I n d . Eng. C h e m . Res. 1989,28, 75-83
75
PROCESS ENGINEERING AND DESIGN Control of Distillation Columns with Low Relative Volatilities M a r k V. Finco* and William L. L u y b e n Process Modeling and Control Center, Department of Chemical Engineering, Lehigh University, 11 1 Research Drive, Mountaintop Campus, Bethlehem, Pennsylvania 18015
Richard E. Polleck S u n Refining and Marketing Company, Marcus Hook, Pennsylvania 19061
Distillation columns t h a t separate close-boiling components have the distinctive dynamic feature of very large time constants. This paper reports the results of a dynamic study of this type of low relative volatility distillation system. A propylene/propane column (C, Splitter) a t the Sun Refining and Marketing Company’s Marcus Hook, PA, refinery was used as a specific example. The propylene/propane separation is a n extremely important one in itself, but the conclusions from this study should be applicable t o a wide range of “super-fractionator” situations: low relative volatility, high reflux ratio, and large number of trays. Experimental steady-state and dynamic plant data were used t o obtain steady-state and dynamic models. Then computer simulation studies were performed for a number of conventional and nonconventional control structures. The two best configurations were (1)the reflux ratio-boilup ratio (RR-BR) scheme suggested by Shinskey and (2) an unorthodox distillate-bottoms (D-B) scheme. The latter uses fewer sensors and is less complex, but it is more fragile. If any sensor fails or any valve saturates, the D-B scheme will not work. The D-B scheme was installed on the Sun Oil commercial C3 Splitter in November 1987, using a Honeywell TDC 2000 system. Its ability to provide effective control has been demonstrated. Override controls have been used t o reduce the fragility of the D-B structure t o valve saturation. There are a large number of distillation columns that separate very close-boiling materials. These “superfractionator” applications include the separation of a number of important isomers, some alcohols, mixed butylenes, and ethyl benzenelstyrene. Probably the most common and commercially most important example is the separation of propylene and propane. This separation occurs in almost every refinery and many chemical plants around the world. Columns that make these difficult separations are characterized by very high reflux ratios (greater than lo), large numbers of trays (more than loo), and very long time constants (2-10 h or more). The systems are usually binary. Temperature gradients are very small, so direct composition measurements are usually required. In 1986, Sun Refining and Marketing Company and Lehigh University established a cooperative research program to develop an effective control system for these low relative volatility columns, with the propylene/propane separation as the specific example. A four-part study was carried out: (1) Steady-State Modeling and Analysis. Plant data were collected a t several typical operating pressures. Computer programs were written to calculate operating tray efficiencies from this data. Then rating programs were used to determine steady-state gains, incentives for dual-composition control, effects of various disturbances, and economic incentives for improved control. (2) Dynamic Modeling. Pulse-test data were obtained from the plant column for changes in heat input and reflux flow. A dynamic model was developed that matched the plant data with enough accuracy for comparative control studies.
(3) Control Systems. A number of conventional and nonconventional control structures were evaluated on the dynamic model. Disturbances in feed composition, feed flow rate, and column pressure were imposed, and the ability of each control scheme to reject these disturbances was quantified. (4) Plant Evaluation. The best control scheme was implemented on the commercial column and tested. This paper briefly describes each of these phases. Finco (1987) presents more details of the first three phases of the study. The Sun Oil column studied has 160 trays in two sideby-side shells. Feed is introduced on tray 44 (from the bottom). Twin stab-in reboilers use low-pressure steam as the heat source. The column has no pressure control. Cooling water to the overhead condenser is wide open so that the pressure is minimized a t all times to achieve the largest relative volatility. Typical operating pressures range from 250 psia in the summer to 195 psia in the winter. Distillate product has a minimum specification of 99.5 mol % propylene. Bottoms product goes to LPG (liquified petroleum gas), and any propylene in this stream represents a yield loss.
Steady-State Modeling and Analysis A. Balances and Data. Table I gives steady-state plant data over a typical range of pressures. Total mass and component balances were made using the raw plant data, and they checked quite well. Energy balances were checked by calculating condenser duty in two ways: (1) from an energy balance around the entire column, using the steam flow rate to get the reboiler heat input; and (2) from an energy balance around the condenser, using the
0888-5885/8912628-0075$01.50/0 0 1989 American Chemical Society
76 Ind. Eng. Chem. Res., Vol. 28, No. 1, 1989 Table I. Steady-State P l a n t Data pressure, psia flow rates, barrel/h feed distillate bottoms steam flow rate, lo3 lb,/h reflux ratio compositions, mol % propylene distillate bottoms feed (back-calculated)
z
STEADY S T A T E R A T I N G
H
195
211
250
215 154 62 62.9 12.5
23 1 162 66 66.2 12.8
210 150 63 61.6 14.3
99.64 3.8 71.6
99.60 3.2 73.1
99.60 11.7 74.8
r
n
m
a 140.0 4
> Q
z 132.0
Table 11. Energy Balance Results pressure, psia 195 condenser duty, lo6 Btu/h calcd from steam flow 64.5 calcd from reflux flow 52.2
X
3
211
250
67.7 54.7
61.3 53.0
A
ii W
a: 124.0 0.60
0.68
0.64
FEED
Table 111. Column Design at 100% T r a y Efficiency pressure, psig column designs total no. of trays optimum feed tray actual column total trays feed tray
195
211
250
162 42
163 42
155 36
160 44
160 44
160 44
=
a0
- a,x - a$
0.76
0.80
STEADY S T A T E R A T I N G
reflux flow rate. As summarized in Table 11, these energy balances were off by about 20%. Heat losses could account for only 5 % of this. We were unable to obtain cooling water flow rate and temperature rise data to provide an independent check of the reflux flow measurement. Since it was felt that the reflux flow measurement was more reliable than the steam measurement, the measured reflux ratios were used in the steady-state model. B. Vapor-Liquid Equilibrium. The VLE correlation used in any distillation column study is a very important component. An extensive survey of the literature was conducted to find a simple correlation that incorporated the effects of pressure and composition on relative volatility. Looking ahead to the dynamic simulations, it was also recognized that the VLE calculations should be computationally efficient. Equations 1-4 give the final correlation used. Relative volatility is given as a quadratic function of liquid composition. The coefficients are linear functions of pressure. cy
0.72
COMPOSITION (MOL%)
(1)
2
36.0
+ d iI
3
28.0
J U 0
m
20.0
0.60
0.64
0.68
0.72
FEE0 C O M P O S I T I O N
0.76
0.80
(MOL%)
STEADY STATE R A T I N G
-
14.0
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13.6 \
x
3 J
IL
-n"
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0 H
CZ,
= 1.2855 - 0.000446P
(2)
= 0.088008 - 0.0001035P
(3)
2
U
12.8
X
3 _1
a2 = 0.052215 - 0.00014607P
(4)
where cy is the relative volatility of propylene to propane, x is the liquid composition (mole percent propylene), and P is the pressure (psia). Using this correlation and the plant reflux ratio and composition data given in Table I, three different columns were designed for the three operating pressures. Equimolal overflow and 100% tray efficiencies were assumed. Table I11 shows that the results of these designs give columns that are very close to the actual 160-tray column with feed on tray 44. The conclusion is that the tray efficiencies in the column must be close to 100%. C. Rating Programs. Three types of steady-state rating calculations were made. In the first, the need for dual-composition control was established. In the second, steady-state gains between manipulated and controlled variables were determined. In the third, optimum economic steady-state operating conditions were established.
w LL
12.4
a
12.0 0.60
0.64
0.68
0.72
FEED COMPOSITION
0.76
0.80
(MOL%)
Figure 1. (a, top) Reflux and boilup versus feed composition. (b, middle) Boilup ratio versus feed composition. (c, bottom) Reflux ratio versus feed composition.
(1) Incentives for Dual-CompositionControl. Figure 1gives curves for the required changes in reflux flow rate,
vapor boilup, boilup ratio, and reflux ratio as feed comparison changes, while maintaining distillate and bottoms compositions constant a t specification values ( x D = 99.5 mol % propylene and xB = 2.5 mol % propylene). The normal design feed composition is 70 mol YO propylene. The range of changes in feed composition is 60-80 mol % propylene.
Ind. Eng. Chem. Res., Vol. 28, No. 1, 1989 77 ECONOMIC INCENTIVES
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5
527.0
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\
z
1 - PLANT 1
x"
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521.0
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2520 7 519.0 0.04
0.
0.08
0.12
0.16
BOTTOM COMPOSITION Figure 2. Worth versus bottom composition.
The conclusion from these rating curves (Luyben, 1975) is that none of these variables remains nearly constant, so a simpler single-end control alternative to dual-composition control is not economical. (2) Steady-State Gains. A rating program was used to calculate steady-state gains between controlled and manipulated variables. A very small change (0.07%) was made in one manipulated variable (for example, reflux or heat input), and the resulting new steady-state values of xD and X B were calculated. Typical results are shown in eq 5. The gains in this equation have units of mole percent/mole/ minute. These steady-state gains were used later in the dynamic studies to calculate relative gain arrays.
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=
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-0.011 283 -0.18699
][ ;]
2440
I
20
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40
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80
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GO
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120
TIME (MINI
Figure 3. Plant pulse test compared to model, R pulsed.
(5)
(3) Economic Incentives. To quantify the economic incentive for tighter control (closer to the distillate 99.5 mol % specification) and to find the economic optimum operating conditions, calculations were done to show how product values and operating costs change with different distillate and bottoms compositions. Figure 2 shows a plot of "worth" (the sum of the value of the two products minus steam cost) versus bottoms composition. Three curves are shown at different distillate compositions. The incentive to move closer to the minimum specification value of 99.5 mol % propylene is shown. Also the optimum bottoms composition can be seen to be about 2.5 mol % propylene. Below this value, energy costs increase rapidly. Above this value, yield losses of propylene increases rapidly. The basis for these curves is propylene product at $0.16/lbm,propane bottoms product at $O.ll/lb,, and an energy cost of $5.00/106 Btu. The normal operation of the column averaged about 99.6 mol % distillate and 6 mol % bottoms. Operation at the optimum specifications would result in savings of about $20/h or $150 000/year. Under some conditions, the bottoms composition drifts up to 12 mol %. At this level, the lost profit is $45/h. Dynamic Modeling A. The Column. The column has 160 sieve trays and is built in two side-by-side sections. Liquid is pumped from the base of the top section to the top of the bottom section. This liquid holdup in the base of the top section creates an additional dynamic lag in the system. Tray spacing is 18 in. Liquid flow is two-pass. Cooling water
62
-I
TIHE [HIN)
Figure 4. Plant pulse test compared to model, V pulsed.
is used in the overhead condensers, and the column pressure floats as the weather, time-of-day, and season dictate. B. Experimental Dynamic Tests. Pulse tests in steam and reflux flow rates were made on the plant column. Figures 3 and 4 compare these data with model predictions. It was difficult to make pulses where the response was distinguishable from the background noise without seriously upsetting the column. The distillate composition was insensitive to changes in either reflux or steam. Therefore, X D was the limiting observation for determining pulse magnitude. Note the large experimental time constants observed in this column. C. Model. A simple two-ODE per tray model was used. Equimolal overflow and constant pressures were assumed. The model included three level controllers and two composition controllers. The cycle time of the gas chromatographic analyzers was 5 min. Composition data were delayed and held between sampling times. The tray hydraulic time constant was adjusted to match the plant dynamic data. The comparison between the model and
78 Ind. Eng. Chem. Res., Vol. 28, No. 1, 1989 Table IV. Controller Tuning Constants" loop ~~
structure single end (bottom) single end (distillate) reflux-vapor (R-V) distillate-vapor (D-V) reflux-bottoms (R-B)
distillate
K, = -8325 71 = 50 K, = 2475 71= 192 K, = -5550 71 = 75 K, = 4050 = 84 K, = -75 71
reflux ratio-boilup ratio (RR-BR) distillate-bottoms (D-B)
= 57 K, = -7500 71 = 64 71
bottoms K,=-1915 71= 76
detuning factor 2
Ih
1
K, = -956 7'1 = 152 K, =-1200 71 = 63 K, = 338 71 = 80 K, = 0.40 71 = 58 K, = 360 71 = 69
T
4 _j
1.5 2 1.5 1.5
"All reset times are in minutes. Gains have dimensions corresponding to the following units: compositions in mol % propylene, flows of distillate, bottoms, and reflux in mole/minute, and flow of vapor boilup (steam flow) in lb,/minute.
the plant data was considered good enough for control systems comparative studies.
Control Systems
A number of alternative control structures were compared on the dynamic model. Most of the classical single-end and dual-end composition control schemes were evaluated. A. Steady-State Analysis. Relative gain arrays for three tradition structures were calculated (1)reflux-vapor boilup (R-V), RGA = 25; (2) distillate-vapor boilup (D-V), RGA = 0.08; (3) reflux-bottoms (R-B), RGA = 0.92. These results favor the R-B scheme. The obvious direct material balance scheme (D-V) gives a result which suggests a dynamically poor pairing: control xD with V and control XB with D. B. Controller Tuning. Pulse testing of the model was initially tried in an attempt to determine transfer function models for controller tuning. This approach did not work very well because of the extremely long time constants and the nonlinearity of the process. An experimental approach was finally evolved to tune all the loops for each configuration in a consistent manner. First the ultimate gain and ultimate frequency were found for each loop (with the other composition loop on manual) by using the nonlinear model and increasing the gain of a proportional controller until sustained oscillations occurred. Then the Ziegler-Nichols (ZN) settings were calculated for each loop. Finally a single detuning factor F was used for both loops, increasing reset times and decreasing gains by the same factor, until the closed-loop response of the nonlinear model with all loops on automatic showed reasonable damping coefficients (0.3 or greater). This procedure required a considerable amount of computer time (somewhat more than pulse testing), but it gave very reliable results that gave fair comparisons among the alternative control schemes. Table IV gives the controller settings for all the configurations. Note the long reset times and the detuning factors. C. Composition Control. The primary evaluation of each control structure was based on how well the composition controllers performed for a +5 mol % feed composition disturbance (70-75 mol % propylene). Only results using conventional diagonal multiloop SISO controllers with proportional integral action are presented
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200
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400
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600
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Figure 5. (a, top) §ingle-end bottom structure. (b, bottom) Response of single-end bottom structure.
in this paper. One multivariable structure was studied (Finco, 1987), but no improvement was noted. D. Single-End Control. It is sometimes possible and other times necessary (when an analyzer goes out of service) to control only one end of a column. This eliminates interaction problems and simplifies control. Unfortunately, in this system neither of the single-end control structures gave close enough control of the other end, as predicted by the steady-state rating program. They did, however, show that either end can be controlled well and gave a standard to compare the responses of the dual-
,
Ind. Eng. Chem. Res., Vol. 28, No. 1, 1989 79
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Figure 6. (a, top) Single-end overhead structure. (b, bottom) Response of single-end overhead structure.
Figure 7. (a, top) R-V structure. (b, bottom) Response of R-V structure.
composition control structures. Figure 5a gives the control system when only the bottoms composition is controlled by manipulating steam flow rate. Reflux flow rate is ratioed to feed flow rate. Figure 5b shows the dynamic response for a feed composition disturbance. Bottoms composition is well controlled, but XD goes below specification. Figure 6 gives results when only the distillate composition is controlled by manipulating distillate flow rate: Steam is ratioed to feed flow rate. Now XB rises to a level where propylene yield suffers.
E. Dual-Composition Control. Five control schemes were evaluated. (1)Reflux-Vapor (R-V). Figure 7 gives the structure and the dynamic response for a feed composition disturbance. Neither distillate or bottoms composition is well controlled. The control structure would not be expected to perform well because of the very high reflux ratio. (2) Distillatevapor (D-V). Figure 8 shows the structure and the results. This configuration is the conventional approach for high reflux ratio columns. Its performance is adequate, but XB is not too well controlled and is away
80 Ind. Eng. Chem. Res., Vol. 28, No. 1, 1989
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400
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I
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128.0
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400
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Figure 8. (a, top) D-V structure. (b, bottom) Response of D-V structure.
Figure 9. (a, top) R-B structure. (b, bottom) Response of R-B structure.
from the set point for an extended period. (3) Reflux-Bottoms (R-B). This structure was the one favored by the RGA analysis. Figure 9 shows that =cB is well controlled but XD is not. (4) Reflux Ratio-Boilup Ratio (RR-BR). Figure 10a shows the structure. The reflux ratio is controlled in the top and is reset by the distillate composition controller. Reflux drum level is held by either distillate or reflux flow. The ratio of the steam flow rate to bottoms flow rate is controlled and is reset by the bottoms composition controller. Base level is held by steam flow. This scheme was
suggested by Shinskey (1986). Both of the level controllers must be tightly tuned. Figure 10b shows that the load rejection performance of this scheme is outstanding. It does a much better job in holding xD and xB near their set points. As can be seen in Figure loa, one of the problems with the RR-BR scheme is instrumentation complexity. Four flow measurements must be made and two ratios computed and controlled. Noisy or unreliable flow signals can produce problems. Therefore a simplier system with comparable performance would be desirable.
Ind. Eng. Chem. Res., Vol. 28, No. 1, 1989 81
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128.0
128.0
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Figure 10. (a, top) Reflux ratio-boilup ratio structure. (b, bottom) Response of RR-BR structure.
(5) DistillateBottoms (D-B). A little reflection revealed the fact that we are really manipulating the distillate and bottoms flow rates in the RR-BR scheme if the two level controllers are tightly tuned. Thus, a more simple structure would be to use distillate flow rate to control XD and use bottoms flow rate to control xB. See Figure l l a . This is a control system that has been labeled “inoperable” by all the distillation control experts. It seems to violate overall material balance constraints, but in reality it does not. The two level controllers (base on steam and
0
100
200
300 400 TIME (MINI
500
600
Figure 11. (a, top) D-B structure. (b, bottom) Response of D-B structure.
reflux drum on reflux) force the overall material balance to be satisfied in the long term. Dynamically, of course, there will be a misbalance. This structure had another very important practical advantage for the Sun Oil application. The plant operators had been running this column manually using the D-B structure for several years. The two level loops were on automatic, but the operator would set the flow rates of distillate and bottoms every several hours. The effectiveness of the D-I3 structure for a feed composition disturbance is shown in Figure l l b . It performs
,
82 Ind. Eng. Chem. Res., Vol. 28, No. 1, 1989 99.70-
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Figure 12. D-B structure, bottom set point to 3%.
as well as the RR-BR structure. The D-B structure needs special consideration, however, when any sensor fails or any valve saturates as discussed later in more detail. F. Additional Testing for the D-B Structure. Satisfied that the D-B structure performed well under initial screening, we tested it under more rigorous conditions. Some of these cases, which were similar to actual plant situations, are presented below. All runs were made on the rigorous model with the same linear D-B controllers with no changes in controller settings. (1)Bottoms set point was raised from 2.5 to 3.0 mol % (Figure 12). (2) Distillate set point was raised from 99.5 to 99.6 mol % (Figure 13). (3) Pressure was ramped from 210 to 240 psia in 1 h; then feed composition was raised from 70 to 90 mol % at t = 600 min (Figure 14). (4) Pressure was ramped from 210 to 180 psia in 1 h; then feed composition dropped from 70 to 50 mol % at t = 600 min (Figure 15). As Figures 12-15 show, the D-B structure handled all these rather severe disturbances in good style. The structure continues to give effective control even a t extreme operating pressures and feed compositions.
Fragility of the D-B Structure The D-B scheme works because the base level controller and the reflux drum level controller and the two composition controllers all work in unison to maintain product compositions and overall material balance over the long term. The two composition loops are “nested” with the level loops: one loop depends on the other loop being on automatic in order to produce any effect. Therefore, if either analyzer goes out of service or if any of the four control valves saturates, the D-B structure will not work. For example, you cannot put the xD loop on
300
400
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TIME (MIN)
Figure 13. D-B structure, overhead set point to 99.6%. 99.55
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T I M600 E [MIN) 800
1000
1200
Figure 14. D-B structure, high-pressure operation.
manual. If you do, the system will slowly drift away. This is because the flow rate of distillate is fixed, and no composition control system can work with a fixed product flow rate.
Ind. Eng. Chem. Res., Vol. 28, No. 1, 1989 83 Several weeks were spent in controller tuning since it was decided that it would be prudent t o start with more conservative settings than used on the simulation. After some experience, the settings were gradually tightened and are now close to those found in the dynamic simulations. During start-up, the operation of the scheme was smooth except when a control valve was saturated or a sensor failed. Then the operator had to intervene and manually adjust the distillate and bottoms flow rates. When the column is operated at normal flow rates where valve saturation does not occur, the system runs well. When the system runs at maximum capacity, a maximum flow rate limitation on the reflux valve was encountered. An override controller was installed that pinches back on the column feed rate to keep the reflux valve within its operating range.
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Conclusions An experimental and simulation study of low relative volatility distillation columns has resulted in an unorthodox D-B control structure that performs very well in the face of load disturbances and set point changes. However, this structure lacks integrity, and control loop restructuring must be done when any valve saturates or any sensor fails.
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Figure 15.
D-B structure, low-pressure
operation.
The ability of a control system to remain operable when individual loops are taken out of service is called “integrity”. Clearly, the D-B structure has very little integrity. These restrictions on the D-B structure must be recognized and appropriate precautions taken. Override controllers should be used to handle valve saturation by switching the control structure away from dual-composition control. Analyzer failure also requires a switch to single-end composition control. The RR-BR scheme has somewhat more integrity than the D-B scheme. Keeping reflux ratio constant does let the distillate flow rate change even when the xD loop is on manual. However, more sensors are involved, which increases the chances of sensor failure. Industrial Implementation The proposed D-B control scheme was installed on the Sun Oil C3 Splitter a t the Marcus Hook refinery in November 1987. The control hardware used was a Honeywell TDC 2000.
Nomenclature D-B = XD controlled by distillate flow, XB controlled by bottoms flow, base level controlled by steam flow, reflux drum level controlled by reflux flow D-V = xD controlled by distillate flow, XB controlled by steam flow, base level controlled by bottoms flow, reflux drum level controlled by reflux flow R-V = XD controlled by reflux flow, X B controlled by steam flow, base level controlled by bottoms flow, reflux drum level controlled by distillate flow R-B = xD controlled by reflux flow, ZB controlled by bottoms flow, base level controlled by steam flow, reflux drum level controlled by distillate flow RR-BR = xD controlled by reflux ratio (reflux/distillateratio), xB controlled by boilup ratio (steam/bottoms ratio), base level controlled by steam flow, reflux drum level controlled by reflux flow Registry No. Propene, 115-07-1; propane, 74-98-6.
Literature Cited Finco, M. V. The Modeling and Control of Low Relative Volatility Splitters. M. S. Thesis, Lehigh University, Bethlehem, PA, 1987. Luyben, W. L. Steadystate Energy Conservation Aspects of Distillation Column Control System Design. Ind. Erg. Chem. 1975,14, 321. Shinskey, F. G. Distillation Control Short Course. Lehigh University, Bethlehem, PA, May 1986.
Received f o r review June 29, 1987 Revised manuscript received March 1 1 , 1988 Accepted September 6, 1988
