Effect of Feed Impurity on the Design and Control of a Ternary Two

of processes in which a fresh feed stream contains significant impurities. ... amounts of an impurity, which is product C. With low impurity levels, i...
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Ind. Eng. Chem. Res. 1999, 38, 3430-3437

Effect of Feed Impurity on the Design and Control of a Ternary Two-Recycle Process William L. Luyben* Department of Chemical Engineering, Lehigh University, Iacocca Hall, Bethlehem, Pennsylvania 18015

This paper studies both the steady-state design aspects and the dynamic controllability aspects of processes in which a fresh feed stream contains significant impurities. The ternary process with the reaction A + B f C has a flow sheet consisting of two distillation columns, one reactor, and two recycle streams. One of the fresh feeds contains mostly A but can contain varying amounts of an impurity, which is product C. With low impurity levels, it is logical to introduce the fresh feed directly into the reactor; but if the feed contains large amounts of C, it may be more economical to feed this stream into the distillation column that is separating A and C. For the numerical case studied, impurity levels greater than about 30% favor feeding the fresh feed to the column when the reaction is irreversible. When the reaction is reversible, the impurity level at which the fresh feed should be introduced into the column drops to about 20%. Other kinetic and vapor-liquid equilibrium parameter values will affect these impurity levels. Different control structures may be required in the two cases, and the dynamic controllability may also be different. Control schemes are developed that effectively handle both situations. Dynamic simulations show that introducing the impure fresh feed stream into the column gives a faster dynamic response because it isolates the reactor from disturbances. 1. Introduction Interest in plantwide control has increased rapidly in recent years because of the economic pressures to build more efficient chemical plants. These high-performance plants feature minimum surge capacity, extensive energy integration, “on-aim” control requirements, and more material recycle streams to improve yields and to reduce the production of environmentally unfriendly byproducts. All of these features make the dynamic control of chemical processes much more difficult. Work in the area of plantwide control began with the pioneering work of Buckley1 almost four decades ago. The state of the art and the many unanswered challenges were reviewed in the mid-1980s by Stephanopoulos,2 but little progress was made until the early 1990s, when several workers began to actively address this very important and challenging problem. The literature has been recently reviewed by Skogestad,3 and a book on this subject has been published.4 Other recent papers include work by Ny and Stephanopoulos5 and Zheng et al.6 However, many open research areas remain. One of the most important is exploring the interactions and trade-offs between steady-state design and dynamic controllability. This paper studies one aspect of this type of problem. In many situations the “best” flow sheet and parameter values from a steady-state economic point of view do not represent the best overall design when dynamics are taken into consideration. Other flow sheets or other parameter values (reactor sizes, recycle flow rates, etc.), which may be slightly less economical from a steadystate perspective, may offer significant advantages in terms of dynamic disturbance rejection. In this paper we look at a simple process that typifies the plant topology of many industrial processes. The two * Telephone: 610-758-4256. E-mail: [email protected].

Figure 1. Alternative flow sheets.

reactants enter in two separate fresh feed streams, and one of these streams can contain significant amounts of an impurity. The best steady-state flow sheet depends on the purity of the feed stream. At high to moderate purities, the feed should be introduced directly into the reactor. At low purity, the feed should be introduced into one of the distillation columns. The steady-state design and the dynamic controllability of these alternative flow sheets are studied in this paper. 2. Process Studied The process explored is the same as that studied by Luyben et al.,7 and the conventional flow sheet (FS1) is sketched in Figure 1. The two fresh feed streams of reactants A and B (F0A and F0B) are fed directly into the reactor. The isothermal reaction A + B f C takes place in a single stirred-tank reactor with holdup VR and concentrations zA, zB, and zC. Reactor effluent, with

10.1021/ie990025a CCC: $18.00 © 1999 American Chemical Society Published on Web 08/07/1999

Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 3431

flow rate F, is fed into the first distillation column. The relative volatilities are in the following order: RA > RC > RB. Two columns are needed to separate the two reactants from the intermediate-boiling product. Figure 1 shows several possible flow sheets. In the indirect separation sequence (“heavy-out-first”) the heaviest component B is recycled from the bottom of the first column in stream B1. The lightest component A is recycled from the top of the second column in D2. The alternative separation sequence (the direct or “light-outfirst”) recycles A from the top of the first column and B from the bottom of the second column. The indirect sequence is used in this paper to be consistent with previous work, but similar results are expected with the direct sequence. We want to consider what happens when one of the fresh feed streams is not pure A or B, but it contains some of the product C. This situation arises frequently in plants where the feed stream is produced in an upstream unit. If the impurity in the feed were a completely different component, a different separation system would be required to remove this component while still recycling unconverted reactants and producing the desired product purities. In most cases this means an additional separation unit (e.g., a third distillation column) would be required. This situation has been studied by Belanger and Luyben.8 In this paper we assume the impurity in F0A is component C. A similar case would occur if the C impurity were in the other fresh feed stream F0B. Now the choice is to feed this stream into the reactor or into the first column. Of course these feed locations would switch if the direct separation sequence were being used. See Figure 1. 3. Steady-State Process Design Two steady-state design cases are studied. In the first, the reaction is irreversible (A + B f C). In the second, the reaction is assumed to be reversible (A + B S C). For each of these chemical systems the impurity concentration in the F0A fresh feed is varied from zero to 70 mol %. The following assumptions are made: (1) In all cases the net production rate of product C in the reactor is always 98 (lb mol)/h. When there is an impurity of C in the fresh feed, the total flow rate of product C leaving in stream B2 is increased by the amount of C in the fresh feed. (2) The amounts of the reactants lost in the product stream are constant at Aloss ) 1 (lb mol)/h and Bloss ) 1 (lb mol)/h for all cases. (3) The reactor operates isothermally and with constant molar holdup VR. The optimum design value of the reactor holdup varies with the impurity level z0A(C) and with the flow sheet used. (4) The relative volatilities are constant at RA ) 4, RB ) 1, and RC ) 2. (5) Equimolal overflow, saturated liquid feeds and reflux, theoretical trays, total condensers, and partial reboilers are assumed in the columns. (6) The cost factors and equipment sizing are similar to those used by Luyben,3 with the exception that the reactor capital cost is assumed to be five times that of a plain pressurized vessel. (7) The impurities of the recycle streams from the bottom of column 1 (xB1(C)) and from the top of column 2 (xD2(C)) are 1 mol %. (8) There is no A in the bottom of column 1 and no B in the distillate of column 2, so xB1(B) ) 0.99 and xD2(A) ) 0.99.

(9) Fresh feed F0B is assumed to be pure B. The steady-state design procedure is outlined below for the irreversible and reversible reaction cases. 3.1. Irreversible Reaction Case. 3.1.1. Flow Sheet 1. The reaction rate ((lb mol)/h of C produced) is given by

R ) kVRzAzB

(1)

The specific reaction rate is k ) 1 h-1 and R ) 98 (lb mol)/h. The reaction is first order in the mole fractions of reactants A and B. For a given impurity level z0A(C), an iterative procedure is used to find the value of reactor holdup VR that gives the minimum total annual cost (TAC). For each value of reactor holdup, there are an infinite number of possible designs that correspond to having different values of zB, since it is only required that the product zAzB be constant. Therefore, the optimum values of both VR and zB must be found for each impurity level. The steps in the steady-state design procedure are as follows: (1) Fix the value of VR at a small value. (2) Fix the value of zB at a small value. (3) Calculate the concentration zA from eq 1. (4) Calculate the required fresh feed flow rates.

F0B ) RC + Bloss

(2)

F0A ) (RC + Aloss)/(1 - z0A(C))

(3)

Remembering that the reaction is nonequimolal, the steady-state bottoms flow rate from column 2 is calculated:

B2 ) F0A + F0B - RC

(4)

The compositions of the product stream B2 are xB2(A) ) Aloss/B2 and xB2(B) ) Bloss/B2. (5) The total molar balance and the two component balances around the reactor are:

F0B + F0B + B1 + D2 ) F + RC F0Az0A(A) + D2xD2(A) ) FzA + RC F0B + B12xB1(B) ) FzB + RC

(5)

These equations contain three unknowns: F, B1, and D2. They can be combined to solve first for F.

F0A + F0B + F)

RC - F0B RC - F0Az0A(A) + - RC xB1(B) xD2(A) 1-

zA zB xD2(A) xB1(B)

(6)

Then the other two flow rates can be calculated.

D2 )

FzA + RC - F0Az0A(A)

B1 )

xD2(A) FzB + RC - F0B xB1(B)

(7) (8)

(6) The column 1 distillate flow rate is calculated as D1 ) F - B1. (7) Component balances around column 1 permit calculation of the distillate composition.

3432 Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999

xD1(j) )

Fzj - B1xB1(j) D1

(9)

(8) Now the feed, bottom, and distillate flow rates and compositions are known for both columns. The Fenske equation is used to calculate the minimum number of trays. The actual number of trays is set equal to twice the minimum. (9) The Underwood equations are used to calculate the minimum reflux ratio. For sizing purposes, the actual reflux ratio is set equal to 1.2 times the minimum. (10) The columns are sized using an F factor of 1 Vmax(Fν1/2), where Vmax is in feet per second and Fν is in pounds per cubic foot. Condensers and reboilers are sized using the parameter values given in ref 9. (11) Using an energy cost of $5/106 Btu, the total annual cost is calculated by combining the energy cost with the annual capital cost, using a payback period of 3 years.

TAC ($/year) ) energy cost ($/y) + total capital investment (10) payback period (12) Then the value of zB is varied over a wide range, and steps 3-11 are repeated for each value of zB, generating its corresponding TAC. Then the minimum in the TAC versus zB curve is selected. See Figure 2. (13) Finally, the value of the reactor holdup VR is varied over a wide range, and steps 2-12 are repeated. The minimum in the TAC versus VR curve is selected as the optimum steady-state design for the given feed impurity. Figure 2 illustrates the optimization results for one impurity level (z0A(C) ) 0.6). For a given reactor holdup, increasing zB decreases zA, increases the recycle of component B, and decreases the recycle of component A. More detailed results of this design procedure are presented in the next section. 3.1.2. Flow Sheet 2. When the fresh feed stream F0A is introduced into the second column, the design procedure is slightly modified. The reactor balances are modified as follows:

F0B + B1 + D2 ) F + RC D2xD2(A) ) FzA + RC F0B + B1xB1(B) ) FzB + RC

(11)

These equations contain three unknowns: F, B1, and D2. They can be combined to solve first for F.

F0B + F)

RC - F0B RC + - RC xB1(B) xD2(A) 1-

zA xD2(A)

-

zB

(12)

xB1(B)

Then the other two flow rates can be calculated.

FzA + RC xD2(A)

(13)

FzB + RC - F0B xB1(B)

(14)

D2 ) B1 )

Figure 2. Optimization: FS1; z0A(C) ) 0.60.

The column design procedure is the same as that used with the other flow sheet with the exception of the design of the second column. This column has two feeds with different compositions, so in theory they should be introduced on different feed trays to minimize energy consumption. The Fenske equation can still be used, since the bottom and distillate compositions are known. But the Underwood equations, in their conventional form, use a single feed composition. Since we are using an approximate design procedure and these two feed compositions are not very different (at the moderate to high impurity levels), an average feed composition is used to simplify the calculations. This average feed composition is calculated from the two feeds to column 2: D1 and F0A with their corresponding compositions xD1(j) and z0A(j). 3.2. Reversible Reaction Case. The net reaction production rate of product C in the reactor is now

R ) VR(kFzAzB - kRzC)

(15)

where kF and kR are the forward and reverse specific reaction rates. In the numerical results given below, the values used are kF ) 1 h-1 and kR ) 0.5 h-1. Firstorder kinetics are used for both reactions. In step 3 of the design procedure, eq 16 is used instead of eq 1.

zA )

R/VR + kR(1 - zB) kR + kFzB

(16)

3.3. Results. Figures 3 and 4 give results for the irreversible and reversible reaction cases using the two flow sheets and a range of impurity levels. In flow sheet FS1, the fresh feed is introduced into the reactor. In flow sheet FS2, it is introduced into column 2. These results show that FS1 with the irreversible reaction is less expensive for impurity levels less that about 30 mol %. Above this level, the TAC of FS2 is lower. Most of the parameters in flow sheet FS1 change significantly as the fresh feed impurity changes: column vapor boilups, reactor size, and reactor compositions. However, flow sheet FS2 is quite insensitive to changes in impurity levels. Column 2 vapor boilup is the only parameter that changes as fresh feed impurity varies. A comparison of Figure 3 (the irreversible case) with Figure 4 (the reversible case) shows that as feed

Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 3433

Figure 3. Flow sheet 1 and flow sheet 2; irreversible reactions.

Figure 5. (A) Flow sheet 1 control structure. (B) Flow sheet 1 steady-state conditions.

Figure 4. Flow sheet 1 and flow sheet 2; reversible reactions. Table 1. Design Parameters for Flow Sheets 1 and 2 FS1

FS2

z0A(C) ) 0.3 z0A(C) ) 0.6 z0A(C) ) 0.3 z0A(C) ) 0.6 F0A ((lb mol)/h) F0B ((lb mol)/h) F ((lb mol)/h) VR ((lb mol)/h) zA (mole fraction) zB (mole fraction) B1 ((lb mol)/h) D2 ((lb mol)/h) B2 ((lb mol)/h) NT1 NT2 R1 ((lb mol)/h) R2 ((lb mol)/h) D1/D2 ((lb mol)/h) energy cost (M$/y) capital ($1000) TAC (M$/y)

141.4 99.0 293.0 1600 0.186 0.330 96.66 53.92 142.4 28 28 285.9 228.6 4.0/3.1 419 2344 1,200

247.5 99.0 459.8 2050 0.159 0.300 138.3 73.01 248.5 29 29 467.3 377.4 4.7/3.6 678 2954 1,663

141.4 99.0 226.5 1338 0.212 0.345 77.91 147.6 142.4 27 28 212.4 337.5 3.5/4.2 463 2281 1,223

247.5 99.0 226.0 1343 0.212 0.345 77.76 147.3 248.5 27 29 212.2 465.2 3.5/4.6 533 2396 1,331

impurity increases, the FS2 flow sheet becomes less expensive at lower feed impurity levels, about 20 mol %. Note that the size of the reactor, the reactant concentrations, the column vapor boilups, and the TACs are all larger in the reversible reaction case. Table 1 gives more detailed design information for the two flow sheets at the two feed impurity levels for the irreversible reaction case. It should be note that the

results presented in this paper are applicable to the numerical case studied. The parameter values used are quite typical of many industrial cases, but other kinetic and VLE parameters will affect the results. 4. Dynamics and Control Dynamic mathematical models for the two alternative flow sheets were developed and used to test control structures. The 60 mol % feed impurity case is discussed below. 4.1. Assumptions and Initial Conditions. The design parameters obtained from the approximate steady-state design procedure were used as starting points for the rigorous dynamic simulation. Figures 5B and 6B give the rigorous steady-state conditions found by running the dynamic model out to steady state. The steady-state design procedure specified columns with about 30 trays. For the dynamic study both columns are assumed to have 40 trays to give some flexibility to handle disturbances. Both columns are fed on tray 20. Note that the two feed streams to column 2 have similar compositions for the 60 mol % impurity feed being studied (xD1(A) ) 0.3232 and z0A(A) ) 0.40). The flow sheets were converged by setting the total feeds to the reactor at the design values (see Table 2) and manipulating the vapor boilups to attain the desired product specifications. Figures 5B and 6B show that the impurity levels used were xB2(A) ) 0.0067/0.0094 and xB2(B) ) 0.0011/0.0015 in the two flow sheet cases. The purity levels of the recycle streams in the steady-state design procedure were 99%. In the rigorous dynamic

3434 Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 Table 2. Total Flow Rates to Reactor and Production Rates total A; recycle + fresh feed ((lb mol)/h) total B: recycle + fresh feed ((lb mol)/h) production rate ((lb mol)/h)

FS1

FS2

320.5 237.3 245.1

147.3 176.8 239.7

simulation, the reflux flow rates were adjusted to give C impurity levels in the two recycle streams of about 5% instead of the 1% used in the approximate steadystate design. This was done because these recycle streams have no real fixed specifications and more moderate purities make the dynamic responses of the columns less nonlinear. All of these modifications explain why the steadystate conditions of the rigorous dynamic model are not exactly the same as the approximate design conditions and parameters. Note that the production rate is not directly set in the control scheme, so the production rates of the two steady states shown in Figures 5B and 6B are slightly different. See Table 2. 4.2. Control Structures. Tyreus and Luyben10 gave two control structures that provide effective control of this process. A slightly modified version of their “CS1” control structure is used in this paper. As sketched in Figure 5A for flow sheet FS1, it consists of the following loops: (1) The total recycle of component B (the sum of the flow rates of the bottoms from the first column B1 and the fresh feed F0B) is flow controlled. (2) The column 1 base level is controlled by manipulating the fresh feed makeup F0B. (3) The total recycle of component A (the sum of the flow rates of the distillate from the second column D2 and the fresh feed F0A) is flow controlled by manipulating the fresh feed F0A. (4) The column 2 reflux drum level is controlled by manipulating the reflux flow rate R2, and the reflux ratio is controlled by manipulating the distillate flow rate D2. This structure is used because of the fairly high reflux ratio in this column. (5) The reactor level is controlled by manipulating the reactor effluent flow rate F. (6) The column 1 reflux drum level is controlled by manipulating the distillate flow rate D1, which is fed to column 2. (7) The impurity of component A in the product stream from the bottom of column 2 (B2) is controlled by manipulating vapor boilup in column 2 (V2). The bottoms composition is inferred by using a temperature on tray 5. (8) The impurity of component C in the bottom of column 1 (B1) is controlled by manipulating vapor boilup in column 1 (V1). The bottoms composition is inferred by using a temperature on tray 5. (9) The reflux flow rate in column 1 is ratioed to the column feed flow rate. The ratio is set high enough to prevent too much B from going overhead, even in the worst case situation. This “single-end” control scheme is widely used in industry as an effective and reliable alternative to a more complex and expensive “dualcomposition” control structure. (10) The column 2 base level is controlled by manipulating the bottoms flow rate B2. Both fresh feed streams are fed directly into the reactor in this flow sheet. Figure 5B gives steady-state flow rates and compositions for the optimum steady-

Figure 6. (A) Flow sheet 2 control structure. (B) Flow sheet 2 steady-state conditions.

state design with this flow sheet when the fresh feed stream F0A contains only 40% component A. Figure 6A gives an alternative flow sheet in which the F0A fresh feed is not fed into the reactor but is introduced into the second distillation column. The control structure used for this flow sheet is similar to the previous control scheme with the following exceptions: (1) Fresh feed F0A is fed into the second column and is manipulated to hold the reflux drum level in that column. (2) The recycle flow rate of component A, which is now the distillate product from the second column D2, is flow controlled. (3) The reflux flow rate in column 2 is flow controlled. Note that the fresh feed is assumed to be a saturated liquid, so its flow rate has no direct effect on the reflux drum level. Adding more feed decreases the control tray temperature, and the temperature controller then increases vapor boilup. This increases the reflux drum level. Thus, the temperature loop is “nested” inside the level loop, and the level loop will not work if the temperature loop is on manual. If the feed were entering the column as a vapor, its flow rate would have a direct effect on the reflux drum level, and the loops would not be nested. 4.3. Holdups and Controller Tuning. The liquid holdup on each tray is 3 lb mol, and that in all reflux drums and column bases is 100 lb mol. A 6-s hydraulic time constant is used. The reactor level controller is assumed to be perfect. All other level controllers are proportional-only with gains of 2. The temperature

Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 3435 Table 3. Controller Tuning Constants for the Manipulated Variables V1 and V2 with the Sensor on Tray 5a FS1 SP (mole fraction C) Ku Pu (h) Kc τI (h) FS2 SP (mole fraction C) Ku Pu (h) Kc τI (h)

V1

V2

0.4 0.749 0.0545 0.234 0.120

0.05 8.49 0.0533 2.65 0.117

0.4 0.749 0.0545 0.234 0.120

0.05 5.30 0.0476 1.66 0.105

a Two 0.5 min lags in the composition (temperature) loops; composition transmitter spans ) 10 mol %; valve sizes ) twice the steady-state flow rates.

Figure 9. Flow sheet 1; -20% step change in both recycle flow rates; column 1 reflux flow rate ratioed to feed.

Figure 7. Flow sheet 1; +20% step change in both recycle flow rates; column 1 reflux flow rate fixed. Figure 10. Flow sheet 1; fresh feed composition changed from 60% to 30% component C.

Figure 8. Flow sheet 1; +20% step change in both recycle flow rates; column 1 reflux flow rate ratioed to feed.

measurement dynamics are assumed to be two 0.5 min first-order lags. The temperature controllers are tuned

by running relay-feedback tests to get ultimate gains and periods. Then the Tyreus-Luyben settings are used. In the simulation, compositions on tray 5 are used instead of temperatures. Table 3 gives controller tuning parameters. 4.4. Dynamic Results. Figures 7-11 give results of the dynamic simulations for the FS1 flow sheet with several types of disturbances. In Figures 7 and 8, the flow rates of the two streams fed to the reactor are both increased by 20% at time equal zero. In Figure 7 the reflux flow rate in column 1 is held constant, while in Figure 8 the reflux is ratioed to the column feed flow rate. When the R1/F ratio is not used, too much B goes overhead in column 1 and drives the product over the specification limit of 1%. A 20% increase in reactor feeds results in an eventual production rate increase of about 20%. Figure 9 shows that reductions in total reactor feed flow rates are also effectively handled. In Figure 10 the composition of the fresh feed stream F0A is changed from z0A(C) ) 0.60 to z0A(C) ) 0.30. In Figure 11 both feed composition and total reactor feed flow rate disturbances

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Figure 11. Flow sheet 1; simultaneous changes in recycle flow rates and feed composition.

Figure 14. Flow sheet 2; fresh feed composition changed from 60% to 30% component C.

Figure 15. Flow sheet 2; simultaneous changes in recycle flow rates and feed composition. Figure 12. Flow sheet 2; +20% step change in both recycle flow rates.

are made simultaneously. The control system handles these large disturbances well. Figures 12-15 give results for the FS2 flow sheet with the same disturbances. Note that the product impurities are given in these figures in mol %, not mole fraction. The control scheme handles all these disturbances well. Comparing the responses of the two flow sheets (Figures 8-11 versus Figures 12-15) shows that the FS2 system responds somewhat more quickly. Increasing total reactor feed flow rates yields larger changes in the production rate in FS1 than in FS2, but decreases in total reactor feed flow rates give about the same changes in production rate. The impact of fresh feed composition on production rate is larger in the FS2 flow sheet (Figure 10 versus Figure 14). This occurs because this disturbance has little effect on the reactor and the first column in FS2. In FS1 this disturbance enters the reactor and causes changes in all three units. 5. Conclusion

Figure 13. Flow sheet 2; -20% step change in both recycle flow rates.

In this paper we have studied the effects of an impure fresh feed on both the steady-state economic design and the dynamic controllability. Moderate to high impurity

Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 3437

levels favor feeding the fresh feed stream into one of the columns instead of directly into the reactor. Control schemes were developed for each flow sheet and demonstrated to give effective control in the face of very large disturbances. The control schemes are similar in structure, but the dynamics of the FS2 flow sheet (impure fresh feed fed to a column, not to the reactor) are found to be somewhat faster than those of the FS1 flow sheet (fresh feeds fed to the reactor). Nomenclature A ) reactant component B ) reactant component Bn ) bottoms flow rate from column n ((lb mol)/h) Dn ) distillate flow rate from column n ((lb mol)/h) F ) reactor effluent flow rate, feed to column 1 ((lb mol)/h) F0A ) fresh feed flow rate ((lb mol)/h) F0B ) fresh feed flow rate ((lb mol)/h) FS1 ) flow sheet with fresh feeds fed to reactor FS2 ) flow sheet with impure fresh feed fed to column 2 k ) specific reaction rate of the irreversible reaction (h-1) kF ) forward specific reaction rate of the reversible reaction (h-1) kR ) reverse specific reaction rate of the reversible reaction (h-1) Rn ) reflux flow rate in column n ((lb mol)/h) R ) rate of production of component C in reactor ((lb mol)/ h) TAC ) total annual cost (1000$/y) Vn ) vapor boilup in column n ((lb mol)/h) VR ) reactor holdup (lb mol) xBn(j) ) composition of bottoms from column n (mole fraction component j) xDn(j) ) composition of distillate from column n (mole fraction component j) zj ) composition in reactor (mole fraction component j, j ) A, B, C)

z0A(j) ) composition of fresh feed F0A (mole fraction component j) z0B(j) ) composition of fresh feed F0B (mole fraction component j)

Literature Cited (1) Buckley, P. S. Techniques of Process Control; John Wiley & Sons: New York, 1964. (2) Stephanopoulos, G. Synthesis of Control Systems for Chemical PlantssA Challenge for Creativity. Comput. Chem. Eng. 1983, 7, 331. (3) Skogestad, S.; Larsson, T. A Review of Plantwide Control. Internal Paper N-7034; Department of Chemical Engineering, Norwegian University of Science and Technology: Trondheim, Norway, 1998. (4) Luyben, W. L.; Tyreus, B. D.; Luyben, M. L. Plantwide Process Control; McGraw-Hill: New York, 1999. (5) Ny, C.; Stephanopoulos, G. Plantwide Control Structures and Strategies; Preprints from DYCOPS-5 1998; IFAC: Corfu, Greece, p 1. (6) Zheng, A.; Douglas, J. M.; Mahajanam, R. V. Hierarchical Plantwide Control System Synthesis Procedure and Its Application to an HDA Process. AIChE Meeting, Miami, November 1998. (7) Luyben, M. L.; Tyreus, B. D.; Luyben, W. L. Analysis of Control Structures for Reaction/Separation/Recycle Processes with Second-Order Reactions. Ind. Eng. Chem. Res. 1996, 35, (3), 758. (8) Belanger, P. W.; Luyben, W. L. Plantwide Design and Control of Processes with Inerts. Ind. Eng. Chem. Res. 1998, 37, (2), 516. (9) Luyben, W. L. Dynamics and Control of Recycle Systems. 2. Comparison of Alternative Process Designs. Ind. Eng. Chem. Res. 1993, 32, (3), 476. (10) Tyreus, B. D.; Luyben, W. L. Dynamics and Control of Recycle Systems. 4. Ternary Systems with One or Two Recycle Streams. Ind. Eng. Chem. Res. 1993, 32, (6), 1154.

Received for review January 11, 1999 Revised manuscript received June 23, 1999 Accepted July 2, 1999 IE990025A