Ind. Eng. Chem. Res. 2007, 46, 5175-5185
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Optimum Design of a Column/Side Reactor Process Devrim B. Kaymak Department of Chemical Engineering, Istanbul Technical UniVersity, 34469, Maslak, Istanbul, Turkey
William L. Luyben* Department of Chemical Engineering, Lehigh UniVersity, Bethlehem, PennsylVania 18015
One of the limitations for reactive distillation to be economically attractive is that the temperature range suitable for reasonable chemical reaction kinetics must match the temperature range suitable for vaporliquid equilibrium because both separation and reaction occur in a single vessel. This temperature mismatch problem can sometimes be overcome by considering an alternative process flowsheet that features a distillation column linked with several external side reactors. The column operates at a low pressure and temperatures favorable for separation. Liquid sidestreams from trap-out trays at intermediate locations in the column are pumped to external reactors operating at higher pressure and temperatures that are favorable for chemical kinetics. This paper extends our previous work [Kaymak, D. B.; Luyben, W. L. Ind. Eng. Chem. Res. 2004, 43, 8049-8056] to provide a more rigorous steady-state economic optimization of the column/side reactor flowsheet. Results demonstrate that this configuration has better steady-state economics than conventional reactive distillation in cases where there is a temperature mismatch between reaction and separation. 1. Introduction Economic and environmental issues have pushed the chemical industry to explore technologies that achieve process intensification (smaller inventories of chemicals). Reactive distillation, where reaction and separation units are integrated in a single column, presents an excellent example of process intensification. It has several advantages in some chemical systems, compared to conventional multi-unit flowsheets with separate reaction and separation sections. Investment and operating costs may be reduced. Conversion and selectivity may be increased. Reactive distillation has received much attention in the past decade, in both industry and academia. However, the applicability of reactive distillation is highly dependent on the chemical system at hand, and there are still limited applications of this process. A fundamental difference between reactive distillation and a conventional multi-unit flowsheet is the selection of operating temperatures. In a conventional multi-unit process, optimal temperatures for the reactor and the columns can be set independently. Conversely, this is not the case in reactive distillation because both reaction and separation occur in the same vessel operating at a single pressure. Thus, if reactive distillation is to be attractive, the temperatures that are good for reaction must match the temperatures that are good for vapor-liquid separation. Kaymak et al.1 presented a quantitative economic comparison of reactive distillation versus conventional multi-unit flowsheets. They demonstrated that reactive distillation becomes less attractive as the temperature mismatch increases. 2. External Side-Reactor/Column Process One approach to overcoming the temperature mismatch is to consider a flowsheet that features a distillation column with external side reactors. There have been several papers involving different configurations of combined column/reactor systems. * To whom correspondence should be addressed. Tel.: 610-7584256. Fax: 610-758-5057. E-mail address:
[email protected].
Schoenmakers and Buehler2 published a pioneering paper that mentions the use of external reactors coupled with a distillation column. Two decades later, Jakobsson et al.3 developed a new unit model to design and optimize the column/side reactor flowsheet, instead of solving it iteratively via the sequential modular approach. They used a sequence of interlinked continuously stirred tank reactors (CSTRs) to represent the side reactors. Baur and Krishna4 developed an algorithm to determine the optimal column/side reactor configuration to achieve the maximum conversion. They simulated the case study of methyl acetate production to evaluate their algorithm. The reactors were modeled by a series of CSTRs. They concluded that the conversion level of a reactive column can be matched by choosing the appropriate number of side reactors and the pumparound ratio. They also indicated that the liquid drawoff and return locations to the column should be taken into consideration. Bisowarno et al.5 studied the application of a column/side reactor system for ethyl tert-butyl ether (ETBE) production. The side reactor was represented by a series of CSTRs to model a tubular reactor. Several configurations of this concept were compared with respect to the overall isobutylene conversion and the ETBE purity of the bottom product. They concluded that the column/side reactor concept should be considered during the conceptual design phase. Gadewar et al.6 outlined a methodology to generate feasible partially integrated flowsheets, which have advantages over both a conventional multi-unit flowsheet and a reactive distillation column. Ouni et al.7 compared the column/side reactor configuration with reactive columns, using two different types of industrial examples: tertamyl methyl ether (TAME) production and isobutylene dimerization. They concluded that the performance of the process can be improved when the design parameters in the reactor series are optimized. Ojeda Nava et al.8 examined a column/side reactor configuration with a single reactor for TAME production. They concluded that the column/side reactor configuration can be competitive with reactive distillation. Citro and Lee9 discussed a column/side reactor configuration for the methyl acetate system, where both the liquid and vapor
10.1021/ie070125d CCC: $37.00 © 2007 American Chemical Society Published on Web 06/26/2007
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Figure 1. Vapor pressures: the R390 ) 2 and 0.95 cases. Table 1. Physical and Chemical Parameters parameter 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) liquid density, FL (kg/m3) ideal gas constant (cal/(mol K)) heat capacity, cp (kJ/(kg K)) heat-transfer coefficient, U (kJ/(s K m2))
value 30000 40000 0.008 0.008/(KEQ)366 -41.8 29 50 800 1.987 2.93 0.85
streams are fed to the side reactor and returned to the same trays from which they are withdrawn. They recommended additional feasibility studies. Kaymak and Luyben10 claimed that the treatment by Citro and Lee9 seems to assume unrealistic hydraulics. Because the reactor would have to operate at a higher pressure than the column, the high-temperature vapor streams from the column would have to be compressed, which could be very expensive. Thus, they considered the design of a practical column/side reactor process in which only the liquid goes to the external reactor because pumping liquid is relatively inexpensive. Two different configurations of this flowsheet were explored: side reactors with and without feed-effluent heat exchangers (FEHEs). Some general characteristics and results were discussed. These preliminary results showed that both of these configurations have better economics than a reactive distillation column when there is a mismatch between favorable reaction and favorable vapor-liquid equilibrium temperatures. The current paper extends and refines our previous work on the column/side reactor process. Some of the heuristic assumptions are relaxed, and more-rigorous economic optimization is performed. 3. Process Studied The process considered is taken from our previous papers. In this generic reaction, products C and D are formed by
an exothermic reversible liquid-phase reaction of reactants A and B:
A+BTC+D
(1)
The forward and reverse specific reaction rates follow the Arrhenius law:
kF ) aF e-EF /(RT )
(2)
kR ) aR e-ER /(RT )
(3)
The rate law is based on concentrations given in mole fractions and liquid holdups given 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)
Table 1 gives physical and chemical parameter values. The reverse reaction rate is more temperature-dependent than the forward reaction rate because the reaction is exothermic. The vapor pressure of component j (PSj ) is a function of temperature and is calculated using the Antoine equation:
ln PSj ) AVP, j -
BVP, j T
(5)
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 previously.10 The relative volatilities between all adjacent components are assumed to be equal to 2 at a temperature of 320 K. This
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Figure 2. Column/side reactor process: (A) with feed-effluent heat exchangers (FEHEs) and (B) without FEHEs.
temperature corresponds to typical reflux drum temperature when using cooling water in the condenser.
RC ) 8
(6a)
RA ) 4
(6b)
RB ) 2
(6c)
RD ) 1
(6d)
The relative volatilities are assumed to change with temperature, becoming smaller as temperature increases. The value of the relative volatility of all adjacent components at a temperature of 390 K (R390) is used as a parameter to vary the temperature dependence. The smaller the R390 value, the more temperaturedependent the vapor-liquid system. A temperature of 390 K is chosen because this temperature gives reasonable reaction rates and chemical equilibrium constants for the numerical example considered. Different cases are studied for a range of R390 values. For the R390 ) 2 case, the relative volatilities are independent of temperature. For the R390 ) 0.95 case, the adjacent components switch volatilities as the temperature approaches 390 K, so the desired separation would be infeasible. Figure 1 provides two examples of different temperaturedependent vapor pressures. In the left graph, vapor pressures are constant for all temperatures. In the right graph, the curves get closer as temperature increases. The Antoine constants for the cases considered are listed in Table 2. 4. Flowsheet Configuration The two alternative flowsheets studied in the previous paper are depicted in Figure 2. The only difference between these two configurations is the heat exchangers used between the column and the reactors. The configuration in Figure 2A has heat exchangers to preheat the reactor feed. There are no heat exchangers in Figure 2B. These FEHEs increase the inlet
Table 2. Vapor Pressure Constants vapor-pressure constant
reactant A
reactant B
product C
product D
AVP BVP
12.34 3862.00
R390 ) 0.95 15.80 5189.23
8.89 2534.77
19.26 6516.46
AVP BVP
12.34 3862.00
R390 ) 1.25 14.27 4699.95
10.42 3024.05
16.20 5537.90
AVP BVP
12.34 3862.00
R390 ) 1.5 13.26 4374.90
11.44 3349.10
14.17 4887.80
AVP BVP
12.34 3862.00
R390 ) 2 11.65 3862.00
13.04 3862.00
10.96 3862.00
temperatures to the external adiabatic tubular reactors, so reactor volumes are smaller than those required without FEHEs. The distillation column operates at its optimum pressure and temperature for separation (320 K in the reflux drum). 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, and a rectifying section with NR trays and a total condenser. As shown in Figure 2, several total liquid trap-out trays are installed at several intermediate trays between these two zones. NM trays are present in the middle of the column. No reaction occurs anywhere in the column: reaction only occurs in the external side reactors. The liquid trap-out trays collect all the liquid coming down from upper trays. The vapor from the tray below each trap-out tray flows up through the chimney to the tray above. There is no vapor-liquid contact on the trap-out trays. Liquid from each tray-out tray is pumped to a sufficiently high pressure so that the material remains liquid at the higher temperatures in the external side reactors. The reaction occurs in adiabatic plugflow reactors. Reactor effluents are fed back to the column on the tray below the trap-out tray from which they were withdrawn. The light product C leaves in the distillate, while the heavy product D is removed in the bottoms.
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Table 3. Optimization Results of Distillation Column/Side Reactor Design Value Previous Design parameter design variables NEXT VR (kmol) NS NR NLT design parameters NT VS (mol/s) R (mol/s) Dc (m) Ar (m2) Ac (m2) DR (m) LR (m) capital cost (103$) column tray heat exchanger reactor energy cost (103$/yr) total annual cost, TAC (103$/yr)
R390 ) 0.95
Current Designs R390 ) 0.95
R390 ) 1.25
R390 ) 1.50
R390 ) 2.00
3 60 20 29 5
3 80 17 7 2
3 50 12 7 2
4 35 9 7 1
4 20 7 8 1
60 58.4 63 1.34 86.1 186 0.785 7.85
31 55.86 60.51 1.32 82.16 179.48 0.860 8.60
26 44.95 49.60 1.22 66.11 152.69 0.735 7.35
23 37.71 42.36 1.14 55.46 134.93 0.652 6.53
22 31.66 36.32 1.08 46.57 120.09 0.543 5.42
500
289.3 10.9 341.0 253.0 240.7 538.8
230.5 8.1 302.9 188.8 193.7 437.1
195.5 6.5 276.1 201.6 162.5 389.1
177.3 5.7 252.6 142.3 136.5 329.1
350 214 252 613
Our previous work10 illustrated the interesting tradeoff between heat-exchanger cost and external reactor cost. They found that capital investment is smaller if large external reactors are used without heat exchangers because heat-exchanger area is more expensive that a simple adiabatic reactor vessel. Thus, the configuration addressed in this study is that shown in Figure 2B. 5. Assumptions and Specifications The column/side reactors process has a large number of design optimization variables. Several specifications and assumptions are made to reduce this number to a manageable level. The design objective is to obtain 95% conversion for fixed fresh feed flow rates of 12.6 mol/s of each reactant. The product purities of distillate stream xD,C and bottoms stream xB,D are both 95 mol %. 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, respectively. The reactors are assumed to be adiabatic, and the holdups of all reactors are same. We assume that the number of trays between each liquid trap-out tray is the same. Other assumptions are theoretical trays, equimolal overflow, saturated liquid feeds and reflux, total condenser and partial reboiler. Based on these specifications and simplifying assumptions, there are five optimization variables: (1) the number of external side reactors, NEXT; (2) the holdup of each reactor, VR; (3) the number of trays between each liquid trap-out NLT; (4) the number of the stripping trays, NS; and (5) the number of the rectifying trays, NR. 6. Reactor and Column Equations The tray temperatures of the trap-out trays are the inlet temperatures to the external reactors. The ordinary differential equations (ODEs) of a plug-flow reactor for steady-state adiabatic operation are integrated from zero to the total reactor volume VR, keeping track of how the component
compositions and temperature change along the reactor. These equations are
dxA dxB -(kFxAxB - kRxCxD) ) ) dV dV FEXT
(7a)
+(kFxAxB - kRxCxD) dxC dxD ) ) dV dV FEXT
(7b)
and
where the kinetics vary with temperature and FEXT is the flow rate of liquid to the external reactor (expressed in units of mol/ s). Since the reactor is adiabatic, the temperature is directly related to composition:
Tout ) Tin +
(xin, A - xout, A)(-λ) cp MW
(8)
where xin,A is the mole fraction of reactant A in the feed to the reactor, xout,A the mole fraction of reactant A in the effluent from the reactor, λ the heat of reaction (given in units of kJ/(mol A reacted)), cp the heat capacity (given in units of kJ/(kg K)), and Mw the molecular weight (given in units of kg/kmol). The steady-state vapor and liquid rates are constant through the stripping and rectifying sections because equimolal overflow is assumed. However, because the reaction is exothermic, some vapor is produced as the liquid from the high-pressure 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:
∆VEXT )
QEXT FEXT(xin,A - xout,A)(-λ) ) ∆Hv ∆Hv
(9)
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where ∆Hv is the heat of vaporization (expressed in units of kJ/mol). Thus, there are different liquid and vapor rates in the various sections of the column. The vapor-liquid equilibrium is assumed to be ideal. The column pressures are set using the vapor pressures of pure components (PS) and the liquid compositions in the reflux drum (xD,j) at 320 K (so that cooling water can be used in the condenser). Temperature (Ti) and vapor composition (yi,j) on tray i can be calculated with given pressure P and tray liquid composition xi,j. These bubblepoint calculations can be made using a Newton-Raphson iterative convergence method: NC
P)
xi, j Pi,S j (T ) ∑ j)1
yi,j )
( )
Pi,S j x P i, j
(10)
(11)
Simultaneous solution of the large set of nonlinear and algebraic equations is difficult, especially with the high degree of nonlinearity, which is due to the reaction kinetics. The steadystate solution of these equations is achieved using the relaxation technique. This method is an efficient and robust way of solving this large set of equations. A value of reflux flow rate R is guessed, and the dynamic equations of the system (mole fractions through the column) are integrated in time until steadystate conditions are achieved. For this study, 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). The reflux flow rate is varied until these compositions are achieved. The dynamic component balances for the column are given as follows:
Reflux Drum: d(xD, j MD) ) VNT y NT, j - D(1 + RR)xD, j (12) dt Rectifying and Stripping Trays: d(xi, j Mi ) ) L i+1xi+1, j +Vi-1 yi-1, j - Li xi, j - Vi yi, j (13) dt Intermediate Trays (except reactor effluent return trays): d(xi, j Mi) ) Li+1xi+1, j + Vi-1 yi-1, j - Lixi, j - Vi yi, j (14) dt Reactor Effluent Return Trays: d(xi, j Mi) ) (FEXT - ∆VEXT)xout,i, j + dt Vi-1yi-1, j - Lixi, j - Vi yi, j (15)
Feed Trays: d(xi, j Mi ) ) Li+1xi+1, j + Vi-1yi-1, j - Lixi, j dt Viyi, j + F0j z0i, j (16)
Column Base: d(xB, j MB) ) L1x1, j - BxB, j - VSyB, j (17) dt
Column diameter is set by the largest vapor rate, which is VNT in the top section of the column. Energy consumption is set by the vapor rate VS at the bottom of the column. 7. Design Optimization Procedure A five-dimensional grid search method is used to find the optimum values of the five design optimization variables. The following steps in the design procedure are used: (1) Fix the number of reactors (NEXT) at a small value. (2) Fix the holdup for each reactor (VR) at a small value. (3) Fix the number of trays between each liquid trap-out tray (NLT) at a small value. (4) Fix the number of stripping trays (NS) at a small value. (5) Fix the number of rectifying trays (NR) at a small value. (6) The flow rates of the two fresh feeds are fixed at 12.60 mol/s. (7) The flow rates of the distillate and bottoms are fixed at 12.60 mol/s. (8) The vapor boilup (VS) is manipulated by a proportional controller to control the level in the column base; the reflux drum level is not controlled. (9) The reflux flow rate is manipulated by a PI controller to drive the composition of product C in the distillate to its desired value; this also sets the purity of product D in the bottoms product. (10) The values (xout, Tout, and ∆VEXT) for adiabatic reactors are calculated with eqs 7-9. (11) The liquid and vapor rates through the stripping and rectifying sections are calculated using eq 9, together with the equimolal overflow assumption. (12) The vapor compositions and temperatures on each tray are computed using bubblepoint calculations with eqs 10 and 11. (13) The time derivatives of component material balances are evaluated using eqs 12-17. (14) All ODEs are integrated using the Euler algorithm. (15) Steps 8-14 are repeated until the system achieves the convergence criterion, which is
CC ) max
| |
dxi, j e 10-6 dt
(the largest time derivative of any component on any tray is 320 K are higher than those for the constant relative volatility R390 ) 2 case. Figure 3B gives the composition profiles for three R390 values. All the composition profiles are quite similar, except for component A. The component A profiles have two peaks in all cases; however, the upper peak for the R390 ) 2 case is much larger than that observed for the other R390 cases.
8.1. Case with r390 ) 0.95. Figure 4 displays how the annual capital and energy costs are affected by the variation of two optimization variables: the holdup of reactors (VR) and the number of reactors (NEXT) for R390 ) 0.95 case. A payback period of 3 years is used to calculate the annual capital cost from total capital investment. All cost graphs are plotted versus VR for three different NEXT values, with a fixed total number of trays and a fixed number of stripping and rectifying trays (NT ) 31, NS ) 17, and NR ) 7, respectively). Although the total number of trays in the middle zone is equal for all three NEXT values, the number of trays between each liquid trap-out tray differs because of the different reactor numbers. As the lower left graph in Figure 4 shows, an increase in the number of reactors results in higher reactor cost, and reactor cost increases with increasing reactor holdup. On the other hand, the costs of the column, the heat exchangers (reboiler and condenser), and energy show an exponentially decaying curve as the reactor volume is increased. This is due to the dependence of these costs on the vapor boilup. The increase of the reactor holdups increases the conversion of the reactants. Because less reactant is fed back to the column from the external reactors, the separation is easier for columns. The result is a decrease in
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Figure 4. Effects of reactor numbers and holdups.
Figure 5. Effects of stripping and rectifying tray numbers.
reflux and vapor boilup required to achieve the desired purities of product streams. Therefore, the costs related to the separation decrease as reactor holdup increases. When the columns with different reactor numbers are compared, it can be observed that these separation-related costs decrease as more reactors are used. Because of the decreasing column cost and heat exchanger cost, the capital cost initially decreases with an increase in reactor holdup. However, at some point, the increasing reactor cost becomes more dominant and the total capital cost begins to increase. While the reactor cost increases with increasing number and holdup of reactors, the opposite is true for separation costs. Increasing the reactor number or holdups reduces the separation costs (heat exchanger and column capital costs and energy cost). Thus, there is a minimum in the TAC curve at a certain number of reactors and at a certain value of reactor holdup because of
the classical tradeoff between reactor cost and separation cost. For the R390 ) 0.95 case with constant values for the total number of trays and the number of stripping and rectifying trays, the optimum reactor number is 3, and the optimum reactor holdup is 80 kmol for each reactor. Figure 5 shows the effects of changes in the number of stripping and rectify stages for the R390 ) 0.95 case. All cost figures are plotted versus the number of stripping stages (NS) for four different NR values. The reactor holdups, the number of reactors, and the number of trays between each liquid trapout tray are kept constant at VR ) 80, NEXT ) 3, and NLT ) 2, respectively. Because the number and the holdups of the reactors are kept constant, the reactor costs do not change. The column cost increases as the numbers of stripping and rectifying trays increase. However, the upper right graph in Figure 5 shows that
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Figure 6. Results for column/side reactors process with different R390 values.
Figure 7. (A) Cost results for column/side reactors process with different R390 values. (B) Comparison of alternative processes.
there is a minimum in the energy cost, which is directly related to vapor boilup. The lower right graph shows that the heatexchanger-cost curves track the energy costs directly. As the number of stripping trays increases, the amount of vapor boilup that is required decreases initially. However, increasing the number of stripping trays above the optimum results in an increase of the required vapor boilup. This occurs because the extra separation that occurs with more stripping stages concentrates the products in the middle zone and shifts the chemical equilibrium back to the reactants on the lower part of the middle zone. For example, the concentration of reactant A on the lowest tray of middle zone increases from 0.3711 to 0.4396 as NS is changed from 17 (the optimum) to 22. However, the concentration of product D at the same location decreases from 0.3432 to 0.3073. Therefore, more energy is required to keep component A from leaving in the bottoms. Thus, there is
an optimum stripping tray number that minimizes vapor boilup and the resulting energy cost and heat exchanger cost. A similar effect for reactive columns was discussed by Sneesby et al.11 The change in column costs over the range of separation trays shown in these graphs is relatively large (260 to 360 × 103$/yr) compared to the change in heat exchanger cost (330 to 355 × 103$/yr). Therefore, column cost, which decreases with decreasing numbers of separation trays, is the most dominant factor among the three capital cost factors. Thus, the optimum capital cost shifts to smaller numbers of stripping and rectifying trays, while the optimum energy cost shifts to larger numbers of stripping and rectifying trays. The result is a minimum in the TAC curve at a certain number of stripping and rectifying trays. For the R390 ) 0.95 case with constant reactor number (NEXT ) 3) and constant reactor holdup (VR ) 80 kmol), the
Ind. Eng. Chem. Res., Vol. 46, No. 15, 2007 5183 Table 4. Results for Reactive Distillation Columns with Different Feed Tray Locations Valuea R390 ) 0.95 parameter design variables NS NRX NR NF1/NF2 pressure, P (bar) design parameters NT Vs (mol/s) R (mol/s) Dc (m) Ar (m) Ac (m) capital cost (103$) heat exchanger column tray energy cost (103$/yr) total annual cost, TAC (103$/yr)
optimum design 1
optimum design 2
R390 ) 1.25 optimum design 1
14 68 3 15/82
R390 ) 1.5
optimum design 2
optimum design 1
11 25 5 29/68
12/36
3.75
R390 ) 2 optimum design 1
9 13 6 20/28
10/22
5.50
85
optimum design 2
5 7 5 13/19
6/12
7.00
41
optimum design 2
7/11 8.50
28
17
99.15 103.78 1.53 145.83 285.71
94.76 99.40 1.50 139.38 274.95
68.50 73.14 1.21 100.75 210.48
58.18 62.82 1.13 85.57 185.17
48.82 53.46 1.00 71.81 162.18
42.67 47.31 0.95 62.76 147.09
28.79 33.42 0.80 42.34 112.98
26.65 31.28 0.78 39.20 107.73
474.1 763.0 37.7 427.2 852.2
461.6 747.1 36.6 408.4 823.5
382.4 329.3 12.5 295.2 536.6
348.8 307.4 11.4 250.7 473.2
316.7 198.8 6.4 210.4 384.4
294.6 188.7 6.0 183.9 347.0
240.9 104.5 2.7 124.0 240.1
232.0 101.8 2.6 114.8 227.0
a The results given in the “optimum design 1” column of each R 390 case are the optimum designs with the assumption that feed locations NF1 and NF2 are located at the bottom and top of the reactive zone, respectively. The results given in the “optimum design 2” column of each R390 case are the optimum designs where feed locations are also taken as design optimization variables, while other design variables are kept at their optimum values.
Figure 8. Effect of feed tray locations.
optimum numbers of stripping and rectifying trays are NS ) 17 and NR ) 7, respectively. It is interesting to compare the design obtained in this paper with the approximate heuristic design found in our previous paper.1 The first two columns in Table 3 give a direct comparison. The improved design has fewer trays and larger reactors. The TAC is 13% lower. 8.2. Other r390 Cases. Figure 6 gives optimum design results for the column/side reactors process for a range of temperaturedependent relative volatilities (R390 ) 0.95-2). These results show that there is little change in the optimum number of the reactors. As the reference R390 value decreases, the optimum number of reactors also slightly decreases from 4 to 3. The inlet and outlet temperatures of the reactors decrease as the reference R390 value decreases.
However, lower temperatures are unfavorable for reaction because the reaction rates get smaller. The result is a rapid increase in the required reactor holdups. Lower reference R390 values result in separation that is more difficult, as expected. Thus, there is an increase in the required vapor boilups and the number of stripping trays. Because the operating pressure at the top is kept constant for all R390 cases, there is not a significant change in the number of rectifying trays. Note that the optimum number of stripping trays is larger than the optimum number of rectifying trays. This is caused by the higher temperatures in the lower part of the column, which means lower relative volatilities. Results for these four different R390 cases are given in Table 3. Values of the five design optimization variablessthe number of reactors, the holdup of each reactor, the number of the
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stripping trays, the number of the rectifying trays, and the number of trays between each liquid trap-out traysare shown. Table 3 and the upper graph in Figure 7 show that reducing the reference relative volatility increases both capital and energy costs, which results in an increase of the TAC. The lower graph in Figure 7 compares the economic optimum steady-state design of the column/side reactor process with those of the reactive distillation column and the multi-unit conventional process.10 The reactive distillation column is the most economic alternative for the case R390 ) 2, where no reaction/separation temperature mismatch is observed. The column/side reactor process becomes more attractive as the mismatch of reaction/separation temperatures becomes more severe. Figure 6B shows that the distillation column with side reactor is economically superior for reference relative volatilities of
