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Ind. Eng. Chem. Res. 2008, 47, 8704–8712
Dynamic Control of a Column/Side-Reactor Process Devrim B. Kaymak† and William L. Luyben*,‡ Department of Chemical Engineering, Istanbul Technical UniVersity, 34469, Maslak, Istanbul, Turkey, Department of Chemical Engineering, Lehigh UniVersity, Bethlehem, PennsylVania 18015
If the temperature range suitable for reasonable chemical reaction kinetics does not match the temperature range suitable for vapor-liquid equilibrium, reactive columns are not economically attractive. One way to overcome this temperature mismatch is use a flowsheet that features a distillation column with multiple side reactors. The column operates at a pressure that gives temperatures favorable for separation, while the reactors operate at temperatures (and pressures) favorable for reaction kinetics. This paper discusses the controllability of a column/side-reactor process based on the steady-state design studied by Kaymak and Luyben.1 The performances of two different control structures are explored. The first uses two temperature controllers, one with direct action and the other with reverse action. The second control structure uses an internal composition analyzer. One of the main conclusions is that the opposite actions of controllers in the two-temperature control structure result in a composition breakthrough that moves the column to a different operating condition. The composition and temperature controllers in the second structure have the same action and provide reasonably effective control. 1. Introduction Reactive distillation can yield significant economic benefits in some systems. However, for reactive distillation to be attractive, the temperatures that are good for reaction must match the temperatures that are good for vapor-liquid separation. Therefore traditional reactive distillation is not effective in many chemical systems because of a mismatch in temperatures. Kaymak et al.2 demonstrated quantitatively that reactive distillation becomes less attractive as the temperature mismatch increases. To overcome this temperature mismatch, a flowsheet combining a distillation column with external side reactors can be considered where the column operates at temperatures favorable for separation, while the reactors operate at temperatures favorable for chemical kinetics. There are several papers in the literature dealing with the design of combined column/reactor systems.3-7 However, we are not aware of any paper in the literature that discusses the controllability of these column/sidereactor configurations. In this paper we explore the dynamic control of a column/ side-reactor process based on a recent design paper.1 2. Process Studied The process studied has an ideal exothermic liquid-phase reaction where products C and D are formed from the reactants A and B in several side reactors linked to a distillation column. A+BSC+D
(1)
The reactors operate at pressures and temperatures conducive for reaction kinetics. The side reactors are connected to a distillation column that operates at a pressure conducive for vapor-liquid separation. No reaction occurs within the column. The parameter used by Kaymak et al.2 to quantify reaction/ separation temperature mismatch is R390, which is a measure of how the relative volatilities among the four components * To whom correspondence should be addressed: E-mail: WLL0@ Lehigh.edu. Tel.: 610-758-4256. Fax: 610-758-5057. † Istanbul Technical University. ‡ Lehigh University.
change with temperature. At a temperature of 320 K, which is typical of the reflux drum temperature in a condenser using cooling water, the relative volatilities between adjacent components are R320 ) 2. As temperature increases, the relative volatilities decrease. A value of R390 ) 1 means that all components have the same relative volatility at 390 K. The temperature of 390 K is selected because this temperature gives favorable kinetics in terms of both the forward specific reaction rate and the chemical equilibrium constant in the numerical case used to illustrate the issues. Although we studied a wide range of R390 values in the design paper,1 in this control paper we only deal with the R390 ) 0.95 case in which there is considerable reaction/separation mismatch. The vapor pressure PjS of component j is a function of temperature as given in the Antoine equation. ln PSj ) AVP,j -
BVP,j T
(2)
where AVP,j and BVP,j are constants over a limited temperature range. The Antoine constants for the case considered here are given in Table 1. The detailed calculations to obtain these values are explained in a previous paper.2 The process configuration is given in Figure 1. There is a distillation column operating at its optimum pressure and temperature for separation (320 K in the reflux drum). The reactants A and B are fed to the column in two pure reactant fresh feed streams F0A and F0B, both with a flowrate of 12.60 mol/s. There are 17 trays and a partial reboiler in the stripping section below fresh feed streams F0A, and a rectifying section with 7 trays and a total condenser above fresh feed streams F0B. There is a middle zone with 7 trays between these two sections, where three total liquid trap-out trays are installed at different locations. The lower and upper trap-out trays are immediately below the fresh feed streams of reactants A and B, respectively. It is assumed that the number of trays Table 1. Vapor Pressure Constants R390
constant
A
B
C
D
0.95
AVP BVP
12.34 3862.00
15.80 5189.23
8.89 2534.77
19.26 6516.46
10.1021/ie701705m CCC: $40.75 2008 American Chemical Society Published on Web 10/04/2008
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catalyst is 0.5, so the vessel is half-filled with liquid and half-filled with solid. The reaction occurs at the catalyst site, so that is where the heat of reaction affects the catalyst temperature. There is also heat transfer from the catalyst to the liquid. This means that there will be a temperature difference between the liquid and the solid even under steady-state conditions. The energy equation for the solid catalyst in the nth lump is dTcat,n -λFliqVliq ⁄ Mliq ) (kFxA,nxB,n - kRxC,nxD,n) dt FcatVcatCPcat UA (T - Tliq,n) (3) FcatVcatCPcat cat,n The energy equation for the liquid in each lump includes the convective terms associated with flow of liquid in and out of the lump at their respective temperatures. dTliq,n MliqFliq,n UA ) (T - Tliq,n) + (T - Tliq,n) dt FliqVliq liq,n-1 FliqVliqCPliq cat,n (4) Figure 1. Column/side-reactor process.
between each liquid trap-out tray is the same. Thus, the second trap-out tray is at the midpoint of this middle zone. This column is just used for separation; no reaction occurs in any part of the column. The light product C leaves in the distillate, while the heavy product D is removed in the bottoms. The dynamic component balances for the column are given in the design paper.1 All the reaction takes place in three side reactors. These reactors are adiabatic plug-flow reactors, and the holdups of each reactor are the same (VR ) 80 kmol). The vapor from the tray below each trap-out tray flows up through the chimney to the tray above with no vapor-liquid contacting. Each liquid trap-out tray collects all the liquid coming down from the tray above the trap-out tray. Liquid from each trayout tray is pumped to a high enough pressure so that the material stays liquid at the higher temperatures in the external side reactors. Reactor effluents are fed back to the column on the tray below the trap-out tray from which they were withdrawn. Since we are interested in the dynamic behavior of the system for this control paper, the tubular reactor model used in the flowsheet must be dynamic, not just steady-state as in the design paper. The spatial variation in temperature and composition variables is approximated by using a lumped model. With a reasonable number of lumps, the lumped model gives a steady-state profile similar to the real steady-state profile we get using the rigorous steady-state equations. A lumped model of a distributed system is equivalent to using a series of CSTRs to approximate a tubular reactor. Each lump has its dynamic component and energy balances with variables needed to be numerically integrated in time: dT/ dt, dx/dt, etc. In these reactors, both the process liquid and the catalyst have thermal capacitance, so the temperatures of these two phases can be dynamically different in each lump with heat transfer between the solid and liquid phases. Of course the liquid compositions change dynamically from lump to lump because of the convective flows in and out and because of the reaction. The kinetics used is based on the volume of the liquid. That brings up the issue of specifying the amount of liquid and the amount of solid catalyst in a given total vessel volume. It is assumed that the void volume of the
The last term in both of these energy balances comes from the heat transfer between the catalyst and the liquid. Two assumptions have been made to calculate the values of heat transfer coefficient U and area A needed for these equations: (i) the temperature difference between the liquid and solid is ∼1.5 K at steady state, and (ii) the catalyst particles are spherical with a 0.002 m diameter. The reaction directly affects the compositions in the liquid phase. The forward and reverse specific reaction rates follow the Arrhenius Law. kF ) aFe-EF ⁄RTcat
(5)
kR ) aRe-ER ⁄RTcat
(6)
The overall reaction rate is based on concentrations in mole fractions and liquid holdups in moles. To avoid confusion, the specific reaction rates used in this paper (with the reactor halffull of catalyst) are twice those used in the design paper in which catalyst was not considered. Fliq,n dxi,n ) (x - xi,n) ( (kFxA,nxB,n - kRxC,nxD,n) dt FliqVliq ⁄ Mliq i,n-1 (7) Since the reaction is exothermic, some vapor is produced as the liquid from the high-pressure reactor flashes into the low-pressure column. This results in an increase of the vapor flow rate at each external reactor location and a corresponding decrease of the liquid rate below the external reactor location. The quantity of this vapor is calculated from the heat generated by the reaction occurring in the external reactor, the flow rate of material into the reactor and the thermal properties. The steady-state vapor and liquid rates are constant through the stripping and rectifying sections since equimolal overflow is assumed. However, there are different liquid and vapor rates in the middle sections of the column. The physical and chemical parameter values are given in Table 2. Figure 2A gives the composition and temperature profiles for column. The left graphs are steady-state results using rigorous ordinary differential equation models for the three reactors. The right graphs are steady-state results using the lumped reactor model. The column profiles are essentially identical. Figure 2B gives composition and temperature profiles for each of the three reactors using either the rigorous reactor
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3. Control Structures
Table 2. Physical and Chemical Parameters activation energy of reaction forward reverse specific reaction rate at 366 K forward reverse heat of reaction, λ heat of vaporization, ∆Hv molecular weight of the mixture, Mliq catalyst density, Fcat liquid density, Fliq ideal gas constant catalyst heat capacity, CPcat liquid heat capacity, CPliq heat-transfer coefficient, U heat-transfer area, A
cal/mol 30000 40000 kmol/(s-kmol) kJ/mol kJ/mol g/mol kg/m3 kg/m3 cal/(mol-K) kJ/(kg-K) J/(kg-K) kJ/(s-K-m2) m2
0.016 0.016/(KEQ)366 - 41.8 29 50 2000 800 1.987 0.50 2.93 0.02 749
model (solid lines) or the lumped reactor model (dashed lines). These profiles are quite similar.
In practical applications it is desirable to use inferential temperature measurements whenever possible instead of direct composition measurements. Composition analyzers have higher cost, require more maintenance, and can introduce deadtime into the control loop. Therefore, we first explore a control structure that does not have any composition analyzer. The performance of this two-temperature control structure will then be compared with a structure that uses a composition analyzer. The control structures are single-input-single-output (SISO) structures with PI controllers for temperature and composition and P-only controllers for levels with gains of 2. The Tyreus-Luyben tuning method is used to tune the temperature and composition controllers. The ultimate gain and ultimate period necessary for this method are obtained using the relayfeedback test. Two first-order measurement-lags of 60 s each are used in all temperature loops, while a 3 min deadtime is
Figure 2. (A) Composition and temperature profiles for column, (B) composition and temperature profiles for reactors (length ) 8.6 m).
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used for the composition analyzer. All the control valves in the process are designed to be half-open at steady state. The effectiveness of the control structures studied in this paper is demonstrated by using dynamic simulations and subjecting the processes to production rate changes (∆F0j or ∆VS) and feed composition disturbances (∆z0A and ∆z0B). As with any control system, factors such as criticality of the online analyzers and failure of measurements would need to be considered in any actual plant installation. These factors have not been considered in this study. 3.1. Control Structure CS7. Control structure CS7 is based on a paper by Roat and co-workers8 and is shown in Figure 3. Two temperature controllers manipulate the two fresh-feed flowrates to maintain the temperatures on two trays. Reboiler heat-input is flow controlled and serves as the productionrate handle. The base level is controlled by manipulating the bottoms flowrate, while the reflux drum level is controlled
Figure 3. Control structure CS7.
Figure 4. Gains and SVD for CS7.
by the reflux flowrate. Reflux ratio is controlled by measuring the reflux flowrate, multiplying this by the reciprocal of the desired reflux ratio and sending this signal to a remote-set cascade flow controller on the distillate stream. The column pressure is assumed to be constant and controlled by condenser heat removal. Note that the liquid levels on the three trap-out trays are held constant by manipulating the three valves in the liquid streams from the reactors back to the column (controllers not shown in Figure 3). The pressures in the liquid-filled reactors are set by the pump head. The selection of the trays to temperature control is the main issue in this structure. From the rigorous steady-state simulation, the gain matrix between the inputs (two fresh-feed flowrates) and the outputs (the temperatures on all trays) is calculated numerically. Using these steady-state gains, the locations of the most sensitive trays whose temperatures are to be controlled are selected by applying singular value decomposition (SVD) analysis. Some engineering judgment must be also exercised in this selection. The procedure is discussed in detail in a previous paper.9 The steady-state gains (KF0A and KF0B) between tray temperatures and feed flow rates and their related SVD results for CS7 structure are given in Figure 4. The steady-state gains between tray temperatures and the F0A feed are negative (an increase in feed flowrate decreases tray temperature) throughout the column except for a small region in the lower stripping section that has very small positive values. On the other hand, the steady-state gains between tray temperatures and the F0B feed are mostly positive, especially at the most temperature sensitive regions. Note that the most sensitive temperature measurements to the change in the fresh feed streams are in the rectifying section with a negative maximum at tray 27 for F0A and with a positive maximum at tray 26 for F0B. However, since these two trays are so close to each other, it is not possible to use both of them. To overcome this problem, we look for secondary sensitive regions for both gains (second peaks that are smaller than the biggest ones). By looking at the curves in Figure 4, these secondary peaks are found in the upper stripping section (tray 16 for both gains). Although the problem defined above may be solved by selecting one of these trays to pair with one of the fresh feed stream, a bigger problem still exists. While
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both primary and secondary sensitive trays have negatiVe gains for changes in F0A, the gains are positiVe for changes in F0B. Therefore there will be a difference in the actions of control loops, and this may result in difficulties for this control structure. Kaymak and Luyben9 pointed out that the actions of the two temperature controllers used in a reactive distillation column should be the same (e.g., both positive). Controlling an upper tray in rectifying section by manipulating the fresh-feed flowrate F0B (the upper-feed flowrate) and controlling a tray in the stripping zone by manipulating the fresh-feed flowrate F0A (the lower-feed flowrate) sounds more reasonable than the reverse. Therefore the F0A/T16 and F0B/T26 pairings are first selected as the control loops instead of the alternative pairings of F0A/T27 and F0B/T16. Figure 5 gives relay-feedback test results for both loops used in this structure. Note the difference in the time scales for the two loops. Although the amplitude and period look reasonable for the F0A/T16 pairing, the shark-tooth shape of the tray 26 temperature response is characteristic of a process with inverse response. This is confirmed by the controller gain and reset time values calculated from test data. As given in Table 3, the values for the F0A/T16 loop have reasonable values. However, the controller for tray 26 has an unrealistically large reset time of 8624 min. Therefore, the alternative structure with the F0A/T27 and F0B/ T16 pairings is checked by applying the relay-feedback test. This structure also results in inverse response as revealed in the huge reset time of the F0A/T27 loop. Thus, switching the pairing does not help solve the problem. Figure 6 shows the response of CS7 to (5% step changes in production rate (vapor boilup) using the F0A/T16 and F0B/T26 pairings. The response of the system is stable, but it takes a long time for T26 temperature to go back to its setpoint for both positive and negative disturbances. Such a long time to settle down is a problem related to the inverse response and the huge reset time. A bigger problem is that even fairly small 5% disturbances result in large changes in the purities of the product streams xD,C and xB,D. While one of the purities settles down to a new steady state above its setpoint, the other one goes to a new steady state that is far below its setpoint. This problem occurs because the two temperature controllers in the CS7 structure give different initial responses because of their opposite actions. An increase in vapor boilup
Figure 5. Relay-feedback test results for CS7 pairings.
Table 3. Tuning Parameters for Control Structure CS7 pairing
span
KC
τI
F0A/T16 F0B/T26
10 10
1.37 0.06
37.95 8624
produces an increase in the temperature on both control trays (tray 16 and tray 26). The tray 16 temperature controller has direct action, so it increases the F0A feed flowrate. However, the tray 26 temperature controller has reverse action, so it decreases the F0B feed flowrate. Not enough reactant B is added in a timely enough manner to prevent light reactant A from going to the upper section of the column. Once this breakthrough occurs, the column moves to a different operating condition where the impurity of A in the distillate stream increases and product purities are lower. Thus, we can conclude that control structure CS7 is not a good choice for controlling this column/side-reactor process. 3.2. Control Structure CS5. As mentioned in the previous section, it is desirable to use inferential temperature measurements instead of direct composition measurements whenever possible. However, the results show that the control structure CS7 is not an effective control structure at least for the process studied here, which is the optimum economic steadystate design. It appears that some direct composition information about reactant inventory inside the system is required for a more effective control system since the column is designed for neat operation. Thus, another control structure CS5 that includes one composition analyzer is explored in this section. This control structure differs from control structure CS7 only in how the fresh feed streams and the reboiler heat inputs are manipulated. Figure 7 shows that the temperature of a tray near the bottom of the column is used to infer bottoms product purity, and it is controlled by manipulating the vapor boilup. Tray 16, which has the biggest steady-state gain (KVS) in the stripping section, is selected. Distillate purity is not controlled. The fresh feed F0B is flow controlled and serves as the production rate handle. A composition analyzer is used to detect the inventory of component A in the system. Feedback can be used to prevent the gradual buildup or depletion of reactant A. Thus, the flowrate of the other fresh feed F0A is manipulated by a composition
Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008 8709
Figure 6. A (5% step change in production rate handle ∆VS.
controller than maintains the concentration of component A on a selected tray. To see which tray is the best for detecting component A concentration, a disturbance sensitivity approach was explored. The compositions of both products are driven to their correct values by varying reflux ratio and heat input at different feed flowrates. The composition and temperature profiles have to change to give “perfect” composition control of the two products. The changes of composition of component A through the column at ( 20% of original feed flowrates are shown in Figure 8. From this figure, the tray with the least changing composition (tray 20) is selected as the preferred one to control by manipulating the flowrate of the other fresh feed F0A. This tray is also the effluent of the second (middle) reactor returned back to the column. Figure 9 gives relay-feedback test results for both loops: F0A/xA,20 and VS/T16. The amplitudes and periods look
reasonable for both loops. These results are also confirmed by the controller gain and reset time values given in Table 4. There is no inverse response (huge reset times) problem. There is also no action-related problem because both loops have the same action. The unusual spikes in the composition on tray 20 are caused by the step changes in the F0A feed, which is pure component A and is fed directly on tray 20. To check the effectiveness of this control structure, quite large (20% step changes in the production rate (fresh-feed stream F0B) are applied to the system. Figure 10 shows the response of the CS5 structure to these disturbances. Both controlled variables go back to their setpoints for both positive and negative disturbances in a short time. Also, even with these very large (20% step changes, the purities of the product streams xD,C and xB,D settle down smoothly to steadystate values that are within (1% of the 95% specification value. Therefore the CS5 structure is a much better choice for controlling this column/side-reactor process compared to CS7 structure. The responses of CS5 with tray 20 composition controlled for changes in feed compositions are given in Figures 11 and
Figure 7. Control structure CS5.
Figure 8. Disturbance sensitivity results.
8710 Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008
Figure 9. Relay-feedback test results for CS5 pairings. Table 4. Tuning Parameters for Control Structure CS5 pairing
span
KC
τI
F0A/xa,20 VS/T16
0.5 10
4.79 1.30
49.87 7.04
12. In Figure 11 the composition of the fresh feed F0A is changed from pure A to either 95 mol % A with 5 mol % B (solid lines) or 90 mol % A with 10 mol % B (dashed lines). Control structure CS5 handles this type of disturbance quite well. The purities of both products are maintained within 1% of the desired 95% specification. However, as the impurity amount is increased to 10 mol % B, the purity of the bottoms stream xB,D moves to the limit of the specifications which is 1% below from the setpoint. Thus, it can be said that this purity of the bottoms stream will deviate by more than 1% for larger feed composition disturbances. Figure 12 gives the responses of CS5 to 3% and 5% impurities of A in fresh-feed stream F0B. The control structure keeps product purities within 1% of their specified values for
Figure 10. Step change ((20%) in production rate handle ∆F0B.
the 3% feed stream impurity. However, the purity of the distillate stream xD,C goes out of the specification limits for a 5% feed stream impurity. 4. Conclusion Two different control structures have been studied for the control of a column/side-reactor process with three external reactors. The chemical system studied has two reactants and two products and operates without any excess reactant. The effectiveness of each control structure is demonstrated using disturbances in production rate and fresh-feed compositions. For the first control structure CS7, two tray temperatures are controlled by manipulating the two fresh-feed streams. The vapor boilup (or reboiler duty) is the production rate handle. Simulation results indicate that this control structure is not a good choice for controlling this process. The main problem is the disharmony between the actions of the loops. While one of the loops has a direct action, the other loop has a reverse action.
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Figure 11. Impurity of B in fresh feed composition ∆z0A.
Figure 12. Impurity of A in fresh feed composition ∆z0B.
A secondary problem is that one of the loops shows the characteristic of a process with inverse response. For the second control structure CS5, an internal composition analyzer is used, and the fresh feed stream F0B is the production-rate handle. This control structure shows better responses to disturbances because of several reasons. First, a composition analyzer that supplies information about reactant inventory inside the system that can be used to improve the controllability in a “neat” process. In addition, the similarity in the actions of the two loops and the absence of the inverse response behavior result in a more effective control structure compared to CS7. In a previous paper,10 the same control structures have been used for a reactive distillation column in the same two reactants-two products system. Although the column/sidereactor process and the reactive distillation column are different in terms of reaction-separation interactions, similarities have been observed in their dynamic responses to
control structures CS5 and CS7. For both flowsheets the use of control structure CS7 results in similar conflicts between the actions of the loops and inverse response problems for one of the loops. These problems affect the robustness of control structure CS7 significantly. On the other hand, control structure CS5 could easily handle disturbances that are typical in most chemical processes for both the column/side-reactor process and the reactive distillation column. We have not explored in this paper the possibility of changing the design to provide a more controllable process. Instead of using the economic optimum design, controllability may be improved by changing design parameters such as the number and size of reactors and the number of trays in the various sections of the column. The suboptimal design may result in a process that can be controlled by the two-temperature control structure, which would eliminate the need for analyzers. We plan to explore this possibility in a future paper.
8712 Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008
Nomenclature A ) heat transfer area between catalyst and liquid (m ) aF ) pre-exponential factor for the forward reaction (mol-sec-1mol-1) aR ) pre-exponential factor for the reverse reaction (mol-sec-1mol-1) AVP ) vapor pressure constant B ) bottoms flow rate in the column (mol-sec-1) BVP ) vapor pressure constant CPcat ) heat capacity of catalyst (kJ-kg-1-K-1) CPliq ) heat capacity of liquid (kJ-kg-1-K-1) D ) distillate flow rate in the column (mol-sec-1) EF ) activation energy of forward reaction (cal-mol-1) ER ) activation energy of reverse reaction (cal-mol-1) F0j ) fresh feed flow rate of reactant j (mol-sec-1) Fliq,n ) flow rate of liquid in lump n (mol-sec-1) KC ) controller gain kF ) specific reaction rate of forward reaction (mol-sec-1-mol-1) kR ) specific reaction rate of reverse reaction (mol-sec-1-mol-1) KEQ ) equilibrium constant KFoj ) steady-state gain related to the fresh feed j (K-mol-1-sec) Mliq ) molecular weight of the liquid mixture (kg-kmole-1) PSj ) vapor pressure of component j (bar) R ) perfect gas law constant (cal-mol-1-K-1) R ) reflux flowrate (mol-sec-1) t ) time (sec) Tcat,n ) temperature of catalyst in lump n (K) Tliq,n ) temperature of liquid in lump n (K) Ti ) column temperature on tray i (K) U ) heat transfer coefficient between catalyst and liquid (kJ-s-1m-2-K-1) Vcat ) volume of catalyst in each lump (m3) Vliq ) volume of liquid in each lump (m3) VR ) molar holdup of the reactor (moles) VS ) vapor boilup (mol-sec-1) xB,j ) bottoms composition of component j in liquid (mole fraction j) xD,j ) distillate composition of component j in liquid (mole fraction j) xi,j ) composition of component j in liquid on tray i (mole fraction j) 2
xi,n ) composition of component i in lump n (mole fraction i) z0i,j ) composition of fresh feed stream i (mole fraction j) Greek Symbols R390 ) relative volatility at 390 K λ ) heat of reaction (kJ-mol-1) Fcat ) catalyst density (kg-m-3) Fliq ) liquid density (kg-m-3) τI ) reset time (min)
Literature Cited (1) Kaymak, D. B.; Luyben, W. L. Optimum design of a column/side reactor process. Ind. Eng. Chem. Res. 2007, 46, 5175–5185. (2) Kaymak, D. B.; Luyben, W. L.; Smith, O. J. Effect of relative volatility on the quantitative comparison of reactive distillation and conventional multi-unit systems. Ind. Eng. Chem. Res. 2004, 43, 3151– 3162. (3) Schoenmakers, H. G.; Buehler, W. K. Distillation column with external reactors - an alternative to the reaction column. Ger. Chem. Eng. 1982, 5, 292–296. (4) Jakobsson, K.; Pyha¨lahti, A.; Pakkanen, S.; Keskinen, K.; Aittamaa, J. Modelling of a side reactor configuration combining reaction and distillation. Chem. Eng. Sci. 2002, 57, 1521–1524. (5) Gadewar, S. B.; Tao, L.; Malone, M. F.; Doherty, M. F. Process alternatives for coupling reaction and distillation. Chem. Eng. Res. & Des. 2004, 82, 140–147. (6) Ouni, T.; Jakobsson, K.; Pyha¨lahti, A.; Aittamaa, J. Enhancing productivity of side reactor configuration through optimizing the reaction conditions. Chem. Eng. Res. & Des. 2004, 82, 167–174. (7) Citro, F.; Lee, J. W. Widening the applicability of reactive distillation technology by using concurrent design. Ind. Eng. Chem. Res. 2004, 43, 375–383. (8) Roat, S. ; Downs. J.; Vogel, E.; Doss, J. Integration of rigorous dynamic modeling and control system synthesis for distillation columns. In Chemical Process Control-CPC III; Elsevier: Amsterdam, The Netherlands, 1986. (9) Kaymak, D. B.; Luyben, W. L. Evaluation of a two-temperature control structure for a two-reactant/two-product type of reactive distillation column. Chem. Eng. Sci. 2006, 61, 4432–4450. (10) Kaymak, D. B.; Luyben, W. L. Quantitative Comparison of dynamic controllability between a reactive distillation column and a conventional multi-unit process. Comput. Clum. Eng. 2008, 32, 1456–1470.
ReceiVed for reView December 13, 2007 ReVised manuscript receiVed August 14, 2008 Accepted September 2, 2008 IE701705M
