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Extensions of the Simultaneous Design of Gas-Phase Adiabatic Tubular Reactor Systems with Gas Recycle Francisco Reyes and William L. Luyben* Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015
Luyben studied the simultaneous design of a simple gas-phase tubular reactor system with a single feed stream and independent reactor preheating and cooling for a reversible reaction. Reyes and Luyben studied an irreversible reaction system with a reactor feed preheating system (feed-effluent heat exchanger and furnace) but assumed equimolal concentrations of reactants in the recycle gas. A simple separation was assumed in both of these studies. Reyes and Luyben recently explored systems with more realistic separation systems (a distillation column) for gasphase tubular reactors with liquid recycle and with a dual recycle system. This paper extends this work for two cases: (1) the reversible reaction system is explored with a realistic feed preheating system and with two fresh feed streams, and (2) the irreversible reaction system is studied for nonequimolal reactant concentrations. The exothermic gas-phase reaction A + B S C occurs in an adiabatic tubular reactor. A gas recycle returns unconverted reactants from the separation section consisting of a simple separator in which product C is removed in the liquid phase and reactants A and B are recycled in the gas phase back to the reactor inlet. Optimum steady-state economic designs are shown to lead to poor dynamic responses. Slight modifications of the plant design lead to a much more easily controlled plant. In the reversible case, the additional furnace heat input leads to a better dynamic performance. In the irreversible case, a higher reactor inlet temperature improves dynamics. 1. Introduction The use of adiabatic gas-phase tubular reactors is very widespread in industrial chemical and petroleum processes. The steady-state design and dynamics of tubular reactors have been studied in many papers over the last several decades. Most of this work has considered the reactor in isolation. Few papers have looked at the plantwide aspects of tubular reactor systems, either from a steady-state perspective or in terms of the overall dynamics of the system. These systems present fascinating design problems because of the many tradeoffs. The most important is the tradeoff between the reactor size (capital investment) and the recycle flow rates (compressor and separation section capital investment and energy costs). Many of these reactors operate at high temperatures, so some type of feed preheating system is required. Unlike continuous stirred tank reactor (CSTR) systems in which the feed temperature is usually unimportant, both the design and the control of tubular reactors are strong functions of the temperature of the inlet stream to the reactor. Thus, the design of the feed preheating system is important and has plantwide implications. Our research into these types of systems has been presented in several papers. Luyben1 studied the simultaneous design of a simple gas-phase tubular reactor system with a single feed stream and independent reactor preheating and cooling for a reversible reaction. Reyes and Luyben2 studied an irreversible reaction system with a reactor feed preheating system (feedeffluent heat exchanger and furnace) but assumed * To whom correspondence should be addressed. E-mail:
[email protected]. Telephone: 610-758-4256. Fax: 610-7585297.
equimolal concentrations of reactants in the recycle gas. A simple separation was assumed in both of these studies. Reyes and Luyben3,4 recently explored systems with more realistic separation systems (a distillation column) for gas-phase tubular reactors with liquid recycle and with a dual recycle system. In this paper we extend this work to consider several more realistic situations. Both the reversible system and the irreversible system are extended to relax some of the simplifying assumptions of the initial studies. 2. Process Studied Figure 1 gives a sketch of the plantwide process studied. In all cases the two fresh feed streams F0A and F0B of pure reactants are in the gas phase. These fresh feeds are combined with a gas recycle FR and sent to a feed preheat system consisting of a feed-effluent heat exchanger (FEHE) and a furnace. Cold feed can be bypassed around the FEHE and mixed with the hot stream to control the blended temperature Tmix. The gas-phase reactor is a packed adiabatic plug-flow reactor. The reactor effluent is cooled, and the product C condenses and is removed from a separator drum in stream L. The gas from the drum, containing only A and B, is compressed and recycled. Reactants A and B are noncondensable, so they are not present in L. Product C is nonvolatile, so it is not present in FR. Two different reaction systems are studied in the following sections: a reversible reaction and an irreversible reaction with moderate activation energy (69 710 kJ/kmol). Table 1 gives the kinetic parameters. The following design specifications were used for both cases: 1. The product flow rate (stream L) from the separator is fixed at 0.12 kmol/s.
10.1021/ie000603j CCC: $20.00 © 2001 American Chemical Society Published on Web 12/23/2000
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Figure 1. Optimized flowsheet of a reversible reaction case. Table 1. Parameter Values component molecular weight, kg‚kmol-1 heat capacity, kJ‚kmol-1‚K-1
A
B
C
15
20
35
30
40
70
Irreversible Reaction Case heat of reaction, -23 237 kJ‚kmol-1 specific reaction rate, 0.19023e-69710/8.314T kmol‚s-1‚bar-2‚kgcat-1 Reversible Reaction Case -14 000
heat of reaction, kJ‚kmol-1 specific reaction rate of the forward reaction, kmol‚s-1‚bar-2‚kgcat-1 specific reaction rate of the reverse reaction, kmol‚s-1‚bar-1‚kgcat-1
30e-94000/8.314T 157500e-108000/8.314T
2. The reactor operating pressure is 50 bar, with a pressure drop around the gas loop of 5 bar. 3. The FEHE minimum approach temperature is 10 K. 4. The flash drum and the fresh feed temperatures are 313 K. The mass heat capacity of all components is assumed to be equal to 2 kJ‚kg-1‚K-1. This means that the product of the mass flow rate and the mass heat
capacity is constant for any stream and equals the sum of the product of the component molar flow rates times the corresponding molar heat capacities. Thus, despite the fact that molar flow rates of individual components may vary (for example, in the reactor), the term F C yjcpj is constant, where F is the total molar flow ∑j)A rate, yj is the mole fraction of component j, and cpj is the molar heat capacity of component j. 3. Reversible Reaction System 3.1. Optimum Steady-State Design. Figure 2 illustrates an important characteristic of the reversible reaction case. We may have a low product flow rate as a result of reactor inlet temperatures that are either too low or too high. This occurs because at lower temperatures both forward and reversible reaction rates are small, while at higher temperatures, the equilibrium constant of the exothermic reaction decreases. Figure 2 also illustrates that to meet the desired production rate we can increase either the reactor size (Wcat is the weight of the catalyst in the reactor) or the recycle flow rate FR. The optimum steady-state design involves a tradeoff between these two parameters. The lower graphs in Figure 2 give the amount of bypassing of cold feed around the FEHE that occurs in each one of the designs. These percentages are quite small ( 7) for the optimum design (where Tin ) 440 K). This high-temperature sensitivity can be modified in several ways. As shown in Figure 13, changing the yA,in/ yB,in ratio reduces the reactor gain. This occurs because the reactant that is at low concentration acts as a
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Figure 14. Responses of the suboptimum design under CS3 to Tin variations.
Figure 15. Responses of the suboptimum design under CS3 to FR variations.
limiting reactant and helps to add some self-regulation to the system. The increase in the temperature increases the specific reaction rate, but the overall rate of reaction depends on both k and the product of the mole fractions yAyB. So, if A is the limiting reactant, yA decreases and slows up the reaction. The result is a reduction in the reactor gain, as can be seen in Figure 13 for yA,in/yB,in ratios of 0.1 and 10.
However, there is a high economic penalty (higher TAC) for designs with yA,in/yB,in ratios that are not about unity. Figure 13 shows that TAC increases by about 70%. Another alternative is to increase reactor inlet temperature Tin. If Tin is increased from its steady-state optimum of 440 K to 465 K, the reactor gain is reduced by 60%. This reduction occurs because the higher inlet
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Figure 16. Impact of the furnace on the irreversible reaction case design. Table 2. Steady-State Design Conditions
AX, m2 Fin, kmol‚s-1 FB, kmol‚s-1 FR, kmol‚s-1 MD, kmol P, bar P1, bar P2, bar QF, MW QX, MW Tin, K Tmix, K Tout, K TH,out, K T2, K TAC, 106 $/year Wcomp, MW Wcat, m‚tons yA,in, mole fraction yC,in, mole fraction yA,out, mole fraction yC,out, mole fraction yA,R, mole fraction yC,R, mole fraction
reversible reaction case
irreversible reaction case
5297 2.59 0.357 2.35 740 50 45 50 1.75 15.8 515 495 533 358 321 1.72 0.65 41.9 0.511 0.0 0.487 0.049 0.512 0.0
4074 2.21 0.326 1.97 631 50 45 50 0.0 11.5 465 465 500 355 321 1.27 0.55 41.9 0.401 0.0 0.366 0.057 0.388 0.0
temperature requires a higher recycle flow rate, which means lower per pass conversion and a less sensitive reactor. The impact on the TAC is 24%. The amount of FEHE bypassing is still high, so no furnace is required. The process is redesigned for Tin ) 467 K and yA,in/yB,in ) 0.647. The complete flowsheet details are given in Table 2. A good dynamic performance is achieved for (10 K changes in Tin and (25% changes in FR as seen in Figures 14 and 15. Notice that increasing the inlet temperature results in an increase in the production rate. However, increasing the recycle flow rate results in a somewhat unexpected decrease in the production rate. This effect was discussed by Reyes and Luyben2
and occurs because of the drop in the reactor exit temperature. A third alternative for improving the dynamics of the system was also investigated. It was thought that the use of a furnace in the reactor preheat system might improve the control of the process. This turned out to be incorrect. The major problem is the reactor gain, and adding a furnace actually increased the reactor gain. The use of a furnace pushes the design to smaller recycle flow rates so that less energy is used in the furnace. The decrease in the recycle flow rate means higher per pass conversion and a more sensitive reactor. Figure 16 shows these effects. 5. Conclusion The optimum design of a plant with a gas-phase reactor and a gas-phase recycle involves tradeoffs between reactor costs and compression costs. Controllability may force us to include a furnace to provide an additional control handle when the FEHE bypass turns out to be low. Such a situation is typical of cases with a small reactor temperature rise, with reversible reaction systems being a good example. An economic penalty invariably results if a furnace is used, so the final design is usually not the optimum design in the case of reversible reactions. Large reactor temperature rises are possible for irreversible reactions, so the use of a furnace may not be required. However, irreversible reaction systems can show high-temperature sensitivity (large reactor gains), which can lead to poor dynamic controllability. Redesign of the process away from the steady-state optimum may be required for dynamic stability. The use of higher reactor inlet temperatures or the use of a limiting reactant can improve dynamics but produce a penalty in increased costs.
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Nomenclature A ) reactant component AX ) FEHE area, m2 B ) reactant component C ) product component cpj ) vapor heat capacity of species j, kJ‚kmol-1‚K-1 Fin ) reactor feed stream flow rate, kmol‚s-1 Fout ) reactor exit stream flow rate, kmol‚s-1 Fj ) flow rate of component j, kmolj‚s-1 FB )bypassed flow rate at FEHE, kmol‚s-1 FR ) recycle flow rate, kmol‚s-1 F0,A ) fresh feed flow rate of reactant A, kmol‚s-1 F0,B ) fresh feed flow rate of reactant B, kmol‚s-1 k ) specific reaction rate of an irreversible reaction, kmol‚s-1‚bar-2‚kgcat-1 kB ) specific reaction rate of a reversible reverse reaction, kmol‚s-1‚bar-1‚kgcat-1 kF ) specific reaction rate of a reversible forward reaction, kmol‚s-1‚bar-2‚kgcat-1 KR ) reactor temperature gain L ) product flow rate, kmol‚s-1 Mav ) average molecular weight of a gas loop, kg‚kmol-1 MD ) flash drum liquid holdup, kmol MF ) furnace gas holdup, kmol P ) reactor pressure, bar Pj ) partial pressure of component j, bar P1 ) suction pressure of the compressor, bar P2 ) discharge pressure of the compressor, bar QF ) furnace heat duty, kW QTOT ) total preheat duty of the reactor feed, kW QX ) rate of heat transfer at FEHE, kW R C ) rate of production of C, kmol‚s-1‚kgcat-1 Tav ) average temperature of a gas loop, K Tin ) reactor inlet temperature, K Tmix ) furnace inlet temperature, K Tout ) reactor exit temperature, K TC,in ) inlet temperature to FEHE on the cold side, K TC,out ) exit temperature from FEHE on the cold side, K TH,out ) exit temperature from FEHE on the hot side, K
T0 ) fresh feed streams temperature, K T1 ) compressor suction temperature, K T2 ) compressor discharge temperature, K TAC ) total annual cost, 106$/year Vgas ) volume of the gas loop, m3 w ) catalyst weight, kg Wcomp ) gas compressor power, kW Wcat ) total weight of the catalyst, kg yj,in ) composition of the j component in the reactor feed stream, mole fraction yj,out ) composition of the j component in the reactor exit stream, mole fraction yj,R ) composition of the j component in the recycle stream, mole fraction Greek Letters γ ) ratio of heat capacities λ ) heat of reaction, kJ/kmol of C produced
Literature Cited (1) Luyben, W. L. Design and Control of Gas-Phase Reactor/ Recycle Processes with Reversible Exothermic Reactions. Ind. Eng. Chem. Res. 2000, 39, 1529. (2) Reyes, F.; Luyben, W. L. Steady-State and Dynamic Effects of Design Alternatives in Heat-Exchanger/Furnace/Reactor Processes. Ind. Eng. Chem. Res. 2000, 39, 3335. (3) Reyes, F.; Luyben, W. L. Design and Control of a Gas-Phase Adiabatic Tubular Reactor Process with Liquid Recycle. Ind. Eng. Chem. Res. 2000, submitted for publication. (4) Reyes, F.; Luyben, W. L. Design and Control of Tubular Reactor Systems with Both Gas and Liquid Recycles. Ind. Eng. Chem. Res. 2000, submitted for publication. (5) Douglas, J. M. Conceptual Design of Chemical Processes; McGraw-Hill: New York, 1988. (6) Luyben, W. L. Effect of Kinetics, Design and Operating Parameters on Reactor Gain. Ind. Eng. Chem. Res. 2000, 39, 2384.
Received for review June 22, 2000 Accepted November 8, 2000 IE000603J
