I N D U S T R I A L A N D ENGINEERING CHEMISTRY
2592
pilot plant than in the laboratory. This would tend to produce a higher gas yield and a lower coke yield. The laboratory data are presented on a loss-free basis; the pilot plant results involve losses of 4 to 7%. The laboratory gas was condenscd a t a lower temperature than that prevailing in the pilot plant after-condenBer. This is reflected in a slightly lower specific gravity for the laboratory gas as compared with the pilot plant gas. The results indicate, therefore, that the coking characteristics of a particular stock in the pilot plant can be reliably evaluated by its performance in the laboratory coking unit. Figures 8, 9, and 10 show that the quality of the liquid produced in the laboratory compares well except for the virgin asphalt with that of the comparable pilot plant stock. In the case of the virgin asphalt, thc laboratory unit produced a much lower boiling and lower specific gravity liquid. hlore efficient condensation of the liquid product in the laboratory may account for some of this, but it is possible that a good part of the discrepancy is due to differences in the charge stock.
Enginnyring
Vol. 43, No. 11
ACKNOWLEDGMENT
The authors are greatly indebted to N. K. Anderson of the Deep Rock Oil Corp., Cushing, Okla., for making possible participation in the pilot plant operation, and for making available the feed stock samples, the pilot plant data, and certain analytical information. LITERATURE CITED
(1) "A.S.T.M. Standards," Part 111-A,
Test 086-46,p. 155,Phila-
delphia, American Society for Testing Materials, 1946.
(2) Zbid., Test D189-46, p. 120. (3) Zbid., T e s t D271-46, p. 31. (4) Ibid., Test D287-39, p. 191. (5) Curran, M. D..Oil Gas J.,48,No. 15, 100 (1949). (6) Foster, A. L..Nutl. Petroleum News, 25,26 (1933). (7) Petroleum Refiner, 16, 63 (1937). (8) Watkins, J. C.,Chem. & Met. Eng., 44, 153 (1937). (9) Ziegenhain,W.T . , Oil Gas J.,30,16 (1931). RECEIVED December 12, 1950. Presented before the Sixth Southwest Regional Meeting of the AMERICAN CHEMICAL SOCIETY, San Antonio, Tex.. December 1950.
Effect of Column Holdup in Batch Distillation
pocess development
I AND C. J. GARRAHAN* E. I. DU PONT DE NEMOURS & CO., INC., WILMINGTON, DEL.
R. L. PIGFORD', 1. B. TEPE,
T h e effect of column holdup on the sharpness of separation in the batch distillation of binary mixtures at constant reflux ratio was investigated through calculations involving a differential analyzer. Instantaneous values of distillate and residue compositions and of fraction of original kettle charge distilled over were calculated for values of column holdup from 14 to 56Yo of the initial charge, reflux ratios from 3.2 to 10 ( L I D ) , and relative volatilities from 1.15 to 3. A general tendency for the size of the intermediate frac-
tion to increase with increasing holdup was observed. Io the case of certain easy separations characterized by high relative volatility, however, the size of the intermediate cut decreased at first and then increased with increasing holdup. The optimum value of holdup was found to correspond roughly to values which are encountered in commercial batch-distillation operations. In the presence of appreciableholdup, the effect of reflux ratio on size of intermediate cut was found to be less pronounced than would be expected with negligible holdup.
M
In the design of a batch distillation unit the quantity of the intermediate fraction must be determined. This fraction must be collected and redistilled with the next charge in order to obtain semicontinuous production of two nearly pure product fractions. Important variables which determine the size of the intermediate cut include the relative volatility, the reflux ratio, the number of theoretical plates, and the liquid holdup of the column. It has been customary to neglect the effect of column holdup because of the mathematical complexity which is introduced into the design calculations by taking this variable into consideration. There are a number of different ways of approaching the problem of determining quantitatively the effect of column holdup on the sharpness of separation in batch distillation. The most direct method is by experiment. Alternatively, the physical system can be analyzed mathematically. A system of differential equations which expresses the relationships between the important variables can be derived without difficulty. These equations, however, cannot be reduced to useful algebraic form by analytical methods without making certain undesirable assumptions. They can be solved for specific casea by tedioua numerical methods or by graphical methods, but these methods
ETHODS for the deeign of batch distillation equipment are less rigorous than those for the similar operation of continuous distillation, largely because variations of plate compositions with time lead to complex mathematical relationships which cannot be handled conveniently by the techniques of formal mathematics. The extensive development of large-scale computing machinery, which started in recent times with the so-called continuous integraph of Bush et al. (g) and which was accelerated during the war, has made available today a number of large scale computing machines capable of solving mathematical problems heretofore considered too difficult or too time-consuming for solution by conventional methods. In the present work, a typical large-scale computing machine, the differential analyzer located a t the University of Pennsylvania, was used to investigate the sharpness of separation in the batch distillation of binary mixtures. I t is hoped that this work will contribute to a better understanding of the batch distillation operation and to the refinement of batch distillation design methods. 1 Present address, Department of Chemical Engineering, University of Delaware, Newark, Del. Preeent address, Department of Eleotrical Engineering, Swarthmore College, Swarthmore, Pa
*
November 1951
INDUSTRIAL A N D ENGINEERING CHEMISTRY
are very time-consuming. Another approach, one which was employed in the present investigation, is to solve the equations for different representative sets of operating conditions using a largascale computing machine. The effect of column holdup in batch distillation has been studied previously both theoretically and experimentally. Rose, Welshans, and Long ( 11 ) showed how batch-fractionation curves -Le., plots of composition of product us. percentage of still charge distilled over-can be calculated taking holdup into consideration for the limiting case of operation a t total reflux. The
VAPOR
4
1
CONDENSER ( NO HOLD-UP)
1
2593
dichloride at low reflux ratios. Under the conditions of the Colburn-Stearns tests the effects of holdup were beneficial. In spite of tedious numerical computations, Carlsoa ( 4 ) carried through the calculation of a part of a batch distillation under one set of conditions. He found that holdup had a slightly favorable effect under his assumed conditions, which involved a small holdup of liquid in the column, slightly less than the quantity of the low boiler in the dilute mixture being distilled. Carlson also reported experimental determinations of batch distillation curves obtained both with a packed column and with a multitubular column having relatively less holdup but the same number of transfer units. Both columns were operated at the same reflux ratio. The intermediate fraction obtained with the packed column was only one third to one half as large as that obtained with the multitubular column, presumably because of the greater holdup of the former. The previous work which has been mentioned briefly represents a useful initial effort to demonstrate the influence of holdup, but as has been emphasized (6),“further work is necessary to determine the conditions which control whether holdup is an aid or II hindrance, and the degree of its effect.” FUNDAMENTAL RE LATlON SHIPS
II
H
moles
The fundamental differential equations which govern the transient behavior of a distilling column were derived by Marshall and Pigford ( 9 ) in a form slightly different from that used originally by Colburn and Stearns (6). These equations were used to study the effect of column holdup on the rate of approach to equilibrium of a distilling column operated at total reflux. In the same form the equations proved to be suitable for calculating the effect of holdup in batch distillation. The derivation of these equations for plate columns is given below: Derivation of Differential Equations for Transient Behavior of a Plate-Type Batch Distillation Column. Letting V = vapor rate, moles per hour L
Figure 1. Schematio Diagram of Batch Distillation Column
“
sharpness of separation under these conditions was shown by calculation to decrease with increasing holdup and the size of the intermediate cut increased approximately linearly with holdup expressed as percentage of initial still charge. The conclusions of this work are interesting from a theoretical point of view but are of limited practical value because batch distillations at substantially total reflux usually are carried out only for the separation of close boiling constituents in the laboratory. Smoker and Rose (1.4) extended the theory of Rose and Welshans (10) for batch distillation a t total reflux with negligible holdup to finite reflux ratios. They also reported experimental results for the separation by batch distillation of mixtures of bepzene and toluene with a 1.5% holdup and of benzene and ethylene dichloride with a 2% holdup. Under the reported conditions beneficial effects of holdup were found for the tests with benzene-toluene and little or no effect of holdup was found with benzene-ethylene dichloride. Equations which govern the behavior of a batch distilling column for the general case of operation when the concentrations on all plates and in the kettle change continuously were derived by Colburn and Stearns (6). These authors were unable to obtain a oolution for the equations because of mathematical difficulties. They indicated two opposing influences of holdup on the sharpness of separation and confirmed their deductione from theory by experiments using a small column having seven theoretical plates to separate mixtures of toluene and ethylene
V
-
liquid rate, moles per hour
- L = product rate, moles per hour
and, for simplicity, assumin zero va or holdup, the existence of theoretical plates, the a%sence o f concentration gradients acrose the plates, and constancy of molal liquid holdup and molal flow rates, the following equation is obtained as the reeult of a material balance (see Figure 1):
Letting 0 =
V 2 t S O
-
fraction of initial still contents distilled
-
over and R = LJ = re0uv ratio, Equation 1 can be exV - L pressed as
d3 a R(zn+l - xn) - ( R
So dB
+ l)(l/n -
Absence of holdup in the condenser means that 28
= 97
A material balance around the still shows that -d(Sz,)
= (Vy.
- Lzi)dt
and also that -dS = ( V These are equivalent to
-
L)dl
vn-1)
INDUSTRIAL A N D ENGINEERING CHEMISTRY
2594
s
-d[i;] = de,or S O = 1 - e 5' since e = 0 when - = 1. Eliminating S/S,, and differentiating S O with respect to e.
-d[(I-e)z,]= -(1 -
dx
Oj--d
dl9
Figure 2.
[(l +!?)yo = (1
- Rxi]d@
+R)L/,- R.?i
(5)
-
(6)
Differential Analyzer
The relation betxveen vapor and liquid compositions is
The initial etate of column ordinarily is given by Y,, = zn+l,or xn+l = 1
azn
+ ( a - ljz, , at e
=
0
(8)
The resuking equations are: (1
dx - 0) ($)
= 2.
+ Rzi - ( R + l)yo
The equations were thought to be suitable for graphical calculation of column behavior using a procedure similar to that proposed by Schmidt (8, 12, IS) for heat conduction problems. Some preliminary calculations were made by this method, but convergence was so poor that the time required for a complete solution was judged to be unreasonably long. An investigation into the possibilities of obtaining solutions to the differential equations described using a modern large-scale mechanical or electronic computing machine led to the use of a differential analyzer a t the Moore School of Electrical Engineering, University of PennRylvania, for this purpose. This machine is shown in Figure 2. The differential analyzer is a mechanical analog-type largescale computing machine especially suited to evaluating solutions of ordinary differential equations, and more particularly those which are not amenable to formal mathematical treatment. The values of the variables involved are represented by the angular displacement of rotating shafts. The shafts are interconnected mechanically so that their motion is governed by the equations to be solved. The mathematical units of the machine which control shaft rotation include spur gears for introducing numerical coefficients and scale factors, planetary gears for addition and subtraction, and most important, mechanical integrators which are used to reduce the order of deriva tivw. The excellent descriptions of the differential analyzer which are presented by Bush and Caldwell ($), by Bush, Gage, and Stewart (5), and by Crank ( 7 ) make it unnecessary to discuss this subject further here. The manner in which the differential analyzer was adapted to the solution of the present problem is shown diagrammatically in Figure 3. The University of Pennsylvania differential analyzer has unusual computing facility for a machine of this type but was limited in its application to the present problem to solutions for a column having Eeven theoretical plates. Also because of limits on machine facilities, it was necessary to approximate the true constant relative-volatility equilibrium relationship given in Equation 14 by the simpler equation Z/"
(9)
(10)
= a'zn
I.
SUMMARY O F
(a'
-
1,Jz:
CALCULATED SIEES FRACTIONSO
(15)
a)
2.23 2.23 2.23 2.23 2.23 2.23 2.23 2 2
L/D 8 8 8
8 3.2 4
H/So 0.0 0.024 0.024 0.029 0.045 0.045 0.045
O F INTERMEDIATE
*e A8 Between 1 7(H/Se), 0.96 Based on and Original 0 8 0.06 Charge 0,220 0.2200 0.269 0.231 0.279 0.238 0.294 0.245 0.490 0.373 0.431 0.328 0.267 0.350 0 . 25Ze 0.252 0.310 0,272 0.380 0,297 0.142 0.14Ze 0.126 0.110 0.132 0.170 0.310 0.198 0.248 0.194 0.720 0.720e 0.834 0.731 28
Konlinear partial differential equations for a packed-batch still can also be derived and can be shown to be similar to Equation 11, considered as a difference-differentia1 equation. An analytical solution t o the equations presented appears to be impoasible because of the nonlinear characteristic of the usual constant relative-volatility equilibrium curve. A solution may be possible for a straight equilibrium line, but this case is of so little practical importance that the work involved, which is b e lieved to be considerable, does not seem to be justified.
-
The arbitrary constant, a', is to be chosen 80 that Equation 15 will agree with Equation 14 as closely as possible. The approximate equilibrium curve reprwented by Equation 15 has the same slope at the origin as the constant-a curve ob-
TABLE
Equation 9 corresponds to the kettle. Equations 10 and 11 correspond to the bottom and top plates, respectively, an equation similar to 10 and 11 existing for each theoretical plate of the column. Condenser performance is represented by Equation 12. Equation 33 is the vapor-liquid equilibrium relationship which takes the following familiar form when relative volatility, a, can be assumed constant:
Vol. 43, No. 11
--
+
2'
0"
0:470
0:45l 0.456 0.475 0.466 0.468 0.463
0.470 0.482 0.473 0.473 0.473
8 0.0 10 0:502 Or478 10 0.02 0.502 0.486 2 10 0.04 3 10 0.0 8 10 0.02 o:6io o:io4 0.518 0.495 0.04 3 10 0.526 0.506 3 10 0.08 3 3.2 0.04 0.518 0.515 1.5 10 0.0 1.5 10 0.02 0:5& o : 5 i g 1.16 10 0.02 .,. 0.500 0.484 a Based on a column having 7 theoretical plates, started a t total reflux. b Values of LI 1.15, 1.5, 2, 2.23, and 3 correepond to a' = 1.14, 1.40, 1.667, 1.760. and, 2.00, respeotively. e Computed mthout help of differential analyzer, using methods described previously (10, 1 4 ) .
...
November 1951
2595
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Y
%
+*+.?-
Q =
-.& RR CI
-C+I
1
1
%*+ R [XI-
f(%JI
Figure 3. Differential Analyzer Setup for Batch Distillation Problem
tained from Equation 14 when a' = a. The constant-a and the approximation curves can be made to coincide a t x = 0.5 if CY' is taken equal to (3a - 1)/( a l ) , which was the condition used in the present investigation. In this case, values of a, from Equation 15 will be less than the constant-a value of y for O
