October 1950
INDUSTRIAL AND ENGINEERING CHEMISTRY
(12)Gallo, G., and Correlli, R., Atti congr. naz. h i m . pura applicata, 1923,257. (13)Gomez, A. V., Ion, 2,197-205 (1942). (14)Grun, A., and Wirth, T., Ber., 53B,1301-12 (1920). (15) Inouye, M., J. C h m . SOC.Japan, 42,1065-72 (1921). (16)Ito, C., and Sato, M., J. SOC.C h m . Ind. Japan, 30, 262-60 (1927). (17)Kobayaahi, K., J . Chm. I n d . (Japan),24,1-26 (1921). (18)Ibid., pp. 1421-4. (19) Kobayashi, K., and Yamaguchi, E., Ibid., 24,1399-1420 (1921). (20)Koo. E.C.. and Chena, 8.M., Chinese Ind., 1,202149(1935). (21) Koo; E.C., and CheLg, S. M., Ind. Research (China),4,466-79 (1935). (22)Koo, E.C., and Cheng, 9. M., J. Chem. Eng. (China),3,348-53 (1936). (23)Lo, T.S.,Science (China),24,127-38 (1940). (24)Lo, T. S., and Teai, L. S., J. Chinese Chem. Soc., 4, 67-71 (1936). (25)Ibid., 5 , 6 6 0(1937). (26)Mailhe, A.,Bull. SOC. chim., 31, 249-52 (1922). (27)Ibid., pp. 567-70. (28)Mailhe, A,, C h k r & I d . , 5,3-5 (1924). (29) Mailhe, A,, Compt. rend., 173,368-9 (1921). (30)Ibid., PP. 658-60.
2145
(31)Ibid., 174,873-4(1922). (32)Ibid., 176,37-9 (1923). (33) rbid., 177,2024(1923). (34) Mailhe, A.,J . usines gat., 47,65-8 (1923). (36) Mailhe, A.,Mat. masses, 14,6223-5,6247-8(1938). (36)Melis, B., Atti congr. m z . chin. ind., 1924,238-40. (37)Nelson, W.L.,“Petroleum Refinery Engineering,” p. 77, New York, McGraw-Hill Book Co., 1941. (38)Oberhaueen, F.,Fr. Patent 682,850(Oct. 7,1929). (39) Petrov, A. D.,Ber,, 64B,1827-34 (1931). (40)Pictet, A.,BUZZ.SOC.chim., 27,641-56 (1920). (41)Pictet, A,, and Potok, J., Helv. Chim. Acta, 2,501-10 (1919). (42) Ping, K.,J. Chinese Chem. SOC.,3, 95-102 (1935). (43)Ibid., pp. 281-7. (44)Sachanen, A. N., “The Chemical Constituents of Petroleum,” p. 99,New York, Reinhold Publishing Corp., 1945. (45)Sato, M.,J . C h m . I d . (Japan),25,13-24 (1922). (46)Ibid., 26,297-304 (1923). (47)Ibid., 30,242-5 (1927). (48) Sato, M.,and Mataumoto, H., Zbid.,30,245-52 (1927). (49)Sato, M.,and Taeng, K. F., Ibid., 29,109-15 (1926). (50) Zelinskii, N. D.,and Levine, R. Ya., J. Applied Chem. (U.9. S.R.),6,20-30 (1923). RSICEIVED June 18, 1949.
BATCH FRACTIONAL DISTILLATION Calculated and Experimental Curves for Batch Distillation with Appreciable Holdup ARTHUR ROSE, R. CURTIS JOHNSON, AND THEODORE J. WILLIAMS The Pennsylvania State College, State College, Pa. Distillation curves showing the change of distillate composition with per cent of charge distilled are calculated by an elementary step-by-step procedure. A corresponding series of experimental distillation curves is also presented. The similarity of groups of experimental and calculated curves is notable. Specific examples are given of the effect of holdup and of charge composition. The results justify efforts to make the rather laborious calculations by a more efficient procedure and to extend the range and degree of correspondence of experimental and calculated curves so as to be able to predict the effect of holdup for batch distillations that are of practical interest.
T
HE course of a batch distillation is described most satisfactorily and completely by curves showing the change of distillate composition as a function of per cent distilled. Various methods of calculating such curves have been suggested for simplified c w s , such as those involving negligible holdup (10-13). Extension of these methods to the case of appreciable holdup has been difficult because of the complexity of the relations involved ( 1 , % 4 , 6-91.
The present paper describes the results of the calculation of entire distillation curves in an elementary step-by-step fashion beginning with the condition of the original system a t the instant product removal is commenced. A corresponding series of experimental distillation curves is also presented. The similarity of groups of experimental and calculated curves is notable. COMPARISON OF CALCULATED AND EXPERIMENTAL CURVES
Some of the results of the present aeries of calculations are shown in Figure 1, left. The curves show the calculated effect of 2.88, 7.2, 14.4, 28.8, and 67.0 mole % holdup (compared with charge) in the batch distillation of an ethylene chloride-toluene mixture (a,2.23; initial composition, 9.0 mole % ethylene chlcride, the more volatile component) with a reflux ratio (LID)of
4 to 1 through a column with still pot and 5 theoretical plates
brought to equilibrium at total reflux before the initial portion of the product was removed. Calculated c w e s by Rayleigh equation procedure for simplified cases of negligible holdup (total reflux and McCabe-Thiele) are also shown for comparative purposes. As expected, the curve for the smallest per cent holdup has the largest initial value for the mole fraction of the more volatile component, under the total reflux conditions assumed for the start of the distillation process. However, the initial steep drop in the curves for small percentage holdup has not been previously noted, nor the crossing and recrossing of the various curves for larger per cent holdup. The curves indicate no great beneficial or detrimental effect of holdup on the sharpness of the break in the distillation curve for the particular conditions of these distillations. I n fact, the curves seem to be misleading as an indication of charge composition. This is probably because the distillate composition is decreasing both because of the shift from total reflux to 4 to l reflux, and because of the exhaustion of the more volatile component. Figure 1, right, shows the corresponding experimental curves obtained in actual distillations with the same mixture, charge composition, and reflux ratio aa for the calculated curves, but with four theoretical plates (not including the still) and with abscissa as weight per cent distilled. Attention is directed to the close similarity between the groups of experimental and calculated curves in Figure 1, even though the number of plates is one leas in Figure 1, right, and the abscissas are mole per cent dietilled in Figure l, left, and weight per cent distilled in Figure l, right. These two m e r e n t scales for the per cent distilled are used because of the considerable inconvenience of using a single scale, and the procedure seems justified by the rather small differences between the two scales. Thus, the difference in molecular
c
-
-I
'\,
a s s b i n g zero holdup. In the case of a finite reflux startup of the distillation, the first
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
October 1950 ASSUMPTIONS
2147
I.01
In addition to the possibility of errors in thecalculated curves from purely arithmetical causes, there are also possible errors due to the assumptions involved. Many of these are the usual simplifying assumptions frequently used in other distillation ralculations.
0,s
Y
I
A
I
1. The column is oper.. ating adiabatically and S 0.2 , , , , , , , [ 0 4 , i . i , i , there is equal mold overLO 1s 10 5 IS 30 3s 0 10 20 30 40 SO w o flow. "OLE PER CENT Of C H I R O E D l l T l L L l O YElDHT PER CENT OF C H I R Q E o I $ T I L L E D f 2. The column consists of five perfect plates Figure 3. Calculated ( l e f t ) and Experimental (right) Curves and a still pot which His mole 7 ' holdup; 5 theoretical plates and still; char e composition. 2.5 mole 570 ethylene chloride in toluene; Le/,. also behaves as a perfect total reflux aogditions at start of diatillation; finite reflux (471) during distillations plate. Rig&, Same BIJ above except H i s weight To holdup; 4 theoretical plates and still 3. The vapor above any plate is in equilibrium with the liquid on that difference in the curve. In the resent work the proper size of the plate. The vapor and li uid compositions are related by the expression y = &/[l +?,a 1)2], where (Y is constant (and unit quantity of distillate was Zetermined by trial. Arithmetical equal to 2.23 in the present work). errors were eliminated by making an over-all material balance of the more volatile component after each ste in the calculations4. The column is fitted with a total condenser which has negligible holdup, and the holdup of vapor and of liquid in i.e., each interval-and by tabulating or pyotting on a raph the auxiliary lines is ne ligible. values for compositions on each plate as well as those of still and distillate, for successive steps or intervals in the calculation. 5. The total h8dup in moles is the same on each plate, and remains unchanged throughout the distillation. Errors in computation inevitably cause irre ular and erratic variations in these compositions and their differences. Unexpected 6. The composition of the liquid on any plate is the same as variations in these values also result from the fact that the that of the liquid leaving the plate. This composition does not quantity of distillate removed is not infinitesimal. These variachange during the interval in which a unit quantity of distillate tions for any one plate are alternately positive and negative aa is removed. 7. When distillate withdrawal is started after a total reflux compared with that expected from extrapolation of values for startup, the resultin decrease in liquid flow down the column preceding intervals. In addition, the variations are alternately reaches the bottom d a t e within a ne ligible period of time compositive and negative on the various plates-i.e., when the compared with the time required for withjrawal of a unit quantity of position on one plate is high, the compositions on the plates above distillate. and below are low. Their magnitudes increese in geometric progression from one interval to the next, unless the variations for any one plate are periodically reduced to negligible proporNone of these assumptions is essential, but their use greatly reduces the labor of the calculations, without introducing major distortions in the resulting curves, so far as can be judged from the agreement between experimental and calculated curves.
I
I
-
BASIC EQUATION
The basic equation for the calculations is that of expressing the decrease of moles of more volatile component in the holdup on any particular plate during a brief interval of time during the batch distillation. This equation is HXn.(i+l)
5
HXn.i
+ (Vy(n--~),i+ L z ( ~ + I ) ,-,
Vy-.,
-
Lzn,
