I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1078
ACKNOWLEDGMENT
Successive integrations by part show that /Tn-1
The major portion of this paper wa8 prepared while the senior author enjoyed a summer research fellowship from the Graduate School of the University of Minnesota. The authors are also grateful to the Graduate School for funds made available for the computational portion of the paper. The calculations were performed by William G. Smith.
exp ( - 7 T ) d T =
0
I
(1
+ yt + yt2 3f
. .. .. . .
Vol. 42, No. 6
I)-+
(27)
LITERATURE CITED
Amundson, N. R., Trans. Am. Iml. Chem. Engrs., 42,939 (1946). (2) Berg, C., and James, I. J., Chem. Eng. Progress, 44, 307 (1948). (3) Boole, G., “Calculus of Finite Differences,”reprint, New York, Stechert & Co., 1931. (4) Brown, G. G., and Souders, M., Oil Cas J , , 31, No. 5, 34 (1932). (6) Churchill, R. V., “Modern Operational Mathematics in Engineering,” New York, McGraw-Hill Book Co., 1944. (6) Eldridge, J . W., Ph.D. thesis, Univ. Minnesota (1949). (7) Federal Works Agency, W.P.A., “Tables of Exponential Functions,” Washington, D.C., Natl. Bur. Standards, 1939. (8) Ibid., “Tables of Sines and Cosines,” 1940. (9) Kirillov, N. I., J . AppliedChem. (U.S.S.R.), 13, 978 (1940). (IO) Kremser, A., Natl. Pdroleum News, 22, No. 2 1 (1930). (11) MacMullin, R. B., and Weber, M., Trans. Am. Inst. Chem. (1)
and hence
-
+;
.....
+-)I -
Engrs., 31, 409 (1935).
Marshall, W. R., and Pigford, R. L., “Applications of Differential Equations to Chemical Engineering Problems,” Newark, Del., Univ. Delaware Press, 1947. (13) Maaon, D. R., Ph.D. thesis, Univ. Minnesota (1949). (14) Murdock, P. G., Chem. Eng. Progress, 44, 856 (1948). (15) Sherwood, T. IC., “Absorption and Extraction,” New York, McGraw-Hill Book Co., 1937. 116) Smoker. E. H.. Trans. Am. Inst. Chem. Enors.. 34.. 165 (1938). . , (17j Tiller, F. M., C h m . Eng. Progress, 44, 299 i1948). (12)
+ Wa! + ha!‘
6 where y = H
From this the steady state solution reduces to
=c---
(1
(K
1
+
Taln
- 8 ) 1 - (1 + ff
(1
(18) (19)
Ibid., 45, 391 (1949). Tiller, F. M., and Tour, P. S., Trans. Am. Inst. Chem. Enpa.,
(20) (21)
Underwood, A. J. V., Chem. Eng. Progress, 44, 603 (1948). Widder, D. V., “LaPlace Transform,” Princeton, N. J., Princeton Univ. Press, 1941.
CY)^+'
40, 319 (1944).
+ re)*
where r is the solvent ratio w/b. No example will be worked using these formulas.
REC~IPED January 8, 1960.
Temperature Studies in Packed liquid-liquid Extraction Tower VICTOR S. MORELLO‘
AND
ROBERT E. BECKMANN
CARNEGIE INSTITUTE OF TECHNOLOGY, PITTSBURGH 13, PA,
D a t a are presented on t h e results of an investigation of
t h e effect of temperature on mass transfer in a lS/e-inch inside diameter packed, countercurrent, liquid-liquid ex-
traction column. The column was packed w i t h 53 inches of 4-mm. glass beads, Ratesof extraction of diethylamine from water, by toluene, were experimentally determined a t 26.8’, 38.5”, 48.5”, and 57.5’ C. w i t h t h e toltiene phase being the dispersed phase for all runs. The over-all film transfer units were resolved i n t o the individual film values. It was determined t h a t the (Ht)value of the water film was approximately zero and t h a t t h e (Ht)value of t h e toluene film decreased f r o m 1.73 f e e t a t 26.8’ C. t o 0.79 foot a t 57.5’C. in accordance w i t h the relation (H,)T = 1.81
- 1.489 X 10-W3
where t is the temperature In C. It has been further demonstrated t h a t fine packing, which Is wetted solely 1
Present address, Dow Chemioal Company, Midland, Mich.
by the continuous phase, is very efficient in liquid-liquid extraction because fine packing presumably flxes t h e size distribution of the droplets, prevents coalescence, and thus malntains a larger interfacial area of contact between the two phases. It reasonably constant interfaclal area is maintained under a l l flow conditions and temperatures, then t h e effect of t h e physical properties of the toluene fllm is represented by the equation
= 1.97
- 0.91
x 10-q~~~~)9.7*
where &oh i s the Schmidt number ( p / p D ) .
R
ELATIVELY few fundamental studies of mass transfer rates in continuous countercurrent liquid-liquid extraction columns have been reported in the past, although interest in such studies has steadily increased in recent years. The effect of temperature on the mass transfer rates in liquid-liquid extraction columns is a problem about which information is almost totally lacking in the literature. In addition to the theoretical interest
1079
INDUSTRIAL A N D ENGINEERING CHEMISTRY
lune 1950
They operated their tower at two temperatures, 18' and 38" C., and correlated all results by the equation:
In Equation 2' the Schmidt number does not appear. Only the 38" C. run of the earlier work checked theae results. In 1943 Brinsmade and Bliss (I) reported on the extraction of
acetic acid from methyl isobutyl ketone with water in a wettedwall tower at two temperatures, 77" F. (25' C.) and 112' F. (45' C.), They separated the over-all fdm resistance into individual film resistances as follows: For core fluid (ketone):
For wall fluid (water):
(4)'2'' P P
E Figure 1.
Schematic Flow Diagram of Equipment Used in Liquid-Llquid Extraction Study
----
A = Feed storage tanks B Toluene phase feed pump C Toluene phase construction head tank D Water phase pump E = Water phase construotlcn head tank F = Flow sight glasaes G Filters H, I = Flow control valves J = Glass extraotion tower K = Interface level control L = Coolers M = Product receiving tanks N Extraotlon column heating jacket 0 El.atrIca1 preheaterr P Atmospheric vents R, 5, T Sample drawoff taps
of how the temperature affects the variables in extraction column performance, there may be an economic advantage in extracting at elevated temperatures because of a more favorable distribution coefficient as well as improved mws tranafer. The resultant decreme in the quantity of extract solution needed brings about a heat economy sufficient to more than offset the increased heat necessary to operate at the higher temperature level. There have been few investigations of the fundamentals of continuous liquid-liquid extraction a t different temperature levels reported in the literature. In 1935, Fallah, Hunter, and Nash (8) reported on a study of the extraction of phenol from kerosene by water in a wetted-wall tower a t two temperatures10' and 38' C. The m&8s transfer coefficient of the kerosene core was shown to be a function of the flow rates, the diffusivity, and the Schmidt number ( p / p D ) . A correlation of the results at tho two temperatures gave the relationship:
In this investigation the water rate was held constant, and it was assumed that changes in the rate of flow of the kerosene core throughout each series of runs had no effect on the water-phase resistance. The kerosene core was shown to be in turbulent flow. Strang, Hunter, and Nash (81) continued a study of this proMem. They investigated the poeaibility that the individual film redstances in one liquid phase might be affected by the flow of the second liquid phase and that the rate of mass transfer through the laminar film of core liquid might therefore be governed to some extent by the rate of flow of the wall liquid.
3
0.00135 (Re),
(3,)"'" (4)
where the Reynolds numbers (Re) are evaluated separately for each fluid stream. No other fundamental liquid-liquid extraction studies at varying temperatures are known to the authors. Particularly lacking are data on commercial-type towers such as packed columns. The difficulty here is that the interfacial area of contact is a function of the size, shape, and nature of the surface of the packing, and affects the mass transfer coefficients as well as the physical properties of the liquid phases. However, recent work with fine packing (10, 95') indicates that fine packing can be used to control the drop size distribution and maintain a constant interfacial area between the two phases. In c o m e packings, on the other hand, the droplets of the dispersed phaae can coalesce in the void spaces and thus reduce the interfacial area of-contact. Thus, if fine packinga can fix the drop size distribution, at least in a limited range of temperatures, the column performance can be evaluated in terms of the flow r a t a and physical properties of the fluids which are readily measurable. In the present study the extraction column waa packed with 4mm. glass beads. Rates of extraction were experimentally determined at four temperature levels, 26.8', 38.5 O, 48.5", and 57.5' C., with the system toluene-diethylaminewater, where the toluene phase was dispersed. This system waa chosen because it Was easy to analyze and the distribution relationships were nearly ideal in the low concentration region studied. EQUIPMENT AND PROCEDURE
Extraction Ap aratus. The e uipment used is shown schematically in &gure 1. I t consistel of an extraction tower and the necemary accessories for maintaining a steady flow of the two phases. The tower ww a glass tube la/$ inches inside diameter and 60 inches long, packed with 53 inches of bmm. soft glass beads, which were dumped wet to ensure the densest arrange ment of random packing. The continuous phase was introduced a t the to of the column throqgh a &mm. glam tube. The dispersed pl?ase waa introduced a t a oint immediately above the y k i n g support t h r o u p a Zmm. dktribution tube. The interace between the two p ases was maintained about 0.5 inch above the packing by means of the inverted U-tube level controller shown. A &inch disengaging space a t the two ends of the column was used to separate the two phases. The extraction column was enclosed with a %inch diameter glass jacket through which water circulated a t a controlled temerature. The two solvent phases were heated by electrical coil eaters to the desired tem erature level before the entered the two ends of the column. &ow rates were regulatedrby means of needle control valves. The two flows were measured volumetrically after they had passed through the column. Concentration changes and mutual solubility were sufficiently low to use exit flow rates as a measure of inlet flow rates.
E
Chemicals. The chemic& used were nitration grade toluene, distilled water, and commercial 98% diethylamine. Initial con-
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1080
Vol. 42, No. 6
Table I. 26.8" C. Experimental Runs Toluene Run No. 15 16 17 18 19 20 21 22 23 24 25 27 31 33 35 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 59 60 61 63 64
Run No. 15 16 17 18 19 20 21 22 23 24 25 27 31 33 35 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 59 60 61 63 64
Inlet, CTa
--
Water Exit,
Inlet,
CTi
CWI
crv CT
Column Temp., Exit,
0
c.
cwa
Top
Bottom
Top
Bottom
0.00954 0.01113 0.01091 0.00676 0.00579 0.00761 0.00818 0,00784 0.01000 0.01034 0.00898 0.00545 0.00420 0,00784 0.00886 0.00898 0.00920 0.00886 0.00818 0,00795
26.5 25.5 25.5 28.5 28.5 28.5 28 29 28.5 28.6 29 25.5 25.5 25.5 25.5 25.5 26 26 27 27.5
24.3 24.3 24.3 27.3 27.3 27.8 27.8 27.8 27.8 27.8
1.446 1.446 1.446 1.278 1.278 1.281 1.254 1.254 1.281 1.281
1.569 1,548 1.552 1.423 1.437 1.383 1.371 1.377 1.348 1.345
27.8 25.3 25.3 24.8 24.8 24.8 25.3 25.3 26.8 27.3
0,00977 0.01125 0.01023 0.00816 0.00489 0.01858 0.01341 0.01091 0,00988 0.00852 0,00739 0.01426 0.01415 0.01131 0,01329
28 26 26.5 26.5 27 28.5 28.5 28.5 28.5 28.5 28.2 28.2 28.2 25.3 26.5 27 27 27.6 27.8
27.8 25.3 25.8 25.8 26.3 27.3 27.3 27.3 27.3 27.3 27.3 27.3 27.3 25.1 26.8 26.8 27.3 27.7 27.7
1.257 1.436 1.436 1.436 1.436 1.436 1.408 1.408 1.350 1,324 1.295 1.410 1.381 1.381 1.348 1.270 1.270 1.270 1.270 1.270 1.284 1.284 1.284 1,449 1.382 1.346 1.346 1.321 1.311
1.363 1.562 1.583 1.561 1,543 1.541 1.505 1.510 1.430 1.404 1.355 1.482 1.466 1.490 1.513 1.340 1.343 1.367 1.380 1.396 1.414 1.337 1.338 1.493 1.373 1.366 1.337 1.312 1.310
A Cm
Concn.. Ib. moles/cu. ft.-0.00886 0,00898 0.00864 0,00676 0.00614 0.00852 0.00875 0.00886 0,00807 0.00909 0,00960 0.00781 0.00648 0.00932 0.00920 0.00898 0.00966 0 I00909 0,00966 0.00954
0 0
0
0 0 0 0 0 0 0 0 0,00023 0.00023 0.00023 0.00023 0,00023 0.00023 0,00023 0,00023 0.00023 0,00023 0.00017 0.00017 0.00017 0.00017 0.00011 0.00011 0.00011 0.00011 0.00011 0.00011 0.00011 0.00011 0.00011 o.Ooo11 0.00011 0.00011 o.Ooo11 0.0001 1
0.01045 0.00920 0.00988 0.00977 0.00602 0.01125 0.01148 0.01062 0,01057 0.01011 0,00977 0.01102 0,01079 0.00977 0.01006 0.01067 0.01102 0.01136 0.01079
Material Balance, yo Error -8.6 3.2 -8.7 4.4 -1.8 -10.1 9.5 -4.1 -13.5 -1.8 -2.1 -11.6 -15.3 -5.7 1.1 2.5 -0.4 -13.2 -4.1 -5.2 3.9 4.0 3.1 -3.4 -2.9 -9.8 4.4 -0.02 0.7 2.0 6.9 1.2 -2.8 2.3 -1.1 1.1 1.1
-0.7 -4.4
0.01386 0,01386 0.01386 0.01358 0.01358 0.01318 0.01318 0.01318 0.01318 0,01318 0.01273 0.01511 0.01511 0.01511 0.01511 0.01511 0.01471 0.01471 0.01471 0.01471 0.01471 0.01437 0.01466 0.01466 0.01500 0.01488 0.01488 0.01488 0.01488 0.01488 0.01488 0.01488 0.01488 0.01488 0.01449 0.01522 0.01522 0.01522 0.01522
0,01432 0.01426 0.01460 0.01432
KWA (Based on Amine Transfer) Average Toluene 0,465 0.490 0.313 0.563 0.507 0.733 0.744 0.798 0.762 0,872 0.435 0.727 1.275 0.911 1.281 1.062 0.986 0.723 0.922 0.922 0.903 0.478 0.458 1.468 1.243 0.499 0.767 1.189 1.581 1.657 1.760 0.214 0.144 0.296 0.424 0.289 0.308 0.340 0.203
0.391 0.528 0,233 0.587 0.499 0.634 0.827 0.756 0,467 0.834 0.419 0.653 1.124 0.853 1.298 1.093 0.981 0.578 0.877 0.866 0.952 0.518 0.483 1.408 1.215 0.465 0.9ofi 1.188 1.597 1.695 2,169 0,242 0.088 0.309 0.394 0.313 0,333 0.306 0.083
2.12, 2.97 2.70 2.03 1.68 2.84 2.67 3.06 8.35 6.53 1.69 1.69 2.75 2.31 3.93 3.50 3.06 2.90 2.62 2.73 3.03 2.88 1.93 3.67 3.15 7.43 6.48 6.05 6.03 5.03 4.86 5.97 5.91 1.33 6.80 6.39 4.96 8.91 7.97
dCV/dCT
(Ht)pV
(Based on Amine Transfer) Average Toluene 4.56 6.05 8.64 3.60 3.32 3.88 3.58 3.77 10.96 7.49 3.88 2.33 2.15 2.54 3.07 3.30 3.10 4.01 2.84 2.96 3.36 6.02 4.21 2.50 2.53 14.90 8.45 5.09 3.82 3.04 2.76 27.86 41.10 4.50 16.04 22.12 16.08 26.26 30.26
0.75 1.05 0.55 2.22 2.07 1.41 1.90 1.63 1.46 1.87 0.61 1.80 3.78 1.63 2.81 2.61 1.77 1.27 1.64 1.75 1.64 1.18 0.86 2.28 5.20 0.77 1.22 2.30 2.96 3.38 4.30 0.44 0.18 0.54 0.71 0.66 .O.52 0.40 0.17
5.43 5.62 11.61 3.46 3.37 4.48 3.22 3.98 17.88 7.83 4.03 2.59 2.44 2.71 3.03 3.20 3.12 5.02 2.98 3.15 3.18 5.55 2.61 3'99 2.59 15.98 7.15 5.09 3.78 2.97 2.24 24.70 66.91 4.30 17.25 20.40 14.90 29.16 96.26
TOP
Bottom
1.302 1.302 1.302 1.152 1,152 1.160 1.134 1.134 1.160 1.160 1.143 1.289 1.289 1.289 1.289 1.289 1.263 1.263 1.212 1.187 1.162 1.263 1.237 1.237 1.212 1.139 1.139 1.139 1,139 1,139 1.153 1.153 1.153 1.299 1.237 1.212 1.212 1.182 1.172
1.470 1.430 1.438 1.354 1.368 1.306 1.288 1.298 1.260 1.252 1.278 1.503 1.539 1.477 1.456 1.454 1.411 1.426 1.351 1.325 1.263 1.368 1.366 1.404 1.452 1.213 1.217 1.265 1,290 1,316 1.339 1,200 1.201 1.380 1.244 1.22 1,200 1.187 1.178
Arithmetic Average 1.386 1.366 1,370 1.253 1.260 1.233 1.206 1.211 1,210 1.206 1.211 1.396 1.414 1.383 1.373 1.371 1.337 1.345 1,282 1.256 1.213 1.316 1.303 1.321 1.332 1.176 1.178 1.202 1.215 1.278 1.246 1.177 1.177 1.340 1.241 1.217 1.206 1.185 1.175
Vw(dcw)
VT dCT A ~ . 3.93 3.86 6.75 1.14 1.03 2.48 1.68 2.23 6.94 4.21 3.34 1.31 1.03 1.96 1.92 1.84 2.31 3.06 2.04 1.95 2.25 3.21 2.92 2.12 0.81 11.42 6.26 3.16 2.47 1.91 1.41 15.88 38.41 3.30 11.90 11.81 11.60 26.07 53.92
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1950
1081
The Chilton and Colburn (8-4) term, ( H l ) o ~or, height of a transfer unit, has the same limitations stated and follows an equivalent relationship,
(H&w = V w / K w a
(7)
Individual film values are more useful and fundamental than over-a11 mass transfer coefficients but are difficult to determine experimentally except where the solute is reasonably dilute and ideal relationships are closely approximated. The simplified form of Colburn’s equation relating over-all to individual transfer units is usually used in practical extraction studies,
‘0
.OS .I .I6 2 .25 .3 .sb CONCN. OF AMINE IN TOLUENE LAYER
Figure 2.
and the corresponding equation based on the other phase, r)
(H&T = ( H J T -!- ( H i ) w v T / m v w
Equilibrium Phase Relations-TolueneDiethylamine-Water
centrations of diethylamine in the water phase were maintained constant in all runs at about 1.75 weight % to eliminate the effect of entering solute concentration (18, 13). Samples from the two phases were analyzed by titration with 0.035 N hydrochloric acid solutions, using bromocresol green aa the indicator. Both the water and the toluene phase samples were analyred directly for amine content after dilution with a large excess of distilled water. It was not necessary to render the toluene-phase sample homogeneous., A favorable equilibrium constant and the excess of dilution water used gave results as good as those obtained by the usual practice of adding ethanol to keep the solution homogeneous. Equilibrium Distribution Data. The equilibrium dietribution
-
cw
ooe5cient, H for mixtures of water and toluene containing up to 4 weight % of diethylamine was determined at various isotherms, and the data were cross plotted for smoothness and consistency. Figure 2 shows a plot of CW?the concentration of diethylamine in the water phase, against CT, the concentration of the amine in the toluene phase, at even temperature intervals.
- -information ( (29 Figure 3 shows a plot of H
Figure 2 was used to obtain the slope m =
where rn is the slope of the equilibrium curve,
(9)
dC w dCr
-.
These two equations provide an interesting method for correlating extraction data under widely varying conditions of flow. Thus, if ( H l ) , w - i s plotted against m V w / V T , a straight line is obtained as a first approximation, the intercept of which on the (H&w axis represents the individual film unit (Ht)w and the slope of the line represents HI)^. However, in practice the interceptzlnd slope are only generally indicative of the film values. In order for them to be true values, these conditions must be met: is, m = dCw - = Cw dCT CT this condition is generally true in dilqte solutions 2. The operatin line is straight; another way to express this condition is that t8e volumetric rate of each solvent phase is constant throughout the column 3. The individual film transfer units are constant and do not vary with flow rates, column packing, and solute and solvent concentrations in the column 1. The equilibrium line is straight-that
The first two conditions are easily met by proper choice of system and concentration. The validity of the third condition must be tested experimentally.
needed in subsequent calculations. against CW. The extraction column was 53 inches long so that equilibrium conditions were approached, particularly a t the higher temperatures; consequently, it was necessary that the equilibrium data be very accurate. CALCULATION OF MASS TRANSFER
The experimental mass transfer results were calculated in terms of the two over-all mass transfer units, K w a and ( H J 0 w , both baaed on the water phase. Mass transfer coefficients ( K w a ’ s ) were related to the rate of mass transfer by the approximate form of Elgin and Browning (7). They showed that where the system does not depart widely from the simple distribution law and where the volume changes, amount extracted, and concentrations involved are not large, the rate of mass transfer for extraction may be written simply:
. ACiog mean =
-
-
(C*WI Cwi) (C*wa In (C*Wl CWl) (C*W, - CWl)
CONCENTRATION OF AMINE IN
- Cwa
Figure 3.
(6)
o
we
I
I
.IO
.eo I
WATER LAYER-%
I
ao I
I
I
.40
-(OM-MOIESILITER)
Equilibrium Phase Relations-TolueneDiethylamine-Water Distribution coefflolent
(H
-
CW/CT)
I 1
INDUSTRIAL AND ENGINEERING CHEMISTRY
1082
Vol. 42, No. 6
Table II. 38.5" C. Experimental Runs Toluene Run No.
Inlet, CT2
66
Run
No. 66
67 68 69 70 72 75 76 77 78 79 80 81 82 83 84 86 90 91 92 94 96 97 98 99 100 101 102 103 104 105 106 107 108 109
Inlet,
c I1
CTI
Conon., Ib. moles/cu. ft.
7
67 68 69 70 72 75 76 77 78 79 80 81 82 83 84 86 90 91 92 94 96 97 98 99 100 101 102 103 104 105 106 107 108 109
Water Exit,
0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021 o.wo21 0.00021 0.00026 0.00026 0.00026 0.00026 0.00026 0 00026 0.00026 O.OOO26
O":K% 0.00026 0.00026
Material Balance, % ' Error
6.1 3.6 0.5 -1.4 -0.3 -8.7 0.7 -11.5 1.2 -12.9 14.6 8.5 16.7 -6.5 3.7 7.8 5.9 -1.1 -2.2 -2.8 -3.1 -9.6 -1.1 -5.9 2.9 6.3 -0.6 -0.3 1.1 0.5 1.1 1 .o -1.1 -0.2 0.01
0.01878 0.01747 0,01469 0.01627 0.01679 0.01327 0.00808 0.00630 0.00666
0.00614 0.01160 0.01133 0.01044 0.01202 0.01207 0.01 165 0.00913 0.01627 0.01690 0.01653 0.01527 0.01007 0.01585 0.01527 0.01585 0.01753 0.01857 0.01742 0.01821 0.01878 0.01873 0.01847 0.01884 0.01862 0 .OM68
0.01480 0.01480 0.01485 0.01485 0.01485 0.01485 0.01459 0.01459 0.01459 0.01459 0.01459 0.01459 0.01459 0.01459 0,01459 0.01459 0.01459 0.01464 0.01464 0.01464 0.01448 0.01448 0.01448 0.01417 0.01417 0.01627 0,01627 0.01627 0.01627 0.01627 0.01627 0.01627 0.01627 0.01627 0.01627
--
Bottom
Top
0.01443 0,01123 0.01459 0,01202 0.01254 0.00352 0.00147 0.00100 0.00089 0.00089 0,00226 0.00199 0.00178 0.00262 0.00278 0,00231 0.00152 0.01181 0.01223 0.01223 0.01333 0.00289 0.01327 0.01091 0.01217 0.01375 0.01438 0.01516 0.01532 0.01517 0.01511 0.01537 0.01516
43 42.5 37.7 39.5 40.5 39.3 39.2 38 38.7 38.9 39.5 39.5 39.5 39.5 39.5 39.5 39 39.8 41.2 40.7 40.5 35.5 40.5 37.7 39.2 38.7 39.7 37.2 39.5 40.1 40,s 38.5 40.5 40 40.5
37 36.5 37.7 37 37 36 39 38.5 38.5 38.5 38 37 37 38 38 38 38 37 37 37 35.5 36 37.5 38 38 37 37 36.5 38 38 38 38 38 38 38
0.739 0,751 0,884 0.830 0.804 0.835 0.839 0.875 0.855 0.848 0.830 0.830 0.830 0.830 0.830 0.830 0.845 0.821 0.783 0.797 0.803 0.964 0.804 0.886 0.839 0 1852 0.822 0.897 0.828 0.811 0 809 0 858 0.802 0.814 0.802
::Ei
I
0.206 0.440 0,0655 0.425 0.368 1.149 3.008 2.150 2.284 1.811 3.397 3.331 3.117 3.124 2.872 3.022 1.947 1.096 0.750 0.631 0.0441 4.964 0.320 1.286 0.850 0.893 0.476 0.644 0.546 0.611 0.632 0.783 0.501 0.343 0.368
I
(HI)OW
EXPERIMENTAL RESULTS
The experimental data taken in this investigation and calculated in accordance with Equations 5 through 9 are shown in Tables I to IV. Each table lists the experimental results for B particular temperature study ~bsfollows: Table I, 26.8' C. (ambient room temperatures); Table 11, 38.5' C.; Table 111, 48.5' C.; and Table IV, 57.5" C. The h a 1 calculated Ht and m k values only are rounded off.
I
VT These temperatures are the arithmetic averages of the temperatures maintained during each series of runs. Average and
11.98 5.35 82.10 8.12 9.68 1.55 1.20 1.26 1.06 1.25 1.00 1.01 0.95 1.36 1.24 1 .09 1.06 7.74 10.44 11.06 37.97 1.67 23.56 5.67 7.76 6.57 12.15 19.00 21.57 19.40 17.66 17.26 25.59 41.16 36.67
Bottoiii
ACm
0.910 0.939 0.836 0.917 0.915 1.044 0.961 0.992 0.994 0 994 0,985 1.031 1.035 0.978 0,974 0,984 0,999 0.017 0.915 0 915 0.968 1.056 0.895 0.886 0.881 0.911 0,909 0.925 0.873 0.874 0.874 0.878 0.874 0 873 0 873
0,004864
0,004964 0.006129 0.004825 0.004968 0.003526 0,003597 0 003397 0,003330 0.003320 0,003294 0.003181 0,003275 0.003399 0.003479 0.003313 0.003358 0.004691 0,004956 0.005020 0.006133 0.003615 0.005625 0.003093 0.004230 0.005263 0.004963 0,004537 0.005473 0.005197 0.005307 0.004105 0.005387 0.005554 0.005673
0.24 0.56
0.12 0.56 0.49 1.37 6.07 5.30 5.20 1.48 4.34 4.21 4.41 3.97 3.72 3.87 3.24 1.41 0.98 0.86 0.08 8.03 0.51 1.17 1.02 1.20 0.57 0.75 0.74 0.76 0.80 0.78 0.64 0.46 0.50
2.47 2.35 5.38 3.45 3.56 1.78 3.62 2.72 2.42 2.26 3.41 3.38 2.95 4.26 3.57 3.29 2.07 8.49 7.83 6.97 1.68 7.78 7.55 7.29 6.60
6.87 5.73 12.24 11.77 11.86 11.16 13.51 12.83 14.12 13.51
dCW/dCT
(Based on Amine Transfer) Average Toluene
15.99 5.72 91.48 7.81 9.59 1.46 1.21 1.18 1.07 1.15 1.08 1.06 1.03 1.31 1.27 1.14 1.10 7.52 9.71 10.04 29.00 1.47 21.97 4.83 8.49 7.67 11.87 18.56 23.41 20.09 18.89 18.67 23.32 40.02 36.70
(Hr.)(S& Ft.) Toluene, Water, VT VW
H = -CT
Top
(Based on Amine Transfer) Average Toluene
0.155 0.412 0 0588 0.442 0.371 1.224 2,996 2.306 2.269 1.961 3.144 3.180 2.864 3.260 2,809 2.891 1.886 1.128 0.807 0.695 0.0578 6.307 0.344 1.511 0.777 0,765 0.487 0.659 0.503 0.590 0.591 0.724 0.550 0.363 0.368
c.
cws
K wa
Flow Rate Cu. Ft./
CiT
Column Temp., Exit,
Top
0.739 0.748 0.849 0,809 0.787 0,813 0.815 0.842 0.827 0,822 0,809 0,809 0,809 0I809 0.809 0.809 0.820 0.802 0.773 0.783 0,787 0.914 0.787 0.849 0.815 0.827 0.804 0.862 0.809 0.795 0.793 0.832 0,787 0.797 0.787
Bottom
0.873 0,882 0.849 0.868 0.868 0.980 0 929 0.962 0.965 0.965 0,939 0.985 0.993 0.928 0.923 0.936 0.961 0.868 0.868 0.868 0.914 1 ,000 0.857 0.843 0.842 0.868 0.868 0 882 0.842 0,842 0.842 0.842 0.842 0.842 0.842 I
Arithmetio Average
0.806 0.815 0.849 0.839 0 I828 0,897 0.872 0.852 0.896 0,894 0.874 0.897 0.901 0.869 0.866 0.873 0.891 0.835 0.821 0.826 0.851 0.957 0,822 0.846 0,829 0.848 0.836
0,872 0.826 0.819 0.818 0.837 0.827 0.832 0.827
8.37 3.43 37.29 5.13 6.06 1.17 0.62 0.44 0.42 0.45 0.69 0.72 0.60 0.93 0.83 0.74 0.57 5.01 6.53 6.72 17.95 0.93 12.19 5.27 5.37 4.14 8.49 14.16 13.23 12.82 11.38 14.51 16.52 24.49 22.29
maximum deviations from stated temperature levels are giveti in Table V. The experimental results for each of the four temperatures were plotted a t ( H I ) ~against R mBw/VT in accordance with Equation 8 and are shown in Figure 4. Marked deviations from a straightline relationship occur a t the lower end of the curve for those points which represent high toluene rates of flow-that is, low flow ratios, These deviations are best shown by plotting
5 VT'
the over-all transfer unit based on the toluene phase against mVw/VT in accordance with the related Colburn equation (9).
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1950
Table 111. Inlet,
NO.
CT8
111 113 115 110 117 118 119 120 121 122 123 125 120 127 128 129 130 131 132 133 134 135 130 137 138 139 140 141 142 143 144 145 140 147 148
0.00010 0.00016 0.00010 0.00010 0.00010 0.00016 0.00010 0.00010 0.00010 0.00010 0.00016 0.00016 0.00016 0.00016 0.00010 0.00010 0.00010 0.00010 0.00010 0.00019 0.00019 0.00019 0.00019 0.00019 0.00018 o.Ooo19 o.ooo19 o.Ooo19 0.00019 0.00019 0.00019 0.00019 0.00019 0:00019 0.00019
Run
No.
111 113 115 110 117 118 119 120 121 122 123 125 120 127 128 129 130 131 132 133 134 135 130 137 138 139 140 141 142 143 144 145 146 147 148
Material Balanoa
% Errd -0.7 -2.4 11.9 -14.7 -1.9 5.7 18.5 1.3 8.9 14.1 -18.5 -1.4 0.5 2.5 3.2 -1.2 1.2 0.7 -1.5 7.0 -1.9 4.5 0.6 -1.3 -0.4 -0.5 1.3 -1.9 -0.4
-1.8
-0.3 -0.8 -2.0 -1.9 -2.1
Water Inlet, Exit, CTi CWl CW, Conon., Ib. moles/cu. ft. 0.00137 0.01400 0.01496 0.01480 0.00048 0.00740 0.00248 0.01850 0.01480 0.0081 1 0.02357 0.01480 0.01258 0.02426 0.01480 0.003 17 0.01780 0.01480 0.00190 0.01049 0.01480 0.00317 0.01480 0.01913 0,00349 0.02146 0.01480 0.00127 0.01480 0.01007 0.00227 0.01459 0.01754 0.01110 0.02293 0.01459 0.01002 0.01459 0.02404 0.01131 0.01459 0.02521 0.01469 0.01110 0.02410 0.01189 0.01490 0.02410 0.01490 0.01 152 0.02595 0.01490 0.01131 0,02558 0.01490 0.01099 0,02537 0.00470 0.01480 0.01970 0.00433 0.01480 0,02029 0.02241 0.01480 0.00087 0.01480 0.00814 0,02325 0.01480 0.01007 0.02367 0.02441 0.01480 0.01089 0.01099 0.02441 0.01480 0.02399 0,01205 0.01194 0.02420 0.01480 0.02464 0.01187 0.01480 0.01300 0.02409 0.01311 0,02404 0.01480 0.01322 0.02438 0.01480 0.01480 0.01317 0.02407 0.01367 0,02385 0.01480 0,01379 0.02302 0.01480
48.5" C. Experimental Runs Column Temp.,
Toluene Run
Exit,
:%%
Kwo
@wed on Amine Transfer) Average Toluene 3.140 3.018 3.981 3.933 3.401 3.028 1.293 1.042 0.373 0.348 4,498 4.057 4.599 5.040 0.248 0.301 8.071 8.517 5.726 6.143 2.080 2.349 1.141 1,100 1.143 1,153 1.148 1.180 1.009 1.072 2.535 2.459 2.874 2.946 2.950 2. $92 2,704 2.682 6.405 0.808 5.347 6.274 5.353 5.569 4.521 4.547 4.236 4.132 3.073 3.048 3.081 3.010 2.380 2.408 2.508 2.370 2.320 2,340 1.275 1.173 1.359 1.340 1.150 1.103 1,364 1.182 1.000 0.857 0.807 0.707
1083
0
c.
CW H * G
Top
Bottom
Top
Bottom'
ACm
47 49 45 53 51 48 49 48 48.5 48.5 40 49 51 51.5 50.6 49.5 51.5 51 51 49 50.5 50 50 49 51 50 50.5 50 51 51 50.5 50.5 49.6 49.6 49.5
40 40 40 47 47 47 47 47.5 47.5 47.5 46 47 47 47 47 47 47.5 47.5 47.5 47 47 47 47 47.6 47.6 47.6 47.5 47.5 47.5 47.5 47.5 47.5 47.6 47.6 47.5
0.049 0,609 0.690 0.535 0.571 0.028 0.009 0.628 0.618 0.018 0.674 0.009 0.571 0.562 0.581 0.598 0.501 0,571 0.571 0.009 0.580 0.589 0.589 0.009 0.571 0.589 0.580 0.589 0,571 0,571 0.580 0.580 0.599 0.599 0.599
0.723 0.705 0.742 0.658 0.652 0.681 0.098 0.071 0.608 0.097 0.719 0.054 0.654 0.653 0.053 0.652 0.643 0.643 0.644 0.068 0.071 0.001 0.658 0.643 0 643 0.043 0.042 0.642 0.042 0.041 0.041 0.641 0.641 0.640 0.040
0.002983 0.002945 0.002190 0.004485 0,004468 0.003314 0.003074 0.002921 0.002399 0.003597 0.002447 0.003003 0.003853 0.003282 0,003547 0.003555 0.003166 0.003005
;:A:
1.09 0.99 4.70 4.20 4.09 4.21 5.37 4.03 3.04 3.74 1.51 1.53 1.91 2.30 3.35 4.40 4.33 0.07 5.96 0.04 11.07 10.22 12.10 10.98 18.12 22.15
The results are shown in Figure 5. The relation between the (H&w plots and the corresponding (H& plots, assuming that the individual Ht's are inddpendent, or nearly so, of the flow rattes, is that the slopes of the curves in Figure 4 become the intercepts of the curves in Figure 5 and, conversely, that the intercepts in Figure 4 become the slopes in Figure 5. Plotted in this manner, the points marked in solid color me seen to deviate to a marked degree from the straight-line behavior of most of the experimental points. During these runs a t B high toluene flow rate, it waa observed that the toluene droplets
Toluene 1.05 0.93 0.69 4.39 10.18 1.17 0.87 1 .09 0.82 1.02 1.13 4.86 4.22 3.98 3.90 5.54 3.93 3.59 3.85 1.43 1.55 1.84 2.28 3.44 4.50 4.43 5.86 8.28 0.11 12.03 10.30 ia.e.8 12.08 21.13 27.10
3.10 3.00 2.50 4.58 3.54 6.46 4.39 0.87 6.97 6.24 2.04 5.30 4.80 4.70 4.25 13.01 11.59 10.74 10.33 9.74 8.20 10.23 10.38 14.21 13.70 13.35 14.47 14.95 14.16 14.12 13.89 13.98 14.98 18.12 19.20
dC W / d CT
(H#)OW
(Based on Amine Transfer) Aversge 1.01 0.92 0.73 5.39 9.49 1.21 0.95
I
0.003212 0,003615 0.003584 0.003574 0.003483 0.003055 0.003916 0.003657 0.003909 0.003059 0.003902 0.004177 0.003852 0.004101 0.003578 0.004031 0.004272
2.80 7.07 1.92 0.88 0.28 3.85 4.20 4.28 4.13 9.28 1.40 0.77 0.82 0.08 0.70 1.01 1.00 1.50 1.51 5.55 4.15 3.90 3.03 2.37 2.18 2.05 1.70 1 ,130 1.60 0.88 0.93 0.84 0.78 0.05 0.57
0.015 0,575 0.079 0.522 0.546 0.593 0.575 0.593 0.584 0.684 0.643 0 ;575 0.546 0.540 0,653 0.500 0.540 0.540 0.546 0 .675 0.553 0.659 0.669 0.575 0.646 0,569 0.563 0.569 0.640 0.640 0.653 0 553 0.506 0.500 0.500 I
Bottoiri 0.715 0.750 0.691 0.628 0.015 0.056 0.075 0.645 0.644 0.079 0,090 0.019 0.020 0,019 0.619 0.018 0.808 0.008 0.609 0.044 0.640 0.633 0.028 0.010 0.609 0.009 0.007 0.607 0.807 0.600 0,005 0.005 0,005 0,005 0.005
Arithmetio Average 0.605 0.003 0.685 0.575 0.581 0.025 0.625 0.019 0.614 0.032 0.670 0.597 0.583 0.680 0.586 0.592 0.674 0.677 0.578 0.015 0.800 0.596 0.594 0.593 0.678 0.584 0.580 0.583 0.677 0.576 0.579 0.579 0,580 0,586 0.586
0.74 0.34 0.89 2.98 7.22 0.89 0.65 0.99 1.04 0.42 1.21 4.14 3.45 3.99 3.55 5.00 4.10 8.97 3.95 1.08 1.18 1.54 2.03 3.65 3.04 3.81 4.70 5.45 4.92 9.21 8.02 9.00 11.23 10.45 19.77
working their way upward through the packing would coalesce and form continuous rivulets on the walls of the column. This effect reduced the interfacial area between the two phases and hence increased the apparent Ht's of these runs. With the high toluene flow rate points removed from consideration as nonrepresentative of the deaired experimental conditions, it is possible to draw a remonably good straight line through the experimental data, which is parallel to the abscissa in the (Ht),,r plots of Figure 5 and which apparently paases through the origin in the (H&w plots of Figure 5.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1084
57b°C. Experimental Runs
Table IV. Toluene
NO.
Inlet, CTi
149 150 151 153 154 155 1p7 108 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174
0.00015 0 ,00015 0 .OOOlB 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00017 0.00017 0.00017 0.00017 0.00017 0.00017 0,00017 0.00017 0.00017 0.00017 0.00017 0.00017 0.00017 0.00017 0.00017
Run
~
Run
Exit, Inlet, CT I CWl Concn., Ib. moles/cu.--.tf 0.02441 0.01458 0,01458 0.02411 0,01639 0.01458 0.01458 0,02729 0.01531 0.01797 0.01531 0.02695 0.01531 0.02995 0.01531 0.03334 0.01531 0.03464 0.01514 0.02238 0.02560 0.01514 0.01514 0.03113 0.01514 0.03317 0.01514 0.03187 0.03209 0.01514 0.03402 0.01514 0.03187 0.01514 0.03306 0.01514 0.03345 0.01514 0.03503 0.01514 0.03458 0.01514 0.03181 0.01514 0,03232 0.01514 0.03317 0.01514
Material
~%
Error 13.2 7.0 27.2 -9.2 9.4 1.5
NO.
149 150 1.51 153 154 155 157 168
-8.4 0.8
2.2 11.5 -3.0 -10.1 -3.1 9.6 14.6 -0.9 3.0 0.3 -2.1
1B9
160 161 162 163 164 164 166 167 168 169 170 171 172 173 171
.0.4
0.1
-1.8 -0.9 -0.4
Water
Column Temp.,
c.
Exit, CR,
Top
Bottom
0.00240 0.00212 0.00110 0.00237 0.00090 0,00256 0.00503 0.01000 0.01062 0.00160 0.002 17 0.00664 0.00876 0.00678 0.00622 0.00978 0.01266 0.01243 0.01232 0.01204 0.01192 0.01317 0.01322 0.01317
55 57.5 56.6 58 54 56 57 58 59 55 56.5 57 58.5 57 58 59 56.5 58 58.5 60.5 59.5 56.5 57 58
57 57 56 57 57.5 57.5 57.5 57.5 57.5 57 57 57.5 57.5 57.5 57.5 57.5 57.5 57.5 57.5 57.5 57.5 57.5 57.5 57.5
Kwa
(Based on l ~ Amine~Transfer) ~ Average Toluene 4.019 4.316 6.432 6.188 3.673 4.149 9.795 9.223 6.823 7.150 7,345 7.410 5,062 4.724 4.701 4.753 4 899 5.069 6.865 7.283 5,966 5,860 4.066 3.663 4.919 5.111 9.752 9.030 6.482 7,200 4,572 4.515 3.922 3.617 2.876 2.853 2.220 2.364 2.175 2.155 2.665 2.706 2.554 2.760 2.694 2.601 2.379 2.459
0
Av. Temp., 0
c.
26.8 38.5 48.5 57.5
Max. Deyation, C. 2,6 4 5 4,5 3 5
A?=. Deviation,
c.
1.1 1.2 1.5 0.7
0.519 0.523 0.550 0.521 0.532 0.512 0.490 0.468 0.467 0.544 0.537 0.481 0.472 0.481 0,483 0.469 0.463 0.463 0.463 0.463 0.464 0.462 0.462 0.462
0.002397 0.002641 0.003047 0,002254 0.002619 0.002401 0 .or12521 0.002778 0.002104 0.002538 0.002514 0.002537 0,002594 0.002047 0.002386 0.002377 0.002266 0.002840 0.003004 0.003386 0.002619 0.0025 15 0.002571 0.002753
1.88 3.09 3.44 3.38 4.64 2.93 1.95 1.59 1.37 3.68 2.56 1.33 1.71 2.78 2.38 1.40 1.24 1.10 0.89 0.93 0.91 0.90 0.92 0.88
3.26 5.56 3.19 8.46 5.22 2.44 6.44 9.75 9.37 5.34 5.20 5.89 9.53 8.98 6.80 9.05 13.33 13.09 11.77 10.27 9.68 16,66 16.47 15.07
dCW/dCT
TOP 0.490 0.457 0,472 0.449 0.500 0.478 0.465 0.449 0.433 0.465 0.472 0.465 0.441 0.465 0.449 0.433 0.472 0.449 0.441 0.409 0.425 0.472 0.457 0.441
Bottom 0.495 0.499 0,530 0.496 0.525 0.478 0.464 0.451 0,451 0.520 0.499 0.507 0.488 0.451 0.451 0.451 0.451 0.451 0.451 0.451 0.451 0.451 0.451 0.451
.4rithmetic Average ' 0.493 0.478 0.501 0.473 0.513 0.478 0,464 0.450 0.442 0.493 0.486 0.486 0.465 0.458 0.450 0.442 0,462 0.450 0.446 0.430 0.438 0,462 0.454 0.446
dCw
E (=) vW
A".
0.85 9.8B 0.47 1.18 0.58 0.99 1.54 2.75 3.03 0.72 0.99 2.16 2.59 1.48 1.29 2.86 4.97 5.37 5.93 4.73 4.66 8.58 8.14 7.67
From the slopes and intercepts of the (Ht),w plots, the following individual film values were determined: Temp., O C.
(HI)w
26.8 38.5 48.5 57.5
0 0 0 0
W T From Figure 4 From Figure 5
1.73 1.55 1.27 0.79
1.45 1.55 1.18
0.80
The corresponding values taken from the ( H t ) o Tplots deviate slightly from those taken from the ( H t ) o wplots mainly because of differences in weighting of points by the least-squares method. A re-examination of the points in Figure 4 indicates a very slight curvature, concave upward, of the best line through the experimental data. This may be due to the effect of the flow rates on the individual film values. However, this condition is more likely due to the fact that the amine in the exit toluene at the high
Deviations from Temperature Levels
0.500 0.460 0.475 0,453 0.516 0.482 0.466 0.453 0.440 0.500 0.474 0.466 0.446 0.466 0.453 0.440 0.474 0.453 0.446 0.421 0.434 0.474 0.466 0.453
(HtlpW
(Based Transfer) ~ on Amlne , Average Toluene 0.81 0.75 0.90 0.87 0.87 0.77 0.92 0.86 0.73 0.76 0.82 0.82 1.27 1.36 2.07 2.05 1.91 La5 0.73 0.78 0.87 0.89 1.45 1.61 1.94 1.86 0.92 0.99 1.05 0.95 2.00 1.98 3 69 3.40 4.59 4.55 4.98 5.30 4.77 4.72 3.58 3.65 6.04 6.52 6.12 6.33 6.34 6.13
A least-squares straight line through these data with liability of error limited to the derived ordinate variable would give slightly positive and slightly negative intercepts in the ( H t ) @ lplots. ~ The ( H ~ ) " plots T likewise indicate that the corresponding intercepts on the (Ht),w plots should be small values or zero. However, an extremely large number of experimental points would have to be taken to justify statistically such an intercept. The precision of measurement is such that one can only say that the intercept is approximately zero. Accordingly, a least-squares straight line through the origin, with the ordinate value only liable to error, was fitted to the data. Runs 54,63,and 64 for the 26.8' C. plot are shown in the plot in Figure 5, though noein Figure 4, in order to keep the plot legible for the scale employed. The runs are included in the statistical weighting of the least-squares line through the esperimental points.
Table V.
Vol. 42, No. 6
v.flow ratios is so near to the equilibrium amine VT
concentration in the inlet water phase that the experimental error of measurement is greater than this difference In these experimental runs, the maximum flow rate ratios, were as
z,
high ss 45 to 1. At these high flow rate ratios, the dispersed phsse approaches its equilibrium concentration to such a close degree that the difference between the actual concentration
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1950
1085
Figure 4.
Experimental Runs
-
&;
-
Helghtd over-all transfer unlt (Ht)ow against Ci(VWvT) where m slo e L d %ulllbrlum v toluene o(urve, phase dCw/dCT and weter phaw flow rater, rwpeotlvely, cu. ft./(hr.) (sq.ft.)
and the equilibrium concentration is less than the precision of measurement of the amine concentration, Since the measured amine concentration in the dispersed phase must necessarily be less than the equilibrium value, the observed result will be an (EQowvalue slightly greater than the true value. A number of investigators, such as ROW,Koffolt, and Withrow ( 1 6 ) have reported deviations in the opposite direction at high
v_. flow ratios, particularly in spray towers. VT
hey explain this
behavior by the breakdown of dispersed phase droplets a t the
high flow rates, which results in a decrease in values. This condition, however, is less likely to occur in packed towers than in spray towers. The leastrsquares lines that were fitted to the experimental data in Figure 4 are shown combined in Figure 6. The effect of temperature in reducing the over-all film transfer units (or increming the ma88 transfer coefficients) is marked. Inasmuch as the effect of temperature changes on the (Ht)ow is relatively small at temperatures near 260 to 300 c,, it is apparent that at room temperature a variation of four or five degrees in the operating temperature will have little effect on the apparent (Ht)ow of operation. INDIVIDUAL FILM VALUES
It haa been stated previously that
4
67.6'C.
4
E'
I-3
s1 2
Ise
EXPERIMNTAL RUN5
s
D
dI
g, 0
0
1
J
1.2
IS
2.0
2.4
'0
A
A
Height of
12
1.6
2.0
2.4
V,/nV,
Vm"W
-
Figure 5. Experlmental Runs 0 normal polntq
over-all transfer unlt (H+T against v T / m V w ; polnta
?Y
-
ooalesoence
a necessary condition for the intercept and slope method to be a measure of the individual film values is that these values be constant under the ex per imen t a1 conditions followed. Other investigators have been unable to break down the over-all into the individual film coefficients because the rate of flow of one or both phases affected these individual film values. Colburn and Welsh ( 6 ) measured individual film values and concluded that the film-transfer unit of the discontinuous phase was practically independent of either flow rate and that of the continuous phase increased with increased flow of that phase and decreased with increased flow of the discontinuous phase. The Colburn equations, 8 and 9, were
1086
INDUSTRIAL AND ENGINEERING CHEMISTRY
60
8
c E 6
u.
I -84
i
w
2
'0
2
4
8
6
IO
12
14
16
absorption and liquid-liquid extraction is meant to be implied, even though the interfacial area of contact of the two phases is relatively constant in gas absorption and similarly, aa postulated further below, in the case of liquid-liquid extraction in a tower filled with fine packing. The effect of temperature on the physical properties of the gas and liquid films are too divergent and complex to permit any such close analogy to be drawn. The above reference to g a absorption is merely brought out further to emphasize the fact that in order to obtain a true picture of the temperature dependency of the individual film coefficients for such mam transfer operations aa gas absorption and liquidliquid extraction, it is necesmy to obtain experimental data a t numerous temperature levels. The experimental curve shown in Figure 7 can be fitted by the following empirical equation,
+'\t Flgure 6. Effect of Temperature on Over-All Transfer Unit (H&w
modified to include a power function of the flow rates which corrected the Ht value of the eontinuous phase. An attempt waa made to apply Colburn's power function equations to the experimental data. Different powers were used, but the film values remained relatively constant. For the toluene film value to be a power function of the flow rates it is necessary that the line fitting the experimental data according to Equation 8 be curved. Similar findings were reported by Hou and Franke (IO). One can conclude from the results of this investigation that the individual film transfer units in this case are affected but slightly by the flow rates, if at all, and that the slopes of the lines in Figures 4 represent the toluene film value, (Ht)*, very closely. A cross plot of ( H J T against temperature is shown in Figure 7. The effect of temperature on the individual film tranafer unit is progrwively more important as the temperature is increased. I n previous work (1, 8, 81) using wetted-wall towers, only two temperatures were employed. In such a case the effect of temperature must necessarily be assumed linear as a fist approximation. I n this investigation it is evident that the temperature effect on individual transfer units is not linear but concave downwards. In a related field, gas absorption in a packed tower, Sherwood and Holloway (19) varied the temperature from 5 O to 40" C. and showed that the individual liquid film coefRcient decreased with increasing temperature but with curvature concave upwards. No inference of a close analogy between gas
VoI. 42, No. 6
(HOT = 1.81
- 1.489 X
10dta.*
(10)
where t is the temperature in " C. The equation is, of course, valid only within the temperature limits 25" to 58' C. and only for the particular system and experimental equipment wed. VARIABLES
Previous work in solvent extraction (1, 6, 8, 8,9, 18, 80, 8f) hm shown that the main variables affecting mass transfer are functions of the physical properties (b,p, and D),the interfaoial area of contact, and the flow rates. In gaa absorption in packed columns the liqllid holdup is fairly constant up to the loading point, so that it is possible to determine the specific area of interphase contact from the liquid velocity. In liquid-liquid extraction in packed columns however the holdup is not constant but in general is a function of the dispersed phase flow rate. The nature of the system, the nature of the packing surface, and the void space all affect the holdup. If this discussion is restricted to the case where only the continuous phase wets the packing and the packing is finely divided, as is true in the present experiments, theoretically the effective area term, a, in the mass transfer coefficient, Ka,is relatively constant over a limited range of flows and temperatures. Several investigators (10,14,17,,%9) have shown that fine packing greatly improves the mass transfer rate, and they have observed that the size of the dispersed phase droplets was relatively constant under the experimental conditions studied. In fine packing the maximum size of the droplets probably is fixed by the size of the
t
zwx
0.6 Oa8*
100
140
180
220
260
300
SCHMIDT NUMBER
>/PO TEMPERATURE- *C.
Figure 7
Figure 8.
Effect of Physical Properties on Mass Transfer
INDUSTRIAL A N D ENGINEERING CHEMISTRY
June 1950
NOMENCLATURE
voids in the packing and coalescence thus is restricted. The present investigation also indicates that high efficiency may be realized from fine packing. It seems reasonable to assume, at least as a fist approximation, that the observed effects on mass transfer are on K in Ka, since a is reasonably constant. Of course, as the drops rise through the packing they are continually changing in size and shape as they make their way through the interstides in the packing. The relative shape of these extended drops may not be the same under all conditions but may average out to the wme effective area term, a, when the packing is sufficiently fine to control drop size distribution. If the assumption of constant effective interfacial area of contact is valid, a correlation of the observed data on ( H I ) Tcan be made on the basis of the effect of temperature on the physical properties ( p , p , and D) of the toluene phase. It has been shown here that flow rates have no measurable effect on H i s under the operating conditions employed. The Schmidt number, p / p D , is a dimensionless grouping of the p, p, and D properties and varies with temperature in liquids (1, 8 ) . Using experimentally determined values of the kinematic viscosity, p / p , and D, calculated by theory and analogy to similar compounds (11, 16, %), the average Schmidt numbers of the toluene phase for the experimental runs were calculated:
26.8 38.5 48.5 57.6
0.632 0.556 0.501 0.458
2.22 2.67 3.04 3.87
x x x
x
10"
interfacial area of contact per cu. ft. of tower, sq. ft./ cu. ft. solute concentration in main stream, Ib. moles/cu. ft. solute concentration in one hase which would be in equilibrium with observei concentration in other phase, Ib. moles/cu. ft. log mean concentration difference, Ib. inoles/cu. ft. tower diameter, ft. diffusion coefficient, qq. cm./sec. acceleration due to ravity, ft./(sec.)(sec.) mass flow rate, Ib.Ahr.)(sq. ft. of empty tower cross section) distribution coefficient, ratio of solute concentration in aqueous phase to that in nonaqueous phase at equilibrium height of a transfer unit, ft. height of an over-all transfer unit, ft. film mass transfer coefficient, lb. moles/(hr.) (sq. ft.) (Ib. moles/cu. ft.) over-all mass transfer Coefficient, lb. moles/(hr.)(cu. ft.)(lb. moleF/cu. ft.) slope of e uilibrium curve, dCw/dCT number ofyb. moles of solute transferred Reynolds num-ber Schmidt numker ( p / p D ) temperature, C . liquid flow rate, cu. ft./(hr.)(sq. ft. of tower cross section) effective volume of column, cu. ft. time, hr. absolute viscosity, cp. density,, g./cc. core fluid over-all toluene phase wall fluid water hase ends o r tower
286 208 166 136
10-6 10-5 10-
5 The kinematic viscosity of mixtures of diethylamine and toluene, saturated with water, may be represented by the following equation: y = (0.84006 - 0.0354331) t(0.008762 f 0.0001667.~
-
-
1087
++ o . r n 7 a z )
tqo.ooooas)re
where y kinematic viscosity, oentistokes; t = C.; and z = mole fraction of diethylainine in a toluene solution saturated with water. This equation is valid for the temperature range 20" to 65O C.and the ooncentration range of 0.0 to 0.40 mole fraction diethylamine.
LITERATURE CITED
Figure 8 shows the results of plotting the Schmidt number against the value of the corresponding individual toluene film transfer unit ( H t ) T . This curve may be represented by the following empirical equation within the limits of the experimental range of temperature: 0.91 x 106 (Ht)r 1.87 -(11) (Sch) *.'*
Brinsmade. D. S., and Bliss, H., Tvans. Am. Inst. Chem. Engrs., 39, 679-713 (1943); 40, 117-18 (1944).
Chilton, T. H., and Colburn, A.'P., IND.ENG.CHEW,27,255-60, 904 (1935).
Colburn, A. P., It$$., 33,459-67 (1941). Colburn, A. P., Trans. Am. Inst. Chem. Engrs.,
35, 211-36,
587 (1939).
-
Colburn, A. P., and Welsh, D. G., Ibid., 38, 179-202 (1942). Comings, E. W., and Briggs, S. W., Ibid., 38, 143-77 (1942). Elgin, J. C., and Browning, F. M., Ib
