Extractive Distillation Optimization using Simulated Annealing and a

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Extractive Distillation Optimization using Simulated Annealing and a Process Simulation Automation Server Xiao-Ling Yang, and Jeffrey Daniel Ward Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00711 • Publication Date (Web): 18 Jul 2018 Downloaded from http://pubs.acs.org on July 26, 2018

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Industrial & Engineering Chemistry Research

Extractive Distillation Optimization using Simulated Annealing and a Process Simulation Automation Server Xiao-Ling Yang and Jeffrey D. Ward* Dept. of Chemical Engineering, National Taiwan University, Taipei 106-07, Taiwan

Abstract In this work, continuous extractive distillation processes were optimized using simulated annealing (SA). The processes were modeled in Aspen Plus and the simulated-annealing optimization algorithm was implemented in MATLAB. For the separation of acetone and methanol, the TAC of the process for each entrainer considered was lower than the initial condition taken from the literature. For the separation of n-hexane and ethyl acetate, NMP, 2-methylpyridine, 3-methylpyridine, DMF, and pyrrole were considered as possible entrainers. The results show that DMF offers the best performance and economic benefit. For the separation of n-hexane and tetrahydrofuran, the candidate entrainers were DMF, NMP, and 2-methylpyridine. DMF was again found to be the most suitable entrainer. The results show that the SA algorithm has the advantage of running automatically and has a high probability to obtain a design near the global optimum. Keywords: Extractive distillation; Azeotropic mixtures; Simulated annealing; Optimization

*

Correspondence concerning this article should be addressed to Jeffrey D. Ward at [email protected].

ACS Paragon Plus Environment

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1. Introduction Separation of homogeneous azeotropic mixtures is a challenging problem in the chemical industry.1 One of the most common ways to separate such mixtures is by extractive distillation.2–7 Widagdo and Seider8 reviewed the column performance of homogeneous and heterogeneous towers.

They presented an algorithm

for

heterogeneous azeotropic distillation design including both steady-state and dynamic simulation. Andersen9 focused on the effect of design on the steady-state operation and the control properties of homogeneous azeotropic distillation. Heat-integrated distillation sequences were studied by Knapp and Doherty.10 For a two-component system, separation using a heavy entrainer is accomplished with two columns: an extractive distillation column and an entrainer recovery column. As is shown in Fig. 1, high purity components A and B can be collected from the tops of the two columns. Also the entrainer can be recovered in the entrainer recovery column and recycled. There are six design variables to be determined: the entrainer flowrate (FE), the total number of stages in the extractive distillation column (N1), the solvent and fresh feed tray locations (NFE and NFF), the total number of stages in the solvent recovery column (N2) and feed tray location of the solvent recovery column (NF2). The extractive column can be divided into three parts: the rectifying section (NR), the


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extractive section (NE), and the stripping section (NS), and N1, NFE and NFF can be expressed in terms of NR, NE and NS. The extractive distillation process has both discrete and continuous variables, so the optimization problem is a mixed integer nonlinear programming problem. Kossack et al.11,12 reviewed MINLP optimization algorithms for extractive distillation flowsheets and applied the method of combining shortcut calculation and rigorous MINLP optimization. This approach gave good performance even without user intervention. Many researchers have proposed global optimization techniques13 including simulated annealing, genetic algorithm, Tabu search14, and particle swarm optimization. Simulated annealing has been applied to many chemical process optimization problems, for example in the optimal design of reactive distillation systems15, pressure-swing distillation systems16 and heat integrated distillation sequences.17 However, in most of these cases, shortcut process design methods (e.g. the Fenske-Underwood-Gilliland equations) are used for column design. We are only aware of a single report of the design of an extractive distillation process using simulated annealing18 and in that work a rigorous process simulator was not used for the process modeling. In this research, the simulated annealing method is applied to obtain the optimal design of three extractive distillation processes that are used for separating minimum-boiling binary azeotropes.



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The simulated annealing code interfaces with a rigorous process simulator (Aspen Plus) via an automation server. 2. Methods 2.1. Simulated annealing The simulated annealing method was originally proposed by Kirkpatrick19 based on the work of Metropolis et al.20 Suman and Kumar21 presented a comprehensive review of simulated annealing (SA)-based optimization algorithms for single-objective and multi-objective problems. The method is based on the concept of annealing in metalwork. Initially, molecules of melts are disordered at high temperature. As the metal cools, at each temperature, the molecules are assumed to be in thermodynamic equilibrium. Also new random values of variables are generated and the system may change to another energy state. For optimization, the energy state is the variable to be minimized, in this work the total annual cost of the process. If the new state has lower energy, this move is accepted. However, if the new state has a higher energy, the move is accepted when the acceptance probability is greater than a random value generated over a uniform distribution (Equation 1). According to the Metropolis criteria, the acceptance probability is defined as follows:

=

− ∆ = − = exp (− )


(1)

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where ∆E is the difference of the normalized energy between the new and the old states. The optimization ends when the temperature reaches the freezing temperature. The procedure for the simulated annealing algorithm is illustrated in Fig. 2: (1) Start with a given initial temperature, final temperature and solution space. (2) Perturb di in the neighborhood to generate a new solution vector dnew. (3) Reevaluate the objection function E(dnew) and calculate ∆E=E(dnew)−E(di). (4) If ∆E≤0, then accept the new value dnew by setting di+1=dnew. If exp(−∆E/T)≥U(0,1), also accept di+1. U(0,1) is a random number between 0 and 1. Otherwise set di+1=di. (5) Return to step 3 until the system reaches thermodynamic equilibrium at temperature T. (6) Decrease the temperature according to the cooling schedule. Then reset i=1 and repeat steps 2–5 until the final temperature is reached. Parameter settings for the SA algorithm have an important impact on the results of the optimization process. Many people including Aarts and Krosr22, Patel et al.23 and Painton and Diwekar24 discussed parameter selection. Parameter selection in this work is described in detail in the supplementary material. 2.2. Implementation of the SA algorithm The Aspen Plus ActiveX Automation Server enables external Windows programs to transfer data to and from Aspen Plus.25 Input variables and results in an Aspen Plus



simulation are organized in a tree structure. Most of the properties of simulation can be accessed through the automation server, but some properties of the simulation are read-only. Most important operations such as changing input variables, connecting blocks in the flowsheet, running a simulation and retrieving results can all be accomplished via the automation server. Matlab can also function as an automation client.26 While running the SA algorithm, one of two special cases may arise that must be handled by the code. One is that the Aspen Plus flowsheet fails to converge, and the other is that the Aspen Plus program crashes. In order to recover from these cases automatically, an improved simulated annealing algorithm was developed. If the flowsheet fails to converge, the algorithm rejects that point and tries another point. The rejected point does not count towards the equilibrium detection. To handle the case where Aspen Plus crashes, a second instance of Matlab is run in the background. The code running in this instance checks periodically to determine if Aspen Plus has stopped responding (crashed). If Aspen Plus has crashed, the Aspen Plus task is killed (using the Windows command taskkill), Aspen Plus is restarted, and the optimization continues from the last successful point. It was observed that the basic SA algorithm sometimes failed to approach the global minimum after a single run. Therefore the procedure was modified as shown in


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Fig. 3 so that the SA algorithm was run several times, each time starting with the ending point from the previous run (or turn). The same optimization parameters (temperature trajectory, etc.) were used for each turn. The procedure is run until no significant change (0.01% for the acetone-methanol separation, 0.1% for the other cases) in the TAC is detected after five turns. 3. Case studies 3.1. Separation of Acetone and Methanol Acetone and methanol have similar normal boiling points (329.2 and 337.5K) and a minimum-boiling azeotrope. Luyben and Chien1 studied three candidate entrainers for the separation: DMSO, water, and chlorobenzene. They studied both steady-state economics and dynamic control of the processes and presented a comparison of the three solvents. The designs that they presented are used as the starting point (initial condition) for the optimization performed in this work. The Txy diagram for mixtures of aceteone and methanol as predicted using the UNIQUAC model is shown in Fig. 4. The model predicts that the minimum-boiling azeotrope at 1 atm occurs at 77.6 mol% acetone and 328.4K. Fig. 5 shows the relative volatility curve for the three candidate solvents calculated using a flash unit in Aspen Plus. For the column design, the solvent feed temperature is 320K and the mixture feed flowrate of all the cases is assumed to be 540 kmol/h of 50/50 mol% acetone-methanol



mixture at 320K. All columns are designed to operate at atmospheric pressure. The purities of the overhead and bottom compositions are achieved by manipulating the reflux ratio and the reboiler duty using the ‘Design Spec/Vary’ feature in Aspen Plus. To facilitate comparison with the work of Luyben and coworkers,1,27 for the separation of acetone and methanol, all TAC calculations are performed using economic basis 1 described in the supplementary material. Fig. 6 shows the actual process flowsheet, and Fig. 7 shows the process flowsheet as it is simulated in Aspen Plus, with a torn recycle stream. 3.1.1. Water as an Entrainer Based on sensitivity tests in Aspen Plus, the constraints on the design variables were specified as 0≤NR≤50, 0≤NS≤50, 2≤NE≤50, 5≤N2≤60, 2≤NF2≤N2−1, 500≤FE≤1500. The TAC given by Luyben for their extractive system is $3,750,000/yr for the same purity of products. The results of the annealing process are shown in Fig. 8. Fig. 8 (a) shows the results after the first run of the SA algorithm. The results indicate that the TAC decreases while temperature decreases and finally a point near the global minimum TAC is obtained. The minimum point from the first run is taken as the starting point of the second run. Fig. 8 (b) shows the annealing result of the second run. The optimal design results for each turn are shown in Table 1. For the following 5 turns, the


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optimal result remains nearly the same as $3,264,600/yr, which is a decrease of 12.94% compared with the initial condition ($3,750,000/yr). Because these results were carried out in the Aspen Plus using a flowsheet with a torn recycle stream (as shown in Fig.7), a validation of the results was conducted. All of the parameters from the SA procedure results were specified manually in Aspen Plus. The results, which are shown in Table 2, indicate a deviation in the TAC of 2.1%. The difference is probably due to impurity in the recycle stream. 3.1.2. DMSO as an Entrainer DMSO has much higher boiling point than both of the components to be separated. The acetone product and the methanol product are held to be 99.95 mol%, which is slightly higher than the case when water is used as solvent, because the solvent is more effective so a higher purity product can more easily be obtained. The same values of parameters for the SA algorithm were used. The constraints on the design variables are specified as: 0≤NR≤50, 0≤NS≤50, 2≤NE≤50, 5≤N2≤60, 2≤NF2≤N2−1, 100≤FE≤1000. The optimum design and economics are shown in Table 3. The TAC decreases to 2,422,900 $/yr, which is a decrease of 12.53% compared to the starting point. A comparison of the results between the flowchart with the torn recycle stream and the complete flowchart is shown in Table 4. There is a 0.29% deviation between the results. 3.1.3. Chlorobenzene as an Entrainer



In this system, methanol is collected overhead in the extractive distillation column and acetone is collected overhead in the solvent recovery column. The same values of parameters for the SA algorithm were used and the constraints on the design variables were specified as 0≤NR≤50, 0≤NS≤50, 2≤NE≤50, 5≤N2≤60, 2≤NF2≤N2−1, 500≤FE≤2500. The TAC decreases to 3,216,600 $/yr as shown in Table 5, which represents a decrease of 34.75% compared with the starting point (4,930,000 $/yr). Table 6 shows the deviation of 2% between the flowsheet with the torn recycle stream and the complete flowsheet. For this case, to connect the recycle stream in Aspen Plus using the same parameters from SA results, the constraint on the composition of chlorobenzene in the recycle stream was increased from 99.90mol% to 99.99mol%. Therefore, the energy consumption in the second column increased slightly compared to the former systems. 3.2. Separation of N-hexane and ethyl acetate N-hexane and ethyl acetate are used as organic solvents in pharmaceutical industry and form a homogeneous minimum-boiling azeotrope. According to Acosta et al.,28 the azeotropic mixture boils at 338K with a mole fraction of n-hexane equal to 0.657. Fig. 9 shows the Txy diagram for mixtures of n-hexane and ethyl acetate at 1 atm using the UNIQUAC equation with, which indicates an azeotrope with a composition of 66mol% n-hexane at 338.3K. Fig. 10 shows the relative volatility curve for different solvents. It


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can be seen from the figure that the relative volatility with the solvent DMF is larger than that with NMP, 2-methylpyridine, 3-methylpyridine and pyrrole. Pyrrole has the worst performance, so the others are taken as the candidate solvents. For the simulation, the feed is taken to be 100kmol/h of 66.87mol% n-hexane and 33.13mol% ethyl acetate. For this separation, all TAC calculations are performed using economics basis 2 as described in the supplementary material. 3.2.1. DMF as an Entrainer DMF is the most effective entrainer considered for this mixture and high product purities can be achieved using this entrainer. The n-hexane and ethyl acetate products are specified to be 99.5mol% pure, and this is achieved in part by holding the bottoms composition in the extractive column of 0.1mol% n-hexane. The range of the design variables was determined based on sensitivity analysis in Aspen Plus as 0≤NR≤50, 0≤NS≤50, 2≤NE≤50, 5≤N2≤60, 2≤NF2≤N2−1, 50≤FE≤250. Then a SA-based optimization was performed. The results after each turn are shown in Table 7. In this study, the TAC of all the overall process with DMF solvent using extractive distillation is 918,080$/yr. The computation time was about four hours. 3.2.2. NMP as an Entrainer Yuan et al.29 considered NMP as an entrainer and presented an optimum design with the mass fraction of the light component (n-hexane) in this mixture reaching



99.00%. In our research, the n-hexane product and ethyl acetate product are specified to be 99.50mol% pure. Higher purities are selected because the solvent is so effective that the purities can be obtained with little increase in energy cost. The parameters for the SA process were the same as before and the constraints on the design variables were specified as 0≤NR≤50, 0≤NS≤50, 2≤NE≤50, 5≤N2≤60, 2≤NF2≤N2−1, 50≤FE≤300. The values of the design variables after each turn are shown in Table 8. The values fluctuate from turn to turn as the solvent concentration in the recycle stream changes (ranging from 99.90 mol% to almost 100%). However higher solvent composition in the recycle stream increases the energy consumption and cost of the second column. So in the optimum design, the solvent composition is set to be 99.90mol%. After eight turns of SA, the TAC decreases to 1,032,600 $/yr, a 12.30% decrease from the initial result of 1,177 300$/kmol. The computing time was almost 9 hours which is significantly higher than the case using DMF solvent. 3.2.3. 2-Methylpyridine as an Entrainer 2-methylpyridine is a less effective solvent, so achieving 99.50mol% purity for each product requires a greater solvent flowrate. As before, the bottoms composition in the extractive column is fixed at 0.01mol% n-hexane. The parameters of the SA algorithm are set the same as before and the constraints on the design variables were specified as 0≤NR≤50, 0≤NS≤50, 2≤NE≤50, 5≤N2≤60, 2≤NF2≤N2−1, 50≤FE≤300.


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We were unable to find a reliable value for the cost of this entrainer in the open literature, therefore the design was optimized for two different values of the entrainer cost: 50$/kmol and 300$/kmol. When solvent cost is set at 50$/kmol, the values of all the design parameters after each turn are listed in Table 9. After six turns of the SA procedure, the optimized TAC is 1,265,200$/yr, which is a decrease of 17.46% compared to the result after the first turn. The optimum solvent flowrate is 181 kmol/h. When the solvent cost is set as 300$/kmol, the design results after each turn, presented in Table 10, show that the TAC decreases to 1,563,600$/yr. The optimum solvent flowrate in this case is 187 kmol/h, which is very close to the result when the solvent cost is 50$/kmol. 3.2.4. 3-methylpyridine as an Entrainer When 3-methylpyridine is used to separate the mixture an even greater solvent flow rate is required to achieve the desired 99.50mol% n-hexane purity and 99.50mol% ethyl acetate purity. To implement the SA procedure, the same SA parameters and design variable constraints used for the 2-methylpyridine case were adopted. Again we were unable to find a reliable value for the cost of this entrainer in the open literature, therefore the design was optimized for two different values of the entrainer cost: 50$/kmol and 300$/kmol. The results using an entrainer cost of 50$/kmol



are shown in Table 11, and the results using solvent cost of 300$/kmol are shown in Table 12. The optimal solvent flow rate is similar for both cases. 3.3. Separation of N-hexane and Tetrahydrofuran N-hexane and tetrahydrofuran are widely used as solvents in industry and the boiling points are very close (339.1K for THF, 341.4K for n-hexane). Vapor-liquid equilibrium data for the binary mixture n-hexane-THF have been reported in the literature.30 A minimum boiling temperature azeotrope with an average mass fraction of n-hexane equal to 0.4309 and a temperature of 336.17K at 100kPa was reported, which is very close to the results using the UNIQUAC model for this system. Fig.11 gives the Txy diagram for the binary system. Yuan et al.29 proposed four candidate entrainers according to the polarity principle. The dielectric constant of tetrahydrofuran is higher than that of n-hexane. N,N-dimethylformamide(DMF), N-methyl-2-pyrrolidone(NMP), 2-methylpyridineand 3-methylpyridine were chosen as potential entrainers since their dielectric constant is higher than that of tetrahydrofuran. Fig.12 shows the relative volatility curve between n-hexane and tetrahydrofuran after adding different entrainers. From this figure, it is clear that NMP is the most effective entrainer and 3-methylpyridine is the least effective entrainer. In order to enhance the relative volatility between the mixture components, only NMP, DMF and 2-methylpyridine were considered in this work. The feed flowrate


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was taken to be 100 kmol/h with a composition of 38.41mol% n-hexane, which is close to the mixture azeotropic point at 1 atm. The design flowsheet was shown by Yuan et al.29 N-hexane is produced at high purity in the top of the extractive distillation column and tetrahydrofuran is collected at high purity in the distillate of entrainer recovery column. The n-hexane product is specified to be 99.50mol% pure, while tetrahydrofuran product is held greater than or equal to 99.50mol% to make the simulation converge more easily. For this separation, TAC calculations were performed using economic basis 2 as described in the supplementary material. 3.3.1. NMP as an Entrainer NMP has a much higher boiling point than either DMF or 2-methylpyridine and should be the most effective solvent based on the relative volatility calculations. Yuan et al.29 present an optimized design of an extractive distillation process which produced n-hexane with a purity of 99.10%. They also provided the number of stages in each column, the feed stage locations and solvent-to-feed ratio. In this work, their results were used as a starting point. The range of variable settings are shown as 0≤NR≤50, 0≤NS≤50, 2≤NE≤50, 5≤N2≤60, 2≤NF2≤N2−1, 50≤FE≤500. Table 13 gives the detailed results for each turn. The minimum TAC obtained by SA procedure is 1,726,800 $/yr, which is a decrease of 1.51% compared with the initial result.



3.3.2. DMF as an Entrainer DMF has the same effect on the n-hexane-tetrahydrofuran system: n-hexane is driven overhead in the extractive column and tetrahydrofuran can be captured by the solvent and later separated in the entrainer recovery column. The same SA parameters are used for this case and constraints on the design variables are specified as 0≤NR≤50, 0≤NS≤50, 2≤NE≤50, 5≤N2≤60, 2≤NF2≤N2−1, 50≤FE≤350. The design variable parameters and economics of the optimum results are shown in Table14. The minimum TAC obtained by the SA procedure is 909,440 $/yr, which is a decrease of 24.85% compared with the results of the first turn. 3.3.3. 2-methylpyridine as an Entrainer The parameters of SA optimization were set the same with the other cases, and the constraints on design variables are specified as 0≤NR≤50, 0≤NS≤50, 2≤NE≤50, 5≤N2≤60, 2≤NF2≤N2−1, 250≤FE≤500. The annealing process and results using solvent cost of 50$/kmol are shown in Table 15. Another comparison using solvent cost of 300$/kmol is presented in Table 16. The optimum values of the design variables using 2-methylpyridine solvent are substantially larger than those using NMP and DMF solvents, because the required solvent flow rate is relatively high. 3.4. Results and discussion


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The separation of methanol-acetone system using extractive distillation was optimized by the improved SA method. The results using three different solvents are compared with base-case designs presented in the literature. A 12.94% decrease is achieved using water, a 12.53% decrease is achieved using DMSO and a 34.75% decrease is achieved using chlorobenzene. Table 17 shows the comparison of the new results. DMSO is found to be the best entrainer for the system, consistent with the previous research. Similarly, the other two azeotropic mixtures are separated using extractive distillation processes designed using the same SA method. The initial points are randomly chosen and the total optimization procedure takes approximately 5-6 hours. For n-hexane-ethyl acetate system as shown in Table 18, using DMF as the solvent results in lower cost compared with other solvents when n-hexane and ethyl acetate products are specified to be 99.95mol% pure. For the n-hexane-tetrahydrofuran system as shown in Table 19, minimum TAC obtained using DMF solvent is 909,440 $/yr, which is much lower than for other solvents. 4. Conclusion The design of several extractive distillation processes using Aspen Plus as an automation server was studied in this work. A simulated annealing algorithm was written in MATLAB which functioned as the automation client. For each case, suitable



parameters for the optimization algorithm and suitable ranges for the design variables were determined. Three separations were studied: acetone and methanol, n-hexane and ethyl acetate, and n-hexane and tetrahydrofuran. The results show that the proposed method is quite suitable for the design of different extractive distillation processes. The method can be programmed automatically and saves considerable time compared to manual optimization by sequential iteration. Simulated annealing with multiple turns can be used to determine if there is a better solution in the neighborhood of the solution found after the first turn. Starting the algorithm from different initial conditions increases the likelihood that the global optimal result is obtained. The n-hexane-ethyl acetate case and n-hexane-tetrahydrofuran case demonstrate that the relative volatility and the price of each entrainer are important factors for choosing the best entrainer. Acknowledgement This work was funded by the Taiwan Ministry of Science and Technology under grant 105-2221-E-002-208-MY2. Supporting Information Additional information about the economic calculations, parameters used in the simulated annealing algorithm, and detailed representative results for the design of one two-column process are available in the Supporting Information. This information is available free of charge via the internet at http://pubs.acs.org/.


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Garcia-Herreros, P. and J. M. Gomez (2011). "Optimization of the Design and Operation of an Extractive Distillation System for the Production of Fuel Grade Ethanol Using Glycerol as Entrainer." Industrial & Engineering Chemistry Research 50(7): 3977-3985.

[19]

Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. science, 220(4598), 671-680.

[20]

Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equation of state calculations by fast computing machines. The journal of chemical physics, 21(6), 1087-1092.

[21]

Suman, B., & Kumar, P. (2006). A survey of simulated annealing as a tool for single and multiobjective optimization. Journal of the operational research society, 1143-1160.


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[22]

Aarts, E. H., & van Laarhoven, P. J. (1985). Statistical cooling: A general approach to combinatorial optimization problems.

[23]

Patel, A. N., Mah, R. S. H., & Karimi, I. A. (1991). Preliminary design of multiproduct noncontinuous plants using simulated annealing. Computers & Chemical Engineering, 15(7), 451-469.

[24]

Painton, L. A., & Diwekar, U. M. (1994). Synthesizing optimal design configurations for a Brayton cycle power plant. Computers & chemical engineering, 18(5), 369-381.

[25]

ASPEN Plus. User Guide (Version 10.2). Aspen Technology, Inc., 2000

[26]

MATLAB External Interfaces. The MathWorks, Inc. 2013.

[27]

Luyben, W. L. (2008). Comparison of extractive distillation and pressure-swing distillation for acetone− methanol separation. Industrial & Engineering Chemistry Research, 47(8), 2696-2707.

[28]

Acosta, J., Arce, A., Martínez-Ageitos, J., Rodil, E., & Soto, A. (2002). Vapor− liquid equilibrium of the ternary system ethyl acetate+ hexane+ acetone at 101.32 kpa. Journal of Chemical & Engineering Data, 47(4), 849-854.

[29]

Yuan, S., Zou, C., Yin, H., Chen, Z., & Yang, W. (2015). Study on the separation of binary azeotropic mixtures by continuous extractive distillation. Chemical Engineering Research and Design, 93, 113-119.

[30]

XIE, Q., WAN, H., & GUAN, G. F. (2010). Isobaric vapor-liquid equilibrium for tetrahydrofuran-water-n-hexane system. Chemical Engineering (China), 4, 018.



Page 22 of 40

Tables Table 1 Optimal design result of SA algorithm in each turn using water solvent Conventional

SA(first turn)

SA(second turn)

NR

24

39

39

NS

17

15

15

NE

15

30

30

N2

26

31

31

NF2

14

21

21

1100

850

842

Capital cost(10 $)

3.03

3.28

3.29

Energy

2.72

2.18

2.17

3.75

3.27

3.27

Entrainer 6

6

cost($10 /yr) TAC($106/yr)

Table 2 Comparison of results before and after joining stream using water solvent

C1

C2

Cooler Total system

Results before

Results after

joining stream

joining stream

ID(m)

2.40

2.45

QR(MW)

8.78

9.11

QC(MW)

7.63

7.96

ID(m)

1.68

1.68

QR(MW)

5.90

5.91

QC(MW)

5.80

5.80

1.08

1.08

Total capital(10 $)

3.29

3.33

Total

2.17

2.23

3.27

3.34

QHX(MW) 6

6

energy($10 /yr) TAC($106/yr)


Page 23 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3 Optimal design result of SA algorithm in each turn using DMSO solvent Conventional

SA(first turn)

SA(second turn)

NR

3

3

3

NS

13

18

18

NE

20

29

30

N2

17

11

11

NF2

8

5

5

750

471

459

Capital cost(10 $)

2.08

2.2644

2.2896

Energy

2.08

1.6698

1.6597

2.77

2.4246

2.4229

Entrainer 6

6


Table 4 Comparison of results before and after joining stream using DMSO solvent

C1

C2

Cooler Total system

Results before

Results after

joining stream

joining stream

ID(m)

2.01

2.05

QR(MW)

6.83

6.86

QC(MW)

5.11

5.14

ID(m)

1.69

1.69

QR(MW)

4.37

4.37

QC(MW)

3.02

3.02

2.90

2.90

Total capital(10 $)

2.28

2.29

Total

1.66

1.67

2.42

2.43

QHX(MW) 6

6




Page 24 of 40

Table 5 Optimal design result of SA algorithm in each turn using chlorobenzene solvent Conven

SA(1st

SA(2nd

SA(3th

SA(4th

SA(5th

SA(6th

tional

turn)

turn)

turn)

turn)

turn)

turn)

NR

16

32

31

26

30

32

30

NS

12

11

16

16

15

16

16

NE

16

21

28

32

31

32

31

N2

18

18

18

20

21

20

19

NF2

10

7

7

8

9

8

7

Entrainer

1900

1252

1029

1001

1001

993

994

Capital

3.48

3.3666

3.3162

3.3132

3.3429

3.3651

3.3240

3.78

2.3392

2.1390

2.1252

2.1142

2.0960

2.1086

4.93

3.4614

3.2444

3.2296

3.2285

3.2177

3.2166

6

cost(10 $) Energy 6

cost($10 / yr) TAC($106/ yr)

Table 6 Comparison of results before and after joining stream using chlorobenzene solvent

C1

C2

Cooler Total system

Results before

Results after

joining stream

joining stream

ID(m)

2.79

2.80

QR(MW)

10.27

10.33

QC(MW)

5.88

5.95

ID(m)

2.05

2.12

QR(MW)

3.96

4.25

QC(MW)

4.08

4.35

4.10

4.10

Total capital(10 $)

3.32

3.36

Total

2.11

2.16

3.22

3.28

QHX(MW) 6

6



Page 25 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 7 Optimal design result of SA algorithm in each turn using DMF solvent 1st turn

2nd turn

3th turn

4th turn

NR

23

17

17

22

NS

17

12

18

8

NE

12

8

11

21

N2

16

16

14

13

NF2

10

10

8

7

198

173

102

71

Column cost(10 $)

9.5087

8.8768

8.0291

7.4141

Make-up entrainer

2.0463

2.0079

1.7350

1.6416

2.7332

2.4635

1.6432

1.2502

TAC($10 /yr)

11.8280

11.1310

9.9285

9.1808

D1(n-hexane)

0.9950

0.9950

0.9950

0.9950

D2(Ethyl acetate)

0.9950

0.9950

0.9950

0.9950

B2(entrainer)

0.9990

0.9990

0.9990

0.9990

Entrainer 5

5

cost(10 $) Cooler cost104 $) 5

Table 8 Optimal design result of SA algorithm in each turn using NMP solvent 1st turn

2nd turn

3th turn

4th turn

5th turn

6th turn

7th turn

8th turn

NR

5

5

9

8

11

12

8

7

NS

5

7

6

8

10

9

9

8

NE

6

7

7

9

9

11

10

11

N2

39

40

38

31

26

19

9

10

NF2

11

8

5

5

7

11

4

5

Entrainer

157

150

150

117

121

116

106

100

Column

9.0211

8.7508

8.5218

7.5384

7.5771

7.3195

6.8955

6.7787

2.4183

2.4989

2.5618

3.0471

2.9584

3.0471

3.2145

3.3202

3.3385

3.2227

3.2161

2.6229

2.6792

2.5720

2.3693

2.2665

TAC($106/yr)

1.1773

1.1572

1.1405

1.0848

1.0803

1.0614

1.0347

1.0326

D1(n-hexane)

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

D2(Ethyl

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9990

0.9990

0.9990

0.9990

0.9990

0.9990

0.9990

0.9990

5

cost(10 $) Make-up entrainer cost(105 $) Cooler cost104 $)

acetate) B2(entrainer)



Page 26 of 40

Table 9 Optimal design result of SA algorithm in each turn using solvent cost 50$/kmol 1st turn

2nd turn

3th turn

4th turn

5th turn

6th turn

NR

11

9

14

11

9

10

NS

39

32

33

24

13

14

NE

29

25

29

31

43

38

N2

31

10

37

51

32

25

NF2

11

9

9

20

10

10

Entrainer

211

213

219

198

181

181

Column cost(106 $)

1.4457

1.2804

1.2723

1.2481

1.1793

1.1799

Make-up entrainer

6.0103

6.6533

5.6109

5.9325

6.7374

6.1429

Cooler cost104 $)

2.7038

2.7610

2.8078

2.6531

2.4096

2.3832

TAC($106/yr)

1.5328

1.3746

1.3565

1.3340

1.2708

1.2652

D1(n-hexane)

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

D2(Ethyl acetate)

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

B2(entrainer)

0.9990

0.9990

0.9990

0.9990

0.9990

0.9990

4

cost(10 $)


2nd turn

3th turn

4th turn

5th turn

6th turn

NR

22

31

33

31

14

13

NS

32

22

21

15

22

18

NE

21

23

26

35

46

43

N2

35

42

36

32

32

24

NF2

24

24

20

21

14

8

247

246

223

208

174

187

Column cost(10 $)

1.4670

1.3468

1.3196

1.2996

1.2203

1.1934

Make-up entrainer

3.9253

3.2562

3.3142

3.3521

3.4552

3.4585

3.0690

3.0926

2.8452

2.6787

2.3389

2.4389

TAC($10 /yr)

1.8903

1.7033

1.6794

1.6616

1.5892

1.5636

D1(n-hexane)

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

D2(Ethyl acetate)

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

B2(entrainer)

0.9990

0.9990

0.9990

0.9990

0.9990

0.9990

Entrainer 6



Page 27 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



2nd turn

3th turn

4th turn

5th turn

6th turn

7th turn

NR

10

6

7

6

7

7

6

NS

35

42

20

16

16

16

15

NE

20

22

30

43

53

51

50

N2

40

34

32

22

22

21

22

NF2

13

10

15

8

8

8

8

Entrainer

448

435

413

302

284

285

289

Column

1.7300

1.6873

1.5369

1.4037

1.4042

1.4042

1.3995

4.5841

5.6174

5.3438

5.6479

5.3870

5.3720

5.6708

5.4399

5.2671

5.0398

3.8804

3.6989

3.7033

3.7495

1.8303

1.7962

1.6407

1.4990

1.4951

1.4949

1.4937

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9990

0.9990

0.9990

0.9990

0.9990

0.9990

0.9990

6

cost(10 $) Make-up entrainer cost(104 $) Cooler 4

cost10 $) TAC($106/yr ) D1(n-hexane ) D2(Ethyl acetate) B2(entrainer)



Page 28 of 40


2nd turn

3th turn

4th turn

5th turn

6th turn

7th turn

8th turn

NR

11

10

10

9

8

8

8

8

NS

28

23

20

15

16

19

16

16

NE

24

22

25

30

34

34

50

44

N2

35

28

29

32

31

31

22

22

NF2

14

12

7

14

11

11

8

8

Entrainer

421

439

423

384

362

342

292

304

Column

1.6160

1.6080

1.5692

1.5041

1.4703

1.4607

1.4107

1.4100

2.8168

2.7755

2.8179

2.9231

3.0101

3.0459

3.1601

3.1003

5.1402

5.2572

5.1128

4.7581

4.5351

4.3369

3.7799

3.9006

TAC($106/yr)

1.9490

1.9381

1.9022

1.8440

1.8167

1.8086

1.7609

1.7591

D1(n-hexane)

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

D2(Ethyl

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9990

0.9990

0.9990

0.9990

0.9990

0.9990

0.9990

0.9990

6

cost(10 $) Make-up entrainer cost(105 $) Cooler cost104 $)



Page 29 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 13 Optimal design result of SA algorithm using NMP solvent in each turn 1st turn

2nd turn

3th turn

NR

5

5

5

NS

15

16

16

NE

16

17

16

N2

18

8

8

NF2

6

4

4

105

92

94

Column cost(10 $)

7.4536

7.1771

7.1751

Make-up entrainer

9.8422

9.8812

9.8777

2.3719

2.1149

2.1507

TAC($10 /yr)

1.7533

1.7273

1.7268

D1(n-hexane)

0.9950

0.9950

0.9950

D2(Ethyl acetate)

0.9950

0.9950

0.9950

B2(entrainer)

0.9990

0.9990

0.9990

Entrainer 5

5


Table 14 Optimal design result of SA algorithm using DMF solvent in each turn 1st turn

2nd turn

3th turn

4th turn

5th turn

6th turn

NR

17

17

13

13

18

24

NS

9

11

13

15

18

22

NE

44

46

46

41

36

20

N2

31

12

12

11

11

11

NF2

25

8

7

7

7

7

295

207

184

176

131

121

Column cost(10 $)

10.3460

8.8285

8.3443

8.1710

7.9666

7.8154

Make-up entrainer

1.3772

1.2802

1.6184

1.6358

1.2217

1.0936

Cooler cost104 $)

3.7782

2.7971

2.5538

2.4643

1.9680

1.8533

TAC($105/yr)

12.1020

10.3880

10.2180

10.053.

9.3851

9.0944

D1(n-hexane)

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

D2(Ethyl acetate)

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

B2(entrainer)

0.9990

0.9990

0.9990

0.9990

0.9990

0.9990

Entrainer 5

5

cost(10 $)



Page 30 of 40


2nd turn

3th turn

4th turn

5th turn

6th turn

7th turn

NR

8

11

8

9

9

9

8

NS

17

16

21

20

25

23

19

NE

37

36

42

56

56

53

23

N2

41

35

35

30

20

20

21

NF2

13

11

10

11

8

8

9

Entrainer

433

442

418

355

366

353

370

Column

1.6021

1.6012

1.5501

1.5054

1.5016

1.4971

1.4917

0.9727

0.2111

1.4626

2.4787

2.2497

2.5165

2.4417

4.7859

4.8168

4.6107

4.0261

4.0518

3.9397

4.0933

1.6597

1.6514

1.6109

1.5704

1.5646

1.5616

1.5571

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

0.9990

0.9990

0.9990

0.9990

0.9990

0.9990

0.9990

6

cost(10 $) Make-up entrainer cost(104 $) Cooler 4

cost10 $) TAC($106/yr ) D1(n-hexane ) D2(Ethyl acetate) B2(entrainer)


Page 31 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



2nd turn

3th turn

4th turn

NR

14

14

10

10

NS

19

28

32

15

NE

45

44

40

43

N2

28

23

22

22

NF2

18

10

9

10

410

400

421

401

1.5691

1.5344

1.5522

1.5185

5.6621

7.1136

4.9176

7.6819

4.4886

4.3648

4.5342

4.3655

TAC($106/yr)

1.6706

1.6491

1.6467

1.6390

D1(n-hexane)

0.9950

0.9950

0.9950

0.9950

D2(Ethyl

0.9950

0.9950

0.9950

0.9950

0.9990

0.9990

0.9990

0.9990

Entrainer 6

Column cost(10 $) Make-up entrainer cost(104 $) Cooler cost104 $)




Page 32 of 40

Table 17 Design results with different solvents C1

C2

Cooler Total system

Water

DMSO

Chlorobenzene

NR

39

3

30

NS

15

18

16

NE

30

30

31

ID(m)

2.45

2.05

2.80

QR(MW)

9.11

6.86

10.33

QC(MW)

7.96

5.14

5.95

N2

31

11

19

NF2

21

5

7

ID(m)

1.68

1.69

2.12

QR(MW)

5.91

4.37

4.25

QC(MW)

5.80

3.02

4.35

QHX(MW)

1.08

2.90

4.10

Entrainer

842

459

994

Capital

3.33

2.29

3.36

2.23

1.67

2.16

3.34

2.43

3.28

6

cost(10 $) Energy 6



Page 33 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 18 Design results of n-hexane and ethyl acetate system with different solvents DMF

NMP

2-methyl

2-methyl

3-methyl

3-methyl

pyridine

pyridine

pyridine

pyridine

NR

22

7

10

13

6

8

NS

8

8

14

18

15

16

NE

21

11

38

43

50

44

N2

13

10

25

24

22

22

NF2

7

5

10

8

8

8

Entrainer

71

100

181

187

289

304

53.489

421.90

50

300

50

300

Column cost(10 $)

7.4141

6.7787

11.799

11.934

13.995

14.100

Make-up entrainer

1.6416

3.3202

0.6143

3.4585

0.5671

3.1003

1.2502

2.2665

2.3832

2.4389

3.7495

3.9006

TAC($10 /yr)

9.1808

10.3260

12.6520

15.6360

14.9370

17.5910

D1(n-hexane)

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

B1(n-hexane)

0.0001

0.0005

0.0001

0.0001

0.0001

0.0001

D2(ethyl acetate)

0.9950

0.9950

0.9950

0.9950

0.9950

0.9950

B2(recycled

0.9990

0.9990

0.9990

0.9990

0.9990

0.9990

Entrainer cost 5

5


entrainer)



Page 34 of 40

Table 19 Design results of n-hexane-THF system with different solvents DMF

NMP

2-methylpyridine

2-methylpyridine

NR

24

5

8

10

NS

22

16

19

15

NE

20

16

23

43

N2

11

8

21

22

NF2

7

4

9

10

Entrainer

121

94

370

401

Entrainer cost

53.489

421.90

50

300

7.8154

7.1751

14.9170

15.1850

1.0936

9.8777

0.2441

0.7682

Cooler cost104 $)

1.8533

2.1507

4.0933

0.4366

TAC($105/yr)

9.0944

17.2680

15.5710

16.390

D1(n-hexane)

0.9950

0.9950

0.9950

0.9950

D2(ethyl acetate)

0.9950

0.9950

0.9950

0.9950

B2(recycled entrainer)

0.9990

0.9990

0.9990

0.9990

Column cost(105 $) Make-up entrainer cost(10

5

$)


Page 35 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figures

Figure 1 The two column process for extractive distillation

Figure 2 Flowchart for SA algorithm



Figure 3 Optimization procedure

Figure 4 Txy diagram for acetone and methanol at 1atm.


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Figure 5 Relative volatility curve

Figure 6 Proposed design flowsheet of acetone and methanol mixture



Figure 7 The flowsheet simulated in Aspen Plus (a)

(b)

Figure 8 The annealing processes for the system: (a) result of 1st turn. (b) result of 2nd turn


Page 38 of 40

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Figure 9 Txy diagram for n-hexane and ethyl acetate at 1atm.

Figure 10 Relative volatility curve

Figure 11 Txy diagram for n-hexane-THF at 1 atm.

Figure 12 Relative-volatility curve



For Table of Contents Only


Page 40 of 40

Extractive Distillation Optimization using Simulated Annealing and a

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