Effect of Relative Volatility on the Quantitative Comparison of Reactive

A previous paper presented a quantitative economic comparison of reactive ... between temperatures conducive to good reaction (kinetics and equilibriu...
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Ind. Eng. Chem. Res. 2004, 43, 3151-3162

3151

PROCESS DESIGN AND CONTROL Effect of Relative Volatility on the Quantitative Comparison of Reactive Distillation and Conventional Multi-unit Systems Devrim B. Kaymak and William L. Luyben* Process Modeling and Control Center, Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015

Oliver J. Smith IV Air Products and Chemicals, Inc., Allentown, Pennsylvania 18195

A previous paper presented a quantitative economic comparison of reactive distillation with a conventional multi-unit system for a wide range of chemical equilibrium constants. Assuming constant relative volatilities (R ) 2), reactive distillation was shown to be less expensive than the conventional process. This paper extends this work to explore how the relative volatilities affect the design of these flowsheets in two ways: (1) relative volatilities between adjacent products and reactants are reduced, and (2) relative volatilities are temperature dependent. A fundamental difference between the two flowsheets is the ability in the conventional process to adjust the reactor temperature and distillation column temperatures completely independently, which is not possible in the reactive distillation process. Results show that when relative volatilities are temperature dependent and decrease significantly as temperatures approach those required for reasonable reaction rates, the reactive distillation column becomes more expensive than the conventional flowsheet. 1. Introduction Reactive distillation has received more and more attention in the literature because it offers economic advantages in some chemical systems. Recent books by Doherty and Malone1 and Sharma and Mahajani2 present detailed discussions of the technology and its current status. A recent paper by Kaymak and Luyben3 reviewed the literature dealing with reactive distillation and conventional multi-unit reaction/separation/recycle systems. A quantitative comparison of the optimum economic steady-state designs of the two alternative processes was presented, using the total annual cost (TAC) as the objective function. Ideal vapor-liquid equilibrium was assumed with constant relative volatilities. The effect of the chemical equilibrium constant was explored. This paper is an extension of the previous work that explores the effects of changes in relative volatilities on these two flowsheets. Two types of changes in relative volatilities are considered. First, the relative volatilities among adjacent products and reactants (RCA and RBD) are reduced from the fairly large value of 2 used in the previous work. They are still assumed to be constant. Results show that this change has only a slight effect on the comparison of the flowsheets. The second type of change in the relative volatilities is to make them temperature dependent. This is a much more significant and realistic situation. A fundamental difference between reactive distillation and a conven* To whom correspondence should be addressed. Tel.: (610) 758-4256. Fax: (610) 758-5057. E-mail: [email protected].

tional flowsheet is the selection of operation temperatures. In the conventional system, the reactor temperature can be set at an optimum value and distillation temperatures can be independently set at their optimum values by adjusting the column pressures. In reactive distillation, these temperatures are not independent. Therefore, the design of a reactive distillation column requires a tradeoff between temperatures conducive to good reaction (kinetics and equilibrium constants) and temperatures favorable for vapor-liquid separation. Thus, this temperature dependency of the relative volatilities will emphasize the important differences between the two processes. 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 follow the Arrhenius law

kF ) aFe-EF/RT

(2)

kR ) aRe-ER/RT

(3)

respectively. The rate law is based on concentrations in mole fractions and liquid holdups in kmoles. The forward reaction rate is specified as 0.008 kmol‚s-1‚kmol-1 at 366 K. The reverse reaction rate at this temperature is calculated by taking a specific value

10.1021/ie040051v CCC: $27.50 © 2004 American Chemical Society Published on Web 05/05/2004

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Figure 1. Detailed system flowsheet for the conventional design. Table 1. Physical Data for Processes activation energy of reaction cal‚mol-1 forward reverse specific reaction rate at 366 K kmol‚s-1‚kmol-1 forward reverse average heat of reaction, λ cal‚mol-1 average heat of cal‚mol-1 vaporization, ∆Hv molecular weight of g‚mol-1 the mixture, Mw ideal gas constant cal‚mol-1‚K-1

30 000 40 000 0.008 0.008/(KEQ)366 -10 000 6944 50 1.987

of (KEQ)366.

(kR)366 ) (kF)366/(KEQ)366

(4)

Both reaction rates are temperature dependent, and note that the ratio of kF to kR is not equal to (KEQ)366 at temperatures different from 366 K because of the difference of activation energies. The reverse reaction rate is more temperature dependent than the forward reaction rate because the reaction is exothermic. Parameter values are given in Table 1. Details of the design equations, procedures, optimization strategies, assumptions, and numerical methods are given in our previous paper.3 A single value of the chemical equilibrium constant is used in this paper: (KEQ)366 equal to 2. The relative volatilities, under base-case conditions, are such that the lightest component is one of the products (C) and the heaviest component is the other product (D). Reactant component A is lighter than the other reactant B. Thus, the relative volatilities are

RC > RA > RB > RD

(5)

This means that two distillation columns are required in the conventional flowsheet. Product C is removed

from the top of one column, and product D is removed from the bottom of the other column. The recycle stream contains the two reactant components. It should be emphasized that both 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 both processes. 2.1. Conventional Multi-unit Process. Figure 1 gives the flowsheet of the conventional multi-unit process. The reaction occurs in a continuous stirred tank reactor with holdup VR. There are two fresh feed streams F0A and F0B that contain pure reactants A and B, respectively, while a recycle stream D2 returns from a downstream unit. The reactor effluent contains a multicomponent mixture, and two columns are needed to separate the two products from the intermediateboiling reactants. A direct separation configuration is used. Reactor effluent is fed into the first distillation column, and product C is produced in the distillate D1. There is some impurity of component A in this stream. Bottoms B1 is fed to the second column, which produces a bottoms B2 that is mostly product D with a little impurity of B. The distillate D2 contains mostly reactants A and B, with some impurities of both C and D. This stream is recycled back to the reactor. For this process, it is assumed that there is equimolal overflow in distillation columns, which means that neither energy balances nor total balances are needed on the trays for steady-state calculations. Other assumptions are isothermal operation of the reactor, theoretical trays, saturated liquid feed and reflux, total condensers, and partial reboilers in the columns. When temperature-dependent volatilities are studied, bubblepoint calculations are made to determine temperatures and vapor compositions, given the pressure and liquid composition.

Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 3153 Table 2. Vapor-Pressure Constants for Constant rCA and rBD Cases RCA ) RBD

constant

A

B

C

D

1.250

AVP BVP AVP BVP AVP BVP AVP BVP AVP BVP

12.34 3862 12.34 3862 12.34 3862 12.34 3862 12.34 3862

11.65 3862 11.65 3862 11.65 3862 11.65 3862 11.65 3862

12.57 3862 12.67 3862 12.75 3862 12.91 3862 13.04 3862

11.43 3862 11.34 3862 11.25 3862 11.09 3862 10.96 3862

1.375 1.500 1.750 2.000

reasonable tray liquid heights (about 0.1 m). The reaction rates depend on the holdup of the liquid on the reactive trays. The column diameter is set by the maximum vapor velocity. 3. Relative Volatilities For an ideal mixture, Raoult’s law relates the partial pressure of a component in the vapor phase to its liquidphase composition and vapor pressure. The vapor pressure PS of a component is a function of temperature and can be calculated from a two-parameter Antoine equation over a limited temperature range Figure 2. Reactive distillation column.

The same approximate design procedure as that used in previous work is applied for the conventional system. The numbers of trays in the columns are set equal to twice the minimum, and the reflux ratios are set equal to 1.2 times the minimum. 2.2. Reactive Distillation Column. The reactive distillation process 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. The light reactant A is fed to the bottom tray of the reactive zone, while the heavy reactant B is introduced at the top of the reactive section. The light product C leaves in the distillate, while the heavy product D is removed in the bottoms. Because the light reactant A is quite volatile compared to B and D, it goes up through the column after being fed on the bottom tray of the reactive zone, and there is very little of component A in the stripping section. Likewise, heavy reactant B goes down through the column after being fed on the top tray of the reactive zone, and there is very little of component B in the rectifying section. Thus, the primary separation in the stripping section is between B and D. In the rectifying section, it is between C and A. The steady-state vapor and liquid 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 rate increases up and the liquid rate decreases down through the reactive zone. Other assumptions are saturated liquid feed and reflux, total condenser, and partial reboiler. Reactive tray holdup Mi is assumed to be 1000 mol, which gives

lnPS ) AVP - BVP/T

(6)

where AVP and BVP are constants. A component having a higher vapor pressure at a given temperature than another component is more volatile. The relative volatility Rij for an ideal mixture is equal to the ratio of the vapor pressure of component i to the vapor pressure of component j.

Rij ) PSi /PSj

(7)

3.1. Constant Relative Volatilities. If the vapor pressures of an ideal mixture have the same temperature dependence (the BVP constants are the same for all components), the relative volatilities are constant. Table 2 gives the vapor-pressure constants used for several cases that we will explore under these conditions. The relative volatilities between adjacent products and reactants (RCA and RBD) are equal and constant but are varied for each case (from 1.25 to 2) to study the effect of smaller R’s on the two flowsheets. The AVP coefficients of reactants A and B are kept constant. The AVP coefficient of product C is reduced, and that of product D is increased. This reduces the relative volatilities between adjacent products and reactants (RCA and RBD). The volatility RAB between reactants A and B is constant at 2 for all cases. Figure 3 gives vapor-pressure lines for two cases. The left graph is the base case, where all of the relative volatilities are constant at 2. The lines are parallel because the coefficient BVP’s are the same for all components. The relative volatilities are independent of the temperature, so they are constant throughout the distillation column, despite having temperatures that change from tray to tray in the column. The right graph in Figure 3 gives vapor-pressure curves for the case in which the RCA and RBD values are still constant but are reduced to 1.25. 3.2. Temperature-Dependent Relative Volatilities. In the conventional multi-unit system, the reactor temperature can be set at an optimum value and

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Figure 3. Vapor pressures for the constant relative volatility case with RCA ) RBD: (a) 2; (b) 1.25.

Figure 4. Temperature profile of the optimum reactive column design for constant RCA ) RBD ) 2.

distillation temperatures can be independently set at their optimum values by adjusting the column pressures. The column pressures are set using the vapor pressures PS of the pure components at 320 K and the liquid compositions in the reflux drum xD,j so that cooling water can be used in the condenser. However, in reactive distillation, these reaction and distillation temperatures are not independent because both reaction and separation occur in the same vessel. To study the effect of temperature dependency of relative volatilities on the steady-state design of both flowsheets, the relative volatilities between adjacent

products and reactants (RCA and RBD) are kept constant at 2 at a temperature of 320 K. This means that the distillation columns of the conventional system can operate at the same pressures as those used in the basecase conditions. However, the relative volatilities of all components are now assumed to be temperature dependent. This is achieved by reducing the relative volatilities at some higher temperature. This temperature is selected to be 390 K, which is 70 K higher than the reflux drum temperature. The 390 K temperature is selected because the average reactive zone temperature for the

Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 3155

Figure 5. Vapor pressures for the temperature-dependent relative volatility case with R390: (a) 1.25; (b) 0.95. Table 3. Vapor-Pressure Constants for the Temperature-Dependent rij Case R390

constant

A

B

C

D

0.95

AVP BVP AVP BVP AVP BVP AVP BVP AVP BVP AVP BVP

12.34 3862.00 12.34 3862.00 12.34 3862.00 12.34 3862.00 12.34 3862.00 12.34 3862.00

15.80 5189.23 15.52 5097.78 14.99 4927.86 14.27 4699.95 13.26 4374.90 11.65 3862.00

8.89 2534.77 9.18 2626.22 9.71 2796.14 10.42 3024.05 11.44 3349.10 13.04 3862.00

19.26 6516.46 18.68 6333.56 17.62 5993.72 16.20 5537.90 14.17 4887.80 10.96 3862.00

1.00 1.10 1.25 1.50 2.00

base case is around 390 K, as shown in Figure 4. In this base case, the RCA and RBD volatilities are constant and equal to 2. Now we will vary the value of R390 over the range from 0.95 and 2. The vapor-pressure coefficients of component A are kept constant for all R390 cases. Therefore, the slope of the vapor-pressure line for component A is the same for all cases, as shown in Figure 5. Then the BVP coefficients of the other three components are calculated so as to reduce the relative volatilities to the specified values at 390 K. Table 3 gives the values of all of the vapor-pressure constants for the six cases considered. Figure 5 gives vapor-pressure lines for two cases: R390 ) 1.25 and 0.95. The lines are not parallel, getting closer as the temperature increases. As the right graph in Figure 5 shows, the vapor-pressure lines actually cross each other at a certain temperature for the R390 ) 0.95 case. In the conventional flowsheet, the relative volatilities will be slightly lower as we move down the column because of the increase in tray temperatures. In the reactive distillation column, it will not be possible to operate at a pressure that gives favorable reaction conditions (around 390 K) because these temperatures would make it impossible to maintain the required separation.

As examples of vapor pressures of real components, Figure 6 shows plots for methyl acetate, methanol, and water. These vapor pressures are temperature dependent. The ratio of the vapor pressures for methyl acetate and methanol is 2.06 at 273 K but drops to 1.06 at 373 K. The ratio of the vapor pressures for methanol and water is 6.26 at 273 K but drops to 2.37 at 473 K. Because both of these systems are nonideal with liquidphase activity coefficients greater than 1, the ratio of the vapor pressures is not equal to the relative volatility. 4. Optimum Steady-State Designs The design objective is to obtain 95% conversion for fixed fresh feed flow rates (F0A and F0B) of 12.6 mol‚s-1 and product purities of both components C and D of 95%. The details of the assumptions, specifications, and steady-state design procedures used for both process flowsheets are given in the previous paper.3 On the basis of these specifications and simplifying assumptions, there are three optimization variables for the conventional multi-unit process: (1) molar holdup in the reactor VR, (2) composition of the reactant B in the reactor zB, and (3) reactor temperature TR. For reactive distillation, there are three optimization variables for the constant relative volatility case: (1) the column pressure P, (2) the number of reactive trays NRX, and (3) the number of separating (stripping/rectifying) trays NS ()NR). For the constant relative volatility case, the numbers of stripping and rectifying trays are assumed to be equal because the relative volatilities between the components being separated in the two sections are the same. However, this simplifying assumption cannot be applied for the temperature-dependent relative volatility case because the temperatures in the stripping and rectifying sections are different. Therefore, one more optimization variable is needed in this case; i.e., the optimum values of both the number of the stripping trays NS and the number of rectifying trays NR must be determined.

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Figure 6. Vapor pressures of several real components.

Figure 7. Optimization results of the conventional process for different constant Rij.

The same design and optimization procedures as those used in the previous paper were extended to these cases. Identical sizing correlation, capital costs, and energy costs were used to find the minimum TAC, which includes both annual capital and energy costs assuming a payback period (βpay) of 3 years.

TAC ) energy cost +

capital investment βpay

(8)

5. Results and Discussion 5.1. Constant Relative Volatilities. As the first type of change, the relative volatilities between adjacent products and reactants (RCA and RBD) are varied in the range of 1.25-2 for both design flowsheets. As expected, the lower volatilities yield designs with more trays in both of the conventional columns and in the reactive distillation column. The more expensive separation costs also push the designs to have larger reactor volume and to consume more energy (higher vapor boilups).

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Figure 8. Optimization results of reactive distillation for different constant Rij cases. Table 4. Optimization Results of the Conventional Design (Constant rCA and rBD)

Table 5. Optimization Results of the Reactive Distillation Design (Constant rCA and rBD)

RCA ) RBD 1.250 design variables TR (K) VR (kmol) zB design parameters column 1 NT1 VS1 (mol‚s-1) R1 (mol‚s-1) DC1 (m) AR1 (m2) AC1 (m2) P1 (bar) column 2 NT2 VS2 (mol‚s-1) R2 (mol‚s-1) DC2 (m) AR2 (m2) AC2 (m2) P2 (bar) capital cost ($103) reactor heat exchanger column tray energy cost ($103/year) TAC ($103/year)

1.375

1.500

RCA ) RBD 1.750

2.000

358.0 357.5 0.190

361.0 227.5 0.200

363.0 177.5 0.200

366.0 123.0 0.200

367.0 102.5 0.225

45 109.41 96.81 1.80 160.93 268.59 1.63

31 81.26 68.66 1.51 119.51 199.48 1.80

24 65.87 53.27 1.34 96.89 161.72 1.94

17 49.78 37.18 1.12 73.22 122.20 2.27

13 39.56 26.96 0.97 58.18 97.11 2.57

44 104.54 85.88 1.99 153.77 256.64 1.02

30 77.19 57.06 1.70 113.54 189.50 1.02

23 63.50 42.49 1.54 93.39 155.88 1.03

16 50.13 27.72 1.36 73.73 123.06 1.06

13 44.42 21.54 1.30 65.34 109.06 1.03

481.8 936.2 1137.9 54.9 922.0 1792.2

363.6 770.2 705.5 29.2 682.8 1305.6

311.5 675.1 508.0 18.9 557.5 1062.0

247.3 570.7 326.0 10.5 430.5 815.4

221.3 509.6 245.8 7.3 361.9 689.9

Figure 7 gives the results for the conventional multiunit process. As relative volatilities get smaller and separation becomes more difficult, it becomes attractive to have higher concentrations of products in the column feed and lower concentrations of reactants. This higher conversion requires larger reactors. Because lower reactor temperatures increase the equilibrium constant KEQ and help to increase conversion, the optimum reactor temperature decreases as the relative volatility decreases. The lower temperature also requires larger reactors to achieve the desired conversion.

design variables NR and NS NRX P (bar) design temperatures (K) base reactive zone (avg) reflux drum design parameters NT VS (mol‚s-1) R (mol‚s-1) DC (m) AR (m2) AC (m2) capital cost ($103) heat exchanger column tray energy cost ($103/year) TAC ($103/year)

1.250

1.375

1.500

1.750

2.000

7 24 7.00

7 17 7.75

6 13 8.00

6 9 8.50

5 7 8.50

406.2 386.9 364.0

414.4 390.9 363.9

419.5 391.7 362.6

429.2 394.5 359.4

434.7 394.2 355.2

38 48.69 53.33 1.01 71.62 161.85

31 42.99 47.62 0.94 63.22 147.84

25 39.10 43.73 0.90 57.50 138.29

21 32.47 37.11 0.83 47.76 122.03

17 28.82 33.45 0.80 42.38 113.06

316.3 255.5 8.8 209.8 403.3

295.8 201.3 6.4 185.2 353.1

281.3 161.9 4.9 168.5 317.8

255.7 123.3 3.6 139.9 269.5

241.0 104.5 2.7 124.2 240.3

Because the concentrations of the reactants in the reactor effluent are lower, there is less recycle D2 as the relative volatilities decrease. More trays are required, and vapor boilups are higher. Optimum results for the conventional process with constant relative volatilities are summarized in Table 4. These are the optimum designs in terms of the three design optimization variables: reactor temperature, reactor holdup, and composition of component B in the reactor. As relative volatilities decrease, both capital and energy costs get higher. The reactor cost increases because of the increase of the reactor holdup. The heatexchanger cost and energy cost increase because of the higher vapor boilups. Because separation is more difficult for components with small Rij, the biggest increase occurs in the capital cost of the column shell and trays because of the large increase in the number of trays.

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Figure 9. Comparison of the TACs of both design flowsheets for constant relative volatilities.

Figure 8 gives the results for the reactive distillation flowsheet. Reducing the relative volatilities between adjacent products and reactants increases the vapor boilup and the number of trays. The optimum pressure is lower because this lowers temperatures in the reactive section, which increases the equilibrium constant. Note that there is a large increase in the number of reactive trays. This occurs because the lower temperature requires more reaction holdup. Results for different relative volatility cases are given in Table 5. These are the optimum designs in terms of the three design optimization variables: number of separation trays, number of reactive trays, and column pressure. Reducing the relative volatility increases both capital and energy costs. Figure 9 gives the TAC comparison of both design flowsheets for the constant relative volatility cases. The optimum steady-state design of the reactive distillation column has a significantly lower TAC than the conventional process for all values of RCA and RBD studied. The cost differential between the flowsheets increases as the relative volatility decreases. 5.2. Temperature-Dependent Relative Volatilities. The second type of change in the relative volatilities is making them temperature dependent. The temperature dependence illustrated in Figure 5 is used in these studies. A. Conventional Process. In each of the distillation columns of the conventional flowsheet, geometric average relative volatilities are calculated from the reflux drum and base temperatures. The operating pressure is fixed by specifying the reflux drum temperature of 320 K so that cooling water can be used in the condenser. The vapor pressures of the pure components and liquid compositions in the reflux drum and column base are known, so the relative volatilities can be calculated at both locations and averaged.

(R)geometric ) xRrefluxRbase

(9)

Figure 10 and Table 6 give optimum design results for the conventional process over a range of temperature-dependent relative volatilities. Because the column relative volatilities are only slightly lower than those of the constant relative volatility case, we assume that the three design optimization variables are the same as those of the constant relative volatility case. The slightly lower relative volatilities produce small increases in the number of trays, the reflux ratio, and the vapor boilup in both columns. There is a small increase in the recycle flow rate (D2). Reflux drum temperatures are constant for both columns for different values of R390. However, base temperatures actually decrease slightly as the reference relative volatilities decrease from case to case. This occurs because of the way we have modified the vapor pressures. The vapor-pressure constants for component A have been held constant. The BVP coefficients of the other three components have been modified to make the relative volatilities decrease with temperature. This produces a higher vapor pressure for component D at higher temperatures than it has in the constant relative volatility situation. Figure 10 shows that the relative volatilities RCA and RBD decrease as the reference R390 decreases. B. Reactive Distillation. Figure 11 and Table 7 give optimum design results for the reactive distillation process for a range of temperature-dependent relative volatilities. As the reference R390 decreases, the optimum pressure decreases. This occurs because lower pressure helps the vapor-liquid equilibrium because it lowers temperatures and hence increases relative volatilities. However, lower temperature is unfavorable for reaction because the reaction rates are too small. The result is a rapid increase in the required number of reactive trays. Note that the optimum number of stripping trays is larger than the optimum number of rectifying trays.

Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 3159

Figure 10. Results for the conventional process with different R390’s. Table 6. Optimization Results for the Conventional Process (Temperature-Dependent rij)a R390 design parameters column 1 NT1 VS1 (mol‚s-1) R1 (mol‚s-1) DC1 (m) AR1 (m2) AC1 (m2) column 2 NT2 VS2 (mol‚s-1) R2 (mol‚s-1) DC2 (m) AR2 (m2) AC2 (m2) capital cost ($103) reactor heat exchanger column tray energy cost ($103/year) TAC ($103/year) a

0.95

1.00

1.10

1.25

1.50

2.00

16 47.40 34.80 1.06 69.72 116.36

16 47.13 34.53 1.05 69.30 115.71

16 46.55 33.95 1.05 68.47 114.28

15 45.58 32.98 1.04 67.04 111.89

15 43.17 30.57 1.01 63.49 105.98

13 39.56 26.96 0.97 58.18 97.11

16 51.55 28.66 1.38 75.82 126.55

16 51.17 28.28 1.38 75.27 125.62

16 50.52 27.63 1.37 74.30 124.01

15 49.57 26.69 1.36 72.92 121.70

15 47.98 25.10 1.33 70.58 117.80

13 44.42 21.54 1.30 65.34 109.06

221.3 567.1 313.8 10.1 426.4 797.2

221.3 564.7 312.7 10.0 423.6 793.2

221.3 560.0 310.6 9.9 418.3 785.6

221.3 552.8 291.9 9.1 410.0 768.4

221.3 537.5 285.4 8.9 392.8 743.8

221.3 509.6 245.8 7.3 361.9 689.9

For all R390 cases, VR ) 102.5 kmol, P1 ) 2.57 bar, and P2 ) 1.03 bar.

This is caused by the higher temperatures in the lower part of the column, which means lower relative volatilities. While cases are considered in which the reference R390 approaches and even drops below 1, the actual relative volatilities in the reactive column do not get too close to 1. If they did, the required separation would become impossible. Figure 12 illustrates the point. The average relative volatility through the reactive zone is 2 for the base case (R390 ) 2) because they are constant. However, the average relative volatilities in the reactive zone get smaller as the value of R390 decreases. The decrease of the column temperature prevents the relative volatilities from becoming too small. As shown in Figure 11, the average temperature in the reactive zone for the R390

) 0.95 case is 354 K. This gives relative volatilities equal to 1.34. It should be remembered that, at any temperature, all of the relative volatilities are the same among the adjacent components. Results for different R390 cases are given in Table 7. These are the optimum designs in terms of the four design optimization variables: column pressure and number of stripping, rectifying, and reactive trays. Reducing the relative volatility increases both capital and energy costs. Figure 13 gives a direct comparison of the TACs of both design flowsheets for the temperature-dependent cases. There is a small increase in TAC for the conventional multi-unit process as the relative volatilities

3160 Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004

Figure 11. Results for reactive distillation with different R390’s. Table 7. Optimization Results of the Reactive Distillation Design (Temperature-Dependent rij) R390 0.95 design variables NS NRX NR P (bar) design temperatures (K) base reactive zone (avg) reflux drum design parameters NT VS (mol‚s-1) R (mol‚s-1) DC (m) AR (m2) AC (m2) capital cost ($103) heat exchanger column tray energy cost ($103/year) TAC ($103/year)

1.00

1.10

1.25

1.50

2.00

14 68 3 3.75

13 58 3 4.00

12 41 4 4.50

11 25 5 5.50

9 13 6 7.00

5 7 5 8.50

363.0 354.4 335.9

365.8 356.6 338.1

371.4 361.4 341.8

381.4 369.3 347.9

398.8 380.7 353.7

432.8 394.2 353.2

85 99.15 103.78 1.53 145.83 285.71

74 94.03 98.66 1.48 138.30 273.14

57 83.58 88.22 1.37 122.93 247.49

41 68.50 73.14 1.21 100.75 210.48

28 48.82 53.46 1.00 71.81 162.18

17 28.82 33.45 0.80 42.38 113.06

474.1 763.0 37.7 427.2 852.2

459.5 656.4 31.0 405.2 787.5

428.9 490.9 21.2 360.2 673.8

382.4 329.3 12.5 295.2 536.6

316.7 198.8 6.4 210.4 384.4

241.0 104.5 2.7 124.2 240.3

decrease, but there is a very rapid increase for the reactive distillation process. Figure 13 also shows how the reactor temperature in the conventional process and the average temperature in the reactive section of the reactive distillation column change as the temperature dependence changes. At base-case conditions with R390 ) 2 (no temperature dependence), the optimum reactor temperature in the conventional process is 367 K, and we assume that this does not change for other values of R390 as discussed above. At base-case conditions with R390 ) 2 (no temperature dependence), the optimum average reaction zone temperature in the reactive distillation is 394 K. This is higher than the conventional reactor temperature because the reactive distillation column is removing products from the reaction zone, so a smaller chemical

equilibrium constant can be tolerated (higher temperature). The conventional process, in which no products are removed from the reaction zone, is favored by lower reactor temperature because it gives a higher chemical equilibrium constant. However, as the value of R390 decreases, the optimum average reaction zone temperature in the reactive distillation decreases because the separation is becoming more difficult as the temperature increases. These results clearly illustrate the fundamental difference between a conventional process and a reactive distillation process. In a conventional process, temperatures for reaction and temperatures for separation can be independently set. This is not true for reactive distillation. Therefore, reactive distillation is not eco-

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Figure 12. Average relative volatilities of the reactive zone for different R390’s.

Figure 13. Comparison of the TACs and reaction temperatures for temperature-dependent relative volatilities.

nomical for systems in which the temperatures for reaction and for separation are not similar. 5.3. Some Results for Real Chemical Systems. Some confirmation of the results presented in the paper can be seen in several papers that compare conventional processes with reactive distillation for real chemical systems. Two papers have been found that make such a comparison and provide sufficient detail about process conditions. A. MTBE Process. Sneesby et al.4 provide a description of the conventional process. There are two reactors in series, the first operating at 90 °C and the second at 50-60 °C. The lower temperature in the second reactor

gives a higher equilibrium constant because the reaction of methanol and isobutene to produce MTBE is exothermic. The temperature in the reactive zone of the reactive distillation process is about 70 °C. Thus, the conventional and reactive distillation processes have similar temperatures. Therefore, we would expect the reactive distillation process to be more economical, which is indeed the case. B. Toluene Disproportionation Process. Stitt5 compares a conventional process to produce benzene from toluene with a reactive distillation process. Several steady-state economic indicators are used to show that

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the reactive distillation process “does not prove to be a fruitful development opportunity ... due to economic considerations.” The reactor temperature in the conventional process is 400 °C (vapor-phase reaction). The separation section consists of several distillation columns operating at normal temperature levels for the benzene/toluene separation. The reactive distillation column has a temperature of about 280 °C in the reactive zone. To achieve this temperature, the column must operate at 30 bar. The difference between the conventional reactor temperature and the reactive distillation temperature indicates that the optimum temperature for reaction is different from the optimum temperature for separation. Therefore, we would expect that the reactive distillation column would not be inherently superior to the conventional process, which is precisely what Stitt found. 6. Conclusion The effects of relative volatility on the design of two different flowsheets are quantitatively studied. The economically optimum steady-state designs of a multiunit reactor/column/recycle process and a reactive distillation column are compared. Two types of changes in relative volatilities are considered: (1) the constant relative volatilities between adjacent products and reactants (RCA and RBD) are varied over a range of values, and (2) the relative volatilities are made temperature dependent (decreasing with increasing temperature). For the case with constant relative volatilities, three optimization variables are used to find the optimal results for both systems. The conventional system has the reactor holdup, the reactor temperature, and the composition of reactant B in the reactor as optimization variables, while the reactive column configuration has the number of separation stages, the number of reactive stages, and the column pressure. For the temperaturedependent case, the reactive distillation process has one more optimization variable because the numbers of stripping and rectifying trays are not the same since the relative volatilities in the higher temperature stripping section are smaller than those in the rectifying section. For the constant relative volatilities case, the optimum steady-state design of the reactive distillation column has a lower TAC than the conventional multiunit system for all five values of RCA and RBD studied, with increasing differences as the values of relative volatilities decrease. For the temperature-dependent case, the TAC of the reactive distillation process increases rapidly when the temperature dependence of the relative volatilities is large. The TAC of the conventional process changes only slightly. These results demonstrate the inherent limitation that characterizes the reactive distillation process. Temperatures that are good for reaction must correspond to temperatures that are good for vapor-liquid separation. In a conventional process, the temperatures in the reaction section and the separation section can be independently set so that optimum operation of each is possible.

Future work will compare the dynamic controllability and the flexibility 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 condenser (m2) AR ) heat exchanger area for reboiler (m2) AVP ) vapor-pressure constant B ) bottoms flow rate in the column (mol‚s-1) BVP ) vapor-pressure constant D ) distillate flow rate in the column (mol‚s-1) DC ) diameter of the column (m) EF ) activation energy of the forward reaction (cal‚mol-1) ER ) activation energy of the reverse reaction (cal‚mol-1) F ) effluent flow rate from the reactor (mol‚s-1) F0j ) fresh feed flow rate of reactant j (mol‚s-1) 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 NR ) number of rectifying trays NRX ) number of reactive trays NS ) number of stripping trays NT ) number of trays in the column P ) column pressure (bar) S ) vapor pressure of component j on tray i (bar) Pi,j R ) reflux flow rate (mol/s) TAC ) total annual cost ($‚year-1) Ti ) column temperature on tray i (K) TR ) temperature of the reactor (K) VR ) molar holdup of the reactor (mol) VS ) vapor boilup (mol‚s-1) xB,j ) bottoms composition of component j in liquid xD,j ) distillate composition of component j in liquid zj ) mole fraction of component j in the reactor z0j ) fresh feed mole fraction of component j Greek Symbols R ) relative volatility Rij ) relative volatility of component i to component j R390 ) relative volatility at 390 K βpay ) payback period (year)

Literature Cited (1) Doherty, M. F.; Malone, M. F. Conceptual Design of Distillation Systems; McGraw-Hill: New York, 2001. (2) Sharma, M. M.; Mahajani, S. M. Industrial Applications of Reactive Distillation. In Reactive DistillationsStatus and Future Directions; Sundmacher, K., Kienle, A., Eds.; Wiley-VCH: Weinheim, Germany, 2003. (3) Kaymak, D. B.; Luyben, W. L. A Quantitative Comparison of Reactive Distillation with Conventional Multi-Unit Reactor/ Column/Recycle Systems for Different Chemical Equilibrium Constants. Ind. Eng. Chem. Res. 2004, in press. (4) Sneesby, M. G.; Tade´, M. O.; Datta, R.; Smith, T. N. ETBE Synthesis via Reactive Distillation. 1. Steady-State Simulation and Design Aspects. Ind. Eng. Chem. Res. 1997, 36, 1855-1869. (5) Stitt, E. H. Reactive Distillation for Toluene Disproportionation: A Technical and Economical Evaluation. Chem. Eng. Sci. 2002, 57, 1537-1543.

Received for review February 12, 2004 Accepted April 2, 2004 IE040051V