Method for Evaluating Single-End Control of Distillation Columns

Department of Chemical Engineering, Lehigh University, Bethlehem, ... This single-end distillation control structure is widely used in industry becaus...
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Ind. Eng. Chem. Res. 2009, 48, 10594–10603

Method for Evaluating Single-End Control of Distillation Columns William L. Luyben* Department of Chemical Engineering, Lehigh UniVersity, Bethlehem, PennsylVania 18015

Distillation columns are, in an ideal situation, controlled using a dual-composition structure in which the light-key impurity in the bottoms and heavy-key impurity in the distillate are both maintained at the specified values. This structure minimizes energy consumption. However, it is often almost as efficient to use one-end control of either a composition or a temperature. This single-end distillation control structure is widely used in industry because of its simplicity and because it avoids dynamic interaction between the two competing loops. Because distillation columns have two control degrees of freedom, another variable besides the single temperature or composition must be selected among several alternatives. Usually these choices involve a ratio so that feed rate changes can be effectively handled. However, different ratio schemes handle feed composition changes with different degrees of effectiveness. The two most commonly used are either a refluxto-feed ratio (R/F) or a reflux ratio (RR). The purpose of this Article is to present a methodology for deciding if single-end control can be effective and, if so, which ratio should be used. A steady-state simulation is used in which the two product purities (or impurities) are held constant as feed composition is varied around the design value. Plots are made of the two ratios (R/F and RR). If one of these curves shows little sensitivity to feed composition, it should be used in a single-end control structure. If both ratios show significant change, a dual control structure (two compositions, two temperatures, or one of each) is required to handle feed composition disturbances. 1. Introduction 1.1. Steady-State Design. The design of a distillation column starts with the specification of the desired purities of the product streams. In a simple two-product column with a bottoms product and a distillate product, the distillate contains primarily the lightkey component with a small amount of the heavy-key component as impurity. Lighter-than-light key components coming in with the feed are also present in the distillate, but the column cannot affect their compositions in the distillate. The distillate composition is xD(j). The bottoms contains primarily the heavykey component with a small amount of the light-key component as impurity. Heavier-than-heavy key components coming in with the feed are also present in the bottoms, but the column cannot affect their compositions in the bottoms. The bottoms composition is xB(j). The two design specifications are typically the impurity levels in the two products. So the specification for the distillate is xD(HK), and the specification for the bottoms is xB(LK). Once these specifications have been established, the designer must find the optimum column configuration that satisfies some criterion. Minimization of total annual cost is often used because it balances capital and energy costs. Given the conditions of the feed, there are three design optimization variables: pressure, total number of trays, and feed tray location. Because lower pressure means higher relative volatilities in most chemical systems, pressure is usually set at the lowest value that still permits the use of cooling water in the condenser. This translates into a minimum reflux-drum temperature of 120 °F (50 °C), from which the column pressure can be calculated from the distillate composition. This is a bubble-point calculation if the distillate is liquid or a dew-point calculation if the distillate is vapor. However, if there is a maximum temperature limitation in the system due to polymerization, thermal degradation, materials limitations, or other issues, the pressure must be selected such * To whom correspondence should be addressed. Tel.: (610) 7584256. Fax: (610) 758-5057. E-mail: [email protected].

that the temperature in the bottom of the column does not exceed this high limit. A bubble-point calculation using the bottoms composition at the maximum allowable temperature gives the column pressure. At this pressure and using the distillate composition, the temperature in the reflux drum can be determined. Refrigeration may be required if this temperature is lower than that attainable using cooling water. In the examples used in this Article, we illustrate both of these methods for selecting column pressure. Finding the optimum number of trays in the column involves evaluating the trade-off between energy cost, which decreases as more trays are used, and capital costs, which increase as more trays are used. The energy cost is primarily reboiler heat duty, because cooling water costs are much smaller than steam costs. However, if refrigeration is used in the condenser, the condenser duty represents a very significant energy cost. The capital costs include the column shell and the two heat exchangers (reboiler and condenser). A straightforward approach to find the optimum trays is to evaluate a number of cases over a range of total number of trays. Total annual cost is the sum of the energy cost ($/yr) plus the capital investment ($) divided by a payback period (giving the annual capital cost $/yr). Annual energy cost and annual capital cost are plotted versus total trays NT. Energy cost decreases with increasing NT. Capital cost is high with very few trays (near the minimum number of trays) because, although the column is short, the column diameter is large and the heat exchanger areas are large. However, as the number of trays increases away from the minimum, the capital cost initially decreases because of the reduction in diameter and heat exchanger areas. Eventually the height of the column begins to increase more rapidly than the diameter and heat exchanger areas decrease. The capital cost then begins to increase as NT increases. Therefore, the total annual cost reaches a minimum at the optimum number of trays. Note that the feed tray location is optimized at each value of NT by finding the feed stage that minimizes reboiler heat input.

10.1021/ie900778r CCC: $40.75  2009 American Chemical Society Published on Web 09/28/2009

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The final result is a column that produces the two products at their specified purities for the minimum total annual cost. 1.2. Control Structure Alternatives. Once the column has been designed, an effective control structure must be developed. A host of alternative control schemes have appeared in the literature, and the control engineer’s job is to find one that is simple and effective. We discuss below some of the most commonly used structures. A. Dual-Composition Control. Theoretically, a dualcomposition control scheme would be used with the impurity levels of both product streams controlled by manipulating two input variables. Reboiler heat input and reflux are the two most commonly used, with the other input variables used to control pressure (condenser cooling water), reflux-drum liquid level (distillate), and column base liquid level (bottoms). Of course, other structures are used when more appropriate, For example, if the reflux ratio is high, the reflux-drum level should be controlled by manipulating reflux. The distillate flow rate would then be used for composition control or set by a reflux ratio scheme. The flow rate of the distillate should never be fixed. This violates the first law of distillation control. Product compositions cannot be maintained if product flow rates are held constant. Dual-composition control requires two online composition measurements, which are expensive, somewhat unreliable, and often introduce significant deadtime into the loop. The two composition controllers are also interacting because both manipulated variables (QR and R) affect both controlled variables (xB(LK) and xD(HK)). The tuning of these two interacting controller must account for this dynamic interaction. Tuning each loop independently (with the other on manual) will not guarantee stable response when both are on automatic. There are several methods for tuning interacting loops, but the simple way to handle the problem is to tune the “fast” loop first with the other loop on manual. The fast loop is usually the one using reboiler duty because vapor changes affect controlled variables more quickly than do reflux flow rate changes due to liquid hydraulic lags. The other loop is then tuned with the first loop on automatic. This “sequential” tuning accounts for the interaction. B. Dual-Temperature Control. In some situations, it is possible to infer compositions using temperatures. If the column temperature profile has trays near the top and also near the bottom where the temperature is changing significantly from tray to tray, a dual-temperature scheme may be effective. Temperature measurements are reliable and inexpensive, and they do not introduce large lags or deadtimes into the loop. Therefore, temperature control dynamics are faster than composition control dynamics, so tighter control is possible. The two temperature loops are interacting, and controller tuning must take this interaction into account. If the temperature profile displays only one section of the column with temperatures changing significantly from tray to tray, dual-temperature control cannot be used. A structure that controls one temperature and one composition may be required. An example of this situation is given in one of the examples considered in this Article. In addition, cascade control schemes can be used in which a secondary temperature controller receives its set point from a primary composition controller. C. Single-End Control. Most industrial distillation columns do not use dual-composition or dual-temperature control. The reason for this popularity is that a simple single-end structure can often provide near-optimum control with less complexity and less sensitivity to changing conditions (improved robustness). A temperature (or composition) on an appropriate tray is

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controlled, usually with reboiler heat input. This leaves one other variable to be set. The two most common variables are a fixed reflux to feed ratio (R/F) and a fixed reflux ratio (R/D). Implementing the R/F structure is achieved by placing a flow controller on the reflux. The feed flow rate is measured, and the signal is sent to a multiplier whose output is the desired reflux flow rate. This signal becomes the set point of the reflux flow controller, which is on cascade. Implementation of the RR structure depends on what is controlling the reflux-drum level. In a low-to-modest (5) reflux ratio column, reflux-drum level is controlled by the reflux. So a flow controller is placed on the distillate. Reflux flow rate is measured and the signal sent to a multiplier (constant ) 1/RR) whose output is the desired distillate flow rate. This signal becomes the set point of the distillate flow controller, which is on cascade. The question to be answered is under what conditions and with what systems is single-end control adequate? This Article addresses this problem. 2. Methodology The first thing to recognize is that if the column is only going to see disturbances in feed flow rate, the dual schemes are not necessary and any single-end control structure can handle changes in feed flow rate, provided some ratio scheme is used. Neglecting changes in tray efficiencies and changes in pressures, all flow rates ratio up or down in direct proportion to feed. At the new steady-state conditions, the temperatures and composition profiles do not change from their original values. Product purities are at their specified values when any temperature or composition is held constant. Therefore, throughput changes do not require dual schemes. However, feed composition changes produce different temperature and composition profiles at the new steady state if the products are maintained at their specifications. Therefore, the assessment of which ratio scheme is best must look at feed composition disturbances. The basic idea of the proposed method is to set up a steadystate simulation that holds the two products at their specifications (xD(HK) and xB(LK)) as feed composition is changed. In Aspen Plus, the “design spec/vary” feature is used to maintain the product impurities by varying distillate flow rate and reflux ratio. The feed compositions of the light and heavy key components are varied around the base-case design values. The required changes in R/F and RR are plotted versus feed composition. If one of these curves shows little sensitivity to feed composition (curve is flat), it indicates that holding this ratio may be able to accommodate feed composition changes when using a single-end control structure. If both ratios show significant changes, a dualcomposition (temperature) structure may be required to handle feed composition disturbances. This idea was developed over two decades ago by Chiang and Luyben.1 The present Article provides an illustrative example of its application in a plantwide control problem. Hopefully, this Article will serve to introduce the current generation of control engineers to the method, which they may find useful in assessing distillation control structures. A more recent paper2 used the method to illustrate that the

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Figure 1. Styrene process.

Figure 2. Txy diagram for ethyl benzene/styrene.

most effective distillation control structure depends on feed composition. For the given chemical system and desire separation, over certain feed composition ranges single-end control is sometimes adequate, and over other feed composition ranges dual temperature (composition) is required.

3. Illustrative Examples Two distillation columns are considered to illustrate the procedure and to discuss several other distillation control concepts. The columns are based on a styrene process studied

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Figure 3. Product column temperature profile.

Figure 4. Product column composition profiles.

by Vasudevan et al.3 Figure 1 shows the process flowsheet. Process details are available from the cited paper. Fresh ethyl benzene is mixed with steam (to reduce the partial pressure of ethyl benzene) and fed into a two-stage heater/adiabatic tubular reactor system. The main reaction is the endothermic decomposition of ethyl benzene to styrene and hydrogen. In addition there are several side reactions producing benzene, toluene, and carbon dioxide. The per-pass conversion of ethyl benzene in the reaction section is about 66%, so the recovery and recycle of ethyl benzene in the separation section is required. The reactor effluent is cooled and fed into a decanter. The aqueous phase and a gaseous stream of light components are removed. The organic phase contains mostly unreacted ethyl benzene and styrene with small amounts of benzene and toluene. The mixture is fed into a two-column distillation system to produce high-purity styrene (99.7 mol %), recover the ethyl benzene, and remove the other products. The control of these two distillation columns illustrates the application of the proposed

method. Note that an “indirect” separation configuration is used in this system (heaviest component removed in the first column). The throughput variable in this process is the total ethyl benzene fed into the reactions section (the sum of the fresh ethyl benzene feed and the ethyl benzene recycle from the second distillation). The column control structures will be tested by making large changes in this throughput variable. 3.1. Product Column C1. A. Steady-State Design. The organic phase from the decanter is fed into C1, the product column. The bottoms stream B1 from this column is the styrene product. The distillate D1 is ethyl benzene and light components. Because styrene polymerizes at temperatures around its atmospheric boiling point (145 °C), the product column is run under vacuum (10 kPa in the reflux drum and 50 kPa in the base), giving a base temperature of 121 °C. The bottoms product is 99.7 mol % styrene. The distillate is designed to have a composition of 1 mol % styrene, which ends up being recycled

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Figure 5. EB/styrene feed composition sensitivity analysis for product column.

back to the reactor in the ethyl benzene recycle stream from the second column. The separation of ethyl benzene is very difficult with a relative volatility not much greater than 1 (Figure 2 shows the Txy curve at 101 kPa). Therefore, the column has many trays (82 stages), and the reflux ratio is fairly high (4.8). Feed is introduced on stage 35 (using Aspen notation of numbering from the top with the reflux drum as stage 1). This is a very large column (diameter 4.86 m) for the specified fresh feed of 152.6 kmol/h ethyl benzene. The reflux-drum temperature is 41 °C, which is about at the limit for using cooling water. A partial condenser is used, which produces a vapor product of mostly light components that are removed through a compressor and a liquid distillate that is sent on to the downstream column.

B. Control Structure. Temperature cannot be used in this column because the boiling points of the key components are so close (136.2 and 145.2 °C for ethyl benzene and styrene, respectively). Figure 3 shows the temperature profile, and Figure 4 gives composition profiles. The drop in temperature between the top tray and the reflux drum is due to the lighter-than-light components in the feed. In the section where the ethyl benzene/styrene separation is occurring, temperatures are affected more by the changes in pressure than by changes in compositions. This conclusion can be drawn by comparing the slope of the temperature profile in the section of the column in which compositions are changing very little (stages 60-80) with the slope of the temperature profile in the section in which compositions are changing significantly (stages 10-50). These slopes are almost the same, which indicates temperature is being affected more by pressure than by compositions. This is the usual situation in a vacuum column separating close-boiling components. Therefore, a composition measurement is required. Direct control of the composition of a high-purity product, such as is the case in this column, is difficult because of the highly nonlinear response of the system. The impurity of ethyl benzene in the bottoms stream is only 0.3 mol %. Distillation wisdom recommends that it is more effective to control a composition at some intermediate tray location where the composition of the impurity is larger and the response is more linear. Figure 4 gives the composition profiles in the product column. We select the composition of ethyl benzene on stage 60 (9.09 mol %) to control by manipulating reboiler heat input.

Figure 6. Plantwide control structure. Table 1. Controller Parameters product column CC1 recycle column CC2 (base) recycle column CC2 (ratio) recycle column TC2 (base) recycle column TC2 (Kc ) 10) SP transmitter range OP OP range deadtime KC τI (min)

0.0909 EB 0-0.2 EB

0.0635 T 0-0.2 T

0.0635 T 0-0.2 T

129 °C 100-200 °C

129 °C 100-200 °C

29.8 GJ/h 0-100 GJ/h 5 min 0.23 54

4.80 GJ/h 0-10 GJ/h 5 min 0.13 36

0.000499 GJ/kg 0-0.001 ratio 5 min 0.20 32

0.295 ratio D2/R2 0-0.5 ratio 1 min 6.7 41

0.295 ratio D2/R2 0-0.5 ratio 1 min 6.6 26

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Figure 7. Product column responses to 20% changes in total ethyl benzene flow rate.

Figure 8. Txy diagram for toluene/ethyl benzene.

The question still remains, do we need a dual-composition control structure? Figure 5 gives results of the proposed feed sensitivity analysis methodology. The first two columns in the table show the range of the ethyl benzene and styrene compositions in the feed to this column. The third column in the table shows the required changes in reflux flow rate while keeping the bottoms composition at 0.3 mol % ethyl benzene and the distillate composition at 1 mol % styrene. The changes in the reflux flow rate are less than 1% of the design value over the entire range of feed compositions. The fourth column in the table shows the required changes in the reflux ratio. The RR changes by over 25%. Therefore, the analysis clearly

suggests that a fixed R/F control structure should be much better in handling feed composition disturbances than a fixed RR control structure. Figure 6 shows the entire plantwide control structure for the styrene process, including the controls used for the product column C1. The pressure in the column is controlled by manipulating condenser heat removal. The flow rate of the gas from the reflux drum is flow controlled by manipulating steam flow to the turbine driving the compressor. The set point of the gas flow controller is reset to maintain a fixed gas-to-feed ratio. Base level is controlled by manipulating bottoms B1. Refluxdrum level is controlled by manipulating distillate D1.

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Figure 9. Recycle column temperature profile.

A deadtime of 5 min is used in the stage 60 composition loop. The controller is tuned by running a relay-feedback test and using Tyreus-Luyben tuning rules. The first column in Table 1 labeled “CC1” summarizes the parameters of this composition controller. All level loops used proportional control with gains of 2. Figure 7 gives the responses of the product column for 20% increases and decreases in the flow rate of the total ethyl benzene (the sum of the fresh ethyl benzene feed and the ethyl benzene recycle, the bottoms B2 of the second column). The solid lines are 20% increases, and the dashed lines are 20% decreases. Notice that the column sees simultaneous disturbances in its feed flow rate F1 and its composition z1(j). An increase in the total ethyl benzene increases the F1 feed flow rate, decreases the concentration of styrene z1(S) in the feed, and increases the concentration of ethyl benzene z1(EB) in the feed. An increase in throughput produces more styrene product (the bottoms B1 of the product column). The purity of this stream xB1(S) is shown in the second graph on the right. It remains close to the specified value of 99.7 mol % styrene. The composition of the styrene impurity in the distillate xD1(S) stays close to the design value of 1 mol % (bottom graph on right). An effective control structure has been developed for the product column, which handles large disturbances in both feed flow rate and feed composition. It features an R/F ratio scheme and the control of a composition at an intermediate tray in the column. 3.2. Recycle Column C2. A. Steady-State Design. The liquid distillate from the product column D1 is the feed to the recycle column C2. This column removes the light components (mostly benzene and toluene) in the distillate and recovers the ethyl benzene in the bottoms for recycle back to the reaction section. The design specifications are 1 mol % ethyl benzene in the distillate and 1 mol % toluene in the bottoms. The column runs at 120 kPa, giving a reflux-drum temperature of 81 °C,

Figure 10. Toluene/ethyl benzene feed composition sensitivity analysis for recycle column.

which is more than adequate for the use of cooling water. The separation is not difficult as the Txy diagram shown in Figure 8 indicates. The normal boiling points are 110.6 and 136.2 °C for toluene and ethyl benzene, respectively. The column has 38 stages and is fed on stage 16. The reflux ratio is 3.38. B. Control Structure. The temperature profile in the recycle column is shown in Figure 9. There is little temperature change in the stripping section, but there is a section in the rectifying section that can be used for temperature control. Therefore, only one temperature can be used. Can single-end control be effective, and, if so, what ratio scheme is best? Figure 10 gives the results of the feed composition sensitivity analysis for the recycle column. The feed compositions of toluene z2(T) and ethyl benzene z2(EB) are varied (first two columns in the table). The distillate impurity of ethyl benzene is held at 1 mol %, and the bottoms impurity of toluene is held at 1 mol %. The required changes in reflux flow rate and reflux ratio are shown in the third and fourth columns of the table. It is clear

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Figure 11. Recycle column composition profiles.

Figure 12. Recycle column responses to 20% changes in total ethyl benzene flow rate.

that both of these ratios change quite significantly. Reflux flow rate changes by 24% and reflux ratio changes by 21% over the range of feed compositions. Therefore, a single-end control structure cannot handle feed composition disturbances, and a dual structure is required. Because only one temperature can be controlled, the other controller must control a composition. Because the bottoms contains only a small concentration of the impurity toluene (1 mol %), an intermediate tray is selected (stage 30) to measure and control the toluene composition (6.35 mol %)

so that nonlinearity issues can be avoided. Figure 11 gives the composition profiles in the recycle column. The composition controller manipulates reboiler heat input. The temperature on stage 10 in the rectifying section is controlled by manipulating the reflux ratio. Because the reflux ratio is fairly high (3.38), the reflux-drum level is controlled by reflux and the distillate is ratioed to the reflux (see Figure 6). A deadtime of 5 min is used in the stage 30 composition loop, and a deadtime of 1 min is used in the stage 10 temperature

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Figure 13. Effect of QR/F ratio and high gain in reflux-drum level controller for the recycle column with a 20% increase in total ethyl benzene flow rate.

Figure 14. Aspen Dynamics process flow diagram.

loop. The temperature controller is tuned first, because it has a smaller deadtime, by running a relay-feedback test and using Tyreus-Luyben tuning rules. Next, with the temperature controller on automatic, the composition controller is tuned by running a relay-feedback test and using Tyreus-Luyben tuning rules. The second and fourth columns in Table 1 labeled “CC2 (base)” and “TC2 (base)” summarize the parameters of these two controllers. All level loops use proportional control with gains of 2. Figure 12 gives the responses of the recycle column for 20% increases and decreases in the flow rate of the total ethyl benzene

(the sum of the fresh ethyl benzene feed and the ethyl benzene recycle). The solid lines are 20% increases, and the dashed lines are 20% decreases. Notice that the column sees simultaneous disturbances in its feed flow rate F2 (D1) and its composition z1(j) (xD1(EB)). An increase in the total ethyl benzene increases the F2 feed flow rate to the recycle column and results in larger distillate and bottoms flow rates. The feed composition does not change a great deal. The impurity of ethyl benzene in the distillate xD2(EB) stays very close to its specified value of 1 mol % (second graph on the right). However, the composition of the toluene impurity in

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Figure 15. Controller faceplates.

the bottoms xB2(T) (bottom graph on right) shows a large transient deviation for the 20% increase in total ethyl benzene fed to the reaction section. This occurs because the feed to the column F2 is the distillate from the product column D1, and this stream shows a fairly large and rapid change. The feed is liquid, so it significantly affects the bottoms composition. This transient deviation can be greatly reduced by using a reboiler heat input to feed ratio control scheme. The composition controller then resets the ratio. Figure 13 shows the effect of switching to a QR2/F2 ratio scheme for a 20% increase in throughput. The solid lines are the base case without a ratio. The dashed lines are with the ratio. The transient deviation in the toluene impurity in the bottoms xB2(T) (bottom graph on right) is greatly reduced. However, now the transient disturbance of ethyl benzene in the distillate xD2(EB) (middle graph on the right) is greatly increased. The rapid increase in vapor boilup drives more ethyl benzene overhead before the temperature controller can catch it. The basic problem is the tuning of the reflux-drum level controller. Notice that the temperature controller changes the distillate flow rate through the D2/R2 ratio. Yet the reflux changes only slowly if a proportional level controller with the conventional gain of 2 is used. The dynamics of the temperature control loop can be improved by using a higher gain in this level control application. The effect of using a gain of 10 is shown in the dotted curves given in Figure 13. The transient disturbance of ethyl benzene in the distillate xD2(EB) (middle graph on the right) is greatly reduced. Notice in Table 1 that the integral time of the temperature controller is reduced from 41 to 26 min. The tight level control produces faster changes in reflux when the changes in vapor boilup affect reflux-drum level, which help to reduce the impact of vapor boilup on the distillate composition. These results illustrate a general distillation control principle, enunciated by Greg Shinskey4 four decades ago, that tight refluxdrum level should be used when reflux controls level and distillate controls temperature. Figure 14 shows the Aspen Dynamics process flowsheet for the entire styrene process with all controllers and ratios installed. Figure 15 shows the controller faceplates. Notice that the controller output signal from the composition controller CC2 on the recycle column is a ratio QR2/F2 (in GJ/kg as required by Aspen Dynamics). The controller output signal from the temperature controller TC2 on the recycle column is a ratio (D2/R2).

An effective control structure has been developed for the recycle column, which handles large disturbances in both feed flow rate and feed composition. It features a dual control scheme with one temperature controller and one composition controller. A high gain is used in the reflux-drum level loop to speed up changes in the flow rate of reflux and improve temperature control performance. 4. Conclusion A procedure has been presented for deciding if single-end control of distillation column can be effective and for selecting a ratio scheme. The application of the methods is useful in developing control structures that handle feed composition disturbances. Any ratio structure is capable of handling feed flow rates disturbances, at least from a steady-state point of view. Other distillation control concepts are also highlighted. Control of a high-purity product can lead to nonlinearity problems and can be avoided by controlling a composition on an intermediate trays that has a larger composition. When refluxdrum level is controlled by reflux, a large gain should be used if the distillate is used to control a temperature or composition. The flow rate of a product stream (distillate or bottoms) should not be fixed in a control structure but be able to change to accommodate changes in throughput and feed composition. Two distillation columns in a plantwide environment of a styrene process have been used as illustrative examples for the application of the methodology and the distillation control principles. Literature Cited (1) Chiang, T. P.; Luyben, W. L. Incentives for dual composition control in single and heat-integrated binary distillation columns. Ind. Eng. Chem. Fundam. 1985, 24, 352–359. (2) Luyben, W. L. Effect of feed composition on the selection of control structures for high-purity binary distillation. Ind. Eng. Chem. Res. 2005, 44, 7800–7813. (3) Vasudevan, S.; Rangalah, G. P.; Murthy Konda, N. V. S. N. Application and evaluation of three methodologies for plantwide control of the styrene monomer plant. Ind. Eng. Chem. Res., submitted. (4) Shinskey, F. G. Process Control Systems; McGraw-Hill: New York, 1967.

ReceiVed for reView May 14, 2009 ReVised manuscript receiVed June 30, 2009 Accepted September 13, 2009 IE900778R