- Email: [email protected]
Heat transfer in three-phase fluidized beds
Powder Technology. @ Elsevier Sequoia
Heat Transfer
C. G. J. BAKER, Faculty
in Three-Phase
Fluidized
E. R. ARMSTRONG*
of Engineering
(Received
195 - 204 Lausanne - Printed in the Netherlands
21(1978)
S-A.,
Science.
195
Beds
and M. A_ BERGOUGNOU
L’niuersity
of
Western
Ontario.
London.
Ont.
(Canada)
Aprii 31, 1978)
Heat transfer coefficients h have been measured in two-phase (water-air, water-glass beads) and three-phase (water-air-glass beads) fluidized beds. Experiments were performed over a wide range of Iiquid and gas flowrates in a 0.24 m diam. column fitted with an axially mounted cylindrical heater. Four solids were employed ranging in size from 0.5 to 5 mm. Typical maximum values of h in the threephase, liquid-gas, liquid-solid and liquid beds were approximately 4800, 4300, 3800 and 1300 W/m’K respectively. In the three-phase beds h generally increased with liquid and gas velocity and with particle size. Correlations are presented to calculate h in the different beds.
INTRODUCTION
Many chemical engineering operations involve contact between two or more different phases. In certain cases, the transfer of heat to or from the multiphase mixture is an integral part of the operation_ In order to estimate the required heat exchange area, a knowledge of the appropriate heat transfer coefficients is required_ Although data on heat transfer rates between an exchange surface and a single phase, liquid or gas, are readily available, information on heat transfer to multiphase media is relatively scarce. In the present study, heat transfer and individual phase holdup measurements have been performed in a three-phase fluidized bed_ In this device, solid particles are fluidized *Present address: Proctor and Gamble of Canada Ltd., Hamilton, Ontario LSN 3L5.
by the cocurrent flow of a liquid and a gas. The heat transfer took place between the bed and an axially mounted cylindrical
heat exchange surface- Previous studies of heat transfer in three-phase fluid&d beds [1 - 31 are rather limited in their scope. This paper describes the results of a more wide-ranging series of esperiments which have been reported in part elsewhere [4] _ Complementary measurements were also performed on liquid-fluidized beds and liquid-gas beds.
EXPERIMENTAL Equipment
Experiments were carried out in the cylindrical plexiglas column shown schematically in Fig. 1, which is described in
detail elsewhere [5]. It consisted of four main sections, namely the working section, the liquid outlet header, the grid and the
s Column
b c c e
heater Reservoir Orl:nceMzter Rotamzrers
Fig. 1. The equipment.
196
liquid distributor box. The overall combined height of these sections was 3.35 m. The working section of the column, located between the grid and the outlet header, was 2.75 m high and 0.2d m i-d. Eighteen static pressure taps were positioned at regular intervals up the column wall. Each tap was connected to a water manometer. A second row of 29 taps through which thermocouples could be inserted was located diametrically opposite the pressure taps. -4 total of five 6.35 mm diam. by 0.2 m long copperconstantan thermocouples encased in stainless steel sheaths were employed to sense the bed temperature_ The output from the thermocouples was simultaneously monitored by a temperature recorder and a potentiometer. The top of the working section protruded into a concentrically mounted outlet header. It thus acted as a weir over which the liquid flowed. thereby maintaining an approximately constant head in the coIumr__ The liquid exited from the outlet header through two hoses which were valved to enable varying proportions of the flow to be either returned to the feed reservoir or sent to the drain. The grid, which served to distribute evenly the gas and the liquid and also to support the fluidized solids, was constructed from a 19 mm aluminum plate_ The liquid entered the distributor box and passed through 112 liquid orifices each 3.2 mm in diameter drilled through the grid. The gas entered the bed through 20 grid holes l-6 mm in diameter. These were fed by 6 feedpipes drilled horizontally in the grid_
TABLE
The water employed in the experiments was pumped through the system by a centrifugal pump. The flow was regulated by a globe valve and measured with a calibrated orifice meter. To facilitate smooth regulation of the water flow, a valved by-pass line was located between the pump and the column and served to direct any excess flow back to the feed reservoir. This tank, and also the column, could be supplied with mains water when required Laboratory compressed air was fed to the column by way of an oil filter, a pressure regulator, and one of two calibrated rotameters. Both rotameters discharged through globe valves into a common line connected to the air manifold on the grid. A check valve in this line served to prevent any backflow of water into the rotameters. The solids used in the experiments were glass beads having nominal diameters of 0.5, 1,3 and 5 mm. The properties of these particles, as well as the quantity of each employed in the experiments, are summarized in Table 1. The heater assembly (Fig. 2) consisted of a bcylinder 0.063 RI in diameter and 0.25 m high. Four 0.013 m diam. by 0.24 m long 1500 W/240 V electric heating elements were located in wells symmetrically drilled inside this cylinder_ A voltmeter and an ammeter were included in the supply circuit to enable the power drawn by the eIements to be determined. Three 1 mm d&n_ by G-30 m long copperconstantan thermocouplcss were used to sense the surface temperature of the heater. They
1
Properties of the glass beads Xominal
Size
Density
size (mm)
distribution
Ps (kg/m”)
0.5
0.2 - 0.6
mm,
31’15 __
In
Bed weight (kg)
3.08
31.8
117
2.82
21.8
ReO
1.8
8.9
>10 WC?? in the range 0.3 -0-5
mm
1.0
SIOllOSiZC+d
2955
10.1
3.0
Monosized
2491
25-9
654
2.62
38.6
5.0
Monosized
2484
50.0
1500
2.70
38.6
197
--CLummurn
Shell
Fig. 3. The heater. were mounted in 1.6 mm wells and soldered in place flush with the heater surface. The three thermocouples were positioned 120” apart and separated by 0.05 m height intervals. The brass cylinder was surmounted by a hollow aluminum shell 0.30 m long which housed the necessary connections in the heater and thermocouple ieads. The two sections were separated by a 0.03 m thick highdensity nylon disc and viton O-rings. The disc prevented heat loss from the heater to the shell and also acted as a seal. The electrical leads and thermocouple wires exited through the top of the sealed shell and passed out of the top of the column. In order to prevent any accidental leakage of water into the shell, it was maintained at a pressure slightly above that in the column by means of compressed air. A 0.15 m long highdensity nylon cone was attached to the bottom of the heater- Its purpose was to promote a fully developed thermal boundary layer at th x heater surface. To this end, the surface of the cone was randomly roughened with coarse sandpaper. The heater assembly was supported by a stainless steel wire bohed to the top of the aluminum shell. It was maintained in position along the column axis by spring-loaded rods attached to its top and bottom. &fZASUREMENT
OF
THE
HEAT
TRANSFER
COEFFICIENTS At the start of an experiment, the water and air flowrates were set to the desired
values. The heater was then located vertically along the column axis in the centre of the fluidized bed. In the case of liquid-gas beds, the centre of the brass cylinder was positioned about 0.76 m above the grid. Preliminary experiments showed that the heat transfer coefficient did not vary with the location of the heater in the bed [5] _ The power supply to the heating elements was then switched on. The total power drawn was maintained constant at approsimately 5 kW and was determined by recording the voltage and current. The quantity of water being recycled to the feed reservoir was then set. Make-up water was supplied from the mains to maintain a constant temperature in the reservoir. The column was allowed to run at a given set of conditions for approsimately 15 minutes. This time was far greater than that required to reach steady state_ During this period, the three heater surface temperatures and the five bed temperatures were continuously recorded. Bulk bed temperatures were measured a short distance upstream and downstream of the heater. Three bed temperatures were also taken at a radial distance of about 6 mm from the top, middle and bottom of the brass cylinder. From time to time, the temperature readings were doublechecked with the potentiometer, which was considerably more accurate than the recorder. However, the latter provided more precise values of the average temperatures over the period of the run than could be obtained by spot measurements with the potentiometer. The heat transfer coefficient h was calculated from the standard relation Q= hA&T
(1)
In this equation Q is the power input to the heaters as given by the product of the voltage and current The power factor was taken as unity since the heater was a purely resistive load. The effective heat exchange area A, was the surface area of the brass cylinder, namely O-0507 m2_ The temperature difference AT was taken as the difference between the average of the three heater surface temperatures and the average of the bulk bed temperatures upstream and downstream of the heater. The reproducibility of the results was generally better than I 5%. The heat transfer
19s
coefficients calculated from eqn. (I) were susceptible to errors in the measurement of both the total heat input and the temperature difference_ The accuracy of these parameters was estimated to be better than f 3% and = 12% respectively [ 53 _Thus, values of h are accurate to within i 15%.
?IIEXSI_iREMEXT
OF PHASE
HOLDUPS
The individual phase holdups were determined from the static pressure profiles along the Iength of the column. At high air rates the observed pressures tended to fluctuate about their steady-state values as a result of small changes in liquid level above the outlet weir. This therefore affected all the manometers simultaneously and, in order to capture the true pressure profile, they were photographed at */so s. The actual height of liquid in the manometers was then determined by projecting the developed negative onto a screen and recording the values. A minim-tirn of two pressure profiles was obtained approximately five minutes apart for each set of experimental conditions. The liquid and gas holdups were calculated from the equations [S, 71: Et fEgIE*
= 1.0
(2)
in which lC and es are the only unknown c,uantities. In the liquid-gas beds, E, is zero and H was taken arbitrarily as 2-44 m_ The reproducibility of the holdup measurements was better than I 4% 153 _
RESULTS
In this study, measurements of phase holdups and heat transfer coefficients were performed in liquid-gas beds, and in liquid and three-?-phasefluidized beds. The ranges of liquid and gas velocity employed in the experiments are summarized in Table 2. Extensive data on the individual phase hoIdups obtained in a ewe-dimensional column have been published by Kim et al. [6, 7]_ In the present investigation, liquid holdups observed in the liquid-gas beds were in excellent agreement with Kim’s results. In
TABLE
2
Liquid and gas velocity System
Liquid-gas Liquid-sotid (all particle sizes) Liquid-gas -0.5 mm bzads Liquid-gas -1 mm beads Liquid-gas -3 mm beads Liquid-gas -Z mm beads
ranges
Liquid velocity range (mm/s) s-
92
Gas velocity range (mm/s) 0 - 23s
6 - 126 8
o-
17
40 - 105
0 - 178
40 - 126
0 - 23s
40 - 126
O-238
the liquid-fluidized beds, the majority of ec values were about 5 - 10% higher than predicted by Kim’s correlation_ However, with the 5 mm beads this discrepancy was of the order of 25%, presumably as a result of wall effects. In the case of the three-phase fluidized beds, the present values of eC and (eC + eg) were respectively about 20% and 10% higher than those of Kim. These discrepancies are not unreasonable considering the differences in the geometry of the two columns. Some preliminary measurements of heat transfer coefficients were made with liquid alone flowing through the column_ The values of these coefficients were found to be about double those predicted from the SiederTate equation [8] _ This is probably not unreasonable since the Sieder-Tate equation is strictly valid only for fully developed turbulent flow inside tubes having a large length to diameter ratio. It is not known how closely this equation describes the convective losses resulting f?om the flow of fluid around a small cylindrical heater such as that employed in the present experiments_ In any event, the existence of a fully developed thermal boundary layer was not met. This was confirmed by temperature measurements made 6 mm from the heater surface. With liquid alone, the temperature increased with vertical height. In contrast, in the two- and three-phase beds, it remained essentially constant and equal to the bulk bed temperature, indicating the existence of a very thii, fully developed boundary layer. From these considerations alone, the coefficients calculated from the Sieder
199
Tate equation would be expected to be significantly lower than the experimental values. End effect corrections [8] were not possible in this case because of the geometry of the system. A further probable reason for the discrepancy is the turbulence induced by the high velocity liquid jets emanating from the grid. This would undoubtedly increase the heat transfer coefficient but its effect cannot be assessed quantitatively. Liquid-gas beds Figure 3 shows a plot of the heat transfer coefficient against superficial gas velocity for three different liquid rates. As may be seen, introducing the gas into the flowing liquid resulted in a marked increase in the heat transfer coefficient. This increase was initially extremely rapid but became less marked at the higher gas rates. Under these conditions, the coefficients measured in the liquid-gas beds were approximately 3.5 times those observed with the flowing liquid alone. It may also be noted that h w’.z extremely insensitive to the liquid velocity in the range studiedA Ieast-squares analysis of the data yielded the following correlation: h =
15g2~~_026~0_170 g
(4)
In this equation V, and V, are in mm/s and h is in W/m2K_ The multiple correlation coefficient was 0.9919 for 106 data points. No attempt was made to obtain a dimensionless correlation, as only the liquid and gas rates were varied. The majority of data published on heat transfer in vertical cocurrent liquid-gas flow
were obtained at fluid velocities much higher than those employed in this study. However, Groothuis and Hendal]9] and Kudirka ef al. [lo] both performed experiments on the water-air system at velocities not very far removed from the present ones. The agreement between the present data and those of Groothuis and Hendal is escehent 151. For example, at the lowest liquid and gas velocities employed, 150 mm/s, these authors obtained a coefficient of about 4200 W/m2K. The value calculated from eqn. (4) is 4250 W/m’K_ In contrast, the corresponding result obtained by extrapolating the data of Kudirka et ai. was 5300 W/m’K. However, the minimum superficial liquid and gas velocities employed by these authors were about 300 and 1000 mm/s respectively; it is therefore probable that extrapolation of these data into the present range is not valid. Liquid-fluidized beds Plots of heat transfer coefficient against superficial liquid velocity for the beds of glass beads fluid&d by water are shown in Fig_ 4. As may be seen, h initially increased with liquid velocity, went through a maximum, and then decreased with further increases in the liquid rate. The same trend was observed for all particle sizes_ The ratio of the maximum heat transfer coefficient to the value observed at the same liquid velocity in the absence of solids increased with particle size. Its values were 2.78, 3.34 and 3.42 for the 1, 3 and 5 mm beads respectively_ The velocity at which the peak heat transfer coefficient occurred increased with particle size.
c
I
0
Fig. 3. Plots of heat transfer coefficient velocity in liquid-gas beds.
against gas
” r,
59
lmm 3rr.r
5mm
beacs
bcaas beads
Xl0
U[.mm/s
150
Fig. 4_ Plots of heat transfer coefficient velocity in liquid-fluidized beds.
against liquid
Maxima were also observed in plots of the heat transfer coefficient against liquid holdup [5] _ These occurred at holdups of approsimately 0.75 for the 1 mm beads and O-6 for the 3 and 5 mm particles. These observations are qualitatively in complete accord with previous fmdings for liquid-fluidized beds [ll - 14]_ The present data were correlated by the equation h = ~323~-~~=d;~sa
(5)
The multiple regression coefficient was 0.9982 for 120 data points. The experimental values of h could also be correlated by Iog(Sr-Regaa) = -1.908~,
f O-1367
(6)
with a correlation coefficient of 0.9799 for - 22 data points_ The Stanton and Reynolds numbers were evaluated at the average bulk temperature of the liquid in the column. A plot of 10g(St-R&~~) against ep is shown in Fig. 5 wliich illustrates the good agreement between the data and eqn. (6)- AIso shown in tt,is figure is the correlation of Wasmund and Smith [ll] for glass beads fluidized by water: Iog(St-.12eEss) = -1.75~~
f 0.11
(7)
This equation consistently predicts somewhat higher coefficients than were observed in this study. At a liquid holdup of 0.45, the discrepancy was about 10%; at a holdup of 0.9 it was about 30%. Brea and Hamilton [123, who measured heat transfer coefficients in beds of glass beads (0.5 - 2 mm) fluidized by water and
glycerol-water mixtures, data by the equation
correlated
their
Nu = 0.943(d,/d,)“-151+-o-53,Re~“” _ [Ey9”‘(l
-
Eu)o-4”]
(8)
In the present case, this equation yielded results which were almost identical to the correlation of Wasmund and Smith and are consequently omitted from Fig. 5 for the sake of clarity. Richardson et al. 1133 carried out similar experiments on a variety of solids fluidized by dimethyl phthalate. It i-_ of interest to note that, despite the markedly different coefficient obtained with the higher Prandtl number fluid, the slope of their plot of log(St-Reg-33) against ey was identical to that obtained in the present study_ It would thus appear that the value of the intercept in eqn. (6) is a function of the fluid properties and perhaps the geometry of the systemThree-phase
fluidized
beds
As may be seen in Figs. 6 - 8, the heat transfer coefficient in three-plate fluidized beds increased with gas velocity for all liquid velocities and particle sizes studied. The increase was initially quite rapid. However, at the higher gas rates it became less marked and h appeared to approach a maximum_ As may be deduced from these figures, plots of the heat transfer coefficient against liquid rate exhibited maxima. The same trend, it will be recalled, was observed with liquid-fluidized beds.
0
, 1600 0
E o
Imm be&s q=Llmrr/s UL=67mnvs UL=S6mws
700
_
200
Ug .mm/s Fig_ 5. Plot of log(St-Re$33)
liquid-fkidized
beds.
against Iiquid hoIdup in
Fig. 6_ Plots of heat transfer coef’ficient against gas veIocity in three-phase fluidized beds of 0.5 and 1 mm beads_
XJOO
A==
0
3-rm-abeads lJ,=41mm/s
x <
I
33000 r-
pzp/p
‘-I
I 1
L)=92mm/s_
T 0
0 ug= Omws e U~=16mn/s r u j
Ug=59nm/s _ ug =iIS mm/s Ug =237mmf 5
1
Fig. 7. Piots of heat transfer coefficient against gas velocity in three-phase fluidized beds of 3 mm beads.
Fig. 10. Plots particle size.
0 a
0
%
Smm beads q=Ll
mm/s
U~=92mm/s
Ut=126mm/s
’
tTICFJS
Fig_ 8. Plots of heat transfer coefficient against gas velocity in three-phase fluidized beds of 5 mm beads.
Fig. 9. porosity
Plots
of heat transfer coefficient against
in three-phase fluid-ked beds: open points -
U, = 16 mm/s; shaded points -
UQ
=
119 mm/s.
Typical plots of h against the total holdup or porosity (cy + Q) in three-phase fluid&d beds are shown in Fig. 9. These data were obtained at various liquid rates while holding the gas rate constant_ As may be seen, the heat transfer coefficient went through a maximum which shifted to Iower porosities with increasing particle size. However, little shift was observed at high gas rates on in-
of heat transfer
coefficient
against
creasing the particle diameter from 3 to 5 mm. At any given particle size, the effect of increasing the gas velocity was to shift the maximum to a higher porosity. Plots of h against particle size d, are shown in Fig. 10. The result of introducing solids into a liquid-gas bed (d, = 0) was, in general, to increase the vaIue of the heat transfer coefficient. A notable exception to this was observed at the higher gas rates where the coefficient went through a local minimumThus, under these conditions, h was smaller in the three-phase bed than in the corresponding Iiquid-gas bed_ As may be seen, this is onIy true for particle sizes up to about 1.5 mm. At liquid rates Iower than that shown in the figure, this local minimum was observed to occur at lower gas rates and also to be extended to a larger particle size. It was also generally observed that h was relatively insensitive to d, at values of the latter exceeding 3 mm, particularly at high gas rates. As may also be seen in Fig. 10, three-phase fluidized beds always exhibited larger values of h than liquid-fluidized beds. Although increasing the gas rate at larger particle sizes resulted in a larger value of h in the threephase fluidized beds, the difference between this value and the corresponding liquidsolid coefficient was essentially independent of particle size- However, for smalI particles, this difference decreased with increasing particle size up to about 1.5 mm. The heat transfer coefficients in liquid-gas beds were generally larger than those in the liquidfluidized beds at gas velocities less than about 60 mm/s-
2G2
The three-phase heat-transfer data were correlated by the equation in which h is expressed in W/m’K, U, and U, In mm/s and d, in mm. The multiple correlation coefficient was O-9974 for 246 data points- Attempts to formulate a correlation of similar form to eqns. (6) and (7) for liquidf’uidized beds were unsuccessful_ Moreover, %tclusion of bed porosity as an additional independent variable in eqn. (9) resulted in only a marginal improvement in the correlation coefficient. Published data on heat transfer coefficients in three-phase fluidized beds are estremely limited_ (pstergaard [I] noted that the injection of air into a bed of glass spheres fluidized by water resulted in a marked increase in the heat transfer coefficient. He observed that this increase was largest at the lowest liquid rates and was particularly marked near the minimum fluidizing velocity_ The same trends were observed in this study. Viswanathan et al. 131 measured heat transfer rates in beds of 649 and 928 pm quartz particles fluidized water and air. Their experiments were carried out at a constant bed height, which was achieved by simultaneously changing the water and air rates over relatively narrow ranges_ The initial marked increase in h resulting from the injection of air into the bed was again noted As in the present study, the heat transfer coefficient was observed to increase with particle size_ Typical values were of the order of 5100 W/m’K, which is slightly higher than those obtained in this work_ However, the experimental technique employed by Viswanathan et al. makes a meaningful comparison with the present data difficult.
DISCUSSION In this study, heat transfer coefficients have been measured in three-phase fluidized beds over a relatively wide range of experimentdl conditions_ PreIiminary correlations are presented which enable h to be estimated, at least in beds of glassbeads fIuidized by water and air_ Further work is of course necessary to extend these correlations to other systems. In addition, measurements of
heat transfer coefficients in the corresponding two-phase beds enable some conclusions to be drawn regarding the heat transfer mechanisms in the three-phase beds. In liquid-fluidized beds, the motion of the particles results in an erosion of the thermal boundary layer [ 133 _ At low liquid velocities, movement of the particles is restricted and their enhancement of the heat transfer coefficient is small. With increasing liquid rates, the particle velocity increases, resulting in a corresponding increase in h_ At even higher liquid velocities, this effect is counteracted by the reduced particle concentration. This explains the maximum observed in plots of h against UC and cL and the particular importance of the latter parameter. In liquid-gas beds, the increase in the heat transfer coefficient can also be attributed to increased turbulence about the heat eschange surface. This turbulence appears to be dependent largely on the gas content of the bed since both lg and h increased rapidly at first and then levelled off at high gas rates 151. By combining the effects of solids and gas, a reasonable explanation for the trends in the heat transfer coefficient in three-phase fluid&d beds can be offered. Introducing gas into a liquid-solid bed does not drastically change its porosity. It can therefore be assumed that the individual effect of the solids is not significantly changed. However, the presence of the gas increases the turbulence, resulting in an increased heat transfer coefficient. On increasing the gas rate, as in the liquid-gas bed, the gas holdup becomes essentially constant and thus it is reasonable to assume that its effect on the turbulence also becomes constant. The result is a large initial increase in the heat transfer and a levelling off at high gas rates. This is illustrated in Fig. 11, in which the difference between the film coefficients in three-phase beds and the corresponding liquid-solid bed, Ah,, is plotted against U,. The typical curves in this figure were obtained from the appropriate correlations, eqns. (5) and (9). As noted previously, three-phase fluid&d beds are seen to exhibit greater heat-transfer coefficients than the Iiquid-soIid bed under all conditions_ As with liquid-fluidized beds, decreasing UQ and dp both resulted in an increase in Ah,. However, the variation of this parameter with particle size was smalI
203
the solid particles, thereby reducing the turbulence at the heater surface. This study has clearIy iIIustrated the esceIIent heat transfer characteristics of three-phase fIuidized beds. The values of the heat transfer coefficients ranged up to four times as Iarge as those measured with the liquid alone flowing in the column. Moreover. fouIing of the heater was observed to be retarded by the presence of the solids. These favourable characteristics would certainly support the use of a three-phase fluidized bed for promoting catalytic reactions in which the heat effects are large. Fig. 11. Plots of ah, phase fluidized beds.
against gas ve!ocity
in threeCONCLUSION
Ug . mm/s Fig. 12. PI&s of Afz, phase fluidized beds.
against
gas velocity
in three-
at low rates. Thus the enhancement due to the presence of gas is greatest when it is introduced into a bed of incipiently fluidized particles. The same conclusion was reached by Qstergaard Cl]. The enhancement of the heat transfer coefficient in three-phase beds due to the presence of solids is illustrated in Fig. 12, in which Ah, is plotted against U,. Again, the appropriate correlations, eqns. (4) and (9), were employed to calculate Ah,. As may be seen, this parameter decreased rapidly with increasing gas rate but increased with particle size and liquid rate. In all cases, the trend for ti, to become negative at high gas rates was observed. Under these conditions the heat transfer coefficient in the three-phase bed is smaller than that in the corresponding Iiquidgas bed- The reason for this is not clear, but it may result from the hindrance of the gas by
The following conclusions can be drawn from the results of the present study: (1) in liquid-gas beds, the heat transfer coefficient initially increased rapidly with gas rate but levelled off at high flows. Liquid velocity had only a minimal effect on h_ (2) In the case of Iiquid-fiuidized beds, the presence of solids enhanced the heat transfer coefficient, which increased with d,. Plots of h against V, and eP exhibited masima and a linear relationship was observed between Iog(St-Reg33) and ek. (3) In most cases, the heat transfer coefficient in three-phase beds increased with particle size and with liquid and gas velocity. The value of h in these beds always esceeded that in the corresponding liquid-solid bed and normally exceeded that in the corresponding liquid-gas bed. However, with smaI1 particles and high gas rates, the liquid-gas coefficient e_xceeded that in the three-phase bed_
ACKNOWLEDGEMENTS
The authors would like to thank the National Research Council of Canada for a grant in aid of research to Dr. C_ G. J. Baker which made this work possible.
LIST
4 C, 4
OF
SYMBOLS
surface area of heater
specific heat of liquid hydraulic diameter of annulus
particle diameter acceleration due to gravity heat transfer coefficient expanded bed height, or height of test section in liquid-gas beds thermal conductivity of liquid esponent in Richardson-Z&i equation, Re = Re& Nusselt number, hd, ?Q pressure drop across fluidized bed, or across test section in liquid-gas beds Prandtl number, Cp~Jk~ heat transfer rate Reynolds number, Ucd,pc/pc Reynolds number, UrodpPr/pc Stanton number, h/pkC,UL superficial veIocity of gas superficial velocity of liquid terminal velocity of particles in liquid difference between heat transfer coefficient in three-phase fluidized bed and that in liquid-fluid&d bed with the same d, and L’( difference between heat transfer coefficient in three-phase fIuidized bed and that in a liquid-gas bed with the same U, and U, temperature difference between heater surface and bed gas holdup liquid holdup solids hoIdup liquid viscosity
PE PL PS
gas density Iiquid density solids density
REFERENCES 1 K. Gsterg-iard, in Fluidization, Sot_ Chem. Ind., London, 1963, p_ 6S_ 2 R. P_ Van Driesen and N. C. Stewart. Oil Gas J., 62 (1964) lOO_ 3 S. Visuranathan. A. S. Kaker and P. S. Murti, Chem. Eng. Sci.. 20 (1965) 903. 4 E. R. Armstrong. C: G_ .I_ Baker and M. A. Bergougnou. in D. L. Keaims (Ed.). Fluidization Technology. Vol. 1, Hemisphere Publishing Corp., Washington. 1976, p_ 453. hl.E.Sc. Thesis, Univ. of 5 E. R. Armstrong, Western Ontario, 19i5_ 6 S. D. Kim. C. G. J. Baker and hI_ A_ Bergougnou, Can. J_ Chem. Eng.. 50 (19i2) 695. F S_ D. Kim. C. G. J. Baker and hr. A. Bergougnou. Can. J. Chem. Eng.. 53 (1975) 134. 6 W. L. McCabe and J. C. Smith, Unit Operations of Chemical Engineering, hIcGraw-Hill. New York. 3rd edn.. 1976, pp_ 318 - 320_ 9 H. Groothuis and W_ P. Hendal. Chem. Eng. Sci., 11 (1959) 212. 10 A. A. Kudirka, J. Grosh and W. McFadden. Ind. Eng_ Chem. Fundam., 4 (1966) 339_ 11 B. Wasmund and J. W. Smith, Cao_ J_ Chem. Eng_, 45 (1967) 156. 12 F. M_ Brea and W_ Hamilton. Trans._ Inst. Chem. Eng., 49 (1971) 196. 13 J_ F_ Richardson, hI_ N. Romani and K. J. Shakiri, Chem. Eng. Sci.. 31 (1976) 619. 14 R. D. Pate1 and J. h’,. Simpson. Chem_ Eng. Sci.. 39 (1977) 6i.
Heat Transfer
C. G. J. BAKER, Faculty
in Three-Phase
Fluidized
E. R. ARMSTRONG*
of Engineering
(Received
195 - 204 Lausanne - Printed in the Netherlands
21(1978)
S-A.,
Science.
195
Beds
and M. A_ BERGOUGNOU
L’niuersity
of
Western
Ontario.
London.
Ont.
(Canada)
Aprii 31, 1978)
Heat transfer coefficients h have been measured in two-phase (water-air, water-glass beads) and three-phase (water-air-glass beads) fluidized beds. Experiments were performed over a wide range of Iiquid and gas flowrates in a 0.24 m diam. column fitted with an axially mounted cylindrical heater. Four solids were employed ranging in size from 0.5 to 5 mm. Typical maximum values of h in the threephase, liquid-gas, liquid-solid and liquid beds were approximately 4800, 4300, 3800 and 1300 W/m’K respectively. In the three-phase beds h generally increased with liquid and gas velocity and with particle size. Correlations are presented to calculate h in the different beds.
INTRODUCTION
Many chemical engineering operations involve contact between two or more different phases. In certain cases, the transfer of heat to or from the multiphase mixture is an integral part of the operation_ In order to estimate the required heat exchange area, a knowledge of the appropriate heat transfer coefficients is required_ Although data on heat transfer rates between an exchange surface and a single phase, liquid or gas, are readily available, information on heat transfer to multiphase media is relatively scarce. In the present study, heat transfer and individual phase holdup measurements have been performed in a three-phase fluidized bed_ In this device, solid particles are fluidized *Present address: Proctor and Gamble of Canada Ltd., Hamilton, Ontario LSN 3L5.
by the cocurrent flow of a liquid and a gas. The heat transfer took place between the bed and an axially mounted cylindrical
heat exchange surface- Previous studies of heat transfer in three-phase fluid&d beds [1 - 31 are rather limited in their scope. This paper describes the results of a more wide-ranging series of esperiments which have been reported in part elsewhere [4] _ Complementary measurements were also performed on liquid-fluidized beds and liquid-gas beds.
EXPERIMENTAL Equipment
Experiments were carried out in the cylindrical plexiglas column shown schematically in Fig. 1, which is described in
detail elsewhere [5]. It consisted of four main sections, namely the working section, the liquid outlet header, the grid and the
s Column
b c c e
heater Reservoir Orl:nceMzter Rotamzrers
Fig. 1. The equipment.
196
liquid distributor box. The overall combined height of these sections was 3.35 m. The working section of the column, located between the grid and the outlet header, was 2.75 m high and 0.2d m i-d. Eighteen static pressure taps were positioned at regular intervals up the column wall. Each tap was connected to a water manometer. A second row of 29 taps through which thermocouples could be inserted was located diametrically opposite the pressure taps. -4 total of five 6.35 mm diam. by 0.2 m long copperconstantan thermocouples encased in stainless steel sheaths were employed to sense the bed temperature_ The output from the thermocouples was simultaneously monitored by a temperature recorder and a potentiometer. The top of the working section protruded into a concentrically mounted outlet header. It thus acted as a weir over which the liquid flowed. thereby maintaining an approximately constant head in the coIumr__ The liquid exited from the outlet header through two hoses which were valved to enable varying proportions of the flow to be either returned to the feed reservoir or sent to the drain. The grid, which served to distribute evenly the gas and the liquid and also to support the fluidized solids, was constructed from a 19 mm aluminum plate_ The liquid entered the distributor box and passed through 112 liquid orifices each 3.2 mm in diameter drilled through the grid. The gas entered the bed through 20 grid holes l-6 mm in diameter. These were fed by 6 feedpipes drilled horizontally in the grid_
TABLE
The water employed in the experiments was pumped through the system by a centrifugal pump. The flow was regulated by a globe valve and measured with a calibrated orifice meter. To facilitate smooth regulation of the water flow, a valved by-pass line was located between the pump and the column and served to direct any excess flow back to the feed reservoir. This tank, and also the column, could be supplied with mains water when required Laboratory compressed air was fed to the column by way of an oil filter, a pressure regulator, and one of two calibrated rotameters. Both rotameters discharged through globe valves into a common line connected to the air manifold on the grid. A check valve in this line served to prevent any backflow of water into the rotameters. The solids used in the experiments were glass beads having nominal diameters of 0.5, 1,3 and 5 mm. The properties of these particles, as well as the quantity of each employed in the experiments, are summarized in Table 1. The heater assembly (Fig. 2) consisted of a bcylinder 0.063 RI in diameter and 0.25 m high. Four 0.013 m diam. by 0.24 m long 1500 W/240 V electric heating elements were located in wells symmetrically drilled inside this cylinder_ A voltmeter and an ammeter were included in the supply circuit to enable the power drawn by the eIements to be determined. Three 1 mm d&n_ by G-30 m long copperconstantan thermocouplcss were used to sense the surface temperature of the heater. They
1
Properties of the glass beads Xominal
Size
Density
size (mm)
distribution
Ps (kg/m”)
0.5
0.2 - 0.6
mm,
31’15 __
In
Bed weight (kg)
3.08
31.8
117
2.82
21.8
ReO
1.8
8.9
>10 WC?? in the range 0.3 -0-5
mm
1.0
SIOllOSiZC+d
2955
10.1
3.0
Monosized
2491
25-9
654
2.62
38.6
5.0
Monosized
2484
50.0
1500
2.70
38.6
197
--CLummurn
Shell
Fig. 3. The heater. were mounted in 1.6 mm wells and soldered in place flush with the heater surface. The three thermocouples were positioned 120” apart and separated by 0.05 m height intervals. The brass cylinder was surmounted by a hollow aluminum shell 0.30 m long which housed the necessary connections in the heater and thermocouple ieads. The two sections were separated by a 0.03 m thick highdensity nylon disc and viton O-rings. The disc prevented heat loss from the heater to the shell and also acted as a seal. The electrical leads and thermocouple wires exited through the top of the sealed shell and passed out of the top of the column. In order to prevent any accidental leakage of water into the shell, it was maintained at a pressure slightly above that in the column by means of compressed air. A 0.15 m long highdensity nylon cone was attached to the bottom of the heater- Its purpose was to promote a fully developed thermal boundary layer at th x heater surface. To this end, the surface of the cone was randomly roughened with coarse sandpaper. The heater assembly was supported by a stainless steel wire bohed to the top of the aluminum shell. It was maintained in position along the column axis by spring-loaded rods attached to its top and bottom. &fZASUREMENT
OF
THE
HEAT
TRANSFER
COEFFICIENTS At the start of an experiment, the water and air flowrates were set to the desired
values. The heater was then located vertically along the column axis in the centre of the fluidized bed. In the case of liquid-gas beds, the centre of the brass cylinder was positioned about 0.76 m above the grid. Preliminary experiments showed that the heat transfer coefficient did not vary with the location of the heater in the bed [5] _ The power supply to the heating elements was then switched on. The total power drawn was maintained constant at approsimately 5 kW and was determined by recording the voltage and current. The quantity of water being recycled to the feed reservoir was then set. Make-up water was supplied from the mains to maintain a constant temperature in the reservoir. The column was allowed to run at a given set of conditions for approsimately 15 minutes. This time was far greater than that required to reach steady state_ During this period, the three heater surface temperatures and the five bed temperatures were continuously recorded. Bulk bed temperatures were measured a short distance upstream and downstream of the heater. Three bed temperatures were also taken at a radial distance of about 6 mm from the top, middle and bottom of the brass cylinder. From time to time, the temperature readings were doublechecked with the potentiometer, which was considerably more accurate than the recorder. However, the latter provided more precise values of the average temperatures over the period of the run than could be obtained by spot measurements with the potentiometer. The heat transfer coefficient h was calculated from the standard relation Q= hA&T
(1)
In this equation Q is the power input to the heaters as given by the product of the voltage and current The power factor was taken as unity since the heater was a purely resistive load. The effective heat exchange area A, was the surface area of the brass cylinder, namely O-0507 m2_ The temperature difference AT was taken as the difference between the average of the three heater surface temperatures and the average of the bulk bed temperatures upstream and downstream of the heater. The reproducibility of the results was generally better than I 5%. The heat transfer
19s
coefficients calculated from eqn. (I) were susceptible to errors in the measurement of both the total heat input and the temperature difference_ The accuracy of these parameters was estimated to be better than f 3% and = 12% respectively [ 53 _Thus, values of h are accurate to within i 15%.
?IIEXSI_iREMEXT
OF PHASE
HOLDUPS
The individual phase holdups were determined from the static pressure profiles along the Iength of the column. At high air rates the observed pressures tended to fluctuate about their steady-state values as a result of small changes in liquid level above the outlet weir. This therefore affected all the manometers simultaneously and, in order to capture the true pressure profile, they were photographed at */so s. The actual height of liquid in the manometers was then determined by projecting the developed negative onto a screen and recording the values. A minim-tirn of two pressure profiles was obtained approximately five minutes apart for each set of experimental conditions. The liquid and gas holdups were calculated from the equations [S, 71: Et fEgIE*
= 1.0
(2)
in which lC and es are the only unknown c,uantities. In the liquid-gas beds, E, is zero and H was taken arbitrarily as 2-44 m_ The reproducibility of the holdup measurements was better than I 4% 153 _
RESULTS
In this study, measurements of phase holdups and heat transfer coefficients were performed in liquid-gas beds, and in liquid and three-?-phasefluidized beds. The ranges of liquid and gas velocity employed in the experiments are summarized in Table 2. Extensive data on the individual phase hoIdups obtained in a ewe-dimensional column have been published by Kim et al. [6, 7]_ In the present investigation, liquid holdups observed in the liquid-gas beds were in excellent agreement with Kim’s results. In
TABLE
2
Liquid and gas velocity System
Liquid-gas Liquid-sotid (all particle sizes) Liquid-gas -0.5 mm bzads Liquid-gas -1 mm beads Liquid-gas -3 mm beads Liquid-gas -Z mm beads
ranges
Liquid velocity range (mm/s) s-
92
Gas velocity range (mm/s) 0 - 23s
6 - 126 8
o-
17
40 - 105
0 - 178
40 - 126
0 - 23s
40 - 126
O-238
the liquid-fluidized beds, the majority of ec values were about 5 - 10% higher than predicted by Kim’s correlation_ However, with the 5 mm beads this discrepancy was of the order of 25%, presumably as a result of wall effects. In the case of the three-phase fluidized beds, the present values of eC and (eC + eg) were respectively about 20% and 10% higher than those of Kim. These discrepancies are not unreasonable considering the differences in the geometry of the two columns. Some preliminary measurements of heat transfer coefficients were made with liquid alone flowing through the column_ The values of these coefficients were found to be about double those predicted from the SiederTate equation [8] _ This is probably not unreasonable since the Sieder-Tate equation is strictly valid only for fully developed turbulent flow inside tubes having a large length to diameter ratio. It is not known how closely this equation describes the convective losses resulting f?om the flow of fluid around a small cylindrical heater such as that employed in the present experiments_ In any event, the existence of a fully developed thermal boundary layer was not met. This was confirmed by temperature measurements made 6 mm from the heater surface. With liquid alone, the temperature increased with vertical height. In contrast, in the two- and three-phase beds, it remained essentially constant and equal to the bulk bed temperature, indicating the existence of a very thii, fully developed boundary layer. From these considerations alone, the coefficients calculated from the Sieder
199
Tate equation would be expected to be significantly lower than the experimental values. End effect corrections [8] were not possible in this case because of the geometry of the system. A further probable reason for the discrepancy is the turbulence induced by the high velocity liquid jets emanating from the grid. This would undoubtedly increase the heat transfer coefficient but its effect cannot be assessed quantitatively. Liquid-gas beds Figure 3 shows a plot of the heat transfer coefficient against superficial gas velocity for three different liquid rates. As may be seen, introducing the gas into the flowing liquid resulted in a marked increase in the heat transfer coefficient. This increase was initially extremely rapid but became less marked at the higher gas rates. Under these conditions, the coefficients measured in the liquid-gas beds were approximately 3.5 times those observed with the flowing liquid alone. It may also be noted that h w’.z extremely insensitive to the liquid velocity in the range studiedA Ieast-squares analysis of the data yielded the following correlation: h =
15g2~~_026~0_170 g
(4)
In this equation V, and V, are in mm/s and h is in W/m2K_ The multiple correlation coefficient was 0.9919 for 106 data points. No attempt was made to obtain a dimensionless correlation, as only the liquid and gas rates were varied. The majority of data published on heat transfer in vertical cocurrent liquid-gas flow
were obtained at fluid velocities much higher than those employed in this study. However, Groothuis and Hendal]9] and Kudirka ef al. [lo] both performed experiments on the water-air system at velocities not very far removed from the present ones. The agreement between the present data and those of Groothuis and Hendal is escehent 151. For example, at the lowest liquid and gas velocities employed, 150 mm/s, these authors obtained a coefficient of about 4200 W/m2K. The value calculated from eqn. (4) is 4250 W/m’K_ In contrast, the corresponding result obtained by extrapolating the data of Kudirka et ai. was 5300 W/m’K. However, the minimum superficial liquid and gas velocities employed by these authors were about 300 and 1000 mm/s respectively; it is therefore probable that extrapolation of these data into the present range is not valid. Liquid-fluidized beds Plots of heat transfer coefficient against superficial liquid velocity for the beds of glass beads fluid&d by water are shown in Fig_ 4. As may be seen, h initially increased with liquid velocity, went through a maximum, and then decreased with further increases in the liquid rate. The same trend was observed for all particle sizes_ The ratio of the maximum heat transfer coefficient to the value observed at the same liquid velocity in the absence of solids increased with particle size. Its values were 2.78, 3.34 and 3.42 for the 1, 3 and 5 mm beads respectively_ The velocity at which the peak heat transfer coefficient occurred increased with particle size.
c
I
0
Fig. 3. Plots of heat transfer coefficient velocity in liquid-gas beds.
against gas
” r,
59
lmm 3rr.r
5mm
beacs
bcaas beads
Xl0
U[.mm/s
150
Fig. 4_ Plots of heat transfer coefficient velocity in liquid-fluidized beds.
against liquid
Maxima were also observed in plots of the heat transfer coefficient against liquid holdup [5] _ These occurred at holdups of approsimately 0.75 for the 1 mm beads and O-6 for the 3 and 5 mm particles. These observations are qualitatively in complete accord with previous fmdings for liquid-fluidized beds [ll - 14]_ The present data were correlated by the equation h = ~323~-~~=d;~sa
(5)
The multiple regression coefficient was 0.9982 for 120 data points. The experimental values of h could also be correlated by Iog(Sr-Regaa) = -1.908~,
f O-1367
(6)
with a correlation coefficient of 0.9799 for - 22 data points_ The Stanton and Reynolds numbers were evaluated at the average bulk temperature of the liquid in the column. A plot of 10g(St-R&~~) against ep is shown in Fig. 5 wliich illustrates the good agreement between the data and eqn. (6)- AIso shown in tt,is figure is the correlation of Wasmund and Smith [ll] for glass beads fluidized by water: Iog(St-.12eEss) = -1.75~~
f 0.11
(7)
This equation consistently predicts somewhat higher coefficients than were observed in this study. At a liquid holdup of 0.45, the discrepancy was about 10%; at a holdup of 0.9 it was about 30%. Brea and Hamilton [123, who measured heat transfer coefficients in beds of glass beads (0.5 - 2 mm) fluidized by water and
glycerol-water mixtures, data by the equation
correlated
their
Nu = 0.943(d,/d,)“-151+-o-53,Re~“” _ [Ey9”‘(l
-
Eu)o-4”]
(8)
In the present case, this equation yielded results which were almost identical to the correlation of Wasmund and Smith and are consequently omitted from Fig. 5 for the sake of clarity. Richardson et al. 1133 carried out similar experiments on a variety of solids fluidized by dimethyl phthalate. It i-_ of interest to note that, despite the markedly different coefficient obtained with the higher Prandtl number fluid, the slope of their plot of log(St-Reg-33) against ey was identical to that obtained in the present study_ It would thus appear that the value of the intercept in eqn. (6) is a function of the fluid properties and perhaps the geometry of the systemThree-phase
fluidized
beds
As may be seen in Figs. 6 - 8, the heat transfer coefficient in three-plate fluidized beds increased with gas velocity for all liquid velocities and particle sizes studied. The increase was initially quite rapid. However, at the higher gas rates it became less marked and h appeared to approach a maximum_ As may be deduced from these figures, plots of the heat transfer coefficient against liquid rate exhibited maxima. The same trend, it will be recalled, was observed with liquid-fluidized beds.
0
, 1600 0
E o
Imm be&s q=Llmrr/s UL=67mnvs UL=S6mws
700
_
200
Ug .mm/s Fig_ 5. Plot of log(St-Re$33)
liquid-fkidized
beds.
against Iiquid hoIdup in
Fig. 6_ Plots of heat transfer coef’ficient against gas veIocity in three-phase fluidized beds of 0.5 and 1 mm beads_
XJOO
A==
0
3-rm-abeads lJ,=41mm/s
x <
I
33000 r-
pzp/p
‘-I
I 1
L)=92mm/s_
T 0
0 ug= Omws e U~=16mn/s r u j
Ug=59nm/s _ ug =iIS mm/s Ug =237mmf 5
1
Fig. 7. Piots of heat transfer coefficient against gas velocity in three-phase fluidized beds of 3 mm beads.
Fig. 10. Plots particle size.
0 a
0
%
Smm beads q=Ll
mm/s
U~=92mm/s
Ut=126mm/s
’
tTICFJS
Fig_ 8. Plots of heat transfer coefficient against gas velocity in three-phase fluidized beds of 5 mm beads.
Fig. 9. porosity
Plots
of heat transfer coefficient against
in three-phase fluid-ked beds: open points -
U, = 16 mm/s; shaded points -
UQ
=
119 mm/s.
Typical plots of h against the total holdup or porosity (cy + Q) in three-phase fluid&d beds are shown in Fig. 9. These data were obtained at various liquid rates while holding the gas rate constant_ As may be seen, the heat transfer coefficient went through a maximum which shifted to Iower porosities with increasing particle size. However, little shift was observed at high gas rates on in-
of heat transfer
coefficient
against
creasing the particle diameter from 3 to 5 mm. At any given particle size, the effect of increasing the gas velocity was to shift the maximum to a higher porosity. Plots of h against particle size d, are shown in Fig. 10. The result of introducing solids into a liquid-gas bed (d, = 0) was, in general, to increase the vaIue of the heat transfer coefficient. A notable exception to this was observed at the higher gas rates where the coefficient went through a local minimumThus, under these conditions, h was smaller in the three-phase bed than in the corresponding Iiquid-gas bed_ As may be seen, this is onIy true for particle sizes up to about 1.5 mm. At liquid rates Iower than that shown in the figure, this local minimum was observed to occur at lower gas rates and also to be extended to a larger particle size. It was also generally observed that h was relatively insensitive to d, at values of the latter exceeding 3 mm, particularly at high gas rates. As may also be seen in Fig. 10, three-phase fluidized beds always exhibited larger values of h than liquid-fluidized beds. Although increasing the gas rate at larger particle sizes resulted in a larger value of h in the threephase fluidized beds, the difference between this value and the corresponding liquidsolid coefficient was essentially independent of particle size- However, for smalI particles, this difference decreased with increasing particle size up to about 1.5 mm. The heat transfer coefficients in liquid-gas beds were generally larger than those in the liquidfluidized beds at gas velocities less than about 60 mm/s-
2G2
The three-phase heat-transfer data were correlated by the equation in which h is expressed in W/m’K, U, and U, In mm/s and d, in mm. The multiple correlation coefficient was O-9974 for 246 data points- Attempts to formulate a correlation of similar form to eqns. (6) and (7) for liquidf’uidized beds were unsuccessful_ Moreover, %tclusion of bed porosity as an additional independent variable in eqn. (9) resulted in only a marginal improvement in the correlation coefficient. Published data on heat transfer coefficients in three-phase fluidized beds are estremely limited_ (pstergaard [I] noted that the injection of air into a bed of glass spheres fluidized by water resulted in a marked increase in the heat transfer coefficient. He observed that this increase was largest at the lowest liquid rates and was particularly marked near the minimum fluidizing velocity_ The same trends were observed in this study. Viswanathan et al. 131 measured heat transfer rates in beds of 649 and 928 pm quartz particles fluidized water and air. Their experiments were carried out at a constant bed height, which was achieved by simultaneously changing the water and air rates over relatively narrow ranges_ The initial marked increase in h resulting from the injection of air into the bed was again noted As in the present study, the heat transfer coefficient was observed to increase with particle size_ Typical values were of the order of 5100 W/m’K, which is slightly higher than those obtained in this work_ However, the experimental technique employed by Viswanathan et al. makes a meaningful comparison with the present data difficult.
DISCUSSION In this study, heat transfer coefficients have been measured in three-phase fluidized beds over a relatively wide range of experimentdl conditions_ PreIiminary correlations are presented which enable h to be estimated, at least in beds of glassbeads fIuidized by water and air_ Further work is of course necessary to extend these correlations to other systems. In addition, measurements of
heat transfer coefficients in the corresponding two-phase beds enable some conclusions to be drawn regarding the heat transfer mechanisms in the three-phase beds. In liquid-fluidized beds, the motion of the particles results in an erosion of the thermal boundary layer [ 133 _ At low liquid velocities, movement of the particles is restricted and their enhancement of the heat transfer coefficient is small. With increasing liquid rates, the particle velocity increases, resulting in a corresponding increase in h_ At even higher liquid velocities, this effect is counteracted by the reduced particle concentration. This explains the maximum observed in plots of h against UC and cL and the particular importance of the latter parameter. In liquid-gas beds, the increase in the heat transfer coefficient can also be attributed to increased turbulence about the heat eschange surface. This turbulence appears to be dependent largely on the gas content of the bed since both lg and h increased rapidly at first and then levelled off at high gas rates 151. By combining the effects of solids and gas, a reasonable explanation for the trends in the heat transfer coefficient in three-phase fluid&d beds can be offered. Introducing gas into a liquid-solid bed does not drastically change its porosity. It can therefore be assumed that the individual effect of the solids is not significantly changed. However, the presence of the gas increases the turbulence, resulting in an increased heat transfer coefficient. On increasing the gas rate, as in the liquid-gas bed, the gas holdup becomes essentially constant and thus it is reasonable to assume that its effect on the turbulence also becomes constant. The result is a large initial increase in the heat transfer and a levelling off at high gas rates. This is illustrated in Fig. 11, in which the difference between the film coefficients in three-phase beds and the corresponding liquid-solid bed, Ah,, is plotted against U,. The typical curves in this figure were obtained from the appropriate correlations, eqns. (5) and (9). As noted previously, three-phase fluid&d beds are seen to exhibit greater heat-transfer coefficients than the Iiquid-soIid bed under all conditions_ As with liquid-fluidized beds, decreasing UQ and dp both resulted in an increase in Ah,. However, the variation of this parameter with particle size was smalI
203
the solid particles, thereby reducing the turbulence at the heater surface. This study has clearIy iIIustrated the esceIIent heat transfer characteristics of three-phase fIuidized beds. The values of the heat transfer coefficients ranged up to four times as Iarge as those measured with the liquid alone flowing in the column. Moreover. fouIing of the heater was observed to be retarded by the presence of the solids. These favourable characteristics would certainly support the use of a three-phase fluidized bed for promoting catalytic reactions in which the heat effects are large. Fig. 11. Plots of ah, phase fluidized beds.
against gas ve!ocity
in threeCONCLUSION
Ug . mm/s Fig. 12. PI&s of Afz, phase fluidized beds.
against
gas velocity
in three-
at low rates. Thus the enhancement due to the presence of gas is greatest when it is introduced into a bed of incipiently fluidized particles. The same conclusion was reached by Qstergaard Cl]. The enhancement of the heat transfer coefficient in three-phase beds due to the presence of solids is illustrated in Fig. 12, in which Ah, is plotted against U,. Again, the appropriate correlations, eqns. (4) and (9), were employed to calculate Ah,. As may be seen, this parameter decreased rapidly with increasing gas rate but increased with particle size and liquid rate. In all cases, the trend for ti, to become negative at high gas rates was observed. Under these conditions the heat transfer coefficient in the three-phase bed is smaller than that in the corresponding Iiquidgas bed- The reason for this is not clear, but it may result from the hindrance of the gas by
The following conclusions can be drawn from the results of the present study: (1) in liquid-gas beds, the heat transfer coefficient initially increased rapidly with gas rate but levelled off at high flows. Liquid velocity had only a minimal effect on h_ (2) In the case of Iiquid-fiuidized beds, the presence of solids enhanced the heat transfer coefficient, which increased with d,. Plots of h against V, and eP exhibited masima and a linear relationship was observed between Iog(St-Reg33) and ek. (3) In most cases, the heat transfer coefficient in three-phase beds increased with particle size and with liquid and gas velocity. The value of h in these beds always esceeded that in the corresponding liquid-solid bed and normally exceeded that in the corresponding liquid-gas bed. However, with smaI1 particles and high gas rates, the liquid-gas coefficient e_xceeded that in the three-phase bed_
ACKNOWLEDGEMENTS
The authors would like to thank the National Research Council of Canada for a grant in aid of research to Dr. C_ G. J. Baker which made this work possible.
LIST
4 C, 4
OF
SYMBOLS
surface area of heater
specific heat of liquid hydraulic diameter of annulus
particle diameter acceleration due to gravity heat transfer coefficient expanded bed height, or height of test section in liquid-gas beds thermal conductivity of liquid esponent in Richardson-Z&i equation, Re = Re& Nusselt number, hd, ?Q pressure drop across fluidized bed, or across test section in liquid-gas beds Prandtl number, Cp~Jk~ heat transfer rate Reynolds number, Ucd,pc/pc Reynolds number, UrodpPr/pc Stanton number, h/pkC,UL superficial veIocity of gas superficial velocity of liquid terminal velocity of particles in liquid difference between heat transfer coefficient in three-phase fluidized bed and that in liquid-fluid&d bed with the same d, and L’( difference between heat transfer coefficient in three-phase fIuidized bed and that in a liquid-gas bed with the same U, and U, temperature difference between heater surface and bed gas holdup liquid holdup solids hoIdup liquid viscosity
PE PL PS
gas density Iiquid density solids density
REFERENCES 1 K. Gsterg-iard, in Fluidization, Sot_ Chem. Ind., London, 1963, p_ 6S_ 2 R. P_ Van Driesen and N. C. Stewart. Oil Gas J., 62 (1964) lOO_ 3 S. Visuranathan. A. S. Kaker and P. S. Murti, Chem. Eng. Sci.. 20 (1965) 903. 4 E. R. Armstrong. C: G_ .I_ Baker and M. A. Bergougnou. in D. L. Keaims (Ed.). Fluidization Technology. Vol. 1, Hemisphere Publishing Corp., Washington. 1976, p_ 453. hl.E.Sc. Thesis, Univ. of 5 E. R. Armstrong, Western Ontario, 19i5_ 6 S. D. Kim. C. G. J. Baker and hI_ A_ Bergougnou, Can. J_ Chem. Eng.. 50 (19i2) 695. F S_ D. Kim. C. G. J. Baker and hr. A. Bergougnou. Can. J. Chem. Eng.. 53 (1975) 134. 6 W. L. McCabe and J. C. Smith, Unit Operations of Chemical Engineering, hIcGraw-Hill. New York. 3rd edn.. 1976, pp_ 318 - 320_ 9 H. Groothuis and W_ P. Hendal. Chem. Eng. Sci., 11 (1959) 212. 10 A. A. Kudirka, J. Grosh and W. McFadden. Ind. Eng_ Chem. Fundam., 4 (1966) 339_ 11 B. Wasmund and J. W. Smith, Cao_ J_ Chem. Eng_, 45 (1967) 156. 12 F. M_ Brea and W_ Hamilton. Trans._ Inst. Chem. Eng., 49 (1971) 196. 13 J_ F_ Richardson, hI_ N. Romani and K. J. Shakiri, Chem. Eng. Sci.. 31 (1976) 619. 14 R. D. Pate1 and J. h’,. Simpson. Chem_ Eng. Sci.. 39 (1977) 6i.