T. W. Gilbert University of Cincinnati Ohio 45221
The "Push Through" Design for Solvent Extraction Separations
Courses in chemical separation methods are now commonplace in many college and university chemistry curricula. Several texts have appeared to serve these courses. A typical starting point for these is a discussion of solvent extraction equilibria. The mathematical development of multistage distribution processes serves as a good preliminary topic before launching into the complexities of chromatography. The subject of countercurrent separations is almost invariably illustrated by a discussion of the Craig method and apparatus. In many texts this is the only example treated. While the Craig method is certainly invaluable when applied to complex mixtures of compounds which are difficult to separate. it must he admitted that the apparatus is not frequentiy encountered in many otherwise well-equipped research laboratories. Consequently, the use of this as the only example of countercurrent distrihution nrocesses mav he misleadina as to their possibilities. ~ 6 "Push e ~ h i o u ~ method h" of solvent extraction separations described by Peppard ( I ) has found wide use in the processing of radionuclides and is applicable to many other situations as well. It represents one special case of countercurrent extraction technology, and certainly deserves wider attention than i t has thus far received. This method has the advantages of being conceptually simple, only a few separatory funnels are required, and the concepts of recovery and separation factors are easily introduced and understood. The aim of this article is to point out the virtues of this technique and, more importantly, to show that countercurreot processes may he used to advantage with ordinary laboratory glassware. The discussion of the "push through" design makes the subsequent discussion of the Craig method much easier while also providing the opportunity to make comparisons. It should be noted here that there are many other experimental designs which could also he discussed. For further information on these. see the article hv Peppard ( I ) . In the examples to follow t h e t&ninology and notation of Sandell (2) is adopted. It is assumed throughout the discussion that the distribution ratios of the solutes are constant under the experimental conditions used, and that the ratio of phase voiumes is also constant Notation
Solutes. Two solutes, A and B, are considered. For convenience, A is taken to represent the constituent to be isolated in as pure a form as possible. Consequently, B represents an impurity. Phases. Organic, subscript o; aqueous, subscript w . Concentrations. The concentration of A in the organic phase in all molecular and ionic forms is indicated by [A],. Other concentrations are defined similarly. Dktribution ratios. Dn = [A],/[Alu,,De = LBlo/[Blu Phase uolurnes. Organic, V,; aqueous, V,,. Phase uolurne ratio. r = V,,/V,
'It should be noted that the term "separation factor" has far many years been used in the literature for the ratio of the distribution ratios, uir., 3 = Dll/D*. It has been pointed out, however, that this quantity is not a good measure of the separability of two substances, and, indeed, can be very misleading (2, 31. Accordingly, the definition above, which is a true measure of separahility (2), is adopted. 822
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Journalof Chemical Education
Figure 1. Operational sequence.
Solute quantities. Moles (or, grams) of A in an individual organic phase = (QA),. Moles (or, grams) of A present in the original mixture = QA'. Males (or, prams) of A in the cambinedarganic phases = x ( Q A ) o . RecouepfaetorforA in theoqanicphase. RA, = x 4 Q a ) , / Q ~ ' Separation factors1 S,,, = RJR,,, = (1 - R,,)lIl - R , , ) ,,t,
Method of Operation
Consider first three separatory funnels each containing a volume V,, of barren organic phase (i.e., none of these organic phases contains any of the solutes to be distributed). See Figure 1 for visualization of the operations to follow. To funnel (1) is added a volume V, of aqueous phase containing all of the solute (both A and B). The funnel is shaken, and after equilibrium is reached, the aqueous layer is transferred to funnel (2). Fresh barren aqueous phase (sometimes called the scrub solution) of volume Vw is then added to funnel (1). The solutions in the two funnels are then brought to equilibrium. The aqueous phase in (2) is transferred to (3); the aqueous phase in (1) is transferred to (2); and fresh barren aqueous phase is added to (1) and the process is continued. It is evident that as many aqueous phases as desired can he "pushed through" the series of three funnels. Also, as manv funnels as desired mav he taken. It will he shown in the mathematical development below that the recovery of anv constituent in the combined aaueous phases will.he improved by increasing the number of these aqueous phases pushed through the series of funnels. The improved recovery is achieved a t the expense of a poorer separation. These two desiderata are thus antagonistic. T o increase the separation, the number of funnels employed must be increased, and this, in turn, results in poorer recovery. It is assumed in these general statements that the phase volume ratio is held constant.
Solute Distribution for the Case of Three Funnels and Five Aqueous Phases
We consider first the distrihution of solute A between the two phases. The distribution of B is mathematically identical except for the numerical difference between Da and DR. Let q = fraction of solute A extracted from the aqueous phase into the organic phase in one contact and p = fraction of solute A remaining in the aqueous phase after one contact with organic phase. Hence, q p = 1. I t is easily shown that q = rD~l(rD.~4 1) and p = l / ( r D ~+ 1). The distrihution of solute A (or B) at equilibrium a t each stage of the stepwise process is shown in Tahle 1. When the five aqueous phases are combined the recovery factor for A in the resulting solution will he given by
+
+
R,,
pql
=
+ 39 + 6q2 + 10gs + 15q4)
(11
The recovery factor by B in the combined aqueous phases will be given by the same equation except for different numerical values of p and q . The General Case
Since any number of aqueous phases and any numher of funnel3 (or, any numher of organic phases, since these are never transferred from one funnel to another) may he used in this experimental design, it is desirable to have general expressions which may he solved for any special case. Let, n = the numher of a particular aqueous phase, m = the number of a particular organic phase, and impose the restraints that, n = 1, 2, 3, . . . a, and rn = 1, 2, 3, . . . c. Thus, in the case discussed previously, a = 5 and c = 3. The form of e m . (1)is seen to be
+
+
q = 1, and RA, R A =~ 1, the corresponding Since p equation for the recovery factor of A in the organic phase is Table 1. The Distribution of Solute at Equilibrium
Organic
(d
(
Aqueous
Organic
(P) (q9) (m) (q9
(PC,) (P') (2pq2)
(P9)
Aqueous
(PP)
(2pW
(pal
Organic
(q8)
(4~')
( ~ P W
Aqueous
(m4)
(4~99
(6psq'I
ozganic
Aqueous
1
()
(1
(1 ()
()
Withdraw
P"
------t
Is+ an "has-
or m
1
2
3
4
5
6
Since B, and B, are of the same form, a single small table may be constructed which will apply to any practical laboratory situation. In Tahle 2 the values of the coefficients B, are found from the appropriate c value and the values of n from n = 1 to n = a. The values of B, are found similarly from the value of a and the values of rn from m = 1 to m = c. For the special case of a = 5, c = 3, the coefficients in the expression for RA, will be 1, 3, 6, 10, 15, and for Rae they will be 1, 5, 15. It is interesting to note in Table 2 that the diagonals of the table turn out to he the coefficients of the binomial distrihution. A comparison with the Craig countercurrent method can now be made. The fractional contents of each tube in the usual method of operation of a Craig apparatus are given by the binomial expansion of the expression ( q + p)" after n extractions and n shifts of the phases. This serves as a demonstration that the binomial distribution is the foundation of any countercurrent extraction process, and the form in which it appears depends simply on the experimental design employed. If for the case, a = 5, c = 3, it is found that the recovery of A or B in the aqueous phase is insufficient, the effect of pushing through one more aqueous phase to improve the recovery is easily calculated. For this case c. remains at 3, and a is now 6. In eqn. (2) it is only necessary to add the term, 2l(rD~/(rDn to the summation. In eqn. (3) the only change required is to change the exponent of the multiplier from 5 to 6. Either of these equations, whichever is the more convenient, can, of course, be used for the calculation since R A , = 1- R A ~ . The direct solution of eqn. (2) or (3) is simple but tedious. 1nstead;if a large numher of values of rD are chosen, the solution of eqn. (2) for %R, may be readily obtained with a computer. Such computations were done for rD in the range 0.01-100, c = 1 to c = 5, and a = 1 to a = 12. The calculations were limited to these ranges for practical reasons; the largest experiment considered ( c = 5, a = 12) requires 60 equilibrations; if more than these are needed, one should probably consider an automatic machine such as the Craig apparatus.
+
wiwldraw A
3rd an nhase
6 ~ 9 '
Table 2. Values of 8, or B,, 73
where B, and B, are the numerical coefficients of the terms in the summations. These terms may be calculated directly from the eqns. (1)-(3)
7
8
9
10
Figure 2. Percentage recovery factors for the combined aqueous phases using three funnels.
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Figure 3. Percentage recovery factors for fhe combined aqueous phases using five funnels.
Figure 4. Fractional separation as a function of the phase volume ratio. Conditions: c = 3. Da = 5. DB = 1
Diagrams such as Figures 2 and 3 may be easily constructed from the calculated results. These enable the conditions reqdired for a given separation to be found quickly and without the need for lengthy calculations. The general procedure is first to set the specifications required for the recovery and the purity of the desired compound. The distribution ratios of the desired compound DA, and the impurity De, must he known or determined experimentally. The ratio of phase volumes to be used must next be found and then the values of a and c needed for the separation.
these authors is different from the one under consideration here. However, since their design is symmetrical, with equal numbers of aqueous and organic phases, maximum fractional separation is achieved using the symmetrical volume ratio condition. Figure 4 shows how the phase volume ratio affects the fractional separation of a pair of substances with different distribution ratios. The results were calculated for three funnels and for different numbers of aqueous phases pushed through. It is seen that the curve maxima are broad, and that since eqn. (5) is somewhat awkward to use, an adequate approximation for practical work is
Selection of the Phase Volume Ratio, r
The ratio of the phase volumes is,an important adjustable parameter in selecting the conditions for achieving a given separation with a minimum of individual phase equilibrations. This was pointed nut by Bush and Denson (4) who calculated that the "fractional separation" was a maximum when the phase volume ratio, r, was set equal to (DADH)-'/~. This relationship is widely used in extraction technology since for a single contact of two phases a "symmetric separation" results. That is, the fraction of A in the lower phase is equal to the fraction of B in the . symmetric condition results upper phase @A = q ~ )The in maximum separation for a single stage, and also for multicontact designs which possess sufficient symmetry. This is not the case, however, for the general "push through" design, and maximum fractional separation is achieved with a phase volume ratio which is not necessarily symmetric. The fractional separation, F,, can be defined as the difference in the recovery factors of A and B in the combined aqueous phases F . = R,,, - R,,,
(4)
.. The optimum phase volume ratio calculated from eqns. (5) and (7) for the condititions of Figure 4 are compared in Table 3. An important distinction between the fractional separation, F, = R H ~R A ~and . the separation factor, S H / . ~ ( ~ , = R H ~ / R Lshould \ ~ , he noted at this point. Figure 4 shows that the fractional separation in each case passes through a maximum as r is increased. The separation factor, SR(AIW). on the other hand, increases continuously with increasing r. S B / A (is~ Ia measure of the true separation (2, 31, and represents the "decontamination" of B with respect to A in the aqueous phase. Since, by its definition, it is a ratio of recovery factors, the absolute values of the recovery factors are irrelevant. In Table 4 are shown some values of S H I A Icalculated ~I for the system of Figure 4. In the case where a = 2 and r is increased to 10, the value of S B / A is I ~increased I to 94 which means that the B in the aqueous phase is decontaminated with respect to A by a factor of 94 (i.e., this indicates a good separation). What
-
Table 3. Calculated Optimum Phase Volume Ratios"
When the expressions for R u and R B (eqn. ~ (2)) are substituted in eqn. (4) and dF,/dr is equated to zero, the optimum phase volume ratio is found to be
where, f = a/(a + c ) , and 0 = D ~ I D HEquation . 5 shows that the optimum phase volume ratio depends not only on the ratio of D* to DH, but also on their absolute magnitudes. For the special case where the number of aqueous phases is equal to the number of organic phases used (i.e., a = c), the value of f is 0.5, and eqn. (5) for this "symmetrical" case reduces to r ~ , m = (D~DJ"'
(6)
which is the same result obtained by Bush and Densen. It is interesting to note that the "diamond" design used by 824
/ Journal of Chemical Education
Table 4. Fractional Separations and Separation Factorsa 0
= 2
0 = 3
the separation factor does n o t indicate is that only 0.28% of the original B i s recovered! The situation becomes clear when one examines t h e seoaration factor S .A. ~.. ~ ,T,h~i s. represents t h e d e c o n t a m i n a t U ~ nof A with respect t o H in t h e oreanic ohase. T h e value of 1.0028 indicates almosl n o separation ( a v a l u e of u n i t y represents zero separation). In o t h e r words, A a n d B a r e both nearly quantitatively ext r a c t e d u n d e r these conditions. B y maximizing F t h e values of S R I A aI n~d I SI\,RI~Ia r e brought more nearly equal. T h i s i s exactly so for a symmetrical separation. The u s e of d i a g r a m s s u c h as Figures 2 a n d 3 (or. exp a n d e d versions t o improve graphical interpolation) can best b e illustrated by working through a couple of examples. Illustration 1 A mixture of isomers containing 60% ethylmalonic acid (A) and 40% glutarie acid (B) is to be separated. The distribution ratios of A and B between water and ethyl acetate are known to be D4 = 2.48, D H = 0.75. It is desired to obtain compound A a t greater than 99% purity. Yield is of secondary importance. Since A is preferred by the organic phase and DA and Dn are not greatly different, a push through extraction in which A is recovered in the organic phase is indicated. As a first trial, the purities of the A recovered in the combined organic phases using three funnels (c = 3) might be calculated. Arbitrarilv. . . a constant IeCoveN of 50% of the orieinal A Dresent ull. be n.sumed t'%l(\,. = Irli,. = 5111.I.'rinc Flzurc 2 the vnlues of r D . fur %H,, = 50 can he f w n d Since I), is kncmn, the phase wlume ratio. I to IE used for 50% recovery is readd" calrulnted for the various numbers of aqueous phases pushed through. By next finding the values of rDs for each case, and then returning to Figure 2, the recovery factors, % R H can ~ . be read directly. The purity of the solute in the combined organic phases can now be found from
.
~
These values are plotted as curve 1 of Figure 5. It is seen that the purity does not meet the required specification of greater than 99%. Also, the purity increases very gradually on going from o = 5 to o = 12. To increase the purity to 99% by pushing through more aqueous phases is abviously impractical. Two alternatives are now available. Some yield may he sacrificed for greater purity (e.g., by making %Rno = 40). or the number of funnels may be increased for greater separation.
If the latter course is chosen with c = 5, and the same procedure followed.using Figure 3, then the results plotted as curve 2 of Figure 5 are obtained. The results show that with five funnels and twelve aqueous phases the desired purity is almost achieved with recovery of 50% of the original A present. If a slight reduction in yield can be tolerated (e.g., %Rho = 45, % R A = ~ 55) then the desired purity might be achieved. For these conditions, the results shown as curve 3 of Figure 5 were found in the same manner. The desired purity is reached using o = 12, and 45% of the original A is recovered. The experiment might he conducted as follows: 10 g of the mixture containing 6 g of A and 4 g of B is dissolved in water saturated with ethyl acetate and diluted to 100 ml. Since for e = 5, a = 12, and %Raw = 55, the value found graphically for rDa is 2.332, the phase volume ratio, r, to be used is 0.940. Hence, five funnels, each containing 94.0 ml of ethyl acetate saturated with water, are set up, and the 100 ml of sample solution is added to the first funnel. After the phases are equilihrated, the aqueous phase is transferred to the second funnel; the subsequent operations follow as outlined in Figure 1. Eleven additional 100-mI portions of water saturated with ethyl acetate are pushed through the set of five funnels. When the organic phases are combined, there will be 470 ml of ethyl acetate containing 6 X 0.45 = 2.7 g of A and 4 x 0.0067 = 0.0268 g of B. When using solvents such as ethyl acetate and water, the presaturation step is necessary because of their appreciable mutual solubility. With other solvents it may not be necessary. Illustration 2 Using the same mixture of isomers as in Illustration 1, the separation under conditions of maximum fractional separation will be examined. This is the case for study when both isomers are of interest, and it is desired to separate them from each other as completely as possible. Arbitrarily, only the separation with five funnels ( c = 5) and with various numbers of aqueous phases will be considered. As has been demonstrated, for maximum fractional separation, the phase volume ratio must he calculated fmm eqn. (5) for each a, c combination. The values of r D and rD. are calculated, and the recovery factors for A and B in the aqueous phase are found graphically fmm Figure 3. Since A collects mainly in the organic phase, and B in the aqueous phase, the recovery factors, %R\, and %Rm, are plotted versus a in Figure 6. The interesting result is that both of these increase continuously with increasing a, prouided that r is set a t rapt using eqn. 5. Note that when c = a, the symmetrical case, % R H=~ %Rn4.Note also that the recovery factors are independent of the ratio of the amounts of A and B in the original sample, but that the purities of the recovered compounds are not. The purities calculated from eqn. (8)
/
P u r i t y (erg)
%Re,
g41.p 1 91
5
6
7
I
I
I
I
8
e
(0
8,
8s
NUUBET1 OF &OUEOYS P W E E S . O
Figure 5. The purity of A recovered in the organic Phase (illustration 1) Conditions: Da = 2.48. De = 0.75, Qs'/Da' = 40160, r is delemined by the preset recovery of A desired. Curve 1: c = 3. %RA, = 50. Curve 2: c = 5. %Rae = 50. Curve3: c = 5. %RA. = 45.
F g w e 6 Recover) taclors and p.ral es 01 A n the organ c Dnase an0 8 n me aa.eobr mare .nder con0 I on9 of nmim.m lracl ona separatoon I w a i o n 21 Cona I ons D, = 2 48 D,, = o 75 OH' 0,' = 40 60 r = r,t leqn. ( 5 ) ) .
Volume 51, Number 12. December 1974 I 825
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