Ind. Eng. Chem. Res. 2004, 43, 8049-8056
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Design of Distillation Columns with External Side Reactors Devrim B. Kaymak and William L. Luyben* Process Modeling and Control Center, Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015
Previous work presented a quantitative economic comparison between a reactive distillation process and a conventional multiunit process for systems in which relative volatilities are temperature dependent. A fundamental difference between these two flowsheets is the ability in the conventional process to adjust reactor temperature and distillation column temperatures completely independently, which is not possible in the reactive distillation process. If the temperature required for reasonable reaction kinetics is not in the same range as that in which vapor-liquid phase equilibrium permits the use of distillation, reactive distillation becomes unattractive. This paper explores a third alternative process that can overcome the problem of reaction/distillation temperature mismatch. The column is operated at its optimum temperature (and pressure). Several liquid trap-out trays collect all the liquid coming down from upper trays. These liquids are pumped to external reactors operating at their optimum temperatures (and pressures). Reactor effluents are returned to the column. Results show that this external-reactor/ column configuration has much better steady-state economics than either reactive distillation or the conventional process when there is a mismatch between optimum reaction and distillation temperatures. 1. Introduction Reactive distillation represents one of the most exciting new technologies in the chemical processing industries. It can result in significant economic benefits in some systems, and it can satisfy the desirable inherently safer design objective of smaller equipment and less inventory of hazardous material (“process intensification”). The recent books by Doherty and Malone1 and Sharma and Mahajani2 present detailed discussions of the technology and its current status. Several papers have appeared that explore hybrid systems of reactors and columns. A paper published over two decades ago by Schoenmakers and Buehler3 appears to be the first to mention the use of external reactors coupled with a distillation column. There has been a flurry of recent papers dealing with several types of reactor/column systems.4-10 Traditional reactive distillation is not effective in many chemical systems because of a mismatch between the temperatures conducive for reaction and those favorable for separation based on vapor-liquid phase equilibrium. A fundamental difference between reactive distillation and a conventional flowsheet is the selection of operating temperatures. In the conventional system, reactor temperature can be set at an optimum value, and distillation temperatures can be independently set at their optimum values by adjusting column pressures. In reactive distillation, these temperatures are not independent. Therefore the design of a reactive distillation column requires a tradeoff between temperatures conducive for good reaction (kinetics and equilibrium constants) and temperatures favorable for vapor-liquid separation. A recent paper by Kaymak et al.11 presented a quantitative comparison of the optimum economic steady-state * To whom correspondence should be addressed. Tel.: (610) 758-4256. Fax: (610) 758-5057. E-mail:
[email protected].
designs of these two alternative processes, using total annual cost as the objective function. A range of temperature-dependent relative volatilities was explored, and results demonstrated that reactive distillation becomes unattractive as the temperature mismatch increases. A recent paper by Citro and Lee12 suggested an alternative process configuration that has the potential to overcome the temperature mismatch problem. To illustrate the idea, let us assume that optimum reaction temperatures are significantly higher than optimum separation temperatures. The toluene disproportionation process discussed by Stitt13 is a good example. Reaction temperature must be above 550 K to have reasonable reaction rates. This forces a reactive distillation column with the chemical components involved (benzene, toluene, and the xylenes) to operate at 30 bar. This is much higher than the pressure that would be chosen for distillation columns making this separation (around 1 bar). Therefore, Stitt concludes that reactive distillation is unattractive. The alternative process discussed by Citro and Lee12 consists of a distillation column with external reactors that are fed with streams from intermediate trays of the column. The distillation column is operated at its optimum pressure and temperature for separation. As shown in Figure 1, total liquid trap-out trays are installed at several intermediate trays around the middle of the column. All the liquid is pumped up to a high enough pressure that it remains liquid at temperatures conducive for reaction. If reactor feed preheating is required, heat exchangers are used to recover the heat generated in the reactor. Thus distillation temperatures and reaction temperatures can be independently set at their optimum values. The treatment by Citro and Lee12 appears to assume unrealistic hydraulics. In their Figure 6 they show both liquid and vapor streams being fed to the external reactor. Since the reactor would have to operate at a
10.1021/ie040124a CCC: $27.50 © 2004 American Chemical Society Published on Web 11/05/2004
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Ind. Eng. Chem. Res., Vol. 43, No. 25, 2004 Table 1. Physical and Chemical Parameters activation energy of reaction (cal/mol) forward reverse specific reaction rate at 366 K [kmol/(s kmol)] forward reverse heat of reaction, λ (kJ/mol) heat of vaporization, ∆Hv (kJ/mol) molecular weight of the mixture, Mw (g/mol) ideal gas constant [cal/(mol K)] heat capacity, cp (kJ/kg‚K) heat-transfer coefficient, U (kJ/s‚K‚m2)
Figure 1. External-reactor/column process.
higher pressure than the column, the high-temperature vapor streams from the column would have to be compressed, which would be very expensive. In this paper, we consider the design of a practical external-reactor/column process in which only the liquid goes to the external reactor. Since pumping liquid is relatively inexpensive, this modified structure should be readily applied to many systems. 2. Process Studied 2.1. Chemistry and Reaction Kinetics. The same components, reaction kinetics and vapor-liquid equilibrium considered in previous papers are used. The chemistry is an exothermic reversible liquid-phase reaction.
A+BSC+D
(1)
The forward and reverse specific reaction rates follow the Arrhenius law.
kF ) aFe-EF/RT
(2)
kR ) aRe-ER/RT
(3)
The rate law is based on concentrations in mole fractions and liquid holdups in moles. The forward reaction rate is specified as 0.008 mol s-1 mol-1 at 366 K. The reverse reaction rate at this temperature is calculated by taking a specific value 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 due to the difference of activation energies. The reverse reaction rate is more temperature dependent than the forward reaction rate since the reaction is exothermic. Parameter values are given in Table 1. Details of the design equations, procedures, optimization strategies,
30 000 40 000 0.008 0.008/(KEQ)366 -41.8 29 50 1.987 2.93 0.85
assumptions, and numerical methods were given in a previous paper.14 A single value of the chemical equilibrium constant is used in this paper: (KEQ)366 ) 2. It is useful at this point to perform some preliminary calculations to establish some reasonable operating conditions and sizes for the external reactors for the numerical case considered in this paper. We use the insight gained to make some preliminary assumptions about reactor temperatures and holdups. Figure 2 shows the effects of reactor volume VR and temperature on the conversion that is achieved in two types of plug-flow reactors. Figure 2A gives results for an isothermal plug-flow reactor that is fed with a 50/50 mixture of reactants A and B. Different reactor sizes and temperatures affect conversion. At low temperatures, conversion is low because the specific reaction rates are small. For a given reactor size, conversion initially increases as temperature increases. However, since the reaction is exothermic, the chemical equilibrium constant decreases as temperature increases. Thus, an equilibrium constraint is reached. The maximum conversion for a 2000 mol reactor occurs at about 390 K. In these calculations, the reactor temperature is constant down the length of the reactor. Figure 2B gives results for an adiabatic plug-flow reactor with pure reactant feeds. Now the temperature increases down the length of the reactor. The abscissa of these graphs is the reactor inlet temperature. The maximum conversion for a 2000 mol reactor occurs with an inlet temperature of about 366 K, giving an outlet temperature of 420 K. The feed is a 50/50 mixture of reactants, and the conversion is about 18%. Figure 2C shows the situation when the feed composition is perhaps more typical of what the composition in the middle of the distillation column would be: 30 mol % A, 30 mol % B, 20 mol % C, and 20 mol % D. Now the maximum conversion of a 2000 mol reactor occurs with a reactor inlet of 380 K, giving an outlet temperature of 390 K. On the basis of these preliminary results, we fix the outlet temperature of the external reactors at 390 K. Since we found in our previous paper that a reactive tray holdup of 1000 mol achieved reactive tray compositions that were close to chemical equilibrium, we assume that the streams leaving the external reactors are all at chemical equilibrium. A 2000 mol reactor is assumed for sizing the reactor to evaluate capital costs. In a later section of this paper, we will relax this assumption and explore the effects of external-reactor size and outlet temperature by rigorously modeling the plug-flow reactor and not assuming that the reactor effluent reaches chemical equilibrium.
Ind. Eng. Chem. Res., Vol. 43, No. 25, 2004 8051
Figure 3. Vapor pressures; R390 ) 2 and R390 ) 0.95. Table 2. Vapor Pressure Constants R390
const
A
B
C
D
0.95
AVP BVP AVP BVP AVP BVP AVP BVP
12.34 3862.00 12.34 3862.00 12.34 3862.00 12.34 3862.00
15.80 5189.23 14.27 4699.95 13.26 4374.90 11.65 3862.00
8.89 2534.77 10.42 3024.05 11.44 3349.10 13.04 3862.00
19.26 6516.46 16.20 5537.90 14.17 4887.80 10.96 3862.00
1.25 1.5 2
In the reactive distillation column and in the externalreactor/column system, the distillate contains product C and the bottom contains product D. The vapor pressure PSj of component j is a function of temperature as given by the Antoine equation:
ln PSj ) AVP,j -
Figure 2. (A) Isothermal PFR. (B) Adiabatic PFR: pure A and B in feed. (C) Adiabatic PFR: zA ) zB ) 0.3 in feed.
2.2. Phase Equilibrium. The relative volatilities of the reactants (A and B) and the products (C and D) are
RC > RA > RB > RD
(5)
This means that two distillation columns are required in the conventional flow sheet. Product C is removed through 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.
BVP,j T
(6)
where AVP,j and BVP,j are constants over a limited temperature range. A range of temperature-dependent relative volatilities are considered, which are the same as those studied earlier.11 Various degrees of temperature dependence are achieved by setting the relative volatilities to 2 for all adjacent components at a temperature of 320 K. This is the reflux-drum temperature when cooling water is used in the condenser, so the optimum column temperatures range from 320 K in the top to about 360 K in the base. Then the relative volatilities are set at different values at a higher temperature (390 K). This is the temperature that gives reasonable reaction rates and chemical equilibrium constants for the numerical example considered. The various cases are denoted by R390 values, which range from 2 (the constant R case) to 0.95 (where separation becomes infeasible at temperatures near 390 K). Figure 3 gives the vapor pressure curves at these two extreme cases. Table 2 lists the Antoine constants for the cases considered. 2.3. External-Reactor/Column Process. Figure 1 shows the process configuration. There are three total liquid tray-out trays. The vapor from the tray beneath each trap-out tray flows up through the chimney to the tray above. There is no vapor-liquid contacting on the trap-out tray. The two fresh feed streams of reactants A and B are fed into the column at the trays immediately above the lower and upper trap-out trays.
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Liquid from each tray-out tray is pumped up to a high enough pressure that the material stays liquid at the higher temperatures in the reactors. Although not exhaustively studied, several cases were run with fewer and additional trap-out trays, and results indicated that three external reactors is the optimum number. The locations of the trap-out trays were also varied, and those reported appear to be the optimum. Heat exchangers are used to preheat the reactor feed. The reactors are assumed to be adiabatic and the reaction is exothermic (λ ) -41.8 kJ/mol), so the hotter reactor effluent can be used in the feed-effluent heat exchanger (FEHE). The actual heat-exchanger configuration will vary for different chemical reactions. Endothermic reactions would require a heat source to preheat the feed to the reactor. In some systems a heat exchanger may not be required if the external reactor can be made large enough to achieve the desired extent of reaction even with low reactor inlet temperatures. There is an interesting tradeoff between heat-exchanger cost and external-reactor cost. This will be discussed further in a later section of this paper, but at this point it is worth emphasizing that the use of external reactors offers two advantages: 1. Reaction and separation temperatures can be independently set. 2. Reactor size can be easily and inexpensively made as large as necessary. In traditional reactive distillation, liquid holdup on trays is limited by tray hydraulics. The height of liquid on the tray cannot be made too large because of the effect on pressure drop. Liquid heights over about 0.1 m are unrealistic. The reactors could also be cooled (or heated) instead of operating adiabatically. This option is not considered in this paper because the capital cost of adiabatic reactors is much lower than the multi-tube vessels required for cooled reactors. Equimolal overflow is assumed in the distillation column, which means that neither energy balances nor total balances are needed on the trays for steady-state calculations. However, since the reaction is exothermic, some vapor is produced as the liquid from the highpressure reactor flashes into the low-pressure column. This results in an increase of the vapor flow rate at each external-reactor location and a corresponding decrease of the liquid rate below the external-reactor location. The quantity of this vapor is calculated from the heat generated by the reaction occurring in the external reactor, the flow rate of material into the reactor, and the thermal properties (heat capacity cp ) 2.93 kJ/kg‚ K and heat of vaporization ∆Hv ) 29 kJ/mol).
∆Vext )
QRext Fext(xin,A - xout,A)(-λ) ) ∆Hv ∆Hv
(7)
where Fext is the flow rate of liquid to the external reactor (mol/s), xin,A is the mole fraction of reactant A in the feed to the reactor, xout,A is the mole fraction of reactant A in the effluent from the reactor, and λ is the heat of reaction (-41.8 kJ/mol of A reacted). Thus there are different liquid and vapor rates in the various sections of the column: (1) the rectification section from the top tray down to the upper trap-out tray (where FOB is fed); (2) between the upper and middle trap-out trays; (3) between the middle trap-out tray and the lowest trap-out tray (where FOA is fed); (4)
Figure 4. (A) Composition profiles; R390 ) 0.95. (B) Temperature and vapor flow rate profiles; R390 ) 0.95.
the stripping section from the column base up to the lowest trap-out tray. Figure 4 gives composition, temperature, and vapor flow rate profiles in the external-reactor/column system for the R390 ) 0.95 case. Other assumptions are theoretical trays, saturated liquid feeds and reflux, total condenser, and partial reboiler. Bubble-point calculations are made on each tray and in the reboiler to determine temperatures and vapor compositions, given the pressure and the liquid compositions. Column diameter is set by the vapor rate VNT in the top section of the column. Energy consumption is set by the vapor rate VS at the bottom of the column. The heat exchangers upstream of the external reactors are sized by the following procedure: 1. The composition and temperature of the liquid from the trap-out tray are known. 2. The reactor exit temperature is fixed at 390 K, and the composition of the reactor effluent is calculated by assuming chemical equilibrium. 3. The conversion in the reactor and the heat generated by reaction QRext are calculated. 4. The reactor inlet temperature Tin is calculated from an energy balance around the adiabatic reactor. Now
Ind. Eng. Chem. Res., Vol. 43, No. 25, 2004 8053 Table 3. Optimization Results for Conventional Process R390a 0.95 design parameters, column 1 NT1 VS1 (mol/s) R1 (mol/s) DC1 (m) AR1 (m2) AC1 (m2) design parameters, column 2 NT2 VS2 (mol/s) R2 (mol/s) DC2 (m) AR2 (m2) AC2 (m2) capital cost ($103) reactor heat exchanger column tray energy cost ($103/yr) TAC ($103/yr)
1.25
1.5
Table 4. Optimization Results of Reactive Distillation Design R390
2 0.95
16 47.40 34.80 1.06 69.72 116.36
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
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
221.3 552.8 291.9 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
a For all R 390 cases: VR ) 102.5 kmol; TR ) 367 K; P1 ) 2.57 bar; P2 ) 1.03 bar.
the inlet and outlet temperatures of the cold stream in the FEHE are known. 5. The heat-transfer rate QHE in the FEHE is calculated from the cold stream temperature increase (reactor inlet temperature minus tray temperature). 6. The exit temperature of the hot stream leaving the FEHE is calculated knowing its inlet temperature (390 K) and the heat-transfer rate QHE. 7. Now all the temperatures are known, so a log-mean temperature difference ∆TLM is calculated and the heattransfer area is calculated using the overall heattransfer coefficient U ) 0.85 kJ/s‚K‚m2. The steady-state solution of the nonlinear simultaneous algebraic equations is achieved by using a relaxation technique. Fresh feeds and both product flow rates are all fixed at 12.6 mol/s. A value of reflux flow rate R is guessed, and the dynamic equations of the system are integrated in time until steady-state conditions are achieved. A 95% conversion is desired, so the composition of C in the distillate xD,C must be 95 mol % (as well as the composition of D in the bottoms). Reflux flow rate is varied until these compositions are achieved. 3. Results for Conventional Process and Reactive Distillation It should be emphasized that all three of the processes considered in this work have identical feeds and produce identical products. Economic factors (energy cost and capital cost of columns, reactors, and heat exchangers) are the same in all processes. Table 3 summarizes previous results14 for the conventional multiunit process, which has a large reactor (102.5 kmol) and operates at 367 K. The temperature is low so the chemical equilibrium constant is large, but the small specific reaction rate requires a large reactor holdup. The two distillation columns operate at 2.57 and 1.03 bar, respectively, corresponding to reflux-drum temperatures of 320 K. Component C, the lightest component, is the distillate in the first column. The distillate in the second column is a mixture of components A and B and is recycled back to the reactor. As the value of R390 decreases from the base case of 2, the
design variables NS NRX NR P (bar) design temperatures (K) base reactive zone (avg) reflux drum design parameters NT VS (mol/s) R (mol/s) DC (m) AR (m2) AC (m2) capital cost ($103) heat exchanger column tray energy cost ($103/yr) TAC ($103/yr)
1.25
1.5
2
14 68 3 3.75
11 25 5 5.50
9 13 6 7.00
5 7 5 8.50
363.0 354.4 335.9
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
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
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
design of the conventional multiunit process does not change significantly. Column energy consumptions increase somewhat because the relative volatilities decrease slightly at the higher temperatures in the lower sections of the columns. This increases column capital costs (shell, reboiler, and condenser). However, the total annual cost (TAC) increases only slightly. Thus, the conventional process can fairly easily handle the reaction/separation temperature mismatch problem. However, this is not the case in a reactive distillation column. Results are summarized in Table 4. As the value of R390 decreases from the base case of 2, the design of the reactive distillation column changes drastically. The optimum operating pressure decreases significantly. This occurs because temperatures must be kept low so that relative volatilities do not get too near unity. The lower temperatures require more holdup in the reactive zone because of the small specific reaction rates. This results in a very large increase in the number of reactive trays. The holdup on each tray is limited by liquid height constraints to 1000 mol. Note that under base-case conditions (R ) 2) the temperatures in the reactive zone of the reactive column are higher than those in the conventional process. This occurs because in the reactive distillation column the products are being removed, which helps to drive the reaction toward the products. Therefore, the smaller chemical equilibrium constant that exists at the higher temperature can be tolerated. Energy consumption increases drastically because of the lower relative volatilities. The economic impact of these effects is a large increase in TAC. Thus the reactive distillation column cannot handle the reaction/ separation temperature mismatch. 4. Results for External-Reactor/Column Process Results are given in Table 5 for a range of values of R390. In all these cases, three external reactors are used with outlet temperatures of 390 K and assuming chemical equilibrium in the mixture leaving the reactors. The three trap-out trays are not counted in the total number of theoretical trays since no separation occurs on them. Column pressure is 2.57 bar for all cases.
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Table 5. Optimization Results of External-Reactor Design R390 design variables NT Next location VS (mol/s) R (mol/s) P (bar) temperatures (K) reactor exit reactor inlet reflux drum reaction heats (kJ/s) HX duties (kJ/s) HX area (m2) column DC (m) LC (m) AR (m2) AC (m2) capital cost ($103) column column HX reactors (3) reactor HX energy cost ($103/yr) TAC ($103/yr)
0.95
1.25
1.5
60 30/35/40 65.3 70 2.57
40 20/25/30 50.5 55.5 2.57
40 20/25/30 44.5 49.3 2.57
40 15/20/25 48.3 53 2.57
390 381/377/369 320 110/137/253 393/311/258 51.2/25.7/12.5
390 376/373/369 320 142/148/211 258/203/205 10.1/13.2/14.7
390 374/371/366 320 142/148/214 213/156/159 16.0/9.93/7.93
390 367/376/359 320 201/136/165 47/159/177 2.42/13.2/12.5
1.40 43.9 96.3 203
1.27 29.3 75.0 168
1.21 29.3 65.6 152
1.25 29.3 71.3 162
524 373 25.7 176 281 655
341 324 25.7 124 219 495
325 302 25.7 100 192 447
335 316 25.7 88.3 208 467
4.1. Case with r390 ) 0.95. Let us consider the R390 ) 0.95 case shown in Table 5. A 60-tray column is found to minimize TAC. This column has three trap-out trays located below trays 30, 35, and 40. There are more trays in the stripping section than in the rectifying section because of the higher temperatures and the resulting lower relative volatilities. The reflux flow rate required to achieve the desired 95% conversion (and product purities) is 70 mol/s. The column diameter is 1.4 m, the condenser area is 203 m2, and the reboiler area is 96 m2. The three heat exchangers upstream of the external reactors have areas of 51, 26, and 12 m2 for streams from trays 30, 35, and 40, respectively, with a total capital cost for all three heat exchangers of $176,000. With a fixed reactor exit temperature, more conversion in the external reactor produces a lower reactor inlet temperature. This means larger differential temperature driving forces and smaller areas in the FEHE. Thus more conversion is occurring in the highest external reactor (below tray 40) since its area is the smallest. The heat generated from the reactions in the three external reactors with feeds from trays 30, 35, and 40 are 110, 137, and 253 kJ/s, respectively. The corresponding reactor inlet temperatures are 381, 377, and 369 K, respectively, which give progressively larger ∆TLM values. As shown in Figure 4A, the concentrations of reactants A and B are both high on tray 40, while product concentrations are low. This explains the high reaction conversions in the top external reactor at tray 40 and its small heat-transfer area. At trays 35 and 30, the concentrations of A are higher, but the concentrations of B are much lower. Product C and D concentrations also change. The net effect is lower conversions in these lower reactors. Each external reactor has 2000 mol of holdup, which corresponds to a vessel with diameter DR ) 0.25 m, assuming an aspect ratio (L/D) of 10. The capital cost of this vessel is $8,600, giving a capital cost for the three reactors of only $25,800. Note that the reactors are much less expensive than the heat exchangers. In a
2
Figure 5. Comparison of alternative processes.
later section we consider in more detail the tradeoff between heat-exchanger size and reactor size. The TAC of the external-reactor/column process for R390 ) 0.95 is $655,000/yr. This is much less than the TAC of the conventional process ($797,000/yr) and the reactive distillation column ($852,000/yr). 4.2. Other Values of r390. Looking at the other columns in Table 5 for increasing values of R390, we can see that the column requires fewer trays and less energy and that the total annual cost decreases as the value of R390 increases, except for the last column where R390 ) 2. Figure 5 compares the total annual costs of the three alternative processes over a range of values of R390. When there is no reaction/separation temperature mismatch at values of R390 ) 2, the reactive distillation column is economically the best of the three. For systems with large mismatch of reaction/separation temperature (at values of R390 ) 0.95), the externalreactor/column process is economically superior.
Ind. Eng. Chem. Res., Vol. 43, No. 25, 2004 8055 Table 6. Optimization Results of External-Reactor Design with Various Reactor Sizesa reactor holdup (kmol) design variables VS (mol/s) R (mol/s) column DC (m) AR (m2) AC (m2) reactors (3) DR (m) LR (m) capital cost ($103) column column HX reactors (3) energy cost ($103/yr) TAC ($103/yr) a
40
50
60
70
80
63.3 68
60.3 65
58.4 63
57.7 62.5
57.2 62
1.38 93.4 198
1.36 88.9 191
1.34 86.1 186
1.33 85.2 185
1.33 84.4 184
0.686 6.86
0.739 7.39
0.785 7.85
0.827 8.27
0.864 8.64
517 367 166 273 630
507 357 191 260 618
500 350 214 252 613
498 348 235 249 616
496 347 255 247 620
Figure 6. External reactors without FEHE.
NT ) 60; NRX ) 30/35/40; P ) 2.57 bar; LC ) 43.9 m.
5. Nonequilibrium External Reactors In all the cases considered up to now, we have assumed that the effluent streams leaving the external reactors have attained chemical equilibrium. We have also assumed that the optimum outlet temperature is 390 K, that the reactor holdup is 2000 mol, and that an FEHE will be used. However, the results so far have indicated that increasing external-reactor holdup is much cheaper than providing heat-exchanger area. Therefore, now we will explore the steady-state economics of an external-reactor/column process in which heat exchangers are not use, reactor holdup is a design optimization variable, and the reactor effluent is not at chemical equilibrium. First, a value of reactor holdup is selected. The inlet temperatures to the external reactors are the corresponding tray temperatures. The plug-flow reactor ordinary differential equations for adiabatic operation are integrated from zero to the total reactor volume Vtotal, keeping track of how the component compositions and temperature change with length down the reactor. These equations are
dxA dxB ) ) -(kFxAxB - kRxCxD)/Fext dV dV dxC dxD ) ) +(kFxAxB - kRxCxD)/Fext dV dV
(8)
where the kinetics vary with temperature. Since the reactor is adiabatic, the temperature is directly related to composition.
T(V) ) Tin +
(xin,A - xA(V))(-λ) FcpM
(9)
Results for the R390 ) 0.95 case are given in Table 6 and Figure 6 over a range of reactor holdups. As the size of the external reactors is increased, the required reflux decreases. This means lower energy cost and lower capital cost of the column shell, reboiler, and condenser. However, the cost of the reactors increases. The minimum TAC occurs with an external-reactor holdup of 60 kmol. The TAC of this configuration (with no reactor preheating and large reactors) is $613,000/year and
should be compared with the TAC of the previous configuration (with heat exchangers and smaller reactors) of $655,000/yr. Typical reactor inlet and outlet temperatures in this configuration are about 348 and 367 K, respectively. The capital cost of the three 60 kmol reactors is $214,000. Their diameter is 0.785 m, and their length is 7.85 m. In comparing the two alternative flow sheets, the energy cost is reduced from $281,000 to $252,000/year, the column capital cost is reduced from $524,000 to $500,000, and the reboiler/condenser capital cost is reduced from $373,000 to $350,000. However, the capital cost of the reactors increases from $25,700 to $214,000. Reactor heat exchangers are eliminated, which saves $176,000. Thus it may be more economical to avoid expensive heat exchangers by using large reactors. 6. Conclusion In chemical systems with temperature mismatches between reaction and separation, the use of a distillation column, operating at one temperature level, and external reactors, operating at a different temperature level, should be considered. The results of the case study presented in this paper demonstrate that the use of external reactors coupled with a distillation column can significantly reduce capital and energy costs in chemical systems in which the optimum temperature for reaction is significantly different from the optimum temperature for distillation. Nomenclature aF ) preexponential factor for the forward reaction (mol‚s-1‚mol-1) aR ) preexponential factor for the reverse reaction (mol‚s-1‚mol-1) AVP ) vapor pressure constant B ) bottoms flow rate in the column (mol/s) BVP ) vapor pressure constant cp ) heat capacity (kJ‚kg-1‚K-1) D ) distillate flow rate in the column (mol/s) EF ) activation energy of forward reaction (cal/mol) ER ) activation energy of reverse reaction (cal/mol) F ) effluent flow rate from the reactor (mol/s) Fext ) flow rate through external reactor (mol/s) F0 j ) fresh feed flow rate of reactant j (mol/s) kF ) specific reaction rate of forward reaction (mol‚s-1‚mol-1) kR ) specific reaction rate of reverse reaction (mol‚s-1‚mol-1)
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KEQ ) equilibrium constant M ) molecular weight (kg‚kmol-1) NR ) number of rectifying trays NRX ) number of reactive trays NS ) number of stripping trays NT ) number of trays in the column P ) column pressure (bar) PSj ) vapor pressure of component j (bar) QRext ) heat generated by reaction in external reactor (kJ/ s) TAC ) total annual cost ($/yr) Tin ) temperature of reactor inlet stream (K) Tout ) temperature of reactor outlet stream (K) Tn ) column temperature on tray n (K) TR ) temperature of reactor (K) U ) overall heat-transfer coefficient in heat exchanger (kJ‚s-1‚K-1‚m-2) VNT ) vapor flow rate from top tray (mol/s) VR ) molar holdup of the reactor (mol) VS ) vapor boilup (mol/s) Vtotal ) total holdup in external reactor (mol) xB,j ) bottoms composition of component j in liquid (mole fraction j) xD,j ) distillate composition of component j in liquid (mole fraction j) xin,A ) composition of stream entering external reactor (mole fraction A) xout,A ) composition of stream leaving external reactor (mole fraction A) z0 N,j ) composition of fresh feed stream N (mole fraction j) Greek Symbols R ) relative volatility Rij ) relative volatility of component i to component j R390 ) relative volatility at 390 K λ ) heat of reaction (kJ/mol) ∆Hv ) heat of vaporization (kJ/mol) ∆Vext ) vapor generated in external reactor (mol/s)
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) Schoenmakers, G.; Buehler, W. K. Distillation Column with External Reactorssan Alternative to the Reaction Column. Ger. Chem. Eng. 1982, 5, 292-296. (4) Jakobsson, K.; Pyhalahti, A.; Pakkanen, S.; Keskinen, K.; Aittamaa, J. Modelling of a Side Reactor Configuration Combining Reaction and Distillation. Chem. Eng. Sci. 2002, 57, 1521-1524. (5) Schoenmakers, G.; Bessling, B. Reactive Distillation Process Development in the Chemical Process Industries. In Reactive Distillation; Sundmacher, K., Kienle, A., Eds.; Wiley-VCH: Weinheim, Germany, 2003; Chapter 2. (6) Okasinski, M. J.; Doherty, M. F. Simultaneous Kinetic Resolution of Chiral Propylene Oxide and Propylene Glycol in a Continuous Reactive Distillation Column. Chem. Eng. Sci. 2003, 58, 1289-1300. (7) Krishna, R. Hardware Selection and Design Aspects for Reactive Distillation Columns. In Reactive Distillation; Sundmacher, K., Kienle, A., Eds.; Wiley-VCH: Weinheim, Germany, 2003; Chapter 7. (8) Baur, R.; Krishna, R. Distillation Column with Reactive Pumparounds: an Alternative to Reactive Distillation. Chem. Eng. Process. 2004, 43, 435-445. (9) Ojeda Nava, J. A.; Baur, R.; Krishna, R. Combining Distillation and Heterogeneous Catalytic Reactors. Chem. Eng. Res. Design 2004, 82 (A2), 160-166. (10) Ouni, T.; Jakobsson, K.; Pyhalahti, A.; Aittamaa, J. Enhancing Productivity of Side Reactor Configuration Through Optimizing the Reaction Conditions. Chem. Eng. Res. Design 2004, 82 (A2), 167-174. (11) Kaymak, D. B.; Luyben, W. L.; Smith, O. J. Effect of Relative Volatility on the Quantitative Comparison of Reactive Distillation and Conventional Multi-Unit Systems. Ind. Eng. Chem. Res. 2004, 43, 3151-3162. (12) Citro, F.; Lee, J. W. Widening the Applicability of Reactive Distillation Technology by Using Concurrent Design. Ind. Eng. Chem. Res. 2004, 43, 375-383. (13) Stitt, E. H. Reactive Distillation for Toluene Disproportionation: A Technical and Economical Evaluation. Chem. Eng. Sci. 2002, 57, 1537-1543. (14) Kaymak, D. B.; Luyben, W. L. Quantitative Comparison of Reactive Distillation with Conventional Multi-Unit Reactor/ Column/Recycle Systems for Different Chemical Equilibrium Constants. Ind. Eng. Chem. Res. 2004, 43, 2493-2507.
Received for review April 16, 2004 Revised manuscript received July 26, 2004 Accepted September 15, 2004 IE040124A
