Optimization and Control of Extractive Distillation with

· 117 ·

December 30, 2016

1　Introduction

Benzene is much in demand in modern petroleum and petrochemical operation. High-purity benzene is re-quired as the raw material for manufacture of cyclo-hexane, toluene, chlorobenzene, styrene and phenol. Additionally, benzene is also the starting material for synthesis of pesticides, dyes and pharmaceuticals. How-ever, benzene easily forms an azeotrope with cyclohex-ane, which cannot be completely separated in a single distillation column. There are some major distillation techniques applied in industry to separate azeotropes, such as azeotropic distillation, extractive distillation and pressure-swing distillation[1-2]. Since the mixture of ben-zene and cyclohexane is pressure-insensitive, it is dif-ficult to separate this mixture into two pure components through the conventional pressure-swing distillation. Azeotropic distillation and extractive distillation are the most commonly used methods to separate aromatic/ali-phatic mixtures. In azeotropic distillation or extractive distillation, a third component is added into the system as the entrainer, and the separation system often includes a separation column and an entrainer recovery column. Consequently, the conventional distillation processes for benzene/cyclohexane mixture separation are expensive and cumbersome. To separate the benzene/cyclohex-ane mixture, Qin, et al.[3] proposed a novel extractive

distillation process that operates the entrainer recovery column under vacuum, while the low temperature in the condenser of entrainer recovery column would result in a consequent increase in the operating cost. An extrac-tive dividing wall column was developed to separate the benzene-cyclohexane mixture by Sun, et al., and the results have showed that the energy requirement can be reduced by 22%[4].Heat integration of distillation process has been widely studied. There are two kinds of heat integration suited to the pressure swing distillation process: one combines the condenser in the high pressure column with the reboiler in the low pressure column, and the other combines the rectifying section in high pressure column with the strip-ping section in low pressure column[5]. Large energy sav-ings for the separation of close-boiling mixtures can be achieved in the above-mentioned heat integration, and the corresponding steady state and dynamic characteristics

have been studied extensively in recent years[6-12].Luyben[13] compared the pressure-swing distillation and extractive distillation with and without heat integration for acetone-methanol separation system, and the results

Optimization and Control of Extractive Distillation with Heat Integration for Separating Benzene/Cyclohexane Mixtures

Li Lumin; Tu Yangqin; Guo Lianjie; Sun Lanyi; Tian Yuanyu(State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Qingdao 266580)

Abstract: In this work, the extractive distillation with heat integration process is extended to separate the pressure-insensi-tive benzene-cyclohexane azeotrope by using furfural as the entrainer. The optimal design of extractive distillation process is established to achieve minimum energy requirement using the multi-objective genetic algorithm, and the results show that energy saving for this heat integration process is 15.7%. Finally, the control design is performed to investigate the system’s dynamic performance, and three control structures are studied. The pressure-compensated temperature control scheme is proposed based on the first two control structures, and the dynamic responses reveal that the feed disturbances in both flow rate and benzene composition can be mitigated well.Key words: extractive distillation; heat integration; optimization; genetic algorithm; dynamic simulation

Received date: 2016-07-11; Accepted date: 2016-09-09.Corresponding Author: Prof. Sun Lanyi, Telephone: +86-13-854208340; Fax: +86-53-286981787; E-mail: [email protected].

China Petroleum Processing and Petrochemical Technology 2016, Vol. 18, No. 4, pp 117-127Simulation and Optimization

· 118 ·

showed that the total annual cost of extractive distilla-tion system was by 15% lower than that achieved by the pressure-swing distillation. In order to achieve the heat integration of extractive distillation process, the pressure of entrainer recovery column should be increased to ob-tain the required temperature difference.The heat integration in extractive distillation is possible for benzene/cyclohexane mixture separation. Therefore, this heat-integrated scheme is introduced to save the ener-gy requirement and reduce the fixed capital investment by operating columns at different pressures. This paper will focus on the optimization and control of extractive distil-lation with heat integration for separating benzene/cyclo-hexane mixtures. In this context, the optimum design of the flowsheet is proposed to achieve the minimum energy requirement by using the multi-objective genetic algo-rithm method. Then three control structures are proposed to effectively stabilize this optimum design. Finally, some conclusions are presented in the last section.

2　Steady-State Design

2.1　Process design

The extractive distillation is applied to separate the benzene-cyclohexane system, and the proposed flowsheet is presented in Figure 1, which contains two columns, viz.: an extractive distillation column (EDC) operating at atmospheric pressure and an entrainer recovery column (ERC) operating under a pressure of 6 atm. The reflux-

drum temperature in HP column is 425 K with the purity of benzene distillate reaching 99.7 mol%, and the base of the extractive column is 409 K, thus there is a reasonable 16 K as the differential temperature driving force to size the reboiler/condenser heat exchanger. The Non-Random Two-Liquid (NRTL) model, which can predict this ter-nary system very well[14], is used to calculate the related physical properties. In this paper the extractive distillation was simulated using Aspen Plus with the following data: the feed consists of 750 kmol/h of benzene and 250 kmol/h of cyclohexane.

2.2　Sensitivity analysis

The parameters analyzed in this study cover the following items: the operating pressure of high-pressure (HP) col-umn, the reflux ratio (RR) of low-pressure (LP) column, the entrainer temperature (ET), and the entrainer to feed ratio (E/F).Figure 2 shows the influence of the operating pressure inside the HP column on the total duty in the process and the temperature difference between the bottom of LP column and the top of HP column. It is observed that the increase of operating pressure in the HP column results in a significant rise in the temperature difference during heat transfer, which means a corresponding decrease in the heat transfer area. However, attention should be paid to the increasing total energy requirement in this proposed process. This is because high operating pressure causes more liquid fraction in the feed stream of HP column,

Figure 1　Process flow diagram for extractive distillation with heat integration

Li Lumin, et al. China Petroleum Processing and Petrochemical Technology, 2016, 18(4): 117-127

· 119 ·

which means greater energy requirement at the reboiler.The effect of reflux ratio in the LP column on the cy-clohexane composition and the condenser and reboiler duties are presented in Figure 3. It can be seen that the greatest cyclohexane composition is obtained at a reflux ratio in the range of between 5.0 and 10.0, with a differ-ence among them being no more than 0.05. It is noticed that the cyclohexane composition in the distillate does not change significantly when the reflux ratio is greater than 5.0. Indeed, an apparent decrease in the product compo-sition occurs due to the increasing reflux ratio without entrainer in the LP column. It is also possible to observe from Figure 3 the effect of reflux ratio on the condenser and reboiler duties.The energy requirement is significantly effected when the entrainer temperature varies in the range from 280 K to 380 K (see Figure 4). This is because less energy is required to vaporize the liquid at the bottom when the entrainer is fed at higher temperature. As the entrainer

feed temperature is higher, more furfural is transferred to the vapor phase and the liquid flow to the bottom is less. However, no apparent influence on the product purity can be observed until the entrainer feed temperature is higher than 340 K. When the entrainer temperature is higher than 340 K, the cyclohexane and benzene contents in the distillates are lower. This could be ascribed to the lower furfural content in the rectifying section of LP column, resulting in less cyclohexane separated in the distillate.Figure 5 shows the effect of the entrainer to feed molar ratio (E/F) on the distillate composition and reboiler duty. Based on the above analysis, the reflux ratio is maintained at a constant value (3.2). It can be seen that both of the reboiler duties in LP column and HP column show signifi-cant increase with a rising E/F ratio. Moreover, increasing values of the product purity can be obtained when the E/F ratio is less than 2.0. Nevertheless, when the E/F ratio is higher than 2.0, no significant effect on the product purity can be observed.

Figure 2　Effect of pressure in HP column on the total energy requirement and the temperature difference between the reboiler of LP column and the condenser of HP column

Figure 3　Effect of reflux ratio in LP column (R1) on the cyclohexane composition (XD1) in the distillate of the

extractive distillation and heat duty of LP column

Figure 4　Effect of entrainer temperature on the energy requirement and the product composition in the distillate of

the extractive distillation

Figure 5　Effect of entrainer to feed molar ratio (E/F) on the product composition and reboiler duties in the extractive

distillation column


· 120 ·

2.3　Optimization of extractive distillation process

The application of multi-objective genetic algorithm to optimize the extractive distillation columns has been pub-lished in recent papers[4, 15-16]. In this paper, the extractive distillation processes with and without heat integration are optimized using multi-objective genetic algorithm to achieve minimum energy requirement. Evaluation of the objective function using multi-objective genetic algorithm with constraints, coupled with Aspen Plus[17] as a design tool, can obtain the expected results. Instead of obtaining one optimal design, a set of optimal designs is obtained through this procedure with integration of the Pareto front. In this way, the engineer can choose a trade-off by picking some points along the Pareto front. For the sake of optimization of multivariable functions, the stochastic optimization methods present a reasonable computational effort and they just need to calculate the objective func-tion without problem reformulation.As a thermodynamic equivalent of the extractive distilla-tion with heat integration, two coupled RADFRAC units are used in Aspen Plus. The manipulated variables include the heat duty, the reflux ratios, the total number of stages, the location of the feed, and the extracting agent flow.In terms of multi-objective optimization, there are three objectives to minimize, namely: the number of stages of the total columns, the heat duty of the sequences and the extracting agent flow, which are in competition and con-strained by the desired purity and recovery in each prod-uct stream, therefore the objectives must be optimized si-multaneously. This problem can be expressed as follows:

where Ni is the number of stages in the column i, QR is the total heat duty, including the reboiler heat duties of LP col-umn and HP column and the condenser heat duty of the HP column, QR,i is the heat duty of column i, FEA is the extract-ing agent flow, RRi is the reflux ratio of column i, NF,i is the

feed stage number of column i. yk→ and xk

→ are the vectors of obtained and required purity and recovery for the com-ponent k, respectively. For the case of extractive distilla-tion with heat integration, 2 000 individuals and 40 gen-erations are chosen as parameters of the genetic

algorithm, with crossover and mutation fraction equating to 0.80 and 0.05, respectively. The procedure is carried out as follows. Firstly, a feasible initial design of the ex-tractive column is given as an original solution to the al-gorithm of each run. The algorithm generates N individu-als (i.e., new designs) based on the initial solution to make up the first population. The manipulated variables of each of the N individuals are sent to Aspen Plus to per-form the simulation, and then Aspen Plus gives the values of objective functions and constraints for each individual to the algorithm. The population is divided into subpopu-lations in terms of the number of satisfied constraints with the retrieved information, and at this time the best indi-viduals can satisfy the c constraints, followed by those in-dividuals that reach c-1 constraints, etc. Inside each sub-population, the individuals are ranked according to the value of the fitness function. The original objective func-tions can be optimized through the classification of the population, which can also minimize the difference be-tween the required and obtained constraints (recoveries and purity). Finally, a set of optimal designs of the extrac-tive column is obtained. More detailed information about this algorithm and its link to Aspen Plus can be found in the original work[17].Figure 6 shows the Pareto front for the benzene/cyclo-

hexane mixture, which includes the objectives to mini-mize the following, viz.: the heat duty of the sequence, the extracting agent flow and the total number of stages. Finally, 20 optimal designs are observed that make up the Pareto front, indicating that an extractive distillation

Figure 6　Pareto front of the extractive distillation for benzene/cyclohexane mixture


· 121 ·

column with heat integration can perform the extractive separation. These optimal designs can satisfy the specified purity and recoveries with the lowest energy consumed. In our work, the energy requirement is the criterion for meeting our particular needs, and then a design with the minimum reboiler duty is chosen as the final design. The optimum results of the heat integrated extractive distil-lation are compared with that of the conventional two-column process as shown in Table 1. The number of stages for the LP column and the HP column is 35 and 19, respectively. The recycle solvent returns back to the stage 8 and the feed flows to the stage 19. The number 3.80 is chosen as the reflux ratio of the LP column. As for the HP column, the value of reflux ratio is set at 1.40. In addition, the extracting agent flow rate is 2 500.12 kmol/h. It can be seen that under the above conditions, the total energy requirement of the heat integrated extractive distillation process is 33 461.12 kW, and the corresponding energy saving can reach 15.7% as compared with the conven-tional extractive distillation process.

Table 1　Optimum results of the conventional two-column design and the extractive distillation column with heat

integration design

Configurations

Conventional extractive distillation

Extractive distillation with heat integration

EDC ERC LP HP

Operating pres-sure, MPa

0.1 0.1 0.1 0.6

Total number of stages

34 11 35 19

Feed location 20 7 19 10

Entrainer feed location

8 - 8 -

Reflux ratio 3.74 1.72 3.80 1.40

Entrainer flow-rate, kmol/h

2 698.25 - 2 500.12 -

Condenser duty, kW

-9 870.96 -17 512.01 -8 749.8 -13 093.70

Reboiler duty, kW

19 502.41 20 211.50 17 697.16 28 857.66

Total reboiler duty, kW

39 713.91 (0%) 33 461.12 (-15.7%)

Figure 7 shows the temperature profiles of the LP and HP columns stipulated in the optimum design. There is a rapid rise in the temperature in the stage 15 of the LP col-

umn, and it is obvious that the stage 12 displays a fairly steep slope for the temperature of the HP column. The profile distinguished features indicate that the stage 15 and the stage 12 are the proper temperature control points for the LP and HP columns, respectively.

3　Control System Design

3.1　�Basic control structure for the extractive distilla-tion (CS1)

The optimized flowsheet is exported to Aspen Dynamics as a pressure-driven simulation after reflux drum and base volumes are sized to provide 5 min of holdup when they are half full, pumps and valves are specified to give ad-equate pressure drop to handle changes in flow rates, and the pressure is checked. Control problem mainly comes from the high interaction through the streams connecting the two columns and the heat transfer through the combined condenser and reboiler[18].

The dynamic system must satisfy two conditions, viz.: firstly, the combined condenser/reboiler duty is related to the heat transfer coefficient, the heat transfer area, and the

Figure 7　(a) LP column temperature profile; (b) HP column temperature profile


· 122 ·

temperature difference between the condenser of LP col-umn and the reboiler of HP column; then, the heat input rate of the LP column reboiler is the sum of the heat re-moval rate of HP column condenser and the heat addition rate in the auxiliary reboiler. The corresponding equations then enter the text editor window as shown in Figure 8.

After the flowsheet equations are compiled, simulation is unable to run because of the over-specification of two variables. To cope with this problem, the heat duties in the condenser of HP column and the reboiler of LP col-umn must be changed from “fixed” to “free”. Figure 9 shows the basic control structure for extractive distillation process with heat integration, the effectiveness of which will be evaluated later.(1) The fresh feed to LP column is flow-controlled (re-verse acting).(2) The reflux drum level in both columns is held constant by manipulating the distillates flow rate (direct acting).(3) The base level in LP column is maintained by manipu-lating the bottom flow rate (direct acting).(4) The base level in HP column is maintained by ma-

nipulating the makeup flow rate (reserve acting).(5) The pressure in LP column is controlled by manipulat-ing the heat removal rate in the condenser (reverse acting).(6) The reflux ratio in HP column is fixed.(7) The temperature for the stage 15 in LP column is con-trolled by manipulating the heat input rate of the auxiliary reboiler (reverse acting).(8) The temperature for the stage 12 in HP column is con-trolled by manipulating the heat input rate in the reboiler of HP column (reverse acting).(9) The total solvent flow rate is controlled using the FC2 controller by manipulating the recycle solvent flow rate (reserve acting).(10) The solvent feed temperature is controlled by ma-nipulating the cooler heat removal rate (reverse acting).The PI controllers are used for all flow loops with the normal settings as shown below: KC=0.5 and τI=0.3 min; all level controllers are P-only with KC=2; all pressure loops are proportional-integral with the default values; the relay-feedback tests are used to determine the ultimate gains and periods of the two temperature controllers, us-ing the Tyreus Luyben tuning. Two deadtime elements are inserted in the two temperature control loops with a dead-time of 1 min. Now the dynamic performance of the basic control struc-ture is evaluated by using the disturbances in feed flow rate and composition. Figure 10(a) gives the dynamic

Figure 8　Flowsheet equations for the partial heat integration

Figure 9　Basic control structure for the extractive distillation process with heat integration


· 123 ·

responses of the control structure to positive and negative 20% step disturbances in feed flow rate in 1 h, and Figure 10(b) shows the responses to positive and negative 10% disturbances in benzene composition in 1 h. It is noted that the basic control structure CS1 presents overshootings for the two kinds of disturbances, and the system takes about 6 h to reach a new steady state. It can be seen from Figure 10(b) that for a 10% decrease in benzene concentration of the fresh feed, a relatively large negative offset from the specified purity occurs in the cyclohexane product, leading to an undesired product. Hence, an improved control structure is needed.

3.2　�Improved control structure with the QR/F ratio and S/F ratio (CS2)

In the improved control strategy, a multiplier block is added to the basic control structure to make sure that the heat input rate of the HP column reboiler is proportional to the feed flow rate. Moreover, if the flow rate or the concen-tration of the fresh feed is changed, the solvent flow rate should also be adjusted so that the products can meet the

specified purity. Thus, the S/F ratio is added in the improved control structure. Figure 11 shows the improved control structure CS2 provided with the QR/F ratio and S/F ratio. New relay-feedback tests are run to determine ultimate gains and periods of the two temperature controllers.Figure 12 shows the effectiveness of this improved control strategy. As demonstrated in Figure 12(a), the large transient deviation of cyclohexane purity decreases from 2.6% to 0.5% at a +20% feed flow rate disturbance when the improved control scheme is used. This is because when the feed flow rate increases, the reboiler duty of HP column also increases rapidly, bringing about evaporation of more vapor from the bottom, which would increase the heat removal rate in the HP column condenser and prevent more benzene from escaping from the bottom. However, because of hydraulics lag in the HP column, the effect of this improvement is not significant.

3.3　�Control structure with pressure-compensated temperature (CS3)

Luyben has described[13,19] the pressure-compensated temperature control of the partial heat-integrated pres-

Figure 10　Dynamic responses for the basic control structure CS1: (a)±20% in feed flow rate; (b)±10% in benzene composition


· 124 ·

sure swing distillation process in detail. In this paper, a pressure-compensated temperature control scheme for extractive distillation with partial heat integration is set up. Implementing the pressure-compensated temperature control in Aspen Dynamics requires the use of a third

equation, which will provide a “pressure-compensated” temperature measurement in the HP column. The pressure in the HP column is not controlled in the heat-integrated system, which floats with operating conditions. A larger temperature difference is required when more heat trans-

Figure 11　The improved control structure CS2 with the QR/F ratio and S/F ratio

Figure 12　Dynamic responses for the improved control structure: (a)±20% in feed flow rate; (b)±10% in benzene content


· 125 ·

fer is needed in the reboiler/condenser, and consequently the pressure in the HP column increases, which also raises the bubble point temperature in the reflux drum. The last equation calculates the signal fed to the deadtime element in the TC2 loop as shown in Figure 13(a), and Figure 13(b) gives the control structure using the pressure-com-pensated temperature.The dynamic performance for this pressure-compensated temperature control structure CS3 is demonstrated in Figures 14. It can be seen from Figure 14 that the cyclo-hexane product purity is maintained to comply with its specification after the disturbance in feed flow rate, while a significant improvement is obtained in the response expressed in terms of the benzene content. In addition, the cyclohexane content can be easily brought back to

its initial level within 4 h as compared with the control structure CS2. The results indicate that the drawbacks of the CS2 can be fairly well rectified by this pressure-compensated temperature control structure.

4　Conclusions

This paper considers the separation of pressure-insensi-tive benzene/cyclohexane azeotrope via extractive distil-lation with heat integration. The partially heat-integrated configuration is developed in Aspen Plus, and then the whole process is optimized using the multi-objective ge-netic algorithm. The simulation results show that the en-ergy requirement for the conventional extractive distilla-tion process and the heat-integrated extractive distillation process is 39 713.91 kW and 33 461.12 kW, respectively,

Figure 13　(a) Aspen Dynamics flowsheet equations for heat integration and pressure-compensated temperature in HP column; (b) The control structure using pressure-compensated temperature CS3


· 126 ·

Figure 14　Dynamic responses for the pressure-compensated temperature control structure: (a)±20% in feed flow rate; (b)±10% in benzene content

and a 15.7% energy saving can be achieved by the heat integration process. Three control structures are proposed for this extractive distillation process. As for the pressure-compensated temperature control structure, the product purity is maintained to comply with the specification with negligible deviations after feed flow rate and composition disturbances, and a robust control can be achieved for this heat-integrated process.

Acknowledgements: This work was supported by the National

Natural Science Foundation of China (grant number 21 476

261); the Key Research and Development Plan Project of Shan-

dong Province (grant number 2015GGX107004) Finally the

authors are grateful to the editor and the anonymous reviewers.

NomenclatureBen—benzene

Cyc—cyclohexane

EDC—extractive distillation column

ERC—entrainer recovery column

F—fresh feed flow rate

FEA—the extracting agent flow

Fur—furfural

KC—controller gain

NF,i—feed stage number of column i

Ni—the number of stages of column i

QR—reboiler heat duty

RRi—the reflux ratio of column i

S—recycle solvent flow rateXD1—cyclohexane composition on the top of the LP columnτI—controller integral time constant

References[1]　� Luyben W L, Chien I L. Design and Control of Distilla-

tion Systems for Separating Azeotropes[M]. John Wiley &

Sons, 2011

[2]　� Lladosa E, Montón J B, Burguet M C. Separation of di-n-

propyl ether and n-propyl alcohol by extractive distillation

and pressure-swing distillation: Computer simulation and

economic optimization[J]. Chemical Engineering and Pro-

cessing: Process Intensification, 2011, 50(11): 1266-1274

[3]　� Qin J, Ye Q, Xiong X, et al. Control of benzene–cyclohex-


· 127 ·

ane separation system via extractive distillation using sul-

folane as entrainer[J]. Industrial & Engineering Chemistry

Research, 2013, 52(31): 10754-10766

[4]　� Sun L, Wang Q, Li L, et al. Design and control of extractive

dividing wall column for separating benzene/cyclohexane

mixtures[J]. Industrial & Engineering Chemistry Research,

2014, 53(19): 8120-8131

[5]　� Huang K, Shan L, Zhu Q, et al. Adding rectifying/stripping

section type heat integration to a pressure-swing distilla-

tion (PSD) process[J]. Applied Thermal Engineering, 2008,

28(8): 923-932

[6]　� Li L, Liu Y, Zhai J, et al. Design and control of self-heat re-

cuperative distillation process for separation of close-boiling

mixtures: n-butanol and iso-butanol[J]. China Petroleum Pro-

cessing & Petrochemical Technology, 2015, 17(4): 111-120

[7]　� Jana A K. Heat integrated distillation operation[J]. Applied

Energy, 2010, 87(5): 1477-1494

[8]　� Chen Y C, Hung S K, Lee H Y, et al. Energy-saving designs

for separation of a close-boiling 1, 2-propanediol and ethyl-

ene glycol mixture[J]. Industrial & Engineering Chemistry

Research, 2015, 54(15): 3828-3843

[9]　� Kiss A A, Olujić Ž. A review on process intensification in

internally heat-integrated distillation columns[J]. Chemical

Engineering and Processing: Process Intensification, 2014,

86: 125-144

[10]　� Zhu Z, Wang L, Ma Y, et al. Separating an azeotropic mix-

ture of toluene and ethanol via heat integration pressure

swing distillation[J]. Computers & Chemical Engineering,

2015, 76: 137-149

[11]　� Yu B, Wang Q, Xu C. Design and control of distillation

system for methylal/methanol separation. Part 2: pressure

swing distillation with full heat integration[J]. Industrial &

Engineering Chemistry Research, 2012, 51(3): 1293-1310

[12]　� Li W, Shi L, Yu B, et al. New pressure-swing distilla-

tion for separating pressure-insensitive maximum boiling

azeotrope via introducing a heavy entrainer: design and

control[J]. Industrial & Engineering Chemistry Research,

2013, 52(23): 7836-7853

[13]　� Luyben W L. Comparison of extractive distillation

and pressure-swing distillation for acetone-methanol

separation[J]. Industrial & Engineering Chemistry Re-

search, 2008, 47(8): 2696-2707

[14]　� Kumar U K A, Mohan R. Quinary and eight-component

liquid–liquid equilibria of mixtures of alkanes, aromatics,

and solvent (furfural)[J]. Journal of Chemical & Engineer-

ing Data, 2013, 58(8): 2194-2201

[15]　� Modla G, Lang P. Removal and recovery of organic sol-

vents from aqueous waste mixtures by extractive and pres-

sure swing distillation[J]. Industrial & Engineering Chem-

istry Research, 2012, 51(35): 11473-11481

[16]　� Modla G. Energy saving methods for the separation of a

minimum boiling point azeotrope using an intermediate

entrainer[J]. Energy, 2013, 50: 103-109

[17]　� Gutiérrez-Antonio C, Briones-Ramírez A. Pareto front of

ideal Petlyuk sequences using a multiobjective genetic

algorithm with constraints[J]. Computers & Chemical En-

gineering, 2009, 33(2): 454-464

[18]　� Huang K J, Nakaiwa M, Takamatsu T. Considering process

nonlinearity in dual-point composition control of a high-

purity ideal heat integrated distillation column, Chinese

Journal of Chemical Engineering, 2001, 9(1): 58-64

[19]　� Luyben W L. Design and control of a fully heat-integrated

pressure-swing azeotropic distillation system[J]. Industrial &

Engineering Chemistry Research, 2008, 47(8): 2681-2695


Documents

Optimization and Control of Extractive Distillation with