ABSORPTION AND
EXTRACTION
S Y M POSlUM Held under the auspices of the Division of Industrial a n d Engineering Chemigtry of the American Chemical Society a t Columbia University, New York, N. Y., December 28 and 29, 1936.
Graphical Design Methods Applied to the Fractional Extraction of Methylcyclohexane and n-Heptane Mixtures
The System
MethylcyclohexaneAni1jne-n-Heptane
K. A. VARTERESSIAN AND M. R. FENSKE The Pennsylvania State College, State College, Pa.
B
phase data a t atmospheric pressure and 25 * 0.05" C. were obtained in this laboratory (8) using aniline as solvent. Reasonable precautions were used to work with pure substances. The methylcyclohexane was obtained from the Rohm &
ECAUSE of the increasing importance of liquid-liquid extraction and the fact that the fundamental principles involved are very similar to if not identical with those of distillation, it i s desirable to compare these two operations when they are applied to the same problem. This paper presents a comparison of fractional extraction and fractional distillation as applied to the separation of a definite binary mixture consisting of n-heptane and methylcyclohexane. Methods are presented for calculating fractional extraction problems where the concept of "reflux" is utilized to obtain sharper separation.
The phase diagram at 25" C. and 1 atmosphere pressure is obtained for the methylcyclohexane-aniline-nsystem heptane. In this system aniline is the solvent in which methylcyclohexane is more soluble than n-heptane; it is possible to separate these two h$drocarbons using fractional extraction with aniline as the solvent. Since mixtures of the two follow Raoult's law, it is also possible t o effect their separation by fractional distillation and thus compare the separation with that obtained by fractional extraction processes. For the case of extraction, the equilibrium data can be ex-
Saturation and Equilibrium Data Vapor-liquid equilibrium data (at constant pressure in the case of distillation) and solvent phase-hydrocarbon phase equilibrium data (at constant pressure and temperature in the case of extraction) are naturally the starting points for computations applied to these two operations as they are commonly employed in practice. Experimental values of vapor-liquid data a t atmospheric pressure for n-heptane and methylcyclohexane are available (X), and it is found (1) that these two hydrocarbons follow Raoult's law at all concentrations with a value of 1.07 for a. The experimental values of solvent phase-hydrocarbon 270
MARCH, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
Haas Company of Philadelphia and was further purified by fractionation in a 35-theoretical-plate glass column using 20 to 1 reflux ratio. The material used had the following con= 100.fjjOC., di0 = 0.7691, and na2 = stants: b. 1.4233. The n-heptane was obtained in a pure stfatefrom the California Chemical Company, Newark, Calif. ; the properties as determined by the Bureau of Standards were given as b. P.,~,, = 98.4" C . , dto = 0.6835, and nz2 = 1.3878. The aniline was obtained from the General Chemical Company of Philadelphia, Pa., and was purified by several redistillations. After purification it had the following properties: di0 = 1.0215 and n2: =1.5858.
.
THE SYSTEM METHYLCYCLOHEXANE HEPTANE ANILINE AT 250 'c AND I ATM.
-
271
refractive indices obtained are plotted against per cent methylcyclohexane in Figure 2. With this set of data, the equilibrium compositions, presented by the tie lines in Figure 1, were obtained as follows: Mixtures of the three components were prepared in such proportions as to separate into approximately equal amounts of the two phases. These were kept in a constant-temperature bath at 25.0"C. for a t least 24 hours, with hourly agitation. From the refractive indices of the separated phases their compositions were determined. The accuracy of this process was checked by several points, where the total composition of the two phases combined was known, by seeing if the tie lines determined as described above passed through the points of total composition. The agreement was good in all cases. The saturation, refractive index, and equilibrium data are presented in Table I.
M
TABLE I.
--
SATURATION 4ND EQUILIBRIUM
-
DATA
-
Solvent Layer -Hydrocarbon Layer --Wt. %Refractive --Wt. %Refractlve Me-cycloindex, Me-cycloindex, hexane n-Heptane ng hexane n-Heptane Saturation Compositions 0 0 92.6 1.3948 0.0 6 2 1 5660 16 6 75.4 1.4012 3.1 4.6 1.5630 20 2 71 8 1.4024 9.9 2 8 1 5555 33 0 58.5 1.4075 12.9 1.6 1 5522 39 2 52.2 1.4105 16.9 0.0 1 5477 48 2 42.7 1.4148 56 5 34.1 1.4185 62 5 27.7 1.4215 73 1 16.2 1.4266 75.7 13.4 1.4278 88.1 0.0 1.4358
nc
M&THYLCYCLOHEXANE
n-HEPTANE
FIGURE 1
Aniline was added to the point of turbidity, at 25.0" C., to mixtures of n-heptane and methylcyclohexane of known compositions and weights. From the weights of aniline added, the compositions of the saturated hydrocarbon layers were determined. The refractive indices of these mixtures were obtained a t the same temperature. Next, mixtures of ,n-heptane and methylcyclohexane of known compositions were added to known weights of aniline, again just to the point of separation of the second liquid phase. From the weights of n-heptane and methylcyclohexane added, the compositions of the saturated solvent layers were determined. The refractive indices of these mixtures were also obtained. The saturation compositions for both phases (hydrocarbons saturated with aniline, and aniline saturated .with hydrocarbons) thus determined are presented in Figure 1; the
.
pressed as a simple equation. Although the simple distribution law does not hold, the ratio of the two distribution coefficients is a constant and this concept is the same as that used in distillation involving the ratio of the two vapor pressures. Relationships are derived for the case of minimum reflux ratio and minimum number of theoretical plates in the extraction process, and graphical means are presented for calculating the intermediate cases. As a definite problem the separation of a 50 weight per cent mixture of n-heptane and methylcyclohexane is considered.
0 0 9.2 18 6 22 0 33 8 40 9 46.0 59 7 67.2 71.6 73 6 83 3 88 1
92.6 83.1 73 4 69.8 57.6 50 4 45.0 30 7 22.8 18.2 16.0 5.4 0.0
Equilibrium Compositions 1.3948 0.0 1.3982 0 8 1.4020 2.7 1.4034 3 0 1.4084 4.6 6 0 1.4115 1.4138 7.4 9.2 1.4201 1.4237 11 3 1.4259 0 12 7 1.4270 13 1 1.4325 15.6 1.4358 16.9
6 2 6.0 5.3 51 4 5 4 0 3.6 2 8 2 1 16 1.4 0 6 0.0
1.5660 1.5651 1,5632 1.5630 1.5612 1.5598 1.5583 1.5564 1.5540 1.5524 1.5520 1.5491 1.5477
Mathematical Relations in Saturation and Equilibrium Data An examination of the exgerimental data reveals several useful relations. First, it is found that the ratio of methylcyclohexane to heptane in one liquid Phase is Proportional to that in the other liquid phase in equilibrium with it:
&= Yh
2m
Pg
where 6 (a constant) = 1.90
The value of p is an average for all the equilibrium points given in Table I (with the exception of the first two and last two points), and has a minimum value of 1.7 and a maximum value of 2.0 for the entire range of compositions. If the solvent (aniline) were removed from the phases in equilibrium with each other, Equation 1 would still hold with the same numerical value of /3:
Figure 3 gives the equilibrium curve on a solvent-free basis. By employing extraction with aniline as a solvent in place of distillation to effect the separation, there has resulted a r e
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272
VOL. 29, NO. 3
THE SYSTEM METHYLCYCLOHE~ANE-AN/L/NE-HEP~~E ATZXOtANDlATM. t ,
1.4180-
!.
.
HYDROCARBON LAYER
14020
/39#.
and the other symbols have their previous meanings. The physical significance of the constants in these equations is obvious. These relations give a complete mathematical definition to the system because, as long as saturated phases are concerned, fixing the composition of any one of the components in any one of the liquid phases will numerically define the compositions of all the rest of the components in the same and the other liquid phases, under equilibrium conditions,
f4
/O
8
The Problem
6
4 0
EXPERIMENTAL
PJINTS
I
I
+ po/NTS CALCULATED 6YMEANS W&UATfO#
/ooX,,,, &R
&
30 f& 7'0 tI0 $0 /dO CENT ~ETmLCYCLOHEXANEIN UPPER &AS€ (Hydrocarbon mase 1
FIGURE4
versa1 of the relative compositions of the two hydrocarbon phases, with a value of 1.90 in place of 1.07 as the measure of ease of separation. Secondly, it is found that the composition of either one of the hydrocarbons in the solvent layer is a definite function of its composition in the hydrocarbon layer in equilibrium with it:
(4)
where am = 0.127, bm = -0.374,
ah =
0.100, bh = 0.536
Figures 4 and 5 show these relations. Finally, i t is found that there is a linear relation between the composition of methylcyclohexaneand that of n-heptane, in either one of the two liquid phases, as is evident from Figure 6: Xh
= ~ H X ,-t- b H
(5)
ms!h -k bs
(6)
Yh =
where
'8
-1.043, bx = 0.926 ms = -0.367, bs = 0.062
T ? ~ X=
Having the vapor-liquid and solvent phase-hydrocarbon phase equilibrium data, the separation of a given mixture by means of each of the two operations of distillation and extraction may be compared. As a definite problem it is proposed to separate a 50 weight per cent mixture of n-heptane and methylcyclohexane into one product containing 90 weight per cent n-heptane and another product containing 90 weight per cent methylcyclohexane. These are to be separated continuously employing fractional distillation or fractional extraction, a t the rate of 100 pounds feed an hour. How would the conditions for their separation (such as heat and solvent required, number of perfect plates, reflux ratio, height of tower, diameter of tower, and point of feed in tower) compare in extraction with those in distillation? With the help of the vapor-liquid data, in conjunction with experimental data for H. E. T. P. (height equivalent to theoretical plate) and for allowable throughput, as well as latent heat values for these hydrocarbons, it is simple to ascertain the conditions for the case of distillation. Therefore, in what follows, only the exactly analogous case of extraction will be presented in any detail. For simplicity, just as it is customary
,
AKD FINAL AMOUNTS AND COMPOSITIONS OF MATERIAL TABLE11. INITIAL AS SPECIFIED BY THE PROBLEM AND DICTATED BY SATURATION VALUESAND MATERIAL BALANCES
No. Item 1 Mixt. to be sewrated 2 Extract prod& 3 Raffinate roduot 4 No. 1 s a d with solvent 5 No. 2 satd. with solvent 6 No. 3 aatd. with solvent 7 Solvent satd. with No. 2 S Solvent aatd. with No. 3
--Amount, Lb.-Mecyolo- Hephexane tane Aniline Total 50 45 5 50 46 5 45 5
50 ~5 4550 5 45 5 45
.... ....
100 50 50 9 . 6 5 ~ 109.65 56.18 6.18 54.22 4.22 345 295 708 758
....
-Compn., Wt. %MecyoloHephexane tane Aniline 50 90 10 45.6 80.0 9.22 13.0 0.66
50 10 90 45.6 8.9 83.0 1.47 5.94
... ...
8.8 11.1 7.78 85.53 93.4
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INDUSTRIAL AND ENGINEERING CHEMISTRY
to deal with feed, distillate, and bottoms a t their boiling points in distillation, so in this case of extraction it is considered that the feed, extract, and raffinate are a t their points of saturation with the solvent. Table I1 gives initial and final amounts and compositions on the basis of material balances and saturation values.
273
and for the exhausting section,
For minimum refl ux:
3 8
$
a
I n distillation the equation corresponding to Equation 9 is also derived for overflow a t the feed, although overflow at the condenser is used on account of equality of overflow throughout the column. This qualification must, however, be recognized in extraction. Applying the data in Table I1 to Equations 7, 8, and 9, respectively :
7
g
6
b5
32 C Q
@ 4
$43 k $
0.456
0.800.
0.089
2
= 1‘90N 0.456
0.456 1.90M 0.0922 0.456 = 0.830 /OOXA,WEIGHT PER CENT n-H€PTANE IN UPPER PHASE (Hydrocarbon Phase)
FIGURE 5
Minimum Reflux and Minimum Number of Perfect Plates For the specified separation there will be necessary a minimum reflux (corresponding to an infinite number of perfect plates available) below which, no matter how tall an extraction column may be, the required separation will not be possible. This minimum reflux ratio is a measure of the amount of solvent that is needed for the desired separation; it should not be identified with the theoretioal minimum amount of solvent; the latter may be obtained by a simple material balance, using the initial composition of the feed, and the final compositions of hydrocarbon layer and of solvent layer, but does not specify any mechanism of separation. On the other hand, for the required separation there will be necessary a minimum number of theoretical plates (corresponding to an infinite reflux) below which, no matter how much solvent is used, separation will be impossible. This minimum number of theoretical plates will be a measure of the minimum height of tower that could be employed and still obtain the specified separation. However, throughput will be nil. Any actual operating conditions will lie between these two limits; therefore it is useful to know these limits, especially since they may often be easily obtained. I n a previous paper (12) an equation was derived for determining the allowable minimum number of plates for any given separation, when working with mixtures in which the compositions of the substances to be separated in one liquid phase are proportional to those in the other liquid phase at equilibrium. It is, of course, the constancy of fl that is really necessary, rather than the proportionality of compositions; the former makes the applicability of the equation more general. Following a similar method of derivation as for the case of distillation (4),an equation may also be derived for determining the allowable minimum reflux ratio, when /3 is constant. For the case of extraction, therefore, the following equations are applicable, whenever ,B is constant. For total reflux, we have, for the enriching section:
(7)
These give N = 3.4, M = 3.4 (a total of 6.8 plates), and (Of /P6)dn. = 1.52. The corresponding values obtained graphically, without the assumption of constancy of p, are N = 3.2, M = 3.8 (a total of 7.0 plates), and (O,/P&,. = 1.50. Finally, it is evident that the ratio of the number of theoretical plates required in distillation to that required in extraction is equal to the ratio of the logarithm of p to that of a; in this particular case this ratio is 9.5 to 1.
Graphical Methods of Solution Whether mathematical relations for saturation and equilibrium values be available or not, graphical methods of solution are very convenient (3, 6, 10, 12).
! ‘Z
Em
3 m AT 25.0“c AND I ATM
PER CENT HEPTANE V.5,
IN SATURATED PHASES (merimento1 Vafuss) 0
Ly) 30 40 50 60 70 80 90 lOOx,, WEIWT PERGENTMETHYLCYUOHEXANE
IO
IN SATURATED PHASE
FIGURE 6
Saal and Van Dyck (9) introduced the concept of reflux in extraction and briefly indicated a method of graphical solution. The following is an amplification of their method and a graphical solution that is strictly comparable to that commonly used in distillation. For clarity the two limiting cases will fist be presented, followed by the more practical case of intermediate operating conditions.
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274
M m m u ~ iREFLUX. Consider the enriching section of the column in Figure 7 . At the cross section just below the feed plate there flows up a hydrocarbon layer, Of, that has practically the same composition, f, as the feed, while there flows down a solvent layer, V,+ of composition f 6 that is in equilibrium with the feed. At the bottom cross section of the column there flows down a terminal solvent layer, V,), the composition of which is represented by e', while there flows up the reflux, O., which is the hydrocarbon layer resulting from the removal of enough solvent from t h e terminal solvent layer to change the latter to a saturated hydroc a r b o n l a y e r ; the composition of t h i s H E r e f l u x i s given b y point e. All interFIQTJRE 7 mediate compositions in the solvent layer lie on the line e l f e , while all intermediate compositions in the hydrocarbon layer lie on the line ef. The problem arises as to what the composition of the solvent layer is a t any cross section of the column for a given composition of the hydrocarbon layer a t the same cross section; in other words, what are the operating line points? To answer this, consider the following : Continuity of operation and material balance dictate that the gain in material of one phase in passing through any section must be equal to the loss in material of the other phase passing in an opposite direction through the same section. This applies to the individual components as well as to the total net material transferred from one phase to the other. Therefore, the net flow in a given direction a t any cross section is a definite quantity of material of definite composition, and is the same for all cross sections. Specifically, the amount of net flow in a downward direction a t the bottom cross section of the column is represented by the difference between the quantity of terminal solvent layer, Ve,,and the quantity of reflux, 0,; its composition is fixed by the magnitude of 0, relative to Vej. (Evidently, the amount and composition of this net downward flow are iden&$
16
3 8
15
h
4
x
8
VOL. 29, NO. 3
tical to those obtained for the mixture obtained by adding the extract product, Pelto the solvent removed, S , as a material balance around the separator shows.) At the cross section just below the feed, the amount of net flow in a downwai-d direction is represented by the difference between the quantity of solvent layer, T7f-1, and the quantity of hydrocarbon laver. 0,. and its composition is fixed by :he magnitude of Of relative to V&. However, in the light of the discussion of the previous paragraph, the net downward flow here must be the same in amount and in composition as that a t the bottom cross section of the column. Now, it is a property of the triangular diagram that the composition resulting from the addition or subtraction of a mixture to or from another mixture will lie on the straight line passing through the two points representI \ \ F R H ing the compositions of the mixtures. Evidentlv, then, the composition of the net downward flow will be given graphically by the intersection, a, of the straight line joining e to e' with the straight line joining f to fe. On the other hand, the amount of this net downward flow is simply S P,,as a material balance around the separator indicates. Having ascertained the amount and composition of this net downward flow, it is a simple matter to obtain the operating line points and the reflux ratio. To obtain the operating line points, straight lines are drawn joining points between e and f on the saturation curve for the hydrocarbon layer with the "operating point," a, and reading the intersection of each line on the saturation curve for the solvent layer. The operating curve (Figure 8) for the section below the feed is thus obtained. Compositions in terms of per cent methylcyclohexane in the saturated phases have been read in this particular instance, although per cent heptane might just as well have been used, provided the equilibrium curve for heptane were employed. I n order to obtain the reflux ratio the properties of the triangular plot may be utilized as follows. From a material balance around the separator there results :
+
=
A.
+ Pe f 0,
14 13
3 I
/O 20 30 40 50 60 70 80 fOoX,,WEfGHT PER CENT bfETHYLCYCLOHEXANE IN HYOROCAR0ON PHASE
' 0
FIGURE8
' 0
IO
/oO%,,
20 30 40 50 60 70 WIGHT B R CENT ME T"YlCYCLOH€XAffE fN HYDROCARBON PHASE
FIQURE9
(10)
-
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INDUSTRIAL AND ENGINEERlNG CHEMISTRY
275
The reflux for this section is determined in a similar way, and the following expressions are derived:
fOOx,,,, WEIGHTf k CENT~~ETHYLCYCLOHEXANE ~ IN #DROCAR6ON
PHASE
FIGURE10
and the composition of S and P. combined is given by operating point a. Therefore, from the triangular plot i t follows that: [S
+ P e ] / O c= ( e e ’ ) / ( a e ’ ) ,and (ae’) + (ee’) = (ne)
Again, O/V and O/P values for intermediate cross sections may be determined if desired by means of the corresponding geometrical relations for the intermediate lines passing through operating point b. These relations fix the relative amounts of all pertinent quantities. TOTAL REFLUX. For this case, operating point a for the enriching section and operating point b for the exhausting section will coincide and will become point A , since the composition of the net downward flow for both sections of the column will be that of the solvent. I n addition, it is evident that at any cross section the hydrocarbon flowing in one direction will be the same in amount and in composition aa the hydrocai-bon flowing in the opposite direction. Thus,
‘Quantities in parentheses indicate distances between points on the triangular plot of Figure 7. Substituting these in Equation 10 and solving for O,/V. , gives:
REFLUX RATIO
(9)vs
THEORETICAL PL AYES
Since it is customary to define reflux ratio as O,/P, rather than O,/V,t, it is desirable .also to obtain an expression for the former. This may easily be done when we consider that S/Pa = (ea)/(aA). Combining this with the other geometrical relations given above:
If the overflow and solvent layer a t the feed Of and V,-,, respectively, rather than a t the extract end of the column be desired, by a method similar to the above it is found that: ‘6
7
8
9
10
/f
NUMeER OF fiEORETItAL
12
’
PLATES
FIGURE11 It is evident that for intermediate cross sections, O/V and O / P values may be obtained, if desired, by means of the corresponding geometrical relations for the intermediate lines passing through operating point a. For the exhausting section of the column, similar treatment yields the “operating point,” b, which is the intersection of the straight line joining r’ to r with the straight line joining f to fa. The reason why this point lies outside the triangle is due to the fact that, although the total net amount of downward flow is positive, the net downward flow of methylcyclohexane and of heptane are negative, which necessitates negative compositions for these substances. Point b may be used, similarly to a, to obtain operating line points for the exhausting section by drawing straight lines joining points on the saturation curve between f and r and point b, and reading the point of intersection of each line with the saturation curve for the solvent layer. The operating curve (Figure 8) for the section above the feed is thus obtained, expressed as per cent methylcyclohexane.
with the specified feed composition, the solvent layer a t the feed cross section will have the composition f’, which is the intersection of a straight line joining f to A with the saturation curve for the solvent layer. Whatever was said in connection with the case of minimum reflux applies also to the case of total reflux when operating point A is substituted for operating points a and b; in other words, when line fA replaces line fab. The data obtained are represented in Figure 9. INTERMEDIATE OPERATINGCASES. It is clear that for cases of practical operating conditions the solvent layer at the cross section of the feed will have st composition, y, somewhere between fa (composition of solvent layer in equilibrium with the feed-case of minimum reflux) and f’ (composition of solvent layer which on a solvent-free basis has the same composition as the feed-case of total reflux). This moves point a up towards A on the line aA,and moves point b down towards A on the line bA. Naturally, the geometrical relationships for O / V , O/P, etc., still remain the same in form but change in value.
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276
For instance, in order to determine the case with a reflux ratio of say 5 , such an operating point, a‘, is chosen on line uA so that (ale’) (eA)/(ee’) (a’A) = 5. A straight line is then drawn joining a‘ and f, the intersection of which with line bA gives the operating point b’ for the exhausting section of the column. A system of straight lines is then drawn passing through point a’ and another system of straight lines passing through point b’. Where each individual line cuts the saturation curves, the per cent methylcyclohexane is read
. 2-
VOL. 29, NO. 3
terial has, however, been considered for both extraction and distillation. The observations were made on a tower about one inch in diameter; the question of channeling or loss in efficiency in larger diameter extraction and distillation columns has not been considered because no data are available. It should be remembered that there is a relatively large amount of solvent phase to be circulated in the case of extraction, since this is analogous to the vapor flow in distillation; despite the dense character of a liquid phase compared to that of a vapor, the amount of hydrocarbon carried by the aniline in a unit time is not exceedingly large because of its low concentration in the aniline phase. I n estimating the heat requirement, it was assumed to be unnecessary to vaporize any aniline in view of its relatively high boiling point in comparison with those of the hydrocaxbons. It is realized that the problem is more than one of simple evaporation but, even if allowances are made for this, it appears that the energy requirement in the case of fractional extraction is still considerably less than in the case of fractional distillation. Instead of evaporating the hydrocarbons from the aniline, other means of separation might be used such as cooling, or the addition of a third substance to cause separation, but these have not been considered here.
Consideration of Multicomponent Systems I n dealing with liquid-liquid extraction in systems of any number of components, we must carefully consider the limiFIGURE12 tations imposed and the possibilities offered by the phase rule. A complete treatment of such systems will not be for each phase, which represents a point on the operating attempted a t present. I n order to indicate, however, the curve. With a reasonable number of such points the shape applicability of the equations developed in a previous paper of the operating curve will be determined, thus enabling ( l a ) as well as in this paper, t o the solution of extraction us to ascertain the number of theoretical plates both below problems involving more than three components, a few reand above the feed. The data for this particular case are marks are necessary. plotted in Figure 10. It should be remembered that in the derivations of the The variation of reflux ratio with the total number of basic equations ( l a ) no assumptions were made as to the theoretical plates necessary for the specified separation is number of components in the system, so that they are quite presented in Figure 11; the corresponding values for distillageneral. However, the path which is taken by each of the tion are given in Figure 12. extraction methods between the initial and final states must be definitely known before a numerical solution is possible. Comparative Data I n other words, the extra degrees of freedom introduced by additional components must be balanced by extra indeTable 111 compares the separation of n-heptane-methylpendent relations between the variables entering the problem. cyclohexane mixtures by distillation and extraction. It is The simple distribution hypothesis offers the most elementary clearly recognized that there is a scarcity of data on the form of such relationships; however, the constancy of fl is efficiency of extraction towers and allowable throughputs. sufficient. The data used here are based on a few experimental observaFor instance if, in the presence of other hydrocarbons, a tions and they should not be considered to be optimum or constant B were found for methvlcvclohexane and heDtane. ultimate or even average results. The same packing maas far as the Separation of these two is con: cerned, Equations 7, 8, and 9 could be used as TABLE111. SEPARATION” OF 12-HBPTANE-METHYLCYCLOIIEXANE they are. I n addition, the basic equation developed ( l a ) for the cocurrent infinite-stage MIXTURES method (the well-known Soxhlet method, in which Conditions of Conditions of Min. Reflux Intermediate Case Total Reflux the amount of solvent phase a t any time in conExtn. Distn. Extn. Distn. Extn. Distn. tact with the hydrocarbon phase is kept exHeat required, B. t. u./hr.b 31,500 164,500 58,200 418,000 m m Solvent lb./hr. 1,045 . ... 2,175 .. . . m .. tremely small) reduces to:
NO. per!ect plates m m 10 95 7 65 42.5 17.6 32.5 m m 25 Height of tower ft 0 OD 2 . 2 2 . 3 m 1.4 1.4 Diam. of tpwer,’ft.h 6.5 60 m m 2.6 23 Reflux ratio, 0dP1 0 Problem: to separate 100 Ib. per hour of a 50-50 n-heptane-methylcyclohexsne mixture into a product of 90 weight % heptane and a residue of 90 weight % methylcyclohexane by extraction and distillation. 6 Only latent heats of the hydrocarbons are considered since it was assumed that sensible heat may be obtained through heat exchange. .4 value bf 137 B. t. u: per Ib. as the latent heat of the hydrocarborn was used. Since aniline IS much higher boilin$ than the hydrocarbons, i t was assumed that evaporation of the hydrocarbons from the amline wassufficient for seoaration. the aniline beinv aesurned to be nonvolatile. 0 prom experimental data (I?) a value of 2.5 ft. per perfect plate was used in extraction. B value of 0.5 ft. per perfeot plate was used in distillation ( 6 ) . The packing material used in both cases was considered t o be one-turn helices, 0.16 in. in diameter, made from No. 26 B. & 6. gage wire. d A superficial vapor velocity in distillation of 1 ft. per second was used. This oorreIn extrrlction a value of 98 Ib. of hydrocarbon sponds t o 735 Ib. of vapor per sq. ft. in solvent per sq. ft. per hr. was u s e based r hr on experimental observation.
.
This equation is analogous to the Rayleigh equation for simple distillation where Raoult’s law applies. It may be put in other useful forms, such as
Equation 16 states that the fraction of methylcyclohexane remaining unextracted is equal t o that of heptane raised to a power equal to p.
MARCH, 1937
INDUSTRIAL AND ENGINEERING CHEMISTRY
Finally, in connection with Equations 7, 8, 9, and 15, it is important to note that all compositions are those of solventsaturated hydrocarbon phases. Compositions on a solventfree basis could, however, be used in all of these equations, if the percentage of solvent in the various hydrocarbon layers remained constant; with Equations 7 and 8 solventfree compositions could be used whether the various hydrocarbon layers had the same percentage of solvent content or not.
Physical Significance of Beta On the basis of Dalton’s law for the vapor phase and Raoult’s law for the liquid phase, it may be shown (13) that a in distillation is the ratio of the vapor pressure of the more volatile substance to that of the less volatile substance, in their pure states a t the same temperature. If, now, it is assumed that in the solvent phase the total osmotic pressure due to the hydrocarbons is the sum of those due to each hydrocarbon individually, and that the osmotic pressure due to each hydrocarbon is proportional to its mole fraction on a solvent-free basis, the proportionality constant being the same for both hydrocarbons, there results the equivalent of Dalton’s law. The equivalent of Raoult’s law would be to assume that in the solvent phase, when the latter is in equilibrium with the hydrocarbon phase, the osrnotic pressure due to each hydrocarbon is proportional to its mole fraction on a solvent-free basis in the hydrocarbon phase; the proportionality constant is the osmotic pressure when each hydrocarbon alone is present in the hydrocarbon phase saturated with the solvent. If these assumptions be valid, p in extraction would then have a value of ( T O ) ~ / ( T O ) , , . Osmotic pressure does not lend itself to as easy measurement as vapor pressure. However, it can be calculated from the following expression based on Raoult’s law and the perfect gas equation (7) :
= same as x,,,, on a solvent-free basis 1 - x = same as ZJ,, on a solvent-free basis
x
?r
where
V
2’
(17)
T = osmotic pressure at absolute temperature, T R = gasconstant V = volume of 1 mole of solvent x’ = mole fraction of solvent in solution
Calculating from the data for the case of each hydrocarbon saturated with aniline, and dividing the osmotic pressures so determined as to obtain their ratio, it is found that this ratio is 1.86, in good agreement with the experimental value of 1.9. It may be remarked that although Raoult’s law may not hold exactly for the hydrocarbons in the solutions where aniline is the solute, it is probable that the deviation of each hydrocarbon from this law is of such order as to result in the equivalent of this law being valid.
Acknowledgment Acknowledgment is due A. R. Esterly and G. A. Ruff for the experimental data on the hydrocarbon-aniline system.
Nomenclature weight fraction methylcyclohexane in solvent phase weight fraction n-heptane in solvent phase weight fraction methylcyclohexane in hydrocarbon phase = weight fraction n-heptane in hydrocarbon phase xh B = relative distribution coefficient y = same as ym, on a solvent-free basis . 1- y = same as u),, on a solvent-free basis y,
y~
x,,,
= = =
~~
N
= number of theoretical plates in enriching section (including feed plate, excluding separator) M = number of theoretical plates in exhausting section (excluding feed plate and mixer) 0, = weight of overflow (hydrocarbon phase) to the feed section, per unit, time P, = weight of extract product (saturated with solvent), per unit time Vf-1 = weight of overflow (solvent phase) from the feed section, per unit time f = composition of feed f. = composition of solvent phase in equilibrium with feed V,’ = weight of solvent phase to separator per unit time e’ A composition of solvent phase to separator 0, = weight of hydrocarbon phase reflux per unit time e = composition of hydrocarbon phase reflux so = solvent fed to mixer per unit time s = solvent removed from separator per unit time a = operating point for enriching section (case of minimum reflux) b = operating point for exhausting- section (case of minimum refluxj r = composition of hydrocarbon phase to mixer r‘ = composition of solvent-phase reflux 0, = weight of terminal hydrocarbon phase per unit time V,! = weight of solvent-phase reflux er unit time P, = weight of raffinate product gaturated with solvent) per unit time A = operatin point for both enriching and exhausting sections &me of total reflux) f’ = composition of solvent phase which differs from the feed only in its solvent content u‘ = operating point for enriching section (intermediate case) b‘ = operating point for exhausting section (intermediate caw)
weigh2 of original hydrocarbon phase (saturated with solvent) = weight of final hydrocarbon phase (saturated with solvent) = weight of methylcyclohexane in original hydrocarbon - phase = weight of methyloyclohexane in final hydrocarbon phase = weight of heptane in original hydrocarbon phase = weight of heptane in final hydrocarbon phase = osmotic pressure due to more soluble solute when it alone saturates the solvent = osmotic pressure due to less soluble solute when it alone saturates the solvent =
I
ml ho ht (?r&
RT 1 = -1n-
271
(m)h
Subscripts : P. = extract product (saturated with solvent) f = feed (saturated with solvent) P, = raffinate product (saturated with solvent) 0 = original material before extraction 1 = final material after extraction
Literature Cited (1) Beatty, H. A., and Calingaert, G . , IND.EKG.CHEM.,26, 504 (1934). (2) Bromily, E . C., and Quiggle, D., Ibid., 25, 1136 (1933). (3) Evans, T. W., Ibid., 26, 860 (1934). (4) Fenske, M. R., Ibid., 24,483 (1932). (5) Fenske, M. R., Tongberg, C. O., Quiggle, D., and Cryder, D. S., Ibid., 28, 644 (1936). (6) Hunter, T . G., and Nash, A. W., J. SOC.Chem. I n d . , 53, 95T (1934). (7) Noyes, A. A., and Sherrill, M. S., “Chemical Principles,” p , 86, New York, Maomillan Co., 1934. (8) Ruff, G. A., and Esterly, A. R., undergraduate thesis, Pa. State College, 1936. (9) Saal, R. N. J., and Van Dyck, W. J. D., Proc. World Petroleum Congress, London, 1933,2,352. (10) Thiele, E. W., IND.ENG.. CHEM.,27, 392 (1935). (11) Varteressian, K. A., and Fenske, M. R . , IND. ENG.CHEM.,28, 928 (1936). (12) Ibid., 28, 1353 (1936). (13) Walker, W. H., Lewis, W. K.. and McAdams. W. H.. “Principles of Chemical Engineering,” 2nd ed., Chap. XVII, New York, McGraw-Hill Book Co., 1927. RECEIVED December 3, 1936.
