 (1977)

Description of Interaction Processes in Agitated Liquid-Liquid

Dispersions

Experimental apparatus Vessel Type: flat-bottomed Diameter: 245 mm Height: 254 mm Volume: 12 i

Baffle Number: 4

Impeller Type: six-bladed disk turbine Diameter: 100 mm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): D/4 Width of impeller blade (i»rallel to shaft): Z>/5

Working fluids and their physical properties Continuous phase: distilled water Dispersed phase: oil mixture of 63% kerosene and 37 % dichlorobenzene (density 0.972 = g/cm ;

viscosity = 1.30 cP) Interfacial tension: a = 42.82 dyne/cm

Experimental conditions Impeller speed: 190'-310 rpm Holdup fraction: 0.025-0.15

Results

g(v) = OMv-^^'D^ N'

1+0

F(t;,t;0 = 2.8xl0-^(t;2/3+t;

exp O.O8c7(l+0)

,/2/3j^^2/9 ^^/2/9jl/2 2)2/3

(1+0)'

exp -1.83x10 ,9 ^lcpcD^ N''

a-^ipy

Notation A(v) D F(v. if)

giv)

N

V, t/

probability density of droplet size v in vessel impeller diameter, cm coalescence frequency of drops of volume v with drops of volume v\ 1/sec breakage frequency of drops of volume v, 1/sec total number of drops revolutions per second, 1/sec drop volume, cm^

NA(v)NA(v')

/i viscosity, g/cmsec p density, g/cm^ a interfacial tension, dynes/cm 0 dispersed phase holdup fraction

Subscripts d dispersed phase c continuous phase

536 Chapter 7. Oth«r subj«cto r«lat«d to multi-phas« systems

Aral, K., Konno, M., Matsunaga, Y. and Saito, S.J. Chem. Eng. Japan, 10,325 (1977) Effect of Dispersed-Phase Viscosity on the Maximum Stable Drop Size for Breakup in Turbulent Flow


Buffle Number: 4 Width: 1.27 cm

Impeller Type: six-blade disk turbine Diameter: D/2 Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): Z>/8 Width of impeller blade (parallel to shaft): D/10 Oft-bottom clearance: D/2


Properties of continuous and dispersed phase Uquids at 22 °C

Continuous phase (Water) Polyvinylalcohol concentration 0.1 g/i Density 1.00 g/cc Viscosity 0.97 cP

Dispersed phase (Polystyrene-o-xylene solution) Polystyrene concentration 0 to 25 wt% Density 0.879 to 0.922 g/cc Viscosity 0.78 to 1,500 cP

Inteifacial tension 22 ± 0.4 dyne/cm



Impeller speed tir 150—820 rpm Reynolds number pcnrWur 10*~6 x 10* Dispersed phase volume fraction 0 less than 0.003 Temperature - 22 ± 1 °C

7.4 Siz« and its distribution of disporsod phaso

Results

- o -

key 0

X

A

Md(cp))rv(rp««^

iBofr 520

l?0

T7Q 1 566 1 35J ] 3016 1 ^41 1 3/6 J

H- 0 50 100 150 200 Stirring Time (min.)

Change of the lai gest drop size during stirring time

E »h

J OSh

ai

[key A

\ o

rv(n>m)] 266 300 1

1 • 1 ^00 1 10 J m J

O-OSl L 10» 102

Hd (cp) 10^

Effect of dispersed-phase viscosity on the miximum

637

J 0.5 0.41

I 0.3 "O

021

0-1 h

0-05

D

4N

key OP&PO

Pd

12IL IZiL

3A S^ OTSI

100 500 1000

"r l»'P"i)

Effect of impeller speed on the maximum (h'op size

10

^ 51

J 3. a:' 1 OOKM-Oa*-

[dmxxlNvi the maximum drop size at iVn Wmaxi r, -0 the maximum drop size at Nn -» 0

|key

ro^ 1 1 • J ro" 1 ^ "0 1 s

n,.(rpf»^

TTO 300 ^00 300 ^00 560 600

investigator 1

present work

Mizoywchi el at.

=-:o*i

o ^

/ ^ <

, D O S^«?* ° D O S D , 2 ^

X

a s '

10 r3 «-2 id' 10* 10 1 10

Correlation of the data by means of the model

638 Chapter 7. Oth«r subjects ralatad to multi-phasa systems

Notation d D L N^ fir

? ^ P a 0

drop diameter tank diameter impeller diameter viscosity group, E^'^d^'^lc impeller speed energy dissipation rate per unit mass viscosity density superficial tension dispersed phase volume fraction

Subscripts c continuous phase d dispersed phase max maximum V volume average

7 ^ Siz« and its distribution off disporsod pliaso 639

Konno, M., Arai, K., Saito, S.J. Chem. Eng. Japan, 10,474 (1977) The Effect of Viscous and Inertial Forces on Drop Breakup in an Agitated Tank

Use of reported data Physical properties of dispersed and continuous phase liquids

System

1*

2*

3*

4

5

6

7

8

Dispersed phase and continuous phase

kerosene water

M.I.B.K. water

n-butanol water

(^-xylene 0.01% PVA in water solution

o-xylene 0.1% PVA in water solution

styrene 0.01% PVA in water solution

styrene 0.1% PVA in water solution

styrene 1% PVA in water solution

Density

0.783 0.998

0.795 0.996

0.838 0.972

0.879 1.00

0.879 1.00

0.862 0.978

0.862 0.978

0.862 0.978

Viscosity Interfacial tension (cP) (dyne/cm)

1.62 1.00

0.59 1.00

3.30 1.28

0.78 0.97

0.78 1.05

0.438 0.42

0.438 0.45

0.438 0.83

50

10.5

1.9

22

19

22

19

15

* Sysstems 1,2 and 3 are reported by Brown et al.

(l)-(3) Brown, D. E. and Pitt K. K., Chm, Etig. 5a., 27,577 (1972) Brown, D. E. and Pitt. K. K., Chm. Eng, Sci., 29,345 (1974)

(4)~(8) Arai, K. et al. J., Chem, Eng, Japan, 10,325 (1977) Matsunaga, Y., PhD Thesis, Tohoku Univ., 1976

Notation d drop diameter L impeller diameter Hr impeller speed p density a interfacial tension

Subscripts c continuous phase max maximum

040 Chapter 7. Oth«r subjects rslatsd to multi-phase systsms

Ross, S. L, Verhoff, E H., and Curl, R. L, Ind. Eng. Chem. Fundam., 17,101 (1978) Droplet Breakage and Coalescence Processes an Agitated Dispersion. 2. Measurement and Interpretation of Mixing Experiments

Experimental apparatus Vessel Type: flat-bottomed Diameter: 11.1 cm Height: 14.0 cm Volume: 1,355 cm^


Impeller Type: six-bladed flat-blade turbine Diameter: 5.1 cm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): Z)/4 Width of impeller blade (parallel to shaft): Z)/5

Working fluids and their physical properties Continuous phase: water with 0.001 N Na3P04 Dispersed phase: 39.0% (by volume) Dowtherm-E/61.9% (by volume) shell No. 3747 Base oil

Fluid properties (22^C)

Density, g/cm^ Viscosity, g/cmsec

Dispersed phase (39.1% by vol. 1.0 - 0.035 Dowtherm-E, 61.9% by vol. SheU No. 3747 Base Oil)

Continuous phase (water 1.0+ 0.019 with 0.001 NNa3P04)

Interfacial tension: 35 dyn/cm

Experimental conditions Dispersed phase fraction: 0.025—0.20 Impeller speed: 160-278 rpm

I i U distribution off liisporsod pliaso

ISO no ISO 210 so zso 270

N,Tpm

Dependence of Sauter mean diameter, dsz, upon impeller Dependence of Sauter mean diameter, d^z, upon speed at various phase fractions. phase fraction at various impeller speeds.

Notation d32 Sauter mean diameter of drops, mm D impeller diameter, mm N impeller speed, 1/min 0 dispersed phase fraction

042 Chapter 7. Othar subj«cto rolatod to multi-phas« systems

Brooks, B. W, T^ans. Instn. Chem. Engrs., 57,211 (1979) Drop Size Distributions in an Agitated Liquid/Liquid Dispersion

Experimental apparatus Vessel Type: dish-bottomed Diameter: 0.10 m Height (including the dished base): 0.13 m

Baffle Number: (a) 3 (b) unbaffled Height: (a) 0.10 m (b)-Width: (a) 0.01m (b)-Clearance of baffle from wall: (a) 0.002 m (b) -

Impeller

four-blade four flat-blade horizontal disc Type propeller turbine

Diameter (m) Number of impellers Number of blades on impeller

Location 0.05 m below the stationary liquid level

Working fluids and their physical properties Continuous phase: water Dispersed phase: molten camauba wax at 90°C (density = 845 kg/m ; interfacial tension of

mutually saturated liquids = 1.13 x 10" N/m) Experimental conditions

Temperature: 90°C Volumetric ratio of dispersed phase to continuous phase at 90°C: 0.1

Measurement technique Sieving of solidified wax

Results

0.044 1 4

0.044 1 4

0.044 1 1

Impeller

Horizontal disc 1.16 Propeller 1.20 Turbine 1.22 Turbine (baffled) 0.6

Notation dm Sauter mean diameter, m N impeUer speed, 1/sec

7.4 Siz« and its distribution ciff dispsrssd pliass 543

Gnanasundaram, S., Degaleesan, T. E. and Laddha, G. S., Can. J. ofChem. Eng., 57,141 (1979) Prediction of Mean Drop Size in Batch Agitated Vessels



Impeller Type: six-bladed straight turbine Diameter: 5 cm Number of impeller: 1 Number of blades on impeller: 6


System

Continuous phase Dispersed phase Interfacial tension (mN/m)

(1) water

n-hexane 45.0

(2)

2mmol/^KOH cyclohexyl formate

10.9

xperimental conditions

System

Impeller speed (1/sec) Holdup Impeller Weber number

(dj?N'pr/r)

(1)

1.67-5.83 0.05-0.33

35-100

(2)

8.33-35.0 0.05-0.5

860-15,200


Results

We < 10,000 Ci = 0.052 A = 4.0 We > 10,000 Ci = 0.39 A = 0

Notation dsz Sauter mean diameter of drops, m dR diameter of impeller, m N impeller speed, 1/sec We Weder number, dimensionless X fractional holdup of dispersed phase pc density of continuous phase, \ig/w? y interfacial tension, N/m

544 Chaptmr 7. OtiMr subjacto i«lat«d to multi-plMis* systMns

McManamey, W. J., Chem. Eng. Sci., 34,432 (1979) Sauter Mean and Maximum Drop Diameters of Liquid-Liquid Dispersions in Tiu-bulent Agitated Vessels at Low Dispersed Phase Hold-Up

Use of the published data

C(3) = 0.221

Values of C(i) for Sauter mean drop diameter with negligible dispersed phase hold-up

Impeller

Four-blade paddle Four-blade paddle Six-blade turbines Six-blade turbines Six-blade turbines Six-blade turbines Six-blade turbines

iPoHD/W)

13 13 25 25 24 25 —

Ca) 0.193 0.18 0.24 0.21 0.206 0.265 0.192

Source

(1) (3) (3) (2) (4) (5) (6)

(1) Vermeulen, T., Williams, G. M. and Langlois, G. E., Chem. Engng. Prog., 1955,5185. (2) Chen, H. T. and Middleman, S., ATC/rE/., 1967,13.989. (3) Calderbank, P. H., Trans. Instn. Chem. Engrs., 1958,36,443. (4) Sprow, F. B., Chem. Etigng. Sci., 1967,22,435. (5) Van Heuven, J. W. and Hoevenaar, J. C, Proc 4th European Symp. Chem React. Engng,

Brussels, p.217. Pergamon Press. Oxford 1968. (6) Brown, D. E. and Pitt, K., Chem. Engng. Sci., 1974,29,345.

Notation d dz2 D N P PMI Po W 9 a

drop diameter, m Sauter mean drop diameter, m unpeller diameter, m impeller speed, 1/sec power input to the impeller, W power input per unit mass in the volume swept by the impeller, W/kg power number, Pip N^D^, dimensionless impeller blade width, m continuous phase density, kg/m^ interlacial tension, N/m

7.4 Siz« aiHl its distribution off disporsod pliaso 645

Takahashi, K., Ohtsubo, E and Takeuchi, H., Kagaku Kogaku Ronbunshu, 6, 651 (1980) Mean Drop Diameters of W/0- and (W/0)/W-Dispersions in an Agitated Vessel



Impeller Type: six flat-bladed turbine Diameter: (1) 3.3 (2) 5.0 (3) 6.7 cm Number of impellers: 1 and 2 Number of blades on impeller: (1)~(3) 6 Off-bottom clearance: lower impeller 2.5 cm upper impeller 7.5 cm

Working fluids Water phase: distilled water Oil phase: kerosene Surface active agent: Span 80

Experimental conditions Temperattire: 25 ± 0.5°C

Measurement technique Microscopy

Results (1) Drop size distributions for the W/0-emulsion were expressed by a

logarithmic normal distribution.

BOO,

600

400

200

,--1200 720 ,4 80

/ ^ 600 500

-400

Type Vol.rotio CsCwt%] - o — WO 1/9 1.0 - • - - {W/O^W (1/91/90 1.0

20 40 60 80

Drop size distributions of water drops in oil and W/0-emulsion drops in water.

546 Chapter 7. Othar subj«cto ralat«d to multi-phas« systems

(2) For W/0 emulsion

rf32 = 2.4xlO*Wr°*

(3) For (W/0)/W emulsion

Notation Cs concentration of emulsifying agent in oil phase, wt% dp drop diameter, ^m d^ Sauter mean diameter of drops, \xm Di impeller diameter, m / probability density of drop diameter in term of number, An/iAdp-ntX 1/cm n number of drops counted nt total number of drops counted N impeller speed, 1/min We Weber number, D?N^pla, dimensionless p density of continuous phase, g/cm^ a interfacial tension between liquid phases, dyne/cm

7.4 Siz« and its distribution off disporsod pliaso 547

Narsimhan, G., Ramkrishna, D. and Gupta, J. P., AIChE Journal, 26,991 (1980) Analysis of Drop Size Distributions in Lean Liquid-Liquid Dispersions

Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.14 m Height: 0.20 m Volume: 3 e


Baffle Number: 4 Width: 0.014 m Length: 0.19 m Clearance of baffle from wall: 0.00635 m

Impeller Type: six-blade paddle Diameter: 0.0762 m Number of impellers: 1 Number of blades on impeller: 6 Width of impeller: 0.009525 m Thickness of impeller: 0.00159 m Off-bottom clearance: 0.04 m

Working fluids and their physical properties Continuous phase: water Dispersed phase:

Density, kg/m^ Interfacial tension, N/m

e c u + t-octane (50-50%) 114.9 46 xlO"^ Anisole + ecu (80-20%) 111.3 29 x lO'^ Chlorobenzene 110.1 37.7 x 10"

Experimental conditions Temperature: 30 ± 0.1°C Agitation speed:

(1) water-CCU + t-octane: 300,420 and 480 rpm (2)water-anisole-*-CCU: 300 rpm (3) water-chlorobenzene: 300 rpm


648 Chapter 7. Oth«r suli|«cto rolatad to multl-phas« systems

Restilts Experimental measurements of transient drop size distribution in a stirred liquid-liquid dispersion

100

H AQ

z " ^ , 0

3 -J O SO

UJ

> "^ <

3

• '• .*.

s

•V'

1 ^

11 • if

1 ?••

IS-

Hf A

! t[*

W if/

# •

lii / ; 1 ;

'7i .;V

1 1/

r

/ 11 '"i

I E - , — J

ITT 1

l-[ ." RPM - 4 8 0 TEMP-30-C

•1 - IMPEl 1 FR-:5 »N F¥S[>Pl F

T n • DISPERSED PHASE-ecu + l y i-OCTANE(50-50%)

I I I CON-H I WATt

riNL :R

OU S PH/ \SE-

LJLOJ

6 » 10" 2 4 6 B 10'

DROPLET VOLUME (cc)

*M

2 * w ^1^ tf r ^

^

e

RPM.300 lEMP.iO'C IMPELLER-3 IN RXDOLE DISPERSED PHASE CD, -I-0C7ANE MSXTURE

• 150-50%) CONTINUOUS PHASE-

1 1 , '[ ; 1

f:

1 [{]/••' [W| _.•'.

'TU\,

i h

[ ^ m ij 4 1 ffl nil

F/ 1/ ( /

Hi M l — '.*! 1

7"

/ /

Hi

M i/iii, /tiHi:

^'Ijillli 1 1 i till 1 l l i l 1 i!{|

1 i i i 1 1 i 1 nil 11

k • « I 4 « • 1

DROPLET >«LUME(cc)

Effect of stirring time on drop volume distribution. Effect of stirring time on drop volume distribution.

Ui

a

^ ' 0

i u

RPM-300 TEMR-30*C A .IMPELLER-3 IN RMXX-E /// OtSPERSED PHASE- / / /

•20%CCL / / / i CONTINUOUS PHASE-/ / / :'

.V«CiTER / / / : ,

1

.•1 •*/

*

*•

r r/ t. 1

W ^m •* •

1 \%

iilj

YM

] .•

it

3 ^ /

*

m %

\A\ / 1 1 /j 1 1

1 '* . l-l 1 •fl

WJ if 1/

11 ^

i

n

DROPLET VOLUME (cc)

to

•0

» -2 10

1" 5?? »

o

Tm RPM-300 TEMR-2 IMPELLER-3 IN VtK

o-c DOLE

DISPERSED PHASE-CHLOROBENZENE

" CONTINUOUS PHASE-WATER

' • f l ^

a j j j / f^ 111/-'**" -•H*.-*''* ]li; J

' 4

m m m 4 n ' .

T 1 1

' I I I

% A ll

WP 1/ 11'[

ill II ||

III III UJ

!

i

Effect of stirring time on drop volume distribution.

» • i6^ DROPLET VOLUME (cc)

Effect of stirring time on drop volume distribution.

7.4 Siz« and its distribution of disporsod piiaso 649

Ali, A. M., Yuan, H. H. S., Dickey, D. S., and Tatterson, G. B., Chem. Eng. Commun., 10,205 (1981) Liquid Dispersion Mechanisms in Agitated Tanks: Part L Pitched Blade Turbine



Baffle Number: 4 Height: 0.091 m

Impeller Type: 45° pitched four-blade turbine Diameter: 0.305 m Number of impellers: 1 Number of blades on impeller: 4 Width of impeller blade: 0.062 m Off-bottom clearance: 0.305 m

Working fluids and their physical properties Continuous phase: water Dispersed phase: oil

Type

Gulf Harmony 69 (115) Gulf Harmony 76 (150N) Gulf Harmony 97 (220)

Oil properties

Viscosity, Pas

0.127 0.167 0.225

Interfacial Tension, N/m

0.036 0.024 0.030

Density, kg/w?

883. 893. 891.

Experimental conditions Rotational speed: 1.22-2.65 1/sec

Measurement technique High speed stereoscopic motion picture

Results

hnpeller tip speeds and vortex velocities.

Agitator Rotational

Speed (s-»)

1.22 1.93 2.56

hnpeller Tip

Speed (m/s)

1.17 1.85 2.54

Convected Angle (rad)

0.314 0.255 0.225

Convected Vortex

Velocity (m/s)

0.360 0.466 0.566

Convected Tip

Velocity Ratio

0.308 0.251 0.222

Swirl Velocity

(m/s)

0.633 0.919 1.178

Circumferential Velocity

(m/s)

0.273 0.453 0.612

Circumferential Tip

Velocity Ratio

0.234 0.245 0.240

650 Chapter 7. Oth«r subjects ralatad to multi-phasa systems

Frame - 9 Tlme^ 4 0 msec

Frome : 19 Time • 9 0 msec

O

Frame: I Time: 0 msec

FrQmt'5 Time: 20msec

Frome: 9 Time: 45 msec

Frame: 32 Time: 154 msec Frame: 13 Time: 6 0 msec

Ligament stretching mechanism for the pitched blade turbine.

Turbulent fragmentation mechanism for the pitched blade turbine.

An oil into water dispersion, created by a pitched blade turbine, was observed using high speed, stereoscopic motion pictures. Two different dispersion mechanisms were responsible for the break-up of the oil drops, even though both mechanisms occurred in the vortex system trailing from the impeller Wade tips. The first mechanism could be described as ligament stretching, since large oil drops were stertched by fluid shear to form elongated ligaments, which subsequently ruptured into small drops. The second mechanism was turbulent fragmentation, where laige oil drops were shattered into laige droplet clouds the instant they entered the trailing vortex system.

7.4 Siza and its distribution off disporsod phase 651

Chang, T. P. K., Sheu, Y. H. E., Tatterson, G. B. and Dickey, D. S„ Chem. Eng. Cornrnun., 10,215 (1981) Liquid Dispersion Mechanisms in Agitated Tanks: Part II. Straight Blade and Disc Style Turbines




Impeller

Type straight blade turbine disc style turbine

Diameter (m) 0.305 0.305 Number of impellers 1 1 Number of blades on impeller 4 6 Width of impeller blade (m) 0.051 0.051

Working fluids and their physical properties Continuous phase: water Dispersed phase: oil

Oil properties

Type

Gulf Harmony 69 (115) Gulf Harmony 76 (150N) Gulf Harmony 97 (220)

Viscosity, Pas

0.127 0.167 0.225

Interfacial Tension, N/m

0.036 0.024 0.030

Density, kg/m3

883. 893. 891.

Measurement technique High speed stereoscopic motion picture

652

Results


tJme »0 trome I time » .125 tec frome 16

time - . 133 sec frome 17

time * .156 sec frome 20

time * JOB sec frome K

Ligament stretching mechanism for the disk style turbine.

Blade Thickness

mm

19 2

Impeller Tip Speed

m/s

0.929 0.811

Effect of blade thickness on dispersion parameters.

Average Discharge Velocity

m/s

0.750 0.888

Maximum Observed Minimum Observed Discharge Velocity Discharge Velocity

m/s m/s

1.160 0.58 1338 0.621

Average Drop Size

nrni

2.67 2.12

7.4 Sizo and its distribution off d isponed phaso 653

TURBULENT• FRAGMENTATION MECHANISM

10 10 10* 10" 10*

Impsllsr Rtynoids Number

X>( KT

Dispersion mechanisms vs. power and impeller Reynolds numbers.

In general, two mechanisms for dispersion, ligament stretching and turbulent fragmentation, are present with pitched blade, straight blade or disc style turbines. The transition between these two mechanisms is probably dictated by turbulence intensity as reflected in impeller Reynolds number, although factors involving relative magnitudes of fluid properties are probably significant.

554 Chapter 7. Oth«r subjects r«lat«il to multi-phas* systams

Rounsley, R. R.,AIChE Journal, 29, 597 (1983) Oil Dispersion with a Turbine Mixer

Experimental apparatus Vessel Diameter: 285 mm Height: 610 mm Volume: 35 i


Liquid contained Height: 410 m Volume: 26.5 i

Impeller

Type

Diameter (m) Niunber of impellers Number of blades on impeller Width of impeller blade

flat blade turbine

114.3 1 6

25

flat blade turbine

114.3 1

12 25

flat blade turbine

152.4 1 6

35

marine impeller

114.3 1 — —

V^orking fluids and their physical properties Continuous phase: water-based polymer solution (viscosity = 0.220 Pasec) Dispersed phase: a mixture of aromatic hydrocarbon and kerosene (viscosity = 0.008-0.010

Pasec) Experimental conditions

Impeller speed: 3.59-14.45 rps Temperature: 31-61°C


Results

Ot£

dz2 N t T V

_ 0.02203|F-18.931°^ ^ ~ J4.41 jyr350 j«0.573 ^0.400

ition impeller diameter, m Sauter mean diameter, ^m impeller speed, 1/sec time, sec temperature, **C volume in vessel, ^

7.4 Siz« and Ks distribution off disporsod piiaso 555

Hong, R 0. and Lee, J. M., Ind. Eng. Chem. Process Des. Dev., 22,130 (1983) Unsteady-State Liquid-Liquid Dispersions in Agitated Vessels


Baffle Number: 4

Impeller Type: six-bladed flat turbine


System

1 2

Dispersed Continuous phase

5 cSt Dow Coming 200 fluid ethyl acetate

water water


System

1 2

Density

Interfac. tension, cont, disp, N/m kg/m^ kg/m^

0.0425 1,000 920 0.006 1,000 894

Viscosity

cont, disp, N-s/m^ N-s/m^

0.0010 0.00460 0.0010 0.00046

Measurement technique Microphotographic technique and hght transmittance method

Results Average drop sizes

% = l+a^-^'

Minimum transition time

Notation dsz Sauter mean droplet diameter, m d32 Sauter mean droplet diameter at steady state, m N impeller stirring speed, 1/min / time, min a, P constants 7 constant

656 Chapter 7. Oth«r subjacto r»lat«il to multi-phas« systams

Mochizuki, M. and Sato, K., Kagaku Kogaku Ronbunshu, 10,49 (1984) Drop Diameter near the Tip of Turbine Impeller



Baffle Number: 4

Impeller Type: six-bladed disk turbine Diameter: 100 mm Number of impellers: 1 Number of blades on impeller: 6

Disk turbine

Impeller Blade width no. BID

Blade length Number of blades Power number LID m Np

1-1 2 3 4

2-1 2 3 4

3 4 5-1

2 3 4

6-1 2 3 4 5

1/8

1/5

1/4 1/3 1/2

1/5

1/5 1/4 1/3 1/2 1/5 1/4 1/3 1/2 1/4 1/4 1/5 1/4 1/3 1/2 1/4

6

6

6 6 6

2 3 4 8

12

2.73 2.85 2.94 2.97 4.41 5.13 5.30 5.30 6.52 8.47 9.72

10.8 11.4 11.5 2.10 2.89 3.57 5.89 6.84


Continuous phase

Deionizated water

Dispersed phase

Toluene + CCh Anisole + Toluene + CCh

Viscosity

He X 10^Pas fidX 10^Pas 0.824-1.09 0.638-0.783

1.04

hiterfadal tension

(TxlO^N/m 35.1-38.1

27.4

Density pd = pc Volume fraction of dispersed phase 0 = 0.25%

7.4 Siz« its distribution off disporsod pliaso 657

Experimental conditions Impeller speed: 75—200 rpm

Results

Ar<200rpm

10

9

8

i 7

Dispersed phase Toluene •CCI^ L/D=1M n^^e

02 a3 OA Blade width B/D M

0-5

Effects of blade width on mean drop diameter and PV.B

Notation B dz2 D D32

L rib

N Np Pv,B We

r P a 0

width of impeller blade, m Sauter mean drop diameter, m diameter of impeller, m (dsi/D) We^^*, dimensionless length of impeller blade, m number of blade rotational speed of impeller, 1/sec power number, dimensionless power input per unit volume assuming power dissipating in impeller region, W/m^ weber number, pN^DVo, dimensionless circulation of vortex filament, mVs viscosity, Pasec density, kg/m^ interfacial tension, N/m volume fraction of dispersed phase


058 Chapter 7. Othar subjects rslatsd to multi-phass systems

Imai, M. and Furusaki, S., Kagaku Kogaku Ronbunshu, 10, 707 (1984) Outer Mean Drop Size of W/0/W Emulsions in Agitated Vessels

Experimental apparatus Vessel Type: (1) (2) flat-bottomed Diameter: (1) 10 (2) 15 cm

Baffle Number: (1) (2) 4 Width: (1)1.0 (2) 1.5 cm

Impeller Type: six-blade turbine Diameter: 3,4,5, and 7.5 cm Number of impellers: 1 Number of blades on impeller: 6 Z):/:6 = 20:5:4

Working fluids and their physical properties Water phase: distilled water Oil phase: Dispersol (density = 823kg/m^; viscosity = 1.9x 10"^ Pasec) Surface active agent: Span 80 (nonionic)

Experimental conditions Hold-up of dispersed phase: 0.02—0.25 Weber number: 300-4,000 Temperature: 298 ± 1K


Results

d32/Z> = 0.057 W «-°-

Notation b blade width, m 32 Sauter mean drop diameter, m or ^m

D impeller diameter, m / blade length , m N agitating speed, 1/sec We Weber number, N^D^p/a, dimensionless p density, kg/w? G interfacial tension, N / m

7.4 Sfz« and its distribution off disporsod piiaso 559

Lee, J. M. and Soong, Y., Ind. Eng. Chem. Process Des. Dev., 2A, 118 (1985) Effects of Surfactants on the Liquid-Liquid Dispersions in Agitated Vessels

Experimental apparatus Vessel Type: round-bottomed Diameter: 0.16 m Volume: 5 i


Impeller Type: six flat-bladed turbine Diameter: 0.0762 m Number of impellers: 1 Number of blades on impeller: 6

Working fluids and their physical properties Continuous phase: water and 20% sugar solution Dispersed phase: Dow Coming 200 fluid, kerosene, and 3-chloropropene

Physical properties of systems' studied at 20°C

fluid

Dow Coming 200 fluid kerosene vinylidene chloride 3-chloropropene water 20% sugar solution

density, kg/m^

920 787

1,213 939

1,000 1,200

dynamic viscosity (Ns)/m2

0.0046 0.0017 0.00033 0.00033 0.0010 0.0021

interracial tension with H20,N/m

0.0425 0.0419 0.0136 0.0209

" System 1,5 cSt Dow Corning 200 fluid-water; system 2,3-chloropropene-water, system 3, vinylidene chloride-water; system 4, kerosene-water; system 5, kerosene-20% sugar solution.

Surfactants: hydroxjrpropyl methyl cellulose, pol3rvinyl alcohol resin, sodium dodecyl sulfate, and ethylhexadecyldimethyl ammonium dromide

Experimental conditions The fraction of dispersed phase: 2—20% by volume Temperature: 20 ±1°C


Results

</32/*=0.05 C, (1+2.316 0) Nwe'^^'^Nf,-''-^^ {dildrY'''^

C,=0.63

QQO Chapter 7. OtiMr subjacto r«lat«il to multf-phas* systems

Notation c. dsi d, dr g N Npr Nwe T Ap P a 0

correction factor Sauter mean droplet diameter, m impeller diameter, m tank diameter, m gravitational acceleration, m/sec^ impeller stirring speed, 1/sec impeller Froude number, pcN^d^/Apdig, dimensionless impeller Weber number, N^d^pdo, dimensionless vessel diameter, m |pr~Prf|,kg/m3 density, kg/m^ interfacial tension, N/m fraction of the dispersed phase, dimensionless

Subscript c d

continuous phase dispersed phase

7.4 Siz« mid its distribution off disporsod piiaso 661

Hong, E 0. and Lee, J. M., Ind. Eng. Chem. Process Des. Dev., 24,868 (1985) Changes of the Average Drop Sizes during the Initial Period of Liquid-Liquid Dispersions in Agitated Vessels


Liquid contained Height:(l) 0.292 (2) 0.387 m

Impeller Type: (a) (b) six-bladed flat turbine Diameter: (a) 0.076 m (b) 0.102 m Number of impellers: (a) 0>) 1 Number of blades on impeller: (a) (b) 6


Systems studied

system dispersed phase continuous phase

1 5-cSt Dow Coming 200 fluid 2 ethyl acetate 3 5-cSt Dow Coming 200 fluid 4 kerosene 5 5-cSt Dow Coming 200 fluid

water water 15% sucrose solution water 30% sucrose solution


density, kg/m^ viscosity, Ns/m^

system

1 2 3 4 5

N/m

0.0425 0.006 0.032 0.0419 0.023

•» ————— cont 1,000 1,000 1,087 1,000 1,131

disp

920 894 920 787 920

cont

0.0010 0.0010 0.0020 0.0010 0.0029

dips

0.00460 0.00046 0.00460 0.00169 0.00460

Experimental conditions The fraction of dispersed phase: 0.05—0.20

Measurement technique Microphotographic technique and light transmittance technique

Results Change of drop size during transition period

. jr V-2 .015

h.ZEE. = 29.70 ^ po^^^^^-o.70 d^ \T)

Minimum transition time

M„^ =1995.3 W//rr'-''F°''(Airf//x.)Fr-^''

552 Chapter 7. Othar subjects r«lat«d to multf-phasa systems

Notation di impeller diameter, m dsz Sauter-mean droplet diameter, m dsl steady-state Sauter-mean droplet diameter, m F Taylor number, We/Re^ dimensionless Fr impeller Froude number, pcd^N VApHg, dimensionless g gravitational acceraletion, m/sec^ H height of liquid in the vessel, m N impeller speed, 1/sec Re impeller Reynolds number pcNdfl^c, dimensionless t time, sec tvm minimum transition time required to reach steady-state drop size, sec T vessel diameter, m We impeller Weber number, NH?pelG, dimensionless Ap pc - pd

^ viscosity, Ns/m^ p density, kg/w? a interfacial tension, N/m

Subscripts c continuous phase d disperse phase

7A Siz« and Its distribution off disporsod pliaso 553

Stamatoudis, M. and Tavlarides, L. L., Ind. Eng. Chem. Process Des. Dev, 24, 1175 (1985) Effect of Continuous-Phase Viscosity on the Drop Sizes of Liquid-Liquid Dispersions in Agitated Vessels


Impeller Type: six flat bladed disk turbine Diameter: 100 mm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft):Z)/4 Width of impeller blade ([MUfallel to shaft): D/5

Working fluids and their physical properties Continuous phase: aqueous glycerol Dispersed phase: (1) kerosene, (2) mineral oil

Physicochemical properties of chemical systems studied

I^QCP

223.1 118.0 44.1 21.9 13.2 3.6

122.6 91.5 53.8 27.3 12.0 3.5

HdfC? Pn g/cw?

Kerosene (d)-Aqueous 1.9 1.5 1.5 1.5 1.6 1.4

1.241 1.231 1.208 1.187 1.171 1.107

pdy g/cm^ a,

Glycerol (c) at 25°C 0.808 0.810 0.801 0.805 0.806 0.804

Mineral Oil (d)-Aqueous Glycerol (c) at 25**C 26.7 26.4 26.4 26.4 26.4 26.4

1.227 1.222 1.211 1.193 1.164 1.100

0.843 0.842 0.842 0.842 0.842 0.842

dynes/cm

27.4 28.3 28.9 28.6 29.2 31.8

31.0 31.6 32.6 33.0 35.6 35.7

Experimental conditions Temperature: 25 ± 0.1°C Holdup of dispersed phase: (1) 0.05 (2) 0.025-0.15 Impeller speed: (1) 200-550 rpm (2) 200-450 rpm Weber numben (1) 401-3772 (2) 330-2209

Measurement technique Photomicrographic means

664 Chapter 7. Oth*r subjects ralat«d to multi-phasa systems

Results Sauter Mean Diameters for Dispersions of Mineral Oil in Aqueous Glycerol

Sauter mean diam (^m) for r (cP) of

rpm

200

250

300

325

350

400

450

0 0.025 0.05 0.10 0.15 0.025 0.05 0.10 0.15 0.025 0.05 0.10 0.15 0.025 0.05 0.10 0.15 0.025 0.05 0.10 0.15 0.025 0.05 0.10 0.15 0.025 0.05 0.10 0.15

122.6

70.8 73.9 85.6 94.1 59.1 66.6 78.1 88.3 54.2 60.6 73.1 82.5 45.4 53.0 62.8 72.7 40.9 48.2 55.1 63.6

91.5

71.0 84.7 96.8

108.3 63.7 69.9 80.6 92.5

51.3 58.0 67.9 79.2 46.5 52.0 60.8 69.7

53.a

125.0 141.4 82.4 89.3

101.2 109.4 72.1 72.7 81.6 89.3

55.0 61.5 70.6 79.5 48.5 54.7 64.3 71.0

27.3

265.6 283.6 261.6 280.7 137.4 135.5 137.0 137.2 85.1 89.0 98.7 90.1

69.3 65.5 68.6 70.7

12.0

299.1 268.6 317.5 329.2 188.6 189.0 202.7 197.5 108.7 118.7 130.0 139.3

85.4 90.8 95.9

107.7

3.5

254.3 256.9 246.2 241.9 162.9 184.1 202.6 174.5 123.5 116.1 155.5 124.0

99.1 112.9 121.5 113.4

20

MfCRAL OL. IN AQUEOUS GUTCEROL

20 4 0 6 0 Hc .cP

6 0 XX3 120

Effect of continuous-phase viscosity on Sauter mean diameter for dispersions of mineral oil in aqueous glycerol at various holdup fractions. iV '=350 rpm, CT=31.0-35.7 dynes/cm, //rf=26.4-26.7 cP. and 455 < NRU < 17.186.

4)20

T -OIS

?jOtO

< AGS

0

REROfiCNE N AOUEOUB GUCEROL

• f

y

- - • - « ^

3S0 RPM

^ >ao5

X J>

• 3-6 c(» • l32cP • 2I.9CP • 44SCP

• 118 cP j

'>H-:.. 100 QO 140 « 0 100 200

Drop size distributions of dispersions of kerosene in aqueous glycerol at various continuous-phase viscosities. ^•=350 rpm, or=27.4-31.8 dynes/cm, /irf=1.4-1.9 cP, and 568 < TV)?,./< 17,292.

7.4 Slz« and its distribution of disporsod pliaso 665

d . IN AQUEOUS GUCEROL

350

y ^' PPM ao5 • •

•

He » 120

273 0 122 6

CP eP CP eP

Drop size distributions of dispersions of mineral oil in aqueous glycerol at various continuous-phase viscosities. i\r*=350 rpm, (7=31.0-35.7 dynes/cm, /irf=26.4-26.7 cP, and 539 < Naej < 16,134.

uisoh

L iwlCRAL O t N AQUEOUS GUCEROL 1

r %. F * V Pc'35cP

[ ^

[9.005—

n>.0025-

L i> 1 • 0025 N O06 U OH) 1 • 0«

N^C*— 9.00

Vv* \

* \ \ SLOPE \ S . \

•Tee > \ \ -159 >A \ -127 ^ A \ -T42 X \ . 1

^ • 0 1 5 — ^ \ \

' • ^

3 0 0

200

1

100

KEROSENE IN AQUEOUS GLYCEROL 1 . • aO-OS 1

. A y 0 M*'3-«cP#SLOPE • • M » \ / y • | i « . l 3 2 e F i S L O P E > > i e O

y * / / A M«-21-0eP,SLOPE*-1-74 / > ? y ^ A 11^441 eP ,SLOPE»-131

X ®

-

-

^ / .s 0 ^

- J -

V \ po Mc -lie.O e P. S L O P E - i 0 5 A > ^ | • M«*229*1 cP. S L O P E - 0 9 e

^ ^ ^

- i 1 • 1 1 1 • 1 . 1 . 1 . 1 300 400

N*. RPM

Hot of In 032 VS. In iV* for a dispersion of kerosene in aqueous glycerol of various viscosities. 346 < Nfyj < 22,233.

250 N*, RPM

Hot of In 032 vs. In 7V *for a dispersion of mineral oil in aqueous glycerol, a=35.7 dynes/cm, pid=26.4 cP, and3,696<^i^,./< 17,193.

3 0 0 ^ MNERAL O L IN AQUEOUS GiyCEROL

200

1

Kc • 273 cP

9 SLOPE

• 0025 -245 • 005 -251 • 010 -2 35 • 0 1 5 - 2 4 6

MNERAL OIL N AQUEOUS ^ V ^ ^ A 6 L

> 122-6 cP

300 350 N^.RPM

Plot of In 032 vs. IniV 'for a dispersion of mineral oil in aqueous glycerol. <T=31.0 dynes/cm, fid==26J cP,and390<^)^,./<721.

250 300

Hot of In 032 vs. In i *for a dispersion of mineral oil in aqueous glycerol, a=33.0 dynes/cm, Hd=26A cP, and 1,065 <i\ri?,./< 2,422.

666 Chapter 7. Oth«r subjects ralatsd to multi-phass systems

Notation a drop diameter, ^m 32 Sauter mean diameter, lLnia?l(Xnia?), \\m

A (a) da fraction of drops of diameter between a and a+da, dimensionless D impeller diameter, cm N* impeller rotational speed, 1/min Nse, I impeller Reynolds number, N*D pla, dimensionless fjL viscosity, cP p density, g/cm^ a interfacial tension, dynes/cm ^ holdup fraction, cm^ of dispersed phase/cm^ of dispersion


7.4 Six* and its distributioii off disp«rs«d phaso 557

Tanaka, M., Can. J. ofChem. Eng., 63,723 (1985) Local Droplet Diameter Variation in a Stirred Tank




Impeller Type: six blade Rushton turbine Diameter: 5.0 cm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 1.5 cm Width of impeller of blade (parallel to shaft): 1.0 cm Off-bottom clearance: 6.0 cm

Working fluids and their physical properties Continuous phase: ion-exchanged water Dispersed phase: 4.6:1 mixture of benzene and carbon tetrachloride

(containing 0.05 wt% sebacyl chloride)

Physical properties of dispersion system (at 20°C)

p.=Prf(kgm-^) 998 /Xr(Pas) 1x10-3 iUrf(Pas) 0.69x10-3 y(Nm-*) 35.1x10-3

Experimental conditions Volume fraction of dispersed phase: 10%

Measurement technique Encapsulation method

Results

dp «: Nr ~^^ for circulation region

dp oc Nr '^'^ for impeUer region

dpi.

dp.

t

hBfl '^~N>*

1/3

/ c

568 Chapter 7. Othar sub|«cts ralatad to multi-plMiso systems

Notation dp dpc

dpi

fc Nr Wc

y 1^ p

droplet diameter, m droplet diameter at circulation region, m droplet diameter at impeller region, m mean circulation frequency, 1/sec impeller speed, 1/sec mean coalescence frequency, 1/sec interfacial tension, N/m viscosity, Pasec density, kg/m^

Subscripts c d


7.4 Siz« and its distribution off dispersed pliaso QQQ

Davies, J. T, Chem. Eng. Sci., 40,839 (1985) Drop Sizes of Emulsions Related to Turbulent Energy Dissipation Rates

Results

rfmw = const X CT + —-— Pc rM

Type of equipment

Fine clearance valves Colloid mills Liquid whistles Turbine impellers

Typical local PM in dispersion region,

Wkg-»

400x10® 0.44x10®

12x10® 6x10^*

Typical local if m-s"

12 1.6 3 0.2

/*,^m

0.22 1.3 0.5 3.6

dma (calc. from eqn.

^m

0.7 10.5 2

70

(D). dwax

(exptl.), ^m

~1 6 2

50

(exptl.), |Lmi

--0.05 0.1

<0.1 12

•McManamey W. J., Chem EngngSci. 1979,34,432. eqn.(l) du^=x(a/pcr'Pjf^

Notation maximum drop size in emulsion, \im

dnan minimum drop size in emulsion, \im Ik Kolmogoroff eddy length, fun

PM power input (=rate of energy dissipation) per unit mass of liquid locally, W/kg if turbulent fluctuation (eddy) velocity, m/sec Hd viscosity of dispersed liquid, Nsec/m^ Pc density of continuous liquid, kg/m^ a interfacial tension, N/m

670 Chapter 7. Oth«r suli|«cts rwlatoil to multi-pluis* systems

Lagisetty, J. S., Das, P. K., Kumar, R. and Gandhi, K. S., Chem. Eng. Sci., 41, 65 (1986) Breakage of Viscous and Non-Newtonian Drops in Stirred Dispersions

Experimental apparatus Vessel Type: flat-bottomed Diameter 14.5 cm Height: 20 cm


Baffle Number 4 Width 1.45 cm

Impeller Type: six bladed disk turbine Diameter T/2 Number of impellers: 1 Number of blades on impeller 6 Length of impeller blade(perpendicular to shaft): T/B Width of impeller blade(parallel to shaft): T/10 Off-bottom clearance: T/2

Working fluids and their physical properties Continuous phase

Desctiption

Water

Kerosene

/ (Poise)

0.01

0.021

P (g/cm^

1.0

0.78

Description

Polystyrene in styrene 10-30% by wt 100 ml of CMC in water (25%) + 60 ml of 2% PVA CaCOs aqueous suspension (59.5% CaCOa + 2.00% polyvinyl alcohol)

K g/icms'-')

0.43-37.50

14.5

0.137

Dispersed phase

n

1

2/3

1

a (dynes/cm)

20

50

45.2

P (g/cm^

0.88-0.92

1

1.47

Experimental conditions Impeller speed: 3.33—10 rev/s Reynolds number of the continuous phase: 1.5 x 10*~5 x 10* Dispersed phase volume fraction: 0.02 Temperature: 26°C

Measm^ment technique Microscopy

7.4 Six* and its distribution off disp«rs«d phas* 572

Results

^ = 0.0mi+a2il>y^(Wer''

^ ^ 0.125(1+a2(l>)'HWer'^

fl2=4.0 Notation

d32 Sauter mean diameter, cm dma maximum drop diameter, cm D impeller diameter, cm N impeller speed, 1/sec T vessel diameter, cm We Weber number, N ^D pda, dimensionless pc density of continuous liquid, g/cm^ a interfacial tension, dynes/cm 0 dispersed phase hold up

572 Chapter 7. Oth«r subj«cte r»lat«d to multi-plMistt systems

Calabrese, R. V, Chang, T. P. K. and Dang, R T.AIChE Journal, 32,657 (1986) Drop Breakup in Turbulent Stirred-Tank Contactors Part I: Effect of Dispersed-Phase Viscosity

Experimental apparatus Vessel Type: (l)-(4) flat-bottomed Diameter: (1) 0.142 (2) 0.213 (3) 0.312 (4) 0.391 m

Liquid contained Height: (1) 0.142 (2) 0.213 (3) 0.312 (4) 0.391 m

Baffle Number: (1M4) 4 Width (1)~(4) r/10 Off-bottom clearance: T/20 Clearance of baffle from wall: (1)~(4) T/30

Impeller Type: (1)~(4) six blade Rushton turbine Diameter: (1) 0.0711 (2) 0.1064 (3) 0.1562 (4) 0.1956 m Number of impellers: (1)~(4) 1 Number of blades on impeller: (1)~(4) 6 Length of impeller blade(perpendicular to shaft): (1)~(4) L/4 Width of impeller blade(parallel to shaft): (l)-(4) L/5 Off-bottom clearance: (1)~(4) T/2

Working fluids and their physical properties Continuous phase: water Dispersed phase: five different grades of silicone oils (viscosities = 0.1 ~ 10 Pasec)

Fluid physical properties at 25°C

Dispersed phase, silicone oils

Actual viscosity Density /xj, Pas prf, kg/w?

0.0960 0.486 0.971 4.43

10.51

Interfacial tension a,N/m

960 0.0378 971 0.0378 971 0.0378 973 0.0378 975 0.0378

Continuous phase, distilled water

Viscosity, //r = 0.893 x 10 Density, pr = 997 kg/m^

-3 Pas

7.4 Siz« and its distribution of disporsod piiaso 573

Experimental conditions 13,000 <Re< 101,000 U<We< 0.50 0.065 < g- < 0.50

Impeller speed: 0.93—5.95 rps Temperature: 25°C


Results For the moderate-viscosity data

[ota B Do D32 L N N„-T Re We r Mrf Pc Pd G

^^[l + BNnf" Do

Nri^{pclpdf^lidt"D]L^/a For Nri< I 5 = 11.5

tion constant Sauter mean diameter of an inviscid drop Sauter mean diameter impeller diameter impeller speed viscosity group vessel diameter Reynolds number, pcN^LVa, dimensionless Weber number, pcNLVjicf dimensionless average power input per unit mass viscosity of dispersed phase density of continuous phase density of dispersed phase interfacial tension

674 Chapter 7. Other subjecto r»lat«il to multi-phasa systems

Calabrese, R. V, Wang, C. Y. and Bryner, N. ?.,AIChE Journal, 32,677 (1986) Drop Breakup in Turbulent Stirred-Tank Contactors Part III: Correlations for Mean Size and Drop Size Distribution

Experimental apparatus Vessel size, impeller size, working fluids, and experimental conditions are summarized in the following table

Data set for mean drop size correlation

L,m L/T N,rps <T,N/m

/ii/, Pas /Ar, Pa-s prf, kg/m^ pc, kg/m^

^ Re^PcNLViic We = pcN^LVa Vi^ipc/pif'^H^NL/a

Calabrese e a/. (1986)

60

0.071-0.196 0.5 0.93-4.78 0.0378

0.096-0.486 0.00089 960-975 997

< 0.0015 13,000-101,000 44-1,137 0.326-5.90

Wang e/of. (1986)

knietal. (1977)**

Chen and Middleman Sprow (1967)***

Number of Experiments

146

0.071-0.156 0.5 1.42-4.67 0.00021-0.047

0.00081-0.459 0.00052-0.00089 834-985 792-997

< 0.002 14,000-83,000 54-70,960 0.0041-602.8

25

0.064 0.5 3.00-14.33 0.022

0.00078-0.520 0.00097 879-922 1,000

< 0.003 12,470-59,570 104-2,368 0.0071-22.6

110

0.051-0.152 0.21-0.73 1.33-16.67 0.00475-0.0483

0.00052-0.0258 0.00089-0.00127 703-1,101 993-1,001

0.001-0.005 12,000-104,000 70-2,000 0.0024-1.18

(1967)****

8

0.064 0.29 4.17-33.33 0.0418

0.00051 0.00099 692 1,005

0.005 17,060-136,440 107-6,840 0.0039-0.031

*Data reported for lu > 0.5 Pas are not included here. **Data reported for u = 1.5 Pas are not included here. And et al, report Dnu. It is assumed that D32 - 0.6 Dnn.

***Entire data set as reported by Chen (1966). ****Data reported for > 0.005 are not included here.

References: Calabrese, R. V. et al,,AIChE Journal, 32,657 (1986) Wang, C. Y. et al,MChE Journal, 32,667 (1986) Arai, K. et al„ Chem. Eng, Japan, 10,325 (1977) Chen, H. T. et al„AIChE Journal, 13,989 (1967) Sprow, F. B., Chem, Eng. Sci, 22,435 (1967)

Results

^ = 0.053 W e-' ' [1+0.91 Vi^-"]^''

i^ . i^- i . . . 1+erf [ 0.23 V2 P.

Z>32 0.23 A/2F exp -[i-'-J a

7.4 Siztt and its distribution off disporsod piiaso 575

Notation D diameter of drop Dz2 Sauter mean diameter Fp cumulative volume frequency L impeller diameter N impeller speed Pt, probability density function for drop volume T tank diameter We tank Weber number, pcN^LVc, dimensionless /ir viscosity of continuous phase ^ viscosity of dispersed phase pc density of continuous phase Pd density of dispersed phase G interfacial tension 0 volume fraction of dispersed phase

676 Chapter 7. Othar subjects r»lat«d to multi-phas« systems

Konno, M. and Saito, S.J. Chem. Eng. Japan, 20,533 (1987) Correlation of Drop Sizes in Liquid-Liquid Agitation at Low Dispersed Phase Volume Fractions

Use of reported data

^32/1. = 0.3 W€-^^\l+0.60m'''/Ref'^)

Re^pcNlIl^d

10^

10 '0)

1.3) • Present outhors

• Colobrese el al. ^^

X y'^%^^)

^6\ 10

v*^*^/-

10^ 10 10 10 10

Correlation oidsz (Symbols with tick marks indicate the data of 5-h agitation and the others the data of about 1- to 2-h agitation.)

1) Arai, K., M. Konno, Y. Matsunaga and S. Saito:/. Chem, Eng. Japan, 10,325 (1977). 2) Calabrese, R. V., C. Y. Wang and N. P. Bryner AIChEJ,, 32,677 (1986). 3) Knono, M., M. Aoki and S. Saito:/ Chem. Eng. Japan, 16,312 (1983).

Notation d^z Sauter mean drop size L impeller diameter N impeller speed ^4 viscosity of dispersed drop Pc density of continuous phase G interfadal tension

7.4 Siz» and its distribution off disporsod piiaso 577

Chatzi, E. G., Gavrielides, A. D. and Kiparissides, C, Ind. Eng. Chem. Res., 28,1704 (1989) Generalized Model for Prediction of the Steady-State Drop Size Distributions in Batch Stirred Vessels




Impeller Type: six-blade turbine Diameter: DT/2 Disk diameter: 5Z>r/4 Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): Di/4 Width of impeller blade (parallel to shaft): Di/5 Off-bottom clearance: Di/3

Working fluids and their physical properties Continuous phase: water Dispersed phase: styrene

Numerical values of the system's physical properties

fluid

water, 25 C

styrene, 25*=*C water, 50* 0

styrene, 50X

density, g/cm^ 0.9971

0.9014 0.9881

0.8792

viscosity, cP

0.9147

0.7303 0.5502

0.4591

interfacial tension, mN/m

11.5

7.4

Experimental conditions Temperature: 25 and 50°C Dispersed-phase volume fl:action: 0.01,0.02 and 0.03 Impeller speed: 150,200,250 and 300 rpm


573 Chapter 7. Oth«r subj«eto nilatad to multi-pluisa systems

Results

d^/Di =0.0165 (1+11.940) iNwe)f'''^

or

</32/Z>/=0.056 (l+lO.970)(ArH.e)f°«'

Notation dz2 steady-state Sauter mean diameter, cm Db DT impeller and tank diameter, respectively, cm N* impeller speed, 1/sec (Nwe)T Weber number of main flow, pdNyD^la, dimensionless Pc continuous phase density, g/cm^ G interfacial tension, dyne/cm 0 dispersed-phase volume fraction

lA Siz« and its distributloii off disp«ni«d phaso 679

Okufi, S., Perez de Ortiz, E. S. and Sawistowski, H., Can.]. ofChem. Eng., 68,400 (1990) Scale-up of Liquid-Liquid Dispersions in Stirred Tanks


System




Impeller Type

Diameter (cm) Number of impellers Number of blades Length of impeller blade (cm)

(perpendicular to shaft) Width of impeller blade (cm)

(parallel to shaft) Impeller blade thickness (nrni) Off-bottom clearance (cm)

(1)

flat-bottomed 11

11

4 LI


T/3 1 6

D/4

D/5

0.79 D

(2)

flat-bottomed 22

22

4 2.2


T/3 1 6

D/4

D/5

1.59 D

(3)

flat-bottomed 44

44

4 4.4


T/3 1 6

D/4

D/5

3.18 D

Working fluids Continuous phase: water Dispersed phase: (a) n-heptane

(b) n-heptane containing different concentrations of di-(2-ethylhexyl) phosphoric acid in an aqueous solution of sodium sulphate

Experimental conditions Impeller speed: 317--1,000 rpm Dispersed phase volume fraction: 0.1^0.4

Results

tank diameter impeller Weber number, pcN^DVo, dimensionless density of continuous phase, kg/m^ interfacial tension, N/m dispersed phase volume fraction

32 = 0.126(1 + 2^) FTe- - L- - Z)

Notation d^ Sauter mean diameter, m D impeller diameter, m Do reference impeller diameter, m N stirrer speed, 1/sec L impeller diameter ratio, Z)/Z)o,

dimensionless

T We

Pc a 0

5g() Chapter 7. Othar subjacto r«lat«d to multi-phas« systems

Chatzi, E. G., Boutris, C. J. and Kiparissides, C, Ind. Eng. Chem. Res., 30, 536 (1991) On-Line Monitoring of Drop Size Distribution in Agitated Vessels. 1. Effects of Temperature and Impeller Speed

Experimental apparatus Vessel Type: capped round-bottomed Diameter: 15 cm


Impeller Type: six-blade turbine Diameter: 5 cm Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 5 cm

Working fluids and their physical properties Continuous phase: distilled water Dispersed phase: styrene Suspending agent: polyvinyl alcohol


iV'rpm

200 300 200 300 200 200 300

r,°c 23 25 30 30 50 60 60

(Nweh

269 604 273 614 291 301 678

(NRe)T

20,635 30,953 23,004 34,506 33,285 38,845 58,267

Volume fraction of dispersed phase: 0.01 Concentration of suspending agent: 0.1 g/i

Measurement technique Laser diffraction technique

Results Effects of temperature and impeller speed on drop size distribution (1) The system assumed characteristic bimodal distributions within a very short time. (2) Increasing the agitation rate caused a shift of two peaks of the distributions. (3) An increase in temperature resulted in a size reduction and narrowing of the laige-size peak

of the distribution. (4) The steady-stage mean drop size

d^/Di = 0.045 (±0.003) (Nwe)f''-^

(5) Minimum transition time required for the system to reach dynamic equilibrium

/nim.0.1=3.19xlO^(Ar»..)f"

7.4 Size and its distrilnition off dispersed piiase gg2

Notation dsz Sauter mean diameter, cm 32 steady state Sauter mean diameter, cm

Di impeller diameter, cm N* impeller speed, 1/sec (NReh Reynolds number, N*Df/Vm, dimensionless iNwe)T Weber number, pc (NyDiVa, dimensionless inm.0.1 m i n i m u m t rans i t ion t ime r equ i red to r e a c h (dsz-(1^2)/d^z =0.1, m in

Vm mean kinematic viscosity, cmVsec G interfacial tension, dyne/cm

g32 Chapter 7. Other subjects related to multi-phase systems

Chatzi, E., G., Boutris, C. J. and Kiparissides, C, Ind. Eng. Chem. Des.y 30, 1307 (1991) On-Line Monitoring of Drop Size Distributions in Agitated Vessels. 2. Effect of Stabilizer Concentration

Experimental apparatus Vessel Type: capped round-bottomed Diameter: 15 cm


Impeller Type: six-bladed fan turbine Diameter: 5 cm Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 5 cm

Working fluids and their physical properties Continuous phase: distilled water Dispersed phase: styrene Suspending agent: polyvinyl alcohol

Physical properties of the dispersed and continuous phases (styrene and water, respectively)

r.°c 25 30

50 60

Pm

IXm

Cm, g/L

0.1 0.01 0.05 0.1 0.1 0.01 0.05 0.1 3

--pdip + p

= Mc/ ( l -

pc, g/cm^

0.9971 0.9957

0.9881 0.9832

r ( l - 0 )

flcCP

0.890 0.797

0.546 0.466

0 ) t l + 1.5//rf0/(/Xrf+Alc)]

pd, g/cm^

0.9014 0.8970

0.8792 0.8704

//rf.cP

0.729 0.681

0.531 0.475

pm, g/cm^

0.996 0.995

0.987 0.982

flm,C?

0.905 0.811

0.556 0.474

(T,^, dyn/cm

17.3 24.1 19.4 17.0 15.8 22.9 17.8 15.3 3.8

7.4 Siz« and its distribution off disponiod pliase 683


Cm, g/L

0.01

0.05

0.1

3

N\Tpm

200 300 200 300 300 300 200 300 200 300 200 200 300 200 300

r,°c 30 30 60 60 30 60 25 25 30 30 50 60 60 60 60

(Nweh

194 436 201 453 541 583 269 604 273 614 291 301 678 1,219 2,729

(NReh

23,004 34,506 38,845 58,267 34,506 58,267 20,635 30,953 23,004 34,506 33,285 38,845 58,267 38,845 58,267

11 fV^

17 12 11 8 12 8 18 13 17 12 13 11 8 11 8

Volume fraction of dispersed phase: 0.01 Concentration of suspending agent: 0.01--3 g/i Temperature: 25,30,50 and 60**C

Measurement technique Laser diffraction technique

Results

/fi = 0.046 ±0.002

Minimum transition time required for the system to reach steady state

The exact dependence of parameter kz on the interfacial tension and possibly other physical properties was not determined.

Notation dsz Sauter mean diameter, cm dsz steady state Sauter mean diameter, cm Di impeller diameter, cm ku kz constant N* impeller speed, 1/sec (NReh Reynolds number, N *DflVmy dimensionless iNw^ Weber number of the main flow, pc iN^fD^la, dimensionless ^min, 0.06 t ime requ i red for t h e average drop size to reach 9 5 % of the dzz value

li viscosity, cP Vm mean kinematic viscosity, cmVsec p density, g/cm^ a inteifacial tension, dyne/cm 0 fraction of dispersed phase


684 Chapter 7. Otli«r subjects r»lat«d to multi-phas* systems

CoUias, D. I. and Prud'homme, R. K., Chem. Eng. Set., 47,1401 (1992) Diagnostic Techniques of Mixing Effectiveness: The Effect of Shear and Elongation in Drop Production in Mixing Tanks



Baffle Number: 4 Width: 0.015 m Height: 0.192 m

Impeller

Type

Diameter (m) Number of impellers Number of blades on impellers Length of impeller blade

(perpendicular to shaft) (m) Width of impeller blade (m) Height of impeller blade (m) Off-bottom clearance

Rushton turbine

0.0483 1 6

D/4

D/5 —

0.0483

anchor impeller

0.0483 1 1

• -

0.019 0.113 0.0483

blade (or paddle) impeUer

0.0483 1 2 —

D/S —

0.0483

Working fluids and their physical properties Continuous phase: 3% polyvinyl alcohol in water (density = 1,020 kg/m ; viscosity = 8.43 x 10"

Pasec; surfeice tension = 0.04505 N/m) Dispersed phase:

Dispersed solution

(1)55%MCB+45%T (2) 32% (55% MCB+45%T)

+17% CCI4 + 51% PB (18) (3)PB(18)

26.7% (55% MCB+45%T)+ 12.5% ecu + 60.8% PB (32)

Density kg/an?

990 1,000

920

Viscosity Pasec

0.667x10-' 7.89 xlO-3

0.1

Surface tension N/m

0.03101 0.02920

0.03340

Interfacial tension N/m

0.00367 0.00327

0.01180

T: toluene; MCB: monochlorobenzene; PB: polybutene

Experimental conditions ImpeUer speed: 160,230,300,370,420,470 and 570 rpm


7.4 Siz« and its distribution of disporsod piiaso g35

Results (1) Rushton turbine

dmax/D = 0.384 ( 1 + 1 . 4 0)/>°-^^ We""'^

(2) Blade impeller dn^/D = 0,457(l+1.40)/>°-^2 p -0.71

Notation (imax drop size corresponding to the 9 5 % cumulative point, m D diameter of the impeller, m N rotational speed of the impeller, 1/min p viscosity ratio of t he dispersed and continuous phases, .dimensionless We Weber number , iV^D^p/or, dimensionless fj, viscosity, Pasec p density, kg/m^ c interfacial tension, N / m 0 percentage of the organic phase in the suspension


5g5 Chapter 7. Othar subj«cto ralatad to imilti-phas« systems

Skelland, A. H. P. and Kanel, J. S., Ind. Eng. Chem. Res., 31,2556 (1992) Transient Drop Size in Agitated Liquid-Liquid Systems, As influenced by the Direction of Mass Transfer and Surfactant Concentration

Experimental apparatus Vessel Type: fiat>bottomed Diameter: 0.2135 m Height: 0.2500 m


Baffle Number: 4 Width: 0.019 m Thickness: 0.0025 m

Impeller Type: six flat-blade impeller Diameter: (a) 0.1015 (b) 0.06314 m Number of impellers: (a) (b) 1 Number of blades on impeller (a) (b) 6 Width of impeller blade (parallel to shaft): (a) 0.01262 (b) 0.00764 m Thickness of impeller blade: (a) 0.00247 (b) 0.00152 m Off-bottom clearance: (a) (b) 0.10675 m

Working fluids and their physical properties Continuous phase: deionized water or chlorobenzene Dispersed phase: chlorobenzene or deionized water Solute: tetrabutylammonium bromide (TBAB) Surfactant: octyl phenoxy polyethoxyethanol (Trinton X-100)

Physical and transport properties of water and chlorobenzene at 25^C

density, hquid kg/w?

chlorobenzene 1,083.0 water 997.1

viscosity, diffiisivity of Ns/m^ TBAB,mVs

0.00073 2.62x10-1^ 0.00087 6.24x10-^°

Intertacial tension between chlorobenzene and deionized water correspondmg to a given concentration of triton X-100 at 25^C

solution concn. of surfactant in no. water, g of SAA/L of water

1 0.000 2 0.038 3 0.100 4 2.000

corresp. interfacial tension, dyn/cm

33.5 27.1 21.0 16.0

SAA: surfactant

7.4 Slz« and Ito distribution off disporaod pliaso

Results

687

j 0 1 ^

1 5 o

r '

[.—1 1-

• « R102 di-% phi«.03 o » H 9 9 di"<s. ph2».07 o « R 9 2 dW. |»hi«.03 • * RB9 dj-i phi«.07 N « 220 or 480rpzD 1

• o 1 • 1

• . » o

s — J 1 L..JI 1 1 1 OJD &.0 10i> 15.0 20.0 25.0 90.0 35.0 40.0 45.0

lizne (sec)

i

1 •

1 ° r 8

•

1 • i 1

• « R220 di-s. phi«.03 D « R116 di-s. phi«.07 o«RU0di- iplu- .03 • « RlOe dW. phj«.a7 N •* 220 or 4B0rpm

o 1 • 1

g 0 O

1 1 1 I 8 , 1 , 1

0.0 5.0 10.0 15.0 20.0 2&J0 30.0 95.0 40.0 45.0 time êc)

¥5

• - R240 di-s, phj«.03 o « R243 di-$. phi«.07 o « R1B6 dW. phi».03 • « R201 di«< phi».a7 N » 220 or 460rpm

sL

E5 .E-.

•o'

&0 10.0 ISJO 20.0 2&0 30.0 3S.0 40i> 4SA

Umeêc)

h

L « 1 9 o r •

•

1 J

• «RlBldi-s.phi*.03 o B R241 di-s. jAu=.07 o»R193dKphie.03 • « R205 dH. vhi^Xnr \

N » 220 or 4BDrpm

0

S " o ' • ' • '

OD 5i> 10.0 15J0 20.0 25J0 30.0 351) 40.0 ASXi time êc)

Effect of 0 on the transient daz in the absence of surfactant ("/?" means run, and N for the small (s) and large (1) diameter impellers (di) are 480 and 220 ipm, respectively): (a) for transfer of TBAB from chlorobenzene drops; (b) for transfer of TBAB to chlorobenzene drops; (c) for transfer of TBAB from water drops; (c) for transfer of TBAB to water drops.

688 Chapter 7. OtiMr subjecto ralatad to multi-phas« systems

m o • o

«

<> • *

b « 1 o J M j d 1

m ' o •

D

• •

..—.J U

• -RB9 P->Cir(C3 O-R108 C->DTO5 O.R201 D-x;irfe) • « R205 c-M) irto) IftTf e di and phi, 220rpm

' s -• • "

-^-.J » r 1 I 1 )

¥ 5 h

r * L o

• -R200 Wto)C->D D«R233 Wp)I>->C 0-R216 W(bD->C large di and phi 220rpm

» 0 o o s

..—J 1 i l — U U ^ 0.0 5 ^ 10.0 15.0 S0.0 25.0 30.0 35.0 40.0 45.0

lime (sec) 0.0 5.0 10J> 15.0 20.0 Z&Jb 30.0 35.0 40.0 45.

lime (sec)

h

1 ° o

•«RB1 ir(0)C->D D-R155 WS>)D-->C o«R3B wfcjD-x:

laiige di and pbi« 220rp] m

o a 1

1 " ° 1 — 1 — 1 — I — 1 — 1 — 1 — J —? . . ._ . A

E .

CM "

(Bl

6

6

•

«

S O'

"

a o

o a

a

• -R57 V(D)C->D 0.R13B W(D)D->C

lar:ge di and phi. 220rpm

• S o i _ j 1 1 1 1 1

0.0 bJO 10.0 15.0 20.0 25.0 30J) 35.0 40.0 45.0

time (sec) 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.r

time (sec)

Effects of reversing the direction of dispersion and diffusion on the transient ( 32 for (i/=0.101 m andiS =220 rpm C*R* means run): (a) surfactant-free systems; (b) 0.038 g of SAA/L of H2O; (c) 0.10 g of SAA/L of H2O: (d)2.00gofSAA/LofH2O.

Notation dz2 Sauter-mean drop diameter, m di impeller diameter, m N impeller speed, 1/sec 0 volume fraction of dispersed phase

7.4 Siz« and its distribution off disp«rs«d phas* 539

Nishikawa, M. Kayama, T, Nishioka, S. and Nishikawa, S., Chem. Eng. Set., 49,2379 (1994) Drop size Distribution in Mixing Vessel with Aeration


Liquid contained height: 160 mm


Impeller Type: six-bladed Rushton turbine Diameter: 80 mm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 20 mm Width of impeUer blade (parallel to shaft): 16 nun Off-bottom clearance: 80 mm

Sparger Type: single nozzle Lotion: at the center of bottom plate

Working fluids Conrinuous phase: hot distilled water Dispersed phase: honeybee's wax Gas: air

Experimental conditions Volumetric fraction of dispersed phase: 0.5—30% Superficial gas velocity: 0.083—1.67 cm/sec

Results

dp32 = 0.116£;'^' ei [1+2.8(0/100)''']

dp32 Id = 0.028iSr;''V-''* X [1+2.8(0/100)'^*] Wr^"'

We' = n^d^p/a

Notation d impeller diameter, cm a interfadal tension, g/sec^ dpsz Sauter mean drop size, cm 0 volume fi:action of dispersed n impeller speed, 1/sec phase, % Np power number with no aeration, dimensionless We' mixing vessel Weber number, dimensionless Subscripts e average eneigy dissipation rate per unit mass of a aeration

mixing liquid, cmVsec g agitation p density, g/cm^

690 Chapter 7. Oth«r subjacto ralat«d to multi-phas* systams

Kuriyama, M., Ono, M., Tokanai, H. and Konno, H., Trans. Instn. Chem. Engrs., 74, P ^ A, 431 (1996) Correlation of Transient Sizes of Highly Viscous Drops in Dispersion Process in Liquid-Liquid Agitation


System


Liquid contained Height


Impeller Type

Diameter (m) Number of impellers Number of blades Length of impeller blade (m)



(1)


0.127

4 0.0127

(2)


0.127

4 0.0186

six-bladed Rushton turbine

DI2 1 6

L/4

L/5

D/2

DI2 1 6

L/4

Lib

D/2

forking fluids and their physical properties

Continuous phase 1 (distiUed water added with polyvinylalcohol) polyvinylalcohol concentration 0.1 kg m" Density lO^kgm"^ Viscosity 10"^ Pa s

Continuous phase 2 (distiUed water added with sodium chloride) sodium chloride concentration 0.2 kg mol m" Density lO^kgm"^ Viscosity 10"^ Pa s

Dispersed phase (mixture of silicon oil and tetrabromoethane) Density 10^ kg m" Viscosity 0.0107 to 12.6 Pa s

Interfacial tension between dispersed phase and continuous phase 1 0.016 Nm-^

Interfacial tension between dispersed phase and continuous phase 2 0.038 Nm-^


7.4 Siz« and its distribution off disporsod pliaso 592

Experimental conditions Impeller speed: 2.5—8.31/sec Volume fraction of the dispersed phase: 0.002—0.03 Viscosity of the dispersed phase: 0.0107—12.6 Pasec Temperature: 20°C


Results For final drop size

32 =(l + ai0)rf32

ai = 8.5

For transient drop size

a^ = 16, as = 0.53

Notation 32 Sauter mean drop size, m

dz2 Sauter mean drop size under coalescence conditions, m D vessel diameter, m L impeller diameter, m Nr rotational speed of impeller, 1/sec t agitating time, sec ai, 0(4, OTs constant ^ dispersed phase volume fraction

692 Chapter 7. Othar subj«cto rvlatad to multi-phasa systems

7.4.2 Bubble size and bubble-size distributions

Miller, D. K.AIChE Journal, 20,445 (1974) Scale-Up of Agitated Vessels Gas-Liquid Mass Transfer


System

Vessel Type Diameter Height Liquid height Volume (m^)

Baffle Number Width Thickness Off-bottom clearance

Impeller Type



(parallel to shaft) Thickness of blade Off-bottom clearance

Sparger Type Diameter of ring Hole size Number of holes Hole spacing Orientation

(1)

dish-bottomed 0.1524 0.305 0.1460 0.00252

4 0.0127 0.001588 0.00952

0.1016 1 4

0.01905

0.000794 0.00952

ring 0.00889

0.001588 0.00318 40 10

0.00698 0.0279 down up

(2)

dish-bottomed 0.305 0.610 0.292 0.0252

4 0.0254 0.00318 0.01905


0.001588 80

0.00696 up

0.203 1 4

0.0381

0.001588 0.01905

ring 0.1778 0.00318

20 0.0279

up

0.00635 10

0.0559 up

(3)

dish-bottomed 0.686 1.372 0.657 0.252

4 0.0572 0.00714 0.0429

0.457 1 4

0.0857

0.00357 0.0429

ring 0.406

0.00318 0.00635 50 25

0.0260 0.0516 up down

Units: m Working fluids

Liquid: aqueous solution saturated with CO 2 Gas: air

7.4 Siz« and ito distribution off disporsod pliaso 693

Results F o r stripping of CO 2 from the aqueous solution with air

Mean bubble s ize

Z ) E V = 4.15

0^

0°-' + 0 . 0 0 0 9

,Jjt!f^] ,0.000216 < M 2 ; v i r o

Notation DBM mean bubble diameter , m Pe effective power input, W Ug actual superficial gas velocity, m / s e c Ui bubble terminal velocity of rise, m / s e c V clear liquid volume, m^ pi liquid density, kg/w? a surface tension, N / m 0 fraction gas holdup

xO^

Q94 Chapter 7. Oth«r subj«cto r»lat«d to multi-phas« systems

Figueiredo, M. M. L and Calderbank, R H., Chem. Eng. Sd., 34,1333 (1979) The Scale-Up of Aerated Mixing Vessels for Specified Oxygen Dissolution Rates



Baffle Number: 4

Impeller Type: flat bladed turbine Diameter 0.27 m Number of impellers: 1 Length of impeller blade (perpendicular to shaft): 0.06 m Width of impeller blade (parallel to shaft): 0.06 m



Experimental conditions Power consumption: 0.41 x 10^-4.8 x 10 w/m^ Impeller rotational speed: 4.16'-8.331/sec Superficial gas velocity: 6.34,8.87 and 12.7 x 10" m/sec

Results Interfacialarea arf = 593(P/Vi:)°-25(V;)«- Bubble size dsm = 6H/ad

dm = 3.5 X10'^ m under all conditions Notation

Od gas-liquid interfacial area, m dsm Sauter mean bubble diameter, m H gas holdup (= volume of gas/volume of dispersion) P impeller power dissipation, watt VL volume of liquid, m Vs superficial gas velocity, m/sec

7.4 Siz« and its distribution off disporsod phaso 695

Sridhar, T. and Potter, 0. E., Ind. Eng. Chem. Fundam, 19,21 (1980) Gas Holdup and Bubble Diameters in Pressurized Gas-Liquid Stirred Vessels



Baffle Number 4 Width: 1.2 cm

Impeller Type: six flat-bladed turbine Diameter: 4.5 cm Number of impellers: 1 Number of blades on impeller: 6 Width of impeller blade (parallel to shaft): 0.8 cm Off-bottom clearance: 4.2 cm

Sparger Type: single-hole nozzle Diameter of nozzle: 6 mm Number of nozzles: 1

Working fluids Liquid: cyclohexane Gas: air

Results \0.16

Z)flif=4.15 iPJVf'p'^ JUJU., /^^•' +0.0009

-(^I + 0.000216 U ^ ^ 0.4^02 mm

P^= 0.706 Pindf

or Notation

di impeller diameter, m DBM mean diameter of bubbles, m Et total energy input, W

dispersed phase holdup stirrer speed, 1/sec mechanical agitation power input in gas-liquid dispersion, W mechanical agitation power input in ungassed Uquid, W

Qg volumetric gas flow rate, mVsec

H n

V

p

pa

Pg G

volume of liquid in reactor, m terminal velocity of bubble in free rise, m/sec superficial gas velocity, m/sec hquid density at system conditions, kg/m^ density of air at operating temperature, kg/m^ gas density at system conditions, kg/m^ surface tension, N/m

696 Chapter 7. Oth«r subjaets ff«lat«d to multi-phase systems

Pirthasarathy, R., Jameson, G. J. and Ahmed, N., Trans. Instn. Chem. Engrs., 69, P ^ A, 295 (1991) Bubble Breakup in Stirred Vessels—Predicting the Sauter Mean Diameter

Experimental apparatus Vessel Type: flat-bottomed Diameter 0.195 m



Impeller

System

Impeller type Diameter (m) Number of impellers Number of blades on impeller Width of impeller blade (m)


(1)

six-bladed Rushton turbine 0.065

1 6

D/5

T/3

(2)

flat-bladed impeUer 0.065

1 6

D/S

T/3

Sparger (1) a ring sparger

number of holes: 8 diameters of holes: 0.5 mm

(2) sintered glass disc pore size: 150—250 fim

(3) sintered glass disc pore size: 2—15 jrni

Working fluids and their physical properties Liquid: tap water containing 50 ppm of methyl isobutyl carbinol (surface tension of the liquid =

71.3 mN/m) Gas: air

Experimental conditions Stirrer speed: 2.08-13.33 rps Superficial gas velocity: 2.5 x 10"* -1.25 x 10" m/sec


Results Under non-coalescing conditions

d32^2.0 (P/Vif^'p'^'

7.4 Size and Its distribution off disporsod pliaso g9y

Notation d32 Sauter mean bubble diameter, pm D impeller diameter, m P power consumption, W T tank diameter, m Vi impeller swept volume , nD^ W/4, rn? W blade width, m p density of the liquid phase, kg/m^ a surface tension, N / m

593 Chapter 7. Othar subjacto r«lat»d to multf-phas* systems

Barigou, M. and Greaves, M., Chem. Eng. Scu, 47,2009 (1992) Bubble-Size Distributions in a Mechanically Agitated Gas-Liquid Contactor


Baffle Number: 4

Impeller Type: a standard Rushton turbine Diameter: 0.333 m Number of impellers: 1 Number of blades on impeller: 6 Off-bottom clearance: 0.25 m

Sparger Type: a single tube orifice Diameter of orifice: 19 mm Location: at the center of the tank below the impeller

Working fluids and their physical properties Liquid: deionized water (density = 999 kg/m ; viscosity = 1.00 mPasec; surface tension = 70.99

mN/m) and 0.15 M solution of general-purpose grade sodium chloride Gas: air

Results

AS

D32 (mm)

4.0 i

3J

3.0

25

2.0

1.0 I 100

B Q « 1.64x10-3 m3/s •

o Q » 4.38x10-3 mVs«

A Q « 6.87x10-3 m3/s A

200 N(ipm)

300 400

Effect of i^ and Q on bubUe size: (D, O, A) impeUer region, (•» #, A) region below impeller.

7.4 Size ami iU distribution off disporsod pliaso 699

10

8 i Lfigend

EZ]Mid-plone • I Baffle pLone

0 1 2 3 4 5 6

d (mm)

Overall bubble-size distributions in mid-plane and baffle plane.

- o — Windwaid 100 ipm - • — Windward ISOipm "O Windwaid 250 ipm

—lir— Lccwaid 100 ipm — « — Lcewaid 180 ipm

o--- Leeward 250rpm

3.5 4.0

d32 (mm)

Variation of Sauter bubble diameter near a baffle.

Experimental conditions Air flow rate: 1.64 x 10'^-6.87 x 10" mVsec Impeller agitation speed: 100~390 rpm

Notation d equivalent spherical bubble diameter, mm dzi Sauter mean bubble diameter, mm Dz2 overall Sauter mean bubble diameter, nmi N impeller speed, 1/min 0 air flow rate, mVsec

700 Chapter 7. Othar subjacto r»lat«d to multi-phas* systems

Parthasarathy, R. and Ahmed, N., lyans. Instn. Chem. Engrs., 72, Part A, 565 (1994) Sauter Mean and Maximum Bubble Diameters in Aerated Stirred Vessels



Baffle Number: 4 Width: (1)0.0195 (2) 0.04 m

Impeller Impeller instaUed

Tank (1) (2)

Tank diameter (m) Impeller type

0.195 Rushton turbine

Flat blade impeller Marine propeller

PBD,PBU

0.4 Rushton turbine

PBD, PBU

Impeller details

Impeller No. of biades

Diameter Dim)

Blade Width W(xn)

Blade length L(m)

Pitch/angle of blades

Ruston turbine Flat blade impeller Marine propeller PBD PBU

6 6 3 6 6

r/3 r/3 T/3 r/3 T/3

D/5 D/S

Projected width =Z)/3 Projected width = D/5 Projected width =Z)/5

D/4 D/3 —

D/4: D/4

— — 1.5 45° 45°

(PBD'-iS'* pitched-blade downward-pumping disc turbine, PBU-45*' pitched-blade upward-pumping disc turbine)

Sparger

Tank

Tank diameter (m) Sparger type

Sparger installed

(1) 0.195 ring

porous 0 porous 4

(2) 0.4 ring

porous 4

Sparger details

Sparger Diameter (m)

Ring 2D/3 Porous 0 0.09 Porous 4 0.09

Average pore size (^m)

200 10

Location

half-way between the tank bottom and the impeller

tank bottom directly underneath the impeller

7A Siz« and its distributfon off disp«rs«d phas« 70x

Working fluids and their physical properties Liquid: water containing 50 ppm v/v of methyl isobutyl carbinol (surface tension of the liquid =

71.3 mN/m) Gas: air

Experimental conditions Stirrer speed: 2.08-16.67 rps Superficial gas velocity: 2.5 x 10"*~1.25 x 10"^ m/sec


Results

- ^ = 0.785 dnax

dmxx = 2.55 ^ 3 / 5

{PIVif"p"\

Notation 32 sauter mean or bubble or droplet diameter, \im

dmm maximum bubble or drop diameter, Mm D impeller diameter, m L impeller blade length, m P power demand of the impeller, W T tank diameter, m Vi impeller swept volume, KD^W/4, W? W impeller blade width, m p liquid phase density, kg/m^ a surface tension, N/m

702 Chapter 7. Othmr subj«cto r»lat»il to multi-phas* systems

P^hasarathy, R. and Ahmed, N., Ind. Eng. Chem. Res., 33,703 (1994) Bubble Size Distribution in a Gas Sparged Vessel Agitated by a Rushton Turbine



Impeller Tjrpe: six-bladed Rushton turbine Diameter: 0.065 m Number of impellers: 1 Number of blades on impeller: 6 Width of impeller blade (parallel to shaft): 0.013 m Off-bottom clearance: 0.065 m

Sparger Type: sintered glass disk Diameter: 90 nmi Pore size: 150~250 and 5—15 [im

Working fluids and their physical properties Liquid: tap water containing 50 ppm v/v of methyl isobutyl carbinol (surface tension of the liquid =

71.3 mN/m) Gas: air

Experimental conditions Stirrer speed: 2.08-13.33 rps Superficial gas velocity: 2.5 x 10"*~1.25 x 10" m/sec Temperature: 21 ± 0.5°C


Results The effect of impeller speed on the equilibrium bubble size and size distribution in a stirred

vessel has been studied by using bubbles of known, but different, initial Sauter mean diameters. For bubbles undergoing breakup the size distribution changes as a function of the impeller speed. The original log-normal distribution becomes bimodal due to the generation of smaUer bubbles by the breakup of larger ones in the population. At high impeller speed, the bimodal distribution reverts to unimodal again, but on the lower side of the size scale. This would indicate that the bubbles above a certain size are broken up at each agitation level and attain a new equilibrium distribution, and thus and average size.

703

7.5 Breakage and coalescence

Madden, A. J. and Damerell, G. L.,AIChE Journal, 8,233 (1962) Coalescence Frequencies in Agitated Liquid-Liquid Systems

Experimental apparatus Vessel Type: flat-bottomed Diameter: 51/2 in Height: 6 1/4 in Volume: 1,500 m^


Impeller Type: six-bladed turbine Diameter: 3 in Number of impellers: 1 Number of blades on impeller: 6

Working fluids Continuous phase: toluene containing iodine Dispersed phase: water containing sodium nitrate

Experimental conditions Total volume of dispersed phase: 1.375'-11.0 m£ Impeller speed: 150—300 rpm Temperature: 25°C

Measurement technique Analytical method: determination of iodine

Results 0 oc 5 2 ^

0 oc 7 / - ^

Notation T vessel diameter, in S impeller speed, 1/min Vd total volume of dispersed phase, cc 0 coalescence frequency, 1/sec

704 Chapter 7. OtiMr subjaeto r»lat«il to multi-plMisa systems

Komasawa, I., Morioka, S. and Ohtake, T, Kagaku Kogaku, 34,538 (1970) Studies of the Interaction Rate of Dispersed Phase and Resulting Chemical Reaction in a Stirred Tank

Experimental apparatus Vessel Type: dished-bottomed Diameter: 110 mm Height: 158 mm Volume: 1,380 m^


Impeller Type: six-blade turbine Diameter: 51 mm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 12.5 nun Width of impeller blade (parallel to shaft): 11 nrni Off-bottom clearance: 79 nmi

Working fluids and their physical properties Continuous phase: distilled water containing NaCl

concentration of NaCl = 5 x 10" g-moles/^ Dispersed phase: organic solvents (see table)

Liquid properties for mutually saturated systems at 25°C

Density Viscosity Interfacial tension

System pig/cxc?) /i x 10 (poise) cr (dynes/cm)

38.0

30.2

45.1

28.6

29.9

32.2

3.80

46.0

80% benzen+20% CCU water benzene water CCU water phenetole water CH2CI2 water CHCI3 water cyclohexanone water 64% ts{?-octane-»-36% CCI4 water

1.015 0.9984 0.8725 0.9983 1.583 0.9986 0.9601 0.9980 1.316 1.003 1.479 1.003 0.9470 0.9980 0.9714 0.9990

0.6582 0.9013 0.6028 0.9013 0.9012 0.9013 1.141 0.9013 0.4310 0.9370 0.550 0.9368 0.2019 1.096 0.5780 0.9013

7.5 Br«ak«9* and coal«scmic« 705

Experimental conditions Impeller rotational speed: 340-1,500 rpm Temperature: 24.5 ± 0.5°C Holdup of dispersed phase: 0.05—0.40

Measurement technique Measurement of photo transmission

Results

^y2xlO-''Re''''We^^<l>'''

Notation D diameter of impeller, cm N impeller rotational speed, 1/min Re Reynolds number, pcNDVjirt dimensionless We Weber number, pcN^DVc, dimensionless fir viscosity of continuous phase, g/cmsec Pr density of the continuous phase, g/cm^ a interfacial tension, dyne/cm 0 volume fraction of dispersed phase, dimensionless 0), interaction rate, 1/min

706 Chapter 7. Other subjects relatsd to multHihass systems

Mizoguchi, K., O'Shima, E., Inoue, H. and Inoue, I., Kagaku Kogaku, 37,521 (1973) Break-up and Coalescence Rate of Dispersed Liquid Droplets in an Agitated Vessel


Liquid contained Height: 110 mm Volume of liquid in vessel: 1,000 cc

Baffle Numben4 Width: 11 mm

Impeller Type: six-flat bladed turbine Diameter: 55 nun Number of impellers: 1 Number of blades on impeller 6 Length of impeller blade (perpendicular to shaft): 14 mm Width of impeller blade (parallel to shaft): 11 nun Off-bottom clearance: 55 mm

Working fluids Continuous phase: deionized water containing 0.1 % of PVA stabilizer Dispersed phase: toluene

Experimental conditions Fraction of the dispersed phase: 0.1 Temperature: 32°C

Measurement technique Electron microscopy

Results

at

Notation dv volume mean droplet diameter, cm kc coalescence rate constant, sec°- ^ kd break-up rate constant, sec /cm^ n agitation speed, 1/sec N total droplet number, 1/cm^ t time, sec

7.5 Braakag* and coalesc»nc« yQ7

Shiloh, K., Sideman, S. and Resnick, W, Can. J. ofChem. Eng., 51,542 (1973) Coalescence and Break-Up in Dilute Polydispersions

Experimental apparatus Vessel Type: conical-bottomed Diameter: 20 cm

Impeller Type: six-bladed turbine Diameter: 10 cm Number of impellers: 1 Number of blades on impeller: 6

Working fluids and their physical properties Continuous phase: kerosene (density = 0.78 g/cm ) and kerosene-perchloroethylene mixture

(density = 1.25 g/cm ) Dispersed phase: Na2S04-saturated aqueous solution (density = 1.15 g/cm )


Measurement technique Light intensity measurement

Results Coalescence

(Oi - <!>'''

Breakup

Notation d drop diameter 0 dispersed phase hold-up (Oi coalescence rate (per time and per drop)

708 Chapter 7. Other subjects relateil to multi-phase systems

Brown, D. E. and Pitt, K., Chem. Eng. Sci., 29,345 (1974) Effect of Impeller Geometry on Drop Break-Up in a Stirred Liquid-Liquid Contactor


Impeller

Impeller no.

Type Diameter (m) Number of impellers Number of blades on impeller Length of impeller blade (perpendicular to shaft)(m)

Width of impeller blade (parallel to shaftXm)

1

six 0.10

1 6

0.0315

0.025

2 3

-bladed disc turbine 0.10 0.15

1 1 6 6

0.0315 0.0475

0.050 0.0375

Working fluids Continuous phase: water Dispersed phase: kerosene, methyl iso-butyl ketone and «-butanol

Experimental conditions Volumetric hold-up of dispersed phase: 0.05 Temperature: 20°C

Impeller no. 1 2 3

Rotational speed (rpm) 250-450 250-450 250-450 Np 5.8 9.3 5.8 Ntc 12^3 7^8 3.1

Measurement technique Photo-electric technique

Results

jP.-2/3'l rf^/^nr'M11!^ I = constant.

Notation d32 Sauter mean drop diameter, m N impeller speed, 1/sec Np impeller power number, dimensionless tc circulation time, sec T vessel diameter, m E average energy dissipation rate per unit mass, J / seckg p density of continuous phase, kg/ia? a interfacial tension, J/m^

7.5 Braakag* and coalascanca 709

Mochizuki, M. and Kuroki, K., Kagaku Kogaku Ronbunshu, 5,540 (1979) Observations of the Breakup of a Liquid Drop around Turbine Impeller




Impeller Type: six-bladed Rushton turbine Diameter: 100 mm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 25 mm Width of impeller blade (parallel to shaft): 20 mm Off-bottom clearance: 100 nmi

Working fluids Continuous phase: tap water Dispersed phase: toluene tinted with Sudan HI



Results

a:r«=25mm, //=l/24sec, /,=l/8sec b, c, d: r»=25mm, (r=l/80sec, /,=l/15sec

e:r«=25mm, //=l/45sec, /,=1/15 sec f:r«=25mm, (/ =l/45sec, /,.=1/15 sec

Fig. 1 Multi-exposure photographs of breakup of a drop.

710 Chapter 7. Othar subjects r«lat«d to multi-phasa systems

Fig. 2 Schematic diagrams of the breakup processes of a drop (Fig. 1-b)

Notation Yn radial distance from shaft to nozzle center, mm U time of exposure, sec if time of flashing interval, sec

7.S Braakag» and coal«sc«iic« 71^

Molag, M., Joosten, G. E. H. and Drinkenburg, A. A. H., Ind. Eng. Chem. Fundam.y 19,275 (1980) Droplet Breakup and Distribution in Stirred Immiscible TWo-Liquid Systems


Baffle Number: 4 or unbaffled Width: 0.0145 m

Impeller

Type

Diameter (m)

Number of impeUers Number of blades

on impeller Width Length

turbine

0.0425

1 6

0.0085 0.0106

45° inchned blade

0.0425

1 4

0.0076 —

flat disk

0.090

1 1

— —

cone SO*' «: 0.0325 /: 0.065

1 1

— —

cone 10° «: 0.041 /: 0.055

1 1

— —

f«: upper side /: lower side

Working fluids Continuous phase: 0.1 N NaOH Dispersed phase: a mixture of 71.5 wt% benzene, 25.8 wt% CCI4 and 2.7 wt% sebacoyl dichloride

(the specific gravity is equal to that of the continuous phase) Experimental conditions

Type of impeller Impeller speed (rpm)

turbine, baffled 225-1,300 turbine, unbaffled 225- 800 flat disk, baffled 400-1,300 flat disk, unbaffled 400- 800 inchned blade baffled 400-1,300 inchned blade unbaffled 400-1,000 cone, 30° sht width (nmi) 4 1,300

4 1,300 4 700 4 700 2 700 2 700

cone, 10° sht width (nmi) 4 500-1,300


7X2 Chapter 7. Othar subjects r»lat«d to multi-phas* systems

Results (1) For not two large diameters, droplets in agitated two phase liquid systems will split into two

equal sized daughter droplets. (2) The standard deviation of the drop size distribution will, after relatively few spht-ups, reach a

value of approximately, 0.35, virtually independent on agitator type or speed. (3) Droplet breakup starts at a constant minimal Weber number.

7.5 Braakag« and coalescence 713

Sovov4 H., Chem. Eng. Sci., 36,1567 (1981) Breakage and Coalescence of Drops in a Batch Stirred Vessel—II Comparison of Model and Experiments

Experimental apparatus Vessel geometry and data employed for study

Sets of compared data and corresponding values of parameters

Reference

(2) (7)

(1) (5)

(4) (8) (3) (6)

Impell<

W/D

0.25 0.25; 0.5

0.20 0.20 0.087 0.125 0.125 0.125 0.243

sr

m

6 6

6 6 4 6 6 6 4

Quantity measured

Ud),d^ dsz ^32

dsz X{d),d3z

d32p (0 d32,(0

X(d),d32 X(d),d3z X{d),d^

dsz ^32

dsz

Model parameters

C/G 5.0 5.0 5.0 5.0 5.0 5.0 1.4 3.1 1.0 0.52 3.3 3.3 1.7

C2IO2

5.0 5.0 5.0 5.0 5.0 5.0

11.4 6.8 6.8 6.8 6.6 6.6 6.6

CslO^

7.5 8.0 8.5 8.0 5.0 3.0 6.9

15.1 1.4 0.68 6.0 6.0 2.0

Cs^ lO^

7.5 8.0 8.5 8.0 5.0 3.0 3.0

11.0 1.0 0.5 4.6 4.6 1.5

Sd%da2

6.8 3.6 0.9 2.2 2.4 9.2 7.3 8.3

19 40 21 13 8.6

m=6: six-blade turbine m=4: four-blade paddle

(1) Chen H.T. and Middleman S.,ALCkEJ. 1967,13,989. (2) Brown D.E. and Pitt K., Chem. EtigngSci. 1972,27,577. (3) Park J. Y. and Blair L.M., Chem. Engng Sci. 1975,30,1057. (4) Sprow F.B., Chem. Engng Sci. 1967,22,435. (5) Mlynek Y. and Resnick W., AI.Ch.E.J. 1972,18,122. (6) Vermeulen T., Williams G.M. and Langlois G.E., Chem. Engng Prog. 1955,51,85-F. (7) Brown D.E. and Pit K., Chem. Engng Sci. 1974 29 345. (8) Sprow F.B. ,A/.a.£. / . 1967,13,995.

Results

g(v)^CiV-'''ND'^^exp C20

Csciv'^^-^v'^^^Hv+v')' X2(vy) = exp

(o ~ N^^D^\pJat' = NWe'^'ipJaf

714 Chapter 7. Other subjacto ralat«d to multi-phas« systems

Notation A(d) Cit Czf C3, C5 C'3 = VCz

dsz D g(v) h(v,t/) m N Sd V

V W We Mv,i/) ^ P G

CD

Subscripts c d

frequency distribution of droplet size, 111? model parameter parameter of model Sauter diameter, L impeller diameter, L breakage frequency of drops having volume v^ 1/T collision frequency of drops having volumes v, if, 1/T number of impeller blades rotational frequency of impeller, 1/T mean deviation of diameter of drops, L drop volume, L volume of mixed vessel, L width of impeller blade, L Weber number, N^D^pdOt dimensionless efficiency of collision of drops with volumes v, tf viscosity, M/LT density, WV interfacial tension, M/T^ mean coalescence frequency, 1/T


7.5 Br»aluig» and coal«sc«nc« 725

Narsimhan, G., Nejfelt, G. and Ramkrishna, D., AIChE Journal, 30,457 (1984) Breakage Functions for Droplets in Agitated Liquid-Liquid Dispersions

Experimental apparatus Vessel Type: flat-bottomed Diameter: 0.13 m Height: 0.14 m Volume: 2 X10'^ m


Baffle Number: 4 Width: 0.013 m Length: 0.14 m Clearance of baffle from wall: 6.35 x 10" m

Impeller Type: six-blade turbine Diameter: 0.05 m Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 0.0125 m Off-bottom clearance: 0.03175 m

Working fluids Continuous phase: distilled water presaturated with dispersed phas Dispersed phase: (1) Chlorobenzene

(2) ecu + t-octane (0.5-0.5) (3)Anisole + e c u (0.8-0.2)

Experimental conditions Temperature: 300± IK Agitator speed: 5, 6.67 and 8.33 1/sec


Results \1.78

nv)jf^5.75We-[j,^

Notation L impeller diameter, m N agitator speed, 1/sec V droplet volume, m We Weber number, N'^Dpla, dimensionless r transitional breakage probability, 1/sec p density of continuous phase, kg/m' a interfacial tension, kg/msec

716 Chapter 7. Othmr subjects ralatod to multi-plMis« systems

Bapat, R M. and Tavlarides, L. L, AIChE Journal 31,659 (1985) Mass Transfer in a Liquid-Liquid CFSTR


Baffle Number: 4

Impeller Type: six-blade Rushton turbine Diameter: 51 mm Number of impellers: 1 Number of blades on impeller: 6

Working fluids and their physical properties Continuous phase: distilled water Dispersed phase: qrclohexane-carbon tetrachloride mixture Solute: iodine

Physical properties at 298.15 K

Liquid

Water Cyclohexane Carbontetrachloride Cyclohexane-Carbontetrachloride mixture

Density p, kg/m^

997 770

1,589 970

Viscosity //, Pas

0.00090 — —

0.00082

Inteifacial tension a.N/m

— 0.0468 0.0480 0.0471

Measurement technique Photomicrographic technique

Results

^(«i) = Ci (1+0)^?'

-exp -C2 or(l-H»)^ - ^2/3_5/3 Pd ^ di

1 + 0 (T^(l+0)%a,+«;,

Investigator

Hsia*(1981) Coulaloglou* (1975) Ross «/fl/.* (1978) This work

Breakage and coalescence constants

C,

0.01031 0.00487 0.00487 0.00481

C2

0.06354 0.0552 0.08 0.08

C3, cm

4.5 xlO-^ 2.17x10-^ 2.17 xlO-" 1.9 xlO"^

C4,cm-2

1.891 X10* 2.28 xlO* 3.0 xlO« 2.0 X10*

*As used by Hsia (1981). Hsia, M A and LL. Tavlarides, "A Simulation Model for Homogeneous Dispersions in Stirred Tanks",

Chem. Eng. / . , 20,225 (1980). Coulatoglou, C A , "Dispersed Phase Interactions in an Agitated Flow Vessel", PhD Thesis, RL Inst. Tech,, Chicago,

IL(1975). Cx>u]abglou, C A and L.L. Tavlarides, "Description of Interaction Processes in Agitated Liquid-Liquid

Dispersions", Chem. Eng. Set., 32,1289 (1977). Ross, S.L, F.H. Verhoff and R.L Curl, "Droplet Breakage and Coalescence Processes in an Agitated Dispersion. 2:

Measurement and Interpretation of Mixing Experiments", Ind. Eng. Chem. Fund., 17,101 (1978).

7.5 Brvakag* and coalaseance y^y

Notation a drop diameter, m Cb C2 constants in the breakage frequency function C3, C4 constants in the coalescence frequency function Fifli, aj) coalescence frequency between drops of diameters at and a> 1/sec gift) breakage frequency of a drop of diameter a, 1/sec e power dissipation per unit mass, mVsec^ /x dynamic viscosity, kg/msec p density, kg/m^ G interfacial tension, N/m 0 dispersed phase holdup fraction


718 Chapter 7. Othar subjaeto ralatod to multi-plias* systems

Wang, C. Y. and Calabrese, R. Y.,AIChE Journal, 32,667 (1986) Drop Breakup in Turbulent Stirred-Tank Contactors Part II: Relative Influence of \^scosity and Interfacial Tension

Experimental apparatus Vessel Type: (1)~(4) flat-bottomed Diameter: (1) 0.142 (2) 0.213 (3) 0.312 (4) 0.391 m

Liquid contained Height: (1) 0.142 (2) 0.213 (3) 0.312 (4) 0.391 m

Baffle Number: (1M4) 4 Width: (1)~(4) 7/10 Off-bottom clearance: 7/20 Clearance of baffle from wall: (1)~(4) T/30

Impeller Type: (l)--(4) six blade Rushton turbine Diameter: (1) 0.0711 (2) 0.1064 (3) 0.1562 (4) 0.1956 m Number of impellers: (1)~(4) 1 Number of blades on impeller: (1)^(4) 6 Length of impeller blade(perpendicular to shaft): (1)' (4) L/4 Width of impeller blade(parallel to shaft): (l)~(4)L/5 Off-bottom clearance: (1)~(4) T/2

Working fluids and their physical properties Continuous phase: (a) water (b) 25 % MeOH-H20 and (c) MeOH Dispersed phase: nine different silicone oils

Viscosities of dispersed phase (Pasec) saturated with continuous phase, 25°C

Dispersed phase, Sihcone oil

Nominal viscosity /ii,Pas

0.001 0.005 0.01 0.02

0.05 0.1 0.2 0.5 1.0

Continuous phase, aqueous methanol solutions (Nominal interfacial Tension, O"', N/m)

Water CT'= 0.045

0.00085 0.00428 0.00963 0.0182

0.0424 0.0908 0.185 0.459 1.040

25% MeOH-HzO* CT'= 0.023

0.00081 0.00410 0.00950 0.0174

0.0406 0.0876 0.178 0.406 1.005

Methanol CT'= 0.001

0.00949 0.0174

0.0406 0.0874 0.178 0.403 0.990

•Volume percent of methanol in water.

7.5 Br»akag« and coal«sc«nc« 719

Experimental conditions 1.4<iV<4.7rps 14,000 <i?^< 83,000 54 <FF6< 71,000 0.0041 < Ft < 640 Temperature: 25°C 0.001 < ju i< lPasec 0.001 <cr'< 0.045 N/m


Results For the low to modera te viscosity data

D: = 0.066 W^«-°-" 1+13 .8 7 t ° ^ M ^

Notation Dz2 Sauter mean diameter L impeller diameter N impeller speed Nvi {pclpif^'^iu^^'^DWo Re tank Reynolds number, pcNLV^ Vi tank Viscosity group, (pclpdf^^HdNLIa We tank Weber number, pcN ^LVo F average power input per unit mass or mean energy dissipation rate per unit mass jUr viscosity of continuous phase //</ viscosity of dispersed phase lj!d nominal dispersed-phase viscosity Pc densi ty of continuous phase Pd densi ty of dispersed phase a interfacial tension & nominal interfacial tension

720 Chapter 7. Other subjects ralat«d to multi-phas* systems

Nishikawa, M., Mori, E, Fujieda, S. and Kayama, T.,/. Chem Eng. Japan, 20, 454 (1987) Scale-up of Liquid-Liquid Phase Mixing Vessel




Impeller Type: Rushton-type turbine Diameter: 25 cm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 6.2 cm Width of impeller blade (parallel to shaft): 5.0 cm Off-bottom clearance: 25 cm

Working fluids Continuous phase: distilled water Dispersed phase: honeybees' wax

Experimental conditions Volumetric fraction of dispersed phase = 0.005—0.36


Results For breakup region

^ = 0.OdSN-M^\ 1+2.5-^ <t>"'\\^\ \^\ We'

For coalescence region r ^ \ l /2 1 / \ l /5 f xl/8

Notation d impeller diameter, cm 1 32 Sauter mean drop size, cm

D vessel diameter, cm Do reference vessel diameter, cm n impeller speed, 1/sec Np power number, Pip n^d^, dimensionless P agitation power, gcmVsec^ We' Weber number, n^d^p/a, dimensionless p^ continuous phase Hquid viscosity, g/cmsec Pd dispersed phase hquid viscosity, g/cmsec

(Pdlpc)c viscosity ratio (pc constant), dimensionless

(Pclpdh viscosity ratio (pd constant), dimensionless

p density, g/cm^ a inter£cicial tension, g/sec^ 0 volumetric fraction of

dispersed phase

7.5 Breakage and coalascanca 721

Das, P K., Kumar, R. and Ramkrishna, D., Chem. Eng. ScL, 42,213 (1987) Coalescence of Drops in Stirred Dispersion. A White Noise Model for Coalescence

Results Use of data reported by Madden and Damerell (1962)

K- = 0.11

10°

o-

J

JO-2

/ - ^

.•.-...^ <^«000ll « — (^-0.0055 -»• — ^•QOI I A

J -2.0 2.7 3.4 41 48

ImpeUtr speed, N (rps)

Plot of (Of vs iV with 0 as parameter.

55

Madden, A. J. and DamereU, C. UAIChE Journal, 8,233 (1962) Notation

D diameter of the impeller, cm N impeller speed, 1/sec Pr (Vy if) probability of coalescence between two drops of volume v and 1/ K constant pc density of continuous phase, g/w? G interfacial tension, g/cmsec 0 dispersed phase holdup fraction (Or coalescence rate, 1/sec

722 Chapter 7. Ofhmr subjects ralatad to multi-phass systems

Laso, M., Steiner, L. and Hartland, S., Chem. Eng. ScL, 42,2437 (1987) Dj^amic Simulation of Agitated Liquid-Liquid Dispersions^IL Experimental Determination of Breakage and Coalescence Rates in a Stirred Tank




Impeller Type: six flat blade turbine Diameter: 37 mm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 9 mm Width of impeller blade (parallel to shaft): 7 nun Off-bottom clearance: 37 nmi


Property (measured at 293 K)

Composition

Density Viscosity Interfacial tension

(with water) Contact angle of organic-aqueous interphase

With stainless With glass

Units

vol.%

kg/m^ kg/ms N/m

o

System 1

34.7 CCI4 65.3 «-heptane

1,001.0 0.627x10-^

0.0483

74 61

Dispersed phases

System 2

22.6 CCI4 77.4 1-octanol

999.0 8.439x10"^

0.0167

82 71

System 3

25.1 CCI4 74.9 MIBK

1,001.0 0.684x10-3

0.0185

115 103

Continuous phase

Water

998.2 1.002x10-3

—

— —


7.5 Br»«luig« and e(Mil«sc«iic« 723

Results

^ = 0.118 PTe^-^A'^-^' D

N

N

JL

= 4.04(10^) V we^''a+xr''''z-'

= 2.18(10-'°) D'

-OJSl vO-SO 7-O.OS We^^^X'^Z

Notation flf32 volume-surface diameter, L D impeller diameter, L K}* breakage rate constant, 1/T K' coalescence rate constant, LVT N agitator speed, 1/T V droplet volume, L^ Wv average interaction frequency, 1/T We tank Weber number, N^D^p/Oy dimensionless X holdup of dispersed phase Z Ohnesorge number, ^dlipoDy^, dimensionless IX viscosity, M / L T p liquid density, M / L^ a interface tension, M / T ^


724 Chapter 7. Othar subjects r»lat«d to multi-phasa systems

Das, E K., Ramkrishna, D. and Narsimhan, G.,AIChE Journal, 33,1899 (1987) Effect of Mass Transfer on Droplet Breakup in Stirred Liquid-Liqtiid Dispersions


Baffle Number: 4

Working fluids Continuous phase: 0.1 N KI aqueous solution Dispersed phase:chlorobenzene Transferring agent: iodine


Results

r(v)f£^ = 625We^'Hv/L'

Notation L impeller diameter, m N agitator speed, 1/sec V volume of droplet, m We Weber number, N^L^pc/a, dimensionless r transitional breakage probability, 1/sec p density of hquid phase, kg/w? G interfacial tension, kg/m sec


7.5 Breakage and coal«scmic« 725

Konno, M., Muto, T. and Saito, S.J. Chem. Eng. Japan, 21,335 (1988) Coalescence of Dispersed Drops in an Agitated Tank



Impeller Type: standard six-bladed disc turbine Diameter: 9.3 cm Number of impellers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): L/4 Width of impeller blade (parallel to shaft): L/5

Working fluids and their physical properties Continuous phase: distilled water containing a small amount of sodium chloride (0.1 moMi) Dispersed phase: a mixture of o-xylene and carbon tetrachloride

Phase Density iglcxc?) Viscosity (Pasec)

continuous 1.00 0.00069 dispersed 1.03 0.00089

Experimental conditions The initial impeller speed: 7 rps The reduced impeller speed: 2.3,2.7 and 3.5 rps Volume fraction of the dispersed phase: 0.01,0.02 and 0.05 Temperature: 25°C


Results kAvy) = 13.0«,(rf + rf0'(rf-^0'^'exp(-41.66n?-'^((/rf')'^')

Notation d, d' drop diameter, cm kc (v, v') coalescence frequency of drops with volumes v and v\ cmVsec L impeller diameter, m fir impeller speed, 1/sec


Chatzi, E. G. and Lee, J. M., Ind. Eng. Chem. Res., 26,2263 (1987) Analysis of Interactions for Liquid-Liquid Dispersions in Agitated Vessels

Experimental apparatus Vessel and impeller

System (1) (2)



Baffle Number

Impeller Type Diameter (cm) Number of impellers Number of blades on impeller

flat-bottomed 16

16

six-bladed flat turbine 7.6 1 6

flat-bottomed 29.2

29.2

4

six-bladed flat turbine 10.2

1 6

Working fluids and their physical properties Continuous phase: distilled water and 15% sucrose solution Dispersed phase: 5-cSt Dow Coming 200 fluid and kerosene

system

1 2 3

dispersed phase

5-cSt Dow Coming 200 fluid 5-cSt Dow Coming 200 fluid kerosene

continuous phase

water 15% sucrose solution


system

1 2 3

p, g/cm^

42.5 32.0 41.9

p, g/cm^

cont. disp.

1.000 0.920 1.087 0.920 1.000 0.787

/i, (dyns)/cm^

cont disp.

0.010 0.0460 0.020 0.0460 0.010 0.0169

Surfactant: hydroxypropyl methyl cellulose Experimental conditions

Temperature: 23°C Measurement technique

Microphotography

7.5 BrMikag* and coal«sc«iic« 727

Results Breakage frequency

.«,,.c..(|J%(---|^]

"*-«"ii]""(;;^'^ Cic

Coalescence efficiency

[2' p,n'D'^^d'"

__^ ^cPcfi^D^f dpidp2 1

a^ ydpi+dp2)

^(dpudp2)==exp — Civ a(d}i-^d'p2)(d'pi-^d'p2)

p.n'D'^'dUhidli'^dli')

Notation Ci, C'l, Cn, C'n, Civ, Civ parameters dp droplet diameter, cm D impeller diameter, cm g {dp) breakage frequency of drops of having drop diameter dp, 1/sec n impeller speed, 1/sec A (dpi, dp2) coalescence efficiency of drops of drop diameter dp\ with drops of drop

diameter dp2 jj, viscosity, dynsec/cm^ p density, g/cm^ a interfacial tension, dyn/cm

Subscript c continuous phase d dispersed phase

728 Chapter 7. Othar subjacto related to multi-phasa systems

Kumar, S., Kumar, R. and Gandhi, K. S., Chem. Eng. Sci., 46,2483 (1991) Alternative Mechanisms of Drop Breakage in Stirred Vessels

Experimental apparatus Vessel Diameter: 12.5 cm Height: 20 cm


Impeller Type: six-blade Rushton turbine Diameter: 5.7 cm Number of impeUers: 1 Number of blades on impeller: 6 Length of impeller blade (perpendicular to shaft): 1.5 cm

Working fluids and their physical properties Continuous phase: distilled water Dispersed phase: toluene Suifactant: sodium dodecyl sulphate (0.3% w/w)

Physical properties of the system

Density (kg/m ) Viscosity (kg/msec)

water toluene

1.0 xlO' 0.86 xlO^

1.0x10^ 5.5x10-*

Interfacial tension = 3.881 x 10" N/m

Results

^ = 0.125(1+4^)^-2 FF - -'

idnax)e =

(rfnox), =

Ca,a

25.32iV)Xe

COsCF

113.2iSr'-'ix°-' UVJ

= exp 2 5a4£,+£i(^^^s/3 4.0"/3)

(1)

(2)

(3)

(4)

0.2 0.A 0.6 0.6 1.0

Dispersed phase hold-up

Comparison of overall prediction with experimental data: (O) 5.5 ips, (D) 6.67 rps, (•) 7.83 rps, (A) 9.5 ips.

Notation Ca capillary number, Gfid/2a, dimensionless d drop size, m dnax maximum stable diameter, m D impeller diameter, m G strain rate, 1/sec L blade length, m N stirrer speed, 1/sec We Weber number, pN ^DVa, dimensionless /x viscosity, kg /msec

He emulsion viscosity, kg /msec p density, kg/w? a interfeidal tension, N/m 0 volume fraction of dispersed phase

Subscripts e elongational flow 5 shear flow

7.5 Breakage and coalescence 729

Tobin, T. and Ramkrishna, D.,AIChE Journal, 38,1199 (1992) Coalescence of Charged Droplets in Agitated Liquid-Liquid Dispersions

Experimental apparatus Vessel Type: flat-bottomed Diameter: 5 in Height: 6 in Volume: 2 £

Baffle Number: 4 Width: y2 in

Impeller Type: Rushton-type turbine Diameter: 2 in Number of impellers: 1 Number of blades on impeller: 6

Working fluids and their physical properties Continuous phase: deionized water Dispersed phase: 5% benzene-CCl4 Modifier of the ionic strength of the dispersions: NaCl pH adjuster of the dispersions: dilute HCl and NaOH solutions


Results

£ cooe

! M

T

It : if i»

i i • PH6.C

O P«?.0 • •

A pne.c —

H \ \

* J KL

a o.oo»~

100 200 300 400 500 C0C

Drop Diamttw (p/n)

+t

I

• PH 6.0

O PH7.0

A, PH6.0

ZK .. .raj * ? ? i • i b i ii tti

0 50 100 ISO 200 250 300 2S0 40C

Drop Diamotor (jim)

600 RPM steady-state results for 5% benzene/CCh 600 RPM steady-state results for 5% benzene/CCl4 in water (/=10~4 M). in water (/=10"2 M).

730 Chaptor 7. Oth«r subjects rolat«il to multi-phas« systems

C.01-

o

•

D

5

04

f 1

ii

t, l?i) i ^

i i 1 m omm. —

O lOmln. . . .

A aomin.

D SSrnm. — • •

^"1! • - * - ^ 3 1

0.016-q

C o 5 0.01 -

•

5 o

6

04

•

i TT

i f T 1

i I' IP t [}

1 1 t

• 0 mm. —

Q 10 nun. • •

A 30m*n. — ^

!

200 400 600 M O 1000 1200 1400

Drop OiamMar Oim) 200 400 600 000 1000 1200 1400

Drop Di8m«6r (fim)

800-200 RPM transient results for 5% benzene/CCh 800-200 RPM transient results for 5% benzene/CCh in water (7=10-* M). in water (7=10-=^ M).

OJ012-

c

9

•i : > c. O

01

^

1

^ f7lr,fa

1

if m \ . ' €

1 1 1 1 J •

1 ^

. O

OiMn. —— 1

Stnln. • • •

••• jk

D 100 2 0 0 3 0 0 4 0 0 5 0 0 i S 0 0 7 0 0 6 0 0 6 0 0 Drop DiamM6r (pn)

800-200 RPM transient results for 5% benzene/CCh in water (7=10-* M).

Notation I ionic strength, mol

7.5 Breakage and coalascance 73 ][

Wright, H. and Ramkrishna, D.,AIChE Journal, 40, 767 (1994) Factors Affecting Coalescence Frequency of Droplets in a Stirred Liquid-Liquid Dispersion

Experimental apparatus Vessel Type: flat-bottomed Diameter: 12.7 cm Volume: 2.4 i

Baffle Number 4 Width: 1.3 cm

Impeller Type: six-bladed Rushton impeller Diameter: 5 cm Number of impellers: 1 Number of blades on impeller: 6

Working fluids and their physical properties Continuous phase: water Dispersed phase: 83.9 mol% benzene /16.1 mol% carbon tetrachloride and acetophenone

System

Benzene/carbon tetrachloride (83.9 mol% benzene, 16.1 mol% carbon tetrachloride)

Acetophenone

Density g/cm^

1.074

1.028

Viscosity cP

0.7

1.6

Interfacial tension dyne/cm

35

17

Surfactant: 1% sodium dodecyl sulfate solution Experimental conditions

Dispersed-phase fraction: 0.01,0.05,0.10,0.15 and 0.25 Measurement technique

Computerized image analysis Results

K(vy) = 3.72 X10- (!>'*'NS^iv'"' + v''^')

Notation K{v, v') coalescence frequency of drops with volumes v and v\ iLVsec Nz final impeller speed, 1/min V droplet volume, iL 0 dispersed-phase fraction

733

Chapter 8. Gas-inducing mechanically agitated systems

Martin, G. Q., Ind. Eng. Process Des. Dev., 11,397 (1972) Gas-Inducing Agitator



Experimental conditions Impeller rotational speed: 200'-'360 rpm

Results Gas-induced rate through orifice

v n i / 2

Q^CoAoKi 2g(-k i^] -0.00085^1

Notation Ao area of orifice, ft^ Co conventional orifice coefficient, dimensionless g acceleration due to gravity, ft/sec^ h, liquid head outside orifice when no gas is allowed to flow, ft Ki experimentally determined constant indicating deviation between pressure driving force

across orifice with gas flow from driving force without gas flow, ftVsec Q gas flow rate through orifice, ft^/sec PG gas density, Ibm/ft^ pL hquid density, Ibm/ft^

734 Chapter 8. Gas-inducing machanicaiiy agitatad systems

Joshi, J. B. and Sharma, M. M., Can. J. ofChem. Eng., 55,683 (1977) Mass Transfer and Hydrodynamic Characteristics of Gas Inducing lype of Agitated Contactors

Experimental apparatus Vessel Type: frat-bottomed Diameter: (1) 0.41 (2) 0.57 (3) 1.0 m

Impeller Type: pipe impeller and flattened cylindrical impeller

Survey of design variables studied (/fe = 0,5 = Z)/6,^/r=1.0)

(A) Pipe impeller

Set-up

A B C D E F G H I

Vessel diameter r,(m)

0.41 0.41 0.41 0.41 0.57 0.57 0.57 0.57 1.0

Impeller diameter A(m)

0.2 0.25 0.25 0.25 0.2 0.3 0.38 0.43 0.5

Diameter of impeller pipe A, (m)

0.0318 0.0254 0.0318 0.038 0.0318 0.0318 0.0318 0.0318 0.0318

Number of pipes

2 2

2,4,6 2 2 2 2 2 2

(B) Flattened cylindrical impeller

Set-up

J K L M

Vessel diameter

r,(m)

0.41 0.57 0.57 1.0

ImpeUer diameter A(m)

0.25 0.25 0.395 0.395

Total orifice area on one Blade width impeller blade

WAm)

0.032 0.032 0.05 0.05

i4o, (mm^)

0.5,4.5,12.6,25.2 1 0.5,4.5,25.2

0.5,1.2,4.5,12.6,37.8,63,113.4 4.5,113.4

735

r-®

®A

OH

ys>

®

0H

1.

h<D

.®

I r-

Gas inducing type of agitated contactor: ® Vessel; ® Hollow shaft; (3) Hollow impeller; ® Baffles; © Stator body and seals; @ Orifice on the impeller; ® Gas inlet; ® Bearing housing; ® Pulley; ® Liquid drain.

Working fluids Liquid: aqueous alkaline solutions of sodium dithionite (concentration = 1 kmol/m^) Gas: air

736 Chapter 8. Gas-inducing maclianicaliy agitatad systen

Results (1) Power consumption

P'ND' QOM

(2) Minimum impeller speed at which gas induction occurs

PiVln

"" nOi P'

REYNOLDS NUMBER

Effect of impeller Reynolds number on the values of P'

737

(3) Gas holdup, interfacial area and mass transfer coefficient 0.41<r<1.0, 0.35<Z)/r<0.75, 0.1Z)<5<0.33A HB<0.5T, 3 < AT < 11.7, 0.0003 < 7c < 0.032, the following correlations hold:

a oc iPc /Vf'VS^ for VG < 0.005 aoc (PG /Vf'VS'^ for VG > 0.005

kia oc (PG / Vf^ VS^ for VG < 0.005 ha oc (PG /Vf^VS^ for VG > 0.005

Notation a effective interfacial area per unit clear liquid volume due to surface aeration, mVm^ Ao total cross-sectional area of orifices on one impeller blade, m^ B diameter of impeller from tank bottom, m di diameter of impeller pipe, m D impeller diameter, m g acceleration due to gravity, m/sec^ HB distance of baffle from tank bottom, m HL liquid height above orifice, m Hi static pressure (gauge) on impeller in absence of gas induction, Pa kua liquid side mass transfer coefficient, 1/sec N impeller speed, 1/sec NM minimum impeller speed for onset of gas induction, 1/sec P power consumption in absence of gas, W PG power consumption in gas-hquid dispersions, W P' constant Q rate of gas induction, mVsec T vessel diameter, m Vr impeller tip speed, m/sec VG superficial gas velocity, m/sec W width of flattened cylindrical impeller or turbine impeller, m a constant e average fractional gas-hold-up PL liquid density, kg/m^ ^L hquid viscosity, Pasec

738 Chapter 8. Gas-inducing machanically agitatad systems

Zundelevich, Y.,AIChE. Journal, 25,763 (1979) Power Consumption and Gas Capacity of Self-Inducing Turbo Aerators


Self-inducting aerator principle design (type 1): (1) standpipe, (2) stator, (3) stator blades, (4) rotor blades, (5) rotor.

A-A

Self-inducting aerator principle design (type 2): (1) standpipe, (2) stator, (3) stator blades, (4) rotor blades, (5) upper hollow disk, (6) lower hollow disk, (7) central disk.

739

p°t - T — w-Shaft

Gas

Liquid On

Liquid level

S ^ ^ ^ F ^ I FuL

Ds

Comparative geometry of water jet injector (top sketch) and self-inducting aerator (bottom sketch).

D/T Do Ds ho hs Zs

Design (a) 0.25 0.50 0.6D 1.4D 0.22D 0.1D Q.2D 6 12 30deg Design (b) 0.20,0.25,0.30 0.67D 0.5D 1.25Z) 0.24D 0.12D 0.12D 8 12 30deg


Results

G />

; [77 £wG V ^ « C > ^ _ gH tf,psi7 ' ~"~(ND)2

Notation D Ds C„

EuG

g h hs H N NP

P

aerator's rotor diameter, m aerator's stator diameter, m head coefficient, gH/QJD?, dimensionless gas Euler number, gH/(QG/D 2f, dimensionless gravitational acceleration, m/sec2

rotor blade width, m stator blade width, m aerator submergence, m aerator rotational speed, 1/sec power number, P/pN3D5, dimensionless mechanical agitation pom rer,W

JB- - gH t EA

PN

Po

Qc QL T Z Zs a

r\

P

" (QG/D2)2

pressure of the working liquid (at the nozzle outlet), kg/m sec2

gas pressure at the injector inlet, kg/msec2

aerator gas capacity, m3/sec impeller pumping capacity, m3/sec tank diameter, m rotor blades number, dimensionless stator blades number, dimensionless angle between radius and stator blade, degree impeller pumping capacity, QL/ND3, dimensionless liquid density, kg/m3

740 Chapter 8. Gas-inducing maclianieaily agitatad systems

Sawant, S. B. and Joshi, J. B., Chem. Eng.J., 18,87 (1979) Critical Impeller Speed for the Onset of Gas Induction in Gas-Inducing Types of Agitated Contactors

Experimental apparatus Vessel, impeller dimensions, and systems studied

(1) Air-water systems

Type of impeller r(mm) D(mm) HIT Nrirey/s)

Pipe impeller (two pipes)

Pipe impeller (four pipes)

Flattened cylindrical impeller (angle of attack = 30**)

Cylindrical impeller with single orifice (angle of attack = 30°)

Covered turbine impeller Trianguku: impeller

Flotation cell (Denver type)

Flotation cell (Wemco type)

Twelve-bladed shrouded turbine (covered with stator)

410 410 570 570 570 570

1,000 570 570 410 134 275 410 570

1,000 275

134 134 268

100 m m square 140 m m square 172 m m square

300 (conical bottom)

290

200 250 200 300 380 450 500 300 300 250 60 200 250 395 395 200

60 60 120 70 97 115 50

56

0.88 0.88 0.91 0.91 0.91 0.82 0.88 0.70 0.50 0.91 0.70 0.73 0.88 0.88 0.88 0.73

0.7 0.7 0.7 0.9 0.89 0.94 0.28

0.3 to 0.63

4.3 3.8 5.9 3.5 2.8 2.0 2.4 2.92 2.53 3.65 8.33 3.1 3.15 2.4 3.15 3.3

8.33 9.17 6.50 6.67 5.42 5.0 7.67

(2) Air-water + polyethylene glycol systems

Type of impeller T'(mm) Z)(mm) H/T /x(mPas) Ndrew/s)

Flotation cell (Denver type) 100 mm square

Flotation cell (Wemco type)

140 nun square

300

70

97

50

0.9

0.89

0.012

17.6 26.4 44.0 80.0 17.6 26.4 44.0 80.0 17.6 26.4 44.0 82.0

7.0 7.5 7.8 8.0 5.8 6.0 6.5 6.8 6.2 6.8 7.0 7.6

741

Results

u I • =^-21

Notat ion Z) impeller diameter, mm g acceleration due to gravity, mm/sec^ H liquid height above the impeller, m m Nr critical or minimum impeller speed for the onset of gas induction, 1/sec fXw viscosity of water , m P a s e c /x viscosity of liquid, m P a s e c

742 Chapter 8. Gas-inducing maclianically agitatad systems

Saravanan, K., Mundale, V D. and Joshi, J. B., Ind. Eng. Chem. Res., 33,2226

(1994) Gas Inducing Type Mechanically Agitated Contactors

Experimental apparatus Vessel, impeller, and stator dimensions Vessel Diameter: 0.57,1.0 and 1.5 m

Impeller and stator

unit

impeller nominal diam, m Anrni W,mm

stator A, nmi Wsy mm hsf mm

1

19 0.19

186.5 40.5

260 34 44

2

22 0.22

224.5 43.2

315 40 52

3

33 0.33

327.0 65.5

466 60 77

4

40 0.40

390.0 81.5

560 72 92

5

50 0.550

495.0 104.0

700 90

115

•5 mm thic)( vanes 12 00


743


Summary of condition for runs during gas induction

nmemomc

5,719 5,719 1,019 1,022 1,033 1,519 1,522 1,533 1,540 1,550

Cm 0.095/0.285 0.095/0.285 0.160/0.500 0.160/0.500 0.090/0.500 0.500/0.750 0.500/0.750 0.500/0.750 0.500/0.750 0.500/0.750

min/max

S,m

0.150/0.600 0.150/0.600 0.150/0.600 0.150/0.600 0.150/0.600 0.150/0.600 0.150/0.600 0.150/0.600 0.150/0.600 0.150/0.600

values

N,T/S

4.8/12.8 3.4/8.60 4.5/7.30 3.5/7.80 2.2/7.80 3.2/9.80 2.7/9.10 2.2/7.80 1.7/4.40 1.4/3.30

Qg, nL/s

0.5/7.800 0.96/13.6 1.1/7.300 1.0/16.30 1.0/33.30 0.8/7.900 0.9/12.30 1.0/10.30 1.27/19.4 1.42/20.3

Temperature: 30 ±3°C Results

(1) Critical impeller speed for gas induction For 5 > 0.20, C> 0.25 m, 0.19 < Z) ^ 0.50 m,

0.57 < r ^ 1.5 m and 0.12 <D/T< 0.59

K = 2nR 2gMS-a,)

0, = 1.065 /;2= 0.00342 m' fl,= 0.0394 m

(2) Gas inducing rate

For 0.20 < 5 < 0.75 m, C > 0.145 m, for D <. 0.22 m, 0.01 <2gS/V^< 1.16, 0.124 <D/T< 0.394, 0.19</)<0.50m, 0.57<7<1.5m and 0> 1.0nL/s

XNR^ h(^] 2

-I* = 169.37 mm / ; = 58.28 mm

A7;''= 0.574 0, = 1.101

X/4>, --= 153.781 nm

2g{SU-a,)\

744 Chapter 8. Gas-imlucing machanically agttatad systams

Notation a submergence correction at impeller periphery, m C impeller clearance from bottom, m D impeller diameter, m / conformity factor g gravitational acceleration, m/sec^ / ineffective radius at impeller eye for gas induction process, m N impeUer rotational speed, 1/sec 0 volumetric flow rate, mVsec Qg gas induction rate, mVsec R impeller radius, m 5 submergence of impeller in clear liquid, m T tank diameter, m V impeUer tip velocity, m/sec A gas induction modulus, mm 0 vortexting constant of PTD design, dimensionless

Subscripts c critical state for gas induction g gas, gassed state sp stand pipe

Superscript * scaled parameter

745

Aldrich, C. and van Deventer, J. S. J., Can. J. ofChem. Eng., 73,808 (1995) Modelling of Induced Aeration in Turbine Aerators by Use of Radial Basis Function Neural Networks

Experimental apparatus Vessel Type: flat-bottomed Diameter: 190 mm Volume: 6 i



Impeller

Type Diameter (mm) Number of impeller Number of blades on impeller Disk diameter (mm) Width of blade (parallel to shaft)

six-bladed Rushton (T6) 50 1 6

28 44

twelve-bladed turbine (T12) 57 1

12 36 63

Draft tube

Type Outer diameter (mm) Imier diameter (mm) Slot Size (mm)

Number Space

cylindrical (S80) 80 74

4x64 16

evenly spaced

cylindrical (SlOO) 100 94

4x64 16

evenly spaced


Physical properties of aerated liquids.

Liquid p(kg/m^) /i(mPas) a(mN/m)

Tap water 25% w/w Brine solution 5% w/w Aqueous isopropanol solution 7% w/w Aqueous sucrose solution

25% w/w Aqueous sucrose solution 35% w/w Aqueous sucrose solution 40% w/w Aqueous sucrose solution 49% w/w Aqueous sucrose solution 55% w/w Aqueous sucrose solution 63% w/w Aqueous sucrose solution 95% w/w Aqueous ethanol solution

997 1,190

980 1,026 1,100 1,136 1,176 1,217 1,270 1,304

803

1 2.2 1.90 1.30 2.6 4.10 6.48

16.0 38.7 60 1.38

73 81 37 73 74 75 75 76 76 77 28

746 Chapter 8. Gas-inducing maeiianically agitated systems

Results (1) Critical Froude number

For the six-bkded impeller (T6) N 0.103/ . \ 0.938

Fr.=0.075|-^

For the twelve-bladed impeller (T12) X 0.103/ x0570

^ . = 0 . 1 3 0 ^ j

(2) Rate of induced aeration

Ae=:C(Fr'-Fny'e'"^''-''''\

UJ UJ with a i = 0.616, fl2 =0.178, « 3 = 0.735, ^ 4 = 0.501,

fls = 0.129, fle = 0.268, J7 = 0.268, a^ = 0.302 and C = 45.39

Notation Oi vector of multivariate regression parameters Ae aeration number, QINd^, dimensionless C parameter d impeller diameter, m Fr Froude number, NM^I^, dimensionless Ftc critical Froude number, N?dV^, dimensionless g gravitational acceleration, m/sec^ h impeller submersion depth, m N impeller speed, 1/sec Nc critical impeller speed, 1/sec Q ra te of induced aeration, mVsec T diameter of agitated vessel, m /x viscosity of liquid, m P ^ s e c jUu, viscosity of water, m P a s e c p density, kg/m^ pw density of water, kg/m^ a surface tension, N / m

747

AI Taweel, A. M. and Cheng, Y. H., lyans. Instn. Chem. Engrs., 73, Part A, 654 (1995) Effect of Surface Tension on Gas/Liquid Contacting in a Mechanically-Agitated Tank with Stator

Experimental apparatus Vessel Type: flat-bottomed Dimension: 19 x 19 cm rectangular Height: 25 cm Volume: 10 £

Liquid contained Aerated liquid height: 23 cm

Stator Inner diameter: 12.7 cm Number of bafQes in stator: 12 Standpipe diameter: 4.6 cm

Impeller Type: 8-blade Rushton-type Diameter: 9.6 cm Number of impeller: 1 Number of blades on impeller: 8 Height of impeller blade: 1.9 cm Width of impeller blade: 1.7 cm (M-bottom clearance: 1.5 cm Number of recirculation holes: 4 Diameter of recirculation hole: 0.8 cm

Working fluids Liquid: water containing small quantities (0—40 ppm) of propylene glycol methyl ether Gas: air

Results (1) Gas holdup

(a) the rapidly-coalescent airA^ater system

(b) the additive-containing systems

ec; = 10"-'7V'- OS- (T-"* 750^;\r< 1,500rpm, 2^0G^12^/min 72.7 <(T^ 68.8 mN/m 5<a<40ppm

(2) Interfacial area (a) the rapidly-coalescent air/water system

748 Chapter 8. Gas-inclueiiig maehaiiically agitatad systams

(b) the additive-containing systems

750^iV^ 1,500rpm, 2<Oc^l2^/min 72.7^a^68.8mN/m 5^C^40ppm

Notation a specific interfacial area, 1/m C concentration, ppm N impeller speed, 1/min 0 volumetric flowrate, mVsec or ^/min e gas holdup and local energy dissipation rate G surface tension, mN/m

Subscripts a additive G gas or gassed

749

Saravanan, K. and Joshi, J. B.Jnd. Eng. Chem. Res., 34,2499 (1995) Gas-Inducing-iype Mechanically Agitated Contactors: Hydrodynamic Characteristics of Multiple Impellers


System

Vessel Type Diameter (m) Liquid height (m)


Impeller Type

D/T

W/D B^ (degree)

Ci(m)

C3(m) Sim)

(1)


4 T/10

(2)


4 r/10

(3)


4 r/10

PBTD, PBTU, DT, SBT, PU and PD

0.25-0.33

0.20-0.40 30-90

r/i.5-r/6

0.175-0.45 0.15-1.00

0.19-0.33

0.20-0.40 30-90

r/2-r/io

0.175-0.45 0.15-1.00

0.13-0.33

0.20-0.40 30-90

r/3-r/8

0.175-0.45 0.15-1.00

PBTD: pitched-blade down flow turbine PBTU: pitched-blade upflow turbine DT: disk turbine SBT: straight-blade turbine PU: upflow propeller PD: downflow propeller

750 Chapter 8. Gas-inducing maclianically agitatad systems

List of impellers studied

impeller type

PBTD

PBTU

DT PU

PD

no. of blades (nd)

6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 3 3 3 3 3 3 3

blade width ^(m) 0.057 0.068 0.099 0.120 0.150 0.068 0.068 0.057 0.068 0.099 0.068 0.068 0.068 0.120 0.150 0.045 0.068 0.090 0.045

proj blade width Wp(m)

0.048 0.056 0.080 0.100 0.125 0.056 0.056 0.048 0.056 0.080 0.056 0.056 0.056 0.100 0.125 0.056 0.056 0.056

blade angle B^jdeg)

45 45 45 45 45 30 60 45 45 45 30 60 90 45 45 45 45 45

0.056 ^

impeller diam Dim) 0.190 0.225 0.330 0.400 0.500 0.225 0.225 0.190 0.225 0.330 0.225 0.225 0.225 0.400 0.500 0.225 0.225 0.225 0.225 0.190 0.225 0.330 0.380 0.420 0.500 0.225

"Disk diameter.

1 Smm thicic vonts 12no

Various components of the stator rotor system for gas-inducing impeller.

751


Experimental conditions Impeller speed: 0.30—15.45 rps

Results (1) Critical impeller speed for gas induction

0.15m<5< 1.0m, or 0.10<5/7< 1.4, Ci>0.16m, 0.17 m<C3< 0.45 m for Z): 0.19 m, and 0.28 <Ci/Z)< 2.63, 0.34 <C3/Z)<2.36, 0.01, 0.124 <Z)/r< 0.50, 0.19 < Z) < 0.50 m, 0.57 < T < 1.5 m 0 = 0.935 for PBTD-PU 0 = 0.944 for PBTD-PBTU

(2) Rate of gas induction

[ 07^ J

impeller

single PBTD PBTD-PU PBTD-PBTU BTD-PBTD PBTD-PD PBTD-SBT PBTD-DT

data point

860 1,326

845 342 312 295 295

A'

129.95 133.64 131.42 126.87 127.43 125.10 123.88

a

92.42 273.48 212.21 86.88 90.32 76.77 72.88

A

0.30 0.35 0.35 0.30 0.30 0.25 0.25

0 0.85 0.90 0.90 0.85 0.85 0.85 0.85

0.15m<5< 1.0m, or 0.10<5/r<1.4, Ci>0.16m, 0.17m<C3<0.45m for Z)<0.19m, and 0.28<Ci/Z)<2.63, 0.34 <C3/Z)< 2.36, 0.01 < 2^5 /7 '< 1.06, 0.124 <Z)/r< 0.50, 0.19 <D< 0.50 m, 0.57 < T < 1.5 m, QG > 1.0 nL/s (normal liters per second.)

Notation A

Ci

proportionality constant impeller blade angle to horizontal, degree lower impeller clearance form tank bottom, m (distance between impeller center plane and the bottom)

C3 impeller clearance, m, (center to center distance between two impellers)

D impeller diameter, m g gravitational acceleration, m/sec^ N impeller rotational speed, 1/sec NcG critical impeller speed for gas induction, 1/sec QG gas-induction rate, nL/sec

R S

T V W a X 0

impeller center radius, m submergence of upper impeller in clear liquid, m vessel diameter, m impeller tip velocity, m/sec actual blade width, m gas pumping constant gas induction modulus, nmi vortexing constant, dimensionless

Superscript * scaled parameters

752 Chapter 8. Gas-inducing maciianicaliy agitatad systems

Saravanan, K., Mundale, V D., Pfeitwardhan, A. W. and Joshi, J. B., Ind. Eng.

Chem. Res., 35,1583 (1996)

Power Consumption in Gas-Inducing-iype Mechanically Agitated

Contactors

Experimental apparatus Vessel, impeller, and stator dimensions Vessel

Diameter: 0.57,1.0 and 1.5 m Impeller and stator

unit

impeller nominal diam, m A mm W.mm

stator A, nmi Ws, mm hs, mm

1

19 0.19

186.5 40.5

260 34 44

2

22 0.22

224.5 43.2

315 40 52

3

33 0.33

327.0 65.5

466 60 77

4

40 0.40

390.0 81.5

560 72 92

5

50 0.550

495.0 104.0

700 90

115

-.-(t^.-•5 mm thic|(

vanes 12 no

753


Experimental conditions Summary of conditions for runs during gas induction''

A: Single impeller system

mnemonic Ci(m) 5(m) iV(rotations/s) P(w)

5,719 5,722 1,019 1,022 1,033 1,519 1,522 1,533 1,540 1,550

0.095/0.285 0.095/0.285 0.16/0.50 0.16/0.50 0.16/0.50 0.5/0.75 0.5/0.75 0.5/0.75 0.5/0.75 0.5/0.75

0.15/0.80 0.15/0.80 0.15/0.60 0.15/0.80 0.15/1.00 0.15/0.60 0.15/0.60 0.15/1.00 0.15/1.00 0.15/1.00

4.8/14.5 3.4/9.60 4.5/12.3 3.5/10.8 2.2/9.80 3.2/9.80 2.8/8.10 2.2/7.80 1.7/4.40 1.4/3.33

20/760 20/1,070 20/920 20/1,120 50/1,450

60/840 45/1,350 60/1,500 45/1,450

B: Multiple impeller system

nmemonic

5,719 5,722 1,019 1,022 1,033 1,519 1,522 1,533 1,540 1,550

Ci(m)

0.095/0.285 0.095/0.285 0.16/0.50 0.16/0.50 0.10/0.45 0.38/0.50 0.38/0.50 0.38/0.50 0.38/0.50 0.38/0.50

Csim)

0.17/0.45 0.17/0.45 0.17/0.45 0.17/0.45 0.17/0.45 0.17/0.45 0.17/0.45 0.17/0.45 0.17/0.45 0.17/0.45

5(m)

0.15/0.80 0.15/0.80 0.15/0.80 0.15/0.80 0.15/1.00 0.15/1.00 0.15/1.00 0.15/1.00 0.15/1.00 0.15/1.00

iV^(rotations/s)

5.2/11.62 4.6/9.89 4.5/10.12 3.5/9.75 2.2/8.70 4.9/9.10 4.5/9.10 1.8/6.70 1.7/4.80 1.4/3.30

P(w)

30/1,130 47/1,370 20/1,020 20/1,445 50/1,650

60/840 38/1,350 60/1,550 45/1,730

" Infonnation given as min/max values.

754 Chapter 8. Gas-inducing maclianieaiiy agitatad systams

Results For single impeller system

P-(rr,)(2nN)

C i o = 22.24

= CDO — CDY 1 -

T^= 1.767 Nm 0,=O.84 C;,K=6.71

For multiple impeller system

C*Do - a

Value of various constants for single and multiple impeller systems in the absence of gas induction

impeller combination CD NP

single PBTD PBTD-PBTD PBTD-PBTU PBTD-SBT PBTD~DT PBTD~PD PBTD~PU

80.33 147.27 153.90 307.98 384.44 93.77 86.66

1.12 2.44 2.23 4.67 5.84 1.41 1.26

Value of various constants for single and multiple impeller systems in the presence of gas induction'

impeller combination Xrg CDC CDY

single PBTD PBTD-PBTD PBTD-PBTU PBTD-SBT PBTD-DT PBTD-PD PBTD-PU

1.767 0.762 0.390 0.789 0.927 0.485 0.15

0.841 0.871 0.865 0.865 0.853 0.902 0.849

22.24 47.92 43.21

111.62 146.45

9.11 8.20

6.71 14.09 13.18 27.56 34.87 3.04 2.75

38.87 35.48

7.12

0.65 0.62

0.56

'Upper impeller is PBTD in all cases. PBTD: pitched-blade down flow turbine PBTU: pitched-blade upflow turbine DT: disk turbine

Notation a constant b constant Ci impeUer clearance from tank bottom, m Cs interimpeller clearance, m CDI CDOI CDY drag coefficient D impeller diameter, m F drag force on impeller, N N impeUer rotational speed, Hz Np power number, P/pN^D^, dimensionless P power consumption, W R impeller radius, m

SBT: straight-blade turbine PU: upflow propeller PD: downflow propeller

5 impeller submergence in ungassed liquid, m

W vertical projected width of impeller, m

p density, kg/w? Xrg torque 05 vortexing constants,

dimensionless

Superscript * scaled parameter

755

Saravanan, K. and Joshi, J. B., Can. J. ofChem. Eng., 74,16 (1996) Fractional Gas Hold-up in Gas Inducing IVpe of Mechanically Agitated Contactors


System

Vessel Type Diameter (m) Liquid height (m)


Impeller Type

D/T

W/D B^ (degree)

Ci(m)

C3(m) 5(m)

(1)


4 r/10

(2)


4 r/10

(3)


4 r/10

PBTD, PBTU, DT, SBT, PU and PD

0.25-0.33

0.20-0.40 30-90

r/i.5-r/6

0.175-0.45 0.15-0.70

0.19-0.33

0.20-0.40 30-90

r/2-r/io

0.175-0.45 0.15-0.70

0.13-0.33

0.20-0.40 30-90

r/3-r/6

0.175-0.45 0.15-0.70

PBTD: pitched-blade down flow turbine PBTU: pitched-blade upflow turbine DT: disk turbine SBT: straight-blade turbine PU: upflow propeller PD: downflow propeller

756 Chapter 8. Gas-inducing machanically agitatad systems

List of impellers studied

impeller type

PBTD

PBTU

DT PU

PD

no. of blades (nd)

6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 3 3 3 3 3 3 3

blade width W(m) 0.057 0.068 0.099 0.120 0.150 0.057 0.068 0.099 0.068 0.068 0.068 0.120 0.150 0.045 0.068 0.090 0.045

proj. blade width Wp(m)

0.048 0.056 0.080 0.100 0.125 0.048 0.056 0.080 0.056 0.056 0.056 0.100 0.125 0.056 0.056 0.056

blade angle B^deg)

45 45 45 45 45 45 45 45 30 60 90 45 45 45 45 45 0.056-

impeller diam Dim) 0.190 0.225 0.330 0.400 0.500 0.190 0.225 0.330 0.225 0.225 0.225 0.400 0.500 0.225 0.225 0.225 0.225 0.190 0.225 0.330 0.380 0.420 0.500 0.225

"Disk diameter.

1 Smm thick vonts 12na

3cr ;

H - j^

cutw. ^1 4 I I, 25! J

Various components of the stator rotor system for gas-inducing impeller.

757


Experimental conditions Impeller speed: 0.30—15.45 rpm Temperature: 30°C

Results (1) Gas holdup

c = fl — '^N^Qop.^

^g

Impeller No. of data point

single PBTD PBTD-PBTD PBTD-PD PBTD-SBT PBTD-DT PBTD-PBTU PBTD-PU

860 342 312 295 295 845

1,326

0.00267 0.00261 0.00269 0.00258 0.00251 0.00283 0.00246

1.63 1.66 1.61 1.92 2.01 1.35 1.32

0.48 0.47 0.48 0.39 0.37 0.47 0.52

0.15<5< 1.0, or 0.10<5/7< 1.4, Ci>0.16; 0.17 <C3< 0.45 for Z)<0.19 and Ci/Z)<2.63, 0.34 < Ca < 2.36; 0.01 < 2gS/V^ < 1.06; 0.124<Z)/r<0.5; 0.19<Z)<0.50; 0.57<r<1.5


1-A [2gS\

impeller

single PBTD PBTD-PU PBTD-PBTU PBTD-PBTD PBTD-PD PBTD-DBT PBTD-DT

r 129.95 133.64 131.42 126.87 127.43 125.10 123.88

• a

92.42 273.48 212.21 86.88 90.32

nm 72.88

A

0.30 0.35 0.35 0.30 0.30 0.25 0.25

0 0.85 0.90 0.90 0.85 0.85 0.85 0.85

Notation a, b, c constants A proportionality constant B^ impeller blade angle to horizontal, degree Ci lower impeller clearance form tank bottom (distance between impeller center plane and

the bottom), m Cz impeller clearance (center to center distance between two impellers), m D impeller diameter, m g gravitational acceleration, m/sec^ N impeller rotational speed, 1/sec QG value of gas-induction, mVsec R impeller center radius, m

y53 Chapter 8. Gas-inducing maciianically agitetad systems

s T V w a BG

J^ A Pi 0

submergence of upper impeller in clear liquid, m vessel diameter, m impeller tip velocity, m/sec blade width, m gas pumping constant fractional gas holdup, dimensionless viscosity, kg/msec gas induction modulus, mm density of liquid, kg/m^ vortexing constant, dimensionless

Superscript * scaled parameters

759

Pitwardhan, A. W and Joshi, J. B., Ind. Eng. Chem. Res., 36,3904 (1997) Hydrodynamics of a Stirred Vessel Equipped with a Gas-Inducing Impeller



Impeller and sparger Impeller

Position

Type Diameter (m) Distance from the bottom (m)

upper (gas inducing impeller)

PBTD 0.5 0.8

lower

PU, PBTU, PBTD 0.5 —

PBTD: pitched blade downflow turbine PBTU: pitched blade upflow turbine PU: upflow propeller

UNREACTED GAS

INDUCED GAS

- I — SR^RGED GAS

STANOPIPE

STATOR

IMPELLERS

SPARGER

Schematic of a mechanically agitated gas-liquid reactor equipped with a gas-inducing impeUer.

Sparger Diameter: 0.4 and 1.0 m Hole diameter: 3 nrni Number of holes: 168

760 Chapter 8. Gas-inducing maciianicMily agitated systems

Location of impellers and sparger

set no.

1 2 3 4 5

sparger size (m)

1.00 0.40 0.40 0.40 1.00

distance biw sparger and lower impeUer

0.38 0.38 0.15 0.15 0.15

(m) interimpeUer clearance (m)

0.30 0.30 0.30 0.52 0.52


Experimental conditions Superficial velocity of sparged gas: 0,6,18 and 29 nun/sec

Results The following relationships are valid for

r = 1.5m, Z> = 0.5m, 03//) = 0.6-1.0, V =0-29mm/s, iV = l-3rps, 5 /7 = 0.0-0.47, Fr = 0.03-0.45, i?« = 2xl0^to7.5xl0^ i7 = 0.05-0.13 and FL = 0.2-0.5

(1) Critical impeller speed for gas induction 2

tkNcG = NcG in the persence of sparging - NQG in the absence of sparging

(ANcG)'7t'D'(l>_^ (C^_ 2gS \D fl

sparger and impeller type a\ (s/m)*" az 0L2 (Xi

1.0, PBTD-PBTU 0.127 -0.895 1.226 -1.598 0.4, PBTD-PBTU 36.26 0.409 1.305 effect of 5/7 not studied 1.0, PBTD-PBTD 6.37 -2.55 2.048 -1.873 0.4, PBTD-PBTD 40.56 -1.01 0.937 effect of 5 / r not studied


QG, without sporsinc •XNR- -^M + Saravanan, K. and Joshi, J. B., Ind. Eng. Chem. Res., 34,2499 (1995)

impeller data point r a single PBTD PBTD-PU PBTD-PBTU BTD-PBTD PBTD-PD PBTD-SBT PBTD-DT

860 1,326

845 342 312 295 295

129.95 133.64 131.42 126.87 127.43 125.10 123.88

92.42 273.48 212.21 86.88 90.32 76.77 72.88

0.30 0.35 0.35 0.30 0.30 0.25 0.25

0.85 0.90 0.90 0.85 0.85 0.85 0.85

761

0.15m<5< 1.0m, or 0.10<5/7< 1.4, Ci>0.16m, 0.17 m<C3< 0.45 m for Z)< 0.19 m, and 0.28 <Ci/Z)< 2.63,

0.34<C3/Z)<2.36, 0.01 <2^5/F'< 1.06, 0.124 <Z)/r<0.50, 0.19 <D< 0.50 m, 0.57 < 7 < 1.5 m, QG > 1.0 nL/s (normal liters per second)

1-Qc.with

QG .withoutsparging J

Qs

= piFU •M FL = -

(N-NCG)D'

sparger and impeller type Pi

1.0, PBTD-PBTU 0.4, PBTD-PBTU 1.0, PBTD-PBTD 0.4, PBTD-PBTD

0.654 0.925 0.851 0.651

Ps

0.593 0.706 0.816 0.802

0.456 0.405 0.100

-0.256

(3) Gas holdup

tr sparger and impeller type

1.0, PBTD-PBTU 0.117 0.4, PBTD-PBTU 0.221 1.0, PBTD-PBTD 0.109 0.4, PBTD-PBTD 0.114

Notation A Cs D

m FL FT

g N NCG

P QG

Qs R Re S T V VG

constant interimpeller clearance, m impeller diameter, m flow number, (Qs + QG)/ND^, dimensionless flow number, dimensionless Froude number, N^D/g, dimensionless acceleration due to gravity, m/sec? impeUer rotational speed, 1/sec critical impeller speed for the gas induction, 1/sec power consumption, W rate of gas induction, nL/sec volumetric flow rate of the spaiged gas, nL/sec impeller radius, m Reynolds number, ND^plix, dimensionless impeller submergence, m vessel diameter, m impeller tip velocity, nDN, m/sec superficial gas velocity, m/sec

0.433 0.375 0.430 0.420

-0.132 0.156 0.334 0.192

ai~4 constants a* constant ^1-3 constants EG gas hold-up 771-3 constant A1-3 constant X constant ^ viscosity, Pasec p density, kg/m^ ^ vortexing constant

762 Chapter 8. Gas-imlucing niMshaiiieally agitatad systams

Hsu, Y.-C., Peng. R. Y. and Huang, C.-J., Chem. Eng. Sci., 52,3883 (1997) Onset of Gas Induction, Power Consumption, Gas Holdup and Mass Transfer in a New Gas-Induced Reactor

Experimental apparatus Vessel Type: flat-bottomed Diameter 0.17 m

Liquid contained Height: 1.4-2.1 A

Impeller Type: Diameter: 0.35-0.5 Z)/ Number of impellers: 2

Draft tube Diameter: 0.47-0.59 A

V/////////A

Region UI

Region U

Region I

mnnnm 1 I

Free surface "of liquid

Central gas vortex

Free liquid vortex

Bubble distribution in the gas-induced reactor at gassing condition.

Experimental conditions Impeller speed: 500-1,600 rpm Input gas flow rate: 180-550 n^/hr

— > : Gas

Gas input

77////7/7//\ ^\ Liquid

763

Results (1) Onset of gas induction

Npr.c =0352 Di

(2) Power consumption

: | .=i.22Arr|^^^

(3) Gas holdup OJM

Oil2—1

0.00

(a) n (rpm) 2000

0.06

0.04 H

0.02 H

0.00

1000 (b) n (rpm)

Relationship between gas holdup and impeller speed under different working liquid level, (a) un-gassed; (b) gassed.

754 Chapter 8. Gas-inducing macKanically agitetad systems

Notation D, diameter of the turbine, m Di tank diameter, m g acceleration due to gravity, m/sec^ Hd dynamic liquid level, m Hi clearance of the upper turbine, m Nfy, r Froude number at the onset speed, ticDi/gy dimensionless Npr, c modified Froude number at the onset speed, Npr, cDi/S, dimensionless n impeller speed, 1/min fic onset impeller speed, 1/min P power consumption for agitation under ungassed condition, W Pg power consumption under ungassed condition, W Q inlet gas flow rate, ni/hi S submerged depth of the upper impeller, Hd - //i, m e average gas holdup

765

Author Index

Abrardi, V., Rovero, G., Baldi, G., Sicardi, S. and Conti, R. I l l , 214

Aksan (Sizgek), D., Borak, F. and Onsan, Z. I. 268

Al Taweel, A. M. and Cheng, Y. H. 747 Albal, R. S., Shah, Y. T. and Schump , A. 371 Albal, R. S., Shah, Y. T., Carr, N. L. and

BeU,A.T. 382 Aldrich, C. and van Deventer, J. S. J. 745 Ali, A. M., Yuan, H. H. S., Dickey, D. S., and

Tatterson, G. B. 649 Alper, E. and Ozturk, S. 439 Aiai, K., Konno, M., Matsunaga, Y. and

Saito, S. 636 Armenante, P. M., Huang, Y.-T.

and Li, T 594,614 Armenante, P. M. and Kirwan D. J. 317 Amia, L. A., McCoy, B. J. and Smith, J. M. 404 Asai, S., Konishi, Y. and Kajiwara, T. 445 Asai, S., Konishi, Y. and Sasaki, Y. 316

Baird,M.H.I.,Rao,N.V.R.and Shen,Z.J. 417

Bakker, A. and Van den Akker, H. E. A. 220 Bakker, A. and Van den Akker, H. E. A. 557 Baldi, G., Conti, R. and Alaria, E. 580 Bapat, P. M. and Tavlarides, L. L 716 Barigou, M. and Greaves, M. 427 Barigou, M. and Greaves, M. 561,698 Barresi, A. and Baldi, G. 587 Bartos, T. M. and Satterfield, C. N. 436 Bates, R. L, Fondy, P. L. and

Corpstein, R. R. 128 Beckner, J. L. and Smith, J. M. 130 Bertrand, J. and Couderc, J. P. 175 Bertrand, J. Couderc, J. P. and

Angelino, H. 167 Birch, D. and Ahmed, N. 229,562 Blasilteki, H. and Rzyski, E. 165 Boon-Long, S., Laguerie, C. and

Couderc, J. P. 311 Bossier, J. A., Farritor, R. E.,

Hughmark, G. A. and Kao, J. T. F. 344 Bourne, J. R. and Butler, H. 6 Bourne, J. R., Buerli, M. and Regenass, W. 257 Bourne. J. R. and BuUer, H. 133 Bowen, R. L. 474 Brennan, D. J. and Lehrer, L H. 89 Brito-DE la Fuente, E., Choplin, L. and

Tanguy P. A. 195 Brooks, B. W. 642 Brown, D. E. and Pitt, K. 629,708 Bruijn, W., van't Riet, R. and Smith, J. M. 201 Bujalski, W., Nienow, A. W., Chatwin, S. and

Cooke, M. 475 Buurman. C, Resoort, G. and laschkes, A. 487

Calabrese, R. V., Chang, T. P. K. and Dang, P. T. 672

Calabrese, R. V., Wang, C. Y. and Bryner,N.P. 674

Calderbank, P. H. 332 Carreau, P. J., Chhabra, R. P. and Cheng, J. 188 Carreau, P. J., Paris., J. and

Gu6rin, P. 102,186,276 Carreau, P. J., Patterson, L and Yap, C. Y. 86 Chandraseluuran, K. and Sharma, M. M. 430 Chandrasekharan, K. and

Calderbank, P. H. 367 Chang, M.-Y., Eiras, J. G. and Morsi. B. L 411 Chang, M. -Y. and Morsi. B. L 410 Chang,T.P.K.,Sheu,Y.H.E.,

Tatterson, G. B. and Dickey, D. S. 651 Chapman, C. M., Gibilaro, L. G. and

Nienow, A. W. 370 Chapman, C. M., Nienow, A. W., Cooke, M.

and Middleton, J. C. 484,509,547,615 Chatzi, E. G., Boutris, C. J. and

Kiparissides, C. 680,682 Chatzi, E. G., Gavriehdes, A. D. and

Kiparissides, C. 677 Chatzi, E. G. and Lee, J. M. 726 Chaudhari, R. V., Gholap, R. V.,

Emig, G. and Hofmann, H. 389 Chavan, V. V. and Ulbrecht, J. 149,151,156 Chen, H. T. and Middleman, S. 625 Cheng, J. and Carreau, P. J. 224 Chundacek, M. W. 583 CoUias, D. L and Prud'homme, R. K. 684 Conti, R. and Sicardi, S. 312 Cooper, R. C. and Wolf, D. 4 Costes, J. and Couderc, J. P. 476 Coukdoglou, C. A. and

Tavlarides, L. L. 634,635 Coyle, C. K., Hirschland, H. E.,

Michel, B. J. and Oldshue, J. Y. 247

Das, P. K., Kumar, R. and Ramkrishna, D. 721 Das, P. K., Ramkrishna, D. and

766 Author Indox

Narsimhan, G. 724 DaviesJ.T. 669 De Maerteleire, E. 255,291 Deimling, A., Karandikar, B. M.,

Shah, Y.T. and Carr,N.L. 374 Deimling, A., Karandikar, B. M.,

Shah, Y. T.and Carr, N. L. 433 Dietrich, E., Mathieu, C, Debnas, H. and

Jenck,J. 448 Ditl, P. and Nauman, E. B. 491 Dutta, N. N. and Pangarkar, V. G. 567,621 Dyster, K. N., Koustakos, E.,

Jaworksi, Z. and Nienow, A. W. 38

Eckert, R. E., McLaughlin, C. M. and Rushton,J.H. 321,497

Edney, H. G. S. and Edwards, M. F. 252,288 Einsele, A. and Finn, R. K. 107 Esch, D. D., D'angelo, P. J. and

Pike, R. W. 598

Hiraoka, S., Kamei, N., Kato, ¥., Tada, Y., Asai, K., Hibino, S. and Yamaguchi, T. 330

Hiraoka, S., Tada, Y., Suzuki, H., Mori, H., Aragaki,T.andYamada,L 328

Hiraoka, S., Yamada, I. and Mizoguchi, K. 16 Hirose, T. and Murakami, Y. 180 Hockey, R. M. and Nouri, J. M. 55 Hong, P. O. and Lee, J. M. 655,661 Hozawa, M., Yokohata, H., Imaishi, N. and

Fujinawa, K. 462 Hsu, Y.-C, Peng. R. Y. and Huang, C.-J. 762 Hudcova, v., Machon, V. and

Nienow, A. W. 211,522 Hudcova, v., Nienow, A. W.,

Haozhung, W.and Houxing, L 517 Hughmark, G. A. 360

i Imai, M. and Furusaki, S. 658 Ito, S., Ogawa, K., and Yoshida, N. 12

Farritor, R. E. and Hughmark, G. A. 359,459 Femandes, J. B. and Sharma, M. M. 319 Figueiredo, M. M. L. and

Calderbank, P. H. 356,504,544,694 Foft, L, ValeSovd H. and Kudma, V 142 Frijhnk, J. J., Bakker, A. and Smith, J. M. 511 Frobes, D.-H. and Bohnet, M. 282 Frobese, D.-H. and Bohnet, M. 269

Gibilaro, L. G., Davies, S. N., Cooke, M., Lynch, P. M. and Middleton, J. C. 386

Gnanasundaram, S., Degaleesan, T. E. and Laddha, G. S. 643

Godfrey, J. C, Reeve, R. N., Grilc, V. and Kardelj, B. 605

Godleski, E. S. and Smith, J. C. 127 Gosman, A. D., Lekakou, C, Politis, S., Issa,

R. L and Looney, M. K. 69 Gosman, A. D., Lekakou, C, Politis. S., Issa,

R. L and Looney, M. K. 78 Gray, D. J., Treybal, R. E. and

Bamett, S. M. 171 Gray, D. J., Treybal, R. E. and

Bamett, S. M. 208 Greaves, M. and Barigou, M. 551 GUnkel, A. A. and Weber, M. E. 15

H HaU,K.R. and Godfrey, J. C. 140 Harvey, A. D., Wood, S. P. and Leng, D. E. 57 Hassan, L T. M. and Robinson, C. W. 362,536

Jadhav, S. V. and Pangarkar, V. G. 318 Janzon, J. and Theliander, H. 595 Jaworski, Z., Nienow, A. W. and

Dyster, K.N. 51 Jaworski, Z., Nienow, A. W., Koutsakos, E.,

Dyster, K. and Buialski, W. 37 Joosten, G. E. H., Schilder, J. G. M. and

Broere, A. M. 578 Joosten, G. E. H., Schilder, J. G. M. and

Janssen, J. J. 428 Joshi, J. B. and Sharma, M. M. 734 Joshi, J. B., Pandit, A. B. and

Sharma, M. M. 109 Judat, H. 368 JureCiC, R., BeroviC, M., Steiner, W. and

Koloini, T. 378

Kamei, N., Hiraoka, S., Kato, Y., Tada, Y., Shida, H., Lee, Y. -S., Yamaguchi, T. and Koh, S.-T 191

Kaminoyama, M., Saito, F. and Kamiwano, M. 34

Kamiwano, M. Saito, F. and Kaminoyama, M. 24

Kara, M., Sung, S., Klinzing, G. E. and Chiang, S. H. 373

Karandikar, B. M., Morsi, B. I., Shah, Y. T. and Carr,N.L. 387,391

Kataoka, H. and Miyauchi, T. 456 Kawase, Y. and Moo-Young, M. 397 Kawase, Y., Araki, T., Shimizu, K. and

Miura, H. 454

Author lnd«x 767

Khang, S. J. and Levenspiel, 0. 91,470,471 Kizil9e9, F. A. Onsan, Z. I. and Borak, F. 274 Kojima, H., Uchida, Y., Ohsawa, T. and

Iguchi, A. 444 Koloini, T., Plazl, I. and

2umer,M. 233,446,565 Komasawa, I., Morioka, S. and Ohtake, T. 704 Komori, S. and Murakami, Y. 27 Konno, M. and Saito, S. 676 Konno, M., Aral, K., Saito, S. 639 Konno, M., Muto, T. and Saito, S. 725 Kraume, M. 106 Kuboi, R. and Nienow, A. W. 21 Kuboi, R., Komasawa, I., Otake, T. and

Iwasa, M. 308 Kumar, S., Kumar, R. and Gandhi, K. S. 728 Kung, D. M. and Harriott, P. 280 Kuriyama, M., Arai, K. and Saito, S. 263 Kuriyama, M., Inomata, H., Arai, K. and

Saito, S. 17 Kuriyama, M., Ohta, M., Yanagawa,

K., Arai, K. and Saito, S. 262 Kuriyama, M., Ono, M., Tokanai, H. and

Konno, H. 690 Kurpiers, P., Steiff, A. and

Weinspach, P.-M. 295,301,303 Kushalkar, K. B. and

Pangarkar, V. G. 450,452

Lagisetty, J. S., Das, P. K., Kumar, R. and Gandhi, K.S. 670

Lai, P., Kumar, S., Upadhyay, S. N. and Upadhya,Y.D. 314

Laso, M., Steiner, L. and Hartland, S. 722 Ledakowicz, S., Nettelhoff. H. and

Deckwer, W.-D. 381 Lee, J. C. and Meyrick, D. L. 336 Lee, J. C. and Meyrick, D. L. 531 Lee, J. M. and Soong, Y. 659 Levins, D. M. and Glastonbury, J. R. 306 Linek, V., Benes, P., Sinkule, J. and

Moucha, T. 416 Linek, V., Moucha, T. and

Sinkule, J. 226,425,559 Linek, V., Sinkule, J. and Benes, P. 413 Loiseau, B., Midoux, N. and

Charpentier,J.-C. 204 Loiseau, B., Midoux, N. and

Charpentier,J.-C. 539 Lu, W.-M. and Ju, S.-J. 209,520

M Machoii, V., Fof t, L, AntoSova, E.,

Spanihel, B. and Kudma, V. 524

Madden, A. J. and Damerell, G. L 703 Mak, A. T. C. and Ruszkowski, S. W. 490 Manikowski, M., Bodemeier, S., LUbert, A.,

Bujalski, W. and Nienow, A. W. 80 Marrone, G. M. and Kirwan, D. J. 435 Martin, G. Q. 733 Matsumura, M., Masunaga, H.,

Haraya, K. and Kobayashi, J. 160,206,541 Matsumura, M., Masunaga, H. and

Kobayashi, J. 460 Mavros, P. Xuereb, C. and Bertrand, J. 46 Mavros, P., Naude, L, Xuereb, C. and

Bertrand. J. 62 McManamey, W. J. 473,644 Mehta, V. D. and Sharma, M. M. 339 Meister, D., Post, T., Dunn, L J. and

Bourne, J. R. 357 Meister, D., Post, T., Dunn, L J. and

Bourne, J. R. 545 Metzner, A. B. and Otto, R. E. 120 Metzner, A. B., Feehs, R. H., Ramos. H. L.,

Otto, R. E. and Tuthill, J. D. 121,123 MiUer, D. N. 305,348,481,534,692 Miller, S. A., Ekstrom, A. and

Foster, N.R. 405 MiUs, D. B., Bar, R. and Kirwan, D. J. 443 Mishra, V. P. and Joshi, J. B. 39,41 Miyachi, M., Iguchi, A., Uchida, S. and

Koide, K. 432 Mizan, T. I., Li, J., Morsi, B. L, Chang, M.-Y.,

Maier, E. and Singh, C. P. P 467 Mizoguchi, K., O'Shima, E., Inoue, H. and

Inoue, I. 706 Mizushina, T., Ito, R., Koda, S., Kabashima, A.,

Hiraoka, S. and Nakamura, T- 278 Mizushina, T., Ito, R., Murakami, Y. and

Kiri,M. 239,244 Mizushina, T., Ito, R., Murakami, Y. and

Tanaka, S. 241 Mlynek, Y. and Resnick, W. 630,631 Mochizuki, M. and Kuroki, K. 709 Mochizuki, M. and Sato, K. 656 Mochizuki, M. and Takashima, I. 18,20 Mochizuki, M., Takei, N., Satoh, K. and

Akehata, T. 193 Mochizuki, M., Takei, N., Satoh, K.,

Akehata, T. and Miyauchi, T. 218 Mochizuki, M., Takei, N., Sato, T., Tada, H.,

Sato, K. and Akehata, T. 227 Molag, M., Joosten, G. E. H. and

Drinkenbuig, A. A. H. 711 Molerus, 0. and Latzel, W 488,489,585 Momonaga, M., Hibi, F. and Yazawa, H. 486 Moore, L. P. T., Cossor, G. and

Baker, M. R. 44

768 Author lnd«x

Morud, K. E. and Hjertager, B. H. 82 Moucha, T., Linek, V. and Sinkule, J. 424 Murakami, Y., Fujimoto, K., Shimada, T.,

Yamada, A., and Asano, K. 10 Musil,L.andVlk,J. 581 Myers, K. J., Fasano. J. B. and

Corpstein. R. R. 596

N Nagata, S., Nishikawa, M., Itaya, M. and

Ashiwake, K. 286 Nagata, S., Nishikawa, M., Tada, H. and

Gotoh, S. 146 Nagata, S., Nishikawa, M., Tada, H.,

Hirabayashi, H. and Gotoh, S. 137 Nagata, S., Nishikawa, M. and

Takimoto, T. 250 Nagata, S., Nishikawa, M., Takimoto, T.,

Kida, F. and Kayama, T. 248 Narayanan, S., Bhatia, V. K., Guha, D. K. and

Rao,M.N. 576 Narsimhan, G., Nejfelt, G. and

Ramkrishna, D. 715 Narsimhan, G., Ramkrishna, D. and

Gupta, J. P. 647 Nienow, A. W. 115,574 Nienow, A. W. and Miles, D. 144 Nienow, A. W. Konno, M. and Bujalski, W. 616 Nishikawa, M. Kayama, T., Nishioka, S. and

Nishikawa, S. 689 Nishikawa, M., Kunioka, S., Fujieda, S. and

Hashimoto, K. 293 Nishikawa, M., Mori, F., Fujieda, S. and

Kayama, T. 720 Nishikawa, M., Nakamura, M. and

Hashimoto, K. 366 Nishikawa, M., Nakamura, M., Yagi, H. and

Hashimoto, K. 365,505 Nocentini, M., Fajner, G., Pasquali, G. and

Megelli, F. 414 Nocentini, M., Fajner, G., Pasquali, G. and

MegeUi, F. 553 Novdk, V. and Rieger, F. 135

Obot,N.T. 477 Ogawa, K. and Kuroda, C. 478 Ogawa, K., Yoshikawa, S. and Shiode, H. 75 Ogut, A. and Hatch, R. T. 393 Oguz, H., Brehm, A. and Deckwer, W.-D. 441 Okamoto, Y., Nishikawa, M. and

Hashimoto, K. 483 Okufi, S., Perez de Ortiz, E. S. and

Sawistowski, H. 502 Okufi, S., Perez de Ortiz, E. S. and

Sawistowski, H. Onken, U., Sick, R. and Weiland, P. Oyama, Y. and Endoh, K. Oyevaar, M. H., Bos, R. and

Westerterp, K. R. Oyevaar, M., Zijl, A. and

Westerterp, R.

679 383 199

407

395,548

Pandit, A. B. and Joshi, J. B. 110 Panja, N. C. and Rao, D. P. 406 P^pastefanos, N. and Stamatoudis, M. 181 Parthasarathy, R. and Ahmed, N. 700,702 Parthasarathy, R., Jameson, G. J. and

Ahmed, N. 696 Patterson, W. I., Carreau, P. J. and

Yap, C. Y. 161 Patwardhan, A. W. and Joshi, J. B. 759 Perez, J. F. and SandaU, 0. C. 350 Petela, R. 492 Peters, D. C. and Smith, J. M. 1,85 Pettersson, M. and Rasmuson, A. C. 72 Prasher, B. D. and Wills, G. B. 341

Raghav Rao, K. S. M. S. and Joshi, J. B. 104,197

Raghava Rao, K. S. M. S., Rewatkar, V. B. and Joshi, J. B. 589

Ranade, V. R. and Ulbrecht, J. J. 354 Ranade, V. V. and Joshi, J. B. 32 Rao, K. B. and Murti, P. S. 284 Rewatkar, V. B. and Joshi, J. B. 593,620 Rewatkar, V. B., Deshpande, A. J.,

Pandit, A. B. and Joshi, J. B. 555 Ridgway, D., Sharma, R. N. and

Hanley,T.R. 401 Rieger, F. and Novdk, V 154,469 Robinson, C. W. and Wilke, C. R. 342,346 Ross, S. L, Verhoff, F. H., and Curl, R. L. 640 Rounsley, R. R. 654 Ruchti, G., Dunn, I. J., Bourne, J. R. and

von Stockar, U. 385 Rushton, J. H., Costich, E. W. and

Everett, H. J. 117 Rutherford, K., Lee, K. C,

Mahmoudi, S. M. S. and Yianneskis. M. 49

s Saito, F. and Kamiwano, M. 98 Saito, F., Arai, K. and Kamiwano, M. 100 Sano,Y. and Usui, H. 96,174 Sano, Y., Usui, H., Nishimura, T. and

Saito, E. 253 Sano, Y., Usui, H. and Saito, E. 259,260

Author Index 769

Sano, Y., Yamaguchi, N. and Adachi, T. 309 Saravanan, K. and Joshi, J. B. 749, 755 Saravanan, K., Mundale, V. D. and

Joshi, J. B. 742 Saravanan, K., Mundale, V. D.,

Patwardhan, A. W. and Joshi, J. B. 752 Satoh, K. and Shimada, H. 237 Satoh, K. Shimada, H. and Yoshino, Z. 402,506 Satoh, K., Menju, T., Mochizuki, M. and

Shono, A. 113 Satoh, K, Shimada, H. and Yoshino, Z. 235 Sawant, S. B. and Joshi, J. B. 740 Sawinsky, J., Havas. G. and De^, A. 158 Schafer, M., Yianneskis, M., Wachter, P. and

Durst, F. 66 Schluter, V. and Deckwer, W.-D. 508 Schwartzberg, H. G. and TreybaL, R. E. 572 Sestik. J., iitnf, R. and Hou§ka, M. 178 Shamlou, P. A. and Edwards, M. F. 177 Shamlou, P. A. and Edwards, M. F. 265 Shiloh, K., Sideman, S. and Resnick, W. 707 Shiue, S. J. and Wong, C. W. 92 Skelland, A. H. P. and Kanel, J. S. 612,686 Skelland, A. H. P. and Lee, J. M. 495,602 Skelland, A. H. P. and Moeti, L. T. 325,609 Skelland, A. H. P. and Ramsay, G. G. 500,606 Skelland, A. H. P. and Seksaria, R. 493,600 Skelland, A. H. P. and Xien, Hu 323 Smit, L. 503 Smith, J. M. and Katsanevakis, A. N. 216 Smith, J. M. and Tarry, K. 223 Sovovd, H. 713 Sprow, F. B. 623,627 Sridhar, T. and Potter, 0. E. 363,364,546,695 Stamatoudis, M. and Tavlarides, L. L. 663 Stegeman, D., Ket, P. J., Kolk, H. A., Bolk, J.

W., Knop, P. A. and Westerterp, K. R. 421 Steiff, A. and Weinspach, P.-M. 290,299 Stenbeig, 0. and Andersson, B. 399

Tecante, A. and Choplin, L. 419 Tekie, Z., Li, J., Morsi, B. L and

Chang, M.-Y. 468 Teramoto, M., Tai, S., Nishii, K. and

Teranishi, H. 458 Thring, R. W. and Edwards, M. F. 591 Tobin, T. and Ramkrishna, D. 729

U Uchida, S., Moriguchi, H., Maejima, H.,

Koide, K. and Kageyama, S. 431

Van der Molen, K. and Van Maanen, H. R. E. 472

Van't Reit, K. 358 Van't Riet, K. and Smith, J. M. 13 Vel^ovic, V. B., Bicok, K. M. and

Simonovic, D. M. 465

W Wang, C. Y. and Calabrese, R. V. 718 Wang, K. and Yu,S. 271 Wannoeskerken, M. M. C. G. and

Smith, J. M. 513 Weinstein, B. and Treybal, R. E. 527,529,632 Weisman, J. and Efferding, L. E. 571 Westerterp, K. R., van Dierendonck, L. L. and

deKraa,J.A. 334 Wichterle, K. 588 Winardi,S., Nakao, S. and Nagase, Y. 26 Wong, C.W., Wang, J. P. and

Huang, S. T. 518,618 Wright, H. and Ramkrishna, D. 731 Wu, H. and Patterson, G. K. 30

Takahashi, K. and Nienow, A. W. 525 Takahashi, K., Arai, K. and Saito, S. 169 Takahashi, K., Ohtsubo, F. and

Takeuchi, H. 645 Takahashi, K., Yokota, T. and Konno, H. 97 Takase, H., Unno, H. and Akehata, T. 172 Takase, H., Unno, H. and Akehata, T. 463 Takashima, L and Mochizuki, M. 8 Tanaka, M. 667 Tanaka, M. and Izumi, T. 514 Zundelevich, Y. Tanguy, P. A., Thibault, F., La Fuente, E. B-De., Zwietering, T., N.

Espinosa-Solares, T. and Tecante, A. 60

Xu,G.J.,Li,Y.M.,Hou,Z.Z., Feng, L.F. and Wang, K.

Y

Yagi,H.andYoshida,F. Yap, C. Y., Patterson, W. L and

Carreau, P. J. Yianneskis, M., Popiolek, Z. and

Whitelaw,J.H. Yung, C. N., Wong, C. W. and

Chang, C. L.

Z

296

352

163

23

542

738 479,569

engineering data on mixing ()

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