EngFiYring Process development
Fractional liquid Extraction RELATION BETWEEN BATCHWISE AND CONTINUOUS COUNTERCURRENT EXTRACTION E D W A R D G. SCHEIBEL HOFFMANN-LaROCHE, INC., NUTLEY, N. J.
T
HE separation of com-
T h i s paper presents an equation for calculating the apof the continuous unit. The proach to steady-state conditions for each cycle of a batchlarge number of individual ponents by their differwise countercurrent extraction operation. For a threeoperations required by the ent distribution coefficients stage and a five-stage extraction system, this approach map batchwise technique make between two immiscible solit impractical for commercial be represented by a straight line on a semilogarithmic vents has been the subject of separations requiring more plot. Systems with a larger number of stages show a considerable research in resomew-hat curved line, depending upon the number of than ten stages. cent years. The process i; The conventional method stages, but a general equation of the same form has been particularly applicable to the developed with an empirical constant to represent the best for obtaining a number of separation of nonvolatile comstraight line through the calculated data for these systems. equilibrium stages in a single pounds such as metal salts ( 11, unit is to have the two solThe equation allows estimate of number of cycles required a n d h e a t - s e n s i t i v e comto reach a given fraction of steady state conditions. vents flow continuously and pounds such as vitamins and countercurrently through a antibiotics (3, 5 ) . It is also column. Packing or baffles applicable to the separation are usually inserted in the of a z e o t r o p e s and closecolumn t o increase t h e boiling components (6) which number of equilibrium stages are not readily separable by in the given unit, but even under these conditions relatively fractional distillation. In many such applications this opera,few such stages are obtained when compared to the theoret,ical tion may be more econoniical t)han ext'ractive or azeotropic plates in a distilling column. For this reason, liquid extraction distillattion. has been used commercially only when distillation methods are There are two methods for carrying out, this fractional liquid inapplicable. extraction operation. The original method of batchwise counterAn extraction column incorporating individual mixing sections current liquid extraction is probably still the more popular and packed separating sections has been described ( 7 , 8) which method for laboratory studies because it definitely establishes provides a large number of equilibrium stages in a relatively the number of equilibrium stages in the operation. Earlier invessmall unit. The performance of the co!umn depends upon tigat,ors in this field had considered this technique t'oo cumberseveral operating and design variables ( 7 , 9 ) , and since this is some for laboratory work when a large number of stages vere rethe more desirable method for carrying out the fractional liquid quired. However, a relatively sin~pledevice, developed by Craig extraction operation on a commercial basis, it is necessary in ( 3 , 4),made it possible to carry out a large number of extraclaboratory studies to determine the number of equilibrium st'ages t'ions simultaneously. This device has had extensive application in the given column under the operating conditions. Methods in the separat,ion of antibiotics and in establishing the homogefor calculating this performance have heen presented ( 7 ) . Alneity of preparations. Inasmuch as the importance of t'he fracthough these calculations are necessary for the final design of a tional liquid extraction has received increasing recognition in commercial operation, R preliminary investigation of the process recent years, the applications have been expanded t o numerous by the batchwise technique with a fixed number of stages is freother separations. quently made to demonstrate the application of the process. The Craig extractor handles a limited amount of feed in a In order to interpret properly the results of the batchwise single introduction, and although it is an excellent laboratory operation, it is necessary to study the approach of these operatool, it is impract,ical for commercial production. A commercial tions to the steady state which would then represent, the performoperation would require the continuous introduction of feed and ance of t.he continuous countercurrent operation. the continuous withdrawal of separated products. Such a procThe most convenient patt'ern for the calculation of the batchess has been demonstrated by O'Keeffe, Dolliver, and Stiller ( 5 ) wise operation has been presented by Stene (10). Figure 1 shows in the separat'ion of streptomycins by a batchwise operat,ion, his method applied t o a five-stage ext,raction as described by and by Compere and Ryland (8)who have applied t,he method t o Compere and Ryland (2). The numbering of the cycles differs separation of phenol and picric acid. The advantage of t'he batchfrom that of Stene in that the first cycle is considered that cycle a t wise op' ration for laboratorv studies is that the number of equilibwhich the first product leaves the end stages, and the second rium stages is firmly established for the separation obt'ained, and cycle is that cycle a t which the second product leaves the end it may be used t o predict the performance of a given number of stages. For a single introduction of feed, Figure 1 shows the equilibrium stages available in a continuous countercurrent amounts in each of the streams. If fresh feed is introduced into operation. Also in the case of complex mixtures where present the middle stage a t each cycle, the amount leaving a t any cycle is calculation methods are inapplicable, a comparison of the prodthe sum of all the products which have left the system up to this ucts obtained in the continuous countercurrent device with the cycle in Figure 1. products obtained with a different number of stages in the batchThus, in the fifth cycle shown, the product leaving in t,he light wise operation will give an indication of the performance efficiency
242
+
+
+
+
solvent is p 3 3 p 4 q 9p6q2 27p6q3 81p7y4,and the product leaving in the heavy solvent at this cycle is q3 3pq4 9p2q6 27p3q6 81p'q'. Dividing the f i s t sum by p 3 and the second sum by q3, the identical geometric series is obtained 1 3pq 9p2q2 27p3q3 81p4y4and the tEhterm of the series is ( 3 ~ q ) ~ - 'Since . p and q are both fractions such that p q = 1, it can be seen that the maximum value of 3pq is 0.75, and the series is convergent for all values of p . In a continuous countercurrent fractional liquid extraction, it has been shown ( 7 ) that the concentration of a component in the light liquid at n stages below the top is
+ +
243
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
January 1951
+
+
P'
+
+
+
+
+
CYCLE
I
e
fs
and the concentration of a component in the heavy liquid at m stages above the bottom is 3
Rometsch (6) recognized that when the feed is introduced into the center stage of a column i t is possible to derive a simple relationship for the amounts of the component leaving each end of the column
4
(3)
where the feed stage is n stages above the bottom and n stages below the top, so that the total number of stages in the column is 2n - 1. Based on a unit quantity of feed, it may thus be shown that in continuous countercurrent extraction, the quantity leaving in the light solvent is E"/(E" 1) and the quantity leaving in the heavy solvent is l / ( E n 1 ) . The difference between these quantities and the amounts leaving in each of the cycles of the five-stage batchwise extraction operations previously considered is a measure of the approach to steady-state conditions. It can be shown in this case ( n = 3 ) that by dividing this difference by the amount at steady-state condition which gives the fractional deviation from steady state conditions, a geometric progression is obtained such that
+
5
Figure 1.
+
[ml 3E
=
(4)
Extraction Pattern for Five-Stage Operation with Single Feed Introduction
+
+
+
+
This equation when plotted on semilogarithmic paper gives a straight line aith a slope equal to log 3 E / ( E 1)2 since
(7)
+
3E log 6 = t log ___ (E
+
(5)
A similar derivation may be made for a three-stage extraction column ( n = 2 ) and it ail1 be found that:
[ml
where the total number of stages in the system is 2n - 1. From this relationship, constant r for a seven-stage operation is given as r =
2E
c
=
Consideration of these two equations alone in developing the general relationship will lead to an erroneous conclusion because if E = 1 and the constant is equal to 4, the series will not be convergent, since the deviation 6, so defined, would be unity for all values of t. The deviations for the larger number of stages do not give straight lines on the semilogarithmic plots employed; an attempt has been made to develop an empirical relationship of this form to represent the systems of larger numbers of equilibrium stages. The series for a seven-stage system can be developed by the author's method, and the quantities leaving the end stages will
+
involve the following series: 1 4pq 14p2q2 + 48p3q3 164p4q4 560p6q6 . . . This series approaches a geometric series with a difference of 3.4 p q for each succeeding term. However, the use of this difference for the entire series is not a good approximation because the first few terms contribute the most t o the approach to steadystate conditions. In order to fix the sum of the series to agree with the steady-state conditions, it is necessary to define a constant, T , in a geometric series, such that
+
4E2 6h' (E
+
+4
For a nine-stage operation
and for an eleven-stage operation 7
=
+
+
6E4 _ _ i 5 E 3 20E2 (E 114
+
+ 1523 + 6
(10)
Table I summarizes the variation of this value of T with E for the seven-, nine-, and eleven-stage operations. The variation of T increases as the number of stages increasej. However, when the values of E are large, the process would probably not be
INDUSTRIAL AND ENGINEERING CHEMISTRY
244
NUMBER O f CYCLES
Figure 2.
Vol. 43, No. 1
t
Comparison of Equation 12 with Actual Deviation for Seven-Stage Extraction Operation
studied with a large number of stages because the concentrations a t one end of the extraction train would be too low for accurate analysis. Thus, the values of r for E = 1.0 may be taken as a good average to reproduce the approach of the batchwise operation to steady-state conditions. For E = 1,
Thus, the general expression for the deviation from steady-state conditions may be given as
and the plot of the logarithm of 6 against t will give a line with a slope equal to log 4jE1 - (1/2"-1)/(E 1)*] where 2n - 1is the total number of equilibrium stages in the system. Figure 2 shows the curves calculated according to this equation for a seven-stage system compared to the rigorous summation method of Stene. The differences between the points and the curves are of the order of only a few per cent even a t the unity value for E. For the case of E = 1 where the largest deviations are observed the definition of r is such that at larger numbers of cycles the calculated deviation must approach the actual deviation. Thus, Equation 12 represents the best straight line through the points and gives deviation of the batchwise operations from the steady-state conditions with a good degree of accuracy. The equation may be used to calculate the steadystate conditions after a given number of batchwise cycles. Equation 12 applies to systems in which the distribution coeffi-
+
cient is independent of concentration so that the value of E = L D / H will be constant; in some cases it may be necessary to operate in the very dilute region or, when the distribution coefficients vary, to estimate an average value of D. This is difficult when the variation is large, and the reliability of the equation, in such cases, depends upon the accuracy with which this average value of the distribution coefficient may be estimated. A similar restriction is that the solvent ratio must be the same above and below the feed and when solvent is added with the feed, the values of E above and belolv the feed differ and an average value would also have to be chosen. However, the equation does give an indication of the approach to steady conditions and will allow a preliminary estimate of the number of cycles required to approach within a given per cent of steady conditions-for instance, within 1, 5, or 10% of steady conditions. Such a calculation will thus indicate the reliability of the batchwise data. Figure 3 shows the number of cycles required for an approach to 10% from steady-state conditions. The rigorous calculations as well as Equation 12 also show that the deviations of a component from steady-state conditions are the same a t each end of the extraction system, and thus while over-all material balances may be in error, the stagewise calculations based on the observed terminal concentrations will give the correct number of equilibrium stages. This is particularly significant in studies of continuous-column operation. The equations may be applied t o systems of more than one solute by introduction of the appropriate extraction factor. Equation 12 also indicates that when the optimum solvent ratio (for which El = 1/Ea), is used to fractionate between two components, the approach of each component to steady conditions
January 1951
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
hill be identical] and the product compositions on a solvent-free basis a t the ends of the unit will be the same at steady conditions and a t each cycle. This i s an interesting effect because i t indicates that, with the feed introduced into the center stage, it is not necessary t o reach steady conditions at the optimum solvent ratio in the batchwise operations; i t may be concluded t h a t the same relationship holds in the continuous-extraction column where the changes occur by differential amounts instead of by integral steps.
245
TABLEI. VALUES OF RATIOT , FOR DIFFERENT VALUES OF EXTRACTION FACTOR, E, AND DIFFERENT NUMBERSOF TOTAL STaGES
Total Stages
13xtractio11 Factor, E
7
9 Values of r
1 2 or 0 . 5 4 or 0 . 2 5 10orO.l 9 or 0
3.50 3.56 3.63 3.83 4.00
3.75 3.89 4.20 4.59
5.00
11
__ 3.875
4,lO 4.61 5.27 6.00
The equations derived in this work apply only t o the case of introducing the feed into the center stage. Stene has observed t h a t the relationships for other intermediate feeds become too complex for simple and general representation; also, the general expression for t h e product distribution at steady state becomes much more complex. However, the author’s technique could be applied t o an individual case of this type; when the algebraic expression becomes too complex, numerical values could be applied t o obtain the solution for the particular case under consideration. NOMENCLATURE
D = distribution coefficient = Y / X LD E = extraction factor = -
H
H
= quantity of heavy solvent t o each stage L = uantity of light solvent t o each stage rn = t%eoretical stages below feed in continuous extraction
n = feed stage location-that is, stages from either end of extraction system (2% - 1 = total number of stanes in system) p = fraction of the comgonent passing into the light solvent in fi eachstage = ( E 1) q = fraction of the component passing into the heavy solvent 1 in each stage = (E 1) r = ratio of each term in geometric series t = number of cycles calculated from time first product appears at the end stage (number of product samples colected) X = concentration in heavy solvent Y = concentration in light solvent 6 = fractional deviation from steady state conditions I
+
~
Figure 3. Effect of Number of Stages and Extraction Factor on Cycles Required for 90% Approach to Steady Conditions in Batchwise Extraction
x+
. I
In continuous countercurrent operations such as in packed columns or in columns containing both mixing and separating sections (7,8), the deviation from steady conditions is exceedingly complex t o evaluate theoretically and requires various assumptions t o establish the time for a single cycle. However, Equation 12 indicates that the deviation from steady-state conditions, possibly expressed as the deviation in the material balance on the column at any time, may be correlated according t o a straight line on a semilogarithmic plot against time. This should serve as a useful criterion for predicting the approach of such columns t o steady conditions. Assuming t h a t 1 hour after the first product appeared in the solvent streams from such a column the material balance on the column was 80%] it may be predicted that after 2 hours it will be 9GYo and t h a t 3 hours would be required for the column t o approach within 1%of steady conditions.
+
LITERATURE CITED
(1)Asselin, G. F.,Audrieth, L. F., and Comings, E. C., J. Phvs. & Colloid Chem., 54, 640 (1950). (2) Compere, E. L.,and Ryland,A., IND. ENQ.CHEM.,43,239(1951). (3) Craig, L.C., J.Biol. Chem., 155,519(1944). (4) Craig, L.C., and Post, O., Anal. Chem., 21,500 (1949). (5) O’Keeffe,A. E.,Dolliver, M. A., and Stiller, E. T., J . Am. Chem. SOC.,71,2452 (1949). (6) Rometsch, R., Helu. Chim.Acta, 33, 184 (1950). (7) Scheibel, E.G., Chem. Eng. Progress, 44,681-90,771-82 (1948). (8)Scheibel, E. G.,U. S. Patent 2,493,265(Jan. 3,1950). (9) Scheibel, E. G., and Karr, A. E., IND.ENG. CHEM.,42, 1048 (1950). (10) Stene, S.,Arkiv. Kemi, Mineral. Geol., 18H,No.18 (1944). RECEIVED May 19, 1950.
