NOVEMBER, 1936 *
INDUSTRIAL AND ENGINEERING CHEMISTRY
The agglutinating values of the coal as determined by the Bureau of Mines method (16) are shown in Table VI. These values were not changed significantly by the amount of oxidation to which this coal was subjected. It would appear, therefore, that the plastic range intervals furnish a more sensitive measure of the extent of oxidation of this coal than do the agglutinating values. 1
OF TABLE VI. EFFECT
Sample
OXIDATION O F COAL ON AQOLUTINATIXG
VALUE(16) -4-1
used per kg. d r y coal, grams
A-2
A-3
0.86
2.08
0 2
0.0
A-4
A-5
A-6
A-7
4.73 5.83 7.18 8.79
I n general, oxidation of the coal has an effect very similar t o that obtained by Davis and Hanson ( 7 ) by mixing fine inert material with Pittsburgh bed coal, thereby reducing the fusibility and increasing the strength of the coke produced. Mild oxidation under the conditions used in this work with its attendant increase in coke strength, decrease in tar yield, and fusibility of the coal, apparently destroys some of the fusible coking constituents, of which there is an excess.
1353
Literature Cited (1) Agde, G., and Winter, A,, Brennstof-Chem., 15, 46-50 (1934).
(2) Am. Soo. Testing Materials, Proc. 35, P t . I, 847-53 (1935). (3) Brewer, R. E., and Atkinson, R. G., “Plasticity of Coals, Its Measurement and Relation to Quality of Coke Produced” (in manuscript, 1936). (4) Bunte, K., and Buchner, H., 2. angew. Chem., 47, 84-6 (1934). ( 5 ) Coles, G., and Graham, J., Fuel, 7,21 (1928). (6) Davis, J. D., and B.wne, J. F., J. Am. Ceram. Soc., 7, 809-16 (1924). (7) Davis, J. D., and Hanson, 0. G., IND. ENG.CHEM.,Anal. Ed., 4, 328 (1932). ( 8 ) Francis, W., and Wheeler, R. V., J. Chem. Soc., 1927, 2955. (9) Haldane, J. S., and Makgill, R. H., J. Soc. Chem. I n d . , 53, 359T (1934). (10) Jenkner, A., Kuhlwein, F. L., and Hoffman, E., Gluckauf, 70, 473-81 (1934). (11) Michaelis, P., Ibid., 71, 413-23 (1935). (12) Pamart, C., Chaleur & ind., 15, 329-33 (1934). (13) Parr, S. W., and Milner, R. T., IKD.ENG. CHEM..17, 115 (1925); Fuel, 5, 295 (1926). (14) Porter, H. C., and Ralston, 0. C., U. S. Bur. Mines, Tech. Paper 65 (19143. (15) Rose, H. J., and Sebastian, J. J. S., Fuel, 11, 284-97 (1932). (16) Selvig, TT. h.,Beattie, B. B., and Clelland, J. B., Proc. Am. Soc. Testing Materials, 33, Pt. 2, 741-57 (1933). (17) Strache, H., and Lant, R., ”Kohlenchemie,” Leipsig, rlkademische Verlagsgesellschaft m. b. H., 1924. (18) Yancey, H. F., and Zane, R . E., Bur. Mines, Rept. Investigations 3215 (1933). RECEIVED .4ugust 3, 1936. Presented before t h e Division of Gas and Fuel Chemistry at t h e 92nd Meeting of t h e American Chemical Society, Pittsburgh, P a . , September 7 to 11, 1936. Published by permissi0.n of the Director, U. S. Bureau of Mines. ( K o t subject t o copyright.)
LIQUID-LIQUID EXTRACTION E x a c t Q uant it at ive Relations’
L
IQUID-liquid extraction is constantly employed both in the laboratory and in industry. The ether extraction of organic substances from their aqueous solutions, and the commercial production of absolute ethyl alcohol (9) and of glacial acetic acid (8) are a few examples. With the recent introduction of solvent refining of lubricating oils in the petroleum industry this type of extraction becomes of considerable technical interest. I n industrial work, optimum conditions govern the choice between several alternatives of solvent, of method, and of equipment. Not always will a combination of the most efficient solvent, the most efficient method, and the most efficient equipment, constitute optimum conditions; in fact, this condition may seldom be true. Given a solvent, the method of extraction will largely determine the type of equipment t o be used; the relative advantage of one method over another will mostly be governed by the choice of the solvent; and, for a definite degree of extraction, the necessary amount of solvent will depend on the method used. Yet, no intelligent choice of the proper combination can be made until the interrelations of these different variables are known quantitatively.
Methods of Extraction When a liquid to be submitted to extraction is treated with a suitable liquid solvent, and two layers are formed, one of the 1
T h e first article in this series appeared in August, 1936, pages 928 t o 933
K. A. VARTERESSIAN AND M. R. FENSKE The Pennsylvania State College, State College, Pa.
layers will usually contain a large proportion of solvent and a small proportion of the liquid to be extracted; the other layer will contain a large proportion of the liquid to be extracted and a small proportion of solvent. After such treatment, when the two layers are separated and the solvent is removed and recovered from these layers, what is left of the layer consisting of a large part of the solvent mill be called the “extract,” and what is left of the layer consisting of a large part of the liquid to be extracted Fill be called the “raffinate.” The two layers before the removal of the solvent will be called the “extract layer” and the “raffinate layer,” respectively. Depending upon the relative densities of the extract layer and of the raffinate layer, either one may constitute the top or “light layer,” the other being termed the bottom or “heavy layer.” The various methods of extraction are arranged for convenience as follows: 1. Single-stage 2. Cocurrent contact: a. Multiple-stage b Infinite-stage
3. Countercurrent contact: a. Multiple-stage 6. Infinite-stage
INDUSTRIAL AND EUGINEERING CHEMISTRY
1334
VOL. 28, NO. 11
tinuously fed in countercurrently. The ratio of feed rate of solvent A to that of solvent B is so adjusted as t o equal the ratio of the concentration of the substance C to be separated in solvent B to that in solvent A , under equilibrium conditions. This adjustment retards the dissipation of substance C through the ends of the column which, under such conditions, would be limited only to diffusion, whereas, the dissipation of other substances that might be introduced with C would be augmented, along I I 1 3 one or the other direction of the column, by the fact of their having distribution ratios different from that of substance C. .ix/mt /aye/ Boflhote /ager The combination of conditions which makes 5o/ven/ seporu/or ar m x e r the simplified mathematical treatment justifiPhie number (/ncreoS/ngom‘eri &?e number (/mreos/nyordeer) I able is not commonly realized in industrial practice. Here, a minimum amount of solvent for a definite separation is often the goal; this m e a n s d e a l i n g with concentrated solutions FIQURE1 which, in turn, usually means variation of distribution ratio with concentration. For these By “cocurrent” is meant multiple contact using fresh solmore complicated cases the literature is very recent. vent in each stage. Hunter and Kash (6) extended their computation for the Although in extraction practice various other methods or special case of equilibrium following the distribution law and combinations of methods may be used, the methods listed operating lines having constant slopes t o the more general are selected for mathematical treatment because it is believed case where such simple treatment is not justified. Their these will bring out the essential principles applicable to pracpaper also contains a brief discussion of nonisothermal operatically all extraction methods. tions in the countercurrent multiple-contact method. The use of reflux in countercurrent extraction ail1 reduce I n a valuable article Saal and Van Dyck (IO) pointed out the number of stages necessary for a definite separation, yet it the analogies between distillation and extraction in their main will not introduce any new variables for its mathematical treatment. The two important cases of enriching by reflux and exhausting by reflux will, however, be treated a t least for the case of ideal equilibrium relations and of total reflux. Figure 1 is a diagrammatic presentation of the more imporA system of exact mathematical relatant extraction methods. tions based simply on material balances, and entirely general in applicability, is Previous Investigations worked out for the principal types of extraction. A graphical solution of the The mathematical treatment of extraction methods is not new. Until recently, however, such treatment was confined countercurrent operation on rectangular only to special cases. The assumptions used in the derivacoordinate paper, by means of equilibtion of formulas have limited their applicability to dilute solurium and operating data obtained from tions, where the transfer of the distributed material from one triangular plots of ternary systems, is phase into the other does not sensibly alter the quantity of presented. each phase, and where association, dissociation, or chemical combination do not change the distribution ratio. Using the equilibrium data for the sysFor such cases the computations involved in connection tem chloroform-acetic acid-water and a with the single-contact, the cocurrent multiple-contact, and definite problem, the relative merits of the countercurrent multiple-contact methods of extraction the various methods of extraction are disin condensed ternary systems are well presented by Hunter cussed in the light of calculated data and Nash from both the “theoretical plate” and the “absorption coefficient” viewpoints. The impression might be supported by theoretical expectations ; obtained from their paper, however, that with any given the conclusion is reached that extraction amount of solvent, complete removal of the solute would be methods should not be evaluated in possible if the number of stages were increased infinitely. themselves, apart from the equilibrium That this is not the case and that instead, depending on the relations in the system to which the amount of solvent used and the value of the distribution ratio, a finite percentage removal of the solute is approached method is applied. as the number of stages is increased, will be evident in subseThe conditions for using reflux and the quent parts of this paper where the infinite stage cases are advantages and disadvantages when its considered. use is possible, are briefly discussed. Cornish (1) and associates were concerned with the purifiEnriching and exhausting by total reflux cation of vitamins by means of fractional distribution between two immiscible solvents. The method is batch and are treated mathematically for cases consists in introducing the charge t o be separated a t the where the distribution law is valid. middle of a specially constructed column, a t the extremities of which the two immiscible solvents are uniformly and con-
101
(e),
r
,
IXDUSTRIAL AND ENGINEERING CHEMISTRY
NOVEMBER, 1936
forms. They indicate the possibility of using a graphical method of computation similar to that of RfcCabe and Thiele (7) in cases where, through temperature variations along an extraction column, the combined concentration in the extract layer of the substances to be separated may be kept constant a t all points in the system. This means that the equilibrium curve has to be modified for column temperature gradations. Finally, another investigation by Hunter and Kash (6) is concerned with extraction in complex hydrocarbon systems, such as with the solvent refining of lubricating oils. The equilibrium relations involved in such systems were characterized by empirical measures, such as viscosity-gravity constant, and were utilized in graphical computations for determining the degree of improvement of a charge, submitted to extraction of a given type, such as the cocurrent multiplestage method, using a given amount of solvent. Considering the complexity of the problem, the agreement between predicted and actual values of the degree of improvement of the charge, the amount of raffinate obtained, and the amount of solvent used is good. This method of evaluating equilibrium relations is, however, a t best imperfect, and too great a confidence may not be h a 4 in the estimations made on such a basis. It represents, however, a distinct practical contribution to quantitative treatment in the solvent refining of lubricating oils.
Equilibrium Data Apart from operating data, phase equilibrium composition relations are the only data necessary for the mathematical treatment of extraction methods, under isothermal and isobaric conditions. Although in actual extraction practice, depending on the degree of intimacy of contact between the phases, on their time of interaction, etc., equilibrium conditions may or may not be established yet the relations that would exist a t equilibriuni may always serve as a measure for estimating the e$ciency of the means designed for the purpose of bringing about equilibrium. Since the mathematical relations between the compositions of the phases a t equilibrium are usually complicated, they are frequently represented graphically. At constant temperature and pressure, a two-phase three-component sy4em is conveniently presented by means of a plot on triangular coordinate paper. In the mathematical analysis of the various methods of extraction, for the purpose of clarity, a definite three-component system will form the basis of calculating the relations between the quantities of the different components and phases in-
!&fer
FIGURE 2
1355
FIQURE 3
volved. This system mill be chloroform-water-acetic acid a t 18” C. and 1 atmosphere, The equilibrium data are those of Wright (11, 12). Figure 2 presents them graphically. Curve H K L represents the saturation data: HK gives the compositions of possible heavy layers, and K L gives those of possible light layers. Heavy and light layers which can exist side by side a t equilibrium-i. e. , “conjugate layers”-are joined by straight lines usually termed “tie lines.” Any mixture whose total composition may be presented by a point within the area enclosed by the saturation curve and the side HL of the triangle will form two layers. The compositions of these layers are given by those points on the saturation curve which lie a t the extremities of the tie line passing through the point of total composition. All points of total composition located on one and the same tie line will, at equilibrium, separate into the same pair of conjugate layer compositions. Any mixture whose total composition is represented by a point outside the area referred to above will form an unsaturated mixture and will consist of a single liquid phase.
The Problem Suppose there is a given quantity of a mixture of chloroform and acetic acid of a definite composition, and we desire to reduce the amount of acid in the chloroform to some other definite composition by extracting the acid with water. We can use any desired method of extraction. The main questions with each of the possible methods are how much water must be used, and what, will be the amount and cornposition of the two liquid phases. When water is added to the chloroform-acetic acid mixture, evidently extraction forces will not come into play until enough water has been added to form two liquid layers. This amount of water mill be independent of the method of extraction used, and therefore, as a basis, a mixture of chloroform and acetic acid saturated with water is chosen as the starting material to be extracted. The problem, then, is as follows: One hundred grams of a mixture containing chloroform and acetic acid are saturated with water at 18” C. and atmospheric pressure, The composition, expressed in weight per cent, is ch1oroform:acet’icacid:water = 83.3:11.7:2.0. We desire to reduce the acid concentration from 14.7 to 2.0 per cent. We must find the amount of water necessary for extraction, and the amount and composition of the two liquid phases produced, using different methods of extraction, from the given equilibrium relations. Derivation and Applications of Formulas I n this section formulas are developed which give the relation between the quantities of the various components and phases, using the outlined methods of extraction.
VOL. 28, NO. 11
INDUSTRLQL AND ENGINEERING CHEMISTRY
1356
These formulas are derived on the basis of equilibrium relations and of material balances, so that no assumptions are introduced t o limit their use only to cases where such assumptions will be justified. Moreover, the number of given factors is kept at a minimum, and all variables are expressed in terms of the amount of original charge and the terminal compositions of the various stages. These formulas may be greatly simplified by the use of a variety of mathematical relations between the variables entering into the equations. For convenience, another plot besides the triangular one is used for the calculations. This is represented by Figure 3 which gives the weight per cent of each of the three components in the light layers us. those in the heavy layers a t equilibrium. METHOD1. SINGLE-STAGE.Let il,, C,, and Bo represent the weight of chloroform, acetic acid, and water, respectively, in the original mixture of weight H,;let X,,x,, and 2, be the corresponding compositions in weight fractions. Let this mixture be required to be treated with a weight, S,,of water in order to reduce the acid concentration in the heavy layer to z, the corresponding composition of chloroforni and of water being X,and Z,! as determined from the saturation plot in Figure 2. At this stage the concentrations of the three components in the light layer will be Y,, y, and g,, for chloroform, acetic acid, and water, respectively, as determined from the equilibrium curves in Figure 3. If H, designates the weight of the resulting heavy layer, and L, t h a t of the light layer formed, and material balances are made on chloroform and on acetic acid, we have the equations,
H 2 = 84.80, L2 = 70.98, and SZ = 64.05. This means that = 95.38, and S, = 80.15. The case of equal amounts of solvent used in each stage may be solved by selecting a value of x1 that satisfies this equality, employing the trial-and-error method. For this case there results: HI= 88.70, L1 = 45.90, SI = 34.60, H z = 85.14, LZ = 38.16, and Sz = 34.60. This means t h a t H, = 86.14, LI = 84.06, and S, = 69.20. By extending the formulations to cases of three, four, and more stages, the values of H , L, and S for any stage, n, in a cocurrent multiple-stage system consisting of N stages, are given by the following general formulas:
H, = 84.80, L,
(7) zn-;xn- x,-1 xn LJt= X,din - X"Y,
n-1 Ho
II
i=l
X,-,Y, -
a-IY&
--x,yi - XiYi
(8)
1=1
For the caqe of equal
2
decrements,
- xo
n -
n(Xo
- 2s)
N
(10)
and for the case of equal amount of iolvent used,
s1= 8, = s y - 31
which, solved simultaneously for H,and L,, give
From a total material balance, HJ
+ Lt = H , + Sf
(5)
Substituting in Equation 5 the values of H, and L, given by Equations 3 and 4,respectively, and solving for Sj:
(11)
METHOD2b. COCURRENT INFINITE STAGE. Using this method, the extract layer would continually be removed from contact with the raffinate layer. At a given instant let H be the weight of raffinate layer, L that of the total extract layer formed, and S that of the total solvent used. By material balances, using differential and actual quantities, for acetic acid, for chloroform, and for total material, we ohtain : - H ~ x - x ~ H ytlL -HdX - X d H YdL
(12)
S
(14)
=
H + L
-
H,
(13)
Combining Equations 12 and 13 and integrating, Turning back to the numerical problern, H , = 100, X,= 0.833, xo = 0.147, and x, = 0.020. From Figure 2, X, is 0.970. From Figure 3, y, = 0.084 and Y, = 0.008. Inserting these values in Equations 3, 4, and 6, we obtain H/ = 84.6, L/ = 154.8, and S, = 139.4. METHOD2a. COCURRENT MULTIPLESTAGE. With the two-stage method it is possible to have any desired concentration, xl,of acetic acid in the first stage, provided there results a concentration, x2,in the second stage equal to the final concentration desired. In practice, x1 could be fixed either by using enough solvent in each stage so that the decrements of the acid concentrations in the raffinate layer from one stage to the other are equal, or by using equal amounts of solvent in each stage. I n general, neither the values of x1 nor the amounts of solvent used, determined by these procedures, will be the same. Both possibilities will be considered in the numerical solution of the problem. By material balances around the first and second stages, employing a procedure similar to that used with method 1, in the case of equal acid concentration decrements the following values are ohtained: H I = 91.73, L1 = 24.40, S1 = 16.10,
For the numerical calculation of H,, the right-hand side of Equation 15 may be evaluated by graphical integration, plotvs. x for the first member and 1/Y The relations for x, y, X, and Yare obtained from Figures 2 and 3. The integration of Equation 12 yields, for the amount of extract layer, vs. X for the second member.
Y d (Hx)
-
(16)
The numerical value of the integral may be obtoined by graphical integration plotting l / y vs. Hx,the value of H for each x being obtained from Equation 15.
NOVEMBER, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
Finally S, may be obtained from Equation 14 by substituting in i t the given value of H , and the calculated values of Hf and L,. These calculations give: H, = 84.9, L, = 54.0, and S, = 38.9. METHOD 3a. COUNTERCURRENT MULTIPLESTAGI. Consider a column of a total of N theoretical plates numbered 1, 2, . . , n, . , . A7 from top to bottom. A heavy feed H , is introduced a t the top and withdrawn a t the bottom as heavy product H,; a light feed L Y - is~ introduced a t the Bottom and withdrawn a t the top as light product L1. Making material balance.; around the entire column for acetic acid, for chloroforiii. and for total material, \
+ L N + ~ Y:=V H~ IV ~ ,+Y Llyl H o X o + L.vLiY\+i = H N X . + ~ LiYi Ho + LN+I H N + LI H o ~ o
(17) (18) (19)
Making similar material balances around any plate n,
+ +
+ +
Hn - 1 zn - 1 Ln+t Y ~ + I= Hnzn Lnyn Hn-iXn-i L , + IY,z+i = HnXn LnYt, Hn-i+ LnL1 = Hn
+ Ln
(20)
1357
From the g i v e n v a l u e s of z, a n d z N ,those of X,, yo, Y o ,and XNare read from Figures 2 and 3. Inserting these v a l u e s a s well as the given values of Ho,Ylvfl, and Y,bl (the latter two are zero in this particular problem) in E q u a t i o n s 23, 24, and 25, we obtain: H, = 84.0, L1 = 32.5, and LN-l = 16.5. This nieanq H, = 8 4 . 0 , L, = 3 2 . 5 , a n d S, = 16.5.
(21) (22)
I n addition, X,,yn, and Y , are functions of z,,as plotted in Figures 2 and 3. Under the conditions of the problem, the unknowns in Equations 17, 18, and 19 are: L,+I, H,, LI, y1, and YI. Assuming a reasonable yl, Equations 17 and 18 may be solved for H , and L1,since Y 1will be determined by yl by means of t h e saturation plot of Figure 2. Substituting the values of H Y and L1 thus obtained, in Equation 19, the value of is obtained. With these values of LI and y1, and consequently of Y1, zl, and X1through Figures 2 and 3, the equations for plate 1may then he taken into consideration. Thus Equations 20, 21, and 22 where n = 1, together with the saturation relation between yz and Y z ,will suffice to solve for the four unknowns HI, Lz, ~ 2 and , Y,. This process is continued until the equations for the last plate are taken into consideration. Here lies the test for the correctness of the assumed value for yl. If the assumed value has been correct, the values of H , and originally calculated by Equations 17 and 18 will check those calculated by material balances around the last plate. An alternative test for the correctness of the assumed value for y1 is to see that the value of zN calculated by means of the equations for plate ( N - 1) is identical with its given value. The latter would he a better test if the changes in HN or L,,+l from plate to plate are small. For a column of two theoretical plates, calculations as outlined above give: H I = 88.5, L1 = 56.5, Hz= 85.0, Lp = 45.0, and L,+1 = 41.5. This means H, = 85.0, Lf = 56.5, and Sf = 41.5. METHOD 3b. COUNTERCURREXT INFINITE STAGE. In an extraction tower of infinite height, the difference between the compositions of the raffinate layers, or of the extract layers, from plate to plate becomes exceedingly small a t that end where the material to be evtracted is fed into the tower. This means that the outgoing extract layer may be considered in equilibrium Kith the incoming raffinate layer. Using this concept and making material balances around the entire column, we obtain:
Graphical Solution of Countercurrent Method This method of extraction is likely to be the one used in industry. I n order to visualize the conditions in a countercurrent extraction system, Figure 4 is plotted on the basis of the concentration changes of acetic acid for the case of a column of four theoretical plates. The operating line presents conditions a t the different cross sections of the column. Conditions a t the bottom cross section are presented by point ( z N ,y N + l ) , where zAY is the weight fraction acetic acid in the raffinate layer product (0.020), and y.Y+l is the weight fraction acetic acid in the extract layer feed (0.000). Conditions in the bottom theoretical plate are presented by point (a, y4) since the two layers are a t equilibrium. It is evident that the raffinate layer in the bottom plate and the extract layer in the plate above it (in this case, plate 3) are the resulting two layers from the interaction of the extract layer from the bottom plate and the raffinate layer from plate 3. Where the latter two layers meet in the column is presented by point (z,y4) on the operating line. Briefly, then, the points on the equilibrium curve present conditions in the theoretical plates, whereas the points on the operating line present conditions between the theoretical plates. The equation of the operating line is Y"t1
= L,+1 H* 2"
,+1 X.v + LaL + 1 YNtl -L" _
(26)
where H,,z,v, L N + l ,and ys+l are constants. If, in addition,
H , and L,+1 were also constant (i. e., if the amounts of the
raffinate and extract layers at any section of the column did not change with n, the serial number of the theoretical plate), then Equation 26 would represent a straight line, and would be easily defined by the terminal concentrations, by the concentrations at one end of the column and the ratio of the amount of raffinate layer to that of extract layer, or some such combination. I n case fresh solvent is used, the last term of Equation 26 will disappear, If the amounts of extract and raffinate layers change on their way from one end of the column to the other, the two fixed points (q,, y1) and (sV,y,+l) may not be joined with a straight line, and the problem reduces itself to the drawing of the proper curve between these points. Once this operating line is obtained, it is qimple to ascertain the number of plates by going from the operating line to the equilibrium
INDUSTRIAL AKD ENGINEERING CHEMISTRY
1358
line, then back to the operating line, etc., in a manner analogous to calculations of the same nature in distillation work. The operating line equation is general and may be applied to any of the components in t h e system. I n addition, instead of containing the constants H,x, and LNflyNCI, it may contain the alternative constants H,x, and L1yl. I n other words, an equation of the following type may be had for each of the components involved in the -y,.stem: H N X N- LN+IYN+I = H
- Ln+lYn+~=
n ~ n
H o ~ o- Liyi (27)
From the properties of triangular plots (Figure 5) it is evident t h a t the composition of all mixtures resulting from addition or subtraction of materials involving the composi-
c7goou
xo-l
A\
/
/-%
FIGURE 5. OPERATINGPOIKT AND GRAPHICAL SOLUTIOX
tions presented by points y1 and E, will lie on the straight line passing through these points; the same may be said about point yN+l and rN. Any point such as P that is common to these two lines will, therefore, present the composition of a mixture which may result both by the removal of material of composition yl from that of composition E,, and by the removal of material of composition yN+l from that of composition E,. From Equation 27 i t is evident that P is the point which also gives the composition of the mixture resulting from the removal of material of composition yn+l from that of composition 2,. Consequently, any straight line within the angle yNflPy1, passing through P , will cut the equilibrium line at points x, and yn+l. P , which for convenience will be called the (‘operating point,” may therefore be used for obtaining as many r , and yn+l points as desired, from which the curve for the operating line in Figure 4 may be constructed with any degree of accuracy. As may be expected, the graphical solution may be carried out with the triangular plot alone. A clear presentation of this subject is given by Evans (a).
Reflux under Special Conditions Even with the limiting case of the countercurrent contact method where a tower of infinite height is employed, the best we may expect is an extract layer in equilibrium with the feed to be submitted to extraction. As a rule, the richer the feed in the extractable materials, the richer will be the equilibrium extract layer in these substances, and the sharper will be the separation. The shortcomings of the countercurrent method with no reflux, especially with a feed stock which is poor in the extractable substances, are therefore obvious. What cannot be accomplished with a n infinite height of tower may, however, be accomplished with a little reflux. This is due to the fact that now the outgoing extract layer is given a chance to be in equilibrium, not with the feed, but with a material that is richer in the extractable substances the extract. This, naturally, than is the feed-namely, means sharper separation. There is no question that, with a given solvent, this sharper separation can be attained alterna-
VOL. 28, NO. 11
tively ab the expense of more solvent per unit feed or of its equivalent, more energy of the type used in the recovery of the solvent, such as more heat. Although the advantages of using reflux are evident, considerations of a physico-chemical nature are absolutely necessary for its intelligent utilization. Thus, such factors as the extent to which the constituents of a mixture are soluble in each other and in the solvent, the trend in the distribution of the substance to be separated between conjugate liquid phases, the relatiye densities of saturated solutions of different compositions, etc., shouId be examined before any predictions are made as to the possible results obtainable through the use of reflux. Suppose we wish to separate into its components a mixture of substances B and C, using solvent B , by means of the countercurrent extraction method. If both A and C are partly soluble in B , and if the operating range of raffinate layers is different in density from the operating range of extract layers, it will be possible, through the use of reflux, to obtain either A or C in any desired degree of purity, depending on the number of stages employed, and on the composition and degree of reflux used, provided the extract and the raffinate resulting from any conjugate layers are not identical in composition. If, on the other hand, A is partly soluble and C i s completely soluble in B , it will be possible to separate only A in any degree of purity; this separation is accomplished through refluxing the extract layer (enriching by reflux) or the raffinate layer (exhausting by reflux) depending on the selectivity toward A or C of the solvent used. In cases of this type the use of temperature gradient along the extraction system or the introduction of precipitating agent8 may produce sharper separation of C. The more general case, where both A and C are partially miscible with B, will be considered in the mathematical discussions which follow. To be definite, solvent B will be assumed to be less dense than A and C and to be more selective toward C than toward A . ENRICHING, The operation of refluxing an extract layer by converting i t to a raffinate layer through the removal of some of its: solvent content, will be termed “enriching by reflux.” A scheniatic sketch of such a n operation, using total reflux, is shown in Figure Id. In practice the operation may be continuous or discontinuous (batch) with any desirable degree of reflux. The following nomenclature is used: weight fraction of that constituent toward which the solvent is less selective, in the extract layer = weight fraction of that constituent toward which the soIvent is more select,ive,in the extract layer = same as Y A , in the raffiate layer = same as yc, in the raffiate layer = weight of that constituent toward which the solvent is less selective, in the extract layer = weight of that constituent toward which the solvent is more selective, in the extract layer = same as A‘, in the raffiate layer = same as C’, in the raffiate layer = distribution constant
YA =
yc
xd xc A’ C’
A C
.K
Xow, by the distribution law, YA =
K A X Aand yc = Kczc
where By material balances for C and d around the section including and above any plate, n, for the case of total reflux and steady operation:
UOVEMBER, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
C‘n.-l = C , and A’,,.-l = 4, so that
0-1
(:I)
n):(
(30)
= B(Z)
5 2
9
(32)
n-1
% b
which may be presented in the general form,
(i) n
=
p-1(:)
s5
(33)
I
Equation 33 gives the weight ratio of C to A in the raffinate layer on any plate, n, in terms of the same on the plate which is (n - 1) plates away from it. It is applicable to cases of steady operation, ideal equilibrium relations, and total reflux. Equation 33 is the analog of the one developed by Fenske (3) for cases of fractional distillation where Raoult’s law is applicable; 0,the relative distribution ratio in extraction, replaces a, the relative volatility concept used in distillation. EXHAUSTING. The operation of refluxing a raffinate layer, by converting i t to an extract layer through the addition of more solvent, will be termed “exhausting by reflux.” A schematic sketch of such an operation, using total reflux, is shown in Figure le. With the same type of treatment as that employed for the problem of enriching by reflux (when the material balances for C and -4are around the section excluding and below any plate, m ) , the problem of exhausting by reflux yields t h e equation :
(i) 1
=
p-l(;)
m
(34)
Relative Merits of Extraction Methods It is a serious mistake to evaluate extraction methods in themselves. without considering the particular problem to the solution of‘which they must be applied. Thus, the general belief t h a t countercurrent extraction is in all c i r c u m s t a n c e s superior to cocurrent extraction does not have a sound basis. It k is a result of t h e failure to see $v t h a t an increase in the concen3 tration of a substance in one a liquid phase is not always ac8 companied by a n increase in the $
I dl
Figures 6, 7, and 8 are plotted from data c a l c u l a t e d b y means of the equations developed under the various ext r a c t i o n m e t h o d s . The dotted portions of the curves simply indicate trends. Although the absolute values in
(31)
=
Combining Equations 29 and 31,
(i)
1359
!
s
3
NUHUR 01 J I A C i i
FIGERE 7
other; a c t u a l l y i t i s sometimes accompanied by a decrease. I n order t o show clearly the effect of the various methods of extraction on the important factors entering the specified problem,
FIGURE 8
F 3
these plots may be some$, what in error, because of 2‘ limitations imposed on ac$ c u r a c y by the readings 5 from t h e e q u i l i b r i u m 5 curve, the relative values are remarkably i n l i n e with theoretical expectation, as will be shown in the following discussion. VOCYI P M CfNI CUJCOOU iN DAiilNAii Consider the r e l a t i v e FIGURE 9 a m o u n t s of acetic acid and chloroform i n c o n jugate layers on a water (solvent) free basis, as plotted in Figure 9. These amounts are calculated from the equilibrium data. Arrow a points to the composition of the initial raffinate (original mixture to be extracted, on a water-free basis); arrow b points to the composition of the final raffinate. The ordinate a t b represents the composition of the extract in equilibrium with the final raffinate-in other words, the composition of the extract from the single-stage method. The ordinate a t a, on the other hand, represents the composition of the extract in equilibrium k i t h the initial raffinate; in other words, the composition of the extract from the countercurrent infinite-stage method. The ordinate a t b is greater than that a t a. This fact, of necessity, makes the amount of raffinate from the singlestage extraction greater than that from the countercurrent infinite-stage extraction, since the initial and final concentration in the raffinate and the amount of the initial raffinate are taken the same in the one a4 they are in the other method. During the process of extraction in the cocurrent infinite-stage method the composition of the extract starts with ordinate a t a and ends with ordinate a t b; the average composition finally obtained is a t some point between a and b; computation show:, that this composition is presented by c. Point c has a greater ordinate than either a or b. This means that with the cocurrent infinite-stage method a higher yield of raffinate is obtained than with either the single-stage method or the countercurrent infinite-stage method. The composition of the extract in the cocurrent multiple-stage method will be a t some point betweenbandc, approaching closer to c as the number of stages is increased. Evidently, then, the point may pass through a maximum ordinate, which means a maximum yield of raffinate. Figure 6 indicates that seven units have not been sufficient to pass this maximum. Finally, the fact that the yield of raffinate drops as the number of theoretical plates is increased in the countercurrent method of extraction, is in line with what would be expected;
’
1360
INDUSTRIAL AND ENGINEERING CHEMISTRY
for as the number of plates is increased, the composition of the extract will be nearer a, which means smaller ordinates and therefore smaller yields of raffinate. Under the conditions of the present problem, it will be noted t h a t of all the cases considered, as far as the efficiency of separation of the acid from the chloroform is concerned, the seven-stage cocurrent extraction gives the most desirable result; it yields a greater amount of raffinate than any of the other cases. On the other hand, as far as economy of solvent is concerned, the countercurrent infinite-stage extraction is the most satisfactory. The latter would also be superior, as far as efficiency of separation is concerned; i t would yield more r a f i a t e than any of the other cases if the initial raffinate, instead of being 15 per cent acid, were 5 per cent or less in acid content. Figure 9 shows this clearly and is a result of the fact t h a t the equilibrium curve passes through a maximum above a value of about 5 per cent acid in the raffinate. The importance of this equilibrium curve and of Figures 6, 7, and 8 cannot be overemphasized. Information obtained from them, together with considerations of the relative costs of solvent, of equipment, of stock to be submitted to extraction, of raffinate, of extract, and of other pertinent factors, constitute the important data on which a sound choice of the proper combination of solvent, of method, and of equipment must be based. The conditions under which reflux may be utilized have already been described. Two major points of interest, however, cannot be overestimated from the standpoint of practical applicability: (1) Through the use of proper reflux i t is possible, with a reasonable number of stages, to make separations which would otherwise be impossible even by the use of an infinite number of stages; and (2) in order to separate a constituent from a mixture, the solvent used does not necessarily have to be selectite toward that constituent, if the right type of reflux is used. Such possibilities give reflux a unique place in extraction operations. However, the fact, that these advantages may be had only a t the expense of more solvent or energy per unit charging stock and less throughput of product, must not be overlooked.
Acknowledgment This work is part of a fundamental study on extraction procesqes, supported by the Pennsylvania Grade Crude Oil Association, and is published by permission of the Graduate School of this college.
VOL. 28, NO. 11
Nomenclature Amounts and compositions are expressed on a weight basis; any consistent units of weight may be used, such as grams for amounts and grams per gram for compositions: A = weight of component toward which solvent is less selective (chloroform) C = weight of component toward which solvent is more selective (acetic acid) H = weight of heavy layer per unit time X = weight fraction of A in heavy layer x = weight fraction of C in heavy layer a: = weight fraction of B in heavy layer S = weight of extracting agent or solvent (water) L = weight of light layer per unit time E’ = weight fraction of -4in light layer q = weight fraction of C in light layer = weight fraction of B in light layer $ = total number of stages in a given system n = serial number of extraction stage or plate i = an integer = symbol for multiplication product Subscript’s: = original feed of heavy layer N = last stage where final r a f i a t e layer is produced N 1 = original feed of light layer j = final and total amounts or concentrations (for example, S.v means weight of solvent used in final stage for raffinate: Sr means total weight of solvent used in extraction system consisting of N stiges) 2, . . . n - 1, n, n 1, . . ., N = stage or plate 1, 2, . . . n - 1, n, n 1, . . . N
+
+
+
Literature Cited Cornish, R. E., et al., I N D .ENO.CHEM.,26, 397 (1934). Evans, T. W., Ibid., 26, 860 (1934). Fenske, M. R., Ibid., 24, 482 (1932). Hunter, T . G., and Nash, -4.W., J . SOC.Chem. I n d , 51, 285T (1932).
Ibid.,53, 95T (1934). Hunter, T. G., and Nash, A. TI’., World Petroleum Congr., London, 1933, Proc. 2, 340 (1933). McCabe, W. L., and Thiele, E. W., I N D .ENG.CHEX, 17, 605 (1925).
Othmer, D. F., Trans. Am. Inst. Chem. Engrs., 30, 299 (1933-
341. - _, . Riegel, E. R., “Industrial Chemistry,” 2nd ed., pp. 315-17, New York, Chemical Catalog Co., 1933. Saal, R. N. J., and Van Dyck, W. J. D., World Petroleum Congr., London, 1933, Proc. 2, 354 (1933). Wright, C. R. A,, Proc. Roy. SOC.(London), 49, 174 (1891). I b i d , 50, 375 (1892).
RECEIVEDMay 23, 1936. Submitted by K. A. Varteressian in partial fulBllment of the requirements for the Ph.D. degree in chemical engineering from The Pennsylvania State College, August, 1935.
