Ind. Eng. Chem. Res. 2000, 39, 1271-1278
1271
PROCESS DESIGN AND CONTROL Control of Outlet Temperature in Adiabatic Tubular Reactors William L. Luyben† Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015
Adiabatic tubular reactors are used in many industrial processes. The conventional control scheme for these reactors is to maintain the inlet temperature to the reactor. However, the optimum operation of the entire process (reaction and separation sections) often requires that the reactor be run at the highest possible temperature, which occurs under steady-state conditions at the reactor exit if the reactions are exothermic. The process studied in this paper has the exothermic, irreversible, gas-phase reaction A + B f C occurring in an adiabatic tubular reactor. A gas recycle returns unconverted reactants from the separation section. Four alternative plantwide control structures for achieving reactor exit temperature control are explored. The reactor exit temperature controller changes different manipulated variables in three of the four control schemes: (1) CS1, the set point of the reactor inlet temperature controller is changed; (2) CS2, the recycle flow rate is changed; and (3) CS3, the flow rate of one of the reactant fresh feeds is changed. The fourth control scheme, CS4, uses an “on-demand” structure. Looking at the dynamics of the reactor in isolation would lead one to select CS2 because CS1 has a very large deadtime (due to the dynamics of the reactor) and CS3 has a very small gain. Dynamic simulations demonstrate that in the plantwide environment, with the reactor and separation operating together, the CS3 structure gives effective control and offers an attractive alternative in those cases where manipulation of recycle flow rate is undesirable because of compressor limitations. The on-demand CS4 structure is the best for handling feed composition disturbances. 1. Introduction The literature contains many papers that explore the dynamics of tubular reactors. Open-loop dynamics, stability, and bifurcation phenomena have been studied on a wide variety of reactions in several types of tubular reactors. For example, Luss and co-workers1 have studied the “wrong-way” effect in packed tubular reactors. Much less has been published relating to practical control schemes for tubular reactors. Some examples are Powell,2 Stevens,3 Budman et al.4 and Filho and McGreavy.5 Most of what has been published considers the reactor in isolation with no linkage to other unit operations. There are very few papers that study the development of effective tubular reactor control systems when the entire plant is considered. Reyes-De Leon and Luyben6 have recently explored both the steady-state economics and the dynamic controllability of processes with a tubular reactor, a feed preheat section, and a separation section. The control structure maintained reactor inlet temperature. One of the unique features of tubular reactors, which distinguishes them from perfectly mixed CSTR reactors, is the need to control reactor inlet temperature Tin. In CSTR systems, feed temperature is usually unimportant. However, in tubular reactor systems, feed temperature usually must be kept above some minimum value. If the reactor inlet temperature is too low, the † E-mail:
[email protected]. Phone: 610-758-4256. Fax: 610758-5297.
reaction rates will be so small that the system may “quench” (move to a low-conversion steady state). Therefore, the typical control scheme is to control reactor inlet temperature. This is achieved by adjusting the energy transferred in feed preheating units: feed/effluent heat exchanger bypassing, changing steam flow rate to a preheater, or adjusting fuel to a fired furnace. At the same time, optimum design and operation typically call for running with temperatures in the reactor as high as possible. At the design stage, this minimizes reactor size or recycle flow rate for a given production rate. At the operational stage, this minimizes recycle costs or maximizes capacity. For exothermic irreversible reactions occurring in adiabatic reactors, the highest temperature occurs at the reactor exit under steady-state conditions. Temperatures can be limited by catalyst degradation, the occurrence of undesirable side reactions, materials of construction limitations, safety considerations, and so on. However, direct control of reactor exit temperature is known to be quite difficult in many systems because these systems can exhibit large deadtimes and inverse response. Over two decades ago, Stevens3 discussed an industrial application in which switching from reactor exit temperature control to reactor inlet temperature control eliminated major dynamic stability problems. The system studied was the production of methanol from synthesis gas. This paper studies the problem of selecting the most effective control structure to achieve reactor exit temperature control. Probably the most obvious method
10.1021/ie990667y CCC: $19.00 © 2000 American Chemical Society Published on Web 04/12/2000
1272
Ind. Eng. Chem. Res., Vol. 39, No. 5, 2000 Table 1. Parameter Values and Steady-State Conditions activation energy E (kJ/kmol) heat of reaction λ (kJ/kmol of C) specific reaction rate k @ 500 K (kmol s-1 bar-2 (kg cat.)-1) heat capacities cpA/cpB/cpC (kJ kmol-1 K-1) molecular weights MWA/MWB/MWC (g/mol) production rate (kmol/s of C) recycle gas composition yRA (m.f.) recycle flow rate FR (kmol/s) catalyst weight Wcat (103 kg) reactor inlet temperature Tin (K) reactor outlet temperature Tout (K) furnace inlet temperature Tmix (K) furnace firing rate QF (103 kJ/s) heat exchanger bypass flow rate FB (kmol/s) area heat exchanger (m2) overall heat transfer coefficient U (kJ s-1 m-2 K-1) minimum approach temperature ∆TH (K)
Figure 1. Process flowsheet.
would be to have the reactor exit temperature controller change the set point of the reactor inlet temperature controller. However, this temperature/temperature cascade structure would have to deal with the very unfavorable dynamics between Tin and Tout. The typical packed tubular reactor has a large deadtime between a change in the inlet temperature and its effect on the outlet temperature due to the thermal inertia of the packing. In addition the wrong-way effect or inverse response sometimes exists in these dynamics, which correspond to having a transfer function with a zero in the RHP. Both of these elements (deadtime and positive zero) yield nonminimum phase systems that result in poor performance of feedback control systems. In the following sections, this alternative and three others are explored. 2. Process Studied The process is the same as that studied by Reyes-De Leon and Luyben.6 An 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 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.6-8 Table 1 summarizes important parameter values and steady-state conditions. This is the high activation energy case studied by Luyben8 (E ) 139, 420 kJ/kmol), so the reaction is quite sensitive to temperature. The specific reaction rate k and the overall reaction rate R (kmol/s/kg of catalyst) are given by
k ) Re-E/RT
(1)
R ) kPAPB ) kyAyBP2
(2)
where the partial pressure of component j is Pj ) Pyj (yj
139 420 -23 237 3.309 × 10-8 30/40/70 30/40/70 0.12 0.20 3.10 70.2 478 500 461 2.08 0.280 4 210 0.24 25
) mole fraction of j in the gas phase, P is the total system pressure in bar and T is absolute temperature in Kelvin. The gas recycle has a composition of A that is yRA ) 0.2 (mole fraction) at the initial base-case steady state. This is an important design parameter. 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 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 Luyben8 demonstrates, 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. We assume that the optimum operating pressure is 50 bar and that the normal maximum operating reactor temperature is 500 K. The reactor size is Wcat (kg 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. The beneficial effects of using both bypassing (to prevent reactor runaways by controlling Tmix) and furnace heat input (to prevent reactor quenching by controlling Tin) has been discussed in a previous paper.6 3. Reactor Dynamics Figure 2 shows the dynamic responses of the reactor for changes in inlet temperature, recycle flow rate and fresh-feed flow rate of reactant A. These results are for the reactor in complete isolation from the separation section; i.e., the composition of the recycle gas, the reactor pressure, and inlet conditions are all constant except for the specific disturbance. The effects of the changing reactor outlet conditions on the separation section are not fed back to change reactor inlet conditions. The change in reactor inlet temperature Tin produces a large change in the reactor outlet temperature Tout, but there is a large 5 min deadtime and a slight amount of inverse response. This indicates that adjusting Tin to
Ind. Eng. Chem. Res., Vol. 39, No. 5, 2000 1273
Figure 3. Control structure CS1: manipulate Tinset.
Figure 4. Control structure CS2: manipulate FR.
Figure 2. (A) Isolated reactor: exit temperature. (B) Isolated reactor: exit reactant concentration.
control Tout will give poor performance. In addition, the process gain between Tin and Tout is very large (about 6). This implies that the controller gain must be small to achieve closed-loop stability, which indicates potentially poor performance. The change in the recycle flow rate FR has an immediate and large effect on Tout, so the use of this manipulated variable appears to be an obvious choice. The change in the fresh feed flow rate FOA has an immediate effect on Tout, but the impact is quite small. This low steady-state gain would lead one to the conclusion that the use of FOA as a manipulated variable would be ineffective because very large changes in FOA would be required. 4. Control Structure Alternatives The four alternative control structures explored in this paper are shown in Figures 3-6. In all of these schemes, the following loops are used: (1) Fresh feed FOB is manipulated to control pressure P. (2) Heat exchanger bypass flow rate FB is manipulated to control the blended temperature Tmix. (3) Furnace energy input QF is manipulated to control reactor inlet temperature Tin. (4) Condenser cooling water is manipulated to hold separator temperature constant at 313K. (5) Gas recycle flow rate FR is controlled by adjusting compressor speed
Figure 5. Control structure CS3: manipulate FOA.
(the turbine speed controller adjusts the flow rate of high-pressure steam). In CS1-CS3, separator drum liquid level is controlled by changing the flow rate of liquid product (pure component C). In CS4, an on-demand control structure is used: production rate is set by the flow rate of the product stream leaving the separator drum. Drum level is controlled by manipulating the fresh feed flow rate FOA. In all of these schemes, reactant compositions are not controlled. The span of the reactor exit-temperature controller is 50 K in all cases. The ranges of the manipulated variables are 50 K for Tin, twice the steadystate flow rate for FR, and twice the steady-state flow rate for FOA.
1274
Ind. Eng. Chem. Res., Vol. 39, No. 5, 2000
Figure 6. On-demand control structure CS4: manipulate FOA.
4.1. CS1: Change Reactor Inlet Temperature. Figure 3 shows a scheme in which a temperature/ temperature cascade strategy is used: the controller output signal from the reactor exit temperature controller changes the set point of the reactor inlet temperature controller. First, the reactor inlet temperature controller is tuned as described by Luyben9 and put on automatic. Then a relay-feedback test is run on the reactor exit temperature controller. The ultimate gain is small (0.28) as expected, and the ultimate period is large (15 min). The tuning method proposed by Luyben9 for processes with both deadtime and inverse response is used to calculated the gain (Kc ) 0.051) and reset time (τI ) 2.5). These settings give less sluggish response than Ziegler-Nichols (ZN) tuning. The recycle flow rate is fixed. The flow rate of the fresh feed of component A (FOA) is flow-controlled, which sets the production rate. Note that an increase in production rate will generate more heat in the reactor and require a lower inlet temperature for a constant outlet temperature if the recycle flow rate is constant. This implies that very large changes will be required in compositions to produce the required increase in the yAyB product in the reactor to compensate for the decrease in temperatures in the front end of the reactor. Thus, this control structure can be expected to be unable to handle large increases in throughput. Dynamic simulation discussed below demonstrate this weakness. 4.2. CS2: Change Recycle Flow Rate. Figure 4 gives the control strategy in which the reactor exit temperature controller changes the set point of the recycle flow controller (compressor speed). The reactor exit temperature controller has three 0.5 min lags in the loop to account for temperature measurement, compressor, and turbine lags. Relay-feedback testing gives an ultimate gain of 2.5 min and an ultimate period of 6 min. The Tyreus-Luyben (TL) tuning method is used to calculate controller gain (Kc ) 0.8) and reset time (τI ) 13). The flow rate of the fresh feed of component A (FOA) is flow-controlled, which sets the production rate. Reactor inlet temperature is held constant. With inlet and outlet temperature held constant, changes in production rate are handled by both changes in flow rate through the reactor and changes in compositions. So this control structure should be able to handle large throughput changes. However, changing gas recycle flow rate may be undesirable in some processes. Compressors are sometime quite sensitive to changing loads for mechanical
reasons. In addition, the reaction kinetics often favor operating with maximum recycle flow rate. This can occur, for example, when an undesirable consecutive reaction consumes some of the product. To keep the yield of the desired product high, the concentration of the desired product should be kept low (low per pass conversion). This implies a large recycle flow rate. Therefore, the CS2 structure may not be economically attractive in some processes. 4.3. CS3: Change Fresh Feed Flow Rate. Figure 5 shows the control system in which reactor exit temperature is controlled by manipulating fresh feed flow rate of component A (FOA). When reactor exit temperature decreases, more reactant is added to the system. This increases both reactant concentrations and reaction rates, which tends to raise reactor outlet temperature. Reactor inlet temperature is held constant. The recycle flow rate is fixed. There is no direct production rate handle in this control scheme. Throughput can, in theory, be set by changing either reactor inlet temperature or recycle flow rate, but the latter should be much better for the same reasons discussed in the previous two sections. 4.4. CS4: On-Demand Structure. Figure 6 shows a control scheme that is similar to CS2 (reactor outlet temperature is controlled by manipulating recycle flow rate). However, production rate is set by the liquid product flow rate from the separator drum, and drum level is controlled by manipulating the flow rate of the fresh feed FOA. This on-demand structure might be used when the downstream customer desires immediate responses in the availability of the product stream from this unit. 5. Results Figures 7-11 compare the performances of the four alternative control structures. The disturbances are step changes occurring at time equal to zero. For CS1 and CS2, the disturbance is an increase in the fresh feed flow rate FOA. For CS3, the disturbance is an increase in recycle flow rate FR. For CS4, the disturbance is an increase in the product flow rate from the separator drum. 5.1. CS1. Figure 7 gives results for CS1 in which inlet temperature Tin is manipulated to hold Tout constant. Two cases are shown: +10% and +20% increases in fresh feed flow rate FOA. The smaller production rate change can be handled, but it takes over 3 h to settle out. Note that the inlet temperature must be reduced, so the reactant concentration yRA climbs from 0.2 to about 0.3 to achieve the 10% increase in reaction rate, despite the lower reactor temperatures. However, if the fresh feed is increased by 20%, the system slowly fills up with component A as the reactor inlet temperature is steadily reduced and the yRA concentration steadily increases. After about 4 h, the system shuts down. The product of the two reactants concentrations (yAyB) cannot increase enough to compensate for the lower reactor temperatures. The initial yAyB is (0.2)(0.8) ) 0.16. The highest it can be is (0.5)(0.5) ) 0.25. If reactor temperatures were held constant, the production rate could be increased by 56%: (0.25 - 0.16)/0.16. However, the inlet reactor temperature must be decreased to achieve the same exit temperature with the same flow rate through the reactor at the higher rate of heat generation due to the higher production rate. The
Ind. Eng. Chem. Res., Vol. 39, No. 5, 2000 1275
Figure 7. CS1: 10% and 20% FOA disturbance.
Figure 8. CS2: 20% FOA disturbance.
temperature change through the reactor at the initial conditions is about 501-478 K ) 23 K. If the production rate is increased by 20%, this reactor ∆TR ) Tout Tin must be increased by 20%. Thus, the inlet temperature must drop to 501 - (1.2)(23) K ) 473 K. This 5 K decrease in inlet temperature causes a significant decrease in the specific reaction rate because of the high activation energy used in the numerical example. In processes with lower activation energies (less temperature sensitivity), the CS1 control structure would have more rangeability. The 20% increase in fresh feed causes a peak in the outlet temperature at about 506 K. This rise causes pressure to drop, and this results in a fairly large swing in the FOB flow rate as the pressure controller tries to hold system pressure constant.
5.2. CS2. Figure 8 gives results for CS2 in which recycle flow rate FR is manipulated to hold Tout constant. The disturbance is a 20% increase in fresh feed flow rate FOA. This magnitude of production rate change can be handled by this control scheme. The peak in the exit temperature is smaller (503 K), and the system settles out in about 2 h. The yRA concentration increases from 0.2 to about 0.265. The inlet temperature is held constant in this scheme, so the reactor temperatures do not change. The higher flow rate and the slightly higher concentrations both contribute to the increase in production rate. The recycle flow rate FR gradually increases from 3.1 to about 3.75 kmol/s, a 24% increase in flow rate through the compressor. This would increase the pressure drop through the gas loop (heat exchanger, furnace, reactor
1276
Ind. Eng. Chem. Res., Vol. 39, No. 5, 2000
Figure 9. CS3: 20% FR disturbance.
Figure 10. CS4: 20% product flow rate disturbance.
and condenser) by over 50% [(1.24)2 ) 1.54], so the compressor load would increase substantially. Since the gas compressor is often one of the most expensive parts of the plant and its operating costs are also high, excess compressor capacity may not be designed into the process. Thus, CS2 provides better dynamic control and more rangeability, provided compressor capacity is not limited. 5.3. CS3. Figure 9 gives results for CS3 in which fresh feed flow rate FOA is manipulated to hold Tout. The disturbance is a 20% increase in recycle flow rate. The large step increase in recycle flow rate causes a large drop in reactor exit temperature to a minimum of almost 495 K. Increasing FR has the almost instantaneous
effect of decreasing reactor inlet and outlet temperatures because more material is flowing for the same heat inputs. It takes several minutes for the Tin controller to pick up on the furnace firing. The drop in Tin produces a further drop in Tout after the temperature disturbance has traveled through the reactor. The Tout controller responds by changing FOA. The two curves shown are for two different tuning method: Ziegler-Nichols and Tyreus-Luyben. The ZN settings drive the process back to the set point more quickly, but at the cost of more oscillatory response. The TL settings give a more sluggish response, but the overshoot in the manipulated variable FOA is much less. 5.4. CS4. The on-demand control structure gives the results shown in Figure 10. The disturbance is a 20%
Ind. Eng. Chem. Res., Vol. 39, No. 5, 2000 1277
Figure 11. Feed composition disturbance.
increase in the flow rate of the liquid product from the separator drum. A proportional controller is used on the drum level controller. Note that the response is underdamped, even though the controller is proportional-only. This occurs because the transfer function between the controlled variable (level) and the manipulated variable (fresh feed flow rate) is not a simple integrator. The increase in liquid product flow rate decreases the drum level, and the level controller brings in more fresh feed FOA. This causes the concentration yRA and the reactor outlet temperature to increase. Results are given for two values of level controller gain (Kc ) 1 and Kc ) 2). The higher the gain, the less steady-state change in the drum level, but the more oscillatory the response. One of the advantages of CS4 over the other control structures is that the production rate is directly set,
even for changes in the compositions of the fresh feed. Up to this point, we have assumed that both fresh feeds are pure reactant components. Suppose the composition zOA of the fresh feed stream FOA can change from pure A to a mixture of A and B. Figure 11 compares the responses of all four control structures for a step change in zOA from 100% A to 80% A and 20% B. Control structures CS1 and CS2, which have fixed flow rates of FOA, respond to this disturbance by producing less product. This can be seen by the large reduction in the flow rate of the other fresh feed FOB and occurs because less A is being fed into the system. Reactor outlet temperature drops initially and is slowly driven back to the set point. The yRA concentration decreases to a lower steady-state value since the reaction rate is smaller. In CS1, the reactor inlet temperature increases to achieve the same reactor outlet
1278
Ind. Eng. Chem. Res., Vol. 39, No. 5, 2000
temperature at the lower reaction rate and constant recycle flow rate. In CS2-CS4, reactor inlet temperature is held constant. In CS2, the lower reaction rate results in a decrease in reactor outlet temperature, and the temperature controller decreases the recycle flow rate. Control structures CS3 and CS4 do not fix FOA, so it changes to account for the change in feed composition. In CS3, the recycle flow rate is fixed. The smaller amount of A being fed into the system drops reactant concentration yRA and reactor outlet temperature. The temperature controller brings in more FOA fresh feed to drive the reactor exit temperature back to the set point. Pressure increases and less FOB is brought into the system. In CS4 the product flow rate from the separator is fixed. The decrease in reaction rates makes the separator drum level start to drop, and the level controller brings in more FOA. The recycle flow rate decreases initially to drive the reactor outlet temperature back toward the set point. The process recovers quite quickly, producing the same amount of product while feeding in less FOB and more FOA. 6. Conclusion Four control structures have been compared. Manipulation of reactor inlet temperature appears to be the least attractive scheme. Manipulation of recycle flow rate gives the best control but may be undesirable in some system because of compressor limitations. The ondemand structure provides effective control in the face of feed composition disturbances. 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 cat)-1) Kc ) controller gain KR ) reactor gain Ku ) ultimate gain L ) liquid flow rate leaving separator drum (kmol/s)
P ) total pressure (bar) Pj ) partial pressure of component j (bar) QF ) heat transfer in furnace (kJ/s) QH ) total heat transfer in heat exchanger (kJ/s) RC ) rate of production of C (kmol of C/s) Tin ) reactor inlet temperature (K) Tinset ) reactor inlet temperature set point (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) Wcat ) weight of catalyst (kg) yA,out ) concentration of A in reactor exit (mole fraction) yRA ) concentration of A in recycle (mole fraction) yRB ) concentration of B in recycle (mole fraction) R ) pre-exponential factor ∆TH ) minimum temperature differential in FEHE (K) ∆TR ) temperature differential across reactor (K) λ ) heat of reaction (kJ/kmol of C produced) τI ) reset time constant (min)
Literature Cited (1) Pinjala, V.; Chen, Y. C.; Luss, D. Wrong-way behavior in packed-bed reactors: II. Impact of thermal dispersion. AIChE J. 1988, 34, 10. (2) Powell, B. E. Control of Exothermic Reactions in Packed Bed Reactors. ISA J. 1963, Feb, 45. (3) Stevens, A. D. Stability and Optimization of a Methanol Converter. Chem. Eng. Sci. 1975, 30, 11. (4) Budman, H. M.; Webb, C.; Holcomb, T. R.; Morari, M. Robust inferential control for a packed-bed reactor. Ind. Eng. Chem. Res. 1992, 31, 1665. (5) Filho, R. M.; McGreavy, C. The influence of configuration on controller design of multi-tubular reactors. Comput. Chem. Eng. 1993, 17, 569. (6) 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., submitted for publication. (7) Luyben, W. L. Design and Control of Gas-Phase Reactor/ Recycle Processes with Reversible Exothermic Reactions. Ind. Eng. Chem. Res., in press. (8) Luyben, W. L. Impact of Reaction Activation Energy on Plantwide Control Structures. Ind. Eng. Chem. Res., submitted for publication. (9) Luyben, W. L. Tuning PI Controllers for Processes with Both Inverse Response and Deadtime. Ind. Eng. Chem. Res., in press.
Received for review September 7, 1999 Revised manuscript received March 6, 2000 Accepted March 7, 2000 IE990667Y
