Quantitative Comparison of Reactive Distillation with Conventional

Ind. Eng. Chem. Res. 2004, 43, 2493-2507

2493

PROCESS DESIGN AND CONTROL Quantitative Comparison of Reactive Distillation with Conventional Multiunit Reactor/Column/Recycle Systems for Different Chemical Equilibrium Constants Devrim B. Kaymak and William L. Luyben* Process Modeling and Control Center, Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015

Recent advances in technologies based on process intensification offer different design alternatives for chemical processes including reaction and separation units. An excellent example of process intensification is reactive distillation, which combines reaction and separation units in one piece of equipment. This paper studies the steady-state economic optimum design of a chemical process with a generic exothermic reversible reaction A + B T C + D for two different process flowsheets: a conventional multiunit reactor/separator/recycle structure and a reactive distillation column. Each system is optimized in terms of the total annual cost for a wide range of chemical equilibrium constants, KEQ. In the conventional system, the design optimization variables include the reactor temperature, reactor size, and recycle flow rate. In the reactive distillation system, the design optimization variables include the pressure, number of reactive trays, and number of total trays. The two systems are designed for identical feeds and identical products. Results show that reactive distillation is significantly less expensive (by a factor of up to 3) than the conventional process for all values of the chemical equilibrium constant. 1. Introduction If one of the most important operations in chemical engineering is separation, with distillation columns as its most popular process unit, reactors are the other vital parts of the chemical industry. Since reactor effluents fail to meet specification criteria because of the presence of unconverted materials, reactors followed by several distillation columns with recycle streams back to the reaction section are common in industry. Economic and environmental considerations have encouraged industry to focus on technologies based on process intensification. This is an area of growing interest that is defined as any chemical engineering development that leads to a substantially smaller and more energy-efficient technology.1 An excellent example of process intensification is reactive distillation, which combines reaction and separation units in a single vessel. Reactive distillation can, in some systems, provide an alternative to conventional multiunit flowsheets, which typically include a reactor followed by a separation section with recycles back to the reaction section. Although reactive distillation might be an attractive alternative to the conventional multiunit processes, it can be effective for only a fairly small class of chemical systems because of some inherent limitations. The relative volatilities of the reactants and the products should be such that the products can be removed from the reaction zone of the column easily while the reac* To whom correspondence should be addressed. Tel.: 610758-4256. Fax: 610-758-5057. E-mail: [email protected].

tants remain in the column. This means that the products should be lighter or heavier than the reactants. The temperatures of reaction and separation should be similar because both of these operations occur in the same unit simultaneously. The reaction should be fairly fast, so that the liquid holdups or amounts of catalyst required on each reactive tray are feasible in light of hydraulic limitations (reasonable tray liquid heights). Heats of reaction cannot be too large because of their impact on the vapor and liquid flow rates throughout the reactive zone. For example, if the reaction is exothermic, the liquid flow rates decrease from tray to tray down through the reactive section of the column, and the vapor flow rates increase from tray to tray up through the reactive section. If the heat of reaction is large, hydraulic problems such as weeping or flooding can occur. If reactive distillation is suitable for a chemical system, then this process provides several advantages over the conventional flowsheet. Because products are continuously removed from the reactive zone, the conversion can increase significantly. The selectivity can also be increased because of the continuous separation between reactants and products. A reduction of total investment and operating costs is usually achieved through the simplification of the process flowsheet by the elimination of some process units and direct heat integration between reaction and separation in the same vessel. On the other hand, because reactive distillation systems have a smaller number of control degrees of freedom than conventional multiunit reactor/separation/

10.1021/ie030832g CCC: $27.50 © 2004 American Chemical Society Published on Web 04/17/2004

2494 Ind. Eng. Chem. Res., Vol. 43, No. 10, 2004

recycle systems, they can have worse dynamics, and their controllability can be more difficult. For a given feed flow rate, a reactive distillation column has the same control degrees of freedom as a single conventional column (four control valves give four control degrees of freedom). A conventional multiunit flowsheet has four control degrees of freedom for each column, plus the two control valves on the reactor (coolant flow rate and reactor effluent). One of the most fundamental differences between reactive distillation and a conventional flowsheet is the selection of operating temperatures. In the conventional system, the reactor temperature can be set at an optimum value, and the distillation temperatures can be independently set at their optimum values (by adjusting column pressures). In reactive distillation, these temperatures are not independent. Therefore, reactive distillation has fewer design degrees of freedom to be used to optimize the flowsheet. The application of reactive distillation in the chemical and petroleum industries has increased rapidly in the past decade.2 Following the pioneering paper3 published by Eastman Chemical discussing the reactive distillation of methyl acetate, many other papers and patents have explored the use of this process for other chemical operations. A number of specific chemical systems have been studied in the literature. Chapter 10 of the recent textbook by Doherty and Malone4 presents an excellent summary of 61 different reactive distillation systems. Another list of industrial applications of reactive distillation with 75 examples is given in the first chapter of a recent book on reactive distillation.5 This work states that the most common applications of reactive distillations are etherification and esterification reactions. Although reactive distillation can be effectively used for systems with a wide variety of chemical equilibrium constants, the normal range of values for KEQ is between 1 and 50. Because a reactive distillation column has more design variables than a conventional column, the design of such systems is more difficult. The column pressure, the catalyst holdup on each tray, and the positions of the feed trays are important design considerations. In addition to stripping and rectifying sections, there is one more column section (the reactive zone). Also, the assumption of constant molar overflow is not valid if the reactions are not thermally neutral. Several papers have optimized reactive distillation columns by minimizing the objective function in terms of total annual cost (TAC).6-10 All of these papers proposed different optimization methods for reactive distillation systems and illustrated their methods with examples of specific chemical systems. Only a few papers have appeared in the literature that compare reactive distillation flowsheets with other process flowsheets.11-13 Siirola11 claimed that both the capital and energy costs of the reactive/extractive distillation column design for methyl acetate production are 5 times lower than those of the conventional design. The results in terms of TAC reported by Chiang et al.12 for the amyl acetate process indicated that reactive distillation is 4 times more efficient than the coupled reactor/ separator system. However, Stitt13 claimed that reactive distillation for toluene disproportionation did not offer significant economic benefits. The purpose of this paper is to quantitatively compare the designs of two different process flowsheets: (1) a

conventional multiunit reactor/separator/recycle structure and (2) a reactive distillation column. Both of the flowsheets are designed to achieve the steady-state economic objective of minimum total annual cost for a wide range of chemical equilibrium constants, KEQ. Systematic design procedures for both flowsheets are developed as three-dimensional optimization problems with some heuristic rules and engineering assumptions. The effects of design parameters on the optimum design variables and total annual costs are studied for both process designs. The two flowsheets have identical feeds and produce identical products. The vapor-liquid equilibrium used in this paper is ideal with constant relative volatilities. The rationale for considering ideal systems is to start with a simple system in which the complexities of nonideality do not cloud the issues and the results and some general conclusions are possible. The occurrence of azeotropes is very specific to the particular chemical system considered. We wish to strip away such complexities so that the fundamental differences between the two flowsheets can be fairly compared. Future work will explore the impact of temperature-dependent relative volatilities on the two processes. It is expected that there will be a significant effect on the comparison because of the coupling of the distillation temperatures and the reaction temperatures in the reactive distillation process. In the conventional flowsheet, the reactor temperature and the column temperatures can be set independently. 2. Process Studied The basic process considered consists of a reversible liquid-phase reaction

A+BSC+D

(1)

The forward and backward specific reaction rates, following the Arrhenius law, are given by

kF ) aFe-EF/RT

(2)

kR ) aRe-ER/RT

(3)

The rate law is based on concentrations in mole fractions and liquid holdups in kilomoles. The forward reaction rate is specified as 0.008 kmol s-1 kmol-1 at 366 K. Taking (KEQ)366 equal to 2 as a base case, the reverse reaction rate at this temperature is varied by selecting a range of (KEQ)366 values between 0.5 and 50.

(kR)366 )

(kF)366 (KEQ)366

(4)

Therefore, for different values of (KEQ)366, different values of the preexponential factor aR are calculated. Both reaction rates are temperature-dependent, and the reverse reaction rate is different for each case of (KEQ)366 selected. Note that the ratio of kF to kR is not equal to (KEQ)366 at temperatures other than 366 K because the activation energies are different. Rather, because the reaction is exothermic, the reverse reaction rate is more temperature-dependent than the forward reaction rate. Ideal vapor-liquid equilibrium is assumed with constant volatilities. The volatilities of the components are such that RC > RA > RB > RD. Hence, the reactants are intermediate boiling between the two products, which

Ind. Eng. Chem. Res., Vol. 43, No. 10, 2004 2495

3. Conventional Process Design

Table 1. Physical Data for the Process parameter reaction activation energy forward reverse specific reaction rate at 366 K forward reverse average heat of reaction, λ average heat of vaporization, ∆HV molecular weight of the mixture, Mw ideal gas constant relative volatilities RA RB RC RD vapor-pressure A constantsa AVP 12.34 BVP 3862

units

value

cal/mol 30 000 40 000 kmol/(s‚kmol) cal/mol cal/mol

0.008 0.008/(KEQ)366 -10 000 6944

g/mol

50

cal/(mol K)

1.987 4 2 8 1

B

C

D

11.65 3862

13.04 3862

10.96 3862

ln PSj ) AVP,j - BVP,j/T, with temperature in Kelvin and vapor pressure in bar. a

is the ideal situation for reactive distillation. Kinetic and physical properties and vapor-liquid equilibrium parameters are listed in Table 1 and are taken from Luyben.14 It should be emphasized that the two flowsheets have identical feeds and produce identical products. In addition, the economic factors (energy cost and capital cost of columns and heat exchangers) are the same in the two processes.

Figure 1. Detailed system flowsheet for the conventional design.

Figure 1 presents a detailed flowsheet of the process with notation. The reaction occurs in a continuous stirred tank reactor (CSTR) with holdup VR. There are two fresh feed streams F0A and F0B that contain pure reactants A and B, respectively, and a recycle stream D2 that returns from a downstream unit. The reactor effluent contains a multicomponent mixture because complete one-pass conversion is not achieved. Two columns are needed to separate the two products from the intermediate-boiling reactants. This effluent is fed into the first distillation column to separate product C from unreacted reactants A and B and heavy product D. The product C leaves in the distillate of first column with the desired purity, and other components serve as a feed to the second column. This column produces a bottoms stream of D with the desired purity, and a distillate of unreacted reactants A and B is recycled back to the reactor with a specific amount of product impurities. One of the main problems in developing a steady-state process flowsheet is finding the number of design degrees of freedom, which can be done by subtracting the number of chemical and physical equations (total and component balances, VLE relations) describing the system from the total number of variables (see Table 2). The number of design degrees of freedom for this multiunit process is 12. Subtracting the number of specifications and safety and environmental constraints from the number of degrees of freedom gives the number of design optimization variables. 3.1. Assumptions and Specifications. It is assumed that there is equimolal overflow in the distilla-

2496 Ind. Eng. Chem. Res., Vol. 43, No. 10, 2004 Table 2. Design Degrees of Freedom variables

equations

compositions component balances reactors zj 3 reactor 3 tray liquid xn,j 3∑N trays 3∑N tray vapor yn,j 3∑N bases 6 6 reflux drums 6 reflux drums xD,j base liquid xB,j 6 total balances base vapor yB,j 6 reactor 1 flows bases 2 fresh feeds F0,j 2 reflux drums 2 reactor effluent F 1 VLE vapor boilups Vn 2 trays 3∑N distillates Dn 2 bases 6 bottoms Bn 2 refluxes Rn 2 reactor holdup VR 1 reactor temperature TR 1 numbers of trays stripping NS,n 2 rectifying NR,n 2 total number of variables ) 6∑NT + 38 total number of equations ) 6∑NT + 26 number of design degrees of freedom ) 12

tion columns, which means that neither energy balances nor total balances are needed on the trays for steadystate calculations. Other assumptions are constant relative volatilities, isothermal reactor operation, theoretical trays, saturated liquid feed and reflux, and total condensers and partial reboilers in the columns. Additional assumptions and specifications are as follows: (i) In all cases, the net production rates are set by fixing the fresh feed flow rates of pure components A and B at F0A ) 12.60 mol/s and F0B ) 12.60 mol/s, respectively. (ii) The amount of reactant A lost in product stream D1 is constant at Aloss ) 0.63 mol/s (xD1,A ) 0.05 mole fraction). No B or D is going overhead, i.e., xD1,B ) xD1,D ) 0. (iii) The bottoms product stream B2 contains some amount of component B as an impurity, Bloss ) 0.63 mol/s (xB2,B ) 0.05 mole fraction). No A or C is going out the bottoms, i.e., xB2,A ) xB2,C ) 0. (iv) The impurity of product C in recycle stream D2 is xD2,C ) 0.05. (v) The impurity of component D in recycle stream D2 is xD2,D ) 0.05. (vi) As a result of the previous two assumptions and the fact that C and D have identical stoichiometric coefficients, the concentrations of components C and D in the reactor, zC and zD, are equal for all cases (zC ) zD) but vary in value from case to case. (vii) The column pressures are set using the vapor pressures, PS, of pure components and the liquid compositions in the reflux drum, xD,j, at 320 K (so that cooling water can be used in the condenser). (viii) In each column, the reflux ratio, RR, is 1.2 times the minimum reflux ratio, RRmin, calculated via the Underwood equations. (ix) In each column, the number of stages (or trays), NT, is twice the minimum number of stages, NTmin, calculated via the Fenske equation. (x) Kirkbride’s method is used to find the optimal feed tray location, NF. Through these assumptions, nine of the design degrees of freedom are used as follows: one for the production rate, two for product impurities, two for recycle impurities, and four for total tray numbers and optimum feed tray locations. This reduces the steadystate economic optimization to a three-dimensional

search with the following optimization variables: (1) the molar holdup in the reactor VR, (2) the composition of reactant B in the reactor zB, and (3) the reactor temperature TR. Also, several different specifications for assumptions ii-v are used to investigate the effects of product quality, conversion and recycle impurities on the economically optimal steady-state design. However, these variations do not affect the general structure of the design procedure. A grid-search optimization strategy is used in this work to find the optimum values of the three design optimization variables. Other methods, such as gradient nonlinear programming techniques, could be used. However, the grid method is more robust because a numerical programming method can easily drive the process into an infeasible region in which the specified purities and production rates cannot be achieved. 3.2. Steady-State Design Procedure. The following steps in the design procedure are employed utilizing the material balances and specifying necessary variables. The production rates of components C and D (RC and RD) are given by

RC ) RD ) VR(kFzAzB - kRzCzD)

(5)

(i) Fix the value of reactor temperature TR at a small value. (ii) Fix the value of reactor holdup VR at a small value. (iii) Specify the value of reactor composition zB. (iv) Using the assumption of equal compositions zC and zD in the reactor, calculate the concentration zA by rearranging eq 5 to give

zA )

x[

{

1 kF 4 z + 2(1 - zB) ( 2 kR B kF 4 zB + 2(1 - zB) kR

] [ 2

RC - 4 (1 - zB)2 + 4 VRkR

]}

(6)

(v) Calculate the product concentrations zC and zD in the reactor as

zC ) z D )

1 - zA - zB 2

(7)


(vi) Calculate the distillate product flow rate and compositions for the first column

D1 ) RC + Aloss

(8)

xD1,A ) Aloss/D1

(9)

xD1,C ) RC/D1

(10)

(vii) Calculate the bottoms flow rate and compositions for the second column

B2 ) RD + Bloss

(11)

xB2,B ) Bloss/B2

(12)

xB2,D ) RD/B2

(13)

(viii) Apply a steady-state total molar balance, which can be used because the reactions are equimolar. This balance, the two steady-state component balances, and a mole fraction summation around the reactor are

F0A + F0B + D2 ) F

(14)

F0A + D2xD2,A ) FzA + RC

(15)

F0B + D2xD2,B ) FzB + RD

(16)

xD2,A + xD2,B + xD2,C + xD2,D ) 1

(17) Figure 2. Reactive distillation column.

Solve these four equations for the four unknowns: the recycle stream flow rate D2, the reactor effluent flow rate F, and the reactant compositions in second distillate stream xD2,A and xD2,B. The combination of eqs 14-17 yields

D2 )

(F0A + F0B)(zA + zB - 1) + RC + RD (1 - xD2,C - xD2,D) - zA - zB F ) F0A + F0B + D2 xD2,A )

FzA + RC - F0A D2

xD2,B ) (1 - xD2,C - xD2,D) - xD2,A

(18) (19) (20) (21)

(ix) Use the total mass balance and component balances around the first column to calculate the bottoms flow rate and compositions for that column

B1 ) F - D1 xB1,j )

Fzj - D1xD1,j B1

(22) (23)

(x) Now that the feed, bottoms, and distillate flow rates and compositions are known for both columns, use the Fenske equation to calculate the minimum number of trays. Set the actual number of trays equal to twice the minimum. Then use the Underwood equations to calculate the minimum reflux ratio. For sizing purposes, set the actual reflux ratio equal to 1.2 times the minimum value.

(xi) Using these data, calculate the total annual cost (TAC) by combining the energy cost with the annual capital cost, using a payback period. All of the terms and equations related to the sizing and economy of the process are given in section 5. (xii) Vary the value of zB over a wide range, and repeat steps iv-xi for each value of zB, generating the corresponding TAC. (xiii) Then, vary the value of the reactor holdup over a range, and repeat steps iii-xii. (xiv) Finally, vary the value of the reactor temperature over a wide range, and repeat steps ii-xiii for each temperature. Select the minimum in the TAC as the economically optimum steady-state design for the given (KEQ)366 value. 4. Reactive Distillation Design The reactive distillation alternative is shown in Figure 2. The column is fed with two pure reactant fresh feed streams: F0A and F0B. The column has three zones. There are NS trays and a partial reboiler in the stripping section. Above this section, there is a reactive zone with NRX reactive trays. The third section is the rectifying section with NR trays and a total condenser. Light reactant A is fed to the bottom tray of the reactive zone, while heavy reactant B is introduced at the top of the reactive section. Light product C leaves in the distillate, while heavy product D is removed from the bottoms. Because the light reactant goes up through the column after being fed on the bottom tray of the reactive zone, very little of component A is present in the bottoms. Likewise, heavy reactant goes down through the column after being fed on the top tray of the reactive


zone, so very little of component B is present in the distillate. Thus, the key components are light product C and light reactant A for the rectifying section. For the stripping section, the key components are heavy product D and heavy reactant B. 4.1. Assumptions and Specifications. The optimization of a reactive distillation column has a very large number of design variables. The following are the specifications and assumptions made to reduce the number of design variables for the economically optimum steady-state design: (i) The design objective is to obtain 95% conversion for fixed fresh feed flow rates of 12.6 mol/s. (ii) The product impurity of the distillate stream is xD,A ) 0.05. (iii) The product impurity of the bottoms stream is xB,B ) 0.05. (iv) The two feed points are at the two ends of the reactive zone. (v) The holdups are constant on the reactive trays at 1000 mol and in the other sections of the column at 400 mol. (vi) The numbers of stripping and rectifying trays are equal because the relative volatilities between the components being separated in the two sections are the same. In the rectifying section, the separation is between C and A, where the relative volatility is RC/RA ) 2, and in the stripping section, the separation is between B and D, where the relative volatility is RB/RD ) 2. With these specifications and simplifying assumptions, there are three optimization variables: (1) the column pressure P, (2) the number of reactive trays NRX, and (3) the number of the separating (stripping/rectifying) trays NS (or NR). Specifications ii and iii are changed during the study to investigate the effects of product quality and conversion on the economically optimal steady-state design. However, this does not affect the general structure of the design procedure. 4.2. Steady-State Design Procedure. Simultaneous solution of the very large set of nonlinear and algebraic equations is difficult, especially with the high degree of nonlinearity due to reaction kinetics. The relaxation method is efficient and robust in solving this large set of equations. This method is used to calculate mole fractions and temperature profiles through the column. In general, relaxation methods use the equilibrium-stage model equations in unsteady-state form and integrate them numerically until the steady-state solution is found. Here, the liquid holdups on the trays are assumed constant, i.e., instantaneous hydraulics. A general schematic diagram of an equilibrium tray in the reactive zone, from which the equations for a dynamic model can be derived, is shown in Figure 3. The net reaction rate for component j on tray i in the reactive zone is given by

Ri,j ) νjMi(kFixi,Axi,B - kRixi,Cxi,D)

(24)

where νj is the stoichiometric coefficient of component j. The steady-state vapor and liquid flow rates are constant through the stripping and rectifying sections because equimolal overflow is assumed. However, these rates change through the reactive zone because of the exothermic reaction. The heat of reaction vaporizes some liquid on each tray in that section; therefore, the vapor flow rate increases up through the reactive zone, and

Figure 3. Reactive tray.

the liquid flow rate decreases down through the reactive zone.

Vi ) Vi-1 -

λ R ∆HV i,C

(25)

Li ) Li+1 +

λ R ∆HV i,C

(26)

The dynamic component balances for the column are as follows:

reflux drum d(xD,jMD) ) VNTyNT,j - D(1 + RR)xD,j dt

(27)

rectifying and stripping trays d(xi,jMi) ) Li+1xi+1,j + Vi-1yi-1,j - Lixi,j - Viyi,j dt

(28)

reactive trays d(xi,jMi) ) Li+1xi+1,j + Vi-1yi-1,j - Lixi,j - Viyi,j + Ri,j dt (29) feed trays d(xi,jMi) ) Li+1xi+1,j + Vi-1yi-1,j - Lixi,j - Viyi,j + dt Ri,j + Fizi,j (30) column base d(xB,jMB) ) L1x1,j - BxB,j - VSyB,j dt

(31)

With the equimolal overflow assumption mentioned above, all of the vapor rates, Vi, throughout the stripping section are equal to VS, and all of the liquid rates, Li,


are equal to LS. Analogously, all of the vapor rates, Vi, beginning from the top feed tray throughout the rectifying section and total condenser are VNT, and all of the liquid rates, Li, are equal to LR. The vapor-liquid equilibrium is assumed to be ideal. Column pressure P is optimized for each case. With given pressure P and tray liquid composition xi,j, the temperature Ti, and the vapor composition yi,j can be calculated. This is a bubble-point calculation and can be solved by a Newton-Raphson iterative convergence method. NC

P)

S xi,jPi,j(T) ∑ j)1

S Pi,j yi,j ) x P i,j

(32)

Table 3. Sizing and Economic Basis parameter reboiler heat-transfer coefficient, UR temperature difference, ∆TR condenser heat-transfer coefficient, UC temperature difference, ∆TC energy cost payback period, βpay

units

value

kJ/(s‚K‚m2) K

0.568 34.8

kJ/(s.K.m2) K $/106 kJ year

0.852 13.9 4.7 3.0

can be easily observed from the continuously increasing vapor boilup, and the simulation can be restarted in such cases with new optimization variables. 5. Sizing and Economic Basis

(33)

With a fixed value of the kinetic parameter (KEQ)366, the following steps in the design procedure are used: (i) Fix the column pressure P at a small value. (ii) Fix the number of stripping trays NS and the number of rectifying trays NR at a small value. (iii) Specify the number of the reactive trays NRX. (iv) Fix the flow rates of the two fresh feeds at 12.60 mol/s. (v) Fix the flow rates of the distillate and bottoms at 12.60 mol/s. (vi) Manipulate the vapor boilup VS with a P controller to control the level in the column base. Do not control the reflux drum level. (vii) Manipulate the reflux flow rate with a PI controller to drive the composition of product C in the distillate to its desired value. This also sets the purity of the bottoms product D and the conversion in the reactive zone to their desired values. (viii) Compute the vapor compositions and temperatures on each tray using bubble-point calculations. (ix) Compute the reaction rates with eq 24. (x) Calculate the vapor rates using eq 25 and assuming equimolal overflow through the stripping and rectifying sections. (xi) Calculate the liquid flow rates from eq 26 with the same assumption as in step x. (xii) Evaluate the time derivatives of the component material balances using eqs 27-31. (xiii) Integrate all of the ODEs using the Euler algorithm. (xiv) Repeat steps vi-xiii until the system achieves the convergence criterion, which is CC ) max |dxi,j/dt| e 10-6 (the largest time derivative of any component on any tray is less than 10-6). (xv) With the data obtained, calculate the total annual cost (TAC) by combining the energy cost with the annual capital cost. (xvi) Vary the number of reactive trays over a wide range, and repeat steps iv-xv for each value of NRX, generating its corresponding TAC. (xvii) Then, vary the number of the stripping and rectifying trays over a range, and repeat steps iii-xvi. (xviii) Finally, vary the value of the column pressure over a wide range, and repeat steps ii-xvii for each pressure value. Select the design with the minimum TAC as the economically optimum steady-state design for the given (KEQ)366 value. Depending on the values of optimization variables chosen, the column can leave the feasible region. This

The economic basis for the calculations involves an objective function that sums the capital and energy costs of the process assuming a payback period (βpay) for capital. Total annual cost is defined as

TAC ) energy cost +

capital investment (34) βpay

Table 3 summarizes the economic parameters and the basis of the equipment sizing calculations. The capital costs of individual equipment and the energy cost are estimated using the following equations15

reactor cost ) 52 920DR1.066LR0.802

(35)

column cost ) 17 640DC1.066LC0.802

(36)

tray cost ) 229DC1.55NT

(37)

heat exchanger cost ) 7296AR0.65 + 7296AC0.65 (38) energy cost ) 0.6206∆HVVS

(39)

The terms involved in the TAC equations are calculated from the following set of assumptions and guidelines: (i) The diameter of the reactor is calculated from

DR ) (3.977 × 10-5VR)0.3333

(40)

(ii) The reactor length is assumed to be twice the diameter.

LR ) 2DR

(41)

(iii) Assuming an F factor of 1 in engineering units, the diameter of the column is calculated from the equation

DC ) 1.735 × 10-2

( ) MwT P

0.25

VNT0.5

(42)

(iv) The column height is calculated assuming a 0.61-m (2-ft) tray spacing and allowing 20% more height for base-level volume.

LC ) 0.731 52NT

(43)

(v) The heat-transfer areas of the reboiler and condenser are calculated using the steady-state vapor flow


Figure 4. TAC for the base case of (KEQ)366 ) 2.00 with constant reactor temperature TR ) 367 K.

rates and the heat of vaporization.

VS∆HV AR ) 0.0042 UR∆TR

(44)

VNT∆HV UC∆TC

(45)

AC ) 0.0042

The vapor flow rate in the top tray, VNT, is higher than the vapor flow rate in the reboiler, VS, because of the liquid vaporized through the reactive section. Thus, the heat-transfer areas of the reboiler and condenser are calculated using two different vapor rates. (vi) The two processes are assumed to be equally reliable and to operate for 365 days per year. 6. Results and Discussion 6.1. Conventional Process Design. Figure 4 shows a plot of the total annual cost (TAC) for the base case, (KEQ)366 ) 2, with the constant reactor temperature TR ) 367 K. The TAC is plotted versus the reactor holdup, VR, and the composition of component B in the reactor, zB. The reactor holdup and the reactor composition of component B were varied in increments of 2.5 kmol and 0.025, respectively, yielding a total of 360 different designs. With an in-depth look, Figure 5 displays how several design parameters are affected by the variation of the optimization variables VR and zB, and Figure 6 shows how capital cost and energy cost vary. Both figures are plotted versus zB for three different values of reactor holdup VR with the fixed temperature TR ) 367 K. Figure 5 demonstrates that the reactor effluent contains a higher concentration of reactant components as the reactor size decreases. Thus, there is a need of more vapor boilup to achieve the desired product specifications and an increase in recycle flow rate with smaller reactor holdup. Increasing zB decreases zA for a given reactor holdup. The vapor boilup in the first column, VS1, decreases because there is less A to be separated from C. As the value of zB increases, the vapor boilup in the second column, VS2, starts to increase because there is more B to take overhead. The process can be operated at any point on this curve with the same production rate for this given VR, but the reactor effluent F, the flow rate of bottoms stream B1, and the flow rate of recycle stream D2 will vary, as shown in the lower graphs of Figure 5. There is a value of zB that produces

a minimum reactor effluent flow rate, and this occurs in the region where the compositions of the two reactants are similar because the reaction rate depends on the product of the two reactant concentrations. The optimum design point is shown on each graph as an open circle. Figure 6 shows that a larger reactor size results in a higher capital cost but a lower energy cost because of the lower vapor boilup requirement for all values of zB. From the same figure, it is clear that for all reactor holdups there is a minimum in both the capital cost and energy cost at a specific value of zB at which the concentrations of zA and zB are similar. Thus, there should be a minimum in the total cost around this value of zB because of the tradeoff between increasing capital cost and decreasing energy cost. Figures 7 and 8 provide results for the base case using a range of reactor temperatures as the third optimization variable. All of the results in both figures are the economically optimal steady-state values at the given temperature. The specific reaction rates in the reactor increase with increasing temperatures. Figure 7 shows that increasing the temperature decreases the reactor holdup (VR) for a specified rate of production of C and D. This means that higher temperature results in lower reactor cost, as shown in Figure 8. On the other hand, the column cost, the heat exchanger cost, and the energy cost all depend on the vapor boilups in the system. It can be seen from Figure 7 that there are minima in the vapor boilup curves at certain values of reactor temperature. Because the optimum value of VR decreases with increasing reactor temperature, the per-pass conversion in the reactor decreases. Thus, the reactor effluent F contains more reactant components A and B at higher temperatures. Another reason for the increase in the reactant contents in the reactor effluent is that the equilibrium constant KEQ decreases with increasing temperature for exothermic reactions. More reactants fed to the columns result in an increase in reflux and vapor boilup required to achieve the desired purities of product streams. Therefore, these separation costs increase when the reactor temperature gets high. Because of the decreasing reactor cost, the total capital cost decreases with the increase in temperature up to a certain value. Figure 8 shows, however, that above this temperature, the increasing column cost and heat exchanger cost are more dominant and result in increasing total capital cost. The total annual cost reaches a minimum at a certain reactor temperature because of the tradeoff between reactor cost and separation cost. The optimum reactor temperature for this base-case value of (KEQ)366 is 367 K. The optimum values of the other optimization variables at the optimum temperature are VR ) 102.5 kmol and zB ) 0.225. Other important design parameters are the recycle flow rate D2 (22.89 mol/s) and the composition of component A in the reactor (zA ) 0.2296). Figure 9 presents results for different (KEQ)366 values. The first graph shows that at higher values of (KEQ)366 the total annual cost (TAC) of the system decreases. The optimum temperature increases as the value of (KEQ)366 increases. Reactor holdups decrease for all kinetic cases as the temperatures increase. The lower graphs show that higher values of (KEQ)366 result in lower values of the recycle stream and vapor boilup. The curves of the recycle stream and vapor boilup of second column exhibit minima at certain values of reactor temperature.


Figure 5. Effects of optimization variables VR and zB for the base case of (KEQ)366 ) 2.00 with the constant temperature TR ) 367 K.

Figure 6. Effects of optimization variables VR and zB on design costs for the base case of (KEQ)366 ) 2.00 with the constant temperature TR ) 367 K.

For each kinetic case, the shapes of the curves are similar, but they have minima at different temperatures. For both low and high temperatures, the increase of these flow rates occurs because of the higher reactant compositions in the reactor effluent, as shown in Figure 7 for the base case, (KEQ)366 ) 2. As mentioned before, higher temperatures give smaller reactor holdups VR and lower equilibrium constants KEQ, which give higher reactant concentrations. However, low temperatures give small specific reaction rates, meaning that more reactant leaves the reactor. Therefore, higher vapor boilup is required in the columns to obtain the product streams with specified purities. Optimization results for the conventional design for all cases are summarized in Table 4. These are the optimum designs in terms of the reactor temperature, the reactor holdup, and the composition of component B in the reactor. Optimal operating conditions for the same cases are reported in Table 5. The column pres-

Figure 7. Effects of optimization variable TR for the base-case (KEQ)366 ) 2.00 design.

sures are set using the vapor pressures, PS, of the pure components at 320 K and the liquid compositions in the reflux drum, xD,j. In a conventional multiunit process, the column temperatures can be set independently so as to optimize column efficiency. The reactor temperature can then be independently adjusted to its optimum. This is not the case in reactive distillation because both reaction and separation are occurring in the same vessel, operating at a single pressure. The effect of the conversion design value is explored by increasing the conversion from 95 to 99%. Increasing the conversion means that the product purities increase (less unreacted A and B are lost in the product streams) and the optimum values of all of the design parameters change. Figure 10 gives results for all of the (KEQ)366 cases. The vapor boilup required to achieve 99% conversion increases, as does the flow rate of the recycle stream, D2. The reactor holdups are almost the same for both conversions. These results illustrate that, as


Figure 8. Effects of optimization variable TR on design costs for the base-case (KEQ)366 ) 2.00 design.

Figure 9. Optimization results for different kinetic cases. Table 4. Optimization Results for the Conventional Design (KEQ)366 0.5 design variables TR (K) VR (kmol) zB capital costs ($103) reactor heat exchanger column tray energy cost ($103/year) TAC ($103/year)

1.0

2.0

5.0

10.0

50.0

356.0 362.0 367.0 373.0 379.0 395.0 222.5 145.0 102.5 82.5 60.0 25.0 0.275 0.250 0.225 0.175 0.150 0.110 358.6 630.1 293.3 9.5 502.9 933.4

274.7 565.7 268.1 8.3 425.4 797.7

221.3 509.6 245.8 7.3 361.9 689.9

193.3 444.2 217.9 6.1 292.8 580.0

158.6 407.2 202.4 5.5 256.3 514.2

91.9 341.3 175.0 4.4 195.7 399.9

expected, the TAC of the system increases when a higher conversion is required. Figure 11 shows the effect of impurities in the D2 recycle stream on the total annual cost for the base case, where (KEQ)366 is 2. The impurities of both components

C and D are simultaneously varied from 0.001 to 0.125. The TAC decreases with higher amounts of impurities. The reactor holdup also decreases, whereas the recycle flow rate and vapor boilup of the second column increase. Although there is an initial large decrease in TAC as impurities are increased from 0.001, the change in TAC is not very significant above an impurity value of about 0.05. Therefore, xD2,C ) xD2,D ) 0.05 is used as the base impurity level for other kinetic cases. 6.2. Reactive Distillation Design. Figure 12 shows the effects of separation stages on the economically optimum steady-state design of a reactive distillation column with three different operation pressures. The results are given for the base case, (KEQ)366 ) 2, with a number of constant reactive trays, NRX ) 9. The graph in the middle shows that the column cost increases as the number of separation trays increase. It also shows that a decrease in the operation pressure results in an increase in the column cost for any number of separation trays because decreasing the pressure results in a lower density, which increases the column diameter. The right graph indicates that the higher the number of separation stages, the lower the vapor boilup required. More stripping and rectifying stages provide the required separation while using less energy. Because the temperature of the reactive zone increases with increasing column pressure, it decreases the chemical equilibrium constant, which results in an increase in the amounts of reactant leaving the reactive zone. Therefore, the right graph also shows that operating at higher pressure increases the vapor boilup required to meet desired product specifications. The left graph of Figure 12 shows that there is a minimum in the total annual cost curve at a certain number of separation trays because of the tradeoff between increasing column cost and decreasing costs related to the vapor boilup, such as energy and heat exchanger costs. The overlapping TAC curves for different pressures show that there is an optimum pressure. This occurs because of the competing effects

Ind. Eng. Chem. Res., Vol. 43, No. 10, 2004 2503 Table 5. Optimal Operating Conditions of Conventional Design (KEQ)366 parameter

0.5

1.0

2.0

5.0

10.0

50.0

40.39 82.50 373.00 0.0174 0.0045 0.1947 0.1750 0.3151 0.3151

36.65 60.00 379.00 0.0329 0.0053 0.1655 0.1500 0.3422 0.3422

31.20 25.00 395.00 0.1653 0.0091 0.1035 0.1100 0.3933 0.3933

F (mol/s) VR (kmol) TR (K) kF (s-1) kR (s-1) zA zB zC zD

66.02 222.50 356.00 0.0025 0.0034 0.3005 0.2750 0.2122 0.2122

Reactor 55.81 48.09 145.00 102.50 362.00 367.00 0.0051 0.0090 0.0044 0.0046 0.2662 0.2296 0.2500 0.2250 0.2419 0.2727 0.2419 0.2727

B (mol/s) D (mol/s) VS (mol/s) R (mol/s) P (bar) xD,A xD,B xD,C xD,D xB,A xB,B xB,C xB,D NT NF DC (m) AR (m2) AC (m2)

53.42 12.60 50.56 37.96 2.57 0.0500 0.0000 0.9500 0.0000 0.3596 0.3399 0.0382 0.2623 13 6 1.09 74.36 124.11

Column 1 43.21 35.49 12.60 12.60 44.57 39.56 31.97 26.96 2.57 2.57 0.0500 0.0500 0.0000 0.0000 0.9500 0.9500 0.0000 0.0000 0.3292 0.2933 0.3229 0.3049 0.0354 0.0322 0.3124 0.3695 13 13 6 7 1.03 0.97 65.56 58.18 109.42 97.11

27.79 12.60 34.67 22.07 2.57 0.0500 0.0000 0.9500 0.0000 0.2603 0.2543 0.0273 0.458 13 7 0.90 50.99 85.10

24.05 12.60 31.66 19.06 2.57 0.0500 0.0000 0.9500 0.0000 0.2261 0.2286 0.0238 0.5215 13 8 0.86 46.57 77.72

18.60 12.60 25.62 13.02 2.57 0.0500 0.0000 0.9500 0.0000 0.1397 0.1845 0.0161 0.6596 13 8 0.78 37.68 62.90

B (mol/s) D (mol/s) VS (mol/s) R (mol/s) P (bar) xD,A xD,B xD,C xD,D xB,A xB,B xB,C xB,D NT NF DC (m) AR (m2) AC (m2)

12.60 40.82 66.14 25.33 1.00 0.4706 0.4294 0.0500 0.0500 0.0000 0.0500 0.0000 0.9500 13 8 1.58 97.29 162.38

Column 2 12.60 12.60 30.61 22.89 54.15 44.42 23.54 21.54 0.99 0.98 0.4648 0.4548 0.4352 0.4452 0.0500 0.0500 0.0500 0.0500 0.0000 0.0000 0.0500 0.0500 0.0000 0.0000 0.9500 0.9500 13 13 8 7 1.43 1.30 79.65 65.34 132.93 109.06

12.60 15.19 33.28 18.09 1.00 0.4762 0.4238 0.0500 0.0500 0.0000 0.0500 0.0000 0.9500 13 7 1.12 48.96 81.71

12.60 11.45 27.82 16.37 1.00 0.4749 0.4251 0.0500 0.0500 0.0000 0.0500 0.0000 0.9500 13 6 1.03 40.92 68.30

12.60 6.00 19.80 13.80 0.97 0.4331 0.4669 0.0500 0.0500 0.0000 0.0500 0.0000 0.9500 13 6 0.87 29.12 48.61

of temperature on the reaction rates and the chemical equilibrium constant. For this case, five stripping and five rectifying trays are optimal for all pressures. Figure 13 reveals the effects of the number of reactive trays for the base case with the constant number of separation stages NR ) NS ) 5. The graph in the middle shows that increasing the number of reactive trays results in an increase in the column cost and that higher pressures lead to a lower column cost for any value of NRX. The right graph shows the effects of the number of reactive stages on the vapor boilup. As the number of reactive trays increases, the required vapor boilup initially decreases. However, increasing the number of reactive trays above the optimum results in an increase in the required vapor boilup. This occurs because the extra separation occurring with more stages concentrates the products in the reactive zone and shifts the chemical equilibrium back toward the reactants on the lower and upper reactive stages. This effect was dis-

Figure 10. Effects of conversion for different kinetic cases.

Figure 11. Effects of impurities in the recycle stream for the base case of (KEQ)366 ) 2.0.

Figure 12. Effect of number of separation stages for the base case of (KEQ)366 ) 2 with constant NRX ) 9.

cussed by Sneesby and co-workers.16 For example, the concentration of reactant A on the lowest reactive tray increases from 0.4425 to 0.5179 as NRX is changed from 9 (the optimum) to 11. The concentration of product D at the same location decreases from 0.4817 to 0.4322. Therefore, it takes more energy to keep component A


Figure 13. Effect of number of reactive stages for the base case of (KEQ)366 ) 2 with constant number of separation stages NR ) NS ) 5.

Figure 14. Effects of pressure on the vapor boilup for three different kinetic cases.

from leaving in the bottoms. Thus, there is an optimum number of reactive trays for each pressure that minimizes the vapor boilup, energy cost, and heat exchanger cost. The left graph of Figure 13 shows that there is a minimum in the total annual cost curve at a certain number of reactive trays because of the tradeoff between increasing column cost and decreasing vapor boilup. For this case, nine reactive trays are the optimum for all pressures. This figure also indicates that the optimum pressure is 8 bar for this specific case. Figure 14 shows the effect of operation pressure on vapor boilup. These results are for the three different kinetic cases (KEQ)366 ) 1, 2, and 5 with the number of reactive trays that is optimum for each case. The graph shows that there is an optimum pressure for all three cases that minimizes the vapor boilup. The higher values of (KEQ)366 require lower vapor boilups and operate at higher optimum column pressures. The higher equilibrium constant pushes the reaction to the right. The equilibrium constant decreases with increasing temperature for an exothermic reaction. Therefore, the column can operate at higher pressures when (KEQ)366 is larger. It is possible to conclude from this figure that the sensitivity to pressure increases as the value of (KEQ)366 decreases. Therefore, operating at the

Figure 15. Economically optimum results for three different kinetic cases.

optimum pressure is more important for small values of (KEQ)366 than for large values. This figure shows that the optimum pressures for (KEQ)366 ) 1, 2, and 5 are 6.5, 8.0, and 9.5 bar, respectively. Figure 15 gives the economic optimum steady-state design results for three different values of (KEQ)366. For each case, the optimum pressure that minimizes the vapor boilup is used, and the number of reactive trays is varied over a range to find the minimum total annual cost TAC. The upper graph shows that there is a minimum in the TAC curve at some optimum number of reactive stages. The optimum number of reactive stages decreases with increasing values of (KEQ)366. The column costs and total annual cost decrease as the value of (KEQ)366 increases. Results for five different kinetic cases are reported in Table 6. The table includes the optimum design parameters and costs in terms of the following optimization variables: (i) number of separation trays, (ii) number of reactive trays, and (iii) the column pressure. Also, the temperatures at the top and bottom of different sections are included in this table. Figure 16 shows the composition profile of the optimum design for the base case of (KEQ)366 ) 2. The highest composition of reactant A is at the bottom of reactive zone where A is fed. The other reactant, B, has its highest composition at the top of reactive zone, which is also its feed tray. While the composition of A decreases up through the reactive zone, the composition of product C increases. The reverse occurs for reactant B and product D through the reactive zone. The rest of the column operates as a separation unit. Thus, the composition of heavy product D increases down through the stripping section, and the composition of light product C increases up through the rectifying section. Figure 17 shows the temperature profiles of the optimum designs for the three different kinetic cases (KEQ)366 ) 1, 2, and 5. The temperature profiles of the three cases are similar, with higher temperatures for higher values of (KEQ)366. Fairly significant temperature breaks occur around tray 4 for all cases, and these tray temperatures can be used in control schemes to infer bottoms purity. A similar break occurs at different tray numbers near the top of the column for each case. These temperatures could be used to infer distillate purity. For all kinetic cases, the temperatures show little change in the reactive zone.

Ind. Eng. Chem. Res., Vol. 43, No. 10, 2004 2505 Table 6. Optimization Results of Reactive Distillation Design (KEQ)366 design variables NR and NS NRX P (bar) design temperatures (K) base bottom reactive top reactive reflux drum design parameters NT VS (mol/s) R (mol/s) DC (m) AR (m2) AC (m2) capital costs ($103) heat exchanger column tray energy cost ($103/year) TAC ($103/year)

0.5

1.0

2.0

5.0

10.0

50.0

6 18 5.5

5 13 6.5

5 9 8.0

5 6 9.5

6 4 11.0

5 3 16.0

415.8 382.0 365.1 341.5

423.1 386.7 383.3 346.6

432.8 394.0 393.9 353.2

441.0 400.7 402.6 358.9

449.0 407.7 409.7 363.8

467.6 422.5 428.4 377.3

30 34.86 39.50 0.935 51.28 127.90

23 31.74 36.38 0.873 46.68 120.23

19 28.51 33.14 0.805 41.93 112.30

16 24.36 29.00 0.738 35.83 102.12

265.1 195.5 6.2 150.2 305.9

252.8 146.8 4.3 136.8 271.4

239.7 115.5 3.1 122.8 242.3

222.3 91.8 2.3 105.0 210.5

Figure 16. Composition profile of the optimum design for the base case of (KEQ)366 ) 2.0.

Figure 17. Temperature profiles of optimum designs for different kinetic cases.

Figure 18 illustrates the effect of the conversion on the total annual cost for different pressures. The conversion is increased to 99%, and the optimal results

16 21.37 26.01 0.688 31.44 94.79 209.2 85.1 2.1 92.1 190.9

13 16.24 20.88 0.590 23.89 82.21 185.6 61.1 1.3 70.0 152.7

Figure 18. Effect of conversion for the base case of (KEQ)366 ) 2.0.

at each pressure are given for base kinetic case of (KEQ)366 ) 2. To achieve the required purity, the optimum number of separation stages is NS ) NR ) 7 for this case, which is 2 more than in the 95% conversion system. The optimum number of reactive stages is 13, which is 4 more than in the base case. The optimum pressure is the same (8 bar) as in the 95% conversion case. These results indicate that the TAC of the system increases when a higher conversion is required. 6.3. Comparisons. Comparisons of conventional reactor/separator/recycle and reactive column design configurations at their economically optimum steadystate designs are presented in Table 7 for five different kinetic cases. The results indicate that the TACs of both design configurations decrease as the value of (KEQ)366 increases. The results also show that the reactive distillation column configuration has lower capital and energy costs than the conventional configuration for all kinetic cases. These costs result in lower TACs for the reactive distillation columns compared to the reactor/ column/recycle systems.

2506 Ind. Eng. Chem. Res., Vol. 43, No. 10, 2004 Table 7. Economic Comparison of Two Different Process Flowsheets (KEQ)366 0.5

1.0

2.0

5.0

10.0

50.0

capital cost ($103) conventional 1291.5 1116.8 984.0 861.6 773.6 612.6 reactive column 466.8 403.9 358.4 316.4 296.4 248.1 3 energy cost ($10 /year) conventional 502.9 425.4 361.9 292.8 256.3 195.7 reactive column 150.2 136.8 122.8 105.0 92.1 70.0 TAC ($103/year) conventional 933.4 797.7 689.9 580.0 514.2 399.9 reactive column 305.9 271.4 242.3 210.5 190.9 152.7

7. Conclusion The economically optimum steady-state designs of a multiunit reactor/column/recycle process and a reactive distillation column are compared for different values of chemical equilibrium constants. Identical production targets and prices are used. Three optimization variables are used to find the optimal results for the two systems. The conventional system has the reactor holdup, the reactor temperature, and the composition of reactant B in the reactor as optimization variables, whereas the reactive column configuration has the number of separation stages, the number of reactive stages, and the column pressure as optimization variables. As (KEQ)366 becomes larger, the capital cost and the energy cost decrease for both configurations. These decreases result in a decrease of the TAC for both systems. When compared for different kinetic cases, reactive distillation columns have lower TACs than reactor/column/recycle systems for all values of (KEQ)366. Thus, eliminating a reactor and a column with heat exchangers reduces costs by a factor of 2-3. Ideal phase equilibrium is assumed in this study so that a clean comparison can be made and the systemspecific complexities of azeotropes do not cloud the fundamental issues. The results of this study should provide some general insights and guidance related to the differences between the two alternative flowsheets that arise because of fundamental structural differences and limitations. In this study, we assume that relative volatilities are constant and fairly large (R ) 2). Studies are underway to explore the effects of changes in the relative volatilities on the two flowsheets. Two types of changes will be considered: (1) The relative volatilities between adjacent products and reactants (RCA and RBD) will be reduced. We expect that this will increase the energy requirements in both flowsheets and increase the number of trays in the distillation columns of the conventional flowsheet and the number of stripping and rectifying trays in the reactive distillation column. There will probably be little impact on the optimum reactor temperature in the conventional process. There should be little effect on the optimum pressure of the reactive distillation column. However, the number of reactive stages might change. (2) The relative volatilities will be made temperature-dependent (decreasing with increasing temperature). This should emphasize the important difference between the two processes. Specifically, in the conventional flowsheet, the reactor and column can operate at different pressures. This is not true in reactive distillation. Future work will also compare the dynamics and controllabilities of the two systems.

Nomenclature aF ) preexponential factor for the forward reaction (kmol‚s-1‚kmol-1) aR ) preexponential factor for the reverse reaction (kmol‚s-1‚kmol-1) AC ) heat exchanger area for the condenser (m2) AR ) heat exchanger area for the reboiler (m2) B ) bottoms flow rate in the column (mol/s) D ) distillate flow rate in the column (mol/s) DC ) diameter of the column (m) DR ) diameter of the reactor (m) EF ) activation energy of the forward reaction (cal/mol) ER ) activation energy of the reverse reaction (cal/mol) F ) effluent flow rate from the reactor (mol/s) Fi ) feed flow rate on tray i (mol/s) F0j ) fresh feed flow rate of reactant j (mol/s) kF ) specific reaction rate of the forward reaction (kmol‚s-1‚kmol-1) kR ) specific reaction rate of the reverse reaction (kmol‚s-1‚kmol-1) KEQ ) equilibrium constant LC ) length of the column (m) Li ) liquid flow rate from tray i (mol/s) LR ) length of the reactor (m) LR ) liquid flow rate in the rectifying section (mol/s) MB ) liquid holdup in the column base (mol) MD ) liquid holdup in the reflux drum (mol) Mi ) liquid holdup on tray i (mol) Mw ) molecular weight of all species in the mixture (g/mol) NF ) feed tray in the column NR ) number of rectifying trays NRX ) number of reactive trays NS ) number of stripping trays NT ) number of trays in the column NTmin ) minimum number of trays in the column P ) column pressure (bar) S Pi,j ) vapor pressure of component j on tray i (bar) R ) ideal-gas-law constant (cal‚mol-1‚K-1) Rj ) rate of reaction for component j (mol/s) RR ) reflux ratio in the column RRmin ) minimum reflux ratio in the column Ti ) column temperature on tray i (K) TR ) temperature of the reactor (K) UC ) overall heat-transfer coefficient in the condenser (kJ‚s-1‚K-1‚m-2) UR ) overall heat-transfer coefficient in the reboiler (kJ‚s-1‚K-1‚m-2) Vi ) vapor flow rate from tray i (mol/s) VNT ) molar flow rate from the top of the column (mol/s) VR ) molar holdup of the reactor (mol) VS ) vapor boilup (mol/s) xB,j ) bottoms liquid composition of component j xD,j ) distillate liquid composition of component j xi,j ) liquid composition of component j on tray i yB,j ) bottoms vapor composition of component j yi,j ) vapor composition of component j on tray i zj ) mole fraction of component j in the reactor zi,j ) mole fraction of component j in feed tray i Greek Symbols Rj ) relative volatility of component j βpay ) payback period (year) ∆HV ) average heat of vaporization (cal/mol) ∆TC ) temperature difference in the condenser (K) ∆TR ) temperature difference in the reboiler (K) λ ) average heat of reaction (cal/mol) νj ) stoichiometric coefficient of component j χ ) conversion


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Received for review November 13, 2003 Revised manuscript received February 25, 2004 Accepted March 5, 2004 IE030832G

Quantitative Comparison of Reactive Distillation with Conventional

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