I n d . E n g . C h e m . Res. 1990,29, 59-71
59
Control of Vapor Recompression Distillation Columns Cristian A, Muhrer,? Michael A. Collura,t and William L. Luyben* Chemical Process Modeling and Control Center, Department of Chemical Engineering, Lehigh University, I 1 1 Research Drive, Bethlehem, Pennsylvania 18015
Vapor recompression is being more widely applied in distillation systems because of the very significant savings in energy consumption that it offers in some separations. There have been many papers discussing the steady-state design aspects of vapor recompression columns, but very few papers have discussed the dynamics and control of these more complex and poorly understood systems. This paper reports the results of a detailed, quantitative simulation study of the dynamics of vapor recompression columns. Two specific systems (propylene-propane and ethanol-water) were studied, but we believe the conclusions drawn from these examples are generic. Results show that, despite the complexity added by the vapor recompression design, the process does not require a more complex control structure. The control strategy designed for a conventional column can be applied t o the corresponding vapor recompression column by simply replacing heat input control with compressor control (variable speed, suction throttling, bypass, or variable reboiler area). Pressure is controlled by auxiliary cooling. This simple conclusion should be generic for most vapor recompression columns because the chemical separations for which vapor recompression columns are economical usually involve difficult separations (low relative volatilities). Typical designs feature columns with a large number of trays. This yields time constants of the composition loops that are much slower than the time constants of the pressure loop. Hence, the pressure loop can be tuned for relatively tight control independently from the composition loops. Distillation consumes a large percentage of the energy used in the chemical process industries. Consequently, there is a significant incentive to improve the energy efficiency of this widely applied separation process. Vapor recompression is one technique that can be applied in some separation systems. Vapor recompression has been discussed in the literature for almost half a century (Robinson and Gilliland, 1950). However, heat pump systems in distillation have been commonly accepted by industry only in recent years (Meili, 1987) because of the sharp rise in energy costs in the 1970s. Most of the literature on vapor recompression focuses on the steady-state economic aspects (capital costs, operating costs, and optimum steady-state operating conditions): Null (1976), Mostafa (1981), Quadri (1981), Brousse et al. (1985), Meili and Stuecheli (1987),Ferre et al. (1985), Collura and Luyben (1988). These steady-state designs have shown that vapor recompression is economical in those separations where the following conditions apply: (1)Heat is not available from other process sources (heat integration). (2) Low-temperature operation requires refrigeration. (3) Temperatures are not too high (compressor thermal limitations). (4) Pressures are not too low (large vapor volumes). (5) The temperature difference between the top and the bottom of the column is small (moderate compression ratios). The last item is probably the most restrictive. It limits vapor recompression to separations that have small boiling point differences between the components. Thus, most practical applications of vapor recompression occur in binary systems where the separation is difficult (low relative volatility). The literature covering the dynamics and control aspects of vapor recompression in distillation is very limited. Mosler (1974) and Quadri (1981) give qualitative discussions of control schemes for maintaining column inventories. Nielsen et al. (1988) reported the use of an adaptive multivariable controller in a pilot-plant column with ex-
* Author
to whom correspondence should be addressed. 'Present address: Air Products and Chemicals, Inc., Allentown, PA 18195. 8 Present address: University of New Haven, 300 Orange Av, West Haven, C T 06516. 0888-5885/90/2629-0059$02.50/0
ternal refrigerant. The system separated methanol-2propanol. Dual composition control was successfully implemented using reflux and high pressure in the external heat pump circuit as the manipulated variables. A number of types of vapor recompression designs are possible (Null, 1976), but most applications use direct vapor recompression: process vapor from the top of the column is compressed to a high enough pressure so that it can be condensed in the reboiler-condenser in (or sometime near) the base of the column. Only direct vapor recompression is considered in this paper. There are several types of designs. Figure l a shows a column in which the reflux drum operates at the same pressure as the column. This scheme is used when the column operates at a high enough top temperature so that cooling water can be used in the trim condenser. This configuration minimizes compressor work since only the amount of vapor needed in the reboiler passes through the compressor. Figure l b shows an alternative configuration in which the reflux drum operates at the compressor discharge pressure. This system must be used when the column pressure is too low to permit heat removal with cooling water without further compression. Sometimes two-stage compressors are used. Vapor from the first stage of the compressor is used in the reboiler, and vapor from the second stage is sent to the trim condenser at a high enough pressure so that cooling water can be used for heat removal. The main difference between vapor recompression and conventional distillation is the way in which energy is added to and removed from the column. In a conventional steam-heated, water-cooled distillation column, the dynamic changes in energy addition (reboiler duty) or removal (condenser duty) can be varied independently. In addition, the dynamics of the reboiler and condenser are typically very fast compared to the dynamics of the column. In a vapor recompression column, energy addition and removal are linked together in the reboiler-condenser. The trim cooler does allow for some independent energy removal, but the quantity of energy removed is small compared to the total amount of energy flowing through the column. 0 1990 American Chemical Society
60 Ind. Eng. Chem. Res., Vol. 29, No. 1, 1990
recompression in both of these systems, but particularly in the propylene-propane system, as will be shown later in this paper. These two systems differ in many ways and span the region in which most practical applications of vapor recompression will lie. 1. Pressure. The ethanol-water system operates a t atmospheric pressure. The propylene-propane system operates at 18 atm for a conventional design and at 10 atm for a vapor recompression design. 2. Vapor-Liquid Equilibrium. The ethanol-water mixture has very nonideal liquid behavior and ideal vapor-phase behavior because of the low operating pressure. The propylenepropane mixture behaves as an ideal liquid, but its vapor is nonideal because of the high pressure. 3. Vapor Holdup. Because of the low pressure, the vapor holdup of the ethanol-water system is negligible. Vapor holdup must be considered in the propylene-propane system. 4. Reflux Drum Pressure. A low-pressure reflux drum can be used with ethanol-water; a high-pressure reflux drum must be used with propylene-propane. 5. Temperature Difference across Column. The AT between the top of the column and the bottom of the column is 62 and 22 O F for the ethanol-water and propylene-propane systems, respectively. The A T has a major impact on the economic attractiveness of vapor recompression systems because a large A T implies a high compression ratio and increased compressor power. Vapor recompression is generally considered to be economically viable (late 1980s energy costs) for separations that have A T s that are less than about 60 O F . In light of this, the propylene-propane and ethanol-water systems can be seen as approximating the boundary conditions of the region where economic incentives exist. Because of their representative nature, these systems provide a basis for a general study of vapor recompression. Figure 1. (a, top) High-pressure reflux drum. (b, bottom) Lowpressure reflux drum.
A t the beginning of this study, it was thought that the pressure behavior and the boilup behavior of vapor recompression and conventional columns might be different. In a conventional column, pressure dynamics are normally fast and can be controlled by manipulating condenser duty. Vapor boilup can be directly and independently manipulated by heat input to the reboiler. In a vapor recompression column, the effect of compressor speed on pressure appears to be complex. For example, one would expect an increase in compressor speed to increase the flow through the compressor. This should pull more vapor from the column and decrease the pressure in the column. However, the same increase in speed will increase the heat added to the column and thus increase vapor rates and might produce an increase in column pressure. The net effect of these changes and the speed at which they occur were unknown when this study was initiated. The principal objective of this work was to gain understanding of the dynamics of these vapor recompression systems so that effective control systems could be developed. It appeared that vapor recompression columns were truly multivariable systems of order 3 X 3 (two compositions plus pressure) and that they represented a significant control challenge. Systems Studied Two specific, industrially important separations were examined in detail: ethanol-water and propylene-propane. There are substantial economic incentives for using vapor
Steady-State Design A. Ethanol-Water System. The design and optimum operating parameters for a conventional distillation column a t the base case conditions are shown in Figure 2a. The column contains 78 trays (40% efficiency in the stripping section and 50% in the rectifying section). The reflux ratio (1.75) is 1.1times the minimum. The energy consumption for this design is 117.4 million Btu/h (120000 Ib/h of 50 psia steam). Feed is preheated by overhead vapor and bottoms product. See Muhrer (1989) for more details. The vapor recompression design for the same separation is presented in Figure 2b. The column itself is identical with the conventional one because the operating pressure and reflux ratio are the same. The energy consumption is 8000 hp or 20.4 X lo6Btu/h. Since the top temperature is high enough to use water to condense the excess vapor (the vapor not required to match reboiler duty), it is possible to use a low-pressure reflux drum scheme. The capital investments for the conventional and vapor recompression designs were estimated to be $1.3 and $5.5 X lo6. By use of utility costs of $5/1000 pounds of steam and $0.07/kWh of electricity, the annual energy costs were $5.6 and $3.8 X lo6. These numbers give a 2.3-year pay out time for the incremental investment in going from conventional to vapor recompression systems. The very large capital cost of the vapor recompression system is mostly due to the cost of the compressor. Compressor cost is a function of the compression work required and the volume of vapor that must be handled. For this chemical system, the relatively large temperature difference (62 O F ) between the top and bottom of the column indicates the need for a large compression ratio. For systems with
Ind. Eng. Chem. Res., Vol. 29, No. 1, 1990 61 10000 20 76 ethanol llOF
A
I
1.
351 .l 99% c ;
248.9 5% c; 133.4 F
83% ethanol
73 F 10.9 atm
7 5125
t?
1197 hp
759 1 0.01% ethanol 173 F
FEED
w
!0000
?O B ethanol 110F
1 5% 248.9c
153 F
95 F
17.6 atm
w 99% c =
Figure 3. (a, top) Conventional column, propylene-propane; (b, bottom) vapor recompression column, propylene-propane (numbers inside heat exchangers are lo6 Btu/h; numbers without units along lines are flow rates in lb-mol/h; compositions are mol %).
4
0.01% ethanol 173 F
Figure 2. (a, top) Conventional column, ethanol-water; (b, bottom) vapor recompression column, ethanol-water (numbers inside heat exchangers are lo6 Btu/h; numbers without units along lines are flow rates in lb-mol/h; compositions are mol 9%).
smaller temperature differences, less energy is required and capital cost and pay out time decrease (as in the propylene-propane system). B. Propylene-Propane System. The base case for the conventional propylene-propane distillation is shown in Figure 3a. It is necessary to operate at 17.6 atm (244 psig) in order to use water in the condenser. This pressure is based on a design overhead vapor temperature of 110 OF. This high pressure reduces relative volatility, resulting in a very large column (208 trays, 100% efficiency) and high reflux ratio (13.6). It is not possible to preheat the feed using a column product because the temperatures of these streams are close together. If colder cooling water were available, allowing condensation at 90 OF, the pressure could be reduced to 15.6 atm, resulting in a 4.4% reduction in energy consumption.
The same separation using vapor recompression is presented in Figure 3b. In this case, it is possible to decrease the operating pressure and hence increase the relative volatility. A high-pressure reflux drum scheme is used because of the low top temperature. The temperature in the reflux drum is fixed to provide a 15 OF temperature difference in the reboiler-condenser. This design has a column with 54 fewer trays and an operating pressure 7 atm lower than the conventional column. The energy consumption drops from 27.3 X lo6 Btu/h (steam) to 3.0 X lo6 Btu/h (electricity). The base case design of the conventional column has a capital cost of $1.5 X lo6 and an annual energy cost of $1.2 X lo6. The vapor recompression design has a capital cost of $1.85 X lo6 and an annual energy cost of $0.56 X lo6. The pay-out time for the incremental investment in going from conventional to vapor recompression in this system is only 0.25 year. This is because of the small column AT and high pressure.
Dynamic Models The distillation columns were simulated by using standard column modeling equations. For ethanol-water , the model included two dynamic component balances and one energy balance per tray. For propylene-propane, equimolal overflow was assumed, eliminating the energy balances. The liquid flow rate from each tray was calculated from the Francis weir formula. Details of vaporliquid equilibrium relationships, physical properties, and column dimensions are presented by Muhrer (1989).
62 Ind. Eng. Chem. Res., Vol. 29, No. 1, 1990
Models were derived for the compression section of the process (see Davis and Corripio (1974) for previous work). To model the variable pressure in the column and in the compressor piping, the system was divided into three pats: suction piping, discharge piping, and the compressor proper. Mass balance equations were written for the suction and discharge volumes. These differential equations gave the suction and discharge pressure of the compressor at any point in time:
dPd
-=
di
(F, - F,
RR
\
1.6 -J
m 6
H
a
6
>
1.2
I
-
1
V/F
ZdR Td
-
Fd)-
vd
where F is a molar flow rate, P is a pressure, R is the ideal gas constant, z is a compressibility,Tis a temperature, and V is a volume and for the subscripts c is the compressor, d is the discharge, g is the surge, and s is suction. The suction volume included the effective volume of the column (see Choe and Luyben (1987)). The flows were calculated from algebraic equations. The compressor curves were used to determine F, from the given speed and pressure difference. The vapor leaving the top tray in the column (from the energy equation) and the vapor from the flashing of the hot reboiler condensate gave Fa. The flow rate Fdwas what is being condensed in the reboiler and trim condenser. The bypass flow Fgwas used, if necessary, to avoid surge in the compressor. A. Ethanol-Water System. The column operating pressure was atmospheric in both the conventional and vapor recompression cases, so vapor holdup was a small fraction of the total holdup (2%) and was neglected. Other specific assumptions were (1)constant pressure drop (5.3 mmHg/tray), (2) temperature measurement lag of 15 s, composition measurement dead time of 1min, compressor speed lag of 30 s, heat input lag of 30 s, and (3) compressor polytropic efficiency of 70%. B. Propylene-Propane. Because of the very large number of trays and the long time constants of this system, it was necessary to use as simple a dynamic model as possible. Several simplifying assumptions were made. Due to the high operating pressure, vapor holdup represented about 30% of the total holdup and had to be considered. As a good approximation, additional liquid holdup was added to simulate the impact of the vapor holdup on the column dynamics. This model gave dynamic responses to all disturbances that were essentially the same as the rigorous vapor holdup model proposed by Choe and Luyben (1987). An equimolar overflow model, which removed the need for energy equations, was found to give the same dynamic responses as a rigorous equimolal overflow model for all disturbances except pressure changes. Pressure effects were not seen because vapor flows were not calculated from the energy balance of each tray but were instead assumed constant throughout the column. Since relatively small changes in pressure were seen in the dynamic tests of the column, an equimolal overflow model was used for propylene-propane. The following additional assumptions were made: (1) constant pressure drop (5.3 mmHg/tray), (2) composition measurement dead time of 5 min, compressor speed lag of 30 s, heat input lag of 30 s, and (3) compressor polytropic efficiency of 70%.
Control System Design An effective control system is essential for the efficient
0.12
0.16
0.20
0.24
0.28
0.32
FEED COMPOSITION (MOL FRACTION)
l ' " " " " ' !
i
15.0
t
>
-
U
W
I6
i
11.0
-J
3 Q
Y
I
7.0 0.50
0.54
0.58
0.62
0.66
0.70
FEED COMPOSITION (MOL FRACTION) Figure 4. Steady-state changes in manipulated variables: (a, top) ethanol-water; (b, bottom) propylene-propane.
operation of any process. In this study, multiloop, single-input-single-output controllers (diagonal structure) were found to perform well, so multivariable controllers were not investigated. The controller design procedure employed was similar to that presented by Yu and Luyben (1986). Steady-state "rating" programs were developed for all columns. They were used to determine incentives for dual composition control by plotting the steady-state changes required in all manipulated variables to hold the controlled variables constant for disturbances in feed composition (Luyben, 1975). Disturbances in feed flow rate do not have to be considered because they can be handled with ratio schemes. Figure 4 gives these results for both systems. The curves for ethanol-water show that both vapor boilup and reflux flow must be adjusted to compensate for feed composition disturbances, but the reflux ratio remains almost constant over the range studied. This means that single-end composition control could be used with very little penalty in energy consumption. Singular value decomposition (Moore, 1986) recommended the use of tray 6 temperature. The recommended control system has heat input controlling tray 6 temperature and reflux ratio fixed. Although dual composition was not required for the ethanol-water system, it was examined in the interest of increasing our understanding of the generic behavior of vapor recompression columns. An analyzer was used to measure the top composition instead of inferring it from the temperature because of the poor sensitivity of the temperature on the top trays. Figure 5a shows the control system for
Ind. Eng. Chem. Res., Vol. 29, No. 1, 1990 63
1. conventional column
3.7e-',&
+ 1)(162s + 1) -170e4,%
;[ ]
-5.8e-',%
(1.8s
+ 1)(119Os + 1 7
+ 1)(127s +
323e4.& (1.3s + 1)(40Os + 1) 1)2
1.6e" (0.02s + 1)(19.3s + 112 168 L ( 0 . 6 ~+ 1)(140s + 1 ) 2
-26.6e-S (0.8s + 1)(1510s + 1) 2130 (1211s + 1)(0.08s2+ 0.6s
2. vapor recompression column
[=I:[ B. Propylene-Propane 1. conventional column
[
XD
1=
r
5 .4e-5S
-6. 84e-5s
(1.55s
+ 1)(4310s + 1)
+ 1)J
(0.8s
+ 1)(175s + 1)2-
2. vapor recompression column
-
I;] =
-9.2e-5S (1.5s + 1)(4800s + 1)
(3s
-
+ 1)(115s + 1)2
-0.88 (0.02s + 1)(92s + 1)
7.9e-5s (7s + 1)(141s + 1)2 -2.8e-5S (4.5s + 1)(14s2+ 6s + 1) 1 (4.2s + 1)(11.5s2+ 3s + 1)
the thanol-water separation with vapor re ompression. T e curves in Figure 4b for propylene-propane show that all manipulated variables change significantly as feed composition changes, so dual composition control is required. Several choices of manipulated variables were explored. Finco et al. (1989) studied the control of conventional propylene-propane columns and recommended an unorthodox D-B control structure (distillate flow controls distillate composition, bottoms flow controls bottoms composition, reflux flow controls reflux drum level, and heat input controls bottoms level). Unfortunately, this structure has poor integrity and cannot be analyzed by steady-state methods. The RR-BR structure (reflux ratio controls distillate composition and boilup ratio controls bottoms composition) is equivalent to the D-B structure assuming tight level control. It requires more complex instrumentation and is more difficult to operate (Waller et al., 1988). The D-B,RR-BR, and the more conventional D-QR structures were all studied. Controllers were designed for each case and control performances compared. Only slight differences were found (see Figure 6). Therefore, the widely used D-QR structure was chosen for the conventional column. For the vapor recompression column, a structure that used distillate flow and compressor speed (D-Sp) was used for reasons that will be discussed later in this paper. Figure 5b shows the control system with vapor recompression. These steady-state rating programs were also used to calculate steady-state gains. These were used in obtaining transfer functions so that manipulated variables could be selected and unworkable pairings could be eliminated. Transfer functions of the processes were identified by using the ATV identification procedure (Luyben, 1987). Table I gives the transfer functions for both the conventional and vapor recompression columns for both chemical systems.
(178s +
-0.2'ie-5s 1)(24150s2+ 252s
+ 1)
o.ie-5s
(11s + 1)(78s2+ 10.5s + 1) -0.275 (0.4s + 1 ) ( 1 2 ~+ 1)
-
Table 11. Controller Tuning"
conventional column
Kc TI A. Ethanol-Water
loop
xD-RR TCQR(SJ x D-D
XB-QR(SJ
4.8 0.9
57 9.6
vapor recompression column
Kc
TI
5.0 0.8
37 3.4
B. Propylene-Propane -36 44 -36 -0.385 60 -0.18
37 42
Note: Controller gains were made dimensionless by using valve gains equal to twice the steady-state flow rates and the following transmitter spans: for ethanol-water, X D 0.20, tray 6 100 OF; for propylene-propane, XD 0.05, XB 0.20.
Note that the transfer functions obtained between manipulated variables and pressure have time constants that are much smaller than those for the compositions (see Table IB-2 for propylene-propane). Note also that compressor speed has little effect on pressure; it mostly effects compositions. The Niederlinski index is +3.6 for the pairings xD-D, xB-Sp,and P-F,. The RGA for this system shows that the only pairings that do not give negative RGA elements on the diagonal are those that pair cooling water with pressure:
RGA =
0.240 0.154 0.001
0.893 0.255 -0.148
-0.137 -0.010 1.15
1
It is interesting to note that the Niederlinski index does not show that pressure must be paired with cooling water. It gives a positive index of 36.3 for the pairings xD-S,, xB-Fw, and P-D.
64 Ind. Eng. Chem. Res., Vol. 29, No. 1, 1990
F
q
I
surge
+ B
Figure 5. Control system for vapor recompression column: (a, top) ethanol-water; (b, bottom) propylene-propane.
The multiple SISO controllers were tuned by using the BLT technique (Luyben, 1986). Table I1 gives tuning parameters.
Results for Specific Systems A. Ethanol-Water. The performance was evaluated with the nonlinear model by introducing step disturbances in the feed composition. The results are shown in Figure 7a for the conventional column and in Figure 7b for the vapor recompression column. Constant pressure was assumed in the conventional column since it would typically be vented to the atmosphere through a vent condenser. In the vapor recompression column, the pressure loop was found to be quite fast. Therefore, it could be tuned independently from the composition loops. The control strategy used on the conventional column was found to work quite well on the vapor recompression column. Controller settings were somewhat different because the open-loop behavior of the vapor recompression system was slightly faster than the conventional column (smaller deadtimes and time constants). This behavior could be due to the effect of pressure transients. These results indicated that the control structure used in the conventional column could also operate successfully in the vapor recompression column if compressor control
was substituted for steam flow. B. Propylene-Propane. The performance of the conventional propylene-propane column has already been shown in Figure 6. The same basic structure was used on the vapor recompression column. Compressor speed was used instead of steam flow. Controllers had to be retuned because the dynamics of the vapor recompression column were slightly faster than the conventional. This can be explained by the lower operating pressure, higher relative volatility, and fewer trays. Cooling water flow rate to the trim condenser was used to control the pressure. As shown in Table 11, the time constants of the pressure-to-coolingwater loop were found to be much faster than the composition dynamics. Therefore, the pressure loop was tuned tightly and the composition loops were treated as a 2 X 2 system in the BLT tuning method. The performance of the vapor recompression system for step changes in feed composition is given in Figure 8. The response is slightly faster than that obtained by the conventional column. The manipulated variable movements indicate that the range of controllability could be wider (bigger disturbances could be handled) without running into valve saturation. Thus, both of the separations studied yielded the same conclusion: the control system used on the conventional column could be applied to the vapor recompression column with the simple substitution of compressor speed for steam flow. The effect of a change in compressor speed is primarily to change the vapor rate through the column, not to make large changes in suction or discharge pressures. The discharge pressure must change somewhat to produce the required change in the temperature differential driving force in the reboiler. In the next section, results of studies of several methods for controlling compressor throughput are presented.
Alternative Compressor Control Systems The control strategies for vapor recompression towers presented so far have been designed with a variable-speed compressor. If the compressor is driven by a steam turbine, changing speed is straightforward. However, variable-speed electric motor drives are expensive. Compressor control can be accomplished in several other ways: suction throttling, bypassing flow back into the compressor suction, or varying the heat-transfer area in the reboiler-condenser using a flooded reboiler design (condensate-throttling). In this section, these alternatives will be compared in terms of both steady-state design (energy consumption) and dynamic controllability. The propylene-propane system was used for the comparisons. The compressor was controlled to regulate heat input to the column, thus controlling bottoms composition. Figure 9 shows control schemes for bottoms composition control by using four different compressor control structures. A. Plant Characteristic Curve. In order to analyze the effects of the compressor control alternatives and the compressor characteristic curves on the process, the plant characteristic curve was needed. It was obtained by using a steady-state rating program. The column feed rate was varied while the compositions were held constant to see the result of changing the compressor throughput. Figure 10 gives the compressor characteristic curves as well as the plant characteristic curve. It is interesting to note that the plant curve displays a unique, almost linear relationship between head and flow. This is in sharp contrast to the typical quadratic plant characteristic curve that is usually found in compressor applications. These normal plant curves reflect the second-order relationship
Ind. Eng. Chem. Res., Vol. 29, No. 1, 1990 65 10.0
1
360.0
c
-z E I
p, and a pressure differential exists a t zero flow. Assuming pure propylene and propane products,
This type of almost linear plant characteristic curve should be found in most vapor recompression distillation systems. By use of the approximate equations, the values for m and b of 0.0014 min atm/ft3 and 3.72 atm were calculated. These compared very well with the values found by fitting the data obtained from the rigorous rating program: 0.0012 and 3.75. B. Description of Alternative Compressor Controls. 1. Variable Speed. Compressor speed was adjusted to compensate for process disturbances. Figure l l a shows how the compressor speed must change to maintain compositions when additional heat is required by the column. The discharge pressure must increase to provide the higher temperature differential driving force in the reboiler and the flow must increase. This is achieved by moving the operating point to a higher speed curve. 2. Suction Throttling. The suction throttling strategy adjusts compressor suction pressure to compensate for process disturbances. Figure l l b shows the case when additional heat is required by the column. The operating point moves along a constant speed curve to a higher flow by reducing the pressure difference across the compressor. The higher temperature differential driving force in the reboiler-condenser increases the discharge pressure. The increased opening of the suction valve decreases the pressure drop over the valve and increases suction pressure enough to provide the needed increase in both discharge
Ind. Eng. Chem. Res., Vol. 29, No. 1, 1990 67 50 3
-
I
1
1
-I
0
5-
340.0
3 0
300.3
b1 .
W
! C
