Separation of a two binary-azeotrope acetonitrile-cyclohexane-toluene ternary mixture via continuous triple column extractive distillation with heat integration: design, simulation, and multi-objective genetic-algorithm (MOGA) optimization

ABSTRACT Using a sustainable method for separating azeotropic mixtures, such as extractive distillation, is crucial for environmental and resource sustainability. Cyclohexane, acetonitrile, and toluene are essential solvents in different chemical processes. This ternary mixture has two binary azeotropes between cyclohexane-acetonitrile and acetonitrile-toluene at atmospheric pressures. Using residue curve maps and a uni-volatility line, n-butylbenzene was selected as a viable entrainer for extractive distillation, among other possibilities. Unlike conventional designs, the recycled entrainer was only sent to the first column in this simulation. The wasted energy from the recycled entrainer was used to supply reboilers duty through integration. A 3-D material balance was performed to understand the separation procedures better. High-purity acetonitrile, cyclohexane, and toluene will also be obtained from the first, second, and third columns. Finally, a multi-objective genetic algorithm with 14 key decision variables was utilized to reduce total annual cost (TAC) and CO2 emissions and improve thermodynamic efficiency as objective functions from economic, environmental, and energy efficiency perspectives. Optimized results reveal that a heat-integrated design reduces almost 25% TAC and 46% CO2 emissions compared to conventional extractive distillation and does not significantly affect thermodynamic efficiency. This research could be valuable for separating azeotrope systems from other ternary mixtures.


Introduction
Solvents such as Acetonitrile (ACN), Cyclohexane (CH), and Toluene (T) are frequently used in various chemical processes. [1,2]In the organic Rankine cycle systems, T and CH could be used as sustainable and clean working fluids [3] Furthermore, CH can be a suitable entrainer in various separation processes. [4,5]In the manufacture of nylon, this substance can also be used as a raw material to create cyclohexane anon, adipic acid, and ε-caprolactam [6] T is a common solvent used in chemical, pharmaceutical, dye, and other industries. [7]Toluene derivatives, including xylene, phenylcarbinol, and benzaldehyde, are commonly utilized to produce fuels and pesticides [8] ACN's utility and significance as a raw chemical ingredient and solvent are also undeniable.This substance is a medium-polarity solvent that is miscible with water and dissolves in most organics.It also has relatively low toxicity and chemical reactivity.The synthesis of peptide medicines produces vast amounts of pharmaceutical effluent, including ACN.It is also widely used as a solvent in refineries to purify butadiene. [9,10]As mentioned in previous research, T, CH, and ACN can coexist in the waste of industrial zones. [11]The coexistence of T, CH, and ACN in the pharmaceutical industry is owing to drug synthesis, purification, crystallization, formulation, and delivery systems.Additionally, the chemical manufacturing and petrochemical industries are where T, CH, and ACN can exist simultaneously as waste streams owing to the widespread application of these substances as solvents, intermediates, reaction media, and starting materials for the synthesis of diverse chemicals and polymers.Because of the high probability of this mixture's involvement in numerous sectors, separating and reusing these chemicals is both appealing and required in order to protect the environment and conserve resources for cleaner production.It is challenging to separate each component in this ternary combination as a pure one due to the presence of two binary azeotropes at atmospheric pressure (ACN/CH at 335.64 K and ACN/T at 354.37 K).Separating azeotropic mixtures has been done using a variety of methods.Pressure swing distillation (PSD), [12][13][14][15] azeotropic distillation (AD), [16] and extractive distillation (ED) [17][18][19][20] are the most common techniques.
[23][24] The ED process has been thoroughly examined in a wide range of investigations to separate binary azeotropic mixtures, including vapor-liquid equilibrium data evaluation, [25,26] entrainer selection, [27] energysaving, [28] simulation, optimization, and control of processes. [29]Yan et al. suggested employing various ionic liquids as extractants to separate ethyl acetate and methanol using extractive distillation.Based on the VLE diagram, σ-Profiles, and interaction energy, [EMIM][OAc] was selected as the most efficient entrainer.According to the results, ED with two-stage evaporators and entrainer recovery configuration, and ED with one-stage evaporator and one stripping column and entrainer recovery configuration, are capable of conserving 13.14% and 14.11% of TAC, respectively, compared to conventional ED processes. [30]In a three-column ED process, Duan et al. suggested a unique technique for energy-saving azeotropic binary systems by dividing the feed into two streams, one for the preconcentrator and the other for the extractive distillation column. [31]The performance of the control structures used in the two distillation processes was compared by Wang et al. as they explored the dynamic control of the separation of ethanol and tetrahydrofuran mixtures by ED and partly heat-integrated pressure-swing distillation.They discovered that pressure-swing distillation had high controllability and energy efficiency benefits. [32]This process has recently been extended to include separating ternary azeotropic mixtures, which has attracted interest.Although ED has wide applications in industry, the high energy consumption of this method has led to some strategies to reduce energy consumption as much as possible.Over the last few years, a variety of energy-saving scenarios, including heat-integrated distillation, [33,34] thermal coupling of columns, [35] and heat pump-assisted distillation, [28,36] have been implemented.Recently, heat integration has been employed in various processes to optimize energy usage and cut down operating expenses.This technique involves the integration of heat flows within a process to identify opportunities for heat recovery and reuse, thereby reducing the necessity for external energy sources. [37,38]Han et al. investigated the feasibility of an eco-friendly deep eutectic entrainer for ED, using the COSMO-SAC model and residue curve maps for acetonitrile dehydration.The economic benefits of using this particular entrainer are demonstrated by the study, which found a further reduction in TAC by 3.14% when heat from the hot recycled entrainer stream was used to increase fresh feed temperature during heat integration. [39]urthermore, it is well recognized that entrainer selection significantly impacts energy consumption.Zhao et al. conducted a comparison between two thermally coupled ternary extractive distillation processes for the separation of the ternary azeotropic mixture of tetrahydrofuran/ethanol/ water.They investigated the use of a single-component entrainer (dimethyl sulfoxide) and a mixed entrainer (dimethyl sulfoxide and ethylene glycol).The findings reveal that employing the mixed entrainer can lead to decreased energy consumption and total annual cost in the process. [35]Xu et al. introduced an innovative heuristic predictive model that utilizes TAC and life cycle assessment (LCA) indexes to qualitatively evaluate entrainers in the extractive distillation process.This approach identifies entrainers with superior economic and environmentally sustainable performance by avoiding the formation of new azeotropic or near boiling point systems between the entrainer and heavy components. [40]Aside from these, a variety of optimization algorithms can be used to determine the optimum value of some key parameters to reduce energy consumption as much as feasible.Sensitivity analysis, [41,42] annealing algorithm, [43] sequential iteration optimization method, [44] genetic algorithm, [45][46][47][48] and response surface methodology [49] are examples of the most usable optimization algorithms that researchers employed.To provide a more comprehensive explanation of the efforts undertaken to address the issue of high energy consumption in the ED process, it is pertinent to highlight the following works.Yang et al. utilized a triple-column extractive distillation (ED) technique, both direct and indirect, to separate tetrahydrofuran/ethylacetate/water and they also used computer-aided molecular design to uncover potential entrainers.Based on the results, the indirect separation process with heat integration emerges as the most economically feasible approach. [50]In a separate study conducted by Yang et al., the ternary azeotropic mixture comprising tetrahydrofuran, ethanol, and methanol was successfully separated using direct and indirect ED techniques.To identify suitable entrainers for the separation process based on their volatility line, chlorobenzene and DMSO were screened.By employing the multi-objective particle swarm optimization technique, direct ED sequences are favored over indirect ones due to their ability to minimize TAC, CO 2 emissions, and inherent safety while increasing energy efficiency. [51]Ionic liquids were employed by Li et al. in another study to separate azeotropic mixtures in an eco-friendly manner.
The design and control of the ED process were integrated using a multi-objective NSGA-II optimization technique based on trade-offs between controllability and cost. [52]enzene/isopropanol (IPA)/water ternary combinations were split using single and double reactive ED procedures by Yan et al.Furthermore, the process was optimized with MOGA and TAC, CO 2 emissions, extraction efficiency, and thermodynamic efficiency considered as objective functions.TAC and CO 2 emissions were significantly decreased when compared to conventional triple column extractive distillation (TCED). [53]espite the various research studies outlined, to our knowledge, the separation of ACN/CH/T has been rarely reported and has not yet been process-simulated and evaluated.This work aims to explore the ED process's feasibility of separating complex T, CH, and ACN ternary mixtures using an appropriate entrainer.It belongs to class 2.0 − 2b of Serafimov's topological classes from 26 classes of plausible topological structures for VLE diagrams for ternary mixtures. [54,55]ASPEN Plus V.11 was used to carry out the simulation using the NRTL fluid package.As an energy-saving scenario, heat integration was applied to the process.Finally, the multi-objective genetic algorithm (MOGA) was utilized to find the optimum ED process for a more cost-effective and green strategy to minimize TAC and CO 2 emissions and maximize thermodynamic efficiency by determining design parameters.

Simulation procedure
Fig. 1 illustrates a ternary ACN/CH/T mixture with two binary azeotropes (ACN/CH and ACN/T).Selecting the appropriate entrainer is critical when using the extractive distillation technique to separate azeotropic mixtures. [56]To begin, three relevant entrainers are evaluated for their potential to break the azeotrope.The best one is chosen based on thermodynamic considerations (Section 2-2 contains information about entrainer selection).The process will then be simulated using 3D material balance lines in Aspen Plus V.11, and finally, it will be optimized using a genetic algorithm.Various thermodynamic models such as WILSON, UNIQUAC, and NRTL have been examined using equilibrium data. [11,57,58]The values of root mean square error deviation (RMSD) and average absolute deviation (AAD), shown in Table S1 of the supporting information, are inversely proportional to the correlated model; a better model has lower RMSD and AAD values.It has been determined that the NRTL thermodynamic model can better describe the current system than the others.Therefore, the NRTL model was utilized as an appropriate fluid package in the existing ED process.Table S2 lists the binary interaction parameters of the models for the ACN, CH, and T systems.

Thermodynamic insights via RCMs and entrainer screening
Selecting the most appropriate entrainer is vital for lowering energy consumption rates and changing the product specifications of the ED system. [59]An appropriate entrainer should have some superior properties to break azeotropes efficiently.Apart from being nontoxic and affordable, it should have the ability to enhance the relative volatility of azeotropes.It must also have a high boiling point compared to the feed components, behave as a stable node in the ternary diagram, and not produce any additional azeotrope when mixed with the feed components. [54,60]he uni-volatility line, which is drawn from points with relative volatility equal to 1, can aid in the identification of suitable and cost-effective entrainers. [29]The point where the uni-volatility line intersects the entrainer-feed component line in Fig. S1 is designated as x p .A low x p value suggests a more effective and costeffective entrainer.According to Fig. S1, when applying entrainers, the uni-volatility curve approaches point x p on the border of A-E.As a result, component A can be eliminated from the distillate because it is more volatile than component B in the ABE region.The evaluation of x p "s location provides an initial estimate for the entrainers" separation performance in ED.When the entrainer's flow rate reaches the minimal requirement, the A-B azeotropic mixture can be broken, and the desired product A can be achieved. [61]Detailed explanations can be found in. [22,38,48,49]aterial balance is also an essential concept in the conceptual design of the ED process, as it aids in simulating the process. [61]There are two significant rules to remember when drawing material balance lines.The distillate, feed, and bottom compositions should initially be in a straight line.The second rule is about residue curves.As expected, distillate and bottom composition should always be on the same residue curve.RCMs can't cross each other, and they always move toward rising temperatures along the boiling temperature surface. [62]

Triple-column extractive distillation for separation of ACN/CH/T
In a ternary system with two azeotropes, there are two possible scenarios.In the first scenario, two extractive columns are usually required to break azeotropes and one regeneration column to recycle the entrainer.However, if there is one entrainer that can cause the two binary azeotropes to break and the separated component in the first column was the common component that caused the two binary azeotropes, then one entrainer stream is sufficient to separate the ternary mixture in one extractive distillation column.In the second one, the first, second, and third columns are extractive distillation (EDC), conventional distillation (CDC), and regeneration columns (RC), respectively.However, only the first column serves as extractive distillation. [63,64]The current technique has the requisite requirements for using one extractive distillation tower for breaking azeotropes based on the entrainers utilized and the chemical and thermodynamic characteristics of the input feed.Previous studies have been conducted to demonstrate the economic advantage of the second scenario (single entrainer TCED) compared to the first scenario (double entrainer TCED).In the context of N-hexane/acetone/chloroform separation with DMSO as the entrainer, Guo et al. [65] and Wang et al. [66] determined that the single entrainer TCED configuration is a superior process in terms of control and economics when compared to their respective double entrainer TCED configurations.This superiority arises from the absence of a second entrainer stream, leading to a notable decrease in the cost associated with recovering the entrainer.Additionally, the absence of the second entrainer stream results in an increase in the flow rate of the entrainer introduced into the first distillation column.This, in turn, leads to a further decrease in the economic cost associated with the first distillation column for single entrainer TCED processes.In the case of the ternary azeotrope consisting of acetonitrile, methanol, and benzene, Wang et al. [67] proposed an extractive dividing-wall column as well as conventional triple-column extractive distillation (TCED) processes with double entrainer and single entrainer configurations.A comparison was conducted to evaluate their economic efficiency.The results revealed that the single entrainer TCED scheme outperformed the other alternatives in terms of economic viability.Yang et al. [50] reported that the single entrainer TCED process with heat integration is the best option for the extractive distillation separation of THF/EtAC/ water in terms of economic performance.This configuration achieves high THF purity at a low operating cost.The heat integration further improves the efficiency of the single entrainer TCED process, making it more preferable than the double entrainer TCED process for this separation task.As a result, taking into account economic, environmental, and energy efficiency considerations, the mentioned approach demonstrates reduced energy consumption and a lower TAC; therefore, the utilization of the second scenario in the ongoing simulation is favorable.It should be noted that this decision involves multiple factors, including the capital investment required for equipment and operational costs such as entrainer usage, entrainer recovery, and energy consumption.
The material data in Fig. 2a was acquired by simulating the process, utilizing an NBB entrainer, and conducting multi-objective optimization through a genetic algorithm.The extractive distillation process involved feeding an azeotropic fresh feed consisting of 30% ACN, 30% CH, and 40% T with a flow rate of 100 kmol/h along with an entrainer (shown in Fig. 2a).High-purity ACN was obtained as the top product.The bottom products from the EDC column (CH, T, and entrainer) and CDC column (T and entrainer) were further processed in the CDC and RC columns, respectively, to obtain pure CH and T products.A third column was utilized to separate T from the entrainer, which was then recovered after cooling for recycling back into the first column.To maintain a consistent entrainer-to-feed ratio, an entrainer make-up stream was introduced using a calculator block.Following the completion of the simulation, an optimization process was carried out using the MOGA optimization method by linking MATLAB and Aspen Plus software to optimize seven discrete decision variables and seven continuous decision variables.The objective was to minimize the total annual cost (TAC) and CO 2 emissions while simultaneously maximizing efficiency (η).The final data are shown in Fig. 2a.Similarly, a comparable methodology was employed for Fig. 2b, albeit with the distinction that the optimization focused on the heat-integrated process (the application of this heat integration approach showcases the potential to leverage the thermal energy contained in stream B3 for diverse purposes, such as steam generation or heat exchange operations), and all extra energy costs at the heat-integrated process were removed from the objective function.In this case, due to the fact that the energy extracted from the cooler was used as the energy supplier of the reboilers, by considering total annual cost (TAC), CO 2 emissions, and thermodynamic efficiency (η) as our objective functions, the results of the optimization of this process led to a change in the data of this simulation.Fig. 2b illustrates the final material data.Despite being a leading technique in the chemical industry, distillation is a relatively energy-intensive process.According to the process flow diagram (Fig. 2b), the extractive distillation process with heat integration (HI-ED) is surveyed to reduce energy consumption further.Herein, the heat of the cooler (shown in red) was used to provide column duty.

Total annual cost
In recent years, TAC as an objective function, a suitable criterion for optimizing various processes from an economic point of view, has been exploited as follows. [68]apital costs include the reboiler, condenser, heat exchanger, column trays, and shells.In addition, pipe, valves, and pump costs are ignored due to their low cost compared to other equipment.Furthermore, operating costs include the expense of cooling water and steam.[71] All the needed equations for calculating economic parameters are listed in Table S3.

Thermodynamic efficiency
The thermodynamic efficiency index (η), which is expressed by Equation ( 2), [72] can be efficient in increasing process efficiency.
W min shows the minimum separation work, and LW is the system's lost work as determined by Equations ( 3) and ( 4). [51]ere T 0 is the ambient temperature, ΔH and ΔS are the enthalpy change and the entropy change of the system, respectively.Q R and Q C are the reboiler and condenser heat loads, while T R and T C are the temperatures of the reboiler and condenser, respectively.

CO 2 emissions
Atmospheric carbon dioxide has risen in recent years due to the widespread usage of fossil fuels, with the most severe concern being greenhouse effects, which contribute to global warming. [73]The chemical industry finds extractive distillation to be a valuable separation technique, but it may also have a detrimental effect on the environment, especially when it comes to the release of greenhouse gases like carbon dioxide.The energyintensive feature of extractive distillation is mostly due to the necessity to heat the mixture to boiling point, the use of an entrainer, and its separation.As a result, reducing CO 2 emissions has become a top priority.Equation ( 5) is used to calculate the amount of CO 2 emissions. [74,75]ere α indicates the ratio of the molecular weight of carbon dioxide to carbon (α = 3.67), and NHV denotes the net heat value (NHV = 51600 kJ/kg) using natural gas as a heat source.C% shows the amount of carbon in the fuel (C% = 75.4),and Q fuel (kW) is the amount of heat generated by the combustion of fuel according to the following Equation ( 6). [22]ere λ seq and h seq are the latent heat and the enthalpy of steam transferred to the system, respectively.T FTB ( = 2073.15K) and T stack ( = 453.15K) are flame and stack temperatures, respectively.Process energy consumption is expressed as Q seq .

Constraints
The desired product purities utilized as constraints in the MOGA are specified in Equations ( 7)- (10).
The present simulation was optimized from multiple perspectives via multi-objective optimization.To optimize the suggested process, a stochastic based multiobjective genetic algorithm as a meta-heuristics method is used to identify design operating parameters that may meet all of the constraints and give a quantifiable tradeoff between thermodynamic efficiency (η), TAC, and CO 2 emissions.Classical optimization methods won't guarantee that our solution moves beyond a local optimum to a global optimum.As a result, we use a genetic algorithm to streamline the procedure.Genetic algorithms include (i) creating a random population; (ii) selecting and combining parents to create a population of children; (iii) choosing members of the population to mutate and create a population of mutants; and (iv) combining the original population, children, and mutants to form a new main population. [76]Finally, a set of Pareto-Fronts will be generated, which move along the optimum solutions.Fig. 3 reveals the MOGA optimization procedure for the current process.In this work, we paired a MOGA [77,78] with Aspen Plus software and optimized seven discrete decision variables and seven continuous decision variables.The number of trays in each column (N 1 , N 2 , and N 3 ), the feed stage in each column (NF 1 , NF 2 , and NF 3 ), and the input entrainer tray in the first column (NENT) are all discrete decision variables.Continuous decision variables include the reflux ratio of each column (RR 1 , RR 2 , and RR 3 ), the first and second column's distillate rates (D 1 , D 2 ), the bottom rate of the third column (B 3 ), and the amount of entrainer entry rate into the first column (FENT).The objective functions chosen in this regard are thermodynamic efficiency (η), TAC, and CO 2 emissions; the first should be maximized, while the next two should be minimized, respectively.Additionally, each material's purity is set as a constraint.Table 1 lists all variables and their appropriate bounds based on the sensitivity analysis.

Thermodynamic analysis
Identifying an appropriate entrainer is a crucial step in the ED process.Several potential entrainers were examined to find a feasible one.Many entrainers that had the characteristics mentioned in Section 2-1, however, were discarded owing to the unavailability of binary interaction parameters in the original ternary mixture, the formation of new azeotropes with the initial ternary system, not meeting the requirements of the second scenario, and the inability to eradicate all of the system's azeotropes in the first column.The candidate entrainers in this research  were n-propyl benzene (NPB), n-Butylbenzene (NBB), and 1,3,5-trimethylbenzene (TMB), which are also frequently used as solvents in industry. [79,80]The entrainers used in the process are recycled and never released into the environment.The process of selecting the entrainer involved an initial investigation into the impact of different entrainers on the VLE diagram, specifically examining their deviation from the diagonal.This was followed by utilizing residue curve maps and a uni-volatility line to identify an economically viable entrainer that met the necessary thermodynamic criteria for extractive distillation.Ultimately, by using the best entrainer, a conceptual process design was developed by integrating residue curve maps with three-dimensional material balance lines, enabling the determination of feasible regions and aiding in simulating the process.As shown in Fig. S2, NPB (blue), compared to the other two entrainers, has a low deviation from the diagonal on the VLE of ACN-CH and ACN-T. [81]So, in the following, we will compare the two remaining entrainers.
Fig. 4 shows uni-volatility lines of ACN/CH and ACN/T with TMB and NBB entrainers.It is observed that the azeotropic points of ACN-CH and ACN-T are unstable nodes, while the components TMB and NBB are stable points, and ACN, CH, and T are saddles.
The minimum entrainer required to separate the ACN-CH and ACN-T azeotropes is shown by the univolatility line (α AB = 1) intersecting x p point (as shown in Fig. S1) on the ACN-entrainer side.The value of x p to break the ACN-CH azeotrope is 0.62 for TMB and 0.58 for NBB, as presented in Fig. 4a-b.Also, for the ACN-T azeotrope (Fig. 4c-d), the value of x p is 0.09 and 0.05 for TMB and NBB, respectively.Consequently, NBB may require the minimum entrainer to break the ACN-CH and ACN-T azeotropes and be chosen as the best entrainer among other possibilities.
Based on the notes in Section 2, the reason for breaking two azeotropes in the first column is stated.According to Fig. 4b (CH ACN NBB) and (ACN CH NBB) as lower and upper regions, respectively.Also, CH is more volatile than ACN, but ACN will separate from the top of the column.Because in the (CH ACN NBB) region, no residue curve can get CH, while the existence of a residue curve in the (ACN CH NBB) region that connects to ACN is undeniable.Therefore, by considering the ACN-CH azeotrope, ACN will exit from the top.
On the other hand, about the ACN-T azeotrope, the same argument holds, and again, ACN is the only possible component that exits from the distillate stream (Fig. 4d).So, suppose the above condition happens in the case of the existing two binary azeotropes.In that case, we expect azeotrope to disappear in the first column, and other columns will serve as a common distillation column.As a result, this can significantly reduce investment and current costs.
To illustrate that NBB may be a suitable entrainer for separating the azeotropic system and offering a reasonable entrainer flowrate optimization range, pseudo-vapor-liquid equilibrium diagrams with varied entrainer-to-feed mole ratios (E/F) are demonstrated.The influence of the entrainer (NBB) on the vaporliquid equilibrium phase performances of two binary azeotropes, ACN/CH and ACN/T, is displayed in Fig. S3.As can be seen, the approximate entrainer-tofeed ratio required to avoid azeotrope is around 3 (blue line in Fig. S3).
Figure 5 depicts the novel 3D material balance with RCMs, which aids in a better understanding of the separation steps.Due to the existence of four components, a 3D triangular pyramid-like scheme is required for demonstrating the separation sequence inside the residue curve map when the entrainer is introduced to the ternary mixture, as opposed to the conventional 2D strategies used in prior research. [13,17,82]Following the selection of the best entrainer using a comparison of isovolatility and uni-volatility lines, the residue curve map in Fig. 1 was modified into a 3D map and can be used to illustrate the overall mass-balance lines for the entire separation process.Moreover, the aforementioned figure demonstrates the manner in which the entrainer separates the azeotrope and how pure components are extracted from columns.As can be seen, azeotropic feed and entrainer go into the first column, and M1 is their product point in terms of overall feed composition, according to the lever rule. [51]M 1 is then separated into two streams: D 1 (pure ACN) and B 1 (mainly CH, T, and NBB), both of which have the same straight line and residue curve.The bottom product of the first column is divided into D 2 (pure CH) and B 2 (mainly T and NBB) in the second column.Finally, B 2 is put into the third column to achieve D 3 (pure T) and B 3 (pure NBB) from the top and bottom.

Optimization
The optimization process was performed to minimize TAC and CO 2 emissions and maximize η by the MOGA optimization algorithm in a PC with an Intel® Core™ i7-HQ intel® CPU @ 2.60 GHz, 16 G RAM.The population was set at 300, with crossover and mutation percentages of 80 and 20%, respectively.
To incorporate the thermal aspects of the process, the optimization of the process was initially performed using MOGA.Subsequently, the energy output of the cooler employed to cool the recycle stream, along with the energy needed for the distillation columns' boilers, was determined.Upon comparison of these values, it was discovered that the cooler energy output was found to be inadequate for meeting the required boiler energy of the columns.To rectify this issue, an additional 1.53 MW was incorporated into the required boiler energy based on the disparity between the total required energy and the cooler energy output.The result of the heatintegrated process after optimization shows a significant change in TAC and CO 2 emissions.The utilization of this heat integration approach demonstrates the potential for harnessing the heat energy present in stream B3 for various applications, including steam generation or heat exchange processes.The concept of heat integration with steam generation entails harnessing the residual heat produced by diverse processes to generate steam, which can serve multiple purposes, including power generation, heating, or other industrial applications.The fundamental concept revolves around the extraction of thermal energy from waste streams and its transfer to a working fluid, typically water, in order to generate steam.Through the integration of steam generation with heat recovery, it becomes possible to optimize the utilization of waste heat and decrease the overall energy consumption associated with a plant or system.This method improves energy efficiency, decreases greenhouse gas emissions, and has the potential to generate substantial cost savings through reduced fuel consumption.Furthermore, further investigation of similar approaches conducted by other researchers reveals evidence supporting the utilization of cooler energy as an energy source for the reboiler. [23,83,84]ig. 6 displays the 3D and 2D Pareto fronts obtained after 72 hours of a multi-objective genetic optimization.After three days, there is no new Pareto front with a better solution.According to Fig. 6(b-d), optimum TAC, CO 2 emission, and thermodynamic efficiency are in the range of 1.64-1.82(10 6 $/year), 0.280-0.325(kg/s), and 4.85-5.1%,respectively.It shows that, in the optimum condition, TAC, CO 2 emissions, and thermodynamic efficiency have satisfactory values.Figures S4-S6 show the relationship between the number of stages in each column and the maximum number of solutions found from optimization.Most solutions can be found in 55-57 stages for column 1, 43-50 stages for column 2, and 48-49 stages for column 3, as can be noticed.It shows that those stages are optimum numbers that satisfy our objective functions.So, it's a significant achievement that we can predict the optimum range of stage numbers by simultaneously considering TAC, CO 2 emission, and thermodynamic efficiency, thanks to multi-objective genetic optimization.Since the TAC rises with the increasing number of stages, there are rarely solutions in the upper number of stages.Similarly, the concentration profiles in the column cannot reach the feasibility region imposed by the purity constraints.
The optimal solutions are found in the 2.858-2.866(~3) entrainer-to-feed ratio, according to the results a b c d shown in Fig. S7.Since azeotrope disappears at the E/F of about 3, confirming Fig. S3.The liquid composition and temperature profiles of the three columns at minimum TAC optimum conditions are illustrated in Fig. S8.The azeotrope breaking causes a significant increase in the composition of ACN from the eighth stage to the first stage, and high purity ACN with 99.2 mol% is eventually attained at the first stage (Fig. S8-a).After azeotrope breaking, the CH composition increases from the twentieth to the first stage at the second column, and the first stage is where high purity CH with 99.9 mol% is finally achieved (Fig. S8-b).Similarly, at the first and last stages of the third column, high purity T and high purity entrainer (NBB) were gained, respectively (Fig. S8c).The mole fraction profiles in columns are visualized in Fig. 7.All the parameters in this figure are based on the minimum TAC at the optimized condition.Only the number of stages changes in each scheme to understand the effect of the number of stages on the product mole fraction.The mole fraction of ACN and CH in Fig. 7a reaches 0.99 purity in a sharp movement from stage 54 upwards, suggesting the breakage of azeotropes ACN and CH in the first tower in this number of stages and above.The third component (T) is unaffected by changing the number of stages in the first column.The same happens for CH and T in the second column in Fig. 7b from stage 40 upward, which naturally increases or decreases the number of stages that will not affect ACN.Finally, the number of stages does not affect the purity of T in the third column (Fig. 7c).
Figure 8 depicts the required entrainer flow to achieve higher purity.This figure is also obtained at minimum TAC optimum conditions at different entrainer flow rates.This demonstrates the optimal purity for all three components in the entrainer flow is around 280 (kmol/h).After raising the entrainer flow from the optimal state, the T purity decreased due to the high entrainer to T ratio and the third column's inability to separate this component (which dilutes the T in D 3 ).
Table 2 gives the Pareto-front results for the minimal TAC, minimum CO 2 emission, and highest thermodynamic efficiency as solution 1, solution 2, and solution 3. Results show that the HI-ED design reduces TAC (25%) and CO 2 emissions (46%) compared to conventional ED and does not significantly affect thermodynamic efficiency.The optimization algorithm was run three times to ensure the accuracy of the results.Due to the inherent feature of the genetic algorithm that it doesn't get stuck in local optimum points, similar results were obtained.Also, the process is evaluated from an environmental standpoint by measuring CO 2 emissions.Assuming that the heating requirements were satisfied by natural gas (the CO 2 emissions factor from US-EPA-Rule-E9-5711 is 5.589 × 10 −8 kg/J [85] ), the CO 2 emissions for ED and HI-ED were 0.252 and 0.135 kg CO 2 /kg feed, respectively.Apart from optimization of operating parameters, combining extractive distillation with heat pumps or ionic liquids, introducing side-strippers, applying full heat integration, employing hybrid processes such as pressure swing distillation or extractive dividing-wall columns, and using reactive extractive distillation will further improve the thermodynamic efficiency of the system while reducing exergy loss. [12,45,47,53]Comparing the obtained values with literature to confirm the TAC, CO 2 emission (based on natural gas), and thermodynamic efficiency value interval for the ternary-mixtures ED process ensures that the values are within an acceptable range. [45,61,64,86]][89] The drawbacks of this technology are time consumption, variable product quality, limited scalability, suitability for low-volume items, and inefficiency because the equipment needs to be cleaned and reloaded between batches.The efficiency of the doublecolumn batch distillation process was determined using the TAC, recovery ratio, batch time, and environmental evaluation.The findings indicate a minimum TAC of 460,563 $/year, a total batch time of 24.5 hours, a recovery rate of more than 94%, and 8613.91 kg of CO 2 equivalent global warming potential for a capacity of 7200 kg in optimum conditions. [11]

Conclusion
In this work, the extractive distillation process was simulated and designed to separate the cyclohexane, acetonitrile, and toluene ternary mixture with two binary azeotropes.n-butylbenzene was chosen as the suitable and feasible entrainer from the thermodynamic viewpoint (residue curve maps and uni-volatility line) for this process.The entrainer-to-feed ratio is an essential variable for obtaining high-purity components in the outlet streams.In the current process, the approximate ratio required to avoid azeotrope was around 3, confirmed by both the VLE diagram and optimization result.The conceptual design of the process was developed by a combination of  residue curve maps and material balance lines to determine feasible regions and sequences.From the viewpoints of the economy, the environment, and energy efficiency, a MOGA with 14 main decision factors was applied to the ED process to minimize total annual cost (TAC) and CO 2 emission and improve thermodynamic efficiency as objective functions.Heat integration was achieved by heat from the recycle stream.Besides, the optimization algorithm was utilized to make the ED and HI-ED processes as efficient as possible.Compared to conventional ED, optimized results show that the HI-ED design reduces TAC by nearly 25% (1644910 $/year) and CO 2 emissions by 46% (0.2802 kg/s) while having no considerable effect on the thermodynamic efficiency (5.09%).Eventually, from an environmental perspective, it was established that the CO 2 emissions for ED and HI-ED under optimum conditions were 0.252 and 0.135 kg CO 2 /kg feed, respectively.Overall, the proposed heat-integrated process separates the azeotropic mixture ACN/CH/T cost-effectively and environmentally sustainable.It's worth noting that the proposed simulation and multi-objective optimization method could be valuable for resource recovery from other complex azeotropic ternary mixtures in the future.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Figure 1 .
Figure 1.The ternary diagram of the ACN/CH/T system at 1 atm for class 2.0−2b to Serafimov's 26 topological classes.

Figure 2 .
Figure 2. Process flow diagram of a) conventional triple-column extractive distillation and b) heat integrated triple-column extractive distillation for separation of ACN/CH/T (all the concentrations are based on mole fraction).

Figure 3 .
Figure 3.The MOGA optimization procedure for the ED process.

Figure 4 .
Fig.4shows uni-volatility lines of ACN/CH and ACN/T with TMB and NBB entrainers.It is observed that the azeotropic points of ACN-CH and ACN-T are unstable nodes, while the components TMB and NBB are stable points, and ACN, CH, and T are saddles.The minimum entrainer required to separate the ACN-CH and ACN-T azeotropes is shown by the univolatility line (α AB = 1) intersecting x p point (as shown in Fig.S1) on the ACN-entrainer side.The value of x p to break the ACN-CH azeotrope is 0.62 for TMB and 0.58 for NBB, as presented in Fig.4a-b.Also, for the ACN-T azeotrope (Fig.4c-d), the value of x p is 0.09 and 0.05 for TMB and NBB, respectively.Consequently, NBB may require the minimum entrainer to break the ACN-CH and ACN-T azeotropes and be chosen as the best entrainer among other possibilities.Based on the notes in Section 2, the reason for breaking two azeotropes in the first column is stated.According to Fig.4b, the uni-volatility line (α = 1) divides the triangular diagram into two regions called

Figure 6 .
Figure 6.Effect of parameters on the a)TAC, CO 2 emission, and thermodynamic efficiency in the 3D, b) TAC and CO 2 emission, c) CO 2 emission and thermodynamic, d) TAC and thermodynamic Pareto front.

Figure 7 .
Figure 7. Effect of number of the stage on mole fraction profile a) N 1 , b) N 2 , c) N 3 .

Figure 8 .
Figure 8.Effect of entrainer flowrate on the components mole fraction.

Table 1 .
The lower and upper bounds of key decision variables.

Table 2 .
Design parameters and objective functions for ED and HI-ED processes.