balances were used to find U T O T , reasonable agreement between uTOT and ( V ~ U ~ )would ~ ’ be expected, but a detailed confirmation was thought of interest. The model indicates the velocity decay that would exist in a vessel with injection. At equal flow rates, tangential feed is better than radial feed for heat transfer, but response data indicate fractional inactive volume of nearly the same magnitude a t all the flow rates used here; however, it is shown that the response data criterion < 1 does not necessarily prove the existence of such “dead space.” In this, it is required t o assume a departure from calculable ideality-Le., different tracer concentrations in two feed streams; this is quite acceptable when the configuration is considered. The evaluation of UTOT also shows the possible wide variation of local velocities. Nomenclature
a ] , a2 = parameters defined in text, l j t
A = heat transfer area, sq ft b = parameter defined in text, l j t c = reduced concentration d i = jacket inner diameter, ft d2 = jacket outer diameter, ft D = equivalent diameter, ft D = differential operator in Equation 19, here l j t E = exit age distribution function f = Fanning friction factor h = heat transfer coefficient, Chu/ (hr-sq ft-”C) L = distance along flow path, ft m = heat capacity of water in jacket, Chui0C M = heat capacity of jacket walls, Chuj” C n = number of vessels in series Q = flow rate, cu ft/sec, cu ft/hr R = parameter defined in text, l j t Re = Reynolds number parameter defined in text, l / t s, = cross-sectional flow area, sq ft t = time-sec, hr t = mean residence time, sec, hr t, = measured mean residence time-sec, hr T = temperature, OC
s =
u V w W W
= velocity, ftisec = volume, cu ft = flow rate through jacket, lb,/sec = heat flow /degree
= u: (specific heat of water), 3600 Chu (hr-”C)
z = jacket height, f t Greek letters
0 = u T = @ =
5:
reduced time, t / t density, lb,/cu ft variance reduced vessel wall temperature reduced jacket fluid temperature
Subscripts
c = pertaining to tracer = feed i = in the ith vessel io = at solid-fluid interface in ith vessel o = at nozzle exit, initial condition R = inactive, unmixed TOT = total u: = vessel wall
F
Literature Cited
Bird, R. B., Stewart, W. E., Lightfoot, E. N , , “Transport Phenomena,” 2nd Printing, Wiley, Kew York, N.Y., 1962. Himmelblau, D. M., Bischoff, K. B., “Process Analysis and Simulation,” Wiley, New York, N.Y., p 70, 1968. Hulburt, H. M., Katz, S., Kuo, M. T., Montgomery, W. H., C.I.C. Conference, Hamilton, Ont., November 9-11, 1959. Lehrer, I. H., Ind. Eng. Chem. Proc. Des. Deuelop., 9, 553 (1970). Levenspiel, O., “Chemical Reaction Engineering,” Wiley, New York, N.Y., Chap. 9, 1962. “Perry’s Chemical Engineers’ Handbook,” McGraw-Hill, Kew York, N. Y., pp 5-33 and 5-60, 1963.
RECEIVED for review June 3, 1969 ACCEPTED February 18, 1971
Bed Porosities in Gas-liquid Fluidization Pidaparti Dakshinamurty’, Vangala Subrahmanyam, and Janu Nageswara Rao Chemical Engineering Department, Andhra University, Waltair, India
I
n three-phase (gas-liquid) fluidization, the solid particles are fluidized by an upward cocurrent flow of gaseous and liquid phases. The liquid forms the continuous phase while the gas bubbles through the liquid phase containing the particles. Such an operation is often encountered in chemical process industries where reaction between gas and liquid takes place in the presence of solids, as is the case with heterogeneous catalytic processes like hydrogenation. The importance of such processes has been stressed by Turner (1963). An important property of gas-liquid fluidized bed is the bed expansion as it is related to the volume of the equipment and the residence times of the fluid phases.
I
To whom correspondence should be addressed.
322
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 3, 1971
The reduction in bed porosity in three-phase fluidization was first noticed by Turner (1963). Though he did not offer any explanation, later work in this direction was taken up by Stewart and Davidson (1964) and Ostergaard (1965), and both of them offered explanations for such behavior. Further, Ostergaard and Theisen (1966) have studied the effect of particle size and bed height on porosity reduction. They concluded that bed porosity reduction is greater in beds of small particles than in those with large particles and reduction increases with increasing bed height. Thus, there is every need to extend the range of the variables studied, and t o study the effect of new variables. The present investigation was undertaken to study the effect of particle size, density, liquid surface tension, and flow rates of fluids on bed porosities in three-phase
Bed porosity data of three-phase (gas-liquid) fluidization have been determined for beds of rockwool shot, glass balls, glass beads, iron shot, and sand both in water and kerosine, using air, in a borosilicate glass tube of 5.6-cm diam. The effect of particle size, density, liquid surface tension, liquid viscosity, and flow rates of both gas and liquid on the bed porosity in gas-liquid fluidization, have been studied. The size, density, and gas and liquid flow rates have been varied from 0.1 to 0.7 cm, 2.4 to 7.7 gm/cc, 0.1 to 7.5 cm/sec, and 1 to 20 cm/sec, respectively. The reduction in bed porosity on the injection of a swarm of gas bubbles, was observed in beds of rockwool shot and small glass beads both in water and kerosine and 1/24- and Xz-in. sand in water; while with the other particles no such phenomenon i s perceptible. An attempt was made to correlate the bed porosity data in terms of dimensionless groups. From the present study two equations have been developed for the prediction of bed porosities in gas-liquid fluidized beds, based on Reynolds numbers calculated using terminal velocities of the particles. Both these equations represent the experimental bed porosities satisfactorily. Further, the data for the systems rockwool shot and small glass beads both in water and kerosine and % 4 - and Xa-in. sand systems in water only, are in good agreement with Ostergaard's semiempirical correlation to predict the bed porosities in three-phase fluidized beds.
fluidization. An attempt was made to develop an equation for bed porosity in terms of dimensionless groups. Further, the present data are compared with the data obtained through the method developed by Ostergaard (1965) and the relative merits of both are discussed. Experimental
The present experimental setup consists of a main fluidization tube of borosilicate glass (5.6 cm in diam and 5 ft long). Both water and air are allowed to pass through a calming section, 18 in. long and of the same diameter as the main tube filled with raschig rings (3/sin. diam) and then through a coarse mesh, fine mesh, and a perforated plate supporting the bed before entering the fluidization tube. The introduction of the coarse and fine meshes is with a belief that air entering the main tube will have a uniform bubble size. Densities of bed materials were determined with a specific gravity bottle. The sizes of the regularly shaped particles were determined by determining the average particle volume with the specific gravity bottle. For sand, the particle diameter was taken as the arithmetic average of the apertures of two British standard sieves. The viscosity and surface tension of the liquids were measured with an Ostwald viscometer and torsion balance, respectively. Table I. Systems Studied-Sizes,
The terminal velocities for all the particles are read from the graph given in Brown (1950). Results and Discussion
The systems studied are given in Table I along with the specification of the particle sizes, densities, terminal velocities, and average percent deviations observed. The physical properties of the fluids used are given in Table 11. The experimental bed porosities of the various systems are shown plotted in Figures 1 to 12 against U, (superficial gas velocity based on empty cross section) with Ui', the superficial liquid velocity, as the parameter. The bed voidage is defined as the fractional bed volume occupied by the gas and liquid. An attempt was made, in the first instance, to correlate the present bed porosity data with Ostergaard's method despite method limitations. A comparison between the experimental and calculated bed porosity data according to Ostergaard's method is plotted in Figure 13. The average percent deviation between the calculated and the experimental was 3.7 taking into consideration all the runs of systems 1 to 6 while the percent deviation observed in each system is presented in Table I. I t is evident from Figure 13 that barring a few points, the agreement between the two is satisfactory. I n the case of
Density, and Terminal Velocity of the Particles Av Yo dev between calcd and exptl
No.
1 2 3 4 5 6 7
8 9 10 11 12
System
Rockwool shot-air-water Rockwool shot-air-kerosine X 4 - h . sand-air-water V i 2 - h . sand-air-water Small glass beads"-air-water Small glass beads-air-kerosine Large glass beads-air-water Large glass beads-air-kerosine Glass ballsb-air-water Glass balls-air-kerosine Iron shot-air-water Iron shot-air-kerosine
Density, g/cc
Size Dp, Cm
Terminal velocity of porticle, cm/sec
Authors correlation
Ostergaard correlation
2.7 11 2.7 2.71 2.4 2.4 2.4 2.4 2.26 2.26 7.707 7.707
0.13 0.13 0.106 0.2235 0.3348 0.3348 0.6844 0.6844 0.489 0.489 0.3 0.3
24.0 24.3 16.0 28.0 35.0 36.4 50.0 68.0 43.0 65.0 77.4 105.0
3.66 3.27 5.70 5.65 3.30 6.50 5.40 6.60 2.23 4.50 4.20 4.10
3.57 4.70 3.57 6.40 4.94 1.43
'Glass beads = glass spheres with central cylindrical holes.
Glass balls = glass spheres.
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 3, 1971
323
table II. Physical Properties of the Fluids Used at 30' C Density, g/cc
Viscosity, poise
Surface tension, dynes/cm
0.995 0.8 0.001165
0.008 0.017
71.2 26.0
Fluid
Water Kerosine Air
...
...
Figure 4. c vs. U,
-()7.42
Ui':
0.3
'
I
0
2
I
I
1
3
4
5
System: %J-in. sand-air-water 6.65 8 6.10
05.05
0 4.34
UP
Figure 1 .
0
Ui:
vs. U, plot
System: rockwool shot-air-water 5.05 0 4.18 2.70
8
'
I
1.84
0.4
0
2
I
I
I
I
I
3
4
5
6
U9 07
Figure 5.
1 Ui: Figure 2. t vs. U, plot System: rockwool shot-air-kerosine
Ui
0 5.74 0 4.75 +3.84
0*3 0
2
I U9
0.4
t
3
8
3.08
+ 2.02
0 9.0
vs. U, plot
System: small glass beads-air-water
8
8.0
07.2
0 6.65
0 6.10
these systems high percent deviation noticed in a few points corresponds to high gas velocities. For systems 7 to 12, an Ostergaard correlation shows a minimum deviation of about 10% and the maximum, 32%. Hence, it is not shown in the diagram. I t is concluded that Ostergaard's method could correlate the data of the particles of size 0.1 to 0.33 cm but could not correlate the data if the particle size is more than 0.33 cm. The only exception to this statement is iron shot. Though its diameter is 0.3 cm the reduction in bed porosity is not perceptible and this system could not be correlated by this method. I t is evident from Figures 1 to 6, that, as the particle size is increased from 0.1 to 0.33 cm, the reduction in bed porosity is decreased. Similar behavior is observed by Ostergaard and Theisen (1966). Perhaps the reduction is more pronounced in the case of $$4-in. sand-waterair and rockwool shot-water-air systems. I n the case of % r-in. sand-water-air and !/,2-in. sand-water-air and small glass beads-water-air, as the air velocity, U,, is increased, the error between the calculated and experimental is increased. This may be owing to the limitations of Ostergaard's method. In the case of rockwool shotkerosine-air (barring a few points) and small glass beadskerosine-air, the agreement between the predicted and experimental is good; but in both cases, for a no gas velocity condition, the bed porosities predicted from the equation of Richardson and Jaki (1954) are higher than the experimental. Further, very little bed porosity reduction was observed in these two systems. I n the case of
" T
2
I
0
u!3
4
3
Figure 6. e vs.
5
6
U pplot
0.3
U;:
i ) 10.6
8
0 8.44
9.46
0 7.65
3
2
I
0
System: small glass beads-air-kerosine
5
4
6
U9
0 6.75
Figure 8. e vs. Ug plot System: large glass beads-air-kerosine
Ut':
"" I
0.3' 0
I
I
I
2
3
I
I
4
5
814.6
0.4
0
+12.3
8 12.9
+10.75
09.55
I
1
I
I
I
2
3
4
5
u9
Figure 9. c vs. Upplot
U gplot
System: glass balls-air-water
System: large glass beads-air-water
Ui:
010.55
I
U9
Figure 7. c vs.
+11.2
10.0
0 9.0
0 8.0
rockwool shot-kerosine-air, a small fraction of the particles was attached to the sides of the glass tube in a thin layer and may be responsible for the above effect. With % 4-in. sand-water-air and rockwool shot-water-air systems, relatively large bubbles with a spherical cap shape emerged from the beds carrying with them a very small fraction of the particles; but in the case of s 4 - i n . sandwater-air and small glass beads-water-air systems, the size of the bubbles that emerged from the beds was reduced. The size of the bubbles that emerged in the beds of rockwool shot and small glass beads in kerosine was relatively, a bit smaller. Gradual reduction in the size of the bubbles emerging from the bed was observed when the particle size was changed from 0.107 to 0.3348 cm. The bed porosity reduction in these cases may be due to the large bubbles, with consequent high bubble velocity which in turn increases the wake velocity. Thereby, the velocity of the liquid in the rest of the fluidized bed is lower than the average liquid velocity; pronounced bubble coalescence has been observed in small particle beds. I n these cases, where bed porosity reduction is small, it may be owing to the emergence of small bubbles, which travel with low velocity along with its wake, and, in turn, decrease the difference in velocity of the wake and the liquid in the rest of the bed. The size reduction
Ui':
811.9
0 1 1 . 3
010.5
4
9.0
08.0
of the bubbles emerging from these beds may be owing to disintegration of gas bubbles. I n systems 7 to 12, the gas bubbles emerging from the bed are small, uniform in size, and they move as discrete bubbles in the column toward the outlet. The appearance of the column is similar to a spray column in liquid-liquid extraction. Perhaps, the reduction in bubble size is responsible for the imperceptible bed porosity reduction in these systems. Also, the region of reduction of bed porosity might have been confined to a small range of gas velocities which were not measured in the present work. The net effect is the reduction in bed porosity observed in systems 1 to 6 appears to be absent in systems 7 to 12. I n some cases the opposite effect, that is, a rapid increase in bed porosity for a small gas velocity, was observed. I n all the systems the bed porosity increased as gas velocity is increased, keeping the liquid velocity constant. Also as the liquid velocity was increased the bed porosity increased in all the systems, both in water and kerosine. For a given liquid velocity, the porosity passes through a minimum as the gas velocity is increased. This minimum is displaced toward high gas flow rates as the liquid flow rate is increased. This refers to those systems in which reduction in bed porosity is observed. Similar observations are made by Ostergaard (1965). Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 3, 1971
325
I
0.6 1
i
I/
0.3t
0
I
2
I
I
1
3
4
6
5
0.3
0
2
I
3
U9 System: glass balls-air-kerosine 10.2 0 9.0
0
8 10.9
5
Figure 12. c vs. U, plot
Figure 10. e vs. Ug plot
Ul:
4 u9
0 6.75
7.83
0
U;:
System: iron shot-air-kerosine 18.9 0 15.1 0 13.5
012.8
00
0.7 -
0.6 c\
t X
3 0.5 0-3 0
I
2
3
4
5
6
/eo&
-
.A
&%-
W
Ui:
15.1
t
*
vs. U, plot
System: iro,n shot-air-water 12.9 0 11.9
0
0
&
ma
u9
Figure 11.
O
0 11.3
When the liquid medium is changed from water to kerosine, particles of rockwool shot formed a thin, more or less stagnant, layer on the walls of the tube, which may be owing to the effect of surface tension. I n the case of other particles, no such behavior is observed. I t is evident from the above, that Ostergaard's correlation could not fit the porosity data of all the systems satisfactorily. Hence, an attempt is made to develop an empirical correlation between t , the bed porosity, and dimensionless groups. (The bed porosity is defined as the fractional volume occupied by gas and liquid.) Apparently, the two dimensionless groups ( U [ /Ut) and ( p i U p / ~could ) satisfactorily account for the variation in C. Hence, c can be expressed as a function of these two groups as follows:
To determine the value of the constant, K Z , and the exponents, m and n, in the first instance, experimental values of c are shown plotted in Figures 14 and 15 against ( ~ c ~ Uon~ logarithmic /U) coordinates with U,' as a parameter. (In Figures 14 and 15 data for the systems glass balls-water-air and glass balls-kerosine-air only are shown to illustrate the form of the graph.) The resulting lines for all the systems are parallel and the value of n is 0.08. The intercepts made by such lines were plotted against (UilU,) in Figure 16. Barring rockwool shot in water and kerosine and X4-in.sand in water-i.e., systems 1 to 3-a single straight line could be obtained for all other systems with a slope of 0.6 and intercept of 2.65. For these systems, the Reynolds numbers based on terminal velocity of the particles are greater than 500 and hence, fall in the Newton's law region. Similarly, in Figure 17 the data of systems 1 to 3 could be represented by 326 Ind. Eng. Chern. Process Des. Develop., Vol. 10, No. 3, 197
0.7
I
I
u9 e Figure 14. c vs. (riUg/a)plot P L
Ui:
0 11.9
0.3 1 3X Id4
+
System: glass balls-air-water 11.3 010.5
0
9.0
, 163 /uL
w b 3
"9
0-
Figure 15. e vs. (pAJg/u) plot Uf:
(> 10.9
System: glass balls-air-kerosine 0 10.2 9.0 0 7.83
0 6.75
0.6 -
-
n
50.5
& W
0.5
0.2
0.I
03
UL Ut
0.4
0.4
0.3
Figure 16. Intercepts K vs. (U//Ut)
0 !I'
L-ln, sand-air-water Small glass beads-air-water Small gloss beads-air-kerosine A L a r g e glass beads-air-water A t o r g e gloss beads-air-kerosine
@Glass balls-air-water 0 Glass balls-air-kerosine
2.0 1
1
a
-
e l r o n shot-air-water o l r o n shot-air-kerosine
0.4
0.3
