Plantwide Control of Continuous Multiproduct Processes: Two-Product

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Ind. Eng. Chem. Res. 2003, 42, 1890-1904

Plantwide Control of Continuous Multiproduct Processes: Two-Product Process Kulchanat Kapilakarn† and William L. Luyben* Process Modeling and Control Center, Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015

This paper considers the plantwide control of continuous processes that produce multiple products. A typical example is a process in which there are two reversible reactions producing two products M and D: A + B S M + C and A + M S D + C. The control structure must be able to achieve different production rates of the two products. Several conventional control structures are studied in which the flow rates of the fresh feed streams are fixed or manipulated by level or composition controllers and the production rates of the two products are not directly set. Several “on-demand” control structures are also developed in which both product streams are flow-controlled. The control system must adjust the conditions in the plant and the fresh feed streams to achieve the desired product flow rates. The most effective on-demand control structure requires no reactor composition analyzer and no recycle of product streams. 1. Introduction Many continuous chemical processes feature consecutive or simultaneous reactions that result in the production of multiple products. A typical example is a process in which there are two reversible reactions producing two products M and D.

A+BSM+C A+MSD+C The demand for the two products may vary, so the plant must be designed so that different product ratios can be attained. The optimum steady-state economic design changes as the desired product ratio changes. The control system for the process must also be able to achieve the desired product ratio. This paper discusses the plantwide control of this type of process. The flowsheet includes a reactor, three distillation columns, and (in some cases) three recycle streams. Because the reactions are reversible, chemical equilibrium limits conversion, so the reactor effluent contains significant amounts of unreacted A and B. These components must be recycled back to the reactor from the downstream separation section. If chemical equilibrium results in an amount of one of the products leaving the reactor that is in excess of demand, it may be necessary to also recycle some of the product stream. Several alternative plantwide control structures are developed and compared. Some structures use the conventional approach of setting the fresh feed streams. Other control structures are based on an “on-demand” control objective; i.e., the flow rates of the product streams are flow-controlled, and the control structure must adjust the fresh feed flow rates and conditions throughout the process to satisfy the specified product production rates. * To whom correspondence hould be addressed. E-mail: [email protected]. Phone: 610-758-4256. † Current address: Kulchanat Kapilakarn, Chemical Engineering Department, Prince of Songkla University, Songkla, Thailand, 90112.

Figure 1. Base case.

The design of on-demand plantwide control structures has been the subject of only a few papers in the literature. A general discussion of the inherent disadvantages of on-demand control was presented by Luyben.1 Other on-demand structures for several specific processes have been presented: the Eastman process,2 vinyl acetate process,3 and methylamines process.4 2. Process Studied Figure 1 shows the flowsheet of the process. Components A and B are reactants, component C is a byproduct, and components M and D are the desired products. The desired products leave in the streams D2 and B3. The isothermal continuous stirred-tank reactor (CSTR) is fed by two fresh feed streams (F0A and F0B) and two recycle streams (D1 and RD). The reactor effluent contains all five chemical components and is fed to a three-column distillation separation section. The desired amount of each component can vary with market conditions. The desired product split ratio is defined as a ratio between the amount of product M and the total product amount: M/(M + D). Different ratios give different flowsheets and different control structures. For example, consider the process with relative volatilities of each component assumed to be RA ) 16,

10.1021/ie0205905 CCC: $25.00 © 2003 American Chemical Society Published on Web 03/28/2003

Ind. Eng. Chem. Res., Vol. 42, No. 9, 2003 1891 Table 1. Optimum Design for Several M/(M + D) M/(M + D) product M (lb‚mol/h) VR (lb‚mol) F0A F0B RD (lb‚mol/h) D1 (lb‚mol/h) NT1 NT2 NT3 VS1 (lb‚mol/h) VS2 (lb‚mol/h) VS3 (lb‚mol/h) DC1 (ft) DC2 (ft) DC3 (ft) RR1 RR2 RR3 reactor (106 $) column 1 (106 $) column 2 (106 $) column 3 (106 $) heat ex 1 (106 $) heat ex 2 (106 $) heat ex 3 (106 $) energy (106 $/yr) TAC (106 $/yr)

0.0

0.2

0.4

0.5

0.6

0.8

1.0

0.0 12000 508.65 255.10 0 1580 27 29

50.0 8000 456.89 254.84 0 1147 17 31 30 2274 767 1780 10.64 6.05 9.23 1.11 14.19 2.87 6.65 0.64 0.57 0.86 4.09 2.02 3.49 5.28 11.38

100.0 8000 406.12 254.59 0 696 19 31 30 1923 870 1547 10.42 6.05 9.22 1.76 7.61 2.79 6.65 0.64 0.61 0.80 3.66 2.19 3.18 4.75 10.67

125.0 5000 380.74 254.46 0 883 18 30 30 2356 917 1429 10.61 6.62 8.26 1.67 6.26 2.73 4.96 0.75 0.63 0.76 2.82 1.52 2.03 5.15 9.64

150.0 8000 355.36 254.33 0 1784 19 31 30 4140 1102 1787 15.36 7.25 9.24 1.77 6.26 4.00 6.65 1.10 0.70 0.87 4.56 1.72 2.35 5.41 11.40

200.0 5000 304.59 254.07 400 1448 21 31 30 3729 1183 1556 13.35 7.52 8.62 1.56 4.85 4.08 4.96 1.00 0.73 0.80 3.79 1.80 2.15 7.08 12.16

250.0 12000 253.83 253.81 1000 10448 20 31 30 3172 1463 1995 12.31 8.36 9.76 2.04 4.79 6.82 7.64 0.90 0.82 0.92 3.42 2.07 2.53 7.26 13.35

6053 1738 17.00 9.11 2.83 2.41 8.56 1.66 0.85 5.20 2.31 8.53 14.73

RB ) 8, RM ) 4, RC ) 2, and RD ) 1. If the ratio is zero, we need only product D. The flowsheet will have one reactor and two distillation columns. Any M in the reactor effluent is recycled back to the reactor with A and B in the distillate stream D1 from the first column. If we need only product M, the flowsheet will consist of one reactor and three distillation columns with two recycle streams from the columns back to the reactor (one recycle stream of components A and B and one recycle with component D). Both steady-state economic design and dynamic control of the process depend on the product split ratio. 2.1. Optimum Steady-State Design. Table 1 gives steady-state design conditions and economic results for the optimum flowsheets over a range of product split ratios from 0 to 1. The total production rate of both products is held constant at 250 lb‚mol/h. The two design degrees of freedom (reactor holdup VR and the RD recycle flow rate) are varied for each product ratio to minimize the total annual cost (TAC), which is the sum of the annual energy cost (for providing heat in the column reboilers) and the annual capital cost (assuming a 3-year payback period). Equipment costs are estimated from the correlations given in work by Douglas.5 Product purities are set at 99 mol %, and the impurity of component M in the D1 recycle from the first column is assumed to be 10 mol % for most cases. The effect of the impurities will be discussed below. The numbers of trays in the columns are set at twice the minimum and the reflux ratios at 1.2 times the minimum in the calculation of the steady-state economics. Figure 2 shows that the economic steady-state design indicates that there should be no RD recycle for product ratios of less than about 0.6. For higher ratios (more production of M and less of D), it is economical to recycle some of the bottoms from the third column, which is component D, back to the reactor. Figure 3 shows the effect of the impurity of component M in D1 recycle on the vapor boilup rate VS1 and TAC of the first column with the optimum number of trays

Figure 2. Effect of RD and the product ratio on the recycle flow rate D1 (a) and TAC (b).

at each product ratio and no RD. For low product ratios, a large amount of M is recycled back to the reactor. This implicit recycle is achieved by increasing the impurity of M in the D1 recycle stream. The optimum D1 composition is about 15 mol % M for product ratios between 0.1 and 0.2. If high product ratios (between 0.32 and 0.5) are required, the impurity of M in D1 is about 10 mol %, which is the value used in the base case. 2.2. Base Case for Dynamic Studies. The base case used in the dynamic control studies has a product split ratio of 0.5 (equal amounts of the two products). The optimum reactor holdup for this case is 5000 lb‚mol, and the three columns have 18, 30, and 30 theoretical trays. As shown in Table 2, the results of rating calculations showed that the vapor boilup rates in some of the columns had to increase quite significantly in order to achieve different product ratios using the 5000 lb‚mol

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Figure 3. Effect of xD1,M on the vapor boilup rate VS1 (A) and TAC (B).

proportional-only with gains of 2 for the columns and 10 for the reactor. The reflux flow rates in each column are ratioed to the column feed flow rate. The column feed is measured, this flow signal is multiplied by the desired ratio, and the output of the ratio is the setpoint of the reflux flow controller. The desired ratio is set at the steady-state value. 2.2.2. Reactor. Knowing the conditions in the reactor for various product ratios provides important insight about how the control system must change conditions in the process to achieve different production rates. Figure 5 shows how the compositions of A and B in the reactor must change as the product ratio changes. When more M is desired, the concentration of A in the reactor (zA) must decrease and the concentration of B in the reactor (zB) must increase for the same total production rate. This results in a lower production rate of D from the second reaction because the second reaction depends on the concentration of both M (zM) and B (zB). This information is useful in understanding how alternative control structures can be set up to adjust process conditions to achieve the desired product production rates.

Table 2. Comparison of the Column Vapor Rates for Two Reactor Sizes

3. Control Structure Development

M/(M + D) VR ) 5000 lb‚mol F zA zB VS1 VS2 VS3 D1 xD1,A xD1,B RR1 RR2 RR3

VR ) 8000 lb‚mol

0.4

0.5

0.6

0.4

0.5

0.6

1652 0.345 0.191 1430 730 1745 990 0.575 0.318 0.44 6.21 3.25

1637 0.255 0.270 1250 770 2230 1000 0.417 0.440 0.24 4.86 4.88

1803 0.176 0.388 1420 790 970 1190 0.267 0.586 0.19 4.17 1.71

1448 0.283 0.180 1000 730 1745 788 0.520 0.331 0.28 6.21 3.25

1480 0.207 0.258 958 770 2230 845 0.362 0.451 0.13 4.87 4.88

1590 0.138 0.377 1200 780 920 980 0.223 0.611 0.23 4.15 1.59

reactor. It is unrealistic to assume that column vapor rates can be changed by more than 50%. To achieve more flexibility, the base case reactor holdup was increased to 8000 lb‚mol. The number of trays and the diameters of the columns were fixed at the optimum design values. As shown in Table 2, the required changes in column vapor rates to achieve different product ratios are reduced. 2.2.1. Columns. The initial conditions for the columns in the dynamic simulations were found by using a rigorous steady-state simulation of the columns (the Wang-Henke method). Column base and reflux drum holdups were set at 10 min (at 50% level). Inferential control of product compositions in all columns is achieved by selecting an appropriate control tray. Figure 4a shows the temperature profiles in the three columns. Figure 4b shows the sensitivity of the tray temperatures in column 2 to small changes in heat input and reflux ratio. Using the temperature profiles and the sensitivity results, we selected tray 6 in column 1, tray 23 in column 2, and tray 6 in column 3. Two first-order temperature measurement lags of 1 min are used in all temperature control loops. Relay-feedback tests are used to obtain the ultimate gain and frequency. Then the temperature controllers are tuned using the Tyreus-Luyben tuning rules. All level controllers are

We consider only conventional PI diagonal control structures in this paper and use the plantwide control procedure discussed by Luyben et al.3 to develop alternative basic regulatory control structures. Different control objectives yield different control structures. Process understanding and insight are employed to generate alternative control schemes, whose dynamic performances are evaluated by rigorous simulations. As is the case with all complex multiunit processes with recycles, there are a very large number of alternative control structures. As the “First Law of Plantwide Control” states, it is easy to find a plantwide control structure that does not work! We present several workable control structures in this paper, but there is no claim that any of these are “the best” from any perspective. We only claim that they provide stable operation. If optimum steady-state economic operation is desired, the setpoints of the basic regulatory controllers in these structures can be adjusted by an online optimizer. The following control loops are use in all structures: 1. The reactor temperature is controlled by manipulating the cooling water flow rate. 2. Column temperatures are controlled by changing the reboiler heat inputs. 3. Column reflux flows are ratioed to column feeds. 4. Column pressures are controlled by condenser heat removal. 5. The reflux drum level in the first column is controlled by manipulating the distillate stream D1, which is recycled back to the reactor. 6. The reflux drum level in the third column is controlled by manipulating the distillate stream D3, which is the byproduct component C. The control of the reflux drum level in the second column is different in the various control structures. Similarly, the variables used to control the column base levels vary with the control structure. 3.1. Conventional Control Structures. In the conventional control structure, the production rates of the two products are not directly set. The fresh feed

Ind. Eng. Chem. Res., Vol. 42, No. 9, 2003 1893

Figure 4. (a) Temperature profiles of three columns. (b) Temperature differences of column 2 with 5% ∆VS and 5% ∆RR.

pure fresh feeds F0A and F0B. The stoichiometry of the two reactions requires that

M + 2D ) F0A M + D ) F0B Solving for M and D gives

D ) F0A - F0B M ) 2F0B - F0A

Figure 5. Compositions of A and B in the reactor for different product ratios.

streams are set directly or are manipulated by some other controller (level or composition). The three alternative conventional control structures explored in this work are shown in Figures 6 and 8-10. 3.1.1. Structure CS1. Figure 6 gives the most obvious conventional control structure. The two fresh feed streams (F0A and F0B) are flow-controlled. Setting these two flows fixes the amounts of the two products M and D that will be produced in the plant. Every 1 mol of M produced consumes 1 mol of A and 1 mol of B. Every 1 mol of D produced consumes 2 mol of A and 1 mol of B. If we neglect for the moment the small amount of component B that is lost as an impurity in the D product (stream D2), we can relate the production rates of the two products M and D to the flow rates of the

From the equations above, a limitation on the range of possible values of the ratio between F0A and F0B can be deduced. Physically, the ratio can vary between 1 and 2. If the ratio is 1, the process produces only product D. Figure 7 shows the relationship between the F0A/F0B ratio and the recycle D1 back to the reactor from the first column. In this figure we assume that the first column removes all of components A and B from the top and all of components M, C, and D from the bottom. As we approach either of the limiting cases (all M or all D), the concentration of one of the product components must become very small. This means that the concentrations of the reactants A and B must become very large, which produces a large D1 recycle. The conditions in the reactor (concentrations and flows) and in the columns must adjust themselves to generate exactly these amounts of products in streams D2 and B3. Of course, equipment limitation may limit the achievable range in which the process can operate.

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Figure 6. CS1 conventional control structure.

Figure 7. Relationship between F0A/F0B and D1.

The key loops in the CS1 structure are as follows: 1. The reactor level is controlled by manipulating the flow rate of the reactor effluent F. 2. Reflux drum levels are controlled by distillate flows. 3. Base levels are controlled by bottoms flows. Although this control structure appears to be an obvious and straightforward one, the results presented later show that its performance is unsatisfactory. We should not be too surprised with these results. This structure has the potential to exhibit the “snowball” effect because all of the levels in the recycle loop from the first column are on level control. 3.1.2. Structure CS2. Figure 8 gives a control structure that provides good stable regulatory control of the process. The key loops in the structure are as follows: 1. The reactor level is controlled by manipulating the fresh feed F0B. 2. The reactor composition zA is controlled by changing the fresh feed F0A. 3. The reactor effluent F is flow-controlled. 4. Reflux drum levels are controlled by distillate flows. 5. Base levels are controlled by bottoms flows.

Two modifications of this control structure are also studied. In the first, the composition of A in the distillate of the first column xD1,A is controlled instead of the reactor composition. In the second, the temperature of the top tray in the first column is used to infer the composition of A. These alternatives are shown in Figure 9. The control structure works well, as is shown in the next section. The flow controller in the reactor effluent stream prevents the snowball effect. However, this structure has the disadvantage that the production rates are not directly set. If different flow rates of the product streams D2 and B3 are desired, the two available handles are the setpoints of the composition (or temperature) controller and the reactor effluent flow controller. These would have to be adjusted in an openloop fashion to influence the production rates of the two products. Historical plant data or a model of the process would typically be used to estimate the values of zA and F required. 3.1.3. Structure CS3. Figure 10 gives an alternative control structure that eliminates the need for the composition analyzer. The features of the scheme are as follows: 1. The reactor level is controlled by manipulating the fresh feed F0B. 2. The reactor effluent F is flow-controlled. 3. The fresh feed F0A is ratioed to the reactor effluent flow. 4. Reflux drum levels are controlled by distillate flows. 5. Base levels are controlled by bottoms flows. The key feature is item 3. Fresh feed F0A is changed as the reactor effluent flow is changed. The two handles to adjust the product production rates are the setpoint of the reactor effluent flow controller and the ratio signal. This structure provides stable regulatory control of the process without requiring a composition analyzer.


Figure 8. CS2A conventional control structure.

Figure 9. Modified CS2B/C conventional control structure.

However, it still has the problem of not directly setting product production rates. 3.2. On-Demand Control Structures. In on-demand control structures, the flow rates of the product streams are set. We have looked at several alternatives, as discussed below. It is important to remember that reactor compositions must change to achieve different product ratios. This implies that any on-demand control structure that attempts to hold the composition in the reactor constant will not work.

Three different on-demand control structures are discussed below. In all of these schemes, there are flow controllers on the two product streams D2 and B3. 3.2.1. Structure CS4. Figure 11 shows an on-demand control structure in which the flow rates of the two product streams (D2 and B3) are flow-controlled. Recycle streams of both products (streams RM and RD) are used to control the reflux drum level in column 2 and the base level in column 3. The reactor composition is not controlled. Fresh feed

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Figure 10. CS3 conventional control structure.

Figure 11. CS4 on-demand control structure.

F0B comes in on reactor level control. Fresh feed F0A is manipulated to maintain a constant ratio of the two recycle flows. The ratio of the flow rates of the two recycle streams is calculated and fed into a ratio controller RC as the “PV” signal. The output signal of the ratio controller is the setpoint of the flow controller on the fresh feed F0A.

This scheme is workable, but it has the disadvantage that the use of product recycles increases the energy consumption and increases the load on the columns. 3.2.2. Structure CS5. Figure 12 gives an alternative on-demand control structure in which recycles of products are not used. The basic idea is to develop a relationship that shows how reactor composition zA


Figure 12. CS5 on-demand control structure.

Figure 13. Composition of A in the reactor for different D2 and B3.

must change to achieve different product flow rates D2 and B3. Figure 13 shows this relationship as developed from the steady-state model of the process. The setpoint of the reactor composition is changed by the signal from the “product ratio” function block, given the actual flow rates of the two products D2 and B3. The CS5 control structure is similar to CS2A in the reactor section. However, in the separation section there are important differences. 1. The base levels in all three columns are controlled by adjusting the flow rates of the feed streams to the columns. Thus, the material balance control structure is in the opposite direction to flows through the system; i.e., flows into a unit are manipulated to hold an inventory in the unit. 2. The level in the reflux drum of the second column is controlled by manipulating the setpoint of the temperature controller in the first column. The idea is to adjust the amount of component M that is recycled back

to the reactor in the D1 stream to feed into the second column just the amount of M that is called for by the flow controller on stream D2. For example, if the reflux drum level is rising in the second column, there is too much component M being fed into the column. So, the level controller raises the setpoint of the column 2 temperature controller, which drives more M overhead. This control structure requires a composition analyzer. It also depends on the accuracy of the correlation (Figure 13) between product flow rates and reactor composition. Its effectiveness could also be affected by inaccuracies in flow measurements. The impact of these errors is explored later in this paper. 3.2.3. Structure CS6. Figure 14 gives the final ondemand control structure studied. It is similar to CS5, but it has two important differences: 1. The reactor composition analyzer is eliminated. 2. The flow rate of the fresh feed F0A is simply ratioed to the flow rate of the recycle stream D1 from the first column. This structure evolved from looking at how several variables and ratios of variables had to change to achieve different product flow rates at steady state. As Figure 15 shows, the ratio of F0A to F is fairly constant over a wide range of values of D2 and B3 product flow rates. This process insight led us to try CS6. Table 3 summarizes the important loops and requirements of the various control structures. 4. Results and Discussion Each control structure was subjected to several disturbances, as discussed below. 4.1. Control Structure CS1. Figure 16 gives the results when the conventional CS1 control structure is

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Figure 14. CS6 on-demand control structure. Table 3. Summary of Control Structures mode flow-controlled streams reactor composition analyzer ratio product recycles setpoint of TC1 adjusted

CS1

CS2

CS3

CS4

CS5

CS6

conv F0A and F0B no

conv F yes no no

on-demand F, D2, and B3 no RM/RD yes no

on-demand D2 and B3 yes

no no

conv F no F0A/F no no

on-demand D2 and B3 no F0A/D1 no yes

Figure 15. Ratios between F0A and D1 for different D2 and B3.

used. The disturbances are small changes in the fresh feed flow rate of component A (F0A). One set of curves in Figure 16 shows that the control structure can handle a +10% change in F0A, but it takes more than 10 days for the final changes in the production rates to occur. This very slow response is due to the presence of the recycle between the first column and the reactor. This very sluggish responsiveness would probably be unacceptable with the present industrial requirements for “agile” processes. Note also the snowball effect: a 10% change in F0A causes a 30% change in the flow rate of the D1 recycle. An even more severe problem is shown in the other two sets of curves in Figure 16. The CS1 control

no yes

structure can handle a very small (2%) decrease in F0A, but it cannot handle a modest 5% decrease. The D1 recycle increases to the point that the vapor boilup in the first column reaches its limit, which is set at 3 times the steady-state design value. Thus, this intuitively straightforward control structure does not provide effective control. 4.2. Control Structure CS2. Figure 17 gives the results when the conventional CS2A control structure is used. The disturbances are positive and negative changes in the setpoint of the flow controller on the reactor effluent stream F, which occur at a time equal to 3 h. The control structure is very robust, handling very large changes ((50%). Changing F has a drastic effect on the recycle D1 but has less effect on the flow rates of the fresh feed streams and the product streams. Deceasing F changes the production rates more significantly than increasing F. Reactor composition zA is held constant, and the production rates of both products change by about the same amount. Using the distillate composition or the top tray temperature to control F0A gives the same response as using the reactor composition analyzer for the disturbances in F. Figure 17B shows how the impurities in the two product streams (D2 and B3) are affected by these large disturbances. Although there are momentary large deviations, the column temperature controllers do a good job in returning product purities to close to the


Figure 16. Sensitivity of CS1 to changes in F0A fresh feed flow rate.

Figure 17. (50% change in F for CS2.

Figure 18. (25% change in zA for CS2.

desired levels. Of course, this performance could be improved by using steam-to-feed feedforward control to assist the temperature controllers. For simplicity in comparing the alternative structures, no feedforward control is included in the simulation results. Figure 18 illustrates the effect of changing the setpoint of the reactor composition controller. The original steady-state value is 20 mol % A. The setpoint is

increased to 25 mol % or decreased to 15 mol %. This change has a strong effect on the recycle D1 and on the flow rates of the product streams but has less of an effect on the flow rates of the fresh feed streams. However, the product distribution is altered. Higher zA values produce more of component D (stream B3 increases). Figure 19 compares the responses of CS2A, CS2B, and CS2C when the setpoint of the first column tray

1900


Figure 19. 10% TC1 setpoint change for CS2A, CS2B, and CS2C.

temperature controller (tray 6) is change. Note that in this column there are two temperature controllers for CS2C: one is at the top tray, which controls the composition A in D1, and another is at tray 6, which is used to infer the impurity of B in the bottoms. All structures are workable. Using the composition controller in either the reactor or the column gives the same response. The response when using temperature control is different from that when using composition control; i.e., increasing the temperature setpoint of the first column drives more M up the column, and then the top tray temperature controller increases the flow rate of fresh feed F0A (because if the temperature is high, that means there is less component A in the distillate flow). This causes a higher production of component D. 4.3. Control Structure CS3. Figure 20 gives the results when the conventional CS3 control structure is used. The disturbances are (50% changes in the reactor effluent flow rate F, which occur at a time equal 3 h. The effect of the flow rate F on the production rate is larger than that for CS2. Because the ratio of F0A/F is fixed, a 50% change in F produces an immediate 50% change in the F0A fresh feed. The total production of

Figure 20. (50% change in F for CS3.

products (M plus D) changes more significantly. The D product (stream B3) is more affected than the M product (stream D2), as expected, because a higher concentration of A in the reactor favors the production of D via the second reaction. Notice that the reactor composition and the product flow rates are still slowing changing after 60 h. 4.4. Comparison of Conventional Control Structures. Figure 21 gives a direct comparison between CS2C and CS3 for the +50% increase in F. The larger impact on the production rate of CS3 is clearly shown. The third curves in this figure show the case where the F0A/F ratio is not closed, so there is no change in F0A. Only F has changed, and there is no composition controller. Note that the product distribution changes. For a +50% increase in F, the system ends up producing less M (stream D2 decreases) and more D (stream B3 increases). Figure 21B gives results for a -50% change in F. Notice that the system shuts down when the F0A/F ratio is not closed. The reactor level controller cuts back on the fresh feed F0B, and the system fills up with component A. Figure 22 compares the responses of CS1, CS2C, and CS3 structures when the process has 10 mol % impurity of component B and 90 mol % A in fresh feed F0A. The response is similar to the results of changing the fresh feed F0A flow rate in the sense of the production rate. CS1 fails to handle this change, but CS2C and CS3 are workable for this disturbance. CS2C brings the process to the new steady state faster than CS3. The advantage of CS2C to CS3 is that the production rates of M and D do not change significantly when the process has some impurities in the fresh feeds because CS2C controls the composition A indirectly by the temperature control of the top tray in the first column. 4.5. Control Structure CS4. Figure 23 gives the results for the on-demand control structure in which recycle streams of both products are used. The reflux drum level controller in column 2 manipulates recycle RM and the base level controller in column 3 manipulates recycle RD as the flow rates of the two product streams are varied. We show in these figures the maximum and minimum values of the change in the product flow rate for which the control structure is able to stabilize the system. Only small increases in D2 or decreases in B3 can be handled,


Figure 21. (50% change in F for CS2C, CS3, and CS3 (fixed F0A). Table 4. Limits of Setpoint Changes of On-Demand Control Structures

Figure 22. 10% impurity of B in F0A for CS1, CS2C, and CS3.

while significantly larger changes can be handled in the opposite direction. 4.6. Control Structure CS5. Figure 24 gives the results for the on-demand control structure in which the “product ratio” function block predicts the reactor composition required. This structure can handle very large changes in the individual product production rates. Figure 25 indicates that CS5 is workable even when there are some errors in flow measurement or errors in prediction. The disturbance is a 20% decrease in the flow rate of B3. In Figure 25A, the predicted value of the reactor composition is in error by 10% (both positive and negative), so the setpoint of the reactor composition controller is not the correct. In Figure 25B, the flowrate signal sent to the predictor is in error by (10% (the actual B3 flow rate is not what the predictor uses to calculate the reactor composition setpoint). Despite these errors, the system rides through the disturbance. However, there are some large changes in D1 that may adversely affect the operation of the first column. Similar results were obtained for changes in D2 with the same kinds of errors in prediction or flow measurements. 4.7. Control Structure CS6. Figures 26 and 27 give the results for the on-demand control structure in which

structure

% D2 change

% B3 change

CS4 CS5 CS6

-40, 25 -55, 40 -55, 40

-16, 12 -20, 40 -20, 40

the F0A/D1 ratio is maintained and there is no reactor composition control. The fact that this control structure does not require a composition measurement is a significant advantage. A variety of disturbances were made to test the robustness of this control structure. Figure 26 shows the dynamic results when increases and decreases in the individual product flow rates are made. The system can handle larger increases in either product flow rate than decreases. Figure 27 gives the results when simultaneous 20% changes are made in both product flow rates. 1. Figure 27A: Both D2 and B3 are increased 20%. 2. Figure 27B: Both D2 and B3 are decreased 20%. 3. Figure 27C: D2 is increased 20%, and B3 is decreased 20%. 4. Figure 27D: D2 is decreased 20%, and B3 is increased 20%. All of the fairly large disturbances are effectively handled by the CS6 control structure. 4.8. Comparison of On-Demand Control Structures. Figure 28 compares the results for all on-demand structures when the fresh feed F0A composition changes from 100 mol % A to 90 mol % A and 10 mol % B. All structures are workable. CS4 with the recycle streams of two products takes a longer time than the others to get to the new steady state because the process must detect the change in columns 2 and 3 and adjust the recycle flow rates, RM and RT. The reflux drum level in column 2 is controlled by the temperature setpoint of column 1, and the base levels are controlled by the column feeds for CS5 and CS6. That means level controller signals are opposite to the direction of flows. This is faster than using the recycle product stream to adjust the levels. To set fresh feed F0A, CS5 uses the predictor and reactor composition controller. The controller detects the change in composition A in the reactor and adjusts the fresh feed. Therefore, the response of CS5 is the fastest. In any event, the response of CS6 is faster than CS4. Table 4

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Figure 23. Changes in D2 and B3 for CS4.


Figure 25. CS5 with errors in prediction or flow measurement.

gives the limits of feasible changes in the product flow rates for each of the three on-demand control structures. Changes that are larger than these cannot be handled. 5. Operating Degrees of Freedom This two-product process basically has three operating degrees of freedom (the setpoints of three controllers can

be changed), so different flow rates of the two products can be achieved, provided they lie within the feasible region of the process and its control structure. In the conventional control structures (CS1, CS2, and CS3), besides the control tray temperature in the first column, other operating degrees of freedom are as follows. 1. CS1: flow rates of two fresh feeds F0A and F0B.



Figure 27. Simultaneous changes in D2 and B3 for CS6.

2. CS2: reactor composition zA or the top-tray temperature of the first column and reactor effluent flow rate F. 3. CS3: reactor effluent flow rate F and the ratio of F0A fresh feed to F. There are no recycles of products back to the reactor in these conventional control structures.

The three on-demand control structures use different degrees of freedom and have different ways of recycling excess component M. The 2 degrees of freedom are the specified product flow rates. The CS4 structure explicitly uses two recycle streams (RM from the top of the second column and RD from the bottom of the third column), and these provide an

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degrees of freedom. There is also no unique relationship between the flow rates of the two fresh feeds and the flow rates of the three products; i.e., setting the two fresh feeds does not set the production rates of each of the three individual products because the A and B reactants can be consumed to make different amounts of the three products. Nomenclature

Figure 28. 10% impurity of B in F0A for CS4, CS5, and CS6.

additional 2 degrees of freedom compared to the process with no recycle streams. These additional degrees of freedom in CS4 are the reactor effluent flow rate F and the ratio of product M recycle (RM) to product D recycle (RD). Both the CS5 and CS6 structures have no explicit recycle streams. However, recycle of excess M is achieved by changing the temperature controller setpoint in the first column so more or less M goes overhead in D1 and is recycled back to the reactor. So, the relaxation of holding a fixed tray temperature in the first column provides an additional degree of freedom in CS5 and CS6, beyond the two product flow rates. In CS5 the reactor composition is the additional degree of freedom. In CS6 the ratio of flow rate of fresh feed F0A to the flow rate of D1 recycle is the additional degree of freedom. It is interesting to note that the different control structures will not operate at the identical steady-state conditions for the same product flow rates. This occurs because other combinations of variables can produce the same net production rates of the two products. For example, the reactor effluent flow rate F, the recycle D1 from the first column, the control tray temperature in the first column and the reactor composition can change from structure to structure. However, as discussed earlier in this paper, the two fresh feed flow rates will be identical in all control structures for the same product flow rates because of the stoichiometry.

Bi ) bottom flow rate from the ith column (lb‚mol/h) CC ) composition controller CS ) control structure DCi ) column diameter (ft) Di ) distillate flow rate from the ith column (lb‚mol/h) F ) reactor effluent flow rate (lb‚mol/h) FC ) flow controller FT ) flow transmitter F0A ) fresh feed rate of the A component (lb‚mol/h) F0B ) fresh feed rate of the B component (lb‚mol/h) FLi ) column feed rate to the ith column (lb‚mol/h) LC ) level controller NFi ) feed tray of the ith column NTi ) total number of trays of the ith column PC ) pressure controller ratio ) mulitplier Ri ) reflux flow rate of the ith column (lb‚mol/h) RD ) product D recycle flow rate (lb‚mol/h) RM ) product M recycle flow rate (lb‚mol/h) RR ) reflux ratio SP ) controller setpoint signal TC ) temperature controller TR ) reactor temperature (°F) VR ) reactor holdup (lb‚mol) VSi ) vapor boilup in the ith column (lb‚mol/h) xBi,j ) bottoms composition of the j component from the ith column (mole fraction) xDi,j ) distillate composition of the j component from the ith column (mole fraction) zi ) reactor composition of the i component (mole fraction) Greek Symbols Ri ) relative volatility of the i component ∆RR ) change in the reflux ratio ∆F ) change in the reactor effluent flow rate (lb‚mol/h) ∆F0A ) change in the fresh feed rate of the A component (lb‚mol/h) ∆VS ) change in the vapor boilup (lb‚mol/h) ∆zA ) change in the reactor composition (mole fraction of A)

6. Conclusion and Future Work This paper has compared the dynamic performance of several alternative control structures, both conventional and on-demand. The most obvious conventional control structure, which simply fixes the flow rates of the two fresh feeds, does not provide effective control. It exhibits the snowball effect and can handle only very small disturbances. The most promising on-demand control structure (CS6) requires no reactor composition analyzer and can handle quite large changes (about 20%) in the specified flow rates of either or both products. Future work includes extensions to a process in which there are three consecutive reactions and three products are produced. This case presents a much more challenging situation in which explicit recycles of some of the products may be necessary because of a lack of

Literature Cited (1) Luyben, W. L. Inherent Dynamic Problems with OnDemand Control Structures. Ind. Eng. Chem. Res. 1999, 38, 23152329. (2) Luyben, W. L. Simple Regulatory Control of the Eastman Process. Ind. Eng. Chem. Res. 1996, 35, 3280-3289. (3) Luyben, W. L.; Tyreus, B. D.; Luyben, M. L. Plantwide Process Control; McGraw-Hill: New York, 1999. (4) Luyben, W. L. Plantwide Dynamic Simulators in Chemical Processing and Control; Marcel Dekker: New York, 2002. (5) Douglas, J. M. Conceptual Design of Chemical Processes; McGraw-Hill: New York, 1988.

Received for review August 4, 2002 Revised manuscript received December 30, 2002 Accepted February 13, 2003 IE0205905

Plantwide Control of Continuous Multiproduct Processes: Two-Product

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