heat transfer in incipiently fluidized gas-solids …...heat transfer in incipiently fluidized ......

HEAT TRANSFER IN INCIPIENTLYFLUIDIZED GAS-SOLIDS SYSTEMS

Item Type text; Dissertation-Reproduction (electronic)

Authors Edwards, Richard Modlin, 1920-

Publisher The University of Arizona.

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EDWARDS, Richard Modlin, 1920-HEAT TRANSFER IN INCIPIENTLY FLUIDIZED GAS-SOLIDS SYSTEMS.

University of Arizona, Ph.D., 1964 Engineering, chemical

University Microfilms, Inc., Ann Arbor, Michigan

HEAT TRANSFER IN INCIPIENT LY FLUIDIZED

GAS-SOLIDS SYSTEMS

by

Richard M? Edwards

A Thesis Submitted to the F acuity of the

DEPARTMENT OF CHEMICAL ENGINEERING

In Partial Fulfillment of the Requirements For the Degree of

DOCTOR OF PHILOSOPHY

In the Graduate College

THE UNIVERSITY OF ARIZONA

1963

THE UNIVERSITY OF ARIZONA

GRADUATE COLLEGE

I hereby recommend that this dissertation prepared under my

direction by Richard M. Edwards entitled "Heat Transfer in Incipiently

Fluidized Gas-Solids Systems" be accepted as fulfilling the dissertation

requirement of the degree of Doctor of Philosophy,

issertation Director Date

After inspection of the dissertation, the following members of

the Final Examination Committee concur in its approval and recommend

its acceptance:*

\ 5^/WL . \9

STATEMENT BY AUTHOR

This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in The University Library to be made available to borrowers under rules of the Library,,

Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made0 Requests for permission for extended quotation from or reproduction of this iranuscript in whole or in part may be granted by the head of the

.major department or the Dean of the Graduate College when in their judgment the proposed use of the material is in the interests of scholarship, In all pther instancesf however, permission must be obtained from the author»

SIGNED:

PREFACE

The work reported here was performed in the Chemical Engi

neering Department at the University of Arizona, Tucson, Arizona-

The author wishes to acknowledge the support and encouragement given

by Dr. Donald H. White and the faculty of the department- Special ap

preciation is due Mr. Thomas F- Breen, Technician in the College of

Mines, for his enthusiastic assistance in the design and construction of

the equipment-

iv

HEAT TRANSFER IN INC I PIE NT LY FLUIDIZED GAS-SOLIDS SYSTEMS

by

Richard M. Edwards

ABSTRACT

An investigation of the heat transfer characteristics of a non

uniform cross section, incipiently fluidized gas-solids system has been

carried out0 Previous investigators have reported limited results in

this area indicating the possibility of good heat transfer characteristics

with a low. degree of solids mixingo

A 7-1/2-inch diameter column was employed, using axial,

heated, inserts designed to maintain a constant linear gas velocity through

the column, top to bottom„ The bed height was 48 inches„ Air was used

as the fluidizing medium,, The solids used were spherical glass beads

of 0,000875 inches, 0„ 00222 inches, and 0„ 0059 inches in diameter,,

A condition of minimum fluidization was maintained in each of

18 experimental runs, using the axial insert as the heat transfer ele

ment, Overall heat transfer coefficients were found ranging from about

2 BTU/hr= ft, ̂ 0Fo for the small bead size to about 15 BTU/hr0ft„ ^0Fo

v

for the large bead size., These coefficients correspond to those found

in fixed beds rather than fluidized beds=

The inserts, designed to provide a constant linear gas velocity

throughout the bed, performed satisfactorily allowing uniform incipient

fluidization to be maintained in all cases. Deviations of up to three

percent from design conditions did not affect fluidization quality ad

versely o Based on one case, a deviation from design conditions of 10

percent made uniform incipient fluidization unobtainable0

Recommendations for future work in this area are includedo

vi

TABLE OF CONTENTS

Page

CHAPTER I—INTRODUCTION ... .... 1

CHAPTER H—THEORETICAL CONSIDERATIONS ..... 7

Fluidization Quality ................... ........ 7 Isothermal Insert Design ........... . ..... 11

• Heat Transfer in Fixed Beds ......................... 13 Heat Transfer in Fluidized Beds ... c ... c. .. ..... c.. ... 17 Nonisothermal Insert Design .................... 20 Mixing Studies . . .. c.. ...... . c......... . . 23

CHAPTER HI—EXPERIMENTAL APPARATUS .............. 26

G e n e r a l . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 6 Reactor c . . . . . . o . o o . o o . o c . . o . . . . . . . . . . . o . . . o = . . . . s o . 26 Solids Handling System ................. 33 I n s e r t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 Temperature Measurements .......... .......... 37 Solids . . 39 Utilities . 39

CHAPTER IV—EXPERIMENTAL PROCEDURE .. 42

CHAPTER V—EXPERIMENTAL RESULTS .................. 44

CHAPTER VI—DISCUSSION OF RESULTS ................... 47

Fluidization Quality ................................. 47 Heat Transfer Coefficients ........................... 52 Insert ^Performance o . . . o c c c . . . . c . . . . . . o c o . c . . o . . . . . . 56 Extension of the Design Equation ...................... 68

CHAPTER VH—CONCLUSIONS AND RECOMMENDATIONS ... 70

CHAPTER VIII—APPENDIX ............................... 72

CHAPTER IX—REFERENCES ............................. 120

vii

LIST OF ILLUSTRATIONS

Figure Page

lo Typical pressure drop-flow rate relationship ........... 9

20 Typical heat transfer coefficient representation 16

3o Photograph of apparatus ........... ............ 27

4. Schematic diagram of equipment. ....................... 28

50 Reactor shell details ................ 29

6o Gas distribution system ............. c c ............. 31

7o Typical mixing band relationship ...................... 49

8. Incipient fluidization correlation ............ 51

9. Heat transfer coefficients versus NRe 54

10o Heat transfer coefficients versus Gmf .................. 55

l l o A v e r a g e b e d t e m p e r a t u r e , R u n s 1 a n d 4 . . . . . . . . . . . . . . . 5 8

12o Average bed temperature, Runs 2 and 5 59

13o Average bed temperature, Runs 3 and 6 ............... 60

14c Average bed temperature, Runs 7 and 10 62

15. Average bed temperature, Runs 8 and 11 63

16c Average bed temperature, Runs 9 and 12 64

170 Average bed temperature, Runs 13 and 16 ............. 65

18o Average bed temperature, Runs 14 and 17 ............. 66

190 Average bed temperature, Runs 15 and 18 ............. 67

20o Temperature profile, exit gas, Runs 1 and 4 ........... 75

viii

Figure Page

21. Temperature profile, plane 1, Runs 1 and 4 76

22o Temperature profile, plane 4, Runs 1 and 4............ 77

23o Temperature profile, plane 7, Runs 1 and 4 ............ 78

240 Temperature profile, exit gas, Runs 2 and 5 ........... 79

250 Temperature profile, plane 1, Runs 2 and 5 ............ 80

26. Temperature profile, plane 4, Runs 2 and 5 ............ 81


28. Temperature profile, exit gas, Runs 3 and 6 ........... 83

29. Temperature profile, plane 1, Runs 3 and 6 ....... 84


310 Temperature profile, plane 7, Runs 3 and 6 ............ 86

32. Temperature profile, exit gas, Runs 7 and 10 87

33. Temperature profile, plane 1, Runs 7 and 10 ........... 88



36. Temperature profile, exit gas, Runs 8 and 11 .......... 91

370 Temperature profile, plane 1, Runs 8 and 11 92



40. Temperature profile, exit gas, Runs 9 and 12 .......... 95


42. Temperature profile, plane 4, Runs 9 and 12 ........... 97 ix

Figure Page

CO

o Temperature profile. plane 7, Runs 9 and 12 . ... °.

Figure

64. Temperature difference analysis, Runs 15 and 18

Page

119

LIST OF TABLES

Table Page

1. Insert dimensions ... . .. . . ......... 36

2. Thermocouple locations ............................. 38

3o Bead properties o • * * > • o • • o • o a * o d «• • • • o * a • *« 40

40 Experimental results ..... ................ 45

50 Calculated results ... ................... . .... e..... 46

6 . N o m e n c l a t u r e . . 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3

xi

CHAPTER I INTRODUCTION

The term "fluidlzation" has come to have a special meaning in

the process industries. It describes the situation which occurs when a

fluid is passed upward through a bed of solid particles in such a way

that the resulting fluid-solid mixture behaves as if it were a liquid of

fairly high viscosity„ The term is applied generally to liquid-solid

systems as well as gas-solid systems and to systems in which the solid

particles are just barely suspended by the flowing fluid as well as to

those where the solids are actually being transported by the flowing

fluidc When the particles are barely suspended and no particle motion

is taking place, the system is said to be at the point of "minimum" or

"incipient" fluidizationo When the solids are being transported by the

fluid, the system is called a "dispersed suspension" (18)„

There are nominally three "states" of fluidlzation between

these latter two extremes, depending on the velocity at which the fluid

is traveling through the particle bed (5)„ These are called "quiescent

fluidization, " "dense phase fluidization, " and "dilute phase fluidizationo "

Quiescent fluidization describes the situation in which there is a slight

particle movement in the bed, but no violent mixing action,, Dense phase

fluidization occurs when the fluid velocity is high enough to impart rapid

2

motion to the particles, maintaining, none the less, a well-defined upper

boundary of the bed= When a substantial number of particles are carried a

out of the bed and the upper boundary becomes diffuse, then this upper

area, containing a significantly lower concentration of solids in the fluid,

is in the state of dilute phase fluidization,, In the case of gas-solid sys

tems for a given kind of solid and particle size, the average ratio of the

gas velocity at dilute phase fluidization to that at minimum fiuidization

is about 60 (6)0 If a fluid is passed upward through a bed of solids at a

velocity which is lower than that required for minimum fluidization, the

system is known as a "fixed bedo"

The first commercial fluidized bed process went into operation

in 1942 (4)„ It was a catalytic cracking unit for the production of gaso

lines in which oil vapors passed upward through a bed of catalyst par

ticles., Since that time the major interest in fluidization, as applied to

the process industries, has been in the area of fluidization with gases

rather than liquids,, A very large number of investigators have attempted

to define the fundamentals of these gas-solids systems and the number

of applications to commercial processes has grown continually,, In

addition to the catalytic cracking application, which is now being used

in about 100 cases, gas-fluidized beds are used in many petroleum,

chemical, and metallurgical industries (4)»

The major advantages of fluidized beds are: high heat and

mass transfer rates, good solids mixing, and very simple solids

3

transport equipment,, In some cases disadvantages over fixed bed con

tacting equipment have become apparent: the lack of counter current

flow, solids attrition and carryover, erosion, and the restriction of

gas flow to just that required for fluidization» Fixed bed contactors

have none of these disadvantages but they do, in general, have very low

heat and mass transfer capabilities,,

In the usual form of a fluidized bed reactor a vertical, cylin

drical shaped vessel, is used through which an upward stream of gas is

forcedo The vessel contains solid particles which may or may not re

act in some way with the fluidizing gas, but which are agitated more or

less violently by the gas„ As indicated above, this agitation appears to

improve greatly the mass and heat transfer characteristics over the

situation where the gas does not travel fast enough to move the particles0

In either case, the average linear velocity of the gas stream varies as

it travels from the bottom to the top of the bed- If the bed is at a con

stant temperature, this velocity difference from top to bottom is caused

by the density change in the gas brought about by the difference in total

pressure at different points along the height of the bedo If a temperature

difference in the bed exists because of heat being generated within the

bed or because heat is being transferred to or from the bed, then an

additional effect on the density will result and the linear velocity will

change correspondingly as the gas changes in temperature„

In an ordinary fluid bed system this variation in velocity serves

4

to limit the height of the bed, since a fluidizing velocity at the bottom

of a bed will become a carrying velocity at the top if the pressure drop

is great enough. This limitation is not particularly serious, since there

is a large difference between the minimum fluidizing velocity and mini

mum carrying velocity, and beds of modest height are quite common,

In 1957, attracted by the possibility of combining some of the

advantages of the fluid bed with those of the fixed bed, investigators at

the Y-12 Plant of the Union Carbide Nuclear Company at Oak Ridge,

Tennessee, started work on developing a contactor which would operate

at, or near, incipient fluidization (14, 15)„ In order to maintain this

condition throughout a bed of appreciable height these investigators built

a slightly tapered shell to contain their solids„ This tapered, cylindrical

shell was larger at the top than at the bottom, the wall having an angle

of about four degrees with the axis of the tube, The reported results

were very encouraging, showing as good or better heat and mass trans

fer characteristics than conventional fluid beds operating on the same

processes., At about the same time another team of investigators re

ported improved fluidization performance in tapered beds (23)a Based

on these reports, others became interested in the possibility of varying

the cross section of a reactor from top to bottom and work along these

lines was started at Mallinckrodt Chemical Works in Stc Louis and at

Harwell in England (22, 24), All of these research teams were con

nected in one way or another with the uranium processing industry and,

5

in each case, the solid particles under study were extremely heavy

(U02? UO3,. UF4) and of a very small size (200 mesh and under).

Othmer (19) points out that these two factors made" the results of these

investigations seem more favorable than they really were,, He states

that a uniform cross section will give more uniform fluidity when the

particle sizes and particle densities are in the usual ranges.

The Oak Ridge reports did not define clearly the basis for the

heat transfer coefficients obtained nor the design methods used to de

velop the angle of taper for the reactor shelL The mixing patterns re

ported also raised some interesting questions concerning the counter -

current operation claimed, since high heat transfer coefficients have

ordinarily been associated with particles moving rapidly in relation to

each other.

The research work reported here was undertaken in order to

develop a clear design basis for a varying cross-section fluid bed to

operate at incipient fluidization and to obtain some approximate overall

heat transfer coefficients for use in such a design. Since the construc

tion of a tapered shell reactor is ordinarily too expensive for com

mercial application, and in addition extremely inflexible, the approach

from the beginning has been limited to the development of a tapered in

sert.,

The objective of this investigation was to design an insert for

a particular incipiently fluidized gas-solid system and to test its

6

performance in that system0 The heat transfer coefficients in this sys

tem were to be determined in order to show whether these coefficients

lie in the region of fixed bed coefficients or fluidized bed coefficients=

The flexibility of the insert with respect to its applicability to more

than one particle size was to be evaluated.,

CHAPTER H THEORETICAL CONSIDERATIONS

Fluidization Quality

In any theoretical consideration of incipient fluidization it is

important to recognize that the great amount of work investigating and

correlating the fundamentals in this area has been done in conventional,

constant cross-section equipment. It is well known that, in conven

tional beds, as the gas flow is increased in such a way that the bed

passes slowly from the packed bed to the fluidized bed regime, the

fluidization starts first in the topmost part of the bed0 As the gas flow

is increased, the fluidization of the bed moves downward until the bed

is completely fluido By the time the bottom is fluid the top may or may

not be in the "boiling" or agitated condition, depending mainly on the

height and density of the bed» The reason for this, of course, is that

the gas expands under the influence of the decreasing pressure as it

travels from the bottom to the top of the bed„ Since the bed, consisting

of gas and solids, has the properties of a liquid, this pressure difference

between the top and the bottom is proportional to the product of the height

and the bed density,, In a shallow bed of low density particles, this prod

uct will be small enough to allow the pressure difference and therefore

7

8

the gas density change to be smalL In this case, then, the linear veloc

ity of the gas will be almost the same at the top of the bed as it is at the

bottom and the quality of fluidization will be uniform through the depth

of the bedc In a deeper bed of higher density solid particles there will

be a greater difference in this quality of fluidization from top to bottom

and, in practice, this fact has limited the height of the bed which will

operate satisfactorily. In the design and operation of a fully fluidized

system, a range of velocity of almost two orders of magnitude may be

utilized. In the case of a system which will be incipiently fluidized

throughout, it appears that a range of velocity of only a few percent

exists between the packed bed and the dense phase fluidization condi

tions o

The definition of incipient fluidization is a rather qualitative

one, concerning, as it does, the suspension of particles without causing %

them to move- Many experimenters have found, however, that this

point corresponds to a very definite point in the pressure difference -

mass velocity relationships in the bed„ A schematic representation of

a typical pressure drop-mass velocity relationship is shown in Figure

1 (25)o Note that the flow rate function is that of mass flow rate per unit

area, based on the area of the empty tube. This property is constant

throughout the depth of a conventional fluid bed since the cross section

of the bed is uniform from top to bottom. Leva et al. (11) believed a

better representation of this relation could be made by plotting the log

FLUIDIZATION REGION

VAN HEERDEN,NOBEL,AND

VAN KREVELEN (25)

MASS FlJOW RATE PER UNIT AREA

FIGURE I. TYPICAL PRESSURE DROP-FLOW RATE \

RELATIONSHIP.

' ' : 10

of the pressure drop versus the log of a modified Reynold's Number.,

The modified Reynolds Number was defined as:

The definitions of the terms used will be found in the table of nomencla

ture included in the Appendix as Table 60 Since all of the fundamental

investigations in the area of incipient fluidization have been carried out

under isothermal conditions, NRe is also a constant over the depth of a

given fluid bed, The shape of curves plotted on this basis, then, have

exactly the same shape as the one shown in Figure L The point of in

cipient or minimum fluidization has been universally accepted as the

point of intersection of the line representing the fixed bed performance

and the line showing fluidized bed characteristics,, This point is repre

sented by G0 in Figure 1. Van Heerdenj Nobel and Krevelen (25) have

defined this G0 as the "critical mass velocity,," Experimenters report

ing similar information on nonuniform cross-section beds have observed

exactly the same type of behavior (16, 17, 23, 24)„ K„ J- Miller (17)

confirmed the fact that the intersection point mentioned above and the

qualitative definition are identical in a nonuniform cross-section bed=

He did this by probing the bed and observing particle movement at the

time he was determining the pressure drop versus flow relationships„

The experimental determination of the critical mass velocity is

thus very straightforward.. The calculation of this value with moderate

- 11

accuracy is an old problem and has been investigated by many workers.,

The results of their work had little or no agreement, one with another,

until Leva, Shirai, and Wen (12) brought together the data of ten pre

vious investigationso This correlation covers an extremely wide range

of gases, particle sizes, and particle densities:

Gmf = Cpp2gcPg(Ps ~ Pg>»

For NRe less than 10,, c r 0„0007 NRe"®5^. For NRe above 10, Leva

proposes a more complicated expression for C (7)„ Even this correla

tion, however, is only useful as an approximation, having an agreement

with published data of only about plus or minus 30 percent, No authors

were encountered who commented on the fact that the density of the fluid

is not a constant in any bed of appreciable heights If the bed is not iso

thermal an additional complication arises, that of variable viscosity»

The literature on this subject appears to contain no information on the

range of velocity over which a bed may be incipiently fluidizedo Even

though it is universally considered to be a single-valued point, as a

practical matter there must be a small range of velocity which will pro

vide this conditiono

Isothermal Insert Design

The early work on nonuniform cross-section reactors was

undertaken because the investigators felt that a more constant superficial

12

linear gas velocity would provide a more uniform quality of fluidization

through the reactor.. If this constant linear velocity is the only criteri

on, then an axial insert may be designed to provide the necessary varia

tion in free area from top to bottom.,

In an incipiently fluidized bed, the total pressure at any point

in the bed will be a function of the pressure on the top of the bed, the

density of the bed, and the height of the bed:

P = P t + P b ( H b - H ) 0

If ideal gas behavior is assumed, the pressure and the density of the

gas are related by:

The mass rate of gas flow (W) must be constant and the condition of con

stant linear velocity (V) has been imposed on the design., Since

O - W *JS - VK '

it appears that the quantity (A Pg) must also be constant over the entire

height of the tied., Eliminating the gas density from the previous ex

pressions,

= Pt • Pb(Hb - H)

and

a _ WRT o ' • VMp, t Pb

13

At any point in a cylindrical bed the cross-sectional area of the bed (A)

is related to the reactor diameter (Dr) and the insert diameter (Dj):

A = f

14

and the temperature of the heating surface and that between the gas

leaving and the heating surface,, He found heat transfer coefficients

ranging from about 4 to 100 BTU/hr„ fto ^°F„ He found a very large in

fluence of the ratio of the diameter of the particle to the diameter of the

tube and in general, it appears that this rather definitive work is not

applicable or extendible to ths small particle diameters and relatively

large tubes involved in the current investigation. Later workers chose

to correlate their results based on a modified Nusselt Number.. This

modified Nusselt Number included the diameter of the particle in place

of the usual conduit diameter:

Nu = hPp. k

Finally in 1947 Leva (10) published a generalized correlation for heat

transfer to gases through packed tubes in which he relates the modified

Nusselt Number to the modified Reynold's Number as follows:

h = °-813Bt^r) eexp

inches, and up as large as 0= 003 inches,, Their paper and its results

are widely accepted today and confirm the extension of Leva's data

mentioned above, A schematic representation of the type of informa

tion Baerg et aL reported is illustrated in Figure 2„ Note that the fixed

bed heat transfer coefficients follow a straight-line path at the lower

left-hand edge of the graphs There is an abrupt break in this line and

the fluidized bed performance is indicated by the remainder of the line.

These investigators defined incipient fluidization as the point at which

this break took place. No indication of whether or not the authors be

lieved that this break in the heat transfer-mass flow rate, curve coincides

with the pressure drop-mass flow rate break was given* Leva (8) states

that there is-a sharp increase in heat transfer coefficients between the

fixed bed and the fluid bed and that this can only be caused by the slight

incipient motion of the solids past the heat transfer surface. He also

states that in the case of fixed beds through which air is being passed,

heat transfer coefficients range from about 3„ 5 to 7 BTU/hr=ft. ^0Fo"

Investigators in the area of fixed bed film coefficients used inlet and

outlet temperature differences, usually averaged as a logarithmic mean0

This was considered generally to be a film coefficient even though it was

also generally recognized (20) that the thermal conductivity of the solid

had a very definite influence on the heat transfer coefficient.. This would

appear to indicate that the film coefficients reported by Colburn, Leva,

and Baerg are really forms of an overall coefficient. Levenspiel and

16

BASED ON ROUND SAND OF 0.00106 FT.

DIAMETER

BAERG, KLASSEN, AND GISHLER (2)

MASS VELOCITY (Ibs/hr ft.2)

FIGURE 2. TYPICAL HEAT COEFFICIENT REPRESENTATION

17

Walton (14) in their investigation of heat transfer in fluidized systems

made a certain number of runs in which their system was in the non-

fluidized state., They reported some coefficients for these runs which

range from about 1„ 33 to 8 BTU/hr„ ft„ ^°F„ In general the correlations

of heat transfer information in fixed beds are vague and a definitive

study in this area is lacking., In view of the very definite advantages of

the more recently, developed fluidized beds in so far as heat transfer

and mass transfer are concerned, it is doubtful that this work will be

done. Vener (26), in his report on fixed bed operations, states that

mechanisms for heat transfer in moving bed applications are extremely

complex and not well understood.

Heat Transfer in Fluidized Beds

Othmer (21) points out that there have been more than 35 papers

published over the last ten years pertaining to dense phase heat trans

fer. Of these, over half presented original data, the remainder pre

sented critical reviews, and, of these, only two proposed any general

ized correlation.,

Bannister (1) in 1959 published a literature survey on heat

transfer on beds of fluidized particles0 He presents, in this review, a

rather detailed analysis of the literature on this subject froir: 1943 to

1959o He reviews a total of 86 papers and lists froir these about 35

generalized correlations., His conclusion, after the study of the 86

18

papers and 35 correlations, is that the formulae available for design

purposes in the case of heat transfer equipment give only approximate

information when applied to specific cases„ He feels that the follow

ing six conclusions seem to be agreed upon by most investigators.

lo The thermal conductivity of solid particles does not seem

to be of first importance in affecting heat transfer,

2= The thermal conductivity of the gas or liquid has a con

siderable effect-

3o In a given system, heat transfer increases suddenly when

fluidization sets in and increases to a maximum as the Reynold's

Number is increased. Further increases cause a drop in heat flow,,

4o The above conclusions are valid whatever the form of a

system, that is, whether it is heat transfer to or from a jacket, or

from a heating element surrounding a bed, or whether it is heat trans

fer to or from a probe or surface within the bed, and whether the heat

transfer is to or from the carrier gas or liquido

5„ A thin zone above the support grid in a fluid heated system

shows a temperature gradient. The remainder of the bed shows tem

perature uniformity0

6. It is difficult to generalize, but in a gas fluidized system,

except where hydrogen or helium is used, values of 5 to 450 BTU/hr0ft. ̂

°F„ are encountered„ ;

Experimental work in general has been carried out on small

equipment, beds of less than six inches in diameter being typicaL Only

one, in all the papers reviewed by Bannister, was larger than six incheso

This means that the effect of the side wall no doubt was sometimes se

rious in its effect on fluidization quality, and might very well tend to

invalidate the correlations produced,, Leva (9) publishes for compari

son the correlations of ten investigators. Very little agreement is shown

among these correlations except for the general trend of the curves, in

dicating that the heat transfer coefficient increases with increased mass

velocity., In fact the variation in heat transfer coefficient for a given

mass velocity between the highest and lowest ranges up to about a factor

of seven* Practically all investigators have attempted to correlate their

data based on some relationship between the modified Nusselt Number

and the modified Reynold"s Number. Some have introduced the ratio of

the fluidization velocity at that point to that required for minimum fluid-

ization0 Others have introduced a term to compensate for differences

in bed height, some have included a Prandlt Number^ some have in

cluded the ratio of the tube diameter to the particle diameter, others

have made additional provision for variation in the quality of fluidiza

tion., Leva also presents a generalized correlation in which he has at

tempted to combine the work of four investigators. He feels that it is a

working relationship and takes into account most ordinary situations^ It

is as follows:

20

hDp = 0.16 cPsPsDp 6c lo 5 0= 5 " " 0o 36

k k GDp)|

"mY

In the experimental determination of heat transfer coefficients in fluid-

ized beds it appears that all investigators considered the radial tem

perature gradient to be nil, and calculated film coefficients based on

some average of the bed temperature and the wall temperature., The

more recently accepted method appears to be that of measuring bed

temperatures along the height of the bed and then graphically integrating

the temperature difference between the bed and the wall over the depth

of the fluid bedc This is then reported as a film coefficient

In the case of a fluid bed being heated by an axial element ex>

tending the full length of the bed, an overall heat transfer coefficient

may be defined as follows:

The axial heating element in this case will serve as the insert and must

vary in diameter from top to bottom. In order to make reasonable

simplifications in the design equation derivation, the following assump

tions are made:

Nonisothermal Insert Design

!«, that no heat is lost through the reactor wall.

2c that there is no radial temperature gradient,

21

3c that the overall heat transfer coefficient is a constant

over the height of the reactor, and

4c that the gas temperature and the solids temperature

at any one point in the bed are equaL

This last assumption limits the application of this method of design to

the cases where the amount of heat transferred between the insert and

the bed is large compared to the heat transferred between the solids and

the gasc

Considering a thin, disk-like slice of the bed at any point,

having a thickness of AH, it is apparent that the heat input to it will

be:

U(rTDi AH) (Tt - Tave),

where Tave is the average temperature in the slice under consideration,,

The thin section will have, in general, a temperature difference between

its top boundary and its lower boundary= If this difference is designated

by then the solids, moving downward, will lose heat at the rate of

SCps A To Similarly the gas, moving upward, will gain heat at the rate

of WCpg fcTo Under steady state conditions, then

11(77*^ A H) (Tj - Tave) = (WCpg - SCps) AT«

In differential form, this may be written:

dH - (WCpg - SCps) ^T. "7TUDi (Tj - T)

22

As previously noted, however, Dj is a function of the height and the

temperature:

rt 2 n 2 4 WRT Di = ^ "TTVM-Pt+Pb (%-«!)

Incorporating this egression in the preceding one, the final design

equation becomes:

[dH = (WCpg - SCps) ( dT Oo5

i 2 4WRT I r ru J (t , - t ) |D r - j j -vMpt +pb(Hb - Hj]I

The solution of this equation for the given design problem is

not as difficult as it appears at first inspection. The first step is to in

sert the appropriate values of the given and known quantities, W, S, U,

Dr, Cpg, CpSj, V, M, Tj, pb, and Hb» The procedure then is to

plot

versus T 5

(T,- - T) lD„2 - 4 WRT TTVM [Pt + Pb(Hb " H)]

for various selected values of Ho Graphical integration of this plot will

provide the correct value of T at each of the selected values of H„ Sub

stitution of these values in the expression for Dj will give the design

dimension for the insert

The final design equation is very sensitive in the region where

23

WCp is about equal to SCps and its use in that region is not recom-S

mended* Note that if SCps is larger than WCpg, the longitudinal tem

perature gradient must change sign, thus making the design assump

tions invalid.

Mixing Studies

As mentioned earlier, the improved heat transfer character

istics of fluidized beds have been attributed to the increased particle

motion, Furthermore, it appears that while mixing is very slight in a

fixed bed and very violent in a fluidized bed, the actual mixing pattern

in a bed at incipient fluidization at a time when solids are being removed

at one end of the reactor and introduced at the other is not clearly de

fined,, As an important adjunct to the study of heat transfer in an in-

cipiently fluidized system it appeared that a mixing study was in order.

The testing of an insert for proper behavior necessarily included a study

of the mixing characteristics of the bed.

The usefulness of the nonuniform cross-section bed is tied up

irrevocably with mixing characteristics* Levey et al„ (14, 15) reported

mixing studies in a tapered bed at or near incipient fluidization, which

indicated that the first particle of the feed would not be discharged as

product until after time lapse of approximately 60 percent of the nom

inal retention time,, He further stated that on this basis the reactor

could be operated in a manner equivalent to several counter current

24

stages., His mixing study and conclusions were based entirely on the

percentage of feed appearing in the product as a function of time., A

more definitive study of mixing from the top to the bottom of the bed

was indicatedo

This mixing study was undertaken just prior to the heat trans

fer work» Thorough sampling at various points along the height of the

bed as well as at various points within the bed was necessary in order

to follow the progress of whatever mixing might be taking place0 Since

the state of fluidization is one of a relatively small amount of particle

movement, sampling was done by stopping the gas and solids flow and

carefully inserting sample devices which performed the necessary duty0

At the start of a mixing experiment, the bed was composed of particles

having one identity, and the feed hopper full of particles of another

identity, As the bed was fluidized and the feed particles were allowed

to fall on to the bed, an equivalent amount being removed at the bottom,

certain feed particles mixed with the bed particles and ranged ahead of

others., Likewise, as the bed moved downward, certain bed particles

lagged behindo The distance between this bottom particle of feed and

the top particle of bed was called the "mixing band widtho" The change

in this mixing band width as the interface proceeded down the column

gave a very accurate picture of the mixing performance,, It was also of

considerable interest to find out that, in this type of bed, the particles

move more rapidly down the center, rather than down the walh

25

The method of discharge of the bed particles from the bottom

of the bed was of extreme importance and, depending on the method of

doing this, various mixing characteristics in the bed were observed..

Using sampling planes which were far enough above the discharge point,

the band width measurements were not influenced to any great extent by

the method of discharge.

This mixing study was performed in the Chemical Engineering

Department at the University of Arizona by Miller (14), under the super

vision of the author and the results of that work will be discussed brief

ly later.

CHAPTER m EXPERIMENTAL APPARATUS

General

The experimental apparatus used in this investigation was lo

cated in the Unit Operations Laboratory of the Chemical Engineering

Department at the University of Arizona., Figure 3 is a photograph of

the experimental apparatus,. The arrangement of the various pieces of

equipment is shown schematically in Figure 4„ The general equipment

without the heating devices and temperature measuring equipment was

used by Miller (17) to carry out mixing studies and it is described

rather fully in his thesiso The main items of equipment used were: the

reactor shell for containing the fluid bed along with the necessary gas

distribution system, temperature measuring devicesy and inserts; the

solids handling system for feeding and discharging solids; and the supply

systems for the fluidizing gas and heating steam0

Reactor

A schematic representation of the reactor shell is shown in

Figure 5„ This shell was constructed of a plexiglass tube eight inches

in outside diameter with a one-quarter inch thick walL Its overall

26

FIGURE 3

Photograph of Apparatus

FEED HOPPER

% ROTARY VALVE INFRARED

X LAMPS HEATING COIL HUMIDIFIER

PROBE VIBRATORY FEEDER

.T.C

T.C. (4)

T.C. (4) ROTAMETER

AIR

REGULATOR 100 PSIG

AIR SUPPLY T.C. (4)

FILTER MANOMETER .-T.C. 100 PSIG

STEAM 'SUPPLY T. C.

ROTARY VALVE ROTARY

VALVES TRAP TRAP STEAM

REGULATOR

FIGURE 4. SCHEMATIC DIAGRAM

OF EQUIPMENT.

I

29

8"0.D. PLEXIGLASS

1/4" WALL

1-1/2 GLASS WOOL

INSULATION

INSERT

i

1

PLANE I

PLANE 4

PLANE 7

FIGURE 5. REACTOR SHELL DETAILS

Scale: l"= l'

30

length was 53 inches, allowing a bed height maximum of 48 inches „

Around the periphery of the shell at 7-inch intervals along the length of

the shell were sampling ports = Each sampling plane contained four

ports, 90 degrees aparto The bottom sample port plane was two inches

above the distribution plate0 Six additional planes of sample ports ranged

up the height of the shell with the top plane being four inches below the

top of a 48-inch bed. The top plane of sample ports was designated

plane 1 with the numbers increasing downward to plane 7 at the bottom,,

All of these sample ports were used in the mixing studies, but only the

four in each of planes 1, 4, and 7 were utilized in the heat transfer

study» Each of thsse 12 sample ports provided the access point for

thermocoupleso The details of the gas distribution system at the bottom

of the reactor are shown in Figure 6

REACTOR SHELL

INSERT

SOLIDS DISCHARGI

AIR INLET

STEAM INLET

SOLIDS DISCHARGE

100 MESH SCREEN DISTRIBUTION PLATE

AIR INLET

FIGURE 6. GAS DISTRIBUTION SYSTEM

S c a l e : l " = 2 "

32

chamber,, Two three-eighths inch holes were provided in the very

bottom of the reactor to allow solids dischargee

Plexiglass was chosen for the reactor material because of the

fact that a condition of incipient fluidization was necessary and prac

tically the only means to make sure that no bubbling or agitation of the

bed occurred was by visual observation., In addition, the plenum cham

ber was made of plexiglass in order that constant visual watch could be

kept to make sure that no steam leaks were occurring into the air cham-*

berc This material of construction necessarily limited the temperature

to which the reactor could be heated, but in view of the fact that this

study was a purely exploratory one, it was not considered to be a serious

handicap0 Once better information is available on fluidization quality in

nonuniform cross-section beds, the visual inspection may no longer be

necessary and reactor shells of more conventional material may be usedo *

The 8-inch diameter shell size was chosen because almost all

investigators have reported an adverse influence of the walls in small

tubes. On the other hand, the supply of fluidizing gas available was in

sufficient to provide even minimum fluidization of a reactor bed any

larger than eight inches in diametero The chosen bed height of 48 inches

was purely arbitrary.,

In order to determine whether or not the bed was fluid, a probe

was required, An aluminum rod, one-half inch in diameter and 52 inches

long, was provided for this purpose., Since this probe was used often it

33

was attached to a cord which passed over a pulley located about five feet

above the top of the reactor. The other end of this cord was fastened

at the operator's station and provided an easy, positive method of de

termining fluidization quality,. The rod was frequently lowered into the

bedo If it fell freely all the way to the bottom, the bed was considered

fluidized, if not, an adjustment in gas velocity was madeo

In order to prevent heat loss through the wall of the reactor, a

1-1/2-inch thick layer of glass wool was fitted around the outside.. Small

slits were cut in this insulation to provide inspection ports at appropri

ate pointso These slits were plugged during the operation and were

opened only as required for visual inspection of the bedo

During the mixing studies in this equipment, it was found that

it was very important that the insert be centered exactly and that the

reactor be perfectly verticaL Uniformity of fluidization quality seemed

to suffer seriously if either of these conditions was not satisfied, For

this reason the reactor was carefully leveled and the insert centered

immediately prior to each series of runs.

Solids Handling System

It was important that the solids be fed to the reactor at the top

at a fairly uniform rate. Likewise, it was necessary that the solids

discharge provide uniform withdrawal of material at both sides of the

bottom of the reactor Rotary valves were chosen from this service

34

and after considerable experimentation as described by Miller (17) a

satisfactory valve was designed and builto Each valve was driven by a

separate one-sixth horsepower, variable speed motor., In the case of

the feed rotary valve, it was necessary to provide in addition a small

vibratory feeder.. This feeder served to smooth out the flow of solids

from the rotary valve.. The feed rotary valve discharged into a three-

eighths inch pipe 16 inches long, mounted in a vertical position. The

bottom of this pipe terminated about one-half inch above the bottom of

the trough of the vibratory feeder» This small feeder discharged solids

through a funnel into the center of the top of the bedo Small air-operated

vibrators were placed on each rotary valve to make sure the solids flow

was constant and to prevent bridging., .

The initial work with glass beads, particularly the smaller

glass beads, showed that the generation of static charge might serious

ly interfere with uniform solids feed and discharge* In order to mini

mize this effect, a small evaporative cooler was mounted with the

equipment and a stream of air of high humidity was constantly provided

to the feed hopper., This allowed any static charge to be dissipated be

fore the beads entered the feeding system. Satisfactory operation was

observed in all caseso

The heating of the beads being fed to the reactor was accom

plished by the use of a Glascol heating cord wrapped around the length

of the three-eighths inch pipe between the rotary feeder and the vibratory

35

feeder.. This heater was capable of delivering a thousand watts and was

controlled by means of a variac* In addition, heat was supplied to the

beads by the use of two 250 watt infrared bulbs focused on the beads as

they traveled through the trough of the vibratory feeder. The feed

hopper was made of plexiglass and provided storage for approximately

50 pounds Of glass beads.

Inserts

During the progress of the mixing studies and heat transfer

studies three different inserts were designed and built= Table 1 gives

the dimensions of these three inserts. All three were designed on the

basis of the relationships outlined previously,,

Insert 1 was designed to provide isothermal incipient fluidiza-

tion for the medium sized beads* Insert 2 was designed for the iso

thermal c&se for the large size beads* Insert 3 was designed for the

heat transfer study for large beads flowing through the reactor at 60

pounds per hour* As the experimental work progressed it became ap

parent that these inserts might be used for cases other than the one for

which they were designed. Insert I was used for the mixing study with

the small beads as well as the medium sized beads* Insert 2 was used

for the nonisothermal case of the small beads as well as the mixing

study with the large beads* Insert 3 was used for the nonisothermal

heat transfer work on the medium beads as well as the large beads*

36

TABLE 1 INSERT DIMENSIONS

Height Insert Diameter (inches) "" (inches) ' NOo 1 No0 2 No0 3

46 Oo 64 Oo 70 0o 58 44 Oo 90 Oo 98 Oo 95 42 10 09 lo 20 lo 20 40 lo 26 lo 38 lo 38 38 lo40 lo 54 lo 54 36 lo 52 lo 67 lo 70 34 lo 64 lo 80 1.86 32 lo 75 lo 91 2o 00 30 L85 2.02 2012 28 lo 94 2.12 2o 24 26 2o 03 2.22 2a36 24 2o 11 2o 31 2o 46 22 2o 20 2o 40 20 56 20 2o 27 2,48 20 66 18 2o 34 2o 56 2» 76 16 2o41 2o 63 2o 86 14 20 47 2o 70 2o 96 12 2o 54 2o 77 3o06 10 2o60 2o83 30 16 8 2o 66 2o 89 3.26 6 2o 72 2o 95 3.36 4 2o 78 3.01 3o 46 2 2.81 3o 07 3.56 0 2o 88 3o 12 . 30 72

37

All of the inserts were fabricated from 4-inch diameter aluminum rod.

They were cut to length and an axial hole one-half inch in diameter was

drilled 31 inches into the center of each one- This provided the internal

heat transfer surface for the condensing steam. The rods were then

machined to the required insert dimensions on a lathe equipped for con

tour machining.

Temperature Measurements

Temperature measurements in the bed were made by means of

iron-constantan thermocouples sheathed in a one-sixteenth inch stain

less steel tube0 These thermocouples were inserted through the sample

ports and held in position by means of a standard one-sixteenth inch

tubing fitting. These thermocouples were located with extreme care at

particular points in the bed. A listing of the exact location of each of

these 12 thermocouples is provided in Table 2. Other thermocouples t

were located in the inlet steam line, the inlet gas plenum chamber, the

exit gas stream, and in the incoming bead stream and were mounted

similarly. All 16 of these thermocouples were connected to a Leeds

and Northrup,, Model G, Multiple-point Recorder. Temperatures from

each couple were recorded once every 64 seconds during a run, directly

in degrees Fahrenheit. All 16 thermocouples were calibrated carefully

before use and were found to have a maximum deviation of plus or minus

0o 2 degree Centigrade, and therefore no corrections were applied to

38

TABLE 2 THERMOCOUPLE LOCATIONS

Distance from Thermocouple Location Insert (inches)

1 Plane 7 _ Imbedded 0o 125" 2 " Oo 75 3 " loOO 4 " lo 25 5 Plane 4 Imbedded 0o 125" 6 " 0o75 7 " lo 25 8 " lo75 9 Plane 1 Imbedded 0o 125"

10 " 0o75 11 " Oo 50 12 " 2o00 13 Steam line 14 Inlet air 15 Exit air 16 Solids feed

39

their indicated readingSo

Solids

Three bead sizes were used in this study0 All were very uni

formly spherical in shape and each size covered a very narrow size

range* The two smaller sizes were obtained from Microbeads, In

corporated, of Jackson, Mississippi, The largest beads were obtained

from the Minnesota Mining and Manufacturing Company,, The properties

of thesser beads are shown in Table 3o The beads were inspected peri

odically and were found to suffer no attrition during the mixing and heat

transfer studies..

The mixing study preceded the heat transfer study and involved

the use of dyed beadSo Therefore, all beads used in the heat transfer

study were coated with a very thin layer of Dykem dyeD

Utilities

The gas used for fluidization in all cases was aire The air was

supplied to the apparatus by a compressor which had the capability of

supplying 100 standard cubic feet of air per minute at a pressure of 100

pounds per square incho This air was passed through a large surge

tank, an oil filter, and a pressure regulator into a rotameter having a

capacity of about 60 standard cubic feet per minute at 40 pounds per

square inch pressure. An alternate rotameter having a maximum

40

TABLE 3 BEAD CHARACTERISTICS

Small Medium Large

Diameter (ft.)

Particle density (lbs. /ft, 3)

Bulk density (lbs0/fL3)

Manufacturer

o 000875

1540 9 f

94= 9

Microbeads InCo

o00222

155o 2

93,6

Microbeads Inc»

„ 0059

182o 4

113,0

Minnesota Mining & Mfgo

41

capacity of about 6 standard cubic feet per minute was used for the runs

using the smallest beads. Both rotameters were carefully calibrated

with a standard test meter supplied by the Tucson Gas, Electric Light

and Power Company. This standard test meter was represented by the

company to have an accuracy of plus or minus five-tenths of one per

cent.

The steam used for heating was drawn directly from the lab

oratory supply system of 100 pound per square inch steam,, A trap was

provided immediately before the equipment to remove the major part of

water from the steam. It then passed through a pressure regulator di

rectly into the insert. The insert condensate was discharged through

another trap into a suitable container.

CHAPTER IV EXPERIMENTAL PROCEDURE

A total of 18 runs was made in this heat transfer study utiliz

ing three sizes of beadsf each at three different feed rates0 The gen

eral approach was to make a series of three runs, each of a different

solids feed rate using one size of bead, A duplicate of this three run * I

series was then run at another time. The first run of each series was

made without any bead feed or discharge.. The second run in each case

was made at a feed rate of about 60 pounds of beads per hour, and the

third at about 85 pounds of beads per hour0

Before each series of runs the selected beads were weighed

into the reactor shell and the bed height adjusted to 48 inches with the

fluidizing air at the incipient fluidization velocity. The steam was

turned on and the air flow rate adjusted as required to maintain the

condition of incipient fluidization. As the temperatures in the bed in

creased, frequent adjustment cf the air flow rate was necessary until a

steady state was reachedo

After the temperatures in each section of the bed became rela

tively constant, this condition was maintained for exactly 30 minutes,

after which the conditions were readjusted for the next run. At least

once during this 30-minute period, the thermocouple in the gas stream

42

43

just above the top of the bed was moved in a traverse along a radius of

the reactor tube0

In the case of those runs in which beads were moving through

the reactor, the feed rate was checked at regular intervals and both

product and feed were carefully weighed.. Once the feed rate had been

set, the height of beads in the bed was controlled within plus or minus

one-quarter of an inch of the 48-inch level by adjustment of the speed

of the discharge rotary valve drives0

The most critical part of the experimental activity was that of

maintaining the bed in the incipiently fluidized state., Small slits in the

insulation near the bottom of the reactor allowed inspection at that pointo

Bubbling or fluidization occurring in the upper section of the bed could

be observed by watching the behavior of the upper surface of the beads0

The probe was used periodically to make sure no parts of the bed were

in a nonfluid state° The probe was lowered into the bed at a selected

spoto If it did not drop of its own weight all the way to the bottom, then

the gas rate would be increased until this did happen., Although probing

. was done regularly in all parts of the bed, there was never a time when

the rod would drop at one point and not at anothero

In addition to the recording of the 16 temperatures noted in

Table 2 and the weights mentioned above, periodic notations were made

of the steam pressure, barometric pressure, bed height, feed rate, and

outlet bead temperature.

CHAPTER V EXPERIMENTAL RESULTS

The experimental results obtained in the 18 runs are tabulated

in Table 40 The runs are not listed chronologically, rather they are

grouped so that duplicate runs are adjacent for easier comparison,.

Each reported insert temperature is the reading of a single thermo

couple imbedded one-eighth inch in the surface of the insert at that

plane,, Each reported bed temperature is a calculated average of three

thermocouples located at various distances from the insert,, This av

erage was calculated by graphical integration through appropriate

weighting of a radial temperature profile estimated for each plane from

the three temperature readingso These estimated profiles are shown in

Figures 20 to 55 in the Appendix. *

The calculated results obtained are shown in Table 5„ The

average temperature difference shown was calculated by graphical in

tegration from a temperature difference profile.. This profile was

generated from the average temperatures shown in Table 4. One pro

file was developed for each set of duplicate runs. These are shown in

Figures 56 through 64 in the Appendix,, The values for U, as discussed

later, are given for only one section of the reactor..

44

I

TABLE 4 EXPERIMENTAL RESULTS

Temperatures

TABLE 5 CALCULATED RESULTS

Temperature Difference, Insert to Bed Run Dd (°C) Overall U*

(too) Plane 1 Plane 4 Plane 7 Inlet Ave7*~ (BTU/hr.ft. °F.)

1 o 0708 44o 0 32.0 36.3 54.2 33.4 17.1 4 o 0708 43.7 32.6 37.2 53.0 33.4 17.1

2 o 0708 37o 7 33.5 42.3 43.3 35.1 15.4 5 o 0708 38o 9 33.5 38.1 39.0 35.1 15.4

3 .0708 37.3 32.9 40.4 42.5 36.1 13.9 6 o0708 37.4 33.0 38.9 41.5 36.1 13.9

7 . 0267 37.2 37.4 52.6 54.9 39.4 10 . 0267 39.6 31.3 51.2 56.2 39.4 5.5

8 o 0267 36.3 30.4 56.3 59.2 39.2 11 o0267 31.8 29.8 52.0 55.0 39.2 1*3

9 .0267 25.8 29.7 54.8 58.0 26.0** 2. !•* 12 o 0267 24.0 28o 1 50.6 54.8 26.0** 2. !•*

13 .0105 31.3 26.0 35.6 56.9 30.2

00 o . o

16 .0105 35.2 30.5 41.2 57.6 30.2

00 o . o

14 .0105 20.4 29.9 34.9 53.3 29.7 2.6 17 .0105 26.5 24.8 35.9 57.5 29.7 2.6

15 .0105 26.2 31.9 35.4 55.0 34.8 2o6 18 .0105 20.1 35.7 34.7 56.4 34.8 2o6

* Calculated over plane 7 to plane 4 bed section, except as notedo

** Calculated over plane 4 to plane 1 bed section.

CHAPTER VI DISCUSSION OF RESULTS

Fluidization Quality

Based on the frequent bed probing and the almost continual

visual inspection mentioned previously, it is certain that uniform in

cipient fluidization existed throughout the reactor in all runs0" This was

by far the most important aspeGt of the experimental procedure and was

the primary concern during all experimental runs0 During the prelim

inary heating up period of one run the bed temperature was inadvertent

ly allowed to increase without adjustment of the air flow rate0 The

chart recording bed temperatures showed very graphically the point at

which dense phase fluidization beganc All temperatures in the bed con-

verged to within three or four degrees of one another., Inspection of the

bed at this time showed only a small amount of bubbling* Immediately

upon correction of the air flow rate the temperatures again displayed

the characteristic profiles within a very few minutes0

At the beginning of the first series of runs using the smallest

bead size the reactor contained insert 3, Good fluidization quality was

observed for the first few minutes of heating, but as the bed tempera

ture increased, bubbling occurred at the bottom while the top part of the

48

bed was not fluidc No amount of adjustment, however careful, could

bring about the uniform quality of fluidization realized in the other runs

The attempt to use insert 3 for the small beads had been made based on

the good performance of the medium beads with this insert,

Recognizing finally that uniform incipient fluidization could not

be obtained with this insert, a smaller insert (insert 2) was chosen and

installed in the reactor,, The succeeding runs were quite successful

from the standpoint of uniform incipient fluidization0 Insert 2 provided

approximately 10 percent more free area at the bottom of the reactor

than did insert 3c

The mixing ejqperiments performed by Miller (17) serve as

additional confirmation of the ability of these inserts to permit uniform

fluidization quality from top to bottom,. Miller found that there was

some increase in mixing as the interface between two different colored

beads traveled downward through the bed. This increase, however,

was very modest and the total amount of mixing as compared to ordinary

fluidized bed performance was quite smalh A typical example of his

results is shown in Figure 70 In fluidized bed operation a similar plot,

would show the mixing band width to be practically the entire depth of

the reactor within a very small percentage of the nominal retention

time.

Table 4 includes the tabulation of the fluidizing air rates for

each run., These values show very close agreement between each two

49

SMALL BEADS

MEDIUM BEADS

LARGE BEADS

MILLER, K.J. ( 17 )

DISTANCE FROM TOP OF BED (INCHES)

FIGURE 7 TYPICAL MIXING BAND RELATIONSHIP

50

duplicate runs0 Within each bead size, however, it does show a larger

flow rate requirement for the cases where no solids are moving through

the reactoro This is true with each bead sizea This phenomenon was

caused by the effect of mechanical vibration on the fluidization charac

teristics of the bed0 This effect has not been discussed in the litera-

ture0 It was quite noticeable in this experimentation that a bed which

was operating quite nicely under the condition of incipient fluidization

would immediately show bubbles when vibrators, feeders, or other

mechanical equipment was started in the vicinity„ The relative effect

on the various bead sizes was somewhat differento The large beads re

quired about five percent more air when the vibrators were not operat

ing, the medium beads required only about 3-1/2 percent more air, and

the small beads required as much as 20 percent more air0 In spite of

these differences, however, the values for the incipient fluidization air *

requirements agree quite well with literature values and are quite con

sistent within themselves,, A representation of this comparison is shown

in Figure 8„ The correlations of Leva and Grummer (11), Leva and

Shirai (12), Bearg, et al„ (2), and Van Heerden, et ah (25) are included

for comparison., Note that the experimental results must be represented

on this type of plot as a line rather than a pointo This is necessary be

cause the cross section available for gas flow increases as the gas

travels up through the reactor bedo For this reason the mass flow of

gas per unit area necessarily must decrease* The lines shown represent

51

BAERG (2) 01 LEVA (I I)

EXPERIMENTAL

LEVA (12)^-

H U.

EXPERIMENTAL

52

not only this variation from top to bottom of the bed but the variation

from run to run throughout all work with a particular bead size,,

Heat, Transfer Coefficients

Inspection of the temperature profiles in Figures 19 through

72 show that there is extremely good agreement in similar runs par

ticularly in the lower half of the reactor bed, both in the absolute values

and in the general shape of the curves0 For this reason, reliance has

been placed on the calculation of heat quantities based on the tempera

ture differences within the reactor*,

Further inspection of the temperature profiles mentioned above

will show that the top half of the reactor in all cases but one did not

reach steady state by the time the run was completed,, This fact was

not apparent at the time of the run0 It is equally obvious from the same

information, however, that the lower half of the reactor up to at least

plane 4 was in all cases close to a steady state condition,, For this rea

son heat transfer coefficients and insert performance calculations and

conclusions have been based on the performance bf the lower half of the

bed alonec

The previously mentioned lack of steady state conditions at the

top of the reactor and the concern with entrance effects at the extreme

bottom of the reactor necessitated the choice of the section between

plane 7 and plane 4 in the reactor for determination of heat transfer

coefficientso The quantity of heat transferred through this section was

calculated based on the assumption that the gas temperature and the

bead temperature were equal to each other at every pointo This as

sumption allowed the calculation of the heat gained or lost by the gas

stream and the bead stream between the two planes* This quantity of

heat was then divided by the heat transfer area through that section and

the mean temperature difference between the bed and the insert calcu

lated as outlined previously.. For comparison purposes the heat trans

fer coefficients obtained with the large beads in the three cases were

averaged, Similarly the three coefficients obtained with the small beads

were averagedo In the case of the medium size beads, however, the

difference between the heat capacity of the gas stream and the heat ca

pacity of the bead stream in the moving bed runs were so small that the

accuracy of the calculations was insufficient to place any reliance in the

values obtained, The coefficient obtained in the static bed runs, how

ever, was consistent and is included in the comparisons shown in Figures

9 and 10o Figure 9 shows the comparison of the heat transfer coefficient

correlations of other investigators with the experimental values obtained

in this investigation,. The correlations shown in Figure 9 are in all cases

based on so-called film coefficientso As discussed previously, however,

the universally used method of calculating the temperature difference

was the same as used here0 In reality, their "film" coefficient is a

form of an overall coefficient and the comparison is valido Figure 10

54

FLUIDIZED BED REGION

(2,13). /

COLBURN (3)

EXPERIMENTAL

RESULTS

OTHMER (20)

FIGURE 9. HEAT TRANSFER COEFFICIENTS VERSUS NRe

55

I i i i i |—: 1 j_ _j__ U'-J -jr1

FLUIDIZED BED REGION (2,13)-

COLBUR

LEVA

EXPERIMENTAL

RESUL

OTHMER (20

1000

Gmf (Ibs/hr.ft )

FIGURE 10. HEAT TRANSFER COEFFICIENTS VERSUS Gmf

56

shows the comparison of the experimental heat transfer coefficients

with the correlations of other investigators as a function of minimum

fluidization velocity., This type of correlation eliminates the effect of

variable viscosity and gas density over the length of the bed„ Figure 9,

of course, includes these two terms in a Reynolds Number0 In both

bases it is necessary to show the nonuniform cross-sectional bed data

as a line for each particle size rather than a pointo

Even though both Levey (15) and Robinson (22) reported heat

transfer coefficients at incipient fluidization, their values cannot be

compared directly; they did not give enough information to calculate

either a Reynold's Number or a minimum fluidization velocity. ft

Robinson®s values ranged from 5 to 10 BTU/hr= fto Fo Levey8s se-O

lected values were as high as 50 BTU/hroft, F„ There is some indi

cation that these selected values were actually at velocities higher than

incipient valueso Since the comparisons in Figures 9 and 10 in all cases

are with heat transfer coefficients in fixed beds., it is apparent that heat

transfer coefficients at minimum fluidization are of the order of fixed

bed coefficients rather than fluidized bed coefficients,,

Insert Performance

Insert 3 was designed specifically for the use of large beads

flowing through the reactor at the rate of 60 pounds per hour0 It was

also designed for an inlet air temperature of 40 degrees Centigrade.,

The design involves, as previously discussed, the calculation of a tem

perature profile over the length of the reactor- This is necessary be

cause the linear velocity through the bed depends on the local tempera

ture as well as the pressure., The temperature profiles over the length

of the reactor in the runs using large beads are shown in Figures 11,

12, and 130 For comparison purposes, the calculated temperature pro

file used in the design is included on each figure.. Note that the curves

follow each other through the lower half of the reactor„ Note also that

the inlet air temperatures were in each case higher than the 40 degrees

Centigrade design value0 Recalculation of the temperature profile

based on the specific conditions in each set of runs for the large beads

results in the exact coincidence of the calculated profile with the ob

served profile up to the middle of the reactor,, The difference in the

dimensions of the recalculated insert based on the higher inlet air tem

perature is so insignificant as to be negligible,. It amounted in fact to

approximately five-thousandths of an inch difference on the radius of

the inserto For this reason it was not necessary to fabricate a new in

sert and perform additional tests.,

The design of an insert for the runs using the medium beads

called for dimensions differing only very slightly from the dimensions

of insert 30 These differences ranged from as little as nothing at one

point to a maximum of ninty-thousandths of an inch on the radius of the

inserto This maximum difference amounted to a deviation from the

58

CALCULATED PROFILE

DISTANCE ABOVE BOTTOM OF BED (INCHES).

FIGURE II. AVERAGE BED TEMPERATURE.

R U N S I A N D 4

8 0

70 ADJUSTED DESIGN BASED

o ON 45° C INLET

UJ

ORIGINAL CALCULATED PROFILE o LLJ

BASED ON 40° C INLET

50

40

20 40 30


FIGURE 12. AVERAGE BED TEMPERATURE.

R U N S 2 A N D 5

'i ;S?

60 $

:4 80

70

o

iii

CALCULATED PROFILE

50

40

20 30 40 50


FIGURE 13 AVERAGE BED TEMPERATURE. J 4

RUNS 3 AND 6 j •5 i

•t i I •i j

j I

design velocity of approximately three percent, For this reason insert

3 was used in the medium bead runs0 No difficulty whatsoever was ex

perienced in maintaining good fluidization quality throughout the reactor

in all runs with the medium beads0 A comparison of the temperature

profiles in each of the medium bead runs with the calculated tempera

ture profile is shown in Figures 14, 15, and 16„ The coincidence of

the two profiles is not as good as those shown in the large bead com-

parisonso However4, it appears that the difference between the design

conditions and the experimental conditions were not enough to influence

fluidization quality adversely, and therefore the insert was considered

satisfactory..

As mentioned previously, insert 3 was not satisfactory for the

small beads, the bed showing bubbles at the bottom and a fixed condi

tion at the top0* Since the situation obviously required an insert of

smaller dimensions at the bottom and since no reliable estimate of the

heat transfer coefficient was available, insert 2 was selected for triah

Again, no problems were encountered in obtaining uniform incipient

fluidization in any of the runs with insert 2„ The calculated tempera

ture profile and the observed temperature profile in each run are shown

in Figures 17, 18, and 190 The large difference between the calculated

profile and the experienced profile is due to the rather large difference

in dimension between the design requirements and the actual inserto

The differences in dimensions between design and actual in this case

CALCULATED PROFILE

10 20 30 40


FIGURE 14 AVERAGE BED TEMPERATURE

R U N S 7 A N D 1 0

63

80

70 o

ill

£ 60 CL

UJ

Q LU

50 CALCULATED PROFILE FOR RUNS 7 8 10

40®

20 0 10 30 40 50

DISTANCE ABOVE BOTTOM OF BED (INCHES)..

FIGURE 15. AVERAGE BED TEMPERATURE

R U N S 8 A N D I I

64

80

70 o

LU £E Z>

UJ

50

CALCULATED PROFILE FOR RUNS 789

40®

20 30 40 50 0



. R U N S 9 A N D 1 2

65

80

70

LU

* so

50

CALCULATED PROFILE

40

20 30 50 40 0 10



R U N S 1 3 A N D 1 6

8 0

70

5 60

C5

50®

CALCULATED PROFILE FOR RUNS 13 8 16

40

20 30 40 50



R U N S 1 4 A N D \7

67

CALCULATED PROFILE FOR RUNS 13 a 16


FIGURE 19. AVERAGE BED TEMPERATURE

R U N S 1 5 A N D 1 8

68

ranged up to as much as thirty-five hundredths of an inch on the insert

radius0 The reason that no problems were experienced in maintaining

good fluidization quality was perhaps due to the large temperature rise

in a section of the bed difficult to evaluate with the probe0 It can only

be concluded that the bottom inch or so of the bed was actually in a non-

fluid state0

In the case of the moving bed runs with both the medium beads

and the small beads the difference between the heat content of the gas

and that of the solid was so small that the design equation became in-

operative0 The design in these cases was made only for the static bed

situation,,

j

Extension of the Design Equation

The results discussed above indicate that the use of an insert

will serve to compensate for temperature changes occurring over the

length of a reactor operating in a state of incipient fluidization- The

usefulness of such an insert, however, is not apparent unless it may

be used in a situation where there is a source of heat, or a heat sink

within the reactor itselfo This is the usual case in which a chemical

reaction or change is taking place within the reactor* The extension

of the design to such a case is not difficult. The solution of the design

equations developed would in all but the most simple cases require the

use of computer techniques-

69

If a first order reaction is considered in which there is no

change in the gas volume through the reactor and no change in the spe

cific heats of either the solid or the gas in passing through the reactor,

then the design equation may be extended to the following expression

(considering also that the heat of reaction is constant with temperature):

(WCpg - SCpg) dT dH = ; '

7ru(Ti - T) /d,2 - ̂ £J°'5 - sHJfi e expKa /H 7dH

This equation may be solved by techniques similar to those used in solv=

ing the other design equations, requiring one more intermediate graph

ical integration,,

CHAPTER VII CONCLUSIONS AND RECOMMENDATIONS

The results of this work show that nonuniform cross-section

gas-solids beds operating in an incipiently fluidized condition have

heat transfer capabilities comparable to fixed bed systems, not fluidized

bed systems*. Heat transfer coefficients ranging from 2 to 15 BTU/hr0

ft. ̂ °Fo were found for the transfer of heat between an internal heating

element and the bed, using spherical glass beads of diameters ranging

from o 000875 inches to „ 0059 inches* These values agree well with

previously published fixed bed valueso

A nonuniform cross-section fluid bed can be designed which

will operate under conditions of incipient fluidization0 An equation

which will provide a satisfactory set of dimensions for an axial insert

for this purpose is;

WCpg-SCps f dT / „ — _ — _

J (Ti * T)(-/rVM pt + pb(Hb - H)] This equation becomes invalid at the point where WCpg is not very

70

71

different from SCps and may not be used in that region0

Uniform fluidization can be achieved on systems using inserts

having a deviation from design requirements of as much as three per-

cento Based on the evidence of one trial, a system differing 10 per

cent from optimum design will not give satisfactory performance,.

An extension of the work reported here is in order., Figure 2

shows the possibility of very much higher heat transfer coefficients at

only slightly higher gas velocities,. If only a small amount of additional

mixing occurs at the same time, then the multistage, countercurrent

operation desired is possible with improved heat transfer capabilitieSo

The testing of dense phase fluidization with nonuniform cross-

section beds has been investigated in a very limited way by Robinson,

et ale The equipment used here might be very easily modified to

measure fluidization quality in a fully fluidized system0 One possible

means of determining this property might involve a very careful meas

urement of incremental pressure drops over the height of the bed under

various conditions of fluidization,. If this were done with a properly

designed insert and without any insert there should result a more or

less quantitative indication of the relative uniformity,,

APPENDIX

72

73

TABLE 6 NOMENCLATURE

A g Superficial cross-sectional area, ft0^

Aj = Surface area of the insert, ft0 ^

Cps s Specific heat of the solid, BTU/lbo °F„

Cpg g Specific heat of the gas, BTU/lbo °F

74

NRe o Modified Reynold's Number, dimensionlesso

Nu 2 Modified Nusselt Number, dimensionlesso

P a Pressure, atmD

Pt a Pressure at the top of the bed, atmD

Qi s Heat transferred through insert, BTU/hr0 A

R s Gas constant, fto atm0 /°R lb0 moh

Rf s Leva's bed expansion ratio, dimensionlesso

S s Solids flow rate, lbSc/hr0

Tave = Average bed temperature, °Fo

s Bed temperature, 0Fo

Tj = Insert temperature, 0Fo

U s Overall heat transfer coefficient, BTU/hroft02oF0

v a- Molar volume of gas, fto ®

V a Linear gas velocity, fto /hr„

W s Mass flow rate of gas, lbs» /hr0

j} = Heat of reaction, BTU/lb0

7 s Tb/ Pt Vi(Hb - H), °Fo /atm0

jJi s Gas viscosity, lbSo/ftohro

Tf m Leva's fluidization efficiency, dimensionlesso

Pb s Density of bed, lbs0 /fto ^

Pg s Density of gas, lbs0 /fto ̂

Ps s Density of solid, lbs0 /ft0 ^

100 T © R U N I A V E R A G E 1 - 5 8 . 1 ° C x R U N 4 A V E R A G E T ~ 5 4 . I ° C

O O UJ CC 3 < cc UJ CL

2 UJ

9 0 h -

WALL

5 0

I 2 3

DISTANCE FROM INSERT SURFACE ( INCHES)

FIGURE 20. TEMPERATURE PROFILE.

EXIT GAS RUNS I AND 4

100 r o X

UJ

100

A V E R A G E T - 6 4 . 2 ° C A V E R A G E T - 6 2 . 9 ° C

o R U N • I x R U N 4

9 0

WALL 80

o

Ui 3

UJ CL

UJ

60

5 0

4 0 4 2 3


FIGURE 22.TEMPERATURE PROFILE.

PLANE 4 RUNS I AND 4

100

o R U N I A V E R A G E I - 5 0 . 2 ° C x R U N 4 A V E R A G E I - 4 7 8 ° C

90

WALL 80

o o LU tr id I-< cc UJ CL

60

50

40 4 2 3 0



PLANE 7 RUNS I AND 4

100

0 R U N 2 A V E R A G E T - 5 6 . 3 ° C x R U N 5 A V E R A G E T - 5 6 . 4 ° C

90

WALL 80

cr 70

60

50

40 4 0 2 3


FIGURE 24.TEMPERATURE PROFILE

EXIT GAS RUNS 2 AND 5

100

o R U N 2 A V E R A G E T - 6 2 . I ° C

x R U N 5 A V E R A G E T - 5 9 . 9 ° C

90

80

o o Ld t r 3

60

50

40 4 3 2

DISTANCE FROM INSERT SURFACE . ( INCHES)

FIGURE 25. TEMPERATURE PROFILE

PLANE i RUNS 2 AND 5

A V E R A G E T - 6 5 . C P C A V E R A G E T - 6 3 . 7 ° C

o R U N 2 x R U N 5

CE 70

WALL

40 I 0 12 3


FIGURE 26 TEMPERATURE PROFILE.

PLANE 4 RUNS 2 AND 5

100

9 0

80

LLI c r z> w < CE LL) CL

70

60

50

40

. r~ i i o RUN 2 AVERAGE T-46.5°C x RUN 5 AVERAGE T-46.4°C

0 1

-

1 X

"

—

e

1 1 0 1 2 3


FIGURE 27TEMPERATURE PROFILE.


83

100 I i 1 o RUN 3 AVERAGE T-59.4°C x RUN . 6 AVERAGE T-56.1 °C

90

80 ' WALL-

12 3


FIGURE 28.TEMPERATURE PROFILE


84

100; T

o R U N x R U N

3 A V E R A G E T - 6 2 . 2 ° C 6 A V E R A G E T - 6 I . I ° C

9 0

80

o

IE

H < CE UJ CL 2

7 0

60

5 0

40

WALL, ,

0 1 2 3



PLANE I RUNS 3 AND 6

100,

© R U N 3 A V E R A G E T - 6 6 . 6 ° C x R U N 6 A V E R A G E T - 6 6 . 2 ° C

90

WALL 80

o

60

50

40 0 I 2 3 4




100

o R U N 3 A V E R A G E T - 4 7 . 6 ° C x R U N 6 A V E R A G E T - 4 8 . I ° C

90

WALL 80

70

60

50

40 0 1 2 3 4


FIGURE 31. TEMPERATURE PROFILE.


100

© R U N 7 A V E R A G E T - 5 I . I ° C x R U N 1 0 A V E R A G E T - 4 6 . I ° C

90

WALL 80f—

UJ Q: 70

uj

UJ

60

50

40




100

. 0 R U N 7 A V E R A G E 1 - 6 2 3 ° C x R U N 1 0 A V E R A G E T - 5 5 . 4 ° C

9 0

WALL 80

o o

UJ t r z>

heat transfer in incipiently fluidized gas-solids …...heat transfer in incipiently fluidized ......

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