INDUSTRIAL AND ENGINEERING CHEMISTRY
1068
mined. I n general, their shapes and pusitions of maximum absorption indicate that carotenoids of the alpha configuration predominate. Some cis-isomers are probably present as well as a low proportion of carotenoids of the beta configuration. T o study the relative amounts of different pigments in eggs, the total carotenoids of an egg yolk extract in ether were chromatographed on a 50% magnesia-Super-Gel adsorption column and developed with ether. Relative amounts of pi ent in each zone were estimated by use of wave length 4450 Only about 5% was in the filtrate or carotene fraction, the curve of which indicated high relative absorption in the region below 4300 A. The lower brownish-yellow zone contained 45% of the original pigment, which had a curve almost identical with that of alltrans a-carotene. It was probably luteol. The next zone contained a yellow pigment (15%), the curve of which also resembled that of all-trans a-carotene. The third zone from the bottom was red and contained a pigment (15%) which had absorption properties somewhat intermediate between those characteristic of the all-trans alpha and beta configurations. -4small red zone a t the top of the rolumn was not examined. The pigments of
Vol. 36, .NO. 11
these zones were not purified further.
I n the egg studied, over
75% of the recovered pigments were of the alpha configuration. ACKNOWLEDGMENT
The writers acknowledge with appreciation the assistance of L. F. Green, R. H. Harper, and H. A. Nash in the spectroscopic phases of this work, and of E. L. Johnson with biological assays. They are grateful to the hlidstates Frozen Egg Corporation for cooperation in supplying the eggs used in this investigation, LITERATURE CITED
Hrtuge, S. M., and Zscheile, F. P., Science, 96, 536 (1942). Klose, A . A.,Jones, G. I., and Fevold, H. L., IND.ENG).CHEM.. 35, 1203 (1943).
Kuhn, R., and Smakula, A., 2.phyaiol. Chem., 197, 161 (1931). Nash, H.A., unpublished work in these laboratories, 1943. White. J. W..Jr.. Zbid.. 1942. Zscheiie, F. P., and Henry, R. L., IND.ENO.CEBIM., ANAL.ED., 14, 422 (1942).
Zscheile, F. P., Nash, H. A,, Henry, R. L., and Green, L. F.. Zbid., 16,83 (1944). JOURNALPaper 178, Purdue University Agricultural Experiment Station
BATCH RECTIFICATION Yields at Finite Reflux Ratios R. EDGEWORTH-JOHNSTONE Trinidad Leaseholds Limited, Pointe-a-Pierre, Trinidad, B. W . 1.
A general method is described for calculating yields from batch rectification of binary mixtures under constant distillate conditions for any given final reflux ratio. The method allows for the effect of column holdup. Simplified equations are derived for both binary and complex mixtures which are applicable to certain cases in which holdup is negligible.
N EARLIER paper (a) described a method of calculating the final yield of distillate from batch rectification, allowing for the effect of column holdup, when the reflux ratio is continuously increased to infinity in such a manner as to keep the distillate composition constant. This was termed “batch rectification under constant distillate” (c.d.) conditions. I n the present paper a general method is presented for cases where the final reflux ratio has a finite value. This enables a curve to be plotted showing the relation between final reflux ratio and yield fraction, the R y curve, which is important to the plant designer. Such a curve was, in effect, proposed by Bogart (Z), who carried out a number of McCabe and Thiele constructions a t different reflux ratios, keeping the distillate composition constant, and plotted reflux ratio against composition of residue. He did not, however, allow for the effect of column holdup.
A
BINARY MIXTURES WITH COLUMN HOLDUP
The previous paper (8) showed that the moles of lighter component A held up in the column is equal to Q2,where Q = total moles of the mixture held up per theoretical plate, and L: = a i
+ az + a s . . . . . +
UN
It was further shown that in the special case where the reflux ratio is infinite, 2 can be calculated from up,N , and a. Consider a batch rectification under c.d. conditions in which the final reflux ratio is only moderately high, so that the yield of
distillate is substantially lower than when the final ratio is infinite. The column is assumed to be empty a t the beginning of the operation. If it is not, its contents must be added to the charge, and the quantity and composition of the latter modified accordingly. A McCabe and Thiele construction for the desired final reflua ratio gives the final bottoms composition a,; gives the sum of the final plate-to-plate liquid compositions, al f a2 a: uN = 2; and enables QS, the total column holdup of A , to be calculated. Taking material balances a t the end of the batch rectification:
+ . .... +
P + W = F -&N m Waw = Fat - QZ
+
whence
p,Fa/-‘W ap
- a,
: - N a W &- L a, - a,
Substituting y = Pap/Fu, and &/F = q gives the required yield: .Y=
apI(n/
- a,) - Q a, (a,
(2
- a,)
- Nu,)]
(1)
By carrying out a number of computations of a, for different reflux ratios and repeating the above calculations, the complete R y curve can be drawn, showing the variation of reflux ratio with yield fraction required to maintain a given distillate composition
INDUSTRIAL A N D ENGINEERING CHEMISTRY
November, 1944
Thisis essentially Bogart’s curve ( I ) corrected for column holdup, except that residue composition is replaced by yield fraction, which is more easily observed during the course of rectification. Graphical integration of this curve gives the quantity of reflux which must be vaporized for a given yield of distillate, whence the economic limit of reflux ratio can be decided upon. TABLE I. DATAFOR R y CURVEIN RECTIFICATION OF CHLOROBENZENE AND BROWOBENZENE R ow c Y YO 4
7 12
20
0.443 0.260 0.157 0.117
8.177 7.263
(-0.~6)
O.Sl9 0.663 0.669
6.662 6.190
(-
0.196)
0.476 0.723 0.805
As an example, take the separatjon of chlorobenzene and bromobenzene, using the volatility data published by Young (4). .baume N = 10, a/ = 0.40, up 0.98, Q/F 0 q = 0.01. The Latter is a high value, taken to exaggerate the column holdup effect for purposes of illustration. For rectification a t atmospheric preasure the average value of Q is 1.8898. By carrying out several McCabe and Thiele constructions for d ~ e r e n reflux t ratios, the corresponding values of ol. are found. For each value of a, the plate-to-plate compositions a1 ot 4cr U N are read off and added together to give P. g is then calculated from Equation 1. The Calculations are summarked in Table I. For comparison with y, the yield fraction taking account of column holdup, a calculation has also been made of g,,, the yield fraction for a corresponding value of a, negleating holdup:
-
+
. . . .. +
a,(w
a,(%
- awl - au)
1069
VARIATION IN RELATIVE VOLATILITY
I n continuous distillation it is legit,imate to assume a constant average relative volat8ilityin the column. In batch rectification the value changes during distillation. Plotting a against uu from Young’s data for chlorobenzene and bromobenzene (J),and taking the arithmetic mean of the value in the still (variable) and that at the top of the column (consbant), tfhefollowing values are obtained : a,
a (average) 1.8949
0.40
1.8943 1.8894 1.8867
0.80
0.20 0.16
I n the example given above, it was found that the use of thew values in place of a constant value of 1.8896 produced a change in the R y curve that was barely visible. If, however, the change in relative volatility during distillation is large, the correct average value should be used for each value of uu. SIMPLIFIED EQUATIONS FOR BINARY MIXTURES
For columns having a relatively large number of plates (i.e., in relation to the minimum plates for the particular separation) in which holdup is negligible, simplified equations can be obtained requiring no McCabe and Thiele construction. These are derived from Underwood’s minimum reflux equation (3):
I n batch rectification under c.d. conditions the instantaneoufi reflux ratio R varies with P , the total moles of distillate received; Le., R = dO/dP. ol. is also a function of P . From material balances = SW
Fv/ - Pa, F-P
Putting P/F = p and substituting for a, R - - 1-7J (Y 1
- [-,
0,
(1
or substituting the yield fraction y
a ( 1 - up) - - p (1 - a,)
-
0,)
p (up/a/),
These equations define the manner in which reflux ratio should vary with p and y, respectively, to maintain a constant distillate composition of all in an infinite column. They can be applied with fair accuracy to finite columns in which the value of aN+I is greater than2about 5000 and holdup is negligible. The total vaporization required to secure p. moles of distillate per mole of charge, or a yield fraction of y,, can be calculated by integrating Equation 4. Putting R = d O / d P = do/dp, 04
0.4
0.6
0;s
Y
- a,) - p ( l -a,)
4 1 (1 - a / )
Figure 1. !Finall Reflux R a t i o us. Yield Fraction, without and w i t h Column Holdup, for Chlorobeneenebromobenzene 1
These results are plotted in Figure 1 . The negative value of y for R 4 shows that this reflux ratio is below the required initial value. It can, however, be used for plotting the lower end of the Ry curve and saves calculation of the initial reflux ratio. The Ry. curve corresponde to Bogart’s curve, neglecting column holdup.
1
1
dp
- ap
- a,
J
J
1010
INDUSTRIAL AND ENGINEERING CHEMISTRY
Substituting the yield fraction yr = pr (upla/),
"
a - 1 L
ap
1
-
These equations give the total moles to be vaporized per mole of charge in order to produce pr moles of distillate per mole of charge, or a yield fraction of y, under c.d. conditions. They are applicable to finite columns under the same conditions as Equations 2 and 3-namely, when a N + lis more than 5000 and holdup is negligible.
Vol. 36, No. 11
temperatures are 2.428 and 2.295, respectively. Hence the average relative volatility in the still over the whole operation is 2362, and the mean between this and the relative volatility a t the top of the column is 2.453. This is the value taken for a. To check whether the simplified equations are applicable, evaluate d ' + 1 : 2.45316 = 171,900. Evidently the column can be considered as infinite and the equations apply. The other quantities required are: a1 = 0.474; bj = 0.435; a, = 0.980; y, = 0.99. Substituting in Equation 7 and solving: u = 2.585. That is, 2.585 moles must be vaporized in the still per mole of distillate to secure the desired degree of fractionation of the product and exhaustion of the charge.
SIMPLIFIED EQUATIONS FOR COMPLEX MIXTURES
CONCLUSION
Similar equations can be derived for complex mixtures. Consider a mixture consisting of components A , B , C , etc., from which a distillate is t o be prepared containing a relatively high proportion of A , the lightest component present. A and B are the key components, and the distillate may, without serious error, be assumed to consist of these components only. Provided the components obey Raoult's law, the minimum reflux equation applies to the key components as if they constituted a binary mixturethat is,
The methods presented in this and the previous paper ( d ) rest upon the observation that under constant distillate conditions the equations for batch rectification are very much simplified. Since these are also the conditions for minimum heat input per pound of distillate (for a given final reflux ratio), they represent the most economical procedure as well. For binary mixtures and for complex mixtures, the distillate from which is required to contain a high proportion of the lightest component, a sensitive overhead temperature controller combined with a constant boil-up rate should automatically give the proper R y curve. ACKNOWLEDGMENT
From material balances,
The author wishes to acknowledge valuable criticism from Arthur Rose and to thank the Chairman and Board of Trinidad Leaseholds Limited for permission to publish this paper.
Putting bp = 1 - a, and P/F = p , substituting for aw and bv, and integrating as for binary mixtures,
- aP - ar a - 1
[
l
n
e
p+
a In
b/
b/
- P r (1 1 - up
I
- a,
1
- UP)
(6)
or putting y, = p , (up/af),
J
The above equations are applicable to complex mixtures only when the more volatile of the key components is the lightest material present. They cannot, for example, be applied to petroleum distillation where the distillate has a relatively wide boiling range. As an example of the use of these simplified methods, consider the rectification of a commercial mixture containing the following mole percentages of components: benzene, 47.4; toluene, 43.5; xylenes, 9.1. It is desired to extract 99% of the total benzene in the charge by batch rectification, and the distillate is required to contain 98.0 mole YQof benzene. The column to be used has fifteen theoretical plates. Holdup is negligible. A constant boilup rate will be maintained in the still, and the overhead temperature will be held constant, automatically or otherwise, by continuously increasing the reflux ratio as distillation proceeds. In order to calculate the heat input per gallon of product, and hence the duration and cost of the operation, it is desired to know the total moles which must be vaporized in the still per mole of distillate to secure the desired degree of exhaustion of the bottoms. The temperature at the top of the column will be 80" C. throughout, and the relative volatility of benzene and toluene at this temperature is 2.545. The temperature in the still is estimated 89 96" C. a t the beginning of distillation, 118" C. at the end. The relative volatilities of benzene and toluene a t these
NOMENCLATURE
The nomenclature used is based upon that of Underwood (S), which has certain advantages over the usual x-y system, et+ pecially when applied to complex mixtures. a stands for ,the mole fraction of the most volatile component in the liquid, A for the mole fraction in the vapor. Similarly, b and B refer to the next most volatile component, and so on-for example, a,, b,, Cn+l instead of zaf,X b p , yc,n -I-1. Double subscripts are avoided and the symbols are easier to read. I n the present paper the vapor composition symbols are not required, and capital letters are used to refer to components.
A , B, C, a(, a,, a,
= components in order of decreasing volatility = mole fraction of component A in charge, distillate,
b,,. b,
= mole fraction of component B in charge ,distillate
bf, .
F 0, P , W
N' 0.
P, q
and bottoms, respectively
and bottoms, respectively total moles of charge, reflux, distillate, and bottoms = number of theoretical plates in column =
= OlF, P l F , QlF = final value of p at end of batch rectification = moles of material held up in column per theoretical
plate
reflux ratio = dO/dP moles of distillate obtained divided by moles present in the charge. = theoretical yield fraction corresponding to y, neglecting holdup = value of y corresponding to pr = average relative volatility of components A and B-i.e., arithmetic mean of values in still and top of column throughout distillation , = sum of plate-to-plate liquid compositions, a1 as f a3 . , a.v = instantaneous
= yield fraction-Le.,
.. .. +
+
LITERATURE CITED
Bogart, M. J. B., Trans. Am. Inst. Chem. Engrs., 33, 139 (1937). EdgeworthJohnstone, R.,IND.EN^. CHEM.,35,407 (1943). Underwood, A. J. V . , Trans. Inst. C h a . Engrs. (London), 10,118 (1932).
Young, S., Trans. Chem. SOC.,81, 768 (1902): "Distillation Principles and Processes", p. 44 (1922).
