Ind. Eng. Chem. Res. 1988,27,642-647
642
Lindner, J. Ph.D. Thesis, The Johns Hopkins University, Baltimore, MD, 1988. Nauman, E. B.; Mallikarjun, R. Chem. Eng. J. 1983,26, 231. Olander, R. D. AIChE J. 1960, 6 , 233. Onda, K.; Takeuchi, H.; Okumoto, Y. J . Chem. Eng. Jpn. 1968, 1 , 56. Patwardhan, V. S. Can. J. Chem. Eng. 1978,56, 56. Puranik, S. S.; Vogelpohl, A. Chem. Eng. Sci. 1974,29, 501. Schubert, C. N.; Lindner, J. R.; Kelly, R. M. AIChE J. 1987,32,1920. Shulman, H. L.; Ulrich, C . F.; Wells, N. AIChE J . 1955, 1, 253. Shulman, H. L.; Mellish, W. G.; Lyman, W. H. AIChE J . 1971,17,
631.
Suenson, M. M.; Georgakis, C.; Evans, L. B. Ind. Eng. Chem. Fundam. 1985,24, 288. Treybal, R. E. Mass Transfer Operations; McGraw-Hill: New York,
1980.
van Swaaij, W. P. M.; Charpentier, J. C.;Villermaux, J. Chem. Eng. Sci. 1969, 24, 1083. Yu, W. C.; Astarita, G.; Savage, D. W.; Chem. Eng. Sci. 1985, 40, 1585.
Received for review May 19, 1986 Revised manuscript received November 5, 1987 Accepted November 27, 1987
Multicomponent Batch Distillation. 1. Ternary Systems with Slop Recycle William L. Luyben Process Modeling and Control Center, Department of Chemical Engineering, Mountaintop Campus, 111 Research Drive, Lehigh University, Bethlehem, Pennsylvania 18015
The capacity factor methodology developed by Luyben for binary batch distillation is extended to the separation of ternary mixtures. The processing strategy of recycling the two slop cuts back into the next batch is used. The effects of both design and operating parameters are explored by using digital simulation: number of trays, reflux ratio (both fixed and variable), initial still charge, relative volatility, and product purity. The capacity factor can be used to determine the optimum number of stages and the optimum reflux ratio. Results show little difference in capacity between an optimum fixed reflux policy and a variable reflux policy. Capacity increases with increasing number of trays and increasing relative volatility. Batch processing is becoming increasingly important in many chemical companies as the trend to specialty, small-volume, high-value chemicals continues. Batch distillation columns are frequently an important part of these processes. Batch distillation has the advantage of being able to produce a number of products from a single column. Even though batch distillation typically consumes more energy than continuous distillation, it provides more flexibility and involves less capital investment. A single column can also handle a wide range of feed compositions, number of components, and degrees of difficulty of separation. Since energy costs are not too significant in small-volume, high-value products, batch distillation is often attractive for this class of products. The batch distillation process is characterized by a large number of design and operating parameters to be optimized: the number of trays, the size of the initial charge to the still pot, and the reflux ratio as a function of time (during the product withdrawal periods and during the slop cut periods). In binary separations, there are two products and one slop cut. In ternary separations, there are three products and two slop cuts. Batch time is established by the time it takes to produce the two distillate products and the heavy product left in the still pot at specified purity levels. Most of the work on batch distillation has been limited to the separation of binary mixtures: for example, Luyben (1971),Kerkhof and Vissers (1978), and Gonzalez-Velasco et al. (1987). Ternary batch distillation was studied by Stewart et al. (1973),both theoretically and experimentally. They showed the effects of reflux ratio and number of trays on a measure of separation performance called the average product composition. Van Dongen and Doherty (1985) studied multicomponent, azeotropic, batch distillation. The slop cut in a binary separation can usually be recycled back to the next batch since its composition is often
not much different from that of the feed. The slop cut is the distillate that is removed during the period when the overhead contains too much heavy component to be used in the light product and the material left in the still pot and column still contains too much light component to meet specifications for the heavy product. For ternary systems, there could be two slop cuts. The first will contain mostly the light component and the intermediate component. The second slop cut will contain mostly the intermediate component and the heavy component. In this paper, we assume that both of these slop cuts are recycled back into the next still pot charge. Clearly, this makes little sense from a thermodynamic viewpoint. Alternative operating strategies should be able to improve the efficiency of the system. These include (1) saving up a number of slop cuts and doing binary batch distillations on each of the slop cuts; (2) charging fresh feed to the still pot and feeding the slop cuts into the column at an appropriate tray and at an appropriate time during the course of the next batch; and (3) using the first slop cut to fill up reflux drum (and perhaps the column) prior to the start-up under total reflux conditions in the next batch cycle. The only operating policy to be considered in this paper is recycle of all slop cuts. Although this operation may not be the most efficient, it is certainly the most simple and most widely used in practice. Therefore, it has been used in the initial studies of multicomponent batch distillation. Studies of alternative schemes will be reported in a future paper. Another aspect of batch distillation that becomes much more complex as we move from binary up to multicomponent systems is the question of finding the optimum operating reflux ratio policy. Work on binary systems (Coward, 1967) showed little improvement in going from a constant reflux ratio operation to a more complex constant composition operation or even to the sophisticated
0888-5885/88/2627-06~2~0~.50/0 0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 643
h , I bcf,
W
Figure 1. Configuration and nomenclature in multicomponent batch distillation.
“optimal control” operation using Pontryagin’s Maximum Principle. The reduction in batch time (or energy consumption) was typically less than 5%. Since constant reflux ratio operation is much simplier, it was used exclusively in Luyben’s (1971) work on binary systems. In this paper, two reflux ratio policies are explored. Most of the work will use the simple constant reflux ratio mode of operation, finding the optimum fixed reflux ratio for a given case. The alternative variable reflux ratio policy studied used a simple composition controller to increase the distillate flow rate (and hence reduce the reflux ratio since vapor rate is constant) as the distillate composition rose above the specification purity values during the two product cuts. However, the distillate flow rate was not permitted to drop below some minimum value. The optimum value of this minimum distillate flow rate was determined for each case. The purpose of this paper is to extend the methodology that Luyben (1971) developed for binary batch distillation to multicomponent systems. The performance index of a capacity factor was proposed by Luyben to characterize and quantify the optimum design and operation of binary batch distillation columns. This same capacity concept is shown in this paper to be easily extended to multicomponent batch distillation. This paper presents the results of some initial exploration of the multicomponent batch distillation problem. It is not intended to completely cover the field. Various other aspects of multicomponent batch distillation will be presented in later papers.
System Operation and Nomenclature Ternary systems are considered in this paper. Theoretical trays, equimolal overflow, and constant relative volatilities are assumed. Figure 1 gives a sketch of the system. The total amount of material charged to the column is HBo(moles). This material can be fresh feed, with composition zl,z2, and z3, or a mixture of fresh feed and the two slop cuts. The composition in the still pot at any point in time is xB1,x B 2 , and x B 3 . The instantaneous holdup in the still pot is HB. Tray liquid holdup is assumed constant at 1 mol. Reflux drum holdup is constant at 10 mol. Luyben (1971) showed the effects of holdups in binary systems, and we assume that the same effects apply in multicomponent systems. The vapor boilup rate is V (moles/hour) and is set at 100 for all runs. This is a convenient scaling factor that can be used to determine the energy consumption and column diameter for any production rate. This will be discussed later in more detail. The capacity factors reported in this paper have units of “moles of total products per hour”, and they are based on a column vapor rate of 100 mol/h. The reflux drum, column trays, and still pot are all xBO2, and initially filled with material of composition xBO1, xB03. Vapor boilup is begun, and the column is operated
at total reflux until the concentration of the lightest component in the distillate, x D 1 , reaches the specified purity level. Then distillate product withdrawal is begun at flow rate D. The reflux ratio is held constant throughout the batch cycle in most of the runs, but one type of variable reflux ratio operation will also be considered. The distillate stream is initially the light-component product PI and is withdrawn into a product tank until the average composition of the material in this tank drops to the specified purity level xD;wc. See Figure 1. Then the distillate stream is diverted to another tank, and the first slop cut SI is produced. When the concentration of the intermediate component in the distillate, x D 2 , reaches its specified purity level xD2sPeC, the distillate is diverted to a third tank in which product P2is collected. Material is collected in this tank until one of two events occurs: (1)The purity of the material in the P2tank drops to the specified purity for the product xD$pc. In this event, the distillate stream is diverted into another tank, and the second slop cut S 2 is collected until the average composition of material remaining in the still pot and on the trays in the column meets the purity specification for the heavy product P3,xB;Pec. Note that it is assumed that the liquid on the trays (or packing) in the column drains into the still pot. The material in the S2slop tank and the material in the reflux drum are recycled back to the next batch feed along with slop cut S1. (2) The purity of the material in the still pot and on the trays rises above the purity specification for the heavy product P 3 , In this case, the material in the P2 tank is above its specification. The material in the reflux drum may or may not be above the P2specification. If the average composition of the material in the reflux drum and in the Pztank is above xD2speC, both of these are removed as product P2. If not, the liquid in the reflux drum becomes the slope cut S2 and is recycled back to the next charge. Thus, some batch runs will have two slop cuts and others will have only one. Notice that the initial still pot charge will consist of all fresh feed for the first batch cycle. The initial still pot charge to the second batch cycle will consist of some fresh feed and the slop cuts. Table I gives some results for two cases (product purities of 95 and 99 mol TO),showing how parameters change over the course of the first several batches. It takes about three batch cycles for a pseudosteady-state operation to build up. The fresh feed decreases as the slop cuts come to some steady-state value. The initial composition in the still pot changes from a 0.3/0.3/0.4 mixture to one that is richer in component 2. Thus, the intermediate component is preferentially recycled in the slop cuts. Figure 2 shows the distillate composition profiles for the first three cycles for the case of a 40-tray column with a distillate flow rate of 40 mol/h and 95 mol % product purities (the first case given in Table I). The shapes of the composition time trajectories shift somewhat as the initial still pot composition changes from batch to batch. Notice that there is no S2 slop cut in this case. Figure 3 gives results for the case where only 20 trays are used. The shapes of the composition trajectories are considerable different. A S2slop cut is made on the first cycle, but not thereafter. The second case in Table I produces two slop cuts because product purities have been raised to 99 mol %.
Equations Based on the assumptions of constant tray and reflux drum holdups, constant relative volatilities, and equimolal
644
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988
--
__
- -
--
-0
*
10
~
I
I
I I
I I
2 0
O T
U
- r _ 7
YI
3 c
b
lP
t
1-‘?,as
TIPE
3 0f
O
* c
WURSI
Figure 2. Distillate composition and flow rate trajectories for 40-tray column: (a) first cycle with all fresh feed in initial charge to still pot; (b) second cycle with S1 slop cut first cycle mixed with fresh feed; (c) third cycle, pseudo-steady-stateoperation.
overflow, the equations describing the ternary batch distillation system are still p o t dHB/dt = -D d [ H ~ x ~ ; ] / d=t Rxlj - v y ~ ;
Table I. Effect of Slop Recycle ( N = 40, D = 40, HRO = 300) cycle 1 pi
(1)
j = 1,2
fresh feed
(2)
300 0.3 0.3 0.4 4.52 37.48 0.2072 0.7928 0 0 52.3
XBOl IBO2 xB03
tF
S1 k=l
akXBk
XSll XSl1 xs11
tray n:
SZ CAP
2
3
262.52 0.2884 0.3616 0.3500 4.93 47.24 0.2327 0.7673 0 0 46.5
252.8 0.2894 0.3736 0.3370 5.04 48.88 0.2356 0.7644 0 0 45.4
= 0.95
cvcle 2
1
(5)
xpi
fresh feed xBOl xB02
xE103
tF
Sl XSll xs12 xS13
s2 xs21 %22
xS23
CAP
Capacity Factor The performance index used by Luyben (1971) for binary batch distillation is easily extended to ternary systems. The capacity factor (CAP) of the batch still is defined as the total specification products produced (P1+ P2 P3)divided by the total time of the batch. A 30-min period is assumed to be required to empty and recharge the still pot, so the total batch time is tF + 0.5 h. P , + P2 + P3 CAP = (10) tF + 0.5
+
The total batch time tF includes the time at total reflux
300 0.30 0.30 0.40 5.25 61.44 0.1881 0.8119 0 25.92 0.0003 0.4366 0.5631 36.98
3
4
200.36 0.2587 0.4446 0.2967 5.86 87.32 0.2143 0.7857 0 12.48 0 0.6443 0.3557 31.52
200.20 0.2626 0.4552 0.2822 5.94 88.80 0.2146 0.7854 0 11.08 0 0.7020 0.2980 31.10
= 0.99 212.64 0.2512 0.4116 0.3372 5.64 82.48 0.2122 0.7878 0 17.16 0 0.5213 0.4787 32.68
and the time producing the products and slop cuts. Note that the total products produced will also be equal to the net fresh feed charged to the still pot, which is equal to the total still pot charge minus the sum of the two slop cuts. The capacity factor can be used to determine the optimum column design. As one would intuitively expect, CAP increases as more trays are added to the column for the same vapor rate in the column. This corresponds to the same energy consumption and the same diameter column. Thus, more feed can be processed for the same energy cost. Alternatively, a smaller diameter column and less energy could be used to handle the same amount of material per unit time. Of course, the capital cost of the
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 645
0 55 6
10 0 20c 0
=
I 0 1 0
5 0
, 0
P O
I O
TIME
3 0
1 0
6 0
3 0
I O
$ 0
IHOURSI
TIME
5 0
4 0
(HOURS1
Figure 3. Batch trajectories for 20-tray column: (a) first cycle with fresh feed (b) second cycle with S1and Sz slop cuts from first cycle mixed with fresh feed; (c) third cycle. Table 11. Base Case Conditions and Results (after Three Batch Cycles) initial still charge 300 mol 100 mol/h vapor boilup z1 = 0.30, zZ 0.30, 2 3 = fresh feed composition 0.40 no. of trays 40 a1 = 9, 012 = 3, a 3 = 1 re1 volatilities 40 mol/h distillate flow rate (after initial total reflux operation) time on total reflux 0.45 h time producing product P I 1.96 h time making slop cut S , 1.22 h time making product Pz 1.41 h time making slop S2 0 total distilling time 5.04 h total batch time 5.54 h fresh feed 252.76 mol slop recycles from previous batch Si 47.24, S2 = 0 cycle products produced, mol Pi = 78.56, Pz = 66.28, P3 106.36 slop cuts produced on third batch Si = 48.88, Sz = 0 cycle, mol ~ s l =l 0.2356, ~ ~ =10.7644, 2 composition of S1 *S13 = capacity 45.4 mol of total products/h of total batch time
:
column increases as more trays are added. Therefore, the capacity factor can be used to perform the necessary economic trade-off calculations between capital and energy costs to determine the optimum number of trays and the optimum reflux ratio. An example will be given later in the paper. It is interesting to compare the capacity of a continuous distillation system with that of a batch system for the base case separation: relative volatilities of 9/3/ 1, product purities of 95 mol %, and feed composition 0.3/0.3/0.4. By use of the standard shortcut design procedures for continuous distillation with a reflux ratio of 1.1times the minimum, a total of 100 mol/h of vapor boilup in the two continuous columns would correspond to a feed rate (or capacity) of about 80 mol/h. Each column would require 12 trays. Making this separation in a 20-tray batch distillation with the same energy consumption (100 mol/h of vapor boilup) yields a capacity of about 37 mol/h. If 40 trays are used in the batch column, the capacity is about 45 mol/h. If 80 trays are used, capacity increases to about 55 mol/h. This case illustrates that continuous distillation
-
551
N:68
0:50
CRP
N=28
351
158
Dill0
258
288
380
900
350
HBO
Figure 4. Effect of size of initial charge to the still pot.
I
I: cflp
I
30 30 3s
/ n:w
HBBi380
NSBE
n~0~400
-
~ ~ 0 ~ 3 0 0 HB0:BBe
Ni’l0
N.20 35
NiB0
YB
H80.200 Y5
50
S5
80
D
Figure 5. Effect of number of trays.
~~
30
110
98
60
0
Figure 6. Effect of distillate flow rate on variables to give optimum.
is more energy efficient than batch distillation.
Results The effects of various design and operating parameters have been explored for ternary batch distillation. These
646
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 h:90
HB0=300
Table 111. Comparison of Fixed and Variable Reflux Ratio Operations N 40 20 HBQ 300 200
BRSE C R S E
'15.
I '104
351
tF
03: SI s2
__
a t ! , 20
* ~ _ 30
+
Lf0
4
t-
50
-+
-
60
D Figure 7. Changing design parameters.
CAP tF
DWt SI
sz
CAP
include the size of the initial charge to the still pot, the reflux ratio, the number of trays, the fresh feed composition, the relative volatilities, and the product purities. Table I1 gives the conditions for the base case batch distillation system. The effects of varying parameters from these base case conditions are given in Figures 4-7. All of these results apply to the steady-state conditions that results after there have been at least three recycles of slop cuts back into the fresh feed. Figure 4 shows the effect of the size of the initial charge to the still pot, HBo,on the capacity of batch columns varying in size from 20 to 80 trays. Distillate flow rate D is held constant after the total reflux start-up. Capacity increases with the number of trays N as one would expect. But the initial charge to the still pot has little effect as long as the liquid in the still pot is not depleted before the end of the batch. Thus, the minimum size charge to the still must be increased as the number of trays increases. Figure 5 shows how the optimum fixed distillate flow rate (and corresponding reflux ratio) is obtained for columns of several sizes. The optimum distillate flow rate for the 40-tray column with an initial still pot charge of 300 mol is about 45 mol/h. This corresponds to a reflux ratio of (100 - 45)/45 = 1.2, giving a capacity of about 45 mol/h. Capacity increases as the number of trays is increased. The optimum distillate flow rate increases (reflux ratio decreases) as N increases. Figure 6 illustrates why there is an optimum distillate flow rate. The capacity (CAP), the time to the end of the batch (tF),and the amount of the first slop cut (SI) all vary with distillate flow rate. Batch time decreases as D is increased, but the amount of the slop cut increases. This reduces the amount of products and causes the CAP to go
Variable Reflux Ratio 4.50 40 67.8 10 44.4 Fixed Reflux Ratio 5.04 40 48.9 0 45.4
3.84 30 43.5 10 33.8 3.58 40 42.6 0
38.6
through a maximum. The distillate flow rate that gives the maximum CAP is the optimum. Results me shown for 40- and 60-tray columns. Figure 7 illustrates the effects of changing various system parameters. The base case column (40 trays, initial charge of 300) is used for all the cases. The effect of changing the fresh feed composition from 0.3/0.3/0.4 to 0.1/0.45/0.45 is to decrease capacity and increase the optimum distillate flow rate. As expected, the effect of increasing product purities from 95% to 99% or decreasing relative volatilities is to reduce capacity and reduce the optimum distillate flow rate (increase optimum reflux ratio). See Table I also for information on the higher product purity case. In all of the previous cases, a fiied reflux ratio operation was used. One simple variable reflux ratio scheme was also studied. Figure 8 shows three cycles for a system in which the distillate flow rate is set by a composition controller. A simple proportional controller is used with a gain of lo00 mol/h/mole fraction. When the distillate purity is above the specified value, distillate flow rate is increased in direct proportion to the error signal.
D = Dmin+ K,.[x,, - xV~'] (12) This mode of operation does not give exactly constant distillate compositions, but it captures the feature of having low reflux ratios when the separation is easy and increasing reflux ratios when the separation becomes more difficult. It is also similar to what an actual control system could do on an operating column. The distillate flow rate is not permitted to drop below some minimum value, Dmin,once the total reflux start-up has been completed. The optimum Dminis found by
Figure 8. Batch trajectories for variable reflux operation: (a) first cycle; (b) second cycle; (c) third cycle.
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 647 making runs with different values of D- and selecting the one that maximizes CAP. Table I11 compares the maximum capacity values for the fixed reflux ratio operation with the variable reflux ratio operation for 20- and 40-tray columns. There is little difference between the two policies for the 40-tray column. But for the 20-tray column, the fixed reflux ratio strategy yields a higher capacity (38.6 versus 33.8). The variable distillate operation reduces the batch time but produces larger slop cuts. Since the fixed reflux ratio operation is much simpler than the variable reflux ratio strategy, it would be preferred even if there were some sacrifice in capacity.
Optimum Number of Stages The use of the capacity factor to determine the optimum number of stages is illustrated in the following example. Suppose we want to produce 300 mol/h of total products. If we use 40 trays, Table I11 shows that the capacity (CAP) is 45.4 for the optimum fixed reflux ratio. If we use only 20 trays, capacity drops to 38.6. Since these capacity numbers are given in terms of total products per hour and are based on a vapor rate of 100 mol/h, we can calculate the energy consumptions for the two cases. (1) Case 1: N = 20. From Table 111, CAP = 389.6 at the optimum distillate flow rate of 40. To make 300 mol/h of products, we need [lo0 mol/h of vapor/38.6 mol/h of products][300 mol/h of products desired] = 772 mol/h of vapor boilup required to meet the desired production rate in a 20-tray column. (2) Case 2: N = 40. From Table 111, CAP = 45.4 at the optimum distillate flow rate of 40: [lo0 mol/h of vapor/45.4 mol/h of products] [300 mol/h of products desired] = 661 mol/h of vapor boilup required. Thus, the incremental savings in energy cost is about 14% in adding 20 trays: [(772 - 661)/772] = 0.144. The diameter of the column would also be reduced since the vapor rate is lower. Then we would see if the energy savings give a satisfactory return on investment for the increment capital cost of 20 more trays, less the savings in capital for a smaller diameter column. Note that the procedure also yields the optimum reflux ratio: [reflux/distillate] = [(vapor - distillate)/distillate] = [(loo - 40)/40] = 1.5. One final comment should be made about selecting the optimum number of stages. In many batch columns, the number of trays is not fixed by energy/capital cost trade-offs. If temperature-sensitive materials are being distilled, the pressure in the still pot must be kept below some maximun value. Thus, in many vacuum batch distillation columns, the number of stages is fixed by the total pressure achievable with reasonable condenser pressures. However, the capacity factor is still useful in these cases because it gives the optimum reflux ratio to be used with the given number of stages. Conclusion and Future Work Luyben's capacity factor can be easily extended to multicomponent batch distillation. The effects of various design and operating parameters have been explored for the batch distillation of a ternary mixture. Recycle of slop cuts has been assumed. There is an optimum fixed reflux ratio for each system. The fixed reflux ratio policy appears
to be just as good if not better than the variable reflux policy explored in this paper. Capacity is decreased when relative volatility or number of trays is reduced. Future studies in multicomponent batch distillation will include alternative processing schemes to slop recycle, other variable reflux ratio policies, and wider ranges of parameters such as feed compositions and relative volatilities.
Nomenclature CAP = capacity factor, mol/h D = distillate flow rate, mol/h 03: = optimum value of the minimum distillate flow rate in variable reflux ratio operation, mol/h Dopt = optimum value of distillate flow rate in fixed reflux ratio operation, mol/h H , = tray liquid holdup, mol HB = still pot holdup, mol HBO = initial charge to still pot, mol H R = reflux drum holdup, mol PI = amount of light product, mol P2 = amount of intermediate product, mol P3 = amount of heavy product, mol SI = amount of first slop cut, mol S2= amount of second slop cut, mol tp = duration of distilling portion of batch cycle, h V = vapor boilup, mol/h xBJ = still pot composition, mole fraction of component j xK = specified purity of heavy-component product, mole fraction of component 3 xm! = initial still pot composition, mole fraction of component .l xD,
x8y
= distillate composition, mole fraction of component j = specified purity of light-component product, mole
fraction of component 1
x8r = specified purity of intermediate-component product, mole fraction of component 2 xnJ = liquid composition from tray n, mole fraction of com-
ponent j = composition of f i t slop cut, mole fraction of component
xSlJ
j
xs2, = composition of second slop cut, mole fraction of com-
ponent j yBJ = reboiler vapor composition, mole fraction of component j ynJ = vapor composition from tray n, mole fraction of com-
ponent j zJ = fresh feed composition, mole fraction of component j Greek Symbol aJ = relative volatility of component j (with respect to heavy
component)
Literature Cited Coward, I. Chem. Eng. Sci. 1967,22,503,1881. Gonzalez-Velasco, J. R.; Gutierrez-Ortiz, M. A.; Costresana-Pelayou, J. M.; Gonzalez-Marcos, J. A. Ind. Eng. Chem. Res. 1987,26,745. Kerkhof, L. H.J.; Vissers, H. J. M. Chem. Eng. Sci. 1978,33, 961. Luyben, W. L. Ind. Eng. Chem. Process Des. Dev. 1971, 10, 54. Stewart, R. R.;Weisman, E.; Goodwin, B. M.; Speight, C. E. Ind. Eng. Chem. Process Des. Deu. 1973,12,131. Van Dongen, D. B.; Doherty, M. F. Chem. Eng. Sci. 1985,40,2087.
Received for review June 1, 1987 Revised manuscript received October 14, 1987 Accepted November 30,1987
