Impact of Reaction Activation Energy on Plantwide Control Structures

Ind. Eng. Chem. Res. 2000, 39, 2345-2354

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Impact of Reaction Activation Energy on Plantwide Control Structures in Adiabatic Tubular Reactor Systems William L. Luyben† Department of Chemical Engineering, Lehigh University Bethlehem, Pennsylvania 18015

Chemical reactions with large activation energies present difficult control problems because of the rapid increase in the reaction rate as the temperature increases. This paper explores the impact of activation energy and reactant concentration on both the steady-state economics and the dynamic controllability of a process in which an exothermic, irreversible, gas-phase reaction A + B f C occurs in an adiabatic tubular reactor. A gas recycle returns unconverted reactants from the separation section. Steady-state economics favor the use of high reactant concentrations, but dynamic controllability favors having the concentration of one of the reactants low, particularly with large activation energies. Two control structures are explored, one with the limiting reactant concentration controlled by fresh feed and the other with this fresh feed fixed. The first structure is only effective with low activation energies. The second handles large activation energies, but only when reactant concentrations are not high. 1. Introduction Research in the area of plantwide control has increased rapidly in recent years. Workers in both industry and academia have recognized the industrial importance of this subject. Modern world-class chemical process flowsheets have many features that improve yield and efficiency, while reducing pollution, energy consumption, and capital investment. This is accomplished by making extensive use of material recycles, energy integration, minimum intermediate storage, and complex reaction and separation configurations. All of these features make dynamic control more difficult because the entire plant is interlinked and tightly integrated. Control structures developed for the individual unit operations may fail in the plantwide environment because all of the individual unit operations must “dance together”. In addition, competitive pressures have increased the dynamic performance requirements of many processes. Tight control of product-quality variability via “on-aim” control means that product quality must be maintained within a specified range: too pure is just as bad as not pure enough. This is a tougher job than simply making sure a purity specification is met or exceeded. There has also been an increasing desire to have processes that are more agile and can respond quickly to customer needs. The concept of “just-in-time” manufacturing sometimes requires processes to use “ondemand” control structures in which product flow rates from the last process units are set by customer demand. The control scheme must respond to these production rate changes at the end of the process by making appropriate changes in flow rates in upstream units. Typically this is done by working back sequentially through the process from unit to unit. This on-demand control structure often has inherent dynamic disadvantages (Luyben1), making control more difficult. The literature contains a large number of papers dealing with the steady-state design and the open-loop † E-mail: [email protected]. Telephone: 610-758-4256. Fax: 610-758-5297.

Figure 1. Process flowsheet and control structure CS1.

dynamics of tubular reactors. However, few papers deal with tubular reactors in the plantwide environment. Also there are only a few papers that discuss the closedloop control of such systems. These papers were recently reviewed by Luyben.2 This paper studies the impact of the important kinetic parameter activation energy on plantwide control structures. Different control schemes and different design parameters (reactant concentrations) are shown to be required for processes with different activation energies. 2. Process Studied The exothermic, irreversible reaction A + B f C occurs in a gas-phase, adiabatic tubular reactor. The reactor is packed with a solid catalyst. The flowsheet is shown in Figure 1. The two gaseous fresh feed streams FOA and FOB introduce reactants A and B into the system. The fresh feeds are combined with a gas recycle stream, and the total stream flows through a heat exchanger and furnace before entering the reactor. The hot reactor effluent is used to preheat the feed and then is cooled before entering a separator drum. All of the product C formed in the reactor goes into the liquid phase in the drum and is removed. The vapor from the

10.1021/ie990610b CCC: $19.00 © 2000 American Chemical Society Published on Web 05/13/2000

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Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000

Table 1. Parameter Values activation energy E (kJ/kmol) base case hot reaction heat of reaction λ (kJ/kmol of C) k at 500 K (kmol s-1 bar-2 (kg of catalyst)-1) heat capacities (kJ kmol-1 K-1) cpA cpB cpC molecular weights (kg/gmol) MWA MWB MWC overall heat-tranfer coefficient U (kJ s-1 m-2 K-1) minimum approach temperature ∆TH (K) furnace heat duty/total preheat duty (%) production rate (gmol/s of C)

69 710 139 420 -23 237 3.309 × 10-8 30 40 70 15 20 35 0.24 25 10 0.12

drum, containing only A and B, is compressed and recycled back to the reactor. The details of the steady-state design procedure, parameter values, economics, sizing calculations, and modeling (both steady state and dynamic) are given in previous papers.3,4 Table 1 summarizes important parameter values for the base case (with activation energy E ) 69 710 kJ/kmol) and for the “hot reaction” case (with an activation energy twice that of the base case). The specific reaction rate k at a temperature of 500 K is held constant for each value of E by backcalculating the preexponential factor R.

k ) Re-E/RT

(1)

The reaction rate (R, kmol/s/kg of catalyst) depends on the partial pressures of the reactants

R ) kPAPB ) kyAyBP2

(2)

where the partial pressure of component j is Pj ) Pyj (yj ) mole fraction of j in the gas phase and P is the total system pressure in bar). The gas recycle has a composition of A that is yRA (mole fraction). This is an important design parameter. As the economic analysis discussed in the next section shows, designing for equimolar concentrations of both reactants (yRA ) 0.5) gives the best steady-state economic design because it maximizes the yAyB product, which minimizes the reactor size for a specified production rate of C. As yRA is lowered or raised, with the corresponding larger or smaller yRB ) 1 - yRA, the product of the partial pressures decreases, which means more catalyst is required. However, as the dynamic analysis in a later section shows, operating with high reactant concentrations can increase the potential for reactor runaways and make dynamic control more difficult. Designing for a lower concentration of one of the reactants can improve dynamic control, provided the appropriate control structure is used. This is particularly true for large activation energies. The reactant with the smaller concentration is the limiting reactant. When increasing the temperature raises the specific reaction rate k, the concentration of the limiting reactant decreases. The decrease in the yAyB

Figure 2. Optimum design: (A) base case; (B) hot reaction.

product tends to decrease the overall reaction rate R. This adds a degree of self-regulation to the process. We assume that the optimum operating pressure is 50 bar and that the normal maximum operating reactor temperature is 500 K. Because the reactor is adiabatic, under steady-state conditions the maximum will occur at the reactor outlet. We assume the optimum design uses this maximum outlet temperature because this will minimize reactor size (Wcat, kilograms of catalyst). As shown in Figure 1, heat-exchanger bypassing FB is used to control the temperature Tmix of the blended stream (the furnace inlet temperature) and furnace firing QF is used to control the reactor inlet temperature Tin. An alternative configuration, not studied in this work, would be to bypass cold material all the way around both the heat exchanger and the furnace and control Tin directly with bypass flow. Furnace firing would be fixed. This scheme would give tighter temperature control because simple mixing is involved and the dynamics of the furnace are avoided. However, it is not capable of handling as large disturbances because only bypassing is being used. If a disturbance calls for more heat, the bypass valve can go completely shut and the system may “quench”. The scheme used in this paper manipulates both the furnace firing and the bypass, so both runaways and quenching can be prevented. 3. Optimum Steady-State Design For a given activation energy, maximum reactor exit temperature, pressure, and production rate, the process

Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000 2347

Figure 3. (A) Reactor gain (base case). (B) Outlet conditions (base case). (C) Reactor gain (hot reaction). (D) Outlet conditions (hot reaction). Table 2. Design Parameters base case

hot case

yRA (m.f.)

0.5

0.3

0.2

0.1

0.5

0.3

0.2

0.1

FR (kmol/s) Wcat (103 kg) FB (kmol/s) QF (103 kJ/s) Tmix (K) Tin (K) Tout (K) area (m2) capital (106$) reactor catalyst compressor furnace heat exchanger operating (106$/yr) furnace energy compressor work TAC (106$/yr)

1.8 44.0 0.363 1.06 446 461 500 1780

1.8 49.0 0.342 1.12 448 463 500 1930

1.8 60.0 0.332 1.16 449 464 500 2000

2.0 86.4 0.315 1.20 450 468 500 2410

3.0 52.8 0.317 1.81 459 475 500 3620

3.0 58.4 0.294 1.95 460 477 500 3900

3.1 70.2 0.280 2.08 461 478 500 4210

3.5 102 0.254 2.43 464 481 500 5110

0.425 4.40 0.895 0.650 0.946

0.454 4.90 0.895 0.681 0.996

0.515 6.00 0.895 0.696 1.02

0.646 8.64 0.976 0.777 1.15

0.476 5.28 1.36 0.993 1.50

0.506 5.84 1.36 1.04 1.57

0.568 7.02 1.40 1.09 1.66

0.715 10.2 1.54 1.23 1.88

0.158 0.408 3.01

0.168 0.408 3.22

0.173 0.408 3.62

0.200 0.453 4.72

0.275 0.680 4.16

0.292 0.680 4.41

0.311 0.703 4.92

0.363 0.793 6.33

has two design degrees of freedom: recycle gas composition (yRA) and recycle flow rate (FR, kmol/s). Note that setting the production rate fixes the fresh feed flow rates FOA and FOB. The optimum design is found by the following procedure: 1. Select a value for yRA over the range of 0.5-0.1 (to be optimized).

2. Pick a value of recycle flow rate FR (to be optimized). 3. Calculate the reactor inlet temperature Tin from an energy balance around the reactor from the known heat release (to produce the required product C) and the heat capacity and flow rate of material through the reactor.

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Figure 5. Changes in Tin (hot reaction; yRA ) 0.5).

Figure 4. Changes in Tin (base case; yRA ) 0.5).

4. Calculate the heat-exchanger heat duty, the furnace heat duty (assuming 10% of the total preheating occurs in the furnace), and the bypass flow rate. 5. Calculate the size of the heat exchanger, assuming a 25 K minimum approach temperature and an overall heat-transfer coefficient of 0.24 kJ s-1 m-2 K-1. 6. Calculate the reactor inlet flow rate and compositions from fresh feeds and the recycle. See eqs 3-5. 7. Integrate down the length of the reactor (from w ) 0 and Tin) to a catalyst weight (w ) Wcat) where the temperature is 500 K.

8. Calculate the capital costs of the reactor, heat exchanger, furnace, and compressor. The capital cost of the catalyst is assumed to be $100/kg. Calculate the operating costs of the furnace and the compressor. Calculate the total annual cost by using a payback period of 3 years (see eq 6). Details of the economic assumptions and methods are given by Luyben.4 9. Vary the selected recycle flow rate until the minimum TAC is found. Increasing the recycle flow rate increases the compressor, furnace, and heat-exchanger costs but reduces reactor costs. 10. Find the minimum TAC conditions for different recycle compositions.


Fin ) FR + FOA + FOB

(3)

yin,A )

FOA + yRAFR Fin

(4)

yin,B )

FOB + yRBFR Fin

(5)

TAC ) CompressorEnergyCost + FurnaceFuelCost + (CapitalCostsCompressor, Catalyst, Furnace, HeatExchanger)/3YearPaybackPeriod (6) Results are shown in Figure 2 for the base case activation energy and for an activation energy twice as large. It is clear that steady-state economics favor recycle concentration yRA ) 0.5. The economic incentive is significant. For example, for the base case (Figure 2A), at yRA ) 0.5 the total annual cost TAC ) 3 × 106$/yr. At yRA ) 0.1, the total annual cost is over 50% higher at TAC ) 4.7 × 106$/yr. The reactor size (catalyst weight) increases from 44 000 to 86 370 kg. The optimum recycle flow rate increases slightly from 1.8 to 2.0 kmol/s. For the higher activation energy case, similar results are shown in Figure 2B. Costs are higher because the higher temperature sensitivity requires a higher inlet temperature, resulting in more recycle and a larger reactor. However, again, the optimum steady-state design is for high reactant concentrations. Thus, if we consider only steady-state economics, we would design for reactant concentrations near the 0.5 mole fraction level. However, as we demonstrate in the following sections, dynamic controllability is more difficult at high reactant concentrations, particularly for reactions with large activation energies. 4. Reactor Gains We can gain some insight into the dynamic problems associated with high reactant concentrations by looking at reactor gains. The gain of an adiabatic tubular reactor is defined as the steady-state change in the outlet temperature for a given change in the inlet temperature.

KR ) ∆Tout/∆Tin

(7)

The larger KR, the more likely it is that the feed-effluent heat exchanger/adiabatic reactor system will be openloop unstable. Previous papers4,5 have demonstrated the degradation of control as the reactor gain increases. Reactor gains are calculated for the two activation energy cases and for several reactant concentrations, using the optimum design for each case; i.e., the recycle flow rate that gives the minimum total annual cost for each value of yRA. Conditions at these optimum designs are given in Table 2. The gains are calculated with the reactor in isolation, assuming constant pressure and constant inlet reactor flow rate and composition. The inlet temperature is increased by a specified amount ∆Tin, and the ordinary differential equations describing the steady-state tubular reactor are integrated from w ) 0 to Wcat (the total weight of catalyst at the optimum design conditions). Figure 3 shows the reactor gain and the new steadystate values of the reactor outlet temperature and the concentration of reactant A leaving the reactor as the reactor inlet temperature is increased by several ∆Tin

Figure 6. Changes in Tin (hot reaction; yRA ) 0.1).

values. The reactor is quite nonlinear, so the reactor gain varies with the magnitude of the change in inlet temperature. For small values of ∆Tin, reactor gains increase as ∆Tin increases. However, at very large ∆Tin’s, the gains begin to decrease. This occurs because the concentration of reactant leaving the reactor becomes so low that there is no more reactant left to react. Parts A and B of Figure 3 are for the base-case activation energy. Note that the reactor gains are quite small when reactant concentrations are low but can become as large as 20 when yRA ) 0.5. There is more reactant available, so higher exit temperatures can be

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tants in the recycle loop. The total pressure in the gas loop is calculated from an approximate dynamic total mass balance. Gas enters in the two fresh feeds, and gas is converted into liquid component C in the heat exchanger following the reactor. An average density is used in the gas loop, assuming an average molecular weight of 17.5 kg/kmol and an average temperature of 500 K. The total gas volume in the system Vgtot is the vapor volume in the reactor, separator drum, heat exchanger (shell and tube sides), and furnace.

Total mass balance on the gas loop: 17.5Vgtot

Figure 7. Control structure CS2.

reached. Note that these exit temperatures can be very high when the yRA values are greater than 0.1-0.2 mole fraction A. Parts C and D of Figure 3 give results for the high activation energy case. Reactor gains are much larger and more sensitive to ∆Tin and to yRA. Even when yRA ) 0.1, the reactor gain can exceed 7. 5. Dynamic Simulations 5.1. Dynamic Model. The dynamic model used in previous work3 to simulate the entire process is modified slightly to account for varying concentrations of reac-

dP ) 15FOA + 20FOB - 35FNRyNR,C (0.08314)(500) dt (8) Component A molar balance on the gas loop: d(yRAP) ) FOA - FNRyNR,C (0.08314)(500) dt Vgtot

(9)

Every 1 mol of C produced consumes 1 mol of A. 5.2. Control Structure and Tuning. Figure 1 shows one of the control structures used in this paper. It consists of the following loops: 1. Pressure P is controlled by manipulating fresh feed FOB. 2. Fresh feed FOA is ratioed to FOB. 3. Recycle gas composition yRA is controlled by manipulating the ratio (FOA/FOB).

Figure 8. (A) CS2 (hot reaction; yRA ) 0.1). (B) CS2; changes in Tin (hot reaction; yRA ) 0.1). (C) CS2; changes in Tin (hot reaction; yRA ) 0.1). (D) CS2; changes in FOA (hot reaction; yRA ) 0.1).


Figure 9. (A) CS2; changes in Tin (hot reaction; yRA ) 0.5). (B) CS2; changes in FOA (hot reaction; yRA ) 0.5).

4. The temperature of the blended stream entering the furnace Tmix is controlled by manipulating the bypass flow rate FB. 5. Reactor inlet temperature Tin is controlled by manipulating furnace heat input QF. 6. The separator inlet temperature is controlled by cooling water. 7. The separator level is controlled by liquid product. 8. Recycle flow rate FR is held constant by controlling the compressor speed. Two 30-s lags are included in the pressure loop. Three 6-s lags are included in the temperature and composition loops. Controllers are tuned by getting the ultimate gain and period from a relay-feedback test and using the Tyreus-Luyben settings. 5.3. Results for Moderate Activation Energy. Figure 4 gives results for the base-case activation energy and a recycle gas composition yRA ) 0.5. The disturbance is a step change in the Tin setpoint. Figure 4A shows that quite large changes in the inlet temperature can be handled, but the 15 K change produces a very high peak reactor exit temperature of about 575 K. These large changes in temperature produce large increases in throughput. In fact, the 15 K change pulls in so much fresh feed that the control valve on FOB saturates wide open and pressure cannot be maintained. The composition controller keeps yRA at its setpoint of 0.5 mole fraction. Thus, the control structure shown in Figure 1 (we call this CS1) provides effective control of the

process with a moderate activation energy, even using high reactant concentrations, which are the most economically attractive. It should be noted that there are several productionrate handles with this control structure: reactor inlet temperature, recycle flow rate, and pressure. Changing the recycle gas composition would have little effect because it is at such a high level. 5.4. Results for Higher Activation Energy. Figure 5 gives results for the higher activation energy case (hot reaction) at the high recycle gas composition yRA ) 0.5. Only very small changes in temperature can be tolerated. Reactor runaway occurs easily. Figure 6 gives results for the hot reaction with a low recycle gas composition yRA ) 0.1. The same temperature sensitivity is shown. Note that the capacity of the FOB fresh feed control valve has been doubled, but saturation still occurs. Thus, there is an inherent problem with the CS1 control structure used on this process with these parameter values. The problem is that the composition controller maintains the reactant concentration yRA at its setpoint. As temperatures begin to climb, there is no decrease in the limiting reactant concentration, so the self-regulating effect is lost. To overcome this problem, a new control structure was tested. As shown in Figure 7, the CS2 control structure simply flow controls the FOA fresh feed. The recycle gas composition yRA is not controlled but varies as disturbances affect the process. Figure 8 shows that this control structure provides very effective control for large changes in reactor inlet temperature Tin and very large changes in throughput (as reflected in the FOA flow rate). Figure 8C shows that, as temperatures are increased, the recycle gas composition yRA drops. For example, when the reactor inlet temperature is increased 12 K, recycle gas composition decreases from yRA ) 0.1 to 0.03. The yAyB product has changed from (0.1)(0.9) ) 0.09 to (0.03)(0.97) ) 0.0291, which compensates for the larger specific reaction rate k produced by the higher temperatures. For the 12 K inlet temperature increase, the new steady-state reactor outlet temperature is 512 K. Note, however, that there is a much higher dynamic peak (522 K). Figure 8D shows what happens to recycle gas composition yRA and pressure P for the very large changes in FOA fresh feed flow rate. Pressure initially increases, which reduces the FOB fresh feed. The combination of the increase in FOA and the decrease in FOB produces an increase in recycle gas composition yRA. Because the initial value of yRA is low (0.1), an increase in yRA can produce an increase in the yAyB product. For example, for the 50% increase in FOA, the yAyB product changes from the initial (0.01)(0.9) ) 0.09 to a new steady state of (0.118)(0.882) ) 0.104. So the concentration effect produces an increase in the reaction rate of 0.104/0.09 ) 1.16. However, the reaction rate has increased by a factor of 1.5. What has accounted for this difference? The answer can be found by looking at the change in the reactor exit temperature that occurs. Remember that the inlet temperature is held constant. The increased reaction rate caused by the composition effect produces a larger adiabatic temperature change through the reactor, and this increases reaction rates. In the 50% increase case, the reactor outlet temperature rises from 500 to 510 K. With the large activation energy, this

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temperature increase produces a much larger specific reaction rate k. It should be noted that the CS2 control structure has a direct production rate handle: the FOA fresh feed flow rate. This is another advantage over the CS1 structure in which the production rate can only be set indirectly by changing the reactor inlet temperature, recycle flow rate, or pressure. A logical question at this point is, will the new control structure work for high values of recycle gas composition? To test this, the yRA ) 0.5 case was rerun with the CS2 control structure. Figure 9A shows that the sensitivity to reactor inlet temperature changes is reduced, but dynamic peak temperatures are still quite high. However, the real problem with CS2 at high values of recycle gas composition is shown in Figure 9B. A very small increase in FOA fresh feed flow rate cannot be handled; a process shutdown occurs. The process fills up with A, pressure builds up, and FOB fresh feed is cut off. This occurs because the yAyB product cannot increase above its initial (0.5)(0.5) ) 0.25 value. The reaction rate cannot increase, so temperatures cannot increase either. Therefore, the CS2 control structure cannot work for large recycle gas concentrations. Processes designed for recycle gas concentrations between yRA ) 0.1 and 0.5 were explored to see how high the concentration can be raised before dynamic problems occur. Figure 10 gives results for yRA ) 0.2. Peak

temperatures for the inlet temperature disturbances are higher than those in the yRA ) 0.1 case (539 versus 523 K for the 12 K increase in Tin), and recycle gas composition drops from yRA ) 0.2 to 0.06. Large changes in FOA can still be handled because the yAyB product and reactor temperatures increase. Figure 11 gives results for the yRA ) 0.3 case. The sensitivity to the reactor inlet temperature is quite high, with peak temperatures rising to almost 570 K. Very large swings in pressure and FOB flow rate occur. The process is able to ride through the FOA fresh feed flow rate changes, but recycle gas compositions get quite close to the yRA ) 0.5 level, at which the process will “go over the cliff”. A small decrease in the inlet temperature causes the process to shutdown, as shown in Figure 12, when yRA ) 0.3, but the same disturbance is easily handled in the yRA ) 0.2 case. For the numerical case studied in this paper, the design should probably be based on the yRA ) 0.2 case. It has good dynamic properties and its total annual cost is 4.923 × 106$/yr compared to the optimum of 4.158 × 106%/yr, which is an 18% increase. This modest steadystate penalty should be more than compensated for by the greatly improved dynamic stability. Thus, processes with high activation energies should use CS2 and should be designed for low reactant compositions. Higher activation energies than those



ture fixed, shows that the CS2 control structure provides effective control for moderate values of reactant concentration. The difference is explained by the temperature effects. In the isothermal CSTR case, all of the changes in the reaction rate must come from composition changes. In the adiabatic tubular reactor case, the reactor temperatures along the length of the reactor can change, and this impacts the overall reaction rate. 6. Conclusion

Figure 12. CS2; +50% FOA and -2% Tin (hot reaction; yRA ) 0.2 and 0.3).

studied would probably require even smaller reactant concentrations. It is interesting to compare the results of this study, in which adiabatic tubular reactors are considered, with the findings of Tyreus and Luyben,6 who studied processes with isothermal CSTRs. They found that the CS2 type control structure (with FOA fresh feed flow rate flow controlled) did not work except for quite small limiting reactant concentrations. This study, using adiabatic tubularreactors with only the inlet tempera-

This study has demonstrated the strong impact of the reaction activation energy on the design and control of processes with adiabatic tubular reactors in which irreversible exothermic reactions take place. This process provides another important example of the everpresent conflicts and trade-offs between steady-state economic design and dynamic controllability. When activation energies are low, high reactant concentrations can be used, and this corresponds to the steady-state economic optimum. The CS1 control structure, in which recycle gas reactant composition and reactor inlet temperature are controlled, provides effective control. When activation energies are high, the use of a limiting reactant (low concentration of one reactant) is required to provide the same degree of self-regulation. When temperatures change the specific reaction rate k,

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the concentration of the limiting reactant changes in the opposite direction, and this reduces the change in the overall reaction rate R ) kyRAyRBP2. Therefore, the control structure must be modified to let the concentration of the limiting reactant float. The CS2 control structure achieves this, but the process should be designed for low reactant concentrations. The higher the activation energy, the lower the limiting reactant concentration should be. Nomenclature A ) reactant component B ) reactant component C ) product component E ) activation energy (kJ kmol-1) FB ) bypass flow rate (kmol/s) FOA ) fresh feed flow rate of reactant A (kmol/s) FOB ) fresh feed flow rate of reactant B (kmol/s) FR ) recycle flow rate (kmol/s) k ) specific reaction rate (kmol s-1 bar-2 (kg of catalyst-1) KR ) reactor gain Ku ) ultimate gain L ) liquid flow rate leaving the separator drum (kmol/s) P ) total pressure (bar) Pj ) partial pressure of component j (bar) QF ) heat transfer in the furnace (kJ/s) QH ) total heat transfer in the heat exchanger (kJ/s) RC ) rate of production of C (kmol of C/s) TAC ) total annual cost ($/yr) Tin ) reactor inlet temperature (K) Tset in ) reactor inlet temperature setpoint (K)

Tmix ) blended bypass and heat-exchanger temperature (K) Tout ) reactor exit temperature (K) U ) overall heat-transfer coefficient in FEHE (kJ s-1 m-2 K-1) Vgtot ) gas volume in the system (m3) Wcat ) weight of the catalyst (kg) R ) preexponential factor ∆TH ) minimum temperature differential in FEFE (K) ∆TR ) temperature differential across the reactor (K) λ ) heat of reaction (kJ/kmol of C produced) τI ) reset time constant (min)

Literature Cited (1) Luyben, W. L. Inherent dynamic problems with on-demand control structures. Ind. Eng. Chem. Res. 1999, 38, 2315-2329. (2) Luyben, W. L. Control of outlet temperature in adiabatic tubular reactors. Ind. Eng. Chem. Res. 1999, 39, 1271-1278. (3) Reyes-De-Leon, F.; Luyben, W. L. Steady-state and dynamic effects of design alternatives in heat-exchanger/furnace/reactor processes. Ind. Eng. Chem. Res. 1999, submitted for publication. (4) Luyben, W. L. Design and control of gas-phase reactor/ recycle processes with reversible exothermic reactions. Ind. Eng. Chem. Res. 1999, in press. (5) Luyben, W. L. Effect of kinetic, design and operating parameters on reactor gain. Ind. Eng. Chem. Res. 1999, in press. (6) Tyreus, B. D.; Luyben, W. L. Dynamics and control of recycle systems. 4. Ternary systems with one or two recycle streams. Ind. Eng. Chem. Res. 1993, 32 (6), 1154.

Received for review August 1, 1999 Revised manuscript received March 30, 2000 Accepted April 6, 2000 IE990610B

Impact of Reaction Activation Energy on Plantwide Control Structures

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