Ind. Eng. Chem. Res. 1989,28, 1873-1878 The University of Texas a t Austin, Aug 1986. Tedder, D. W.; Ekkles, A. J.; Ferster, P. J.; Tawik, W. Y. Continuous Fermentations and Product Recovery by Liquid-liquid Extraction. Proceedings of Biotech 84, p 177, 1984. Vermeulen, T.; Moon, J. S.; Hennico, A.; Miyauchi, T. Axial Dispresion in Extraction Columns. Chem. Eng. Prog. 1966,62,95.
1873
Wilke, C. R.; Chang, P. Correlation of Diffusion Coefficients in Dilute Solutions. AZChE J. 1955,1 , 264.
Receiued for review December 9, 1988 Revised manuscript received June 26, 1989 Accepted August 15, 1989
Preliminary Design of Sieve Tray Extraction Columns. 1. Determination of the Column Diameter. Flooding Velocities in Sieve Tray Extractors J. Antonio Rocha,* J. Carlos CBrdenas, Cbar Sosa, and Jorge Rosales Instituto Tecnol6gico de Celaya, Departamento de Zngenieria Quhica, Celaya, Gto., Mexico
Experimental data from this project and other sources have been used to obtain three correlations for predicting the flooding velocities in sieve tray extractors. One correlation was obtained using the analogy between distillation and extraction. This correlation showed an average relative deviation of 22%. The second and third equations were obtained by dimensionless analysis and a least-squares fit of the physical properties and geometric and hydrodynamic parameters that most affect the performance of sieve tray extractors. These equations presented an average relative deviation of 11’3’0 and 13% The three correlations were used to estimate the flooding velocities and the diameters of the sieve tray extraction columns working a t 60% flooding.
.
In recent years, liquid-liquid extraction has gained increased attention as a commercial separation method in the process industry, as has been shown by Humphrey et al. (1984). Although liquid-liquid extraction has been practiced for many years, its study, investigation, and development have been rather poor. Pilot plant experimentation is still needed to design most industrial equipment. In the classification of nonmechanically agitated contactors, the sieve tray extractor has an important role due to the relatively high throughputs, the moderate efficiency, and the simplicity of construction and operation, which is similar to the well-known sieve tray distillation column. The operation of a sieve tray liquid-liquid extraction column, where the light liquid is the dispersed phase, is shown in Figure 1. The heavy liquid flows downward through such a extractor horizontally across each tray and through the downcomers from tray to tray. The light liquid issues from the perforations in each tray in the form of jets or drops (drop formation), rises through the heavy liquid in the form of drops (drop rise), enters into a flocculation zone, and subsequently coalesces into a layer of light liquid which accumulates immediately under each tray. In a previous paper, Rocha et al. (1986) have shown that the optimum mass-transfer efficiency in sieve tray extractors is obtained at a high velocity of the dispersed phase, but if this velocity is increased, the extractor may flood. Flooding in sieve tray extractors occurs when the flow rate of the dispersed phase is prevented from flowing through the column and is dragged out by the flow rate of the continuous phase. Flooding can also arise if the flocculation zone expands to fill the stage. Correlations to predict the flooding velocities in sieve tray extractors seem important because they could permit us to fix the proper flow to a good mass-transfer efficiency and also to estimate the column diameter.
reported in the literature are limited. A small comment about the most important work done in this field of research is as follows: Mewes and Pilhofer (1979) presented the load limits and the operational range of sieve tray extractors as a function of extractor geometry and physical properties of the system. Although no experimental data are reported, their “load diagrams” plot the volumetric flow rates of both phases in a dimensionless form by using eq 1-A and 1-B.
r
L
-
J
Hirschmann and Blass (1984) performed investigations with the test system 1-butanol/succinic acid/water, on account of its low interfacial tension, namely, 1.75 dyn/cm. The investigations started by studying the drop formation as the main process. The results thus obtained were applied to a specified design of the sieve tray column with downcomer. Holden (1984) performed an experimental project to study the influence of geometric variables and physical properties of the system on the flooding velocities. He used two different systems (toluene/water, and methyl isobutyl ketone/water) in a 0.1-m-diameter glass column. Dawodu et al. (1984) and Oloidi and Mumford (1985) carried out some studies on the hydrodynamic parameters of sieve tray extractors in a 0.45-m-diameter glass column. The correlations they proposed to predict the drop diameter distribution and operational holdup were mostly applicable to the system they used. Rocha et al. (1985), using basically the experimentaldata of Holden (1984), proposed an approximate correlation to predict the flooding velocity of the continuous phase. The equation is as follows:
Previous Work The studies and investigations on flooding velocities in sieve tray extractors are scarce. The experimental data 0888-5885/89/2628-1873$01.50/0
1113
0 1989 American Chemical Society
1874 Ind. Eng. Chem. Res., Vol. 28, No. 12, 1989 O u i e t l i g h t phase
Table I. Data Sources for Flooding Velocity Studies in Sieve Tray Extraction Columns reference system tray spacing, m data pts d, m toluene/water 0.102 0.174,0.246,0.350 49 Holden (1984) 21 MIBK/water 0.102 0.174,0.346 Holden (1984) butanol/water 0.075 0.200,0.412 13 Hirschmann and Blass (1984) Clairsol/water 0.450 0.340,0.380 11 Oloidi and Mumford (1985) Rocha and Isopar/water 0.425 0.304 9 Seibert (1987) 34 present work MIBK/water 0.246 0.200,0.400 29 present work toluene/water 0.246 0.200,0.400,0.600
t Main interface
Table 11. Physical Properties of Systems in the Data Sources Inlet
Outlet heavy phase
l i g h t phase
M
-
Figure 1. Sieve tray extractor with the light liquid as the dispersed phase.
Oloidi et al. (1986) presented a summary of the experimental work carried out by Dawodu et al. (1984) and Oloidi and Mumford (1985) in the 0.45-m-diameter glass column. They proposed correlations to predict the operational holdup, height of the coalesced layer, and drop diameter. They showed several experimental flood points for plate hole sizes of 3.17 and 6.35 mm.
Experimental Equipment For the realization of this study, a stainless steel distillation column was adapted as the sieve tray extractor by the collocation of a distributor for the light phase at the lower part of the column and a cylindrical section on the head of the column to permit (1) the separation of the light phase from the continuous phase, (2) the entrance of the heavy phase and the exit of the light phase, and (3) the installation of a level glass window and a level control for the main interface. The column has a diameter of 0.25 m and a total height of 7.4 m. A diagrammatic representation of the column and the peripheral equipment is shown in Figure 2A, and a view of the geometry of one plate is shown in Figure 2B. It must be noted that the device used to seal the exit of the downcomer when the column was operating as a distillation column still remains in most of the experimental runs when operated as the extractor. This provided an additional resistance to the flow of the heavy or continuous phase. The differences found when the extractor worked without these seals were that, for the toluene/water system, the flooding velocities decreased, while for the MIBK/water system, there was no change. Equipment Operation A typical run to flood the column took about 1 h. A sequence of the steps involved is described below. Step 1. Filling the Column. The extracton column is first filled with water (the heavy phase), letting the air leave through a vent valve. The light phase is then introduced through the distribution at the lower part of the column by pumping in the light phase and opening the outlet valve for the heavy phase. Step 2. Starting the Operation. When an appropriate amount of light phase has been built up a t the top
toluene/water MIBK/water Clairsol/water butanol/water Isopar/water
862 813 783 846 862
992 999 998 985 992
0.00056 0.00069 0.00180 0.00340 0.00054
0.0011 0.0011 0.0011 0.0014 0.0090
0.025 0.008
0.035 0.002 0.020
of the column, pumping of the heavy phase is started, and the outlet valve for the light phase is opened. The desired volumetric flow rates are adjusted. The interface level controller helps steady state to be reached by adjusting the inlet of the heavy phase. Step 3. Increasing One of the Flows and Waiting for the Results. At the start of the operation, both flows are low, and usually one is a t the desired value. Then in order to approach flooding, the flow of the other is increased in steps, letting it reach steady state or the flooding conditions. For steady-state conditions, measurements of the volumetric flow rate are performed for dispersed and continuous phases by measuring the time required to fill a receptacle of known volume. The point of flooding is reached when a second interface is formed at the bottom of the column, which is detected by the level glass window. After this point, if one of the flows is increased, the light phase will be strongly entrained with the exit of the heavy phase. Step 4. Shutdown of the Operation. When flooding is detected, all the flows in and out of the column are shut off, and the material inside the column is allowed to settle. The procedure just described was repeated with different flow rates for the heavy and light phases.
Test Systems and Data Bank The systems used in this study were toluene/water and methyl isobutyl ketone (MIBK)/water, with approximate interfacial tensions of 30 and 10 dyn/cm, respectively. Table I shows the data sources for the flooding velocity studies on sieve tray extraction columns. Table I1 shows the physical properties of the systems used. Tables 111-VI show some of the experimental reported data. Correlation of the Flooding Velocity by Analogy with Distillation The flooding velocity of the gas phase on sieve tray distillation columns was correlated by Fair (1961),plotting on logarithmic scales the parameters 0.5
(3) Rosales (1987), on the basis of the paper by Woodle (1963), applied the analogy between distillation and ex-
Ind. Eng. Chem. Res., Vol. 28, No. 12, 1989 1875 Table 111. Flooding Velocities: Experimental Points (Source: Hirschmann and Blass (1984). System: Butanol/Water)
run P1 P2 P3 P4 P5 P6 P7 P8 Q1 Q2 Q3 64 Q5
udp m/s
UCfr4 s
0.004 34 0.003 97 0.003 47 0.002 87 0.002 60 0.002 27 0.001 68 0.001 23 0.006 06 0.005 07 0.004 10 0.002 30 0.001 13
0.005 75 0.006 22 0.006 72 0.007 43 0.007 86 0.008 40 0.008 98 0.008 88 0.003 37 0.004 50 0.005 63 0.006 72 0.006 72
d,l,
m
0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075
do, m 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015
N O
140 140 140 140 140 140 140 140 140 140 140 140 140
Ht, m 0.2000 0.2000 0.2000 0.2000 0.2000 0.2000 0.2000 0.2000 0.4120 0.4120 0.4120 0.4120 0.4120
Ldoamt
0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.155 0.155 0.155 0.155 0.155
BC 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0220 0.0220 0.0220 0.0220 0.0220
A, 0.0649 0.0649 0.0649 0.0649 0.0649 0.0649 0.0649 0.0649 0.0554 0.0554 0.0554 0.0554 0.0554
Table IV. Flooding Velocities: Experimental Points (Source: Oloidi and Mumford (1985). System: Clairsol 350/Waterl
run N1 N2 N3 N4 N5 01 02 03 04 05 06
Ud.R m/s 0.007 28 0.007 08 0.006 98 0.006 89 0.006 79 0.008 19 0.008 20 0.008 10 0.007 99 0.007 69 0.008 13
Uc,f,m/s 0.006 89 0.007 29 0.007 69 0.007 99 0.008 48 0.008 89 0.009 00 0.008 99 0.008 82 0.009 19 0.009 20
m 0.450 0.450 0.450 0.450 0.450 0.450 0.450 0.450 0.450 0.450 0.450
d,l,
do, m 0.003175 0.003 175 0.003 175 0.003 175 0.003 175 0.006 350 0.006 350 0.006 350 0.006 350 0.006 350 0.006 350
N O
985 985 985 985 985 380 380 380 380 380 380
Hi,m 0.3800 0.3800 0.3800 0.3800 0.3800 0.3400 0.3400 0.3400 0.3400 0.3400 0.3400
Ldoamr
0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120
BC 0.0999 0.0999 0.0999 0.0999 0.0999 0.0999 0.0999 0.0999 0.0999 0.0999 0.0999
A, 0.0490 0.0490 0.0490 0.0490 0.0490 0.0756 0.0756 0.0756 0.0756 0.0756 0.0756
Bc 0.0243 0.243 0.0243 0.0243 0.0243 0.243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243
A, 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479
Table V. Flooding Velocities: ExDerimental Points (Present Work. System: Toluene/Water)
run R1 R2 R3 R4 R5 R6 R7 R8
s1
s2 s3 s4 s5 S6 T1 T2 T3 T4
u1 u2 N1 u4 u5 U6 u7 U8 u9 u10 u11
Ud,ft m/s
0.009 29 0.007 96 0.005 30 0.006 63 0.004 64 0.003 98 0.002 65 0.002 65 0.010 39 0.007 96 0.006 36 0.005 30 0.003 98 0.001 32 0.010 61 0.003 98 0.004 82 0.001 43 0.016 66 0.014 49 0.006 23 0.006 60 0.001 07 0.001 65 0.006 53 0.005 13 0.001 10 0.009 80 0.001 05
Uc,f,m/s 0.002 65 0.003 98 0.004 64 0.005 30 0.00663 0.007 96 0.009 29 0.01061 0.003 81 0.005 20 0.005 34 0.005 48 0.006 15 0.006 63 0.004 82 0.005 34 0.005 30 0.005 72 0.005 40 0.004 76 0.006 10 0.006 23 0.009 52 0.008 33 0.006 66 0.007 32 0.007 75 0.005 20 0.008 33
m 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246 0.246
do, m 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047 0.0047
traction, considering the dispersed and continuous phases in extraction as the gas and liquid phases in distillation. He plotted the equivalent parameters on logarithmic paper and found good agreement with his experimental data. He also found that the interfacial tension had no significant influence on the flooding velocity represented by (3). His proposition to predict the flooding velocity for the dispersed (and light) phase is, then, by using Figure 3, which is a plot of the following parameters:
NO 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128
128 128 128 128 128 128 128 128 128 128 128 128 128 128
H,,m 0.2000 0.2000 0.2000 0.2000 0.2000 0.2000 0.2000 0.2000 0.4000 0.4000 0.4000 0.4000 0.4000 0.4000 0.6000 0.6000 0.6000 0.6000 0.4000 0.4000 0.4000 0.4000 0.4000 0.4000 0.4000 0.4000 0.4000 0.4000 0.4000
Ldown,
0.184 0.184 0.184 0.184 0.184 0.184 0.184 0.184 0.184 0.184 0.184 0.184 0.184 0.184 0.184 0.184 0.184 0.184 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354
His predictions present an average relative deviation of 22% and were calculated with the following equation:
av relative deviation = av
Correlation of the Flooding Velocity by a Least-Squares Fit From reading the papers cited in the Previous Work section and from the experience gained through experimental work, one can find that the physical properties and the geometric and hydrodynamic parameters that most
1876 Ind. Eng. Chem. Res., Vol. 28, No. 12, 1989
affect the operation and flooding velocities of a sieve tray extractor are (1) the superficial velocities of both phases, (2) the densities of both phases, (3) the viscosities of both phases, (4) the interfacial tension of the system, (5) the hole diameter, (6) the diameter of the column, (7) the ratio of downcomer length to plate spacing, (8) the ratio of downcomer area to total column area, (9) the fractional free area, and (10) the plate spacing. The parameters just cited were combined to obtain dimensionless groups and correlated to obtain a total flooding velocity group:
(
?$!!rl):*”(
0.21163
F e e d l o n k h e a v y phose
(6) Heavy p h o s e p r o d u c l
Equation 6 is solved with the normal knowledge of the ratio of the dispersed to continuous phase flow rates, usually set by laboratory tests or by multiplying by an appropriate factor (greater than 1.0) the minimum solvent-to-feed ratio. The estimation of the total flooding velocity shows an average relative deviation of l l % , when calculated with eq 5. A simplified version of eq 6 is Ut,rdOPC - 0.30137( -P C
0.0948
r d 2No/ 4
)
u
0.0593
UC,f (A)
X
This equation presents an average relative deviation of 13% and it has less terms than eq 6.
Influence of Column Diameter on the Flooding Velocity For scale-up purposes, it is of interest to determine how the total flooding velocity changes with the variation in the column diameter. Unfortunately at the present time, the number of available experimental points do not seem to be enough to generate a reliable equation. Application of Correlations for Design Cases It was mentioned before that one of the applications of a correlation for the flooding velocity is the estimation of the column diameter required to perform a specific operation. In this part of the paper, the correlations proposed with (3) and eq 6 and 8 will be used in a typical case of design, based on the concept of flooding velocity and on the recommendation of working the columns at an operational velocity of 60% flooding. From the point of view of a designer, some of the parameters that must be fixed are as follows: (1)the ratio of downcomer area to total area of the column, Adown/Acol, from 9% to 12%; (2) the ratio of downcomer length to plate spacing, Ld,,,/Ht, from 60% to 80%;(3) the diameter of the orifice, do, usually set between 3.17 and 6.35 mm, 4.762 mm being a very common size; (4) the fractional free area, usually set between 5% to 7%; (5) as was stated before, the ratio of the dispersed phase to the continuous phase set as a factor of minimum solvent-to-freed ratio and usually obtained by laboratory tests using small glass
c~-
2 46
Figure 2. (A, top) Flow diagram of the experimental equipment. (B, bottom) Tray and downcomer geometry (scale mm).
equipment of the kind of funnel separators. Normal values of ud/ucreported in the literatre range from 0.1 to 7.0, but the authors know of an industrial sieve tray extractor with a ratio of more than 30. Three cases were chosen to test the flooding correlations. These are as follows. Laddha and Degaleesan (1978) Case. This problem involves an aqueous acetaldehyde solution and vinyl acetate as the immiscilble phases. The volumetric flow rate of the continuous phase is 118 L/min; the ratio of the dispersed phase to the continuous phase is 1.28, assuming a perforation size of 3 mm. Treybal (1980) Case. This problem involves the recovery of acetic acid from an aqueous stream by using isopropyl ether as the solvent in the dispersed phase. The volumetric flow rate of the continuous aqueous phase is 132 L/min. The ratio of the dispersed phase to the continuous phase is 3.18, and a hole diameter of 6.0 mm is recommended.
Ind. Eng. Chem. Res., Vol. 28, No. 12, 1989 1877 Table VI. Flooding Velocities: run UA*, m / s v1 0.01061 v2 0.005 30 v3 0.002 65 w1 0.006 06 w2 0.013 33 w3 0.012 34 w4 0.015 15 w5 0.016 66 W6 0.010 41 w7 0.008 13 W8 0.006 90 w9 0.007 02 w10 0.017 54 w11 0.006 20 w12 0.012 34 W13 0.011 10 W14 0.009 66 W15 0.004 90 x1 0.010 75 x2 0.010 10 x3 0.017 54 x4 0.016 66 x5 0.015 87 X6 0.015 15 x7 0.012 34 X8 0.012 34 x9 0.007 93 x10 0.007 93 x11 0.006 94 Y1 0.015 20 Y2 0.007 93 Y3 0.010 41 Y4 0.010 41 Y5 0.007 93
Experimental Points (Present Work. d,,, m d,, m 0.246 0.0047 0.006 63 0.0047 0.246 0.007 96 0.246 0.0047 0.009 29 0.246 0.0047 0.007 28 0.246 0.0047 0.005 18 0.0047 0.246 0.004 68 0.246 0.0047 0.004 09 0.246 0.0047 0.003 26 0.246 0.0047 0.006 98 0.246 0.0047 0.008 10 0.246 0.0047 0.008 55 0.246 0.0047 0.008 94 0.0047 0.246 0.003 30 0.246 0.0047 0.008 33 0.246 0.0047 0.004 97 0.246 0.0047 0.005 95 0.246 0.0047 0.007 57 0.246 0.0047 0.009 00 0.008 33 0.246 0.0047 0.007 66 0.246 0.0047 0.002 69 0.246 0.0047 0.0047 0.003 20 0.246 0.004 06 0.246 0.0047 0.004 76 0.246 0.0047 0.005 55 0.246 0.0047 0.005 95 0.246 0.0047 0.006 66 0.246 0.0047 0.007 24 0.246 0.0047 0.008 13 0.246 0.0047 0.007 41 0.246 0.0047 0.007 93 0.246 0.0047 0.006 66 0.246 0.0047 0.007 57 0.246 0.0047 0.246 0.0047 0.009 00
U,,m/s
System: MIBK/Water) No H,,m Lh, m 128 0.2000 0.184 0.184 128 0.2000 0.184 128 0.2000 0.184 128 0.4000 0.184 128 0.4000 0.184 128 0.4000 0.184 128 0.4000 0.184 128 0.4000 0.184 128 0.4000 0.184 128 0.4000 0.184 128 0.4000 0.184 128 0.4000 0.184 128 0.4000 128 0.4000 0.184 0.184 128 0.4000 0.184 128 0.4000 0.184 128 0.4000 0.184 128 0.4000 0.184 128 0.2000 0.184 128 0.2000 0.184 128 0.2000 0.184 128 0.2000 0.184 128 0.2000 0.184 128 0.2000 128 0.2000 0.184 0.184 128 0.2000 0.184 128 0.2000 128 0.2000 0.184 128 0.2000 0.184 0.354 128 0.4000 128 0.4000 0.354 0.354 128 0.4000 0.354 128 0.4000 128 0.4000 0.354
B, 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243 0.0243
A. 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479 0.0479
Table VII. Comparison between the Cc.imn Diameters Calculated with the Correlations and the Values Reported in the Literature
calcd system vinyl acetate isopropyl ether/acetic acid/water diisopropyl ether/phenol/water
eq4 1.06 0.97 2.14
eq6 1.15 1.24 2.66
reported eq8 eq8 0.84 0.91 0.98 1.00 2.36 2.43
reference mob 11.1: Laddha and Deealeesan (1978) prob 10.8 Treybal (1980) study case: Rocha and Fair (1986)
extractor against a Scheibel column for the extraction of phenol from a wastewater stream. The volumetric flow rate of the continuous phase is 2809 L/min. The ratio of the dispersed phase to the continuous phase is 10, and a hole diameter of 5 mm was used. In general, the application of the three correlations is straightforward, but care must be taken when using the first correlaton, because the flooding velocity of the dispersed phase is based on the net area of the column (area of the total column minus the area of a downcomer). If the operational velocity is chosen as 60% of the flooding velocity, the equation to calculate the cross-sectional area of the column is r
Figure 3. Prediction of flooding velocity by analogy with distillation.
Rocha and Fair (1986) Case. This problem involves the comparison of the global dimensions of a sieve tray
where Qdis the volumetric flow rate of the dispersed phase. The column diameters calculated by using the three correlations and reported in the literature are shown in Table VII. In Table VII, it is observed that eq 8 is a better predictor than 6 and 4. From these results, it is possible to think that the dimensionless numbers Adown/ACol, Ldom/Ht,and &/& are not as relevant as the other fine parameters
1878 Ind. Eng. Chem. Res., Vol. 28, No. 12, 1989
included in both eq 6 and 8.
Conclusions Three correlations for estimating the flooding velocities in the sieve tray extractors have been developed, one based on the analogy with distillation (eq 4) and the others (eq 6 and 8) based on the total flooding velocity and dimensionless groups. Both eq 6 and 8 give approximately the same average relative deviation. Equation 6 takes into account most of the important parameters on the sieve tray liquid-liquid extractors and was derived in a more rigorous dimensionless analysis. Equation 8 can be considered to be a simplified version of eq 6. Correlations of this kind are useful for determining the ranges of superficial velocities that will provide good mass-transfer efficiency and also for estimating the diameter of the sieve tray extraction column. Good agreement was obtained when the correlations were used to calculate the diameter for the three cases reported in the literature. Acknowledgment Financial assistance for this work was provided by COSNET (Mexico), for project P-730-87, and is gratefully appreciated. We also appreciate the contribution from The University of Texas at Austin.
Nomenclature A, = fractional free area, ( N o ~ d $ / 4 ) / A c o l A = cross-sectional area, m2 B, = ratio Adown/Acol C = continuous phase mass rate, kg/s d = diameter, m D = dispersed phase mass rate, kg/s g = acceleration of gravity, m/s2 G = vapor mass rate, kg/s Ht= plate spacing, m L = liquid mass rate, kg/s Ldown = downcomer length, m N o = orifice number Q = volumetric flow rate, m3/s U = superficial velocity m/s Greek Letters p
= viscosity, kg/(m.s)
h = gradient p = u =
density, kg/m3 interfacial tension, kg/s2
Subscripts
c = continuous phase col = column d = dispersed phase
down = downcomer f = flooding n = net area o = orifice or perforation t = total Superscript
’ = dimensionless Literature Cited Dawodu, F. A.; Mumford, C. J.; Jeffreys, G. V. Hydrodynamics and drop size distributions in a pilot scale sieve plate extraction column. Inst. Chem. Eng., Symp. Ser. 1984,88, 153. Fair, J. R. How to predict sieve tray entrainment and flooding. Pet. Chem. Eng. 1961,33, 211. Hirschmann, K.; Blass, E. Suitability of unpulsed sieve tray columns for liquid-liquid extraction of systems with low interfacial tension. Ger. Chem. Eng. 1984, 7, 280. Holden, S. 0. The effect of hydrodynamic variables in a sieve plate liquid-liquid extraction column. Unpublished report, The University of Texas at Austin, Aug 1984. Humphrey, J. L.; Rocha, J. A.; Fair, J. R. The essentials of extraction. Chem. Eng. (N.Y.) 1984, 91, 76. Laddha, G. S.; Degaleesan, T. E. Transport Phenomena in Liquid Extraction; Tata-McGraw-Hill: New Delhi, India, 1978. Mewes, D.; Pilhofer, T. Prediction of fluid dynamic properties of unpulsed sieve plate extraction columns. Ger. Chem. Eng. 1979, 2, 69. Oloidi, J. 0.; Mumford, C. J. The hydrodynamics of a pilot scale sieve plate extraction column. Paper present a t a Research Meeting, Society of Chemical Industry Extraction and Ion Exchange Group, University of Aston, May 8, 1985. Oloidi, J. 0.;Jeffreys, G. V.; Mumford, C. J. Correlation of design parameters for the sieve plate extraction column. Paper presented at International Solvent Extraction Conference, Munich, 1986. Rocha, J. A.; Fair, J. R. Design Manual for Sieve Tray Extraction Columns, Version 11. Separation Research Program, The University of Texas a t Austin, 1986. Rocha, J. A.; Seibert, F. S. Experiments realized at the Separation Research Program, The University of Texas at Austin, Summer 1987. Rocha, J. A.; Fair, J. R.; Humphrey, J. L. Design Manual for Sieve Tray Extraction Columns. Separation Research Program, The University of Texas a t Austin, 1985. Rocha, J. A.; Humphrey, J. L.; Fair, J. R. Mass transfer efficiency of sieve tray extractors. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 862. Rosales, P. J. Determination experimental de velocidades de inundacion en columnas de platos perforados en extraccion liquido-liquido. M.S. Thesis, Instituto Tecnologico de Celaya, Mexico, 1987. Treybal, R. E. Mass Transfer Operations, 3rd ed.; McGraw-Hill: New York, 1980. Woodle, R. A. The distillation-extraction analogy. Ind. Eng. Chem. 1963, 3, 17.
Received for review July 21, 1988 Revised manuscript received July 10, 1989 Accepted August 31,1989
