Steady-State Economic Comparison of Alternative Tubular Reactor

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Ind. Eng. Chem. Res. 2003, 42, 3304-3320

Steady-State Economic Comparison of Alternative Tubular Reactor Systems Phisit Jaisathaporn† and William L. Luyben* Chemical Process Modeling and Control Research Center, Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015

This paper presents a comparison of the steady-state economics of alternative tubular reactor systems. These alternative designs use different tubular reactor configurations including single adiabatic, multistage adiabatic with interstage cooling, multistage adiabatic with cold-shot cooling, single cooled, multistage cooled with interstage cooling, and multistage cooled with coldshot cooling. The design considers the entire plantwide process: reactor(s), heat exchangers, gas recycle compressor, preheat furnace, condenser, and separator. The chemistry is the exothermic, irreversible, solid catalytic, gas-phase reaction A + B f C, which is carried out in a packed-bed tubular reactor. The economic objective function is total annual cost, which includes annual capital cost (reactor, catalyst, compressor, and heat exchangers) and energy cost (compressor work and furnace fuel). Design and optimization procedures are developed for each alternative design. Optimum operating conditions and equipment sizes are determined. The effect of catalyst cost on the steady-state design is considered. The steady-state design results indicate that the single cooled reactor configuration is the best from the standpoint of steadystate economics. 1. Introduction Tubular reactors are widely used in chemical processes, particularly when reactions are in the gas phase and a solid catalyst is used. Important industrial examples include methanol, amines, ammonia, and sulfur dioxide. Many of these reactions are exothermic, and the management of heat removal is vital for the efficient and safe operation of the process. These reactions often have a maximum temperature limitation. The operation of tubular reactors can be adiabatic or nonadiabatic. Adiabatic operation is carried out in a single-stage reactor or in multistage reactors with intermediate cooling. Multistage operation of adiabatic reactors is more attractive than single-stage operation because higher per-pass conversion can be achieved when reactor temperatures are limited to some maximum value. This results in a smaller overall reactor size and/or less recycle. The intermediate cooling can be done by using interstage heat exchangers or by mixing with a cold stream of unreacted feed (“cold-shot” cooling). Tubular reactors can also be operated nonadiabatically by using small-diameter multiple tubes in parallel with heat transfer from the process phase into a cooling medium. The use of multiple cooled tubular reactors in series is also possible, but as we show in the paper, a single cooled reactor is more economical than multistage cooled reactors. Thus, there are six alternative designs of tubular reactors: single-stage adiabatic, multistage adiabatic with interstage cooling, multistage adiabatic with cold* To whom correspondence should be addressed. E-mail: [email protected]. Tel.: 610-758-4256. Fax: 610-758-5297. † Current address: Department of Chemical and Process Engineering, King Mongkut’s Institute of Technology North Bangkok, 1518 Piboolsongkram Rd., Bangkok 10800 Thailand. E-mail: [email protected]. Phone: 66-2-913-2500 ext 8230. Fax: 66-2-587-0024.

shot cooling, single-stage cooled, multistage cooled with interstage cooling, and multistage cooled with cold-shot cooling. This paper discusses the steady-state design, optimization, and economics of each of these alternative designs. 2. Literature Review Adiabatic and cooled tubular reactors have been studied for many years in several areas such as design, optimization, stability, modeling, and control. Different reactor setups have been used in the literature. Singlestage (adiabatic or cooled) reactors, both packed and unpacked, have been widely studied. Few papers have explored the more complex multistage reactors. Even less work has been reported on tubular reactor systems in a complete plantwide environment in which all of the process components are included in the analysis. 2.1. Isolated Single Adiabatic Reactor or Reactor/Preheater Systems. Pioneering works by Amundson and Bilous1,2 reported the effect of parameters on the sensitivity of empty tubular reactors and optimum temperature gradients. Analytical solutions for some adiabatic reactor problems were provided by Douglas and Eagleton.3 Design and control of feed-effluent exchanger/reactor systems were reported by Douglas et al.4 Stability analysis of fixed-bed reactors with heat feedback was discussed in Silverstein and Shinnar.5 Tyreus and Luyben6 discussed the inverse response, deadtime, and open-loop instability of a reactor coupled with a preheater. They showed that, in contrast to conventional control loops, the use of integral action can improve the closed-loop stability, especially at low frequencies. Luyben7 explained why this dynamic improvement occurs and presented a controller tuning procedure. The chaotic behavior of a similar system was reported in Bilden and Dimian.8 The authors analyzed the stability and multiplicity of a heat-integrated plugflow reactor by using bifurcation techniques. They

10.1021/ie020757u CCC: $25.00 © 2003 American Chemical Society Published on Web 06/11/2003

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developed a design procedure to ensure open-loop stability and to avoid high sensitivity. 2.2. Plantwide Systems with Single-Stage Adiabatic Tubular Reactors. Several studies of tubular reactor systems have been reported in recent years in which the reaction section consists of a single adiabatic tubular reactor. Luyben9 discussed the control of the reactor outlet temperature of a single adiabatic tubular reactor with gas recycle and an irreversible reaction using four different plantwide control structures. Manipulation of the gas recycle flow rate was found to be effective for temperature control but might be undesirable because of compressor limitations. Plantwide design and control of gas-phase adiabatic reactor systems with reversible exothermic reactions were reported by Luyben.10 The economic impact of inert components in the fresh feed stream was reported. Reactor inlet temperature was controlled, and different pressure control schemes were explored. Luyben11 reported the strong impact of reaction activation energy on the design and control of adiabatic tubular reactor systems with irreversible exothermic reactions. One of the conclusions of this study was that the process might have to be designed for “limitingreactant” operation (design for a low concentration of one of the reactants) when activation energies are large. This provides some self-regulation in reaction rate through the reactant concentration dependence, which helps to compensate for the strong temperature sensitivity. Luyben12 explored the effects of kinetic, design, and operating parameters on the reactor gain of feedeffluent heat exchanger/reactor processes. A number of papers (Reyes and Luyben13-16) have explored single-stage adiabatic tubular reactor systems with several types of recycles (gas and/or liquid), several types of reactions (irreversible and reversible), and different separation sections (simple separators or distillation columns). 2.3. Isolated Multistage Adiabatic Tubular Reactors. The criterion for optimal operation of adiabatic tubular reactors with interstage cooling was given by Horn.17 At a specified final conversion, the optimization procedure finds inlet temperatures that minimize the total catalyst volume. The same procedure was developed by Horn18 for multistage adiabatic tubular reactors with cold-shot cooling. Detailed results for the optimal operation of multistage adiabatic tubular reactors with cold-shot cooling were given in Lee and Aris.19 The nonlinear behavior of heat-integrated multibed tubular reactors with interstage cooling was discussed in Bildea et al.20 using bifurcation techniques. 2.4. Plantwide Systems with Multistage Adiabatic Tubular Reactors. Stephens21 investigated a methanol plant consisting of four adiabatic catalyst beds with cold-shot cooling. A dynamic simulation of the closed-loop system was performed. Inlet and exit temperature control schemes were considered. The exit temperature control scheme failed to handle disturbances, but the inlet temperature control scheme was successful. A simple experimental optimization method for the methanol converter was described. Steady-state and dynamic models were reported. 2.5. Isolated Cooled Tubular Reactor. A criterion for the temperature sensitivity of packed-bed tubular reactors was developed by Barkelew.22 Design considerations for tubular reactors with highly exothermic reactions were discussed in Shinnar et al.23 These

authors developed design guidelines for cooled tubular reactors to satisfy requirements on the radial temperature profile, temperature sensitivity, and tolerable pressure drop and investigated the closed-loop dynamics of the reactors subjected to flow maldistribution. They pointed out that a design that violates the requirements can lead to reactor sensitivity and runaway. Filho and McGreavy24 investigated the interactions between coolant flow pattern and reactor behavior and suggested that a new reactor configuration can improve control. 2.6. Plantwide Systems with a Single Cooled Tubular Reactor. A design procedure for a single cooled tubular reactor system was developed by Luyben.25 The steady-state design involves a tradeoff between reactor tube diameter and pressure drop. Optimum designs for different specific reaction rates were reported. The author assumed a fixed tube length of 5 m. This assumption is relaxed in this paper, so tube length becomes a design optimization variable. Luyben26 discussed the effect of design and kinetic parameters on the control of this type of system. His results show that reactor inlet temperature control is more difficult as reaction rates increase because of the smaller reactor size and the resulting smaller heattransfer area. Reactor tube diameter (heat-transfer area) has a significant impact on controllability. Reactant dilution was found to be less effective for providing self-regulation in cooled reactor systems than in adiabatic reactor systems. 3. Process Studied This paper extends the work of Reyes and Luyben13-16 to include multistage tubular reactors. Optimum design procedures are developed for six different flowsheets, and quantitative economic comparisons are made among these alternatives. Each flowsheet produces the same amount of product, operates at the same pressure, and has the same maximum temperature constraint. 3.1. Alternative Flowsheets. The six alternative flowsheets of tubular reactor systems are shown in Figures 1-6. These alternative designs use different reactor configurations, but the separation, recycle, and preheating sections are essentially identical. The alternatives considered are as follows: (1) single adiabatic reactor, (2) multistage adiabatic reactors with interstage cooling, (3) multistage adiabatic reactors with cold-shot cooling, (4) single cooled reactor, (5) multistage cooled reactors with interstage cooling, and (6) multistage cooled reactors with cold-shot cooling. 3.2. Process Conditions and Assumptions. The chemistry in this process is the exothermic, irreversible, solid catalytic, gas-phase reaction A + B f C. The production rate of C is fixed at 0.12 kmol/s for all designs. A feed-effluent heat exchanger (FEHE) is used to preheat the reactor feed stream by recovering heat from the hot reactor effluent stream. A furnace provides additional heat when it is needed and is necessary during plant startup. A bypass valve between the feedeffluent heat exchanger and furnace provides an additional manipulated variable for reactor inlet temperature control. The reactor exit stream is cooled in the FEHE and in a condenser. Product and unreacted reactants are separated in a flash drum in which perfect separation is assumed (no A or B in the liquid product stream with flow rate LC and no C in the gas recycle stream). The compressor operates with a discharge pressure of 50 bar and an efficiency of 75%.

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Figure 1. Flowsheet with an adiabatic reactor.

Figure 2. Flowsheet with multistage adiabatic reactors with interstage cooling.

Figure 3. Flowsheet with multistage adiabatic reactors with cold-shot cooling.

A maximum reactor temperature of 500 K is used in this study. This maximum temperature occurs at the exit of the adiabatic reactors, but in the cooled reactors the maximum usually occurs at an intermediate location along the length of the reactor. Plug flow is assumed, with no radial gradients in concentrations or temperatures.

The gas pressure drop in each heat exchanger and in the furnace is assumed to be 0.5 bar at steady-state design conditions. The pressure drops over the tube side and the shell side of the FEHE are each 0.5 bar. The design pressure drop over the control valve between the FEHE and the furnace is also 0.5 bar. The reactor pressure drop is calculated using the Ergun equation


Figure 4. Flowsheet with a cooled reactor.

Figure 5. Flowsheet with multistage cooled reactors with interstage cooling (NR ) 2).

Figure 6. Flowsheet with multistage cooled reactors with cold-shot cooling (NR ) 2).

and therefore varies with design parameters (number of tubes, diameter of tubes, tube length, and flow through each tube). The energy requirement of the furnace is usually zero for adiabatic reactor cases, as the reactor exit stream at maximum temperature can provide enough heat. Furnace energy is usually required in the cooled tubular reactor systems, which also do not use any FEHE bypassing. In the adiabatic reactor case, the design of the FEHE and the amount of bypassing are determined

by the reactor inlet temperature. A temperature difference of 25 K is assumed for the hot end of the FEHE. The hot reactor effluent enters the hot side of the FEHE at 500 K, so the cold-side exit stream is at 475 K. If the specified reactor inlet temperature is less than 475 K, bypassing is used. 3.3. Reactor Vessels. All reactor vessels in the adiabatic reactor cases are designed with a length-todiameter ratio of 10 so that the assumption of plug flow is reasonable. A ratio of about 2 would minimize vessel

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Figure 7. Two adiabatic reactors with interstage cooling. Figure 9. Cooled reactor.

Figure 8. Multibed adiabatic reactor with cold-shot cooling (NR ) 2).

cost but might lead to flow distribution problems. For a single adiabatic reactor and for multiple adiabatic reactors with intermediate heat exchangers, each reactor is a separate vessel. When cold-shot cooling is used, multiple internal beds are used in a single vessel with a length-to-diameter ratio of 10. For the cooled reactors, the length of each reactor is a design optimization variable (along with the diameter and number of the tubes), and therefore, the length-to-diameter ratio of the vessel is not fixed. 3.4. Cooling via Steam Generation. Figure 7 shows the configuration of two adiabatic reactors in series with an interstage heat exchanger. The temperature reaches a maximum of 500 K at the exit of each reactor. The outlet stream is cooled in an interstage heat exchanger, which generates steam. Boiler feedwater (BFW) is fed on the shell side, and the steam generated is considered a credit in the economics of the process. The value of the steam is a function of the pressure at which it is generated, which depends on the temperature on the process side (hot side) of the heat exchanger. Equation 21 (section 4) is used to calculate the value of the steam. The steam temperature is assumed to be 25 K lower than the process exit temperature (the inlet temperature of the downstream reactor). Note that the reactors can have different inlet temperatures, different diameters and different lengths. An overall heat-transfer coefficient of 0.227 kJ s-1 m-2 K-1 is used in the steamgenerating intercoolers, and a lower overall heattransfer coefficient of 0.142 kJ s-1 m-2 K-1 is used in the FEHE because of the gas-gas heat transfer that occurs in this unit. 3.5. Cold-Shot Cooling. Figure 8 shows the configuration for a two-bed adiabatic reactor process with coldshot cooling. The catalyst beds are mounted in a single reactor vessel because it is more economical than using multiple vessels. The spacing between beds is set at 1 m. The length-to-diameter aspect ratio of the vessel is 10. The hot exit stream from each bed is cooled by mixing it with a cold stream of unreacted feed. Because a multibed reactor must have internal piping, flow distributors, and bed supports, a multibed reactor vessel is more expensive than a simple vessel. According to Diemer,27 each additional bed increases the reactor capital cost by about 25%. Equation 13 (section 4) is used to calculate the cost of multibed reactors. 3.6. Cooled Reactors. Figure 9 shows a cooled reactor, which is assumed to be simply a shell-and-tube heat exchanger. Catalyst is packed inside the parallel tubes. Steam is generated on the shell side, serving as a coolant. The liquid level in the shell is controlled by bringing in BFW to keep the tubes covered. The steamside temperature is constant at all axial locations in the

reactor because the BFW is vaporized at a constant temperature. The temperature of the steam is assumed to be equal to the reactor inlet temperature, as suggested by Westerterp,28 and the temperature of the BFW is assumed to be equal to the steam temperature. The diameter of the reactor tubes is a design optimization variable, but a maximum limit of 0.12 m is used to avoid mechanical and heat-transfer difficulties. The cross-sectional area of the reactor vessel is assumed to be twice the total cross-sectional area of all of the reactor tubes, i.e., the volume in the shell outside the tubes is equal to the total tube volume. 4. Steady-State Model and Economics The reactor is modeled by three ordinary differential equations: a component balance on C, an energy balance, and the Ergun equation for pressure drop. The model is one-dimensional, using the weight of catalyst w as the independent variable, which is related to the length through the catalyst bulk density and tube diameter. Algebraic equations describe reaction kinetics, friction factors, heat-transfer coefficient in the cooled reactors, and compressor work, as detailed below.

Kinetics rC ) kPAPB ) kyAyBP 2

(1)

k ) Re-E/RT(kmol s-1 kgcat-1 bar-2)

(2)

Component balance dFC ) r C, dw

FC(0) ) FC,n

(3)

Adiabatic-energy balance - λrC dT ) , dw cpAFA + cpBFB + cpCFC

T(0) ) Tn

(4)

Cooled-energy balance dT - λrC - 4U(T - Tst)/(FcatDtube) ) , dw cpAFA + cpBFB + cpCFC

T(0) ) Tn (5)

Overall heat-transfer coefficient U ) 0.015 45 + Re )

0.6885 × 10-6 Re DP

(6)

DPVF µ

(7)

Pressure drop 2 dP - fLtubeFV ) , dw D W 105 P

f)

[

(1 - )

3

P(0) ) Pn

tube

1.75 + 150

]

(1 - ) Re

(8)

(9)


Compressor power Wcomp )

[( ) ()

RTSFRγ

PR 0.75(γ - 1) PS T R ) TS

PR PS

(γ-1)/γ

]

-1

Table 1. Design Parameters

(10)

(γ-1)/γ

(11)

Capital costs (see Luyben25 for details) single-bed reactor cost ) 0.035DR1.066LR0.082 ($106) (12) multibed reactor cost ) 0.035DR1.066LR0.082(1 + 0.25NR) ($106) (13) cooled reactor cost ) 2(0.0073)AR0.65 ($106)

(14)

catalyst cost ) $5 or $100 per kg

(15)

log10(furnace cost) ) -2.49 + 0.762 log10(QF) ($106) (16) heat exchanger/condenser cost ) 0.0073AR0.65 ($106) (17) compressor cost ) 0.004 33Wcomp0.82 ($106)

(18)

Energy costs (see Luyben25 for details)

compressor work ) 0.000 613Wcomp ($106 year-1) (20) (21)

where

CF ) -0.000 24Pst2 + 0.0219Pst + 0.634

(22)

Pst ) 0.0023Tst2 - 1.84Tst + 373

(23)

The cost factor in eq 21 is a function of steam pressure. Equation 22 is fitted using data from Douglas.29 The calculation of the steam credit is based on the fuel cost of $5/106 Btu.

Total annual cost (TAC) capital cost ) cost of (reactor + catalyst + furnace + heat exchangers + compressor) (24) operating cost ) cost of (furnace energy + compressor work) - steam credit (25) total annual cost )

F0A ) 0.12 kmol s-1 F0B ) 0.12 kmol s-1 T0 ) 313 K LC ) 0.12 kmol s-1 PR ) 50 bar TS ) 313 K ∆THX ) 25 K ∆PHX ) 0.5 bar µ ) 1.8 kg m-1 s-1 γ ) 1.312 UFEHE ) 0.142 kJ s-1 m-2 K-1 UHX ) 0.227 kJ s-1 m-2 K-1

heat capacity is constant for any stream and equal to the sum of the products of the component molar flow rates times the corresponding molar heat capacities. Thus, despite the fact that molar flow rates of individual components can vary (in the reactor), the term C yjcpj is constant, where F is the total molar flow F∑j)A rate, yj is the mole fraction of component j, and cpj is the molar heat capacity of component j. This relationship is used in the design procedures discussed below to calculate the inlet flow rate from an energy balance around the reactor. 5. Design and Optimization Procedures

furnace energy cost ) 0.000 150QF ($106 year-1) (19)

steam credit ) 0.348FstCF ($106 year-1)

R ) 0.190 38 kmol s-1 bar-2 (kg of catalyst)-1 E ) 69 710 kJ kmol-1 λ ) -23 237 kJ kmol-1 DP ) 0.003 m Fcat ) 2000 kg m-3 ) 0.4 cpA ) 30 kJ kmol-1 K-1 cpB ) 40 kJ kmol-1 K-1 cpC ) 70 kJ kmol-1 K-1 MA ) 15 kg kmol-1 MB ) 20 kg kmol-1 MC ) 35 kg kmol-1 LR/DR ) 10 Tmax ) 500 K

capital cost + payback period operating cost (26)

where a payback period of 3 years is used. Table 1 lists the design parameters. One important physical property assumption is made about heat capacities. The mass heat capacities of all components are assumed to be the same (2 kJ kg-1 K-1). This means that the product of the mass flow rate and the mass

The flow rates, compositions, temperatures, and pressures of the two fresh feeds are fixed and held constant in all designs. Likewise, all designs have the same production rate of product C, maximum reactor temperature, and kinetic parameters. Each of the flowsheets has different design optimization variables. For example, the single adiabatic reactor system has two design degrees of freedom. In theory, any two variables can be selected, and the optimization involves finding the “best” values of these two parameters that maximize or minimize some objective function. We find it convenient to select the reactor inlet temperature T1 and the ratio of the reactants in the reactor inlet stream yA/yB. In a process with NR multiple adiabatic reactors with either intermediate or cold-shot cooling, there are NR + 1 degrees of freedom: the inlet temperature of each reactor and the reactant ratio. In the cooled reactor process, there are four degrees of freedom, which are selected as the tube diameter, tube length, flow rate per tube, and reactant ratio. The details of the design procedures for all of the processes are given below. Once the design optimization variables are selected, the nonlinear programming routine “fminsearch” in Matlab is used to find the optimum values. The steadystate model is simulated using Matlab. The optimization calculations for a four-stage adiabatic reactor system with interstage cooling take about 15 min on a Pentium IV 1.6 GHz personal computer. Each evaluation of the TAC takes about 2.6 s. Computing times for a four-stage adiabatic reactor system with cold-shot cooling are over 4 times larger (about 65 min) because of the additional iterative calculations. Design and optimization procedures for the adiabatic reactor systems and the single-stage cooled reactor system are given below. Procedures for multistage cooled reactor systems are given in Appendix A.

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5.1. Procedure for Single-Stage Adiabatic Reactor System. 1. Pick the reactor inlet temperature T1 and the yA/yB ratio (these design variables are to be optimized). This fixes the reactor inlet composition and temperature. 2. Calculate the reactor inlet flow rate using an energy balance around the reactor, eq 27. The conversion is known, so the heat generated is known. Thus, given the inlet temperature (T1) and the outlet temperatures (Tout ) 500 K), the inlet flow rate to the reactor can be calculated, using the fact that the term C yjcpj applies to both the inlet flow and the outlet F∑j)A flow, which are also related by eq 28. Then, component balances are used to calculate the reactor exit compositions.

0.12λ

F1 )

(27)

C

(Tout - T1)

∑(yjcpj)1

j)A

Fout ) F1 - 0.12 kmol/s

(28)

3. Knowing all of the conditions at the reactor inlet, integrate down the length of the reactor, using the ordinary differential eqs 3, 4, and 8, until the temperature is 500 K. This gives the amount of catalyst required and the composition profiles in the reactor. 4. Calculate the sizes and costs of the reactors, heat exchanges, furnace, condenser, and compressor. All flow rates and temperatures through the entire process are now known, so the heat-exchanger areas can be calculated from energy balances. 5. Evaluate the TAC of the process. 6. Vary T1 and yA/yB until the minimum TAC is obtained using Matlab’s fminsearch function. 5.2. Procedure for Multistage Adiabatic Reactor System with Interstage Cooling. 1. Specify the number of reactors in the system, NR. 2. Pick reactor inlet temperatures T1, T2, ..., TNR and the yA/yB ratio (all NR + 1 variables to be optimized). 3. Calculate the inlet flow rate F1 to the first reactor using an energy balance (eq 29) that is similar to that used for the single adiabatic reactor but modified to account for partial conversion in each reactor. The fraction of the total conversion of the entire reaction section (0.12 kmol/s) that occurs in each reactor is proportional to the ratio of the temperature difference in that reactor to the sum of all of the temperature differences over the NR reactors. Thus, the flow rates in and out of each reactor can be calculated using eq 30. Component balances then yield all compositions throughout the process.

0.12λ

F1 )

NR

(

(29)

C

∑ ∆Tk)[j)A ∑(yjcpj)1]

k)1

n

0.12 Fout,n ) F1 -

∑ ∆Tk

k)1 NR

∑ ∆Tk

k)1

(30)

4. Integrate down the length of each reactor until the temperature is 500 K and obtain the amount of catalyst required for each reactor. 5. Calculate the sizes and costs of all equipment. 6. Evaluate the TAC of the process. 7. Vary T1, T2, ..., TNR and yA/yB until the minimum TAC is obtained. 5.3. Procedure for Multistage Adiabatic Reactor System with Cold-Shot Cooling. 1. Specify NR. 2. Pick T1, T2, ..., TNR and the yA/yB ratio (all NR + 1 variables to be optimized). 3. Guess the temperature of the cold-shot stream TCS. This is the temperature of the stream after the recycle gas (at an initially unknown temperature and flow rate) is combined with the two fresh feed streams. An iteration loop is used through this step until the guessed value and the calculated value are sufficiently close. 4. Solve the set of 2NR linear equations (eqs 31-33 below) for the rate of generation of C in each reactor RC,n (n ) 1, ..., NR), the feed flow rate of the first reactor F1, and the flow rates of cold-shot streams entering other reactors Fm (m ) 2, ..., NR). (See Figure 3.) Equation 31 is the total generation of C in all reactors. Equation 32 is the energy balance around each reactor. Equation 33 is the energy balance at the reactor inlet where the cold stream Fm is mixed with the hot stream leaving the previous reactor at Tout. The outlet flow rate of each reactor can be calculated using eq 34. Component balances are used to calculate all composition throughout the process. NR

∑ RC,n ) 0.12 kmol/s

(31)

n)1 n

∑ j)1

Fj )

λRC,n

(n ) 1, ..., NR)

C

(Tout - Tn)

∑(yjcpj)1

j)A

(32)

m-1

Fj(Tout - Tm) ) Fm(Tm - TCS) ∑ j)1 n

Fout.n )

(m ) 2, ..., NR) (33)

n

Fj - ∑RC,j ∑ j)1 j)1

(34)

Appendix B provides an illustration of these equations for the case with three adiabatic beds in the reactor vessel. When NR ) 3, there are six equations that are linear in the six unknowns. 5. Integrate down the length of each reactor until the temperature is 500 K and obtain the amount of catalyst required for each reactor. 6. Calculate the recycle temperature TR and then calculate TCS. 7. Update TCS and return to step 4. When this iterative loop has converged, continue. 8. Calculate the sizes and costs of all equipment. 9. Evaluate the TAC of the process. 10. Vary T1, T2, ..., TNR and yA/yB until the minimum TAC is obtained.

Ind. Eng. Chem. Res., Vol. 42, No. 14, 2003 3311 Table 2. Steady-State Design Comparisons ($100/kg Catalyst) reactor configuration

NR

TAC ($106/year)

Wcat (103 kg)

FR (kmol/s)

Ltube (m)

Ntube

AR (m2)

single adiabatic staged adiabatic with intercooling staged adiabatic with cold-shot single cooled staged cooled with intercooling staged cooled with cold-shot

1 3 7 1 2 2

3.99 3.41 2.03 1.57 1.83 1.80

78.78 76.98 33.80 31.38 33.22 32.57

1.20 0.38 0.66 0.38 0.42 0.42

8.51 4.66 5.05

190 215 204

564 971 974

Table 3. Steady-State Design Comparisons ($5/kg Catalyst) reactor configuration

NR

TAC ($106/year)

Wcat (103 kg)

FR (kmol/s)

Ltube (m)

Ntube

AR (m2)

single adiabatic staged adiabatic with intercooling staged adiabatic with cold-shot single cooled staged cooled with intercooling staged cooled with cold-shot

1 4 4 1 2 2

1.07 0.74 0.78 0.46 0.66 0.64

142.50 105.52 57.30 41.50 42.66 42.91

0.78 0.16 0.45 0.22 0.29 0.29

8.13 5.37 5.53

226 176 172

692 1067 1073

5.4. Procedure for Single-Stage Cooled Reactor System. 1. Pick the tube diameter Dtube, the length Ltube, the inlet flow rate per tube Ftube, and the yA/yB ratio (four variables to be optimized). 2. Calculate the amount of catalyst per tube, Wtube, from the volume of the tube and the bulk density of the catalyst (2000 kg/m3). 3. Guess T1 ) Tst (inlet temperature ) steam temperature). 4. Integrate down the length of the reactor tube to obtain the temperature profile and the generation of C per tube using eq 5, which is the energy balance with heat transfer. 5. If the peak temperature is not equal 500 K, adjust T1 ) Tst and then return to step 4. 6. Calculate the number of tubes, Ntube, and the total amount of catalyst needed for the total generation of C ) 0.12 kmol/s. 7. Calculate the sizes and costs of all equipment. 8. Evaluate the TAC of the process. 9. Vary Dtube, Ltube, Ftube, and yA/yB until the minimum TAC is obtained. 6. Results 6.1. Summary of Results. Overall comparisons among reactor configurations at their optimum steadystate designs are shown in Table 2 for expensive catalyst ($100/kg) and in Table 3 for inexpensive catalyst ($5/kg). In both cases, the single cooled tubular reactor design has the lowest TAC. This occurs for two reasons: (1) This system requires less catalyst (smaller reactor) because it operates at a higher average temperature, which results from having a higher inlet temperature. The reaction is irreversible. Therefore, the higher the temperature, the larger the specific reaction rate, and the less catalyst required for a given conversion. However, the capital cost of the cooled reactor is higher per unit of volume than that of the simple adiabatic reactor vessels. (2) This system has a lower recycle flow rate because cooling the length of the reactor reduces the problem of exceeding the maximum temperature limitation. An adiabatic reactor requires higher flow rates so as not to exceed this maximum temperature constraint. The lower recycle flow rate results in a smaller compressor, smaller heat exchangers, and lower compression energy cost. The operating

cost advantage is offset somewhat by the need to provide energy in the furnace. The single adiabatic reactor design is the most expensive. It is much cheaper to operate multiple adiabatic reactors in series because this multistage configuration permits smaller recycle flow rates. When the catalyst is expensive, a process with seven adiabatic beds in the reactor vessel with cold-shot cooling is cheaper than a three adiabatic reactor system with interstage cooling. When the catalyst is cheap, a four adiabatic bed reactor with cold-shot cooling is slightly more expensive than four adiabatic reactors with interstage cooling. Multistage cooled reactor systems are more expensive than a single cooled reactor for several reasons. First, the total amount of catalyst is larger because the average temperatures are lower. Second, the multi-unit heat exchangers/reactors are more expensive that a single unit. The detailed results for each reactor configuration are discussed below. 6.2. Single-Stage Adiabatic Reactor System. Figure 10 shows the effect of the reactor inlet temperature, T1, on the total annual cost (TAC), the annual equipment costs, and the operating costs. The optimum inlet temperature is 445.10 K when the catalyst is expensive and 422.47 K when the catalyst is cheap. As the inlet temperature increases, the compression and heatexchanger costs increase because recycle flow rate must be larger for the maximum temperature constraint not to be exceeded. The reactor and catalyst costs decrease initially, but at high inlet temperatures, they begin to increase because of the large pressure drop caused by the high flow rates. Figure 11 shows the effect of the reactor inlet temperature on the operating conditions and the optimum ratio of A and B (yA/yB) in the reactor feed stream. As the inlet temperature increases, the optimum ratio yA/yB decreases, the amount of catalyst decreases and then increases, the recycle flow rate increases, and the FEHE bypass flow rate decreases. No bypass flow is needed when the inlet temperature is 475 K or higher. The system at high recycle flow rate benefits from having more B in the system because the costs associated with heat transfer and compression are lower as a result of the higher heat capacity of B. 6.3. Multistage Adiabatic Reactor System with Interstage Cooling. The contour plot given in Figure

3312


Figure 10. Results for the design with an adiabatic reactor.

Figure 11. Operating conditions for the design with an adiabatic reactor.

12 shows how the TAC varies in a system with two adiabatic reactors with interstage cooling. The reactant ratio yA/yB is fixed at unity in this figure, so there are two design optimization variables, the inlet temperatures of the two reactors T1 and T2. Complete results with various numbers of reactors in the system are listed in Tables 4 and 5 ($100/kg

catalyst) and in Tables 6 and 7 ($5/kg catalyst). These tables list the costs and optimum conditions for each specific number of reactors. When the catalyst is expensive, the minimum TAC is $3,410,000 per year, and the optimum number of reactors is 3. When the catalyst is cheap, the minimum TAC is $740,000 per year, and the optimum number of reactors is 4.

Ind. Eng. Chem. Res., Vol. 42, No. 14, 2003 3313 Table 5. Optimum Operating Conditions for Multistage Adiabatic Reactors with Interstage Cooling ($100/kg Catalyst) parameter

units

NR

Figure 12. Contour plot of total annual cost (two adiabatic reactors with interstage cooling). Table 4. Results for Multistage Adiabatic Reactors with Interstage Cooling ($100/kg Catalyst) parameter

units

NR TAC yA/yB T1 T2 T3 T4

1 ($106/year) 3.99 0.91 (K) 445.10 (K) (K) (K)

capital costs ($106) reactor catalyst compressor FEHE interchangers condenser furnace operating costs compressor steam

2

3

4

3.50 0.94 447.14 457.43

3.41 0.96 448.06 456.80 466.51

3.45 0.97 448.51 456.51 465.04 474.14

0.61 7.87 0.97 0.71 0 0.47 0

0.77 7.57 0.71 0.50 0.17 0.33 0

0.90 7.69 0.59 0.42 0.27 0.27 0

1.03 7.98 0.52 0.37 0.34 0.24 0

0.45 0

0.31 -0.16

0.24 -0.21

0.21 -0.24

($106/year)

As the number of reactors increases, the inlet temperatures increase, the yA/yB ratio increases, and the recycle flow rate decreases, but the overall pressure drop increases because of the added pressure drops in interstage heat exchangers. The decrease in the recycle flow rate reduces the compression and heat-exchanger costs. The amount of catalyst used does not significantly decrease, and it eventually increases as the number of reactors increases because of the high pressure drop. For a specific number of reactors, the optimum design does not have reactors of the same size; the reactors decrease in size going down the train. 6.4. Multistage Adiabatic Reactor System with Cold-Shot Cooling. Results for this case are listed in Tables 8 and 9 ($100/kg catalyst) and in Tables 10 and 11 ($5/kg catalyst). The optimum number of reactors depends on the catalyst cost. When the catalyst is expensive, the optimum number of adiabatic beds in the reactor vessel is 7. When the catalyst is cheap, the optimum number of beds is 4. Using a larger number of small beds gives higher average temperatures because the bed inlet temperatures are higher, and this reduces the amount of catalyst required. As the number of reactors increases, the inlet temperatures increase, the yA/yB ratio increases slightly, the recycle flow rate decreases, the overall pressure drop decreases, and the amount of catalyst decreases. Notice that the optimum design limits the maximum inlet temperature of the first reactor to 475 K so that no

1

2

3

4

1.20 0.28 0.18 42.1 326.1 0.74 6.15 1140 3.35 598

0.59 0.15 0.30 39.5 331.1 0.50 3.54 670 1.92 344

0.38 0.11 0.40 37.3 335.6 0.40 2.63 502 1.43 255

0.27 0.09 0.48 35.2 340.2 0.34 2.17 416 1.18 211

(103 kg) (103 kg) (103 kg) (103 kg) (103 kg)

78.8 78.8

75.8 39.7 36.1

77.0 27.7 26.0 23.3

79.8 22.2 21.0 19.5 17.1

DR,1 DR,2 DR,3 DR,4

(m) (m) (m) (m)

1.71

1.36 1.32

1.21 1.18 1.14

1.12 1.10 1.07 1.03

RC,1 RC,2 RC,3 RC,4

(kmol/s) (kmol/s) (kmol/s) (kmol/s)

0.120

0.066 0.054

0.049 0.040 0.031

0.040 0.033 0.027 0.020

P1 P2 P3 P4

(bar) (bar) (bar) (bar)

48.50

48.50 44.46

48.50 45.22 41.74

48.50 45.64 42.66 39.45

∆P1 ∆P2 ∆P3 ∆P4


5.4

3.54 4.00

2.78 2.99 3.43

2.36 2.48 2.71 3.22

FR Fby XA PS TR Wcomp QHX AHX QC AC

(kmol/s) (kmol/s)

Wcat,total Wcat,1 Wcat,2 Wcat,3 Wcat,4

(bar) (K) (MW) (MW) (m2) (MW) (m2)

Table 6. Results for Multistage Adiabatic Reactors with Interstage Cooling ($5/kg Catalyst) parameter

units

NR TAC yA/yB T1 T2 T3 T4 T5

1

capital costs ($106) reactor catalyst compressor FEHE interchangers condenser furnace operating costs compressor steam

2

3

4

5

0.81 0.92 431.28 437.36

0.75 0.96 435.94 442.31 450.24

0.74 0.98 438.94 445.67 453.31 461.06

0.76 0.99 440.94 447.99 455.46 463.03 470.40

0.88 0.71 0.36 0.45 0 0.38 0

1.01 0.58 0.26 0.35 0.16 0.27 0

1.12 0.54 0.21 0.31 0.26 0.22 0

1.23 0.53 0.19 0.29 0.33 0.20 0

1.34 0.53 0.18 0.28 0.38 0.19 0

0.136 0

0.089 0.071 0.062 0.058 -0.15 -0.21 -0.24 -0.26

($106/year) 1.07 0.87 (K) 422.47 (K) (K) (K) (K)

($106/year)

energy is used in the furnace. The 475 K corresponds to a 25 K minimum differential temperature in the FEHE with 500 K hot gas entering from the reactor. A comparison of the interstage-cooled and cold-shot designs shows that the former has smaller recycle flow rates but more catalyst. Note that the cost of the single vessel with seven catalyst beds in the optimum cold-shot design ($1,340,000, Table 8) is higher than that of the optimum three-vessel design with interstage cooling ($900,000 reactor cost and $270,000 heat-exchanger cost, Table 4).

3314


Table 7. Optimum Operating Conditions for Multistage Adiabatic Reactors with Interstage Cooling ($5/kg Catalyst) parameter

units

NR

1

2

3

4

5

0.78 0.34 0.25 46.1 319.1 0.22 3.77 572 2.96 446

0.36 0.17 0.41 44.6 321.6 0.15 2.40 391 1.57 257

0.22 0.12 0.53 43.2 324.1 0.12 1.91 324 1.13 194

0.16 0.09 0.61 41.6 327.0 0.10 1.67 291 0.92 164

0.12 0.08 0.67 40.0 330.1 0.09 1.53 273 0.81 147

FR Fby XA PS TR Wcomp QHX AHX QC AC

(kmol/s) (kmol/s)

Wcat,total Wcat,1 Wcat,2 Wcat,3 Wcat,4 Wcat,5

(103 kg) (103 kg) (103 kg) (103 kg) (103 kg) (103 kg)

142.5 142.5

116.9 56.2 60.7

108.2 34.9 36.2 37.1

105.5 26.0 26.1 26.2 27.2

106.1 21.5 21.0 20.8 21.1 21.7

DR,1 DR,2 DR,3 DR,4 DR,5

(m) (m) (m) (m) (m)

2.09

1.53 1.57

1.30 1.32 1.33

1.18 1.18 1.19 1.20

1.11 1.10 1.10 1.10 1.11

RC,1 RC,2 RC,3 RC,4 RC,5

(kmol/s) (kmol/s) (kmol/s) (kmol/s) (kmol/s)

0.120

0.063 0.057

0.045 0.040 0.035

0.037 0.032 0.028 0.023

0.032 0.028 0.024 0.020 0.016

P1 P2 P3 P4 P5

(bar) (bar) (bar) (bar) (bar)

48.50

48.50 46.73

48.50 46.79 45.18

48.50 46.81 45.18 43.61

48.50 46.82 45.16 43.54 41.98

∆P1 ∆P2 ∆P3 ∆P4 ∆P5


1.41

1.27 1.10

1.21 1.11 1.02

1.19 1.13 1.07 0.99

1.18 1.16 1.12 1.07 1.01

(bar) (K) (MW) (MW) (m2) (MW) (m2)

6.5. Single-Stage Cooled Reactor System. Figure 13 shows the temperature profiles in the cooled tubular reactor for the optimum designs with the two catalysts. The lengths of the reactors are about the same, and the peak temperature occurs about 5.3 m from the reactor inlet in both designs.

Table 12 gives the results of the optimum designs. The amount of catalyst used in the expensive catalyst case is smaller, so the number of tubes is lower since the tube diameters are about the same. The optimum ratio yA/yB is about 1 for both cases. The optimum recycle flow rate is larger with the expensive catalyst, as expected, which yields an optimum inlet temperature that is higher. It is important to note that the heat-transfer coefficient U in the expensive catalyst case is almost twice that in the cheap catalyst case. This is due to the larger recycle flow rate and higher velocity in the tubes. The heat-transfer areas AR of the two designs are only 20% different because the inlet temperature of the expensive catalyst design is higher, which provides less of a temperature differential. The product UAR has important effects on the dynamic controllability of this system, which will be studied in a future paper. 6.6. Multistage Cooled Reactor System with Interstage Cooling. Results are listed in Tables 13 and 14 ($100/kg catalyst) and in Tables 15 and 16 ($5/kg catalyst). The length and tube diameter are assumed to be the same in all reactors. As the number of reactors increases, the required amount of catalyst and the recycle flow rate increase. This is the opposite of what occurs in the multistage adiabatic design, in which both the recycle flow rate and the amount of catalyst decrease as the number of adiabatic reactors increases. This counterintuitive result can be explained by considering the temperature profiles in a single cooled reactor with those in multiple cooled reactors (with either interstage cooling or cold shot cooling). The average temperature in the single cooled reactor is higher than the average temperature in multiple cooled reactors because the temperature of the feed to each stage has been reduced by the external cooling in the latter case (or by mixing with the coldshot stream). This lower average temperature means that more catalyst must be used. The second factor is the increase in the capital cost of multiple heat exchangers/reactors (three in the twocooled-reactor case) compared to having a single heat exchanger/reactor. These factors cause the optimization to push the design to higher recycle flow rates, trading off reactor cost against compression cost. The higher recycle flow rates permit higher inlet temperatures.

Table 8. Results for Multistage Adiabatic Reactors with Cold-Shot Cooling ($100/kg Catalyst) parameter

units

NR TAC yA/yB T1 T2 T3 T4 T5 T6 T7 T8

($106/year) (K) (K) (K) (K) (K) (K) (K) (K)

capital costs reactor catalyst compressor FEHE condenser furnace

($106)

operating costs compressor

($106/year)

1

2

3

4

5

6

7

8

3.99 0.906 445.10

2.78 0.947 458.31 463.76

2.37 0.965 466.03 469.69 472.71

2.18 0.975 471.40 474.02 476.26 478.16

2.08 0.983 475.00 477.46 479.16 480.63 481.90

2.04 0.989 475.00 480.55 481.82 482.94 483.93 484.81

2.03 0.994 475.00 482.95 483.93 484.81 485.59 486.30 486.94

2.04 0.997 475.00 484.86 485.64 486.34 486.98 487.56 488.09 488.57

0.61 7.87 0.97 0.71 0.47 0

0.74 5.29 0.61 0.52 0.41 0

0.81 4.41 0.48 0.45 0.39 0

0.91 3.95 0.41 0.42 0.38 0

1.03 3.67 0.36 0.40 0.37 0

1.18 3.50 0.33 0.38 0.36 0

1.34 3.38 0.30 0.37 0.36 0

1.53 3.29 0.28 0.36 0.36 0

0.45

0.25

0.19

0.16

0.14

0.12

0.11

0.10

Ind. Eng. Chem. Res., Vol. 42, No. 14, 2003 3315 Table 9. Optimum Operating Conditions for Multistage Adiabatic Reactors with Cold-Shot Cooling ($100/kg Catalyst) parameter

units

NR

1

2

3

4

5

6

7

8

1.20 0.28 0.18 42.1 326.1 324.0 0.74 6.15 1140 3.35 598

0.90 0.10 0.22 43.9 322.9 320.8 0.41 4.40 712 3.10 490

0.79 0.04 0.24 44.8 321.4 319.4 0.31 3.75 571 3.02 450

0.74 0.01 0.25 45.3 320.4 318.6 0.26 3.43 506 2.98 431

0.71 0 0.26 45.7 319.7 318.0 0.22 3.25 471 2.96 420

0.68 0 0.26 46.1 319.1 317.5 0.20 3.10 440 2.94 410

0.66 0 0.27 46.4 318.7 317.2 0.18 3.00 421 2.92 403

0.65 0 0.27 46.6 318.4 316.9 0.16 2.93 409 2.91 399

(103 kg) (103 kg) (103 kg) (103 kg) (103 kg) (103 kg) (103 kg) (103 kg) (103 kg)

78.8 78.8

52.9 24.5 28.4

44.2 13.1 14.6 16.5

39.6 8.5 9.4 10.3 11.4

36.8 6.3 6.7 7.3 7.9 8.6

35.0 6.0 5.0 5.4 5.8 6.2 6.6

33.8 5.8 4.0 4.2 4.5 4.8 5.1 5.4

32.9 5.6 3.3 3.5 3.7 3.9 4.1 4.3 4.5

DR LR,1 LR,2 LR,3 LR,4 LR,5 LR,6 LR,7 LR,8

(m) (m) (m) (m) (m) (m) (m) (m) (m)

1.71 17.11

1.53 6.64 7.70

1.48 3.79 4.24 4.78

1.47 2.51 2.77 3.04 3.36

1.47 1.85 1.96 2.13 2.31 2.51

1.50 1.70 1.43 1.53 1.65 1.76 1.89

1.53 1.58 1.09 1.16 1.24 1.31 1.39 1.48

1.56 1.48 0.86 0.91 0.96 1.02 1.07 1.13 1.19

RC,1 RC,2 RC,3 RC,4 RC,5 RC,6 RC,7 RC,8

(kmol/s) (kmol/s) (kmol/s) (kmol/s) (kmol/s) (kmol/s) (kmol/s) (kmol/s)

0.120

0.057 0.063

0.037 0.040 0.043

0.028 0.029 0.031 0.032

0.022 0.023 0.024 0.025 0.026

0.021 0.018 0.019 0.020 0.020 0.021

0.020 0.015 0.016 0.016 0.017 0.017 0.018

0.020 0.013 0.014 0.014 0.014 0.015 0.015 0.015

P1 P2 P3 P4 P5 P6 P7 P8

(bar) (bar) (bar) (bar) (bar) (bar) (bar) (bar)

48.50

48.50 47.21

48.50 47.95 47.09

48.50 48.21 47.78 47.17

48.50 48.32 48.07 47.74 47.30

48.50 48.36 48.21 48.02 47.77 47.46

48.50 48.38 48.29 48.17 48.02 47.84 47.62

48.50 48.41 48.34 48.26 48.17 48.05 47.92 47.75

∆P1 ∆P2 ∆P3 ∆P4 ∆P5 ∆P6 ∆P7 ∆P8

(bar) (bar) (bar) (bar) (bar) (bar) (bar) (bar)

5.44

1.29 2.33

0.55 0.86 1.33

0.29 0.43 0.61 0.86

0.18 0.25 0.33 0.44 0.59

0.14 0.15 0.19 0.24 0.31 0.39

0.12 0.09 0.12 0.15 0.18 0.22 0.27

0.09 0.06 0.08 0.09 0.11 0.14 0.16 0.19

F1 F2 F3 F4 F5 F6 F7 F8

(kmol/s) (kmol/s) (kmol/s) (kmol/s) (kmol/s) (kmol/s) (kmol/s) (kmol/s)

1.440

0.911 0.231

0.729 0.147 0.156

0.641 0.107 0.113 0.118

0.591 0.084 0.087 0.091 0.094

0.561 0.067 0.070 0.072 0.074 0.077

0.542 0.056 0.058 0.059 0.061 0.063 0.065

0.530 0.048 0.049 0.051 0.052 0.053 0.054 0.056

FR Fby XA PS TR TCS Wcomp QHX AHX QC AC

(kmol/s) (kmol/s)

Wcat,total Wcat,1 Wcat,2 Wcat,3 Wcat,4 Wcat,5 Wcat,6 Wcat,7 Wcat,8

(bar) (K) (K) (MW) (MW) (m2) (MW) (m2)

The optimum length of the tubes in each reactor decreases, but the total reactor length increases. No bypassing is used because the inlet temperature is higher than 25 K less than the hot exit temperatures. Furnace energy is required. The peak temperature occurs at or very close to the reactor exit. The diameter of the reactor tubes is always 0.12 m at the specified limit when the catalyst is cheap. The diameter of the

tube would be larger to reduce compression cost if there were no limit on the tube diameter. 6.7. Multistage Cooled Reactor System with Cold-Shot Cooling. Results for this case are given in Tables 17 and 18 ($100/kg catalyst) and in Tables 19 and 20 ($5/kg catalyst). The results are about the same as those obtained in the interstage cooling case, and the reasons for the pooorer performance compared to that

3316


Table 10. Results for Multistage Adiabatic Reactors with Cold-Shot Cooling ($5/kg Catalyst) parameter

units

NR

1

TAC yA/yB T1 T2 T3 T4 T5

($106/year) 1.07 0.87 (K) 422.47 (K) (K) (K) (K)


($106)

2

3

4

5

0.86 0.92 437.36 446.52

0.79 0.95 446.32 453.08 458.75

0.78 0.96 453.13 458.43 462.88 466.65

0.80 0.97 458.66 462.93 466.53 469.59 472.22

0.88 0.71 0.36 0.45 0.38 0

0.99 0.42 0.26 0.31 0.34 0

1.03 0.33 0.22 0.26 0.32 0

1.13 0.29 0.19 0.23 0.32 0

1.24 0.26 0.18 0.22 0.31 0

operating costs ($106/year) compressor 0.14

0.09

0.07

0.06

0.06

Table 11. Optimum Operating Conditions for Multistage Adiabatic Reactors with Cold-Shot Cooling ($5/kg Catalyst) parameter

units

NR

1

2

3

4

5

0.78 0.34 0.25 46.1 319.1 317.8 0.22 3.77 572 2.96 446

0.57 0.14 0.31 46.5 318.5 316.9 0.15 2.43 321 2.90 372

0.49 0.08 0.34 46.7 318.1 316.4 0.12 1.92 238 2.88 343

0.45 0.05 0.35 46.8 317.9 316.2 0.10 1.68 202 2.87 329

0.43 0.03 0.36 46.9 317.8 316.1 0.10 1.56 183 2.86 322

(103 kg) (103 kg) (103 kg) (103 kg) (103 kg) (103 kg)

142.5 142.5

84.9 39.9 45.0

66.7 19.4 22.3 25.0

57.3 11.8 13.5 15.2 16.8

51.3 8.0 9.2 10.3 11.4 12.4

DR LR,1 LR,2 LR,3 LR,4 LR,5

(m) (m) (m) (m) (m) (m)

2.09 20.90

1.79 7.94 8.94

1.69 4.34 4.97 5.58

1.65 2.77 3.17 3.57 3.95

1.63 1.93 2.19 2.46 2.73 2.99

RC,1 RC,2 RC,3 RC,4 RC,5


0.120

0.054 0.066

0.034 0.040 0.046

0.025 0.028 0.032 0.035

0.019 0.022 0.024 0.026 0.028

P1 P2 P3 P4 P5


48.50

48.50 48.17

48.50 48.37 48.13

48.50 48.44 48.33 48.14

48.50 48.46 48.40 48.30 48.15

∆P1 ∆P2 ∆P3 ∆P4 ∆P5


1.41

0.33 0.69

0.13 0.24 0.43

0.06 0.11 0.19 0.30

0.04 0.06 0.10 0.15 0.22

F1 F2 F3 F4 F5


1.020

0.422 0.145 0.164

0.351 0.102 0.115 0.126

0.312 0.079 0.087 0.095 0.102

FR Fby XA PS TR TCS Wcomp QHX AHX QC AC

(kmol/s) (kmol/s)

Wcat,total Wcat,1 Wcat,2 Wcat,3 Wcat,4 Wcat,5

(bar) (K) (K) (MW) (MW) (m2) (MW) (m2)

0.573 0.236

of a single cooled reactor are the same. A multistage cooled reactor system is more expensive than a singlestage cooled reactor system.

Figure 13. Temperature profile in the cooled reactor. Table 12. Results for the Design with a Single-Stage Cooled Reactor parameter

units

catalyst cost

($/kg)

100

5

TAC Dtube Ltube Ftube yA/yB

($106/year) (m) (m) (kmol/s)

1.57 0.1113 8.51 0.0033 1.017

0.46 (0.12) 8.13 0.0020 1.029

Wcat Ntube FR Fby ∆P PS TC ) Tin Tout XA U V DR AR AHX AC Wcomp QR QHX QC QF

(103 kg)

31.38 190 0.38 0 0.75 46.75 477.33 495.25 0.38 0.246 0.276 2.17 564 942 217 89.46 2.40 3.35 0.61 0.15

41.50 226 0.22 0 0.20 47.30 464.17 489.17 0.52 0.135 0.142 2.55 692 670 159 41.94 2.39 2.38 0.43 0

capital cost reactor catalyst compressor furnace FEHE condenser

($106) 0.90 3.13 0.17 0.15 0.63 0.72

1.02 0.21 0.09 0 0.50 0.59

operating cost compressor furnace fuel steam

($106/year) 0.05 0.02 -0.41

0.03 0 -0.37

(kmol/s) (kmol/s) (bar) (bar) (K) (K) (kJ s-1 m-2 K-1) (m/s) (m) (m2) (m2) (m2) (kW) (103 kW) (103 kW) (103 kW) (103 kW)

The TAC, the amount of catalyst, the recycle flow rate, and the pressure drop increase with the number of reactors. The total heat-transfer area increases on going from one stage to two (by about 50%), but it decreases as more stages are added. The heat-transfer coefficient is also larger because of the high recycle flow rates. These factors might have some advantages for dynamic controllability. 7. Conclusion and Future Work Steady-state design and optimization procedures for alternative plantwide tubular reactor systems have been developed. An economic comparison has been made among these optimum designs. The process with a single cooled tubular reactor is found to be the most economical from a steady-state point of view. The single adiabatic reactor is the simplest system, but it requires a larger reactor and more catalyst. Multiple adiabatic reactors with intermediate cooling

Ind. Eng. Chem. Res., Vol. 42, No. 14, 2003 3317 Table 13. Results for Multistage Cooled Reactors with Interstage Cooling ($100/kg Catalyst) parameter

units

parameter

NR

3

4

NR

1.83 0.1026 4.66 215 0.983

2.02 0.0983 3.56 209 1.012

2.17 0.1036 2.66 197 0.987

TAC Dtube Ltube Ntube yA/yB

($106/year) (m) (m)

1.25 3.32 0.22 0.66 0.09 0.75 0.14

1.50 3.39 0.28 0.67 0.15 0.77 0.18

1.65 3.53 0.30 0.67 0.24 0.77 0.15

capital costs reactor catalyst compressor FEHE interchangers condenser furnace

($106)

0.90 3.13 0.17 0.63 0 0.72 0.15

0.07 0.02 -0.41

0.10 0.03 -0.42

0.11 0.02 -0.40

operating costs compressor furnace fuel steam

($106/year)

0.05 0.02 -0.41

($106/year) 1.57 (m) 0.1113 (m) 8.51 190 1.017

capital costs ($106) reactor catalyst compressor FEHE interchangers condenser furnace ($106/year)


Table 14. Optimum Operating Conditions for Multistage Cooled Reactors with Interstage Cooling ($100/kg Catalyst) units

NR

1

2

3

4

31.38 0.0033 0.38 0 0.38 46.75 318.0 316.1 2.17 564 942 217 89.46 3.35 0.61 0.15

33.22 0.0031 0.42 0 0.37 46.02 319.2 317.0 2.13 971 1023 232 121.79 3.63 0.67 0.14

33.90 0.0032 0.43 0 0.35 45.03 320.9 318.1 2.01 690 1041 238 159.72 3.70 0.71 0.19

35.31 0.0035 0.44 0 0.35 44.63 321.6 318.6 2.06 511 1051 241 176.12 3.73 0.73 0.16

(103 kg) (kmol/s) (kmol/s) (kmol/s)

T1 T2 T3 T4

(K) (K) (K) (K)

477.33

480.14 486.24

483.06 486.31 491.73

481.70 486.60 487.72 490.65

Tout,1 Tout,2 Tout,3 Tout,4

(K) (K) (K) (K)

495.25

500.00 499.15

500.00 500.00 499.85

500.00 500.00 500.00 500.00

RC,1 RC,2 RC,3 RC,4


0.120

0.070 0.050

0.050 0.041 0.029

0.039 0.033 0.027 0.021

P1 P2 P3 P4


48.50

48.50 47.48

48.50 47.47 46.48

48.50 47.63 46.78 45.95

∆P1 ∆P2 ∆P3 ∆P4


0.75

0.52 0.46

0.53 0.49 0.45

0.37 0.35 0.33 0.31

require more vessels and more heat exchangers. Multiple adiabatic reactors with cold-shot cooling require higher recycle flow rates than in the case of the intermediate cooling design. The single cooled reactor is the most economical because the temperatures in the reactor are higher than those obtained in the other configuration (all being limited to a maximum temperature constraint).

1

2

3

4

0.46 (0.12) 8.13 226 1.029

0.66 (0.12) 5.37 176 0.995

0.80 (0.12) 3.80 168 1.008

0.94 (0.12) 3.11 155 0.951

1.02 0.21 0.09 0.50 0 0.59 0

1.33 0.21 0.15 0.57 0.08 0.65 0.01

1.55 0.22 0.18 0.59 0.16 0.67 0.01

1.72 0.22 0.22 0.60 0.24 0.69 0.09

0.03 0 -0.37

0.05 0.0007 -0.39

0.06 0.0005 -0.39

0.07 0.0117 -0.39

Table 16. Optimum Operating Conditions for Multistage Cooled Reactors with Interstage Cooling ($5/kg Catalyst) parameter

units

NR

Wcat,total Ftube,1 FR Fby XA PS TR TCS DR AR AHX AC Wcomp QHX QC QF

(bar) (K) (K) (m) (m2) (m2) (m2) (kW) (103 kW) (103 kW) (103 kW)

units

2

1

TAC Dtube Ltube Ntube yA/yB

parameter

Table 15. Results for Multistage Cooled Reactors with Interstage Cooling ($5/kg Catalyst)

1

2

3

4

41.50 0.0020 0.22 0 0.52 47.30 317.2 315.0 2.55 692 670 159 41.94 2.38 0.43 0

42.66 0.0030 0.29 0 0.46 46.4 318.5 316.0 2.25 1067 809 185 74.14 2.87 0.52 0.0044

43.38 0.0033 0.31 0 0.43 45.8 319.6 316.7 2.20 723 860 194 96.53 3.05 0.56 0.0037

43.64 0.0036 0.33 0 0.44 45.1 320.8 317.5 2.11 546 881 200 119.06 3.13 0.59 0.0783


(103

T1 T2 T3 T4

(K) (K) (K) (K)

464.17

471.82 484.54

474.47 480.48 489.36

478.83 480.86 486.12 490.43


(K) (K) (K) (K)

489.17

500.00 496.58

500.00 500.00 499.28

500.00 500.00 500.00 499.89

RC,1 RC,2 RC,3 RC,4


0.120

0.077 0.043

0.054 0.042 0.024

0.043 0.035 0.026 0.016

P1 P2 P3 P4


48.50

48.50 47.70

48.50 47.74 47.00

48.50 47.73 46.99 46.26

∆P1 ∆P2 ∆P3 ∆P4


0.20

0.30 0.25

0.26 0.23 0.20

0.27 0.25 0.22 0.20

kg) (kmol/s) (kmol/s) (kmol/s) (bar) (K) (K) (m) (m2) (m2) (m2) (kW) (103 kW) (103 kW) (103 kW)

The single cooled reactor process has a total annual cost that is 40-43% of the cost of the single adiabatic reactor process, depending on the catalyst cost. The total annual cost of the single cooled reactor process is 4662% of the cost of the optimum multistage adiabatic reactor process with interstage cooling (three stages for the expensive catalyst and four stages for the inexpensive catalyst). The total annual cost of the single cooled reactor process is 59-77% of the cost of the optimum

3318


Table 17. Results for Multistage Cooled Reactors with Cold-Shot Cooling ($100/kg Catalyst) parameter

units

parameter

NR TAC Dtube Ltube Ntube yA/yB

($106/year) (m) (m)


($106)


($106/year)

2

3

4

1.57 0.1113 8.51 190 1.017

1.80 0.1003 5.05 204 1.012

1.99 0.0996 3.52 203 1.009

2.11 0.1002 2.62 200 0.999

NR TAC Dtube Ltube Ntube yA/yB

($106)

($106/year)

0.90 3.13 0.17 0.63 0.72 0.15

1.25 3.25 0.21 0.63 0.78 0.12

1.48 3.34 0.23 0.62 0.83 0.14

1.61 3.31 0.26 0.63 0.89 0.16

0.05 0.02 -0.41

0.07 0.02 -0.37

0.08 0.02 -0.32

0.09 0.02 -0.29


1

2

3

4

31.38 0.0033 0.38 0 0.38 46.75 318.0 316.1 2.17 564 942 217 89.46 3.35 0.61 0.15

32.57 0.0030 0.42 0 0.36 46.32 318.7 316.6 2.03 974 946 242 111.43 3.36 0.91 0.12

33.43 0.0029 0.45 0 0.35 46.18 319.0 316.9 2.01 671 932 267 125.46 3.31 1.20 0.13

33.11 0.0030 0.50 0 0.32 46.03 319.2 317.2 2.01 496 942 299 146.17 3.35 1.53 0.16

(103 kg) (kmol/s) (kmol/s) (kmol/s)

T1 T2 T3 T4

(K) (K) (K) (K)

477.33

479.37 487.27

481.32 485.46 488.05

482.59 485.31 489.40 491.82


(K) (K) (K) (K)

495.25

499.96 498.86

500.00 500.00 499.91

500.00 500.00 500.00 500.00

RC,1 RC,2 RC,3 RC,4


0.120

0.070 0.050

0.047 0.041 0.032

0.036 0.032 0.028 0.024

P1 P2 P3 P4


48.50

48.50 47.91

48.50 48.09 47.64

48.50 48.18 47.83 47.44

∆P1 ∆P2 ∆P3 ∆P4


0.75

0.59 0.59

0.41 0.45 0.46

0.32 0.36 0.39 0.41

F1 F2 F3 F4


0.621

0.611 0.045

0.599 0.052 0.039

0.606 0.053 0.047 0.039

multistage adiabatic reactor process with cold-shot cooling (seven stages for the expensive catalyst and four stages for the inexpensive catalyst). Cooled tubular reactor systems are known to have high sensitivity and to be difficult to control, especially

1 0.46 (0.12) 8.13 226 1.029

2 0.64 (0.12) 5.53 172 1.035

3 0.76 (0.12) 4.67 141 1.026

4 0.88 (0.12) 3.70 150 1.050

1.02 0.21 0.09 0.50 0.59 0

1.33 0.21 0.13 0.53 0.65 0

1.58 0.22 0.15 0.53 0.66 0

1.88 0.25 0.14 0.48 0.66 0

0.03 0 -0.37

0.04 0 -0.35

0.05 0 -0.33

0.04 0 -0.30

Table 20. Optimum Operating Conditions for Multistage Cooled Reactors with Cold-Shot Cooling ($5/kg Catalyst) parameter

units

NR


(bar) (K) (K) (m) (m2) (m2) (m2) (kW) (103 kW) (103 kW) (103 kW)

($106/year) (m) (m)


units

NR

units

1

Table 18. Optimum Operating Conditions for Multistage Cooled Reactors with Cold-Shot Cooling ($100/kg Catalyst) parameter

Table 19. Results for Multistage Cooled Reactors with Cold-Shot Cooling ($5/kg Catalyst)

1

2

3

4

41.50 0.0020 0.22 0 0.52 47.30 317.2 315.0 2.55 692 670 159 41.94 2.38 0.43 0

42.91 0.0028 0.29 0 0.45 46.97 317.7 315.5 2.22 1073 719 184 62.30 2.60 0.52 0

44.73 0.0033 0.30 0.0001 0.44 46.53 318.4 316.0 2.02 745 721 187 74.80 2.56 0.53 0

50.22 0.0028 0.29 0.0069 0.44 46.7 318.2 315.8 2.08 628 621 187 69.83 2.31 0.56 0


(103

T1 T2 T3 T4

(K) (K) (K) (K)

464.17

470.41 484.18

473.68 482.44 491.43

471.90 479.29 487.41 493.94


(K) (K) (K) (K)

489.17

500.00 496.25

500.00 499.33 498.70

500.00 500.00 499.52 499.47

RC,1 RC,2 RC,3 RC,4


0.120

0.075 0.045

0.055 0.043 0.022

0.044 0.038 0.025 0.013

P1 P2 P3 P4


48.50

48.50 48.23

48.50 48.18 47.84

48.50 48.31 48.10 47.88

∆P1 ∆P2 ∆P3 ∆P4 F1 F2 F3 F4

(bar) (bar) (bar) (bar) (kmol/s) (kmol/s) (kmol/s) (kmol/s)

0.20

0.27 0.26

0.32 0.34 0.31

0.456

0.480 0.045

0.465 0.049 0.023

0.19 0.21 0.22 0.20 0.425 0.054 0.035 0.016

kg) (kmol/s) (kmol/s) (kmol/s) (bar) (K) (K) (m) (m2) (m2) (m2) (kW) (103 kW) (103 kW) (103 kW)

when the activation energy is high. The dynamic controllability of the system has to be investigated, and a design adjustment might be needed to ensure safe and smooth operation. Dynamic comparisons among these alternative designs will be the subject of a future paper.


Appendix A Design and Optimization Procedure. Design and optimization procedures for multistage cooled reactor systems are given below. A.1. Procedure for Multistage Cooled Reactor System with Interstage Cooling. 1. Specify NR. 2. Pick Dtube, Ltube, Ntube, and the yA/yB ratio (all four variables to be optimized). 3. Calculate the amount of catalyst per tube Wtube. 4. Guess the inlet flow rate per tube of the first reactor Ftube,1. 5. Guess the inlet temperature of the first reactor T1 ) Tst,1. 6. Integrate down the length of the first reactor tube to obtain the temperature profile and the generation of C per tube. 7. If the peak temperature is not equal 500 K, adjust T1 ) Tst,1 and then return to step 6. 8. Calculate the generation of C of the first reactor RC,1. 9. Repeat steps 5-8 for the other reactors. 10. Calculate the total generation of C. 11. If the total generation rate is not equal to LC ) 0.12 kmol/s, adjust Ftube,1 and return to step 5. 12. Calculate the sizes and costs of all equipment. 13. Evaluate the TAC of the process. 14. Vary Dtube, Ltube, Ntube, and yA/yB until the minimum TAC is obtained. A.2. Procedure for Multistage Cooled Reactor System with Cold-Shot Cooling. 1. Specify NR. 2. Pick Dtube, Ltube, Ntube, and the yA/yB ratio (all four variables to be optimized). 3. Calculate the amount of catalyst per tube Wtube. 4. Guess the temperature of the cold-shot stream TCS. 5. Guess the inlet flow rate per tube of the first reactor Ftube,1. 6. Guess the inlet temperature of the first reactor T1 ) Tst,1. 7. Integrate down the length of the first reactor tube to obtain the temperature profile and the generation of C per tube. 8. If the peak temperature is not equal 500 K, adjust T1 ) Tst,1 and then return to step 6. 9. Calculate the generation of C of the first reactor RC,1. 10. Guess the inlet temperature of the second reactor T2 ) Tst,2. 11. Calculate the amount of cold-shot F2 from the upstream hot exit temperature Tout,1, the flow rate Fout,1, T2, and TCS. 12. Integrate down the length of the reactor tube to obtain the temperature profile and the generation of C per tube. 13. If the peak temperature is not equal 500 K, adjust T2 ) Tst,2 and then return to step 12. 14. Calculate the generation of C of the second reactor RC,2. 15. Repeat steps 10-14 for the other reactors. 16. Calculate the total generation of C. 17. If the total generation rate is not equal to LC ) 0.12 kmol/s, adjust Ftube,1. 18. Calculate the recycle temperature TR and then calculate TCS. 19. Update TCS and return to step 5. When this iterative loop has converged, continue.

20. 21. 22. mum

Calculate the sizes and costs of all equipment. Evaluate the TAC of the process. Vary Dtube, Ltube, Ntube, and yA/yB until the miniTAC is obtained.

Appendix B Equations in the Cold-Shot Design for NR ) 3. There are six equations and six unknowns (F1, F2, F3, RC,1, RC,2, and RC,3) for the case with three adiabatic beds in the reactor vessel. These equations are

RC,1 + RC,2 + RC,3 ) 0.12 kmol/s F1 )

λRC,1 (Tout - T1)(yAcpA + yBcpB + yCcpC)1

F1 + F2 )

λRC,2 (Tout - T2)(yAcpA + yBcpB + yCcpC)1

F1 + F2 + F3 )

(B1) (B2)

(B3)

λRC,3 (Tout - T3)(yAcpA + yBcpB + yCcpC)1 (B4)

F1(Tout - T2) ) F2(T2 - TCS)

(B5)

F1(Tout - T3) + F2(Tout - T3) ) F3(T3 - TCS) (B6) Note that these equations are linear in the six unknowns, so they can be easily solved. Nomenclature A ) reactant component AC ) heat-transfer area in the condenser (m2) AHX ) heat-transfer area in the heat exchanger (m2) AR ) heat-transfer area in the reactor (m2) B ) reactant component C ) product component CF ) steam cost factor cpj ) heat capacity of component j (kJ kmol-1 K-1) DP ) catalyst pellet diameter (m) DR,n ) diameter of the nth reactor or bed (m) Dtube,n ) tube diameter of the nth reactor (m) E ) activation energy (kJ kmol-1) f ) friction factor Fby ) bypass flow rate around FEHE (kmol/s) FC,n ) flow rate of product C entering the nth reactor (kmol/ s) FEHE ) feed-effluent heat exchanger Fj ) flow rate of component j (kmol/s) Fm ) flow rate of cold-shot stream entering the mth reactor (kmol/s) FR ) recycle flow rate (kmol/s) Fst ) flow rate of generated steam (kmol/s) Ftube,n ) inlet flow rate per reactor tube of the nth reactor (kmol/s) F0j ) fresh-feed flow rate of component j (kmol/s) F1 ) feed flow rate of the first reactor (kmol/s) k ) specific reaction rate [kmol s-1 bar-2 (kg of catalyst)-1] LC ) liquid flow rate of product C leaving the separator drum (kmol/s) LR,n ) length of the nth reactor/bed (m) Ltube,n ) length of reactor tubes in the nth reactor (m) Mj ) molecular weight of component j (kg/kmol) NR ) number of reactors Ntube,n ) number of reactor tubes in the nth reactor P ) total pressure (bar)

3320


PA ) partial pressure of reactant A (bar) PB ) partial pressure of reactant B (bar) Pn ) pressure at the inlet of the nth reactor (bar) PR ) recycle or compressor discharge pressure (bar) PS ) compressor suction pressure (bar) Pst ) pressure of steam (bar) QC ) heat transfer in condenser (kW) QF ) heat transfer in furnace (kW) QHX ) heat transfer in heat exchanger (kW) QR ) heat transfer in reactor (kW) R ) ideal gas constant (bar m3 kmol-1 K-1) rC ) reaction rate of product C [kmol s-1 (kg of catalyst)-1] RC,n ) rate of generation of C in the nth reactor (kmol/s) Re ) Reynolds number T ) temperature (K) TCS ) temperature of cold-shot stream (K) Tin ) temperature at the reactor inlet (K) Tmax ) maximum allowable temperature (K) Tn ) temperature at the inlet of the nth reactor (K) Tout ) temperature at the reactor exit (K) TR ) temperature of the recycle stream (K) TS ) compressor suction temperature (K) Tst ) steam temperature (K) T0 ) temperature of the fresh feed stream (K) U ) overall heat-transfer coefficient in the reactor (kJ s-1 m-2 K-1) UFEHE ) overall heat-transfer coefficient in the feedeffluent heat exchanger (kJ s-1 m-2 K-1) UHX ) overall heat-transfer coefficient in the heat exchanger and condenser (kJ s-1 m-2 K-1) V ) superficial velocity in the tube (m/s) w ) weight of the catalyst (kg) Wcat,n ) total weight of catalyst in the nth reactor (kg) Wcomp ) compressor work (kW) Wtube,n ) weight of catalyst per tube in the nth reactor (kg) XA ) fractional per-pass conversion based on reactant A yA ) composition of reactant A in the first reactor inlet stream (mole fraction) yB ) composition of reactant B in the first reactor inlet stream (mole fraction) R ) preexponential factor γ ) ratio of heat capacities ∆PHX ) design pressure drop in the heat exchanger (bar) ∆Pn ) pressure drop in the nth reactor (bar) ∆THX ) design differential temperature in the heat exchanger (K) ) voidage of bed λ ) heat of reaction [kJ/(kmol of C produced)] µ ) average gas mixture viscosity (kg m-1 s-1) F ) gas density (kg m-3) Fcat ) catalyst-bed density (kg m-3)

Literature Cited (1) Amundson, N. R.; Bilous, O. Chemical Reactor Stability and Sensitivity. II: Effect of Parameters on Sensitivity of Empty Tubular Reactors. AIChE J. 1956, 2, 116. (2) Amundson, N. R.; Bilous, O. Optimum Temperature Gradients in Tubular Reactors. Chem. Eng. Sci. 1956, 5, 81 and 115. (3) Douglas, J. M.; Eagleton, L. C. Analytical Solutions for Some Adiabatic Reactor Problems. Ind. Eng. Chem. Fundam. 1962, 1, 116. (4) Douglas, J. M.; Orcutt, J. C.; Berthiaume P. W. Design and Control of Feed-Effluent Exchanger-Reactor Systems. Ind. Eng. Chem. Fundam. 1962, 1, 253.

(5) Silverstein, J. L.; Shinnar, R. Effect of Design on the Stability and Control of Fixed-Bed Catalytic Reactors with Heat Feedback: I Concepts. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 241. (6) Tyreus, B. D.; Luyben, W. L. Unusual Dynamics of a Reactor/Preheater Process with Deadtime, Inverse Response and Openloop Instability. J. Process Control 1993, 3 (4), 241. (7) Luyben, W. L. External and Internal Open-Loop Unstable Processes. Ind. Eng. Chem. Res. 1998, 37, 2713. (8) Bilden, C. S.; Dimian, A. C. Stability and Multiplicity Approach to the Design of Heat-Integrated PFR. AIChE J. 1998, 44 (12), 2703. (9) Luyben, W. L. Control of Outlet Temperature in Adiabatic Tubular Reactors. Ind. Eng. Chem. Res. 2000, 39, 1271. (10) Luyben, W. L. Design and Control of Gas-Phase Reactor/ Recycle Processes with Reversible Exothermic Reactions. Ind. Eng. Chem. Res. 2000, 39, 1529. (11) Luyben, W. L. Impact of Reaction Activation Energy on Plantwide Control Structures in Adiabatic Tubular Reactor Systems. Ind. Eng. Chem. Res. 2000, 39, 2345. (12) Luyben, W. L. Effect of Kinetics, Design, and Operating Parameters on Reactor Gain. Ind. Eng. Chem. Res. 2000, 39, 2384. (13) 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. (14) Reyes, F.; Luyben, W. L. Extensions of the Simultaneous Design of Gas-Phase Adiabatic Tubular Reactor Systems with Gas Recycle. Ind. Eng. Chem. Res. 2001, 40, 635. (15) Reyes, F.; Luyben, W. L. Design and Control of a GasPhase Adiabatic Tubular Reactor Process with Liquid Recycle. Ind. Eng. Chem. Res. 2001, 40, 3762. (16) Reyes, F.; Luyben, W. L. Design and Control of Tubular Reactor Systems with Both Gas and Liquid Recycles. Ind. Eng. Chem. Res. 2001, 40, 4089. (17) Horn, F. Elektrochemie 1961, 65, 295. (18) Horn, F. Addition by Dr. Horn. Chem. Eng. Sci. 1961, 14, 20. (19) Lee, K. Y.; Aris, R. Optimal Adiabatic Bed Reactors for Sulfhur Dioxide with Cold Shot Cooling. Ind. Eng. Chem. Process Des. Dev. 1963, 2, 300. (20) Bildea, C. S.; Dimian, A. C.; Iedema, P. D. Multiplicity and Stability Approach to the Design of Heat-Integrated Multibed Plug Flow Reactor. Comput. Chem. Eng. 2001, 25 (1), 41. (21) Stephens, A. D. Stability and Optimization of a Methanol Converter. Chem. Eng. Sci. 1975, 30, 11. (22) Barkelew, C. H. Stability of Chemical Reactors. Chem. Eng. Prog. Symp. Ser. 1959, 55, 34. (23) Shinnar, R.; Doyle, F. J.; Budman, H. M.; Morari, M. Design Considerations for Tubular Reactors with Highly Exothermic Reactions. AIChE J. 1992, 38, 1729. (24) Filho, R. M.; McGreavy, C. The Influence of Configuration on Controller Design of Multi-Tubular Reactors. Comput. Chem. Eng. 1993, 17, 569. (25) Luyben, W. L. Design of Cooled Tubular Reactor Systems. Ind. Eng. Chem. Res. 2001, 40, 5775. (26) Luyben, W. L. Effect of Design and Kinetic Parameters on the Control of Cooled Tubular Reactor Systems. Ind. Eng. Chem. Res. 2001, 40, 3623. (27) Diemer, B. DuPont USA, Wilmington, DE. Personal communication, 2002. (28) Westerterp, K. R.; van Swaaij, W. P. M.; Beenackers, A. A. C. M. Chemical Reactor Design and Operation, 2nd ed.; John Wiley & Sons: New York, 1984. (29) Douglas, J. M. Conceptual Design of Chemical Processes; McGraw-Hill: New York, 1988.

Received for review September 24, 2002 Revised manuscript received April 8, 2003 Accepted April 8, 2003 IE020757U

Steady-State Economic Comparison of Alternative Tubular Reactor

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