Reactive Distillation for Fischer−Tropsch Synthesis: Feasible Solution

Jun 22, 2010 - Regions of interest corresponding to different objectives .... represent the feasible solution space for different objectives. Thus, in...
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Ind. Eng. Chem. Res. 2010, 49, 6350–6361

Reactive Distillation for Fischer-Tropsch Synthesis: Feasible Solution Space Seethamraju Srinivas, Sanjay M. Mahajani, and Ranjan K. Malik* Department of Chemical Engineering, Indian Institute of Technology, Powai, Mumbai, 400076, India

Fischer-Tropsch synthesis can be advantageously carried out in reactive distillation (RD) mode. Parametric studies like the effect of reflux ratio, pressure, etc. have been reported in our earlier work [Srinivas et al. Ind. Eng. Chem. Res. 2009, 48, 4719-4730] using Aspen Plus. As an extension of this work, multiparameter sensitivity analysis is performed on a simple RD configuration without side-draws or side-coolers in Aspen Plus, retaining the kinetic and thermodynamic models used previously. A feasible solution space in terms of reflux ratio, pressure, and total catalyst loading is identified and possible reasons for the bounds observed are provided. Changes in the column configuration toward various objectives like maximum conversion, maximum gasoline yield, or selectivity, etc. are also investigated. Regions of interest corresponding to different objectives are represented on a Da-reflux ratio plot. Introduction Reactive distillation (RD) that combines reaction and separation together in a single piece of equipment has some potential benefits to offer when applied to the reaction of Fischer-Tropsch synthesis (FTS) that converts syngas to a wide range of heavy hydrocarbons. The major advantages include temperature control by using the reaction exotherm and simultaneous product separation that enables side-draws, thereby reducing the load on the downstream processing equipment. It also provides flexibility in the choice of both operating (reflux ratio, sidecooler duties, etc.) and design (number of reactive stages, catalyst loading per stage, etc.) parameters to alter the product yields and selectivity. The feasibility of RD for FTS has been shown with the help of simulations in our earlier work1 using a kinetic model which incorporates in it a detailed productdistribution and olefin readsorption.2 A built-in thermodynamic model, PRMHV2, based on the Peng-Robinson equation of state (PR EoS) with Huron-Vidal mixing rules as suggested by Marano and Holder3 is used for phase equilibrium calculations in the Aspen Plus simulations. The effect of various parameters, both design and operating, like reflux ratio, catalyst loading, number of reactive/nonreactive stages, etc. was also analyzed and the changes in performance parameters such as conversion, product yields, and distribution were commented upon. The few important questions that now arise are as follows: (1) What is the optimum configuration (in terms of reflux ratio, condenser pressure, and catalyst loadingsboth total as well as per stage)? The objective could be to maximize conversion or improve selectivity toward a desired fraction like gasoline or diesel, etc. (2) Does the optimum configuration vary as the objective varies? Given a fixed design, is it possible to move from one optimum configuration to another when the target changes? (3) With the background knowledge of sensitivity analysis obtained from parametric studies4 and optimization, is it possible to design a RD column for FTS using a simulation package for a specified target, e.g., definite throughput at a desired conversion level? (4) Is the design generated unique? The aim of this work is to answer the first two questions in the best manner possible. The problems related to design are * To whom correspondence should be addressed. Phone: (022) 2576 7796. Fax: (022) 2572 6895. E-mail: [email protected].

presented in a separate work5 that elaborates the design algorithm proposed along with illustrative examples. The important conclusions from an earlier parametric study for FTS in RD4 are listed below to form a base for further discussion on the results obtained in this work: • There is a trade-off between conversion and liquid yields as the reflux ratio is varied. The conversion is higher at higher values of reflux ratio, but net liquid yields decrease. • The way the catalyst is distributed on the stages, for a given total loading, affects the conversion and product selectivity too. • As the per stage catalyst loading changes due to an increase in the number of reactive stages, there is a change in conversion and product selectivity. • An increase in heat-removal results in a slight decrease on the corresponding stage temperature leading to a fall in conversion and increase in heavy product selectivity. There is no significant change in conversion or product selectivity on altering side-draws or by adding nonreactive stages below the last reactive stage in the column. It only changes the purity of the bottom product. Using Simulators for the Design and Optimization of an RD Column Table 1 presents a concise overview on the use of Aspen Plus for the simulation of RD columns by various researchers. It can be seen that the use of Aspen Plus has mainly been for the purpose of comparing/validating the theoretical model with experimental results and performing what-if studies apart from optimization and design of RD columns. The list presented in Table 1 is not exhaustive and is only indicative of the different types of reactions simulated using Aspen Plus for RD applications. As regards optimization in RD, there has not been much work performed to date. Seferlis and Grievink26 use the technique of orthogonal collocation on finite element (OCFE) in combination with an optimization algorithm to evolve an optimal design for an RD column synthesizing ethyl acetate from ethanol and acetic acid. The use of OCFE avoids considering the individual stages as integers and simplifies the model to be solved. Stichlmair and Frey27 use MINLP optimization to demonstrate the optimized RD configuration in case of methyl acetate and MTBE syntheses. More recently, Gangadwala and Kienle28 apply MINLP optimization for butyl acetate synthesis considering two alternativessa stand-alone RD

10.1021/ie100106u  2010 American Chemical Society Published on Web 06/22/2010

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Table 1. Overview of RD Simulation Work Using Aspen Plus ref 6

description of work presented 7

Jacobs and Krishna; Nijhuis et al.; Hauan et al.

8

Ciric and Miao;9 Ciric and Gu10

Abufares and Douglas11

Perez-Cisneros et al.12

Gonzalez et al.13

Eldarsi and Douglas;14 Kim and Douglas15

Bezzo et al.16

Quitain et al.17 Taylor and Krishna18

Cardoso et al.19

Popken et al.20 Peng et al.21

Smejkal and Soos22 Dhale et al.23 Viveros-Garcia et al.24 Yang et al.25

column and a nonreactive distillation column with side-reactors. Gangadwala et al.29 propose the use of wave functions for model reduction with suitable relaxation methods to reduce the complexity of solving the MINLP formulation and illustrate it for a metathesis reaction in RD. In other works reported in literature, the optimization for RD is performed using different techniques like disjunctive programming,30 genetic algorithms,19 etc. which are not only computationally intensive but also complex. The simulations for FTS in RD until now have been performed using the Radfrac module in Aspen Plus. It is, hence,

Use Aspen Plus to detect and analyze the reasons for multiple steady states (MSS) observed in MTBE synthesis. Reasons for MSS are attributed to initial estimates provided, concentration of n-butene in feed, different kinds of reactive residue curves, and/or interaction between phase and chemical equilibrium. Investigate multiple steady states in the production of ethylene glycol from water and ethylene oxide using homotopy continuation. Synthesize an optimal RD configuration using an mixed integer nonlinear programming (MINLP) formulation to minimize total annual cost using a rigorous tray-by-tray model for the ethylene glycol example. Performed both steady-state and dynamic simulations for MTBE system using Aspen Plus and SPEEDUP, respectively. Comparison with experimental results and dynamic response to step-changes in reflux ratio, etc., are presented. Perform steady-state simulations for MTBE synthesis and ethyl acetate synthesis with emphasis laid on the importance of proper choice of thermodynamic and kinetic models in simulations and their impact on column operation/design. Report a reasonable match between experimental results and simulation for the synthesis of tert-amyl alcohol (hydration reaction) along with parametric studies to find the effect of different operating parameters like feed composition, column pressure, etc. Perform simulation and optimization for an industrial scale RD column used in MTBE synthesis using cost analysis. Four different configurations are studied and the optimal design and operating variables are suggested. Analyze the steady-state behavior of an industrial column for synthesis of propylene oxide from propylene chlorohydrin and calcium hydroxide. Presence of electrolytes in solution and salting-out effects are taken care of. Good agreement between simulated results and real plant data is reported. Perform simulations using Aspen Plus for evaluating a proposed industrial process for the synthesis of ETBE from bioethanol and tert-butyl alcohol in a sequence of two RD columns. Present an extensive review on modeling of reactive distillation covering equilibrium and nonequilibrium stage models, steady-state and dynamic simulations, and a short description of different design methods. Validate the model used in the simulation step of the optimization algorithm by comparison with Aspen Plus simulations for an ethylene glycol RD column. Further illustrate that the proposed simulation/ optimization method has the ability to closely give optimal solutions for RD problems. Compare simulation results using EQ model with experimental data for both methyl acetate synthesis and hydrolysis in a packed RD column, emphasizing the choice of kinetic model used in the simulations. Compare simulation results using EQ and NEQ models implemented in gPROMS independently with Radfrac and Ratefrac for TAME and methyl acetate synthesis. Report excellent agreement between the two cases and point out the merits and demerits of using the EQ or NEQ stage modeling. Compare simulation results of Aspen Plus with Hysys for a RD column having acetic acid and 1-butanol as reactants. Results from either software are reported to predict the pilot-plant data well. Report good agreement between experimental data and simulation results for acetalization reaction involving propylene glycol recovery. Validate a proposed configuration of a RD column obtained from conceptual design for diesel hydrodesulphurization with two reactive zones through rigorous steady-state simulations in Aspen Plus. Use sensitivity analysis to illustrate input and output multiplicities in RD for synthesis of ethylene glycol and ETBE using Radfrac module.

considered easier to continue working with this simulation model for the optimization study. However, owing to the high degree of nonlinearity and complexity arising from the kinetic and thermodynamic models for FTS in RD, the built-in “optimization” utility of Aspen Plus led to convergence issues. One may suggest the use of user-built codes in Fortran or other highlevel languages with MINLP formulations, etc. to solve the optimization problem. While this is possible, it is not considered in the present case because the aim here is to perform analysis that can provide inputs for column design at a preliminary/ conceptual level rather than for the final optimal design, and

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Figure 2. Variation in number of solutions at a fixed pressure as RR and Cat.Wt2 change.

Figure 1. RD configuration for FTS used in sensitivity analysis. 1. Syngas Feed; 2. Vapor Distillate; 3. Liquid Distillate; 4. Bottoms product; 5. Reactive stage loaded with catalyst.

this is illustrated by simultaneous variation of parameters. The paper is organized in the following manner. In a preliminary study, multiparameter sensitivity analysis is performed within a specified range for each parameter, viz. pressure, reflux ratio, and catalyst loading. The reason for the upper and lower bounds on each parameter, if found, will be explored and a suitable way to expand the parameter space will be suggested. The points in the parameter space corresponding to different objectives, like maximum conversion, maximum selectivity toward a product fraction, etc. will be identified in a detailed exercise. Finally, analysis based on the Damkohler number is used to represent the feasible solution space for different objectives. Thus, in a true sense, the exercise presented in this work is inclined toward finding a feasible solution space for different objectives within a certain range of parameters and not the global optimal solution. Preliminary Study The base case for this study is an RD column with no sidedraws or side-coolers (Figure 1). It has four reactive stages with the following catalyst loading: 1.9, 1.8, 0.25, and 0.05 kg. The condenser operates at 25 atm and 35 °C. The column receives syngas feed at the rate of 1000 mol/h with a H2/CO ratio of 2.03 in the feed on its last stage. Further details of this base case can be found in the work of Srinivas et al.1 To start with, three parameters were varied simultaneously as follows using the “sensitivity” block in Aspen Plus: reflux ratio (RR) from 0.215 to 0.36 (0.01); pressure (P) from 15 to 33 atm (1 atm); catalyst weight on the second stage (Cat.Wt2) from 1.9 to 3.8 kg (0.1 kg). The catalyst loading on the other stages is held constant, i.e., 1.8, 0.25, and 0.05 kg on stages 3, 4, and 5, respectively. The selected range for each parameter is such that the upper limit is approximately twice the lower limit. The figures in brackets indicate the increments used. Hence, varying reflux ratio alone results in 15 cases, pressure alone in 19 cases,

and catalyst loading alone in 20 cases. The following parameters are tracked for each case: temperature of the last stage in the column, viz., stage 6, mass flow rates of the distillate (both vapor and liquid) and the bottoms streams, net yields of gasoline and diesel in terms of mass, selectivity toward gasoline and diesel in the liquid product, conversion of CO and H2, average reactive tray temperature, condenser duty, and utility ratio. In total, the three parameters varied together result in 5700 possible cases. It is observed, however, that only 1826 cases result in converged solutions. The reason for the absence of solution is not attributed to convergence or solver-related problems, but to the physics of the process, and is discussed in a latter section. Figure 2 shows the variation in the number of solutions as the reflux ratio and catalyst loading is varied for a given pressure. It is interesting to see that there is a maximum in the number of solutions and the corresponding range of pressure is ∼23-26 atm. Variation in the number of solutions is also observed when the reflux ratio or catalyst loading was kept constant, while altering the other two parameters. Further, it may be noted that despite increasing the reflux ratio by ∼1.7 times from its base case value of 0.215 and the catalyst loading by 2 times from its base value of 1.9 kg, no solutions are possible at the lower and higher end of the pressure spectrum. From parametric studies performed earlier,4 it was concluded that conversion increases as pressure decreases. Thus, at a fixed reflux ratio, it is expected that conversion will be maximum when the catalyst loading is maximum and the pressure is minimum. It may be noted from Table 2 that the minimum pressure corresponding to each reflux ratio is different and no solutions exist below this lower limit of pressure. Table 2 shows the maximum conversion and the respective average reactive tray temperature at different values of reflux ratio for both the observed and expected cases. The values given under maximum conVersion expected show the minimum pressure and the corresponding catalyst weight at which convergence is seen. In most of the cases, the maximum conversion is observed at the minimum possible pressure, except for reflux ratio values of 0.255, 0.285, 0.305, 0.345, and 0.36. The conversion values in the exceptional cases deviate by a maximum of only ∼2% while the temperature deviation is of the order of 20 °C in some cases. It can also be seen that the maximum conversion necessarily does not correspond to the maximum catalyst loading, for e.g., 1.9 kg in case of reflux being 0.255 and 0.285, 2.2 kg for a reflux ratio of 0.36, etc. One may note that the maximum catalyst loading permitted was 3.8 kg which appears in Table 2 only when the reflux ratio is 0.325. The same behavior is seen with the following objectives: maximum gasoline/diesel yield, maximum gasoline/diesel selectivity, and maximum average reactive temperature. It is worth noting that maximizing the yield of gasoline/diesel results in a

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Table 2. Variation in Maximum Conversion maximum conversion observed at

maximum conversion expected at

RR

Pmin (atm)

Cat.Wt2 (kg)

avg reac T (C)

Xco (%)

Pmin (atm)

Cat.Wt2 (kg)

0.215 0.225 0.235 0.245 0.255 0.265 0.275 0.285 0.295 0.305 0.315 0.325 0.335 0.345 0.355 0.36

15 16 17 17 20 19 20 21 21 23 21 22 23 24 24 25

3.6 3.7 3.3 3.1 1.9 3.3 2.7 1.9 2.1 2 3.6 3.8 3.3 3 3.6 2.2

260.8 252.84 253.54 263.62 259.56 250.07 257.44 268.21 271.88 260.56 259.56 247.51 254.15 256.35 250.15 275.12

58.23 57.49 58.45 62.25 60.19 61.15 63.11 64.98 67.78 65.37 68.38 66.38 68.37 69.27 69.23 73.73

15 16 17 17 18 19 20 20 21 21 21 22 23 23 24 24

3.6 3.7 3.3 3.1 3.6 3.3 2.7 3.5 2.1 3.7 3.6 3.8 3.3 3.8 3.6 3.4

configuration which is different from the one that maximizes the selectivity of gasoline/diesel. These observations can be explained by the combined effect of pressure, reflux ratio and catalyst loading. Considering the case in Table 2 when the reflux ratio is 0.285, the difference in conversion between the observed and expected values is 2% with the pressure difference being 1 atm only. However, the catalyst loading almost doubles (from 1.9 to 3.5 kg) and the average reactive tray temperature falls by 20 °C. While the conversion values are comparable, there would be a considerable difference in the product yields. At the observed maximum conversion (avg reac T ) 268.21 °C), the net gasoline yield is 0.064 kg/h and diesel yield is 0.041 kg/h. The respective values at the expected maximum conversion (avg reac T ) 248.22 °C) are 0.155 and 0.271 kg/h, which fall in line with the expectation owing to a lower average reactive tray temperature. One can thus infer the following from the foregoing discussion: (1) There are bounds on each parameter between which a feasible RD design is realized. (2) There appears to be an interval for each parameter wherein the maximum number of solutions is possible. If this can be considered as analogous to flexibility in operating the column, this range should be chosen as the operating zone during the design stage. For example, pressure should be in the range of 23-26 atm (as seen in Figure 2). (3) Results/conclusions from the parametric studies involving sensitivity analysis of a single parameter in isolation cannot be extended to multiparameter sensitivity analysis, as illustrated through the example of conversion in Table 2. It is found that the regions defined by RR, P, and Cat.Wt2 corresponding to maximum gasoline and diesel yields are different. Figure 3 illustrates this finding with the gasoline and diesel yields as a function of P and RR. In all the cases in Figure 3, the top surface represents gasoline and the bottom surface depicts diesel yield. It is interesting to see that there are regions in this space where both the surfaces intersect signifying a change in the behavior of the column toward a response to the combined changes in P, RR, and catalyst loading. In other words, the product distribution shifts from more gasoline and less diesel yields to more diesel and less gasoline yields (Figure 3b and c). To get some more insight, a more detailed study is performed and is discussed in the next section. The reasons for

avg reac T (C)

Xco (%)

249.94

60

248.22

62.51

246.61

64.2

251.63

69.13

260.46

71.72

nonexistence of solutions in parts of the simulation space will then be discussed in the subsequent sections. Generation of a Feasible Solution Space Experiments reported for the kinetics chosen were performed in the following range: temperature 220-269 °C and pressure 10.9-30.9 bar.2 For a detailed analysis, the values of pressure chosen are 20, 22, 24, 25, 26, 28, and 30 atm. The reflux ratio is varied between 0.215 and 0.455 (approximately doubled from the base case value) in increments of 0.01. An additional value of 0.36 is also used that corresponds to the maximum possible reflux beyond which the base case failed to converge. The catalyst weights on each reactive stage are also varied as follows: 1.9-3.8 kg on stage 2 (0.2 kg); 1.8-3.6 kg on stage 3 (0.2 kg); 0.25-0.5 kg on stage 4 (0.05 kg), and 0.05-0.25 kg on stage 5 (0.05 kg). The figures in brackets indicate the step size used. Thus, for a fixed reflux ratio and pressure, the number of solutions possible by simultaneously varying the catalyst weights on all the reactive stages turns out to be 3300. It may be noted that the total catalyst weight is more than doubled from 4 to 8.15 kg as a result. Figure 4 represents the trend in the percentage number of solutions as the catalyst loading is allowed to vary on each stage at different values of pressure. For example, the maximum number of solutions possible at a reflux ratio of 0.365 and 24 atm is 3300 while the number of converged solutions observed is 2356 only. Hence, the percentage number of solutions is 2356/ 3300 which equals 64%. It is interesting to note that allowing the catalyst weight to increase above a total of 4 kg starts resulting in solutions for the base case beyond a reflux ratio of 0.36 as well, which was otherwise not possible in the example presented in the earlier section. Hence, allowing the catalyst loading to be a free variable permits expansion of the solution space. It is further observed that there is a peak in the maximum number of observed solutions in Figure 4. The peak value decreases with increase in pressure and reflux ratio. Table 3 further supports this observation. This is due to the mutual interaction between reflux ratio, pressure, and catalyst loading. An increase in pressure leads to a lowering of conversion while an increase in reflux ratio increases conversion, viz., counteracting in nature. In addition to this, the way the catalyst is distributed between the reactive stages also determines the reaction extent and, hence, the conversion. It is interesting to note that, despite the high catalyst loading provided, there is a minimum and maximum reflux ratio beyond

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Figure 3. (a) Gasoline and diesel yields as a function of P (21-25 atm) and RR (0.215-0.26). (b) Gasoline and diesel yields as a function of P (24-27 atm) and RR (0.265-0.3). (c) Gasoline and diesel yields as a function of P (25-30 atm) and RR (0.3-0.34). (d) Gasoline and diesel yields as a function of P (29-32 atm) and RR (0.335-0.365). Table 3. Percentage of Observed Solutions

Figure 4. Percentage number of solutions obtained as catalyst loading varies.

which no solutions exist. For example, at 25 atm, there are no solutions for a reflux ratio of 0.455 (maximum limit) while no solutions exist below a reflux ratio of 0.325 (minimum limit) in the case of 30 atm. The diagonal pattern for the space in which solutions exist in Table 3 is an interesting feature observed from the sensitivity analysis study. As the pressure increases, there is an increase in both the minimum reflux ratio at which solutions begin to exist and the maximum reflux ratio beyond which solutions cease to exist. This is possibly due to the opposing effects of pressure and reflux ratio on conversion as stated previously. From an operating point of view, one would like the difference between the maximum and minimum reflux ratios to be wide enough. It is observed that the width of the reflux ratio zone remains constant while shifting to the right as pressure increases. Figure 5 illustrates the bounds on the three parameters consideredsreflux ratio, pressure, and total catalyst loading. The cube formed by the bold lines is the simulation

RR

at 20 atm

at 22 atm

at 24 atm

at 25 atm

at 26 atm

at 28 atm

at 30 atm

0.215 0.225 0.235 0.245 0.255 0.265 0.275 0.285 0.295 0.305 0.315 0.325 0.335 0.345 0.355 0.36 0.365 0.375 0.385 0.395 0.405 0.415 0.425 0.435 0.445 0.455

58 68 78 87 92 94 91 84 75 63 49 34 21 11 4 2 1 0 0 0 0 0 0 0 0 0

22 29 37 45 54 64 75 82 87 90 89 82 71 57 44 35 30 17 8 3 1 0 0 0 0 0

2 4 8 13 19 26 34 42 51 59 69 76 79 80 75 71 68 54 41 30 19 11 4 2 0 0

0 0 2 4 7 11 17 23 30 37 46 53 60 65 67 67 65 60 52 43 31 22 12 6 2 0

0 0 0 1 2 4 7 12 17 23 31 39 47 54 60 63 64 65 63 59 53 43 30 20 11 5

0 0 0 0 0 0 0 1 2 4 7 11 16 22 28 31 35 42 49 56 59 59 56 51 43 32

0 0 0 0 0 0 0 0 0 0 0 1 3 5 8 9 12 15 21 28 34 41 46 50 51 49

space considered and the shaded volume within represents the feasible space that resulted in converged solutions. One can also notice seven vertical planes in Figure 5, each of which corresponds to a certain pressure, and draw the following conclusions:

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Study on Bounds

Figure 5. Illustration of bounds.

• Almost the entire range of RR and Wt is covered in the pressure range of 24-26 atm. • At lower pressures, high reflux ratio and high catalyst loading do not give a feasible design. • At higher pressures, low RR does not result in converged solutions and the same is the case with high reflux ratios and high catalyst weights. It now remains to be seen if the solution space in which no converged solutions exist can be expanded further by an additional increase in catalyst weight beyond 8.15 kg. Two such spaces can be identified in Table 3: one encompassing the region (R1) between a reflux ratio of 0.215 and 0.275 and pressure of 28 and 30 atm; the other region (R2) lies between a reflux ratio of 0.445 and 0.455 with the pressure being between 20 and 24 atm. Results from a new set of simulations (details given in section 1 of the Supporting Information) showed that no significant expansion of the solution space is possible for both regions, R1 and R2. It can, therefore, be concluded that there are bounds (maximum and minimum) on the parameters considered heresreflux ratio, pressure, and catalyst weightssboth total and on each stage.

Before going further, the reason(s) for the existence of bounds detected previously are investigated. To start with, the base case having a reflux ratio of 0.215 and pressure of 25 atm was considered. The reflux ratio was decreased until the convergence failed indicating an absence of solution under those conditions. This is observed to be 0.212 and is assumed to be the minimum reflux ratio at that pressure. The pressure is now decreased gradually to 24 atm ensuring convergence is obtained. At this pressure, the minimum reflux ratio is found. This procedure of decreasing pressure and reflux ratio in steps is continued. Table 4 lists the parameters that are tracked during the analysis. At each pressure, the values given are the following: minimum reflux ratio, conversion of CO, the reflux rate (L1), net liquid (which is the sum of the liquid distillate and bottoms streams), percentage of net product as a liquid, the condenser duty, and the average reactive tray temperature in the same order. It is to be noted that, in reality, one may not operate the column at such low pressures owing to the large volumes that will need to be handled and possible mass-transfer limitations. The idea here is to theoretically check for the lowest possible bounds on pressure and the reason for it. As can be seen, the lowest possible pressure is 3.42 atm for a catalyst loading of 4 kg (total) with 0.02101 as the corresponding reflux ratio. No solutions could be obtained by further reduction of any of these three parameters, either alone or in combination. The trends observed in Table 4 fall in line with the earlier conclusions4 that conversion decreases with a decrease in reflux ratio and increases with a decrease in pressure. Since the effect of reflux ratio is more dominant, an overall decrease in conversion is observed with a decrease in pressure. It is evident from Table 4 that the decrease in all the tracked parameters slowly starts to level off as the pressure is lowered. The only source of reflux is from the condensation of the reaction products and a considerable reaction rate is needed to generate products. However, since the reaction is highly exothermic, sufficient removal of reaction exotherm is also necessary to maintain a favorable temperature profile in the column. This requires formation of condensable products like naphtha, etc. rather than light gases at significant levels of conversion. It is inferred that overlapping of these conditions, viz., significant conversion and formation of condensable

Table 4. Minimum Conditions P (atm)

min RR

Xco (%)

L1 (kg/h)

net liq (kg/h)

% liq

Qc (kW)

avg reac T (°C)

25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 3.5 3.42

0.212 0.194 0.177 0.16 0.144 0.128 0.111 0.095 0.083 0.072 0.062 0.054 0.049 0.044 0.039 0.036 0.0325 0.03 0.0276 0.0257 0.0238 0.021 0.02101

39.76 36.98 34.24 31.35 28.54 25.58 22.18 18.75 16.13 13.62 11.21 9.2 8.01 6.75 5.37 4.67 3.63 3 2.34 1.96 1.72 0.876 0.777

0.1841 0.1702 0.1569 0.1434 0.1304 0.1171 0.1029 0.0891 0.0786 0.0688 0.0597 0.0524 0.0477 0.043 0.0383 0.0354 0.0321 0.0297 0.0274 0.0255 0.0237 0.0209 0.0209

0.644 0.604 0.562 0.518 0.474 0.428 0.374 0.319 0.274 0.23 0.189 0.154 0.132 0.109 0.0854 0.0723 0.0547 0.0436 0.0325 0.0256 0.0207 0.00896 0.00787

6.08 5.70 5.30 4.89 4.47 4.04 3.53 3.01 2.59 2.17 1.78 1.45 1.25 1.03 0.81 0.68 0.52 0.41 0.31 0.24 0.20 0.08 0.07

-5.262 -5.014 -4.771 -4.515 -4.266 -4.005 -3.706 -3.405 -3.174 -2.953 -2.742 -2.565 -2.456 -2.349 -2.227 -2.165 -2.074 -2.019 -1.961 -1.927 -1.905 -1.831 -1.822

214.79 213.77 212.89 211.88 210.94 209.87 208.41 206.87 205.88 204.68 203.24 201.94 201.66 200.88 199.25 199.31 197.63 197.15 195.95 196.42 198.04 194.29 192.79

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Table 5. Maximum and Minimum Reflux Ratios As a Function of Pressure P (atm)

RRmin

RRmax

delta RR

20 22 24 25 26 28 30

0.128 0.16 0.194 0.212 0.23 0.266 0.3

0.276 0.306 0.336 0.355 0.365 0.394 0.42

0.148 0.146 0.142 0.143 0.135 0.128 0.12

products, is not possible at the limits found resulting in no solution. This reason holds good for each of the cases in Table 4 as well. A similar exercise is performed to find the maximum reflux ratio corresponding to each pressure and the maximum possible pressure. The maximum possible pressure is 47.3 atm for a catalyst loading of 4 kg (total) with 0.649 as the corresponding reflux ratio. And as expected, the conversion increases with the increase in the reflux ratio overriding the effect of increase in pressure. As the reflux ratio increases, the reaction rates increase owing to a higher average reactive tray temperature. This implies the higher formation of products, and hence, the starvation in reflux rate is not expected. However, higher reactive stage temperatures (∼270-300 °C) push the product spectrum toward methane and other lighter gaseous components which cannot be condensed leading to problems in providing an adequate amount of reflux. Thus, the bounds are observed. It is expected that removal of the reaction exotherm in the high conversion case would lower the reactive stage temperature thereby giving a favorable product distribution that helps expand the feasible solution region, as will be illustrated. To confirm this reason, an additional stream is added as an input to the column in the form of a solvent that can serve both the purposes of reflux as well as heat sink, to the minimum and maximum configurations found. The solvent considered is n-hexadecane (C16H34), and its flow rate is adjusted to allow for convergence of the simulation. In the case of the maximum configuration, the reflux ratio could be increased from 0.649 to 0.654 without any change in the catalyst loading (4 kg) or pressure (47.3 atm). The increase in resulting conversion was ∼2%. Similarly, for the minimum configuration, the reflux ratio could be reduced from 0.021 to 0.001 (almost zero) and the pressure from 3.42 to 1 atm. It is to be noted, however, that under these minimum conditions, the conversion is negligible (∼0.05% for CO) resulting from the low temperatures on the

reactive stages (∼158-172 °C). Table 5 shows that both the minimum and maximum values for the reflux ratio are increasing with an increase in pressure, as concluded in the preliminary study. The difference between the maximum and minimum observed reflux ratios at each pressure decreases as the pressure increases. This difference, however, remains constant in the case of the preliminary study (Table 3). The reason for this discrepancy is the fact that catalyst weight is a free variable in the case of the study in Table 3 while it is not in the case of Table 5. Hence, one can infer that allowing the catalyst distribution to be a free variable during the optimization stage explores the solution space in a larger manner. The configuration considered until now had the following catalyst distribution: 1.9, 1.8, 0.25, and 0.05 kg on stages 2, 3, 4, and 5, respectively. To verify the conclusions arrived at, this study is repeated using a configuration with equal catalyst weights of 1 kg on all the four reactive stages. All the trends of the distributed catalyst loading case are observed with the equal catalyst loading case too. Besides solvent addition, it is interesting to note that exotherm control by adding side-coolers helps in expanding the feasible solution space at the upper limit in the equal catalyst loading case (details in section 2 of the Supporting Information). Objectives and Solution Space: Net Catalyst Weight Varied The cases resulting in converged solutions in Table 3 were analyzed for the following maximization objectives: average reactive stage temperature (1), conversion (2), yields of gasoline (3) and diesel (4), and selectivity of gasoline (5) and diesel (6). It may be noted that maximizing the average reactive stage temperature is not an objective unlike other performance parameters like conversion, yield, and selectivity. It is included to gain some insight only. The constraints in this case are the bounds set on each parameter during the sensitivity analysis study itself, e.g., P varies between 20 and 30 atm, etc. Table 6 presents the values of these parameters for different cases. The first number in the case represents the pressure, and the second represents the objective number. For example, 24p5 indicates that the results correspond to a pressure of 24 atm when the objective is to maximize gasoline selectivity (5). While analyzing the results in Table 6, it is to be borne in mind that the catalyst loading, both on the stages as well as the net loading, is left as a free variable. For the sake of brevity, results at only

Table 6. Performance Parameters at Maximum Objectives Cat.Wt. on stages (kg)

yields (kg/h)

selectivity (%)

conversion (%)

temperature (°C)

case no.

NetCat.Wt. (kg)

2

3

4

5

gasoline

diesel

gasoline

diesel

CO

H2

bottom

avg reac T

reflux ratio

24p1 24p2 24p3 24p4 24p5 24p6 25p1 25p2 25p3 25p4 25p5 25p6 26p1 26p2 26p3 26p4 26p5 26p6

5.35 5.35 7.35 8.15 4.85 4.8 5.9 6.15 7.9 6.95 5.8 5.8 5.65 5.65 7.3 6.95 7.3 5.8

2.7 2.7 3.7 3.8 1.9 2.3 3.2 2.3 3.6 3.8 2.2 1.9 3.5 3.5 3.7 3.8 3.7 1.9

2.6 2.6 3.2 3.6 2.6 1.8 2.4 3.4 3.6 2.4 3.2 3.6 1.8 1.8 3 2.4 3 3.6

0.25 0.25 0.35 0.5 0.3 0.5 0.25 0.4 0.5 0.5 0.3 0.25 0.3 0.3 0.5 0.5 0.5 0.25

0.05 0.05 0.1 0.25 0.05 0.2 0.05 0.05 0.2 0.25 0.1 0.05 0.05 0.05 0.1 0.25 0.1 0.05

0.011 0.011 0.482 0.208 0.342 0.179 0.012 0.011 0.487 0.214 0.467 0.184 0.012 0.012 0.653 0.227 0.653 0.196

0.003 0.003 0.179 0.547 0.131 0.423 0.004 0.004 0.194 0.56 0.095 0.444 0.004 0.004 0.086 0.573 0.086 0.449

2.13 2.13 58.85 21.08 59.69 25.87 2.36 2.26 56.29 20.73 70.29 24.17 2.47 2.47 76.24 21.28 76.24 24.99

0.61 0.61 21.86 55.41 22.79 60.79 0.906 0.95 22.46 54.18 14.35 58.34 0.92 0.92 10.08 53.68 10.08 57.36

84.28 84.28 64.76 64.54 55.24 62.55 84.45 84.72 68.45 65.65 60.05 55.6 84.12 84.12 69.64 67.34 69.64 57.91

45.46 45.46 18.69 18.16 16 18.6 44.56 44.49 20.03 18.65 17.4 15.52 43.63 43.63 20.51 19.24 20.51 16.32

238.94 238.94 202.84 212.84 204.67 221.89 237.47 235.19 204.08 217.69 201.43 210.5 237.19 237.19 194.23 217.45 194.23 210.54

308.89 308.89 222.96 222.38 224.85 248.01 303.21 302.31 226.36 232.15 222.57 215.73 303.25 303.25 232.08 232.83 232.08 217.12

0.425 0.425 0.375 0.385 0.295 0.335 0.435 0.445 0.415 0.385 0.345 0.325 0.435 0.435 0.425 0.405 0.425 0.345

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three pressures are tabulated, viz., at 24, 25, and 26 atm. The observations at other values of pressure are similar. To reiterate, the bounds on the parameters varied are as follows: reflux ratio between 0.215 and 0.455 (0.01), pressure at 20, 22, 24, 25, 26, 28, and 30 atm, catalyst loading on stage 2 between 1.9 and 3.8 kg (0.2 kg), on stage 3 between 1.8 and 3.6 kg (0.2 kg), on stage 4 between 0.25 and 0.5 kg (0.05 kg), and on stage 5 between 0.05 and 0.25 kg (0.05 kg). As a result, the net catalyst loading varies between 4 and 8.15 kg. Note that the feed basis is 1000 mol/h of syngas with H2/CO ratio of 2.03 at 25 atm and 250 °C. Average Reactive Stage Temperature (1) and Conversion (2). Both the maximum average reactive stage temperature and conversion are expected to occur at the maximum reflux ratio, minimum pressure, and maximum catalyst loading as the reaction rates are expected to be the highest under these conditions. At a constant pressure (P), one can see from Table 6 that neither the reflux ratio (RR) nor the catalyst loading (W) is the maximum at any of the three pressures considered. Further, the maximum CO conversion is ∼84% in all cases while the H2 conversion lies between 43.5 and 45.5%. Irrespective of the pressure, there appears to be a combination of reflux ratio and catalyst distribution that can result in the same conversion and approximately the same average reactive stage temperature. The configuration remains the same for both the objectives under the considerations here, except at 25 atm where the catalyst distribution changes slightly (cases 25p1 and 25p2). As expected, a rather high average reactive temperature of ∼300 °C results in methane as the main product and, hence, the yield/ selectivity of gasoline and diesel are negligible. The high utility ratio (moles of H2 consumed per mole of CO) observed also indicates that excessive lighters (in the form of gaseous components) are formed. To conclude, there exists a combination of P, RR, and W that maximizes the conversion and average reactive stage temperature which need not necessarily correspond to the minimum or maximum values as expected. Yields of Gasoline (3) and Diesel (4). It is expected that the average reactive temperature reflects the product distribution and a higher value predicts more gasoline yields vs diesel. However, this does not hold true for the cases shown in Table 6. Cases 24p3 and 24p4 have approximately the same average reactive temperature, and so do the cases 26p3 and 26p4. The temperature is higher in case 25p4 where the diesel yield is maximum, which is contradictory. However, it is to be noted that the reflux ratio and catalyst distribution are quite different in all these cases and it has been shown earlier that a combination of RR, W, and P can lead to such behavior. Among the three pressures, gasoline yield is highest at 26 atm, which has the highest reflux ratio but the lowest net catalyst loading. The corresponding diesel yield is lowest too. In the case of diesel, the highest yield is for 26 atm, which again has the highest reflux ratio and a lower catalyst loading. However, the difference in yields is not very significant for maximum diesel production as compared to the gasoline production. It is also to be noted that the maximum yields come at the expense of conversion, which is lower as compared to the maximum conversion case by ∼20%. Selectivity toward Gasoline (5) and Diesel (6). It is observed that the maximization of yields does not imply the maximization of selectivity. Gasoline selectivity, in this case, is defined as the net production rate of gasoline from the liquid streams as a fraction of the total production rate from the liquid streams. As in the case of yields, the reflux ratio and catalyst distribution are quite different in all the cases. Maximum selectivity toward

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gasoline is observed at 26 atm, which has the highest catalyst loading and the highest reflux ratio among the three pressure values. It is fortuitous in this case that maximum gasoline yield corresponds to maximum gasoline selectivity, which may not always be true. For example, cases 25p3 and 25p5 that correspond to maximum gasoline yield and selectivity have different configurations. Selectivity toward diesel is highest at 24 atm, which has the lowest catalyst loading but an intermediate value for reflux ratio, among the three pressures. Further, the conversion is highest in the case of 24p6. Though the selectivity values for maximum diesel selectivity at different pressures differ by ∼3% only, it is interesting to note the large variations in catalyst distribution and conversion among the three cases. Similar to the case of yields, there is a compromise between maximum selectivity and conversion, which is lower as compared to the maximum conversion case by ∼20%. Between the maximum yield and selectivity cases, the conversions differ by ∼10% too (cases 24p3 and 24p5 for gasoline; cases 25p4 and 25p6 for diesel). It may be noted that, within the range of parameters studied, the best possible solution which maximizes each objective has been highlighted in bold in Table 6. Figure 6 locates the coordinates corresponding to pressure (P), reflux ratio (RR), and total catalyst loading (Wt.) in their varied range for each of the objectives considered. Further, the entire simulation space considered (cube formed by the bold lines) and the feasible space corresponding to the converged solutions (shaded volume within the cube) are also shown. One can infer from the coordinates represented by the symbols for the different objectives in Figure 6 that the solution space corresponding to optimization of these objectives would be different for each with some overlaps between them. It is clearly evident from the foregoing discussion that the number of solutions is quite large while examining each of the objectives. Allowing the catalyst weights on all of the four reactive stages to vary in addition to the pressure and reflux ratio gives seven decision variables to choose from, the seventh being the total catalyst loading. To simplify the task and reduce the search space for optimization, the total catalyst weight was fixed, and the solutions in Table 3 are sorted out and analyzed for different objectives (section 3 of the Supporting Information). Trends similar to the case of total catalyst loading as a free variable are observed from the analysis of fixed total catalyst weight cases. It is seen that fixing the total catalyst weight still results in a large number of solutions with many combinations arising from the individual stage catalyst loads alone. The question of deciding the total catalyst loading also remains to be answered. There is a trade-off observed between the different objectives. For example, increasing product selectivity was at the expense of a decreased conversion. A better way to optimize would hence assign weights to each of the objectives and, finally, optimize the weighted, combined objective function which can be performed as a future part of this work. Thus, it has been shown that different objectives can lead to different configurations. The solution space covered is also quite large compared to the number of variables consideredsreflux ratio (RR), pressure (P), and net catalyst weight (W)sprimarily. Also, we have not considered three other decision variablessside-duties, side-draws, and nonreactive stagesswhich further increase the complexity of the search or the optimization task. However, it has been shown earlier that these three variables do not affect the conversion or product distribution when the choice of P, RR, and W is proper. Hence, they can be added to the search space after the initial simple configuration is decided. The three remaining parameters that were part of our earlier sensitivity

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Figure 6. (a) Coordinates for maximum objectives: avg reac T and Xco. (b) Coordinates for maximum objectives: yields and selectivity.

analysis4 include the design variablessfeed temperature, feed ratio, and the amount of CO2 present in the feed. Since these form the basis for which the optimization task is defined, changing their values would alter the solution space. But, a similar methodology being followed here can be applied for different base conditions of these three variables. Analysis Based on Damkohler Number In the analysis performed until now, it has been shown that the solution space for different objectives is quite large. In addition, the combination of reflux ratio, pressure, and catalyst loading is such that clear bounds on each of them for different objectives could not be resolved. However, the Damkohler number (Da) to an extent is expected to take care of all these three variables. Da is defined as (kmcat/V). The reaction rate constant, k, is evaluated at an average temperature, T. Since the reflux ratio changes affect the stage temperatures, the change of reflux ratio manifests itself through changes in k. The effect of change in pressure will be indirectly reflected in the change

in temperature (bubble point) on the reactive stages. Changes in catalyst loading on the stages result in changes in mcat, if Da on each stage is considered. Before performing the Da analysis, the few simulation cases from the feasible solution space identified are repeated to check for their accuracy and possible existence of multiple solutions (more details in section 4 of the Supporting Information), and the results were convincing. The reference reaction chosen for Da calculations is the methane formation reaction. The value of k can hence be evaluated using the pre-exponential factor and activation energy for the methane formation reaction if T is known. The choice of T is a difficult task owing to the wide-boiling nature of the components present. T is therefore assumed to be the average temperature of the reactive stages and is calculated in two wayssusing a weighted average of the catalyst loading per tray and using an exponential dependence (arising from the calculation of k). Catalyst mass per stage, mcat, is also known as well as the column pressure. The last input needed for Da calculation is the vapor flow rate, V, which is set equal to the feed flow rate. Da calculations on each stage are also performed with T

Ind. Eng. Chem. Res., Vol. 49, No. 14, 2010

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Figure 8. (a) Da number variation with RRsall objectives. (b) Da number variation with RRsyield, selectivity, and cat. loading objectives.

Figure 9. Da number variation with RRschange in objective.

Figure 7. (a) Da variation at maximum avg reac T and Xco. (b) Da variation at maximum yields. (c) Da variation at maximum selectivity and catalyst loading.

taken as the stage temperature and V as the vapor flow rate for that particular stage. However, no conclusions could be drawn from the detailed stagewise Da calculations. Thus, an average Da for the entire column is calculated with T as the average temperature (obtained as explained earlier), mcat as the total catalyst loading in the column and V as the inlet feed rate. Values of Da calculated using the weighted average of catalyst loading and the exponential dependence did not differ significantly. The Da values reported in Figures 7 and 8 are based on T calculated using the weighted average of the catalyst mass. It was expected that each objective when maximized would correspond to a unique value of Da incorporating the effects of pressure, reflux ratio, and catalyst weight. This was not observed,

and therefore, a necessity arose to choose a second dimensionless number to explain the results noticed. Since separation needs to be taken care of, reflux ratio (RR) was chosen as the second parameter. Figure 7 shows the variation in Da when different objectives reach a maximum, as a function of pressure and reflux ratio. Da values are highest when the average reactive stage temperature or conversion is maximized (Figures 7a and 8a) and least when the yields are maximized (Figures 7b and 8b). The reason for the observed discrepancy in the Da values can be attributed to the high temperature (∼300 °C), and consequently, a higher Da resulting from the exponential dependence of the reaction rate constant on temperature when maximum conversion is the objective. Thus, Da is strongly dependent on the temperature, which in turn varies with reflux ratio, and dominates the changes in pressure or catalyst loading. Therefore, we reduce the dimensionality of Figure 7 to two by using RR and Da only in Figure 8. Regions for different maximization objectives are represented in Figure 8 using the maximum and minimum values of Da and RR from the data of Figure 7. It was verified that all the intermediate points for any of the objectives lie in the respective quadrilateral region. It is expected that Figure 8 will provide an idea on the magnitude of change needed in one or more of the parameters (RR, P, or catalyst weight) to move from a region of maximizing one objective to another. Such a case is illustrated using results from an independent design study performed by the authors5 using Figure 9 and Table 7. Cases 1 and 2 are similar in configuration, but case 2 has double the side-draw rates compared to case 1. Cases 3-6 are similarly configured although

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Table 7. Change in Objective for Important Performance Parameters and Liquid and Net Product Selectivity Important Performance Parameters temperature (°C)

case case case case case case

1 2 3 4 5 6

liquid yields (kg/h)

Da

reflux ratio

Xco (%)

Qc (MW)

avg. reac

max

min

gasoline

diesel

wax

0.266 0.308 0.261 0.308 0.337 0.712

0.294 0.355 0.312 0.338 0.355 0.38

50.93 54.56 50.81 54.62 56.83 69.59

-75.064 -78.682 -74.74 -78.82 -81.2 -69.91

221.98 225.18 221.58 225.23 227.23 244.52

245.43 245.84 245.37 245.58 245.69 264.41

197.02 193.98 193.41 201.99 204.96 183.63

2111 1977 1971 2160 2252 2010

4390 4774 4346 4787 5059 4809

3078 3148 3054 3198 3210 1683

Liquid and Net Product Selectivity liquid selectivity (%)

case case case case case case

1 2 3 4 5 6

net product selectivity (%)

Da

gasoline

diesel

wax

light gas

naphtha

gasoline

diesel

wax

alpha

0.266 0.308 0.261 0.308 0.337 0.712

21.65 19.95 21 21.18 21.25 23.53

45.03 48.19 46.32 46.95 47.75 56.29

31.57 31.77 32.55 31.37 30.3 19.71

12.44 13.01 12.4 12.63 13.02 30.81

14.46 14.93 14.43 14.63 14.94 21.17

20.7 20.18 21.05 20.56 20.22 15.33

30.81 31.27 30.62 31.28 31.71 24.21

21.6 20.61 21.51 20.9 20.12 8.48

0.92 0.914 0.92 0.916 0.911 0.853

with different reflux ratios as shown in Table 7. While the bounds in Figure 9 are obtained with a small and simple column (6 stages, 4 reactive stages, 4 kg catalyst, 1 kmol/h of feed, no side-draws or side-coolers), cases 1-6 are evolved using a larger and complex column (70 stages, 48 reactive stages, 48 tons of catalyst, 0.5 million m3/day of feed, two side-draws and 20 sidecoolers). Value of Da for each of the six cases is given in Table 7. Except in Case 6, the Da values are lower than the lower limit of Da used in Figure 9 and hence lie outside the bounds. Nonetheless, one may see the changes in Da as changes are made to the design. For example, as the reflux ratio increases from case 3 to case 6, it may be seen that the maximum selectivity moves from diesel to gasoline with some extrapolation of the bounds in Figure 9. The same is however, not suggested by the selectivity/yield values in Table 7 owing to the difference in the definition of selectivity used in calculations in Table 7 and Figure 9. Alternatively, at a fixed reflux ratio, one may try and find a suitable combination of pressure and catalyst weight so that the Da moves in a vertical manner to switch between the different zones in Figure 9. Calculations of Da were performed using other reactions as reference reactionss formation of hexane, decane, hexadecane, and tetracosane. In all the cases, the trends remain the same with only changes in the absolute values of Da. To conclude, the methodology adopted here for the analysis of maximization of different objectives using Da is quite preliminary in nature and needs further improvement. It is envisaged that tools like Figure 9 will enable one to find a right mix of operating parameters (P and RR) for a given configuration (catalyst loading fixed) when the objective changes. Conclusions Using the “sensitivity” tool in Aspen Plus, it is demonstrated that parameters such as pressure, reflux ratio, and catalyst weight can be simultaneously varied to determine a feasible solution space for FTS in RD. It may be noted that the results from the sensitivity block are accessed directly, and MS-Excel is used to sort the data after accessing these results as well as for further analysis. It is also shown that trying to maximize different objectives like conversion, yield, or selectivity result in solutions lying in different regions of the feasible solution space. There is a trade-off observed between different objectives, for example,

yields of gasoline/diesel improve with a penalty on the attainable conversion level. Thus, a multiobjective optimization is necessary to deal with these trade-offs by assigning weights to different objectives. This is, however, a difficult task considering convergence issues and the number of variables available for optimization. Perhaps, a combination of the simulator with techniques like genetic algorithms may prove helpful in the multiobjective optimization as shown by Vazquez-Castillo et al.31 Through a preliminary analysis based on a Da-reflux ratio plot, it is illustrated that this can guide the designer in a proper choice of the operating parameters under certain constraints. Supporting Information Available: Description of feasible solution space. This information is available free of charge via the Internet at http://pubs.acs.org/. Literature Cited (1) Srinivas, S.; Malik, R. K.; Mahajani, S. M. Feasibility of Reactive distillation for Fischer-Tropsch Synthesis. 2. Ind. Eng. Chem. Res. 2009, 48, 4710–4718. (2) Wang, Y. N.; Ma, W. P.; Lu, Y. J.; Yang, J.; Xu, Y. Y.; Xiang, H. W.; Li, Y. N.; Zhao, Y. L.; Zhang, B. J. Kinetics modeling of FTS over an industrial Fe-Cu-K catalyst. Fuel 2003, 82, 195–213. (3) Marano, J. J.; Holder, G. D. Characterization of FT liquids for VLE calculations. Fluid Phase Equilib. 1997, 138, 1–21. (4) Srinivas, S.; Malik, R. K.; Mahajani, S. M. Feasibility of Reactive distillation for Fischer-Tropsch Synthesis. 3. Ind. Eng. Chem. Res. 2009, 48, 4719–4730. (5) Srinivas, S.; Malik, R. K.; Mahajani, S. M. Design Methodology for Fischer-Tropsch Synthesis in Reactive distillation. Ind. Eng. Chem. Res., submitted for publication. (6) Jacobs, R.; Krishna, R. Multiple solutions in reactive distillation for methyl-tert-butyl ether synthesis. Ind. Eng. Chem. Res. 1993, 32, 1706– 1709. (7) Nijhuis, S. A.; Kerkhof, F. P. J. M.; Mak, A. N. S. Multiple steady states during reactive distillation of methyl-tert-butyl ether. Ind. Eng. Chem. Res. 1993, 32, 3767–2774. (8) Hauan, S.; Hertzberg, T.; Lien, K. M. Why MTBE production by reactive distillation may yield multiple solutions. Ind. Eng. Chem. Res. 1995, 34, 987–991. (9) Ciric, A. R.; Miao, P. Steady State Multiplicities in an Ethylene Glycol Reactive Distillation Column. Ind. Eng. Chem. Res. 1994, 33, 2738– 2748. (10) Ciric, A. R.; Gu, D. Synthesis of nonequilibrium reactive distillation processes by MINLP optimization. AIChE J. 1994, 40, 1479–1487. (11) Abufares, A. A.; Douglas, P. L. Mathematical modeling and simulation of an MTBE catalytic distillation process using SPEEDUP and Aspen Plus. ChERD 1995, 73, 3–12.

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ReceiVed for reView January 17, 2010 ReVised manuscript receiVed June 2, 2010 Accepted June 7, 2010 IE100106U