I
DAVID A. ELLIS Western Division, Research Department, The Dow Chemical Co., Pittsburg, Calif.
Prediction of Multistage Solvent Extraction Operation from Limited Data Curves have been derived to predict recovery in a solvent extraction process from one or two experimental measurements
SOL~NT
extraction systems for the recovery or purification of materials are often operated in several countercurrent stages. In evaluating such systems, as it is not convenient to make a countercurrent study of each possible case, easily measured parameters that can be related to the performance are needed. T h e distribution isotherm and the distribution coefficient, k = j / x , are commonly used to define the behavior of solvents. If a constant value is obtained for k from tests over a wide range of concentrations, the distribution isotherm is linear and the relationship describing the recoveiv in a countercurrent system is relatively simple. Frequently, however, k is not constant, and the distribution isotherm is curved. This curvature may be due to various causes, but it often indicates that the extraction is due to a chemical reaction betiveen the extractant and the extracted substance. so that, as the material extracted increases. the amount of avail-
able extractant decreases. This is analogous to the conditions considered by Langmuir in the derivation of the equation for the absorption isotherm ( 5 ) . Here it was assumed that the curvature was due to the decrease in surface area available for adsorption as the surface because covered with adsorbed gas. When “available extractant concentration” is substituted for “available surface area,” this equation should describe solvent extraction systems limited by extractant availability. A number of solvent extraction systems have been shown experimentally to approximate this equation (7-3) and it is probably generally applicable to systems where the extraction is governed by a single chemical reaction. Some nonlinear distribution curves d o not follow this equation, however-curvature due to deviations from Henry’s law would not be included. T h e Langmuir derivation gives the following distribution equation:
::p;i k =
- Y/Ys.)
(1 1
Km
Figure 2. When number of stages is infinite, predicted recovery approaches that for linear distribution as K, and F decrease
of one extractant molecule for each charge on the extracted species. Thus, it is reasonable to assume y s equal to the molar concentration of extractant divided by the charge. An expression relating R, to a single analysis of one phase is obtained from the Langmuir equation, K = K,(1 - Y ) , and the mass conservation equation, Y = F ( l - X):
This equation may be rewritten in terms of reduced factors:
K = K,(1
Yc 2
I 32
0.6
2.4
9.8
13
L 2 ..
. .’.
~
2.5
0 3
1.3
Figure 1. Distribution curve can b e linearized by Langmuir plot A. B.
Typical curvilinear distribution Langmuir plot of same data as A
- Y)
(2)
T h e equation describes a straight line if K is plotted against Y and the intercept of this line with the K axis is the maxim u m value of the coefficient (Figure 1). Three experimental points should be sufficient to determine whether this relationship holds. Although the distribution coefficient varies over a wide range, the curve is described completely by the values of K , (the limiting extraction coefficient) and 1. (the saturation loading). Two experimental points will establish both values. or a single experimental point will be sufficient for determining K,,, if j Sis known. If ys is not known, and experimental data for only a single point are available, it can be approximated by use of a simple assumption concerning the extracted complex. In most cases, the extracted complex will consist
I t is desirable to be able to relate the extraction coefficients to the recovery attainable in a countercurrent system with a number of stages. iVhere the distribution isotherm is linear, the recovery is easily found fiom the follol\,ing formula due to Kremser ( 4 ) .
In the case of the Langmuir distribution, such a simple formula is not availablr. However, values of the recovery can be determined from the McCabe-Thiele diagram geometrically or calculated algebraically, since the distribution curve can be expressed as a n algebraic relation. This computation has bren made for ‘3 range of values of R, and F using Bendix G-15 computrr. VOL. 52, NO. 3
MARCH 1960
251
although they will serve as a n approximation for cases where the relative extraction of other substances is small. T h e p H and concentration of cations such as sulfate, chloride, or nitrate often have a pronounced effect on K , and y. ( 3 ) . I n continuous multistage operation these concentrations may vary from stage to stage. Thus, even though a Langmuir isotherm is obtained i n experiments where p H , sulfate concentration, etc., are held constant, the actual multistage behavior is often more complex than the simple case treated here.
R
Nomenclature
f
K
ratio or feed ratio = volume of phase x/volume of phasey = reduced feed ratio, F = fxo/yr = extraction coefficient, k = y / x = reduced extraction coefficient, K
k,
= Y/X = limiting extraction coefficient,
K,
=
n
=
R Y?
= = =
X
=
y ys
= x/xo = molar concentration in phasey = limiting molar concentration in
F k
Km
Figure 3. A. B. C.
These curves make possible prediction of recovery in solvent extraction
T h e limiting case, where the number of stages is infinite, is shown in Figure 2. As K , and F decrease, the recovery predicted for the Langmuir distribution approaches that for the linear distribution (Equation 4). Figure 3 4 , shows expected recoveries for single-stage extraction. I n the region belcw and to the right of the shaded area, the recovery is essentially equal to the limiting ( m -stage) case. Thus, i n this region there would be no advantage in using more than one stage. I n the region to the left the operation is identical to that with the linear case. Figure 3,B to F, shows recoveries computed for two to six countercurrent stages. T h e transitional region indicated by the shaded area decreases in size and moves slightly to the left as the number of stages is increased. Thus, the range of conditions decreases, for which increased stages result in iwreased recovery. T o illustrate the use of these curves, assume that a 0.1M extractant solution, i n contact with 10 times its volume of a n aqueous phase containing 1 gram of
252
Km
n
Extraction with a single stage Extraction with two countercurrent stages Extraction with three countercurrent stages
= phase
D. E.
F.
Extraction with four countercurrent stages Extraction with flve Countercurrent stages Extraction with six countercurrent stages
uranium per liter, decreases the aqueous concentration to 0.5 gram per liter. T o determine the recovery in a threestage countercurrent system with aqueous to organic feed ratios of 20 : 1, 10 :1, and 5:1, it is first necessary to determine K,.
X
= x/xO =
T h e value of yd is found by dividing the extractant concentration by 2 , the charge on the UOz++ion. y s = (0.1)/(2) = 0.05M f = 10 =
Ye
(10)(0.0042)/(0.05)
=
0.84
Using these values of X and F , K , is found by Equation 3: K , = 1.45. This value is then used to find R from the curves for three stages (Figure 3,C). T h e values of F corresponding to f = 20, 10: and 5 are 1.68, 0.84, and 0.42. Recoveries of 37, 70, and 9670, respectively, are predicted for the above feed ratios. These curves are applicable only where a single substance is extracted,
INDUSTRIAL A N D ENGINEERING CHEMISTRY
x
phase y
Y
= reduced concentration in phase y = Y/Ys
y,
literature Cited
0.5
xO = 1/238 = 0.0042.M
F =f
x
k,
limit k asy -.0 reduced limiting coefficient, K, = limit K as Y-. 0 number of theoretical equilibrium stages fractional recovery from phase x molar concentration in phase x initial molar concentration in phase x reduced concentration in phase x ,
(1) Bailes, R. H., U. S . .4tomic Energy Comm., Progress Rept. DOW 79 (June 11, 1952). (2) Ellis, D. A . , Long, R . S., Magner, J. E., “Coordination Complexes in
Uranium Solvent Extraction,” Division of Industrial and Engineering Chemistry, 133rd Meeting, ACS, San Francisco, Calif., April 1958. (3) Hassialis, M. D., “Recovery of Uranium from Chattanooga Shale,” Division of Industrial and Engineering Chemistry, Status Rept. RMO-4014 (September 19571 - , -,. (4) Kremser, .4.,.Vat/. Petrol. News 22, 42 (May 21, 1930). ( 5 ) Langmuir, I., J . Am. Chem. SOC. 40,1361 (1918).
RECEIVED for review April 6, 1959 k C E P T E D October 19, 1959 Division of Industrial and Engineering Chemistry, Symposium on Chemistry of Heavy Elements, 135th Meeting, ACS, Boston, Mass., April 1959.
