fluid flow through randomly packed columns and fluidized beds

7/26/2019 Fluid Flow Through Randomly Packed Columns and Fluidized Beds

1/6

Fluid

Flow

through

Randomly

Packed Columns and Fluidized Beds

T h e ra t io o f pressure grad ient t o super f ic ial f lu id ve loc i ty

in

packed colu mns is shown

t o be a l in ear funct i on of f lu id mass f low rate. Th e constants of th e l inear relat ion

involve part i cle specific surface, fract ion al void volum e, and f luid viscosity. These

cons tants can be used t o p redict t h e degree of bed expansion w it h increasing gas f low

af ter th e pressure gradient reaches th e buo yant weight of sol ids per u n i t vo lume of th e

bed. Form al equat ions are developed t h at perm it est i mat io n of gas flow rates corre-

sponding to Inc idence of tur bu lent or two-phase f lu idization-a state of f low i n which

gas bubbles, wit h entrained sol ids, r ise thro ugh t he bed and cause intense c ir culat ion

of solids. A con stant p rod uct of gas viscosity t im es superf icial velocity ma y serve as a

cr i ter ion of a standard state in f lui dized systems used for reactio n k in eti c studies.

SABRI ERGUN

A N D A.

A. ORNING

COAL RESEARCH LAEORATO RY AN D DEPARTMENT O F CHE M I CAL E NOI NE E RI NG,

CA NE 51E I NSTI T UTE

O F

T E CHNOL OOY, PI T T SE URG

H

PA.

HE

use of fluidized beds for kinetic studies of heterogeneous

T eactions offers advantag es in ease of tem pera ture control

even for highly exothermic reactions. However, it is essential to

know the gas velocities needed to produce fluidization, and inter-

pretatio n of da ta requires either a standard st at e of fluidization

or

some basis

of

correction for changes in bed volume and for

nonuniformity of contact between gases and solids. This has re-

quired

a

st ud y of the laws of fluid flow and new experimental d at a

to describe the conditions of gas flow

for

rates ranging continu-

ously from zero through those needed for fluidization.

If the behavior of a packed bed is followed when a gas stream is

introduced from the bot tom, the pressure drop a t first increases

with flow ra te without bed expansion-i.e., th e fractional void

volume remains unchanged. When the flow rat e is sufficient to

cause a pressure gradient equal to t he buoyant weight of th e sol-

ids per unit volume, further increase in flow rat e causes th e bed to

expand-i.e., increases th e fractional void volume-the pressure

drop remaining substantially constant. Up to

a

certain gas flow

rate the expansion does not involve channeling

or

bubble flow,

provided the column

is

subjected to some vibration. In this re-

gion the bed increasingly acquires fluid properties, ceases to

maintain it s normal angle of repose, and can be said to be par-

tially fluidized. Until t he gas flow ra te is sufficient to cause bub-

ble flow, there

is

no

gross

circulation or mixing of solids.

With increasing gas flow rates bubbles appear and t he bed be-

comes fully fluidized-i.e., i t can no longer main tain a n angle of

repose greater than zero-there is no resistance to penetration by

a

solid except buoyancy, and the solids are circulating

or

mixing.

Continued increase in flow ra te causes passage of larger bubbles

with increasing frequency. This fluidized bed is not homogeneous

with regard t o concentration of solids. For this reason, i t can ap-

propriately be described as two-phase fluidization. With in th e

fluidized bed

a

denser but expanded bed constitutes the continu-

ous

phase, while bubbles, which probably contain solids in sus-

pension, constitute the discontinuous phase. Th e relative pro-

portion of these phases varies with flow rat e.

The three distinctly different states-the fixed bed, the ex-

panded bed, and th e fluidized bed-are considered sepa rate ly in

th at order.

THE FIXED BED

Th e fured bed is identical with randomly packed beds involved

in th e determina tion of th e specific surface of fine powders by the

air permeability method

(1,

6-8,

10-18)

and with randomly

packed colunins

( 3 , 5 ,9,16,18-20) as

used in absorption, extrac-

tion, distillation, or catalyti c reactions.

Attempts to determine the specific surface

of

powders by the

air permeability method have led to

a

considerable amount

of

work in connection with the pressure drop through fine powders

and filter beds a t low flow rates. The following equation, based

upon viscosity, was first developed by Kozeny

(IS),

roposed by

Carman

8) or

use with liquids, and later extended b y Lea and

Nurse

(14)

o include measurements with gases:

J t has been found satisfactory for small particles having specific

surfaces less than

1000

to

2000 sq.

cm. per gram. Arne11

(1 )

and

others have modified it to include terms which account for the

changing flow character istics in extrcmely fine spaces,

a

modifics,

tion that

is

not

of

particul ar interest for the present purpose.

On the other hand,

a

considerable amount of work has been

done in correlating data for packed columns

at

higher fluid veloc-

ities where the pressure d rop appears to va ry with some power

of

the velocity, the exponent ranging between 1 and 2. Blake (8

suggested th at this change of relationship between pressure drop

and velocity is entirely analogous to tha t which occurs in ordinary

pipes and proposed a friction factor plot similar to t ha t of Stan

ton a nd Pannell (20). The equat ion used was th at for kinetic ef

fect modified by

a

friction factor which in turn is

a

function o

Reynolds number

(9).

A P = 2jpiu2/Dp 2

where

f = d N R s )

Recent workers

7 , 1 5 )

have included t he effect

of

void fractio

by the addition of another factor in Equation

2.

It is usually

given in t he form

(1 - )m / s 3

where

rn

is either 1

or

2.

A study

of

these different procedures showed tha t

for

fluid

flow

at

low velocities through fine powders, viscous forces account fo

the pressure drop within the accuracy of measurement, wherea

for higher velocities, kinetic effects become more important bu

do not alone account for t he pressure drop without t he aid of fac

tors which in turn are functions

of

flow rate .

This trans ition from t he dominance of viscous to kinetic effect

for most packed systems, is smooth, indicating th at there shou

be a continuous function relating pressure drop t o flow rate.

1179


2/6

1180 I N D U S T R I A L

A N D

E N G I N E E R I N G C H E M I S T R Y Vol.

41, No.

I

W / A , G .

/

( S E C X C M ~ )

0.02 a04 a06 0

F igure 1.

Permeabi l i ty of Beds of Glass and Lead

Spheres

Mat eri al Gas Spheres,

Rlm.

Void

V o l u m e

+ Glass N 0.570 0 330

coz

0.570 0.330

Lead Nz 0.562 0.352

CHI

0.562 0.352

N 0.497 0.350

A v . D i a m .

o f

Frac t i ona l

I

W / A . G / SECJ CM~)

Figure

2.

A i r

Permeabi l i ty

o f

Lead

Shot

(Data

of

Burk e and P lumrn er ,

5 )

A v . Diam. of Fract ional

Spheres , M m . Vo id Vo lume

6.34

3.08

1.48

0.397

0.383

0.374

general relationship ma y be developed, using the Kozeriy assunip-

tion tha t the granular bed is equivalent to

8.

group of parallel and

equal-sized channels, such that the total internal surface and the

free internal volume are equal to the t otal packing surface and th e

void volume, respectively, of the randomly packed bed. The

pressure drop through

a

channel is given by the Poiseuille equa-

tion :

dP/dL = 32 fiux/DZ (3)

t o which

a

term representing kinetic energy

loss,

analogous

to

that

introduced by Brillouin

4 )

or capillary flow, may be added.

dP/dL = 32

pu*/DZ

f

/B

pju*'/Do

4)

Using relationships for cylindrical channels, the number

of

channels per un it are a an d their size can be eliminated in favor of

specific surface and the frac tional void volume by means of t he

following equations:

S , = A - L T D ~ / L T D ~ / ~ ) ~

NirDZ/4

=

aD2

14

2L* = U E

and

This leads to:

(5)

This equation, like many others that relate pressure drop

to

polynomials of t he fluid flow rat e, differs from them in that the

coefficients hav e definite theoretical significancc.

1 1 - e2

dP/dL =

2

(

pu

S + -__

8 3

P/U2S,

For a

packed

b e d , the flow pat h is sinuous and the strea m line

frequently converge and diverge. The kinetic losses, which occu

only orice for the capillary, occur with a frequency t,httt is s tatisti

cally related t o t'lie number of particles per unit length. For thes

reasons, a correction factor must be applied t o each term . Thes

factors may be designated as 01 and p.

Th e values for

a

and

3

can be determined ex;pe~imentally nd

generally app roximates (a/2 )2a,h ich has been proposed on t,heore

cal

grounds ( 12 ) . Experiments with randomly

packed

m:tter

al s

of

known specific surface have led

to

adopt,ioii

of

a value of

for 2a, which is close to the theoretical value of 4.035.

Integration of Equation 6, assuming isothermal espansiori o

an ideal gas, leads

to

the equation:

where

urn

s the superficial velocity

at'

the mean pressure, and

W /

is the mass

f l o ~

ate per unit area

of

the empty tube. Leva

et a

( 1 5 ) reported t'liat' in packed tube s, xlicn the viscous forces a

predominant, the pressure drop is proport,ional to

1

t ) * / e

\-hereas, at higher flow rates , the corresponding dependence upo

the void fraction is

1

- ) / e 3 viliich is just a-ha,t

would

be ex

pected from Equation

7 .

From Equation 7, a plot, of AP: L2im

08.

TV/A would give

straight line, t.he intercept and slope leading to values

of

01 and

Typical

plots

of

data obtained l o test this dependence of pressur

drop on gas flow rate are shown in Figure 1.

Pressure drop measurements ivere made

in a

glass tube,

1

inc

in inside diameter and 30 inches long, fitted with a fritted-gla

disk t o obtain uniform gas flow at the bot tom an d with pressur


3/6

June

1949

I N D U S T R I A L A N D E N G I N E E R I N G

C H E M I S T R Y 1181

size

(19).

These plots demonstrate the validity

of

Equation

7

within the range of experimental accuracy. Values for a and p

for

all

the da ta are given in Table I, together with references to

sources of those data taken from the literature. The lines shown

in Figure 3 for the da ta of Oman and Watson

(19)

are not those

used in determining the constants. These data fell int o high and

low density groups each of nearly, bu t no t quite, t he same frac-

tional void volume. For these dat a, Equation 7 was first divided

by

(1

-

~/e3,

eading to plots with common intercepts conven-

ient for determining a. Similarly, a division by 1 - )/e3 led to

plots with common slopes

for

determining p.

Using the relation for

a

sphere, D

=

6/&, Reynolds number,

N R ~D P U n P j m / ~ ,

an be used totra nsfor mEqu ation7 to th e form

8 )

a l - - e P 1 E

A P / L

=

[ + 96 --l v R a ] s T s Pj,u:

Thus the friction factor would become:

f = a [ 1 + 9 6 " l - ' ]

NR

9)

An examination of the values of

cy

and

P

given in Table I and

of

Equation 8 indicates t he relative importance of the viscosity and

kinetic terms. For Reynolds numbers around

60,

with

E

= 0.35,

the two have nearly equal effects upon pressure drop.' For

N z c

=

0.1, viscosity accounts for

99.8 ,

while for N R ~ 3000, kinetic

effects account for 97 of the pressure drop. Because packed

columns are generally operated in the range from

N R ~

1

to

10,000, both term s are essential in calculations of pressure drop

Mater i al Spheres, Inc h (Approx imate) Although the theoretical development has been based on ran-

-tCeli te spheres 0.25

domly packed beds, th e same treatment can be applied to d at a ob-

-I- Cel i te cy l lndera 0.25.25 0.36.46 tained

(9,

I? ) for geometrically arranged packings. In these

0 Raschig

r i ngs

0.375 0.55 cases the coefficients may differ markedly for different arrange-

0 Berl saddles

0.5 0.71

ments even a t the same frac tional void volume.

e

Figure 3.

Air Permeabi l i ty of Various Materials

(Data

o f

Oman and Watson,

19

Fract ional

A v . Diam. of Void Volume

9 Celi t e spheres 0.25 0.38

0 Cel i te cy l inders

+ Raschig r ings 0.375 0.62

+

Berl saddles 0.5 0.76

0.46

taps at the top and at a point

just above the fritted-glass

disk. Gas flow was measured

with a series

of

capillary flotv-

meters, each calibrated against

wet-test meters. Reproducible

results in this small glass tube

were most easily obtained if

the size range of material in

the bed was not

too

great and

if the bed was thoroughly

mixed by full fluidization be-

fore packing to th e desired

density. Excessive pa c ki ng

generally disturbed the inci-

dence and uniformity of ex an-

sion. A brief summary ofthe

conditions for which experi-

mental d at a were obtained is

as follows: parti cle size, 0.2 to

1.0

mm.; particle density,

1.5,

2.5,

7.8, 8.6, and 10.8 grams

p e r c c . ; p a r t i c l e s h a p e ,

spherical and pulverized; gases

employed, hydrogen, methane ,

nitrogen, and carbon dioxide;

gas

velocities, up to 100 em.

per second.

Figures

2

and 3 show data

taken from the literature for

experiments with air flowing

through beds of lead shot 1.5

to

6.5

mm. in diameter ( 5 ) and

Celite spheres, Celite cylin-

ders, Raschig rings, and Berl

saddles, each ranging from

0.25 to 0.75 inch in nominal

Material

Table I. Coefficients for Pressure Drop Equation

Specific

Sample

Surface, Weight, Void

Fluid Cm.-1 Grams Fraction I

Pulverized coke Different gases 60-370

.

.

0.52-0.64 2.5

Glass beads

Iron shot

Lead shot

Lead shot

Copper shot

Lead shot

Lead shot

Lead shot

Hydrogen 264.0

200 0,343 1. 9

Carbon dioxide

105.2 200

0 . 3 3 0 1 . 8

Nitrogen 105.2

200

0.330 1.9

Nitrogen 127.2 300 0.375 2. 0

Nitrogen 127.2 200 0.375 2. 0

Carbon dioxide 127.2 300 0.375 1 .8

Nitrogen

78.0 200 0.371 2.0

Nitrogen 120.7 500

0.350 1 .9

Carbon dioxide

120.7 500 0.350 1 8

Nitrogen 106.8 300 0.352 1.8

Methane 106.8 300 0.352 1 .8

Air

Air

Air

Air

Air

Air

Air

Air

Nitrogen 75.2 1000 0.364 1.9

Nitrogen 75.2 300 0.364 1.9

Nitrogen 59.75 500 0.366 1.8

Carbon dioxide 90.0 500 0.372 , 1 . 8

Water Different . . 0.380 2.5

w e s

40.6

. .

0,375 2 .0

1 9 . 5 . . 0.383 2.3

19.5 . . 0.390 2 .2

9.57 , . 0.421 2.8

9.57

, .

0.397 2.8

2 7 . 5 . . 0 , 3 0 3

1 . 9

22.2

. .

0.325 2 .5

19.8 . . 0,320 3 .0

. . 0 . 3 7 8 5 . 8

pheres, Celite Air 11 .5

Air 11.5 . . 0.466 5 .8

Cylinders, Celite Air 8. 78 . . 0.365 5 .7

Air

8 . 7 8 , . 0.457. 4.9

Berl saddles, clay Air 11 .55 .,. 0.713 6.6

Air 11.84 . . 0.764 6 .6

Raschig rings, clay Air 12.2 3

. .

0.555 8 .3

Air 12.23 . . 0.622 9.9

Rhombohedral 3a Water 7.56 . . 0.260 2.2

Orthorhombic 4a Water

7 .56 . . 0.395 3 .4

Orthorhombic 2 clear

Water 7.56 . . 0.395 3.3

Orthorhombic 2' blocked

Water 7.56

. .

0.395 8 .7

. . ,

1.7-3.00

a Configurations an d orientations of geometrical packings are described in detail in

B).

Various inateriais Different gases , , , , . .

P

Source

2 . 3

. .

3 . 0

. .

3 . 1 . .

2 . 8 . .

2 . 5 . .

2.6 . .

2 . 5

. .

2 . 7 . .

2 . 7 . .

3 . 1 . .

2.7

. .

3 . 1 . .

3 . 3

, .

3 . 3

. .

2 . 9

. .

2 . 6

2 . 6 cih


4/6

1182

I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y Vol. 41, No. 6

perimentally with glass beads, lead shot, and iron s h o t

with various gases. The curves are drawn according

to Equation

12,

the break points corresponding to eo,

the void fraction

of

the fixed bed.

For relatively shoit columns of fine,

low

density

material, t he

u:

term of Equation 7 can be neglectrd

and Equation 12 can be approximated as:

3 2&fi

(urn

?in,

13)

_ _

1

-

p s g

nhere

the

zero subscript designates value> at the

in-

cidence of expansion. TVithin the range of fractional

void voluines usually cncountered, the left-hand mem-

ber

of

Equation 13 is nearly pioportional t o the Erac-

tional increase in column height. A constant, c, for the

approximate relation

(141

can be chosen such tha t t he calculated values of colunin

_ _ -

J j r - = c -

1 L

I - t

1

O o

Ov3*4 a 12 16 2 2 4 28

32

36

S U P E R F I C I A L V E L O C I T Y ,

U M ,

C M / S E C

Figure

4.

Expans ion of Beds of Glass Beads

height deviate froin the true ralues by

no t

more iliar.

370 in the range from zero to 30% expansion for F ,

greater than

0.35.

Curves drawn according to Equat ion

12

wi t h break poin ts a t

e o )

A v . Diam. of

Gas Spheres, Mm .

This approximation leads

t o

the equation

:

H2

coz

Nz

0.227

0.570

0.570

(16;

THE EXPANDED BED

or for a given bed m d fluid

AL/Lo = constarit urn- um0

(16)

hen the pressure gradient becomes equal to the buoyant

weight of

tmhe

acking pelunit volume of the bed,

Equation 1.3can be written more directly as

(10)

Equation 6 remains valid, the pres-

Thr fractiorial void

dP

dL

= (1

) P a V Y

17 )

the bed begins t o expand.

sure gradient being given in Equation 10.

These equations off er convenient ineaus for determining t he

volume increases with

f low

rate. Eliminating

t,hc

pi urc gradi- expansion of fluidized beds. With a knodedge of the properties

ent betiwen Equat>ions and 10:

of the fluid arid the dcnsit>y nd specific surface of the material,

e

..__

==

~ _ _

3

a s i2fl u,,2;

111, >

?I,, o

1 - E

P d

gives the fract>ionalvoid volunie in terms of t he corre-

sponding velocity, u . This equation is not rigorous as

applied to t he entire column in terms

of

urn, ecause it

neglects the variation in fractional void volume over the

length

of the

bed due

t o

the effect of gas expansion

upon velocity. However, this change in 6 i s nearly

proportional

t o

the one third

power

of velocity, and the

use of urn ives a fitirly accurate average

E

over the en-

tire column. A rigorous solut,ion would involve the

substit,utionof appropria te values of t various lengths

L n Equation 11, plotting t os. L, rid graphically ob-

taining the average e over the entire column. This

procedure

is

hardly warranted , for the use of urn nd the

over-all fractional void volume yields results ivell with-

in t,he liniit,s of experimental accuracy. Therefore,

Equat,ion

11

can be written as:

Independen t knowledge

of S ,

s not essential. Esperi-

mental da ta for the fixed bed give values of (as:) nd

PS,). 8 1 1

dependence upon particle size

and

shape is

involved in these quantities. As illustrated

in

Figures

4

to 6, this relation has been verified ex-

S U P E R F I C I A L V E L O C I T Y , U CM./SEC.

Figure 5.

Expansion of Beds of M e t a l S h o t

(Curves draw n according to Equation 1 2 wi th break po in ts a t

ea

Mater i a l G a s Spheres, M m .

Av. Diam.

of

Iron

Lead

Iron

Na

cox

M ?

0.472

0.497

0.770


5/6

June 1949

I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y

11

can be obtained from Equati on 17 for fluidized systems of fine ma-

terial of

low

density. More generally,

a

single observation of

AL/Lo

will determine th e constant

of

Equation

16.

In t he event

umocannot be obtained from Equation 12 because of lack of in-

formation, ano ther set of values of aL/Lo s.

urn

will determine

urn, s well.

Equation

15

has been verified experimentally for pulverized

coke and for fine glass beads with various gases. Equ ation 16 has

been found to apply more generally, even when the second term

of

Equation

7

cannot be neglected, except tha t th e slope mus t then

be determined experimentally and can no longer be predicted

from a knowledge of

01

and p

T H E FLUIDIZED

BED

As

the gas flow rate is increased, bed expansion continues ac-

cording t o Equatio n

12.

There is a limit, however, to t he homo-

geneous expansion of the bed. At higher flow ra tes pa rt of th e gas

flows throu gh a denser but expanded bed which constitut es a con-

tinuous phase, while the balance of the gas passes through the bed

in bubbles which probably contain solids in suspension. The bub-

bles constitute

a

discontinuous phase. The solids are violently

agitated and th e condition may be termed tu rbul ent or two-phase

fluidization. Increasing flow rate causes

a

larger portion of the

gas to flow in the discontinuous phase, approaching a final limit

with all th e solids in suspension.

With spherical particles, two-phase fluidization was found to

begin when the void fraction exceeded a value

of

about 0.46.

This value is nearly t ha t for th e void fraction for spheres packed

in cubical arrangement, the loosest stable form. This observation

suggests th at two-phase fluidization does not sta rt before the bed

at tai ns th e equivalent of th e loosest stable configuration. The

loosest stable volume was obta ined by fluidizing the bed, cutting

down the gas flow slowly, and observing the volume when the

gas was completely cut off. After the materi al was packed tightly,

gas was let in and th e rat e of

flow

increased slovvly until two-phase

fluidization began. Th e volume at the sta rt of bubble formation

was

the same as t hat obtained by the reverse procedure.

Experiments with closely screened samples of pulverized coke

from

16

to

100

mesh gave loosest stable volumes corresponding

to void fractions from

0.60

to

0.70

and fractional increase in be

height ranging from 15 to

20 .

These estima tes for void fractio

of coke are arbitrari ly based upo n a density of 1.4 for the co

which allows for pore volumes not available for fluid flow. Th

loosest stable packing volumes-Le.

,

loobest bulk density-

for

materials having irregular shapes and surface cannot b

estimated theoretically, but are easily determined as has bee

described.

I n two-phase fluidization, t he denser but expanded phase su

rounding the rising bubbles moves towards th e bottom of th e be

The rising bubbles carry

a

portion of the solids to complete th

pat h of circulation. While the solids circulate, there is no su

stanti al circulation

of

gas.

Because the gas does not flow homogeneously through t

bed, contact time and surface effectively contacted are indete

minate. However, for relatively fine solids of low density, th

final term of Equ ation 7 can be neglected a nd th e expansion equ

tion can be used in th e form of Equat ion

17.

These equations, f

a given bed, depend upon specific gas properties and flow rat

only through the product of viscosity times superficial velocit

For

thi s reason, a constant product of viscosity times superfici

velocity was chosen as a criterion for a stan dard s ta te of fluidiz

tion for a series

of

kinetic stud ies involving gaseous reactions wi

60-

to 100-mesh coke. With a suitabl e correction for the parti

pressure of the reac ting gas component, the resulting r ate co

stants gave a good Arrhenius plot and were direc tly proportion

to the amount

of

coke in the bed.

S U P E R F I C I A L V E L O C I T Y , U C M / S E C

Figure 6. Expansion of Beds of Lead Shot

(Curves

drawn according to Equat ion 12 w i th

break

p o i nt s a t eo)

A v.

Diam. o f

Gas

Spheres, Mm

Nn

HI

NS

0.798

0.562

1.004

SUMMARY

A

general equation has been developed which relates pressu

drop t o gas flowfor fixed beds. The equation shows tha t the rat

of pressure drop to superficial velocity is a linear function of ma

flow rate.

Its

coefficients depend upon fractional void volum

specific surface of packing material, and fluid viscosity. A tran

formation of the equation shows th at the fi iction factor impli

itly involves the fractional void volume and is not a function o

th e Reynolds number alone, as has often been assumed.

A

fixed bed expands with increasing fluid flow after th e pressu

drop equals the buoya nt weight of th e solids per unit area of t h

bed. The general equation for the fixed b

applies also

t o

the expanding bed; the valu

of the coefficients remain unchanged. Her e th

total pressure drop stays constant while th

fractional void volume increases.

A

gener

form of the equation suitable for caIculatio

of

iractional void volume has been given. Wi

suitable approximations equations have bee

developed which permit direct calculation o

such readily observable quantities as fraction

expansion

or

height of th e bed. A knowled

of specific surface of th e solids is n ot necessar

Measurement

of

pressure drop versus flow ra

in the fixed bed, employing any gas at a su

able pressure and temperature,

is

sufficient

determine and

pS,.

The void fraction f

the fixed bed, however, mus t be known.

Expansion is homogeneous until the be

att ain s th e loosest stable configuration of th

solids. With gases, addit ional increase in flo

ra te causes appearance of bubbles. Und

these conditions, th e bed is fluidized (two-pha

fluidization). Th e loosest bulk density of an

packing material can be determined by fluidizi

a

sample with a gas in

a

column and reducin

the

gas

flow slowly. A knowledge of the loo

est bulk density i s sufficient to estimate flo

rates corresponding

to

the incidence of tw

phase fluidination for any gas under any cond

tions of pressure and temper ature.


6/6

1184

I N D U S T R I A L A N D E N G I N E E R I N G

C H E M I S T R Y

Vol. 41,

No.

6

Fo r kinetic s tudies of heterogerieous ieact.ons in fluidized beds,

a constant product

of

gas viscosity times superficial velocity may

serve as a criter ion of a standard st at e of fluidization-Le., it will

ensure a constant st ate of fluidization a t different temperatures ,

pressures, and gas compositions. Use

of

this criterion for a kinetic

study of ste am and oxygen reactions with coke in fluidized beds, to

be reported elsewhere, led to reaction ra tes th at were proportional

t o

the weight of t he coke in the bed an d gave good Arrhenius plot^.

d

=

u =

D , =

D ,

=

L =

V =

LYP.

=

AP

=

s, =

*

=

11

=

I / =

c =

=

3 =

P, =

pr n

=

a =

c =

N O M EN C L AT U R E

cross-sectional area of column,

sq.

cm.

dimensionless constant

diameter of bed, cm.

diameter of a channel, em.

diameter of a spherical particle, em.

length

of

bed, em.

number of channels per unit area of colurnri

Reynolds number

pressure drop, dynes pcr

sq.

cm.

specific surface,

sq.

em. per cc. of solid particle

average velocity through channel, em. per second

superficial velocity,based on emp ty tube , cin. per second

superficial gas velocity a t mean of entrance and exit

weight rat,e of fluid fiom, grams pcr second

dimensionless coefficient

dimensionless coefficient

fractional void volume

density of fluid, grains per cc.

gas density at mean

of

entrance an d exit pressures,

giiiiiis

pressures, cm. per second

-

per cc.

p a = density

of

solid particles, grams per cc

fi =

viscosity of fluid, poise

LITERATURE

CITED

Arnell,

J.

C.,

Can.

J . Research, 24, A-B, 103 (1946).

Becker,

J.

C.,

M.S.

thesis, Carnegie Institute

of

Technology

Blake,

F.E., Trans.Am. nst . Chem.

Engrs.,

14,415

1922).

Brillouin,

M . ,

LeGons sur

la

viscosit6 des liquides et

des gaz,

Burke,

S .

P., and Plummer, w. B.,

IXD. NG.

Hmf.,

20, 119

1947.

Paris, Gauthier-Villars, 1907.

119281.

Carman,

P.

C., J .

SOC.

Chem. Ind. , 57 , 2251 (1938).

I b i d . ,

58,

1-7T

(1939).

Carman, P. C., Trans.

Inst.

C h e m .

Engrs.,

15, 150-66 (1937).

Chilton, T.

H.,

and Colburn,

A.

P., IND.

ENG.

CHEX.,

3,

913

(1931).

Teubner, 1930.

Forchheimer, Ph., Hydraulik, 3 aufl., p. 54, Leipzig,

B.

G

Forchheimer, Ph., Z. B er . deu t . ITLQ.,

5 ,

1782 (1901).

Hitchcock, D. I., J . Gen . P h p i o l . , 9, 755 (1926).

Kozeny, J . ,

S i t zber .

A k a d . Wiss Wien, M a t h . - n a t u ~ w ,

Klame

Lea,

F. M.,

and Nurse,

R.

W.,

J . SOC.C h e m .

Ind.,

5 8 ,

277-831

Leva, Max, and Grummer,

M., Chem. Eng. Progress,

43,

549-54,

Lindquist, E. , Premier Congrbs des Grandes Barrages. Vol. V.

Martin, J.,

Sc.D.

thesis, Carnegie Institute

of

Technology, 1948

Muskat,

M.,

Flow

of

Homogeneous Fluids through Porous Me

Oman, A . O . ,

and

Watson,

K . M., AVatl.Petroleum Sews, 36

Stanton, T.

E., and

Pannell,

J. R., T r a n s . R o y Soc.

(London

136

Aht.

IIa). 271-306 (1927).

(1939).

633-8, 713-18

(1947).

pp. 81-99.

Stockholm, 1933.

dia,

New

York, McGraw-IIill

Book Co.,

1937.

R795-802 (1944).

(A)

214, 199-224 (1914).

RECEIVED anuary 15, Y4 4,

Flow Characteristics

of

Solids-

as

Mixtures

In

a Horizontal and Vertical Circular Con

Th e isot hermal f low characteris t ics of a solids-gas mix-

tu re (alu mi na, s i l ica, catalyst , and air ) are invest igated in

a ho r izon tal and vert ical glass con dui t

17 mm

in ins ide

diamet er for var ious rates of ai r f low and sol ids f low.

Pressure drops across test sections

2.0

fee t in length) are

accurately measured for a ser ies of air f low rates in w hic h

th e ra t io o f so l ids to a i r

is

varied f rom 0 o

16.0

pounds of

solids per pound of air . Th e sol ids (catalyst ) are int ro-

duced i n to t he f low system t hrou gh a mix ing nozzle fed

by a slide valve-controlled weighin g t an k, an d have a size

d is t r i but io n vary ing f ro m par t ic les less than

10

m ic rons t o

URISG World War

11,

one of t he most remarkable develop-

D

ment s in engineering was th e application

of

the continuous

flow process to catalytic synthesis. , The advantages resulting

from a

cont inuous cata lyti c process-continuous regeneration

of

catalyst, control of catalyst activity, reaction rate control result-

ing from the constancy

of

temperature and thorough mixing in

reactors, and finally the economy of long on-stream periods-

need not be discussed here. The fluid catalytic units or today

offer a most at tracti ve means

of

carrying out t he ma ny Fischer-

Tropsch reactions heretofore considered too complex and costly

from a commercial point

of

vieF.

Although a large number

of

fluid catalytic crackers have been

designed a nd successfully operated, there appears t o be a scarcity

of

design information

in

the literature on the hydrodynamic

behavior of multicomponent, multiphase systems.

This particu-

part ic les greater than 220 micro ns. Ai r velocit ies i n t h e

solids-free approach section vary from

50

t o

150

feet per

second. Several typ es of nozzles fo r feeding solids are

invest igated for stabi l i t y of f low in t h e system (absence of

pressure surges) and some qual i tat i ve in for mat io n is pre-

sented on th e type o f nozz le y ie ld ing th e most u n i for m

typ e of mix i ng. Qual i t at ive observat ions on th e f low

in t h e sol ids feed l ine, mix ing nozzle, hor izontal and

vert ical test sect ions, and sh ort and long radi us bends,

and th e behavior of a mult i effect cyclone separator are

discussed.

LEONARD FARBAR

UNIVERSITY

O F

CALIFORNIA. B E R K E L E Y

4,

CALIF.

Iar field of unit operations has been given some consideration in

the past; however, the investigations th at have been reported

are limited in their application to t he fluid units by the fact tha t

studies were limited to particles

of

fixed and relatively large sizes

Considerable

work

has been carried out on the investigation

of

the flow charac teris tics of gas-liquid mixtures 1, 5,

6 )

and

a

certain amount

of

attention

( 3 , 9)

has been given to the pneu-

matic conveyance of relatively large solid particles in which the

size spect rum was rather limited. Gasterstadts ( 5 ) investiga-

tion of th e transportation of wheat app ear s to be the first detailed

stu dy indicating the possibility th at

a

simple relationship may

exist in closed conduits between the pressure drop

of

a single

phase (gaseous) flowing and that encountered when more than

one phase

is

present.

fluid flow through randomly packed columns and fluidized beds

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