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HEAT TRANSFER IN INCIPIENTLYFLUIDIZED GAS-SOLIDS SYSTEMS
Item Type text; Dissertation-Reproduction (electronic)
Authors Edwards, Richard Modlin, 1920-
Publisher The University of Arizona.
Rights Copyright © is held by the author. Digital access to this materialis made possible by the University Libraries, University of Arizona.Further transmission, reproduction or presentation (such aspublic display or performance) of protected items is prohibitedexcept with permission of the author.
Download date 01/04/2021 22:42:27
Link to Item http://hdl.handle.net/10150/284513
http://hdl.handle.net/10150/284513
This dissertation has been 64—6770 microfilmed exactly as received
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
27. Temperature profile, plane 7, Runs 2 and 5 ............ 82
28. Temperature profile, exit gas, Runs 3 and 6 ........... 83
29. Temperature profile, plane 1, Runs 3 and 6 ....... 84
30. Temperature profile, plane 4, Runs 3 and 6 ............ 85
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
34. Temperature profile, plane 4, Runs 7 and 10 ........... 89
35. Temperature profile, plane 7, Runs 7 and 10 ........... 90
36. Temperature profile, exit gas, Runs 8 and 11 .......... 91
370 Temperature profile, plane 1, Runs 8 and 11 92
38. Temperature profile, plane 4, Runs 8 and 11 ........... 93
39. Temperature profile, plane 7, Runs 8 and 11 ........... 94
40. Temperature profile, exit gas, Runs 9 and 12 .......... 95
41. Temperature profile, plane 1, Runs 9 and 12 ........... 96
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
j
27
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
DISTANCE ABOVE BOTTOM OF BED (INCHES).
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
DISTANCE ABOVE BOTTOM OF BED (INCHES).
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
DISTANCE ABOVE BOTTOM OF BED (INCHES).
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
DISTANCE ABOVE BOTTOM OF BED (INCHES).
FIGURE 16. AVERAGE BED TEMPERATURE.
. 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
DISTANCE ABOVE BOTTOM OF BED (INCHES).
FIGURE 17. AVERAGE BED TEMPERATURE.
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
DISTANCE ABOVE BOTTOM OF BED (INCHES).
FIGURE 18. AVERAGE BED TEMPERATURE.
R U N S 1 4 A N D \7
67
CALCULATED PROFILE FOR RUNS 13 a 16
DISTANCE ABOVE BOTTOM OF BED (INCHES).
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
DISTANCE FROM INSERT SURFACE ( INCHES)
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
DISTANCE FROM INSERT SURFACE ( INCHES)
FIGURE 23.TEMPERATURE PROFILE.
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
DISTANCE FROM INSERT SURFACE ( INCHES)
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
DISTANCE FROM INSERT SURFACE ( INCHES)
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
DISTANCE FROM INSERT SURFACE ( INCHES)
FIGURE 27TEMPERATURE PROFILE.
PLANE 7 RUNS 2 AND 5
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
DISTANCE FROM INSERT SURFACE ( INCHES)
FIGURE 28.TEMPERATURE PROFILE
EXIT GAS RUNS 3 AND 6
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
DISTANCE FROM INSERT SURFACE ( INCHES)
FIGURE 29.TEMPERATURE PROFILE.
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
DISTANCE FROM INSERT SURFACE ( INCHES)
FIGURE 30.TEMPERATURE PROFILE.
PLANE 4 RUNS 3 AND 6
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
DISTANCE FROM INSERT SURFACE ( INCHES)
FIGURE 31. TEMPERATURE PROFILE.
PLANE 7 RUNS 3 AND 6
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
DISTANCE FROM INSERT SURFACE ( INCHES)
FIGURE 32.TEMPERATURE PROFILE.
EXIT GAS RUNS 7 AND 10
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>