Economic and entropy production evaluation of extractive distillation and solvent-assisted pressure-swing distillation by multi-objective optimization

Yao Wang, Qing Ye, Jinlong Li, Qingqing Rui, Azhi Yu

Jiangsu Key Laboratory of Advanced Catalytic Materials and Technology, School of Petrochemical Engineering, Changzhou University, Changzhou 213164, China

Keywords: Extractive distillation Solvent-assisted pressure-swing distillation Entropy production NSGA-II algorithm Computer simulation

ABSTRACT Extractive distillation(ED)and solvent-assisted pressure-swing distillation(SA-PSD)are both special distillation processes that perform good at separating pressure-insensitive azeotropes. However, few reported studies have compared the performance of the two processes. In this paper, ED processes with N-methylpyrrolidone (NMP) and dimethlac-etamide (DMCA) as entrainer, SA-PSD process with isopropyl-alcohol (IPA) as solvent and SA-PSD process with partial heat integration (PHI-PSD) are proposed to achieve high purity separation of a mixture of cyclohexane/2-butanol system.The optimal operating conditions of the processes are obtained after optimizing with NSGA-II algorithm when total annual cost(TAC)and the entropy production of process are set as objectives.The optimal results show that the optimal PHI-PSD process has lower TAC by 28.7% and the lower entropy production by 39.5% than the optimal SA-PSD process while the ED process with NMP as entrainer has lower TAC by 50.9% and the lower entropy production by 56.1% than the optimal SA-PSD process. The optimal results show that the ED process with NMP as entrainer has the best economic and thermodynamic efficiency among the four proposed processes in this paper.

1. Introduction

2-Butanol is the most important intermediate in the production of methyl ethyl ketone which accounts for about 90% of the total consumption [1]. In industry, 2-butanol can also be used as a raw material for the synthesis of flavors and dyes, which has important industrial production value.Cyclohexane is an intermediate in the production of cyclohexanone and caprolactam[2].It is also used as a solvent, entrainer, paint stripper and diluent for polymerization reactions. Cyclohexane is an important raw material for many chemical products and fine chemicals. However,cyclohexane forms an azeotrope with 2-butanol and makes it difficult to access high purity products from industrial products or waste water. Due to the presence of azeotropes, ordinary distillation methods cannot separate products that meet the purity requirements.Therefore,special distillation process like extractive distillation (ED), pressure-swing distillation (PSD) have been used to separate mixture with azeotropes.

ED [3–5] is a special distillation process which has been researched and used extensively.The ED process breaks azeotropic mixtures and achieves efficient separation by introducing one or more additional components as extraction entrainers, continuously injecting a different column plate from the fresh feed and changing the relative volatility of the components. Gilet al.[6]used extractive distillation process to separate methanol and acetone with water as the entrainer.They paid attention to the effects of the entrainer to feed molar ratio,reflux ratio,feed stage,entrainer feed stage and entrainer feed temperature to obtain the best design of the extractive distillation column with minimal energy requirements. Liet al.[7] used sulfolane as the entrainer to separate cyclohexane and benzene. The thermodynamic analysis and carbon dioxide emissions indexes are considered to evaluate the energy efficiency and environmental impacts of the modified designs and the separation specification for the two components could achieve 99.9% (mol). Wanget al.[8] conceptually designed several three-column extractive distillation processes which are energy-saving with an integrated distillation column to separate a three-component poly azeotrope with a high component content.

Pressure-swing distillation (PSD) [9–11] is also a special distillation process which have been used widely to separate azeotropic mixtures.PSD makes use of the pressure sensitivity of some azeotropic mixtures.Luyben[12]used PSD process to separate acetone/methanol system which can obtain the products with a purity of 99.5%(mol).In the PSD process,there may be an appropriate temperature difference between the condenser of one column and the reboiler of another column. This is caused by the pressure difference between the different columns which makes heatintegration feasible. Zhuet al.[13] compared full heat integration and partial heat integration to separate benzene/isopropanol/water system. The results showed that both of them can improve the economic performance of PSD process and full heat integration is better from an economic point of view than partial heat integration.

In general, almost all existing studies on PSD have been performed on pressure-sensitive azeotropes. For systems that are not pressure sensitive, conventional PSD is not considered to be a good choice.Jiaoet al.[14]used ED and PSD to efficiently separate ethyltert-butyl ether/ethanol/water system and they obtained the optimal process parameters and process. Knapp and Doherty [15]proposed a new process of PSD in which a component was added as a pressure-swing entrainer. They proved the feasibility of this new PSD process by separating ethanol and water with acetone as the solvent. The introduced solvent needs to form new azeotrope which is pressure sensitive with one of the components to be separated so that the azeotropic composition between the two azeotropes change rapidly with changes in pressure. Liet al.[16]applied this new PSD process to separate phenol and cyclohexanone with acetophenone as the solvent. Qinet al.[17] compared the performance of azeotrope assisted distillation with tetrahydrofuran as pressure sensitive azeotrope and extraction distillation with dimethyl sulfoxide as solvent in the separation of water/isopropyl alcohol azeotrope,so as to explore the performance of azeotrope assisted distillation. The results showed that ED process reduces total annual cost (TAC) and CO2emissions by 51.80% and 36.96%, respectively, compared to PSD. Li and Xu [18] used new PSD process to separate methanol and toluene with chloroform as the solvent and founded that the new PSD process has 5.39%reduction of TAC and 8.32% of energy consumption compared to the ED process. Up to now, many scholarly studies have demonstrated the viability of this new solvent-assisted pressure-swing distillation (SA-PSD) process but there are relatively few studies comparing it with ED process.

It is well known that the entrainer selection is the first and critical step when use ED process and SA-PSD process and it has been studied in detail by many scholars. Daiet al.[19] investigated the impact of different entrainers for separating ternary mixtures containing azeotropes by ED process and the results prove that the performance of ED process is greatly influenced by different entrainers. Modlaet al.[20] investigated the feasibility of SA-PSD and different solvents are compared. Liet al.[21] used the COSMO-SAC model to calculate intermolecular interactions between components and candidate entrainment agents and selected dimethyl sulfoxide (DMSO) to separate ethyl acetate,1,4-dioxane and water.Xuet al.[22]used the vapor–liquid equilibrium(VLE) diagram of different component pairs on different candidate entrainers to determine the impact of different entrainers on the relative volatility of components and selected DMSO to separate acetonitrile,1,4-dioxane and water.There is a lot of literature on the selecting of the entrainer for ED process but less research on the selecting of solvent for SA-PSD process.

The optimization of distillation processes is an important aspect in distillation process design. In general, methods for optimizing distillation processes are broadly divided into two groups: (i) single objective optimization (SOO) [23,24] and (ii) multi-objective optimization (MOO) [25–27]. SOO typically has a single optimal solution in one of objectives while the solution to MOO is not unique but has a set of optimal solutions consisting of many pareto optimal solutions. MOO differs from SOO in the number of objective functions and the way solutions are compared so that for two or more optimization objectives, MOO is generally used[28,29]. Among the many MOO algorithms, the elitist nondominated sorting genetic algorithm (NSGA-II) [30] has been applied to many different chemical processes. NSGA-II algorithm[31]can provide a better distribution of solutions compare to other MOO algorithms and usually has a faster convergence to the nondominated solution called the Pareto Front. Yanet al.[32] conducted a MOO study on the process of mixed reaction ED to separate waste water containing benzene isopropanol and the optimization results proved the superiority of the NSGA-II algorithm.Up to now,total annual cost(TAC)[33]has been frequently used as one of the objectives to assess the economic efficiency of distillation processes in many published papers but the other objective is very variable. Zhaoet al.[34] selected gas emissions as the other objective to assess environment performance of distillation processes. However,few studies have used entropy production in optimization to assess the thermodynamic efficiency of ED and SA-PSD processes. According to the laws of thermodynamics,the greater the entropy production, the lower the thermodynamic efficiency and the process is more irreversible [35]. The lower the entropy production, the higher the thermodynamic efficiency and irreversibility of the distillation process. Benyouneset al.[36]focused on the impact of the operating parameters of the extractive distillation column on the entropy production of the column but they did not consider the entrainer recovery column.

The aim of this study is to achieve the separation of 2-butanol/cyclohexane system by ED and SA-PSD processes and achieve MOO of proposed processes by using NSGA-II algorithm with both economic efficiency and thermodynamic efficiency (i.e.,TAC and entropy production) as two objective functions. Further analysis of the optimization results is carried out to evaluate the economic efficiency and thermodynamic efficiency and obtain an optimal process for the separation of the cyclohexane/2-butanol system.

2. Thermodynamic Method and Entrainer Selection

2.1. Thermodynamic method

Cyclohexane and 2-butanol can’t be separated by ordinary distillation process because of the presence of azeotrope.Therefore,to achieve the separation of the cyclohexane and 2-butanol mixture,ED and SA-PSD are considered. Both of these two processes need to introduce a entrainer/solvent to the system. Aspen Plus V11 is applied to simulate the steady-state process to separate cyclohexane and 2-butanol. It is found that the non-radom two liquid(NRTL) model can accurately describe the non-ideal liquid phase behavior of various components.The binary interactive parameters are predicted using the NRTL model, as shown in Table 1. Binary interactive parameters are defaults in Aspen Plus V11. The diagrams of calculated data and experiment data is shown in Fig. S1.

Table 1Binary interactive parameters from NRTL model

2.2. Entrainer selection

2.2.1. Extractive distillation (ED)

For ED processes, the choice of the most suitable entrainer is critical.The entrainer used should be mutual soluble with the fresh feed and have a much higher boiling point than the feed components. At the same time, the chosen entrainer ought to be capable to eliminate azeotropic phenomenon and not form new azeotrope with the original components. The commonly used methods for selecting entrainers include the empirical method, polarity principle, relative volatility curve, experimental method, computer-aided molecular design, and quantitative structure–activity relationship [37,38].

In this paper,N,N-dimethylformamids (DMF), ethylene glycol(EG),N-methylpyrrolidone (NMP), dimethlac-etamide (DMAC)and aniline are five candidate entrainers for the ED process.

The COSMO-SAC model is widely used in areas such as reactions and separations and it allows the interactions between components to be explored from a microscopic perspective. In general,the σ-profiles of components and candidate entrainers,which presents the hydrogen bond interaction between molecules and it can be calculated by the COSMO-SAC model. There are three areas for σ-profiles which contains hydrogen bond donator area(σ < –0.0082e∙A-2), hydrogen acceptor area (σ > 0.0082e∙A-2) and non-polar area (other). It means a strong hydrogen accept ability of components when the peaks occur in the hydrogen acceptor area. A strong hydrogen donate ability when the peaks occur in hydrogen donator area. The accept/donate hydrogen bond ability presents the combination ability between molecules. Thus, the strong ability to accept hydrogen bond as well as donate hydrogen bond between entrainers and components means a greatly combination ability in them which presents the great separation ability for this entrainer. For the ED process, the σ-profiles of the candidate entrainers and the components to be separated is shown in Fig.1.As shown in Fig.1,the peaks of DMAC,NMP and DMF appear in the hydrogen bond acceptor area while the peak of aniline appears in the hydrogen bond donator area,the peak of EG appears in both donator area and acceptor area. The peak of DMAC and NMP are the highest in the hydrogen bond acceptor area which is an indication of their strong interaction with 2-butanol. Thus,DMAC, NMP and DMF are three suitable entrainers to separate 2-butanol and cyclohexane.

Vapor–liquid equilibrium(VLE)diagram compares the effects of various entrainers on the relative volatility enhancement is an effective method to screen the entrainer. Fig. 2 shows the impact of different entrainers on VLE of cyclohexane/2-butanol with the entrainer to feed mole ratio 0.3. In the absence of entrainer, they-xcurve intersects they=xline, so cyclohexane and 2-butanol form an azeotrope. The further the curve deviates from the diagonal line,the higher the relative volatility of the components will be,which means the better separation impact of the entrainer on the cyclohexane/2-butanol system.It can be seen in Fig. 2 that DMAC,NMP and DMF enhance the relative volatility of components better than aniline and EG.

For further selection,the boiling points and azeotropic temperatures of five candidate entrainers, cyclohexane and 2-butanol are shown in Table 2. Both EG and DMF form binary azeotropes with cyclohexane so that they cannot be used to separate cyclohexane and 2-butanol. The performance of the five candidate entrainers in terms of relative volatility, molecular bonding energy, and whether they form azeotropes are combined. NMP and DMAC are selected as two different entrainers to separate cyclohexane and 2-butanol because that NMP and DMAC are similar for the separation of cyclohexane and 2-butanol in VLE and σ-profile.

Table 2Boiling point of pure components and azeotropes 0.1 MPa

2.2.2. Solvent-assisted pressure-swing distillation

Pressure-swing distillation is a distillation process that exploits the pressure sensitivity of azeotropic mixtures to achieve separation. Composition of the azeotropic mixture to be separated is required to vary considerably with the pressure when use conventional pressure-swing distillation. However, the azeotrope formed by 2-butanol and cyclohexane is less sensitive to pressure changes as shown in Table 2.Thus,conventional pressure-swing distillation is unable to separate 2-butanol and cyclohexane. In this paper, a new pressure-swing process which a component was added as a pressure-swing solvent can be applied to separate cyclohexane/2-butanol system and a new SA-PSD process is designed. Selection of an appropriate pressure-swing solvent is very critical for SA-PSD process, the introduced solvent should form a new azeotrope which is pressure sensitive with cyclohexane and makes the composition for the two azeotropes changed rapidly with changes in pressure.

In this paper, methanol, ethanol, ethyl acetate (EA) and isopropyl-alcohol (IPA) are the four candidate solvents. The σprofiles of these candidate solvents, 2-butanol and cyclohexane are shown in Fig. 3. The peak of EA appears in the hydrogen bond acceptor area while the peaks of IPA,methanol and ethanol appear in both hydrogen bond donator area and hydrogen bond acceptor area.The peak of IPA appears in the most distant area.Fig.4 shows the impact of different solvents on VLE of cyclohexane/2-butanol with a solvent to feed mole ratio 0.5.It can be seen that IPA,methanol and ethanol enhance the relative volatility of components better than EA.

Further selection of candidate solvents is mainly determined by the flow rate of the recycle stream in the SA-PSD process,which is the critical factor affecting the energy consumption. Analysis of azeotropes formed with cyclohexane at 0.1 MPa and 0.7 MPa for each of the four solvents,as shown in Table 3.The more the difference between the mole fraction of the solvent in the azeotrope at 0.7 MPa and 0.1 MPa pressures results in the lower flow rate of recycle stream. Although EA leads to the largest difference in the molar fraction of solvent in the azeotropes, the impact of EA on the relative volatility of the components is the smallest. Thus,IPA is chosen as the solvent for the SA-PSD process on balance.

Table 3Mole fraction of azeotropes at 0.1 and 0.7 MPa

3. Evaluation

3.1. Economic evaluation

Economy is an important index for the evaluation of the feasibility of the distillation process. Total annual cost (TAC) is often considered as an optimization objective. TAC is a common selection criterion for the whole process when evaluating the economic effect,which consists of total operating cost(TOC)and total capital cost (TCC). Recovery period (RP) is three years [39]. By setting the operation hours per year (OH), TOC can be annualized. The equation of TAC is as follows:

The specific calculation methods of TOC and TCC are as follows:

CwaterandCsteamrepresent the cost of cooling water and steam for the entire distillation process. TCC includes the cost of all equipment,Ccolumn,Ccondenser,Creboiler,CheaterandCcoolerwhich are represent the column cost, condenser cost, reboiler cost, heat exchanger cost and cooler cost. The specific details of above cost are shown in Table S1 (in Supplementary Material). It is noted that the other items such as pumps, piping, and valves are ignored because their costs are negligible compared to the cost of major equipment.

3.2. Entropy evaluation

The thermodynamic efficiency of the process can be determined by calculating the entropy production of the process based on the second laws of thermodynamics. The lower the entropy production, the higher the thermodynamic efficiency of the process.Therefore, the entropy production of the entire process (ΔStotal)can be used as another optimization objective. As shown in Fig. 5, the column is adiabatic through the exchange of heat and mass between the liquid flowing in a downward direction and the vapor flowing in an upward direction. All the heat of this column is provided by the reboilerQRand taken away by the condenserQC.

In this paper, the entropy balance method is used to quantify the total entropy produced by the distillation process.The entropy balance accounts for the changes of entropy production in the system which are related to the flow of heat mass across the system boundary. The entropy of the liquid and vapor flow are calculated by equations [36]:

ΔSsectionis the entropy production of column section without reboiler and condenser. ΔSsectionis calculated by the following equation:

ΔSjis the entropy production of each stage and it is calculated by:

ΔSCis the entropy production of the condenser and it is calculated by:

ΔSRis the entropy production of the reboiler and it is calculated by:

ΔScolumnis the entropy production of the entire column. ΔScolumnconsists of ΔSsection, ΔSCand ΔSR. Thus, ΔScolumncan be calculated by:

ΔStotalis the entropy production of the entire process. ΔStotalconsists of all the ΔScolumn, ΔScoolerand ΔSheaterin the process. Thus,ΔStotalcan be calculated by:

ΔScooleris the entropy production of the cooler, it is calculated by:

ΔSheateris the entropy production of the heater, it is calculated by:

Generally, TAC and ΔStotalhave different trends. Thus, in this paper, TAC and ΔStotalare introduced as two different objective functions to optimize the process.

4. Multi-objective Optimization

It is a multi-objective optimization problem to simultaneously optimize both the TAC and the entropy production of the process so that it is difficult to accomplish by Aspen Plus alone. Therefore,NSGA-II algorithm is applied to overcome this multi-objective optimization problem. This algorithm can make multiple objectives in the same process to achieve the optimum and then achieve the trade-off between multiple objectives. The optimization process can be expressed as follow:

wheref1(x,y) andf2(x,y) are the two objective functions TAC and ΔStotal.Xdenotes discrete variables whileYdenotes continuous variables.

4.1. Communication between Aspen Plus and Matlab

NSGA-II algorithm is applied in this paper by communicating Aspen Plus V11 with Matlab 2021B. The communication method between Aspen Plus and Matlab is shown in Fig. 6. For linking Aspen Plus with Matlab, a steady-state simulation in Aspen Plus firstly should be established and saved as a‘*.bkp’file,Matlab generates and sends inputs to Aspen Plus through the COM server.Aspen Plus runs the simulation and notifies Matlab of the results as soon as the simulation has been completed.Viathe COM server,Matlab collects all the outputs from Aspen Plus and performs further optimization. To avoid errors during communications, the simulation in Aspen Plus should not have any warnings or errors.

4.2. NSGA-II algorithm process

The specific steps of the optimization algorithm are shown in Fig.7.In the course of the NSGA-II algorithm,step 1 is to introduce the determined initialized populations as parent production. In step 2, a fast non-dominance sort is performed on the parent production to obtain new populations sorted by crowding distance and rank. Record the data at this point as the first production.The sorted new population obtained in step 2 is used as a mating pool to realize the crossover and mutation in step 3. The method of selection is tournament selection, the method of crossover is simulated the crossover of chromosomes in nature and analogue binary crossover operator is used in this paper.The mutation operation is polynomial mutation which simulates the genetic variation of an organ.In step 4,the results obtained in step 3 are used as offspring production and merged with the parent population. In step 5 an elite strategy is applied to the merged population to process the merged population, and the resulting new population continues to be sorted in a fast non-dominated manner, cycling until the maximum number of iterations is completed.For NSGA-II algorithm,increasing the initial population size will make the distribution of optimization results more intensive,but the corresponding calculation time will increase exponentially.

A single simulation is required for each individual of the population in each production when use NSGA-II algorithm for optimization. In this paper, the size of initial population is set as 60.

4.3. Variables bounds

During the optimization of the ED and SA-PSD process,there are six decision variables.The entrainer/solvent flow rate(E/S)is a continuous variable. The total number of stages in the first column(N1),fresh feed stage of the first column(NF1),the entrainer/solvent feed stage of the first column(NE/NS),the total number of stages in the second column (N2) and the feed stages of the second column(NF2) are the five discrete variables. The variables bounds are initially determined by the initialized population introduced in step 1 of NSGA-II algorithm and the smallest variable in the population as the lower bound and the largest variable as the upper bound.In addition, if the optimization results are found to be outside the variables bounds, we also adjust the variable bounds accordingly.The bounds of these variables are shown in Eqs. (15).

4.4. Constraints

In the optimization process, some constraints should be made when Matlab is used to call Aspen Plus data and then import the data into Aspen Plus. First, make sure that the five discrete variables must be positive integer numbers in Matlab.Then,make sure that Aspen Plus does not report an error. For example,NF1andNE/NSmust be less thanN1,NF2must be less thanN2and all above constraints should be ensure by Matlab. The product purity of cyclohexane and 2-butanol are both specified at 99.9% (mol) and this constraint is developed by the ’Design Specification’ model in Aspen Plus.

4.5. Pareto front

The NSGA-II algorithm generally has more than one noninferior solution. The objective function corresponding to the last non-inferior solutions constitutes the non-inferior optimal objective domain which is also known as the Pareto Front.In this paper,the initialized population size is set to 60,so the set of solutions on the Pareto Front is also 60.Considering the two different objective functions in the ED and SA-PSD processes, further analysis of the Pareto front is required. The objective which produces the least entropy production of the process on the front is chosen as Point A and the objective which produces the least TAC on the front is chosen as Point C.

The point consisting of the minimum TAC and entropy production of the process is the ideal point, but this point is often unreachable during the optimal process. To further provide a balance between the two objectives as the best solution, Point B which is called the Utopia Point is chosen in this paper. Point B is chosen by calculating the distance between all the points on the Pareto Front and the ideal point.

5. Process Design and Optimization

In this paper, steady simulations of the ED and SA-PSD processes are established by Aspen Plus V11. Some of the parameters of the original distillation process are designed as follows:the feed flow rate is set at 100 kmol∙h-1,containing 56%(mol)of 2-butanol and 44% (mol) of cyclohexane and that it approximates to the waste product samples from a pharmaceutical plant. In order to ensure that the low-pressure column operates at a lower pressure drop, the pressure drop across the column stage is set at 0.00027 MPa [10]. The product purity of cyclohexane and 2-butanol are both specified at 99.9% (mol).

5.1. Extractive distillation (ED)

NMP and DMAC are considered to be two close entrainers in terms of the COSMO-SAC model and the effect on the relative volatility of cyclohexane/2-butanol to separate them by ED process.Six decision variables are optimized including the total number of the stages in the extractive distillation column (EDC), the entrainer flow rate, the fresh feed stage of the EDC, the entrainer feed stage of the EDC, the total number of the stages in the ERC and the feed stage of the ERC. TAC and entropy production of the whole ED process are considered as two objectives.

5.1.1. Optimal result with NMP as entrainer

NSGA-II algorithm is used to optimize the ED process which with NMP as the entrainer. TAC and entropy production of entire ED process are set as two objectives. The variation trend of different Pareto Front solutions for the ED process with NMP as entrainer is shown in Fig. 8. It is clear that from 100th to 300th generations, the objective function of the Pareto Front of the optimization decreases so that the optimization needs to be continued.Optimization would be stopped when decision variables no longer produce any meaningful improvement and the optimization process is ought to continue until the 300th production. For the 300th production, Utopia Point B is selected to provide a balance between the two objective functions, where entropy production of entire ED process is 5.642 MJ∙h-1∙K-1and TAC is 6.153 × 105USD∙a–1.

The ED process use NMP as the entrainer under optimum operating conditions is shown in Fig. 9. In this process, there are two columns and the first column is an EDC which operates at 0.1 MPa. The second column is an entrainer recovery column(ERC) which operates at 0.012 MPa. For this optimal process, the EDC has a total of 28 stages, fresh feed enters the EDC from the 18th stage at a flow rate of 100 kmol∙h-1containing 56% (mol)2-butanol and 44%(mol)cyclohexane and the temperature of fresh feed is 30°C.The entrainer NMP is introduced to the EDC from the 5th stage at a flow rate of 34.60 kmol∙h-1.The product D1 containing 99.9%mol cyclohexane is distilled from the top of the EDC at a flow rate of 44 kmol∙h-1.W1 containing 61.7%(mol)2-butanol and 38.2%mol NMP is sent from the bottom of the EDC to the 5th stage of the ERC at a flow rate of 90.60 kmol∙h-1. The ERC has a total of 12 stages.The product D2 containing 99.9%(mol)2-butanol is distilled from the top of the ERC at a flow rate of 56.01 kmol∙h-1.W2 containing 99.9%(mol)NMP is sent from the bottom of the ERC to the cooler C1 at a flow rate of 34.60 kmol∙h-1,cooled to 70°C by C1 and then recycled to the EDC. In order to compensate for the tiny loss of the entrainer,a make-up stream of NMP is added to the system at a flow rate of 0.01 kmol∙h-1.

Fig. 10 shows the entropy production of every stage in the EDC and ERC, it is clear that the entrainer feed stage, the fresh feed stage and the bottom stage of the EDC are three stages where entropy production is more than other stages because of the mixture of entrainer and fresh feed flows with the flows inside the column.

Fig. 1. σ profiles of cyclohexane, 2-butanol and candidate entrainers.

Fig. 2. Effects of different entrainers on vapor–liquid equilibrium（VLE）of cyclohexane/2-butanol at 0.1 MPa with feed mole ratio of 0.3.

Fig. 3. σ profiles of cyclohexane, 2-butanol and candidate solvents.

Fig. 4. Effects of different entrainers on vapor–liquid equilibrium（VLE）of cyclohexane/2-butanol at 0.1 Mpa with feed mole ratio of 0.5.

Fig. 5. Configuration of the column.

Fig. 6. Block diagram showing the communication method between Aspen Plus and Matlab.

Fig. 7. The specific steps of the NSGA-II algorithm.

Fig. 8. (a) The Pareto front of different productions for the ED process with NMP as entrainer and (b) the Pareto front of 300th production of the ED process with NMP as entrainer.

Fig. 9. Optimal ED process with NMP as the entrainer.

Fig. 10. Entropy production of every stage in the EDC and ERC with NMP as the entrainer.

For this optimal process, TAC is 6.153 × 105USD∙a–1of which total operating cost (TOC) is 4.099 × 105USD∙a–1and total capital cost(TCC)is 2.054×105USD∙a–1.Entropy production of entire process consists of the entropy production of the EDC,ERC and cooler C1. According to Eq. (11), the entropy production of the column is the sum of column section, condenser and reboiler. The entropy production of the column section is the sum of the entropy produced by each stage. In this process, the entropy production of the EDC section is 1.949 MJ∙h-1∙K-1while the entropy production of the ERC section is 0.852 MJ∙h-1∙K-1. The entropy production of the EDC section is much larger than the entropy production of the ERC section due to the addition of a large amount of liquid entrainer in the EDC,which results in more heat and mass transfer of the vapor and liquid in the EDC.The entropy production of condenser is contributed by heat transfer between water and the vapor stream.In the EDC,the entropy production of the condenser is 0.767 MJ∙h-1∙K-1while in the ERC is 0.587 MJ∙h-1∙K-1. The entropy production of the reboiler is contributed by heat transfer between low pressure steam and the liquid stream. In the EDC,the entropy production of the reboiler is 0.965 MJ∙h-1∙K-1while in the ERC is 0.242 MJ∙h-1∙K-1. The entropy production of the EDC is 3.681 MJ∙h-1∙K-1while the entropy production of ERC is 1.681 MJ∙h-1∙K-1.The entropy production of the EDC is larger than that of the ERC because of the introduction of NMP in the EDC,which results in a lower thermodynamic efficiency and more irreversibility.

5.1.2. Optimal result with DMAC as entrainer

Fig.11 shows the Pareto Front solutions of different productions and the Pareto Front of 300th production for the ED process with DMAC as entrainer. As well as the process use NMP as the entrainer,when the optimization process continues to the 300th production, the decision variables no longer produce any meaningful improvement and for the 300th production, Utopia Point B is the case where the entropy production of entire process is 8.645 MJ∙h-1∙K-1and TAC is 9.884 × 105USD∙a–1.

Fig.11. (a)The Pareto Front of different productions for the ED process with DMAC as entrainer and(b)the Pareto Front of 300th production for the ED process with DMAC as entrainer.

The ED process with DMAC as the entrainer under the optimal operating conditions is shown in Fig. 12. In this process, the EDC has a total of 75 stages, the entrainer DMAC enters the EDC from the 50th stage at a flow rate of 50 kmol∙h-1. The product D1 containing 99.9% (mol) cyclohexane is distilled from the top of the EDC at a flow rate of 44 kmol∙h-1. W1 containing 52.8% (mol) 2-butanol and 47.1% (mol) DMAC is sent from the bottom of the EDC to the 6th stage of the ERC at a flow rate of 106 kmol∙h-1.The ERC has a total of 21 stages and the operating pressure is set at 0.012 MPa. The product D2 containing 99.9% (mol) 2-butanol is distilled from the top of the ERC at a flow rate of 56.031 kmol∙h-1. W2 containing 99.95% DMAC is sent from the bottom of the ERC to the cooler C1 at a flow rate of 49.97 kmol∙h-1cooled to 70°C and then recycled to the EDC.A make-up stream of DMAC is added into the system at a flow rate of 0.031 kmol∙h-1.

Fig. 12. The optimal ED process for DMAC as entrainer.

Fig. 13 is the entropy production diagram of every stage in the EDC and ERC with DMAC as the entrainer.It is clear that the entrainer feed stage, the fresh feed stage, and the bottom stage of the EDC are still three stages where entropy production is more than other stages.

Fig. 13. Entropy production of every stage in the EDC and ERC with DMAC as the entrainer.

For this optimal process, TAC is 9.884 × 105USD∙a–1of which total operating cost (TOC) is 4.077 × 105USD∙a–1and total capital cost (TCC) is 2.142 × 105USD∙a–1. Same as the ED process with NMP as the entrainer, the entropy production of the EDC section(2.92 MJ∙h-1∙K-1) is larger than that of the ERC section(0.869 MJ∙h-1∙K-1)due to the addition of the entrainer in this process. The entropy production of the condenser in the EDC is 1.85 MJ∙h-1∙K-1while the entropy production of the reboiler in the EDC is 1.41 MJ∙h-1∙K-1.And in the ERC,the entropy production of the condenser is 0.721 MJ∙h-1∙K-1while the entropy production of the reboiler is 0.703 MJ∙h-1∙K-1.Whether in the EDC or ERC,the entropy production of the condenser is larger than the entropy production of the reboiler because of the more heat transfer.According to Eq. (11), the entropy production of the EDC is 6.19 MJ∙h-1∙K-1while the entropy production of the ERC is 2.293 MJ∙h-1∙K-1.

The process parameters and corresponding objective functions for Utopia Point B with NMP and DMAC as the entrainer are listed in Table 4. It can be seen that optimal process with NMP as the entrainer results in better TAC and entropy production than the optimal process with DMAC as the entrainer.

In ED process, the EDC is divided into three sections: entrainer recovery section,rectifying section and stripping section.Entrainer recovery section refers to the stages between the entrainer feed stage and the top of the column where the component of higher relative volatility is concentrated and left as a distillate product.In general, the entrainer recovery section does not have a large number of column stages.As shown in Table 4,entrainer recovery section has 6 stages when NMP is used as the entrainer. However,the entrainer recovery section has 50 stages when DMAC is used as the entrainer and this result is not as expected.Vapor-liquid equilibrium（VLE）of NMP/DMAC and cyclohexane at atmospheric pressure is shown in Fig. 14. DMAC has tangent pinch on the pure cyclohexane end.This is why 50 stages are required for the entrainer recovery section when DMAC is used as the entrainer to obtain high purity cyclohexane. NMP is therefore the best entrainer to separate cyclohexane and 2-butanol. This result indicates that the screening of entrainers in the ED process should analyze not only the impact of the candidate entrainers on the relative volatility of components to be separated by vapor–liquid equilibrium diagrams,but also the relative volatility of entrainer and components to be separated, which has rarely been proposed in the previous studies.

Fig. 14. Vapor–liquid equilibrium (VLE) of NMP/DMAC and cyclohexane at atmospheric pressure.

5.2. Solvent-assisted pressure-swing distillation (SA-PSD)

Up to now, much of the published literature on the separation of pressure-sensitive binary azeotropes has concluded that the SA-PSD process is superior to the ED separation process in terms of energy consumption and economic cost. Thus, in this paper,SA-PSD process with IPA as solvent is designed to compare with ED processes. In this paper, the whole SA-PSD process contains two columns. The first column is a low pressure column (LPC)operating at 0.1 MPa and the second column is a high pressure column (HPC) operating at 0.7 MPa. Six decision variables are optimized in SA-PSD process including the total number of the stages in LPC,the solvent flow rate,the fresh feed stage of the LPC,the solvent feed stage of the LPC, the total number of the stages in HPC and the feed stage of the HPC. TAC and entropy production of SA-PSD process are still considered as two objectives.

5.2.1. Optimal SA-PSD process with IPA as solvent

NSGA-II algorithm is used to optimize SA-PSD process with IPA as the solvent.Fig.15 shows the variation trend of Pareto Front and Pareto Front solution of 300th production for the SA-PSD process with IPA as the solvent. Utopia Point B is the case where the entropy production of entire SA-PSD process is 12.867 MJ∙h-1∙K-1and TAC is 12.539 × 105USD∙a–1.

The flowsheet of the optimal Utopia Point B for this SA-PSD process is shown in Fig.16.In this process,LPC has a total of 35 stages,which operates at 0.1 MPa.Fresh feed enters the LPC from the 22th stage at a flow rate of 100 kmol∙h-1. The recycle stream D2 containing 58% (mol) IPA and 42% (mol) cyclohexane enters the LPC from the 10th stage at a flow rate of 92.106 kmol∙h-1. D1 containing 60.8%(mol)cyclohexane and 39.2%mol IPA is distilled from the top of the LPC at a flow rate of 136.15 kmol∙h-1. The product W1 containing 99.9% (mol) 2-butanol is separated from the bottom of the LPC at a flow rate of 56.05 kmol∙h-1. HPC has a total of 38 stages, which operates at 0.7 MPa. The flow rate of product W2 is 44.044 kmol∙h-1, which contains 99.9% (mol) cyclohexane. A makeup stream is added into the system at a flow rate of 0.094 kmol∙h-1for the trace loss of IPA.

Fig.17 shows the entropy production diagram of every stage in the LPC and HPC for the optimal SA-PSD process. It is clear that in the LPC, the entropy production is only abruptly changed at the feed stage.

For this optimal process, TAC is 12.539 × 105USD∙a–1of which 9.279 × 105USD∙a–1is TOC and 3.26 × 105USD∙a–1is TCC. The entropy production of SA-PSD process is 12.867 MJ∙h-1∙K-1. Theentropy production of the LPC section is 1.95 MJ∙h-1∙K-1. The entropy production of the condenser in the LPC is 2.084 MJ∙h-1∙K-1while the entropy production of the reboiler is 2.781 MJ∙h-1∙K-1.The entropy production of the HPC section is 1.125 MJ∙h-1∙K-1.The entropy production of the condenser in the HPC is 3.365 MJ∙h-1∙K-1while the entropy production of the reboiler is 0.651 MJ∙h-1∙K-1. According to Eq.(11), the entropy production of the LPC is 6.815 MJ∙h-1K-1while the entropy production of the HPC is 5.142 MJ∙h-1∙K-1.

5.2.2. Heat integration of SA-PSD process

There may be a suitable temperature difference between the reboiler in the LPC and the condenser in the HPC because of the significant pressure difference between two columns so that heat integration is feasible for the SA-PSD process. As shown in Fig. 16, the temperature of the condenser in the HPC is 134.28 °C and the temperature of the reboiler in the LPC is 102.02°C.Therefore, the distillate vapor stream from the HPC can be used to heat the bottom of the LPC and the reboiler’s heat duty(2174.73 kW)in the LPC is greater than the condenser’s(1223.24 kW)in HPC.Thus,the partial heat integration method which needs an auxiliary reboiler to make up the lack of heat duty is used in this paper.For simplicity,the SA-PSD process with the partial heat integration is referred to as PHI-PSD process. The same multi-objective optimization is performed at the PHI-PSD process for comparison with the SA-PSD process. During the optimization process, it is found that only 60 optimizations are needed to obtain the relatively optimal Pareto Front which is shown in the Fig. 18. Utopia Point B is the case where TAC is 8.943×105USD∙a–1and the entropy production of the process is 7.746 MJ∙h-1K-1.

Fig. 16. The optimal SA-PSD process for IPA as solvent.

Fig. 17. Entropy production diagram of every stage in the LPC and HPC.

Fig.18. The pareto front of 60th production for the partial heat integration SA-PSD process.

Fig. 19 shows the flowsheet of the optimal PHI-PSD process is shown in. For this process, LPC has a total of 33 stages while HPC has a total of 23 stages. Fresh feed enters the LPC from the 22th stage while the recycle stream D2 enters the LPC from the 10th stage. The overhead stream in HPC provides heat to bottom reboiler in the LPC with the duty of 1223.24 kW which can reduce the steam and cooling water for the two columns.An auxiliary reboiler H1 is required in the HPC with the duty of 925.77 kW to provide the remaining heat by low-pressure steam. Meanwhile, the reboiler in the HPC still use middle-pressure steam. Thus, a massive quantity of heating steam and cooling water can be saved, resulting in 38.6% reduction in TOC and 23.9% reduction in TCC compared to the SA-PSD process.

Fig. 19. The optimal PHI-PSD process for IPA as solvent.

For this optimal process, TAC is 8.943 × 105USD∙a–1of which 5.681 × 105USD∙a–1is TOC and 3.261 × 105USD∙a–1is TCC. The entropy production of PHI-PSD process is 7.746 MJ∙h-1∙K-1. The entropy produced by the column section is similar to that of SAPSD process which indicates that partial heat integration does not affect the entropy production in the column section. The entropy production of the condenser in the LPC is 2.077 MJ∙h-1∙K-1while the entropy production of the auxiliary reboiler in the LPC is 1.182 MJ h-1∙K-1.This result shows that the entropy production of the reboiler in the LPC and the condenser in the HPC is greatly reduced in the PHI-SAD process compared to the SA-PSD process.

6. Results and Discussion

During the optimization of the ED process, it has been found that the ED process with DMAC as the entrainer is inferior to the ED process with NMP as the entrainer. Thus, detailed results on the TAC and entropy production are presented to compare the ED process with NMP as the entrainer, the SA-PSD process and the PHI-PSD process in this section.

6.1. Economic evaluation

TAC, TCC and TOC of the three proposed processes is shown in Fig. 20.TAC of the PHI-SAD process is reduced by 28.7%compared to that of the SA-PSD process.This is because the partial heat integration saves a lot of heating steam and cooling water which results in lower TOC.TAC of the ED process with NMP as the entrainer is reduced by 50.9% compared to that of the SA-PSD process.The introduced entrainer for ED process has a higher boiling point than the system to be separated which means that the entrainer will not vaporize during the ED process which results in reduced TOC. The vapor flowrates at the top of the first column (EDC,LPC) are 57.3 kmol∙h-1and 173.81 kmol∙h-1for the ED process and SA-PSD process which results in lower TOC. Although most of the published literature have concluded that the SA-PSD process is superior to the ED process regarding economic cost,the optimal result is opposite. The ED process with NMP as entrainer is the most economical process for the separation of cyclohexane/2-butanol mixture.

Fig. 20. Economic comparison for TAC, TCC and TOC of the proposed processes.

6.2. Entropy production evaluation

The entropy production of the column section, reboiler, condenser and cooler of four proposed processes is shown in Fig. 21.The entropy production of the PHI-PSD process is reduced by 39.5% compared to that of the SA-PSD process. The energy consumption of the reboiler in LPC is reduced because of the use of the overhead stream in HPC to provide heat to reboiler in LPC.The entropy production of the ED process with NMP as the entrainer is reduced by 56.1% compared to SA-PSD process. This is also because the lower entropy production of reboiler and condenser.The vapor flow rates at the top of EDC is much lower than that of LPC which results in lower energy consumption which is also the reason why the entropy production of ED process is much lower than that of the SA-PSD process.

Fig. 21. Entropy production for different sections of proposed processes.

The entropy production of the ED process is the smallest among the proposed processes which means the ED process with NMP as the entrain has the highest thermodynamic efficiency and irreversibility.

7. Conclusions

In this paper, ED process, SA-PSD and PHI-PSD process are designed for the separation of cyclohexane/2-butanol insensitive azeotropic mixture. TAC and the entropy production of processes are set as two objectives to access economic and thermodynamic efficiency of proposed processes. The pressure-swing solvent IPA and the entrainers NMP and DMAC are selected and their feasibility are demonstratedviathermodynamic by σ-profiles andy-xdiagram.Based on the three selected solvent/entrainers,ED processes with different entrainers, SA-PSD process and PHI-PSD process are proposed. The proposed processes are optimized in terms of TAC and entropy production of the process by the NSGA-II algorithm.The entrainer DMAC is proved inferior to NMP which indicates that the screening of the entrainer should analyze not only the impact of the candidate entrainers on the relative volatility of the components to be separated by the vapor–liquid equilibrium diagram,but also the relative volatility of the entrainer and the components to be separated.

The optimal results showed that TAC of the PHI-SAD process is reduced by 28.7% compared to that of SA-PSD process while the entropy production is reduced by 39.5%. The ED process with NMP as the entrainer reduced the TAC and the entropy production by 50.9% and 56.1% compared with the SA-SAD process. Thus, the ED process with NMP as the entrainer has the lowest TAC and entropy production among the proposed processes, which means this process performed best in economic efficiency and thermodynamic efficiency.Therefore,the ED process with NMP as the entrainer is the best process for the separation of cyclohexane/2-butanol.

Data Availability

The data that has been used is confidential.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (22178030, 21878025, 22078026).

Supplementary Material

Supplementary material to this article can be found online at https://doi.org/10.1016/j.cjche.2023.04.017.