Optimization of Solvent and Extractive Distillation Sequence Considering Its Integration with Reactor

: AbstractThe integration of reaction and extractive distillation system is beneﬁcial for reducing the process cost. A systematic method is proposed to identify the optimal solvent, solvent-to-feed ratio, extractive distillation sequence and reactor operating conditions based on the integration of reactor and extractive distillation. The non-key component matrix method is used to generate the extractive distillation sequences. The proposed method can be used to evaluate different solvents, solvent-to-feed ratios, as well as the extractive distillation sequences; the optimal extractive distillation parameters corresponding to the minimum total annualized cost (TAC) can be identiﬁed considering different operating conditions. For the selective hydrogenation of benzene to cyclohexene process, the minimum total annualized cost of unit desired product, 4.01 $ · kmol − 1 , is achieved when the reactor’s inlet temperature is 333 K, solvent N -Formylmorpholine and sequence S2 are employed, and the solvent-to-feed ratio is 4.


Introduction
Extractive distillation can be applied to separate mixtures that are difficult to separate by common distillation. Different solvents can be used to increase components' relative volatility to different levels, and multiple distillation sequences can be used to achieve the separation. A solvent can make separation easier, while its application might lead to an undesired growth of the heat load of the distillation columns. Different solvent-to-feed ratios lead to varied energy consumption. In view of these characteristics, it is important to select the optimal extractive solvent, solvent-to-feed ratio and distillation sequence.
In chemical process, the mixture to be separated is generally the reactor's effluent or part of it, which changes along reactor operating conditions. Because of this, the total annualized cost (TAC) of the reactor and that of the extractive distillation system changes as well. The identification of optimal extractive solvent, solvent-to-feed ratio and distillation sequence should be based on the integration and optimization of the reactor and the extractive distillation system.
Research on extraction distillation mainly focuses on the choice of solvent and its flowrate. De Figueiredo et al. evaluated the effect of solvent on the separation efficiency and energy consumption [1]. Zhao et al. identified the optimal composition of mixed solvent for a tetrahydrofuran-ethanol-water ternary system [2]. Zhang et al. proposed a method for identifying the optimal solvent on the basis of isovolatility curves [3]. Based on vaporliquid equilibrium diagrams and infinite dilution factors, Wang et al. selected the feasible solvent to separate the specified mixture and targeted the optimal distillation sequence with minimum TAC [4]. In view of controllability and economy, Wang et al. simulated two possible extractive distillation sequences for separating toluene-methanol-water ternary azeotropic mixture to identify suitable flowrate of solvent [5]. Woo and Kim presented a new procedure to search for new solvent using molecular simulation, and evaluated the procedure's performance using highly energy-intensive processes [6]. A multi-objective Table 1. Five distillation sequences separating four-component mixture.
According to the non-key component matrix and the method proposed by Yin and Liu [22], the matrix representing all distillation sequences can be generated, as shown by Equation (2). In this matrix, rows and columns correspond to distillation sequences and splits, respectively, and each element represents a split point.

Calculation of Relative Volatility
The relative volatility between components A i and A j is the ratio of their gas-liquid equilibrium constant, as shown in Equation (3). Under atmospheric or low pressure, the gas can be considered as ideal mixture, and the liquid can be taken as non-ideal, the gas-liquid equilibrium constant can be calculated by Equation (4).
Substituting Equation (4) into Equation (3), Equation (5) is obtained to calculate the relative volatility between components A i and A j after the addition of the solvent, α ij S .
Processes 2021, 9, 565 4 of 17 where K i is the gas-liquid equilibrium constant of component A i ; P denotes pressure. For components A i and A j , γ i and γ j are their activity coefficients and can be calculated by modified UNIFAC model [23]; P i S and P j S are their saturated vapor pressures and can be calculated by Equation (6).
where A i , B i , C i , D i and E i are Antoine constants, and T is temperature.

Shortcut Design of Distillation Column
For extractive distillation column, the mixture to be separated and the solvent are inlet separately, and the latter is added to the upper part of the feed stage. The Fenske equation [24], Underwood equations [25] and Gilliland correlation [26,27] can be used to calculate the plate number and reflux ratio of each column, and these equations are shown in Equations (7)- (10).
Herein, N min is the minimum number of theoretical plates; ξ lk represents the recovery of light key component at the top, and ξ hk represents that of heavy key component at the bottom; α avg S is the average relative volatility of the light-to-heavy key component, and can be calculated by Equation (11); (α D ) S , (α F ) S and (α B ) S are the relative volatility at the top, feed and bottom. R min is the minimum reflux ratio; (α i ) S is the relative volatility of A i to the heaviest component at the average temperature of column; x F(i) and x D(i) are the mole fraction of A i in feed stream and distillate; θ is the root of Underwood equations. q represents the feed thermal state. N T denotes the number of theoretical plates. R is the reflux ratio and R = 1.1 ∼ 2R min .
The position of the feed stage can be estimated by Equation (12) and the Kirkbride equation [28], as shown by Equation (13). (13) where N D and N B are the numbers of theoretical plates above and below the feed, B is the flowrate at the bottom and D at the top. x is the mole fraction, subscripts F, D and B represent the flowrates of the feed, top and bottom products, respectively; subscripts lk and hk represent the light and heavy key components.

Generation of Extractive Distillation Sequence
When solvents are added, extractive distillation columns and solvent recovery columns should be added in each distillation sequence, and the latter usually follows the former. According to this, the extractive distillation sequences can be generated in two steps. In the first step, the separation order of the components (excluding solvent) is generated based on the non-key component matrix introduced in Section 2.1. In the second step, the solvent is added to the column separating the components with smaller relative volatilities, and this column changes to an extractive distillation column; the solvent recovery column is added following this column. The specific steps are as follows: (1) Generate non-key component matrix according to the components to be separated, and identify the separation order; (2) Identify the extractive distillation columns in each sequence, and add the solvent to the column; accompany a solvent recovery column after each extractive distillation column.
The separation of the three-component mixture is taken as an illustrative example. For each pair of components in this mixture, the relative volatility is quite small, and the addition of a solvent is necessary. With a solvent added, the volatility order of these components might be In the first step, the non-key component matrix is identified, as shown by Equation (14).
The mixture needs two extractive distillation columns to separate them, i.e., solvents should be added in each column to form extractive distillation. Finally, two extractive distillation sequences are generated, as shown in Figure 1. In Sequence 1, A 1 is separated first, and then A 2 and A 3 , while in Sequence 2, A 3 is separated first, and then A 1 and A 2 .  If the solvents used in two extractive distillation columns are the same, there is the possibility of merging two solvent recovery columns into one. In Sequence 1 shown in Figure 1, if the solvent used for separating A2 and A3 is same with that used in the first extractive column, the first solvent recovery column with the red dotted box can be omitted, the bottom product of the first extractive distillation column can be directly sent to the second extractive distillation column, and the solvent recovered by the remaining solvent recovery column is recycled to the first extractive distillation column to be reused. The change of flowsheet is shown by a red line. If the solvents used in two extractive distillation columns are the same, there is the possibility of merging two solvent recovery columns into one. In Sequence 1 shown in Figure 1, if the solvent used for separating A 2 and A 3 is same with that used in the first extractive column, the first solvent recovery column with the red dotted box can be omitted, the bottom product of the first extractive distillation column can be directly sent to the second extractive distillation column, and the solvent recovered by the remaining Processes 2021, 9, 565 6 of 17 solvent recovery column is recycled to the first extractive distillation column to be reused. The change of flowsheet is shown by a red line.

Effect of Solvent to Extractive Distillation
Since solvent can increase the relative volatilities between components, the reflux ratio of an extractive distillation column will decrease after its addition, as well as the energy consumption and cost. Different solvents and their flowrates have different effects on components' vapor-liquid equilibrium, even the volatility order. This can be used to evaluate solvents' performance and their flowrates.
The solvent-to-feed ratio (SF) is defined as the ratio of the molar flowrate of solvent (F S ) to that of the mixture (F M ), as shown by Equation (15).
According to Equations (4), (6) and (15), the vapor-liquid equilibrium curves can be plotted to demonstrate the influence of solvent and solvent-to-feed ratio. The acetonitrilemethanol-benzene ternary mixture with three binary azeotropes is taken as an illustrative example; aniline (AN) and chlorobenzene (CB) are candidate solvents. The vapor-liquid equilibrium of pairwise combination among three components are plotted in Figure  2. It can be seen that when solvents are added, the vapor-liquid equilibrium curves are obviously modified, and the binary azeotrope disappears when solvent-to-feed ratio increases. When the solvent is AN, the volatility order from light to heavy is methanol, benzene, acetonitrile; but when CB is used, the order is methanol, acetonitrile, benzene. To give a more intuitive representation, the variations of relative volatilities along the solvent-to-feed ratio are shown by Figure 3. In the calculation, the molar composition of the mixture to be separated is 40% methanol, 30% benzene and 30% acetonitrile. As can be seen, with solvent AN, the relative volatility between benzene and acetonitrile increases slightly along the solvent-to-feed ratio, while that between methanol and benzene increases first and then decreases; with solvent CB, both relative volatilities increase significantly. To give a more intuitive representation, the variations of relative volatilities along the solvent-to-feed ratio are shown by Figure 3. In the calculation, the molar composition of the mixture to be separated is 40% methanol, 30% benzene and 30% acetonitrile. As can be seen, with solvent AN, the relative volatility between benzene and acetonitrile increases slightly along the solvent-to-feed ratio, while that between methanol and benzene increases first and then decreases; with solvent CB, both relative volatilities increase significantly.
To give a more intuitive representation, the variations of relative volatilities along the solvent-to-feed ratio are shown by Figure 3. In the calculation, the molar composition of the mixture to be separated is 40% methanol, 30% benzene and 30% acetonitrile. As can be seen, with solvent AN, the relative volatility between benzene and acetonitrile increases slightly along the solvent-to-feed ratio, while that between methanol and benzene increases first and then decreases; with solvent CB, both relative volatilities increase significantly.  For a given solvent, its flowrate affects both relative volatilities and the load of separation. For different solvents and SFs, the volatility order and the increment of relative volatility are different. In order to identify the optimal extractive distillation sequence and solvent, the intricate influence of solvent to the cost of each extractive distillation sequence needs to be analyzed carefully. For a given solvent, its flowrate affects both relative volatilities and the load of separation. For different solvents and SFs, the volatility order and the increment of relative volatility are different. In order to identify the optimal extractive distillation sequence and solvent, the intricate influence of solvent to the cost of each extractive distillation sequence needs to be analyzed carefully.

Effect of Solvent on Extractive Distillation System
The extractive distillation sequence together with feed preheater, reboilers and condensers compose the extractive distillation system. The selection of solvents and extractive distillation sequences have a great impact on its cost. It is worth conducting an in-depth analysis of their effect based on the TAC, which is shown by Equation (16).
where C CAP is the capital cost of equipment, β is the annual depreciation coefficient; C OP denotes the annualized operating cost of extractive distillation sequence, including the energy cost of the feed heater, reboilers and condensers, and the cost of solvent material. For each column, the shortcut method shown in Section 2.3 is used to calculate reflux ratio and theoretical plates' number. To simplify the optimization, the feed can be taken as a saturated liquid. Detailed calculation of the capital and operating costs of the equipment are introduced in the Appendix A. For the separation of a given mixture, the optimal extractive distillation sequence, suitable solvent and solvent-to-feed ratio can be identified by analyzing the effect of solvent and comparing distillation sequences.
For the methanol-acetonitrile-benzene mixture, when the solvent is AN, A 1 , A 2 , A 3 correspond to methanol, benzene and acetonitrile, respectively; when the solvent is CB, they correspond to methanol, acetonitrile and benzene, respectively. The TACs of all distillation sequences are calculated according to Equation (16) and the detailed calculation procedure introduced in the Appendix A; the variation curves of TAC along the solvent-to-feed ratio are plotted in Figure 4.

Effect of Solvent on Extractive Distillation System
The extractive distillation sequence together with feed preheater, reboilers and condensers compose the extractive distillation system. The selection of solvents and extractive distillation sequences have a great impact on its cost. It is worth conducting an in-depth analysis of their effect based on the TAC, which is shown by Equation (16).
where CCAP is the capital cost of equipment,  is the annual depreciation coefficient; COP denotes the annualized operating cost of extractive distillation sequence, including the energy cost of the feed heater, reboilers and condensers, and the cost of solvent material. For each column, the shortcut method shown in Section 2.3 is used to calculate reflux ratio and theoretical plates' number. To simplify the optimization, the feed can be taken as a saturated liquid. Detailed calculation of the capital and operating costs of the equipment are introduced in the Appendix. For the separation of a given mixture, the optimal extractive distillation sequence, suitable solvent and solvent-to-feed ratio can be identified by analyzing the effect of solvent and comparing distillation sequences.
For the methanol-acetonitrile-benzene mixture, when the solvent is AN, A1, A2, A3 correspond to methanol, benzene and acetonitrile, respectively; when the solvent is CB, they correspond to methanol, acetonitrile and benzene, respectively. The TACs of all distillation sequences are calculated according to Equation (16) and the detailed calculation procedure introduced in the Appendix; the variation curves of TAC along the solvent-tofeed ratio are plotted in Figure 4.   Figure 4 shows that the TACs of all distillation sequences decrease first and then increase along the solvent-to-feed ratio. By comparing TACs corresponding to different solvents, solvent-to-feed ratios and extractive distillation sequences, the minimum TAC is achieved when solvent is CB, solvent-to-feed ratio is 2, and Sequence 2 is applied.   Figure 4 shows that the TACs of all distillation sequences decrease first and then increase along the solvent-to-feed ratio. By comparing TACs corresponding to different solvents, solvent-to-feed ratios and extractive distillation sequences, the minimum TAC is achieved when solvent is CB, solvent-to-feed ratio is 2, and Sequence 2 is applied.

Optimization of Reaction and Extractive Distillation System
In chemical process, the mixture to be separated by distillation sequence is generally the reactor effluent; reactor operating conditions affect its composition, and further affect the separation system. When the extractive distillation is used, solvent and the distillation sequence affect the system's cost. To achieve economic optimization, all these factors should be considered together.
For a reactor with m reactions and n components (A 1 , A 2 , . . . , A n , arranged in the order of decreasing volatility), all reactions can be expressed as Equation (17).
Herein, ν ik represents the stoichiometric coefficient of component A i in reaction k.
According to reaction kinetics, the reaction rate of each component is a function of a reactor's temperature and concentration, as shown by Equation (18).
where r i is the reaction rate of A i , T R is the reactor temperature, and c represents components' concentration.
The flowrate of the reactor effluents can be calculated according to the mass and energy balance equations. Two ideal reactors, plug flow reactor (PFR) and continuous stirred tank reactor (CSTR), are illustrated. For PFR reactor, its mass and energy balances are shown by Equations (19) and (20), respectively. With these two equations integrated, the composition of the reactor effluent can be obtained.
where F i represents the flowrate of A i ; V is the effective volume of reactor; C pi represents the molar heat capacity of A i at constant pressure; U is the heat transfer coefficient; a is the effective heat transfer area per unit of reactor volume; T a is utility temperature for heat exchange of the reactor. w s is the shaft work per unit volume; R k and (∆H R ) k denote the reaction rate and reaction heat of reaction k.
For CSTR reactor carried out under the isothermal condition, the mass and energy balance are shown by Equations (21) and (22). Similarly, the composition of reactor effluent can be obtained based on these equations.
where F p0 is the flowrate of key reactant A p before the reactions, X p is the conversion of key reactant A p , r p is the reaction rate of A p , F 0 is the feed flowrate, S is the heat transfer area, T 0 is the feed temperature. When operating reactor conditions change, the energy consumption and investment of the reactor will change accordingly, as well as the reactor's effluent. The latter affects the extractive distillation sequence. At the same time, the application of different solvents and solvent-to-feed ratios leads to different relative volatilities, different energy consumptions and different costs of the reaction and extractive distillation system.
The TAC of the reaction and extractive distillation system can be calculated according to Equation (16). The investment cost of the system includes the cost of the reactor, distillation column, feed preheater, reboilers and condensers; the operating cost covers the cost of energy supplied to the equipment and the cost of solvent.
In the integration of the reactor and the extractive distillation system, the separation order of the reactor effluent is identified first based on the non-key component matrix method. Then, the addition of solvent is considered, and the extractive distillation columns and solvent recovery columns are configured to form extractive distillation sequences. For a set of given reactor operating conditions, the composition of reactor effluent with maximum desired product is identified through adjusting other reactor operating conditions; then the volatility orders of components are determined after the solvent is added, and the extractive distillation sequences are generated. The reactor and identified extractive distillation sequences constitute different configurations. The TACs of the systems with different reactor operating conditions, candidate solvents, solvent-to-feed ratios and extractive distillation sequences are calculated, and the optimal system with minimum TAC and the corresponding parameters can be identified. The procedure is shown in Figure 5. The calculation can be implemented by MATLAB R2020b.  It should be noted that the proposed method cannot be applied to the system when the distillation column has side stream or the column performs non-sharp split. The reason is that the non-key component matrix can only be used for the simple column with sharp split. Besides, in the integration of the reactor and the extractive distillation system, the recycling of unreacted reactants is not taken into account. These limitations will be improved in further studies.

Case Study
Cyclohexene (HE, C 6 H 10 ) is generally produced by selective hydrogenation of benzene (BZ, C 6 H 6 ). The reactions are shown below [29]: When catalyst Ru-M-B/ZrO2 is used, the reaction rates under high pressure (>4 MPa) are shown by Equations (23) and (24) [29]. The feed flowrate and the inlet concentration of benzene (BZ) are taken as 33.33 mol·s −1 and 0.078 mol·m −3 , respectively.
where r BZ and r H A are the reaction rates of BZ and HA, c BZ is the concentration of BZ, and T R is the reaction temperature. At 298 K and 5 MPa, the reaction heat for reaction 1 and 2 are −95,000 J·mol −1 and −120,000 J·mol −1 , respectively. To simplify the calculation, the molar heat capacity of each component is taken as constant, and the reaction heat for reaction 1 and 2 in reaction temperature can be obtained by Equations (25) and (26).
The reaction system can be taken as a quasi-homogeneous system and the reactor can be taken as PFR. On the basis of Equations (23)-(26), the reactor volume can be adjusted to maximize the target product HE; the flowrate of BZ, HE and HA can be calculated according to the mass and energy balances, as shown by Equations (19) and (20) in Section 4. With the reactor outlet temperature keeping to be 473 K and the inlet temperature (T 0 ) changing from 303 K to 353 K in the step of 10 K, the product composition is calculated and plotted in Figure 6. where C6H12 is cyclohexane (HA). When catalyst Ru-M-B/ZrO2 is used, the reaction rates under high pressure (>4 MPa) are shown by Equations (23) and (24) (24) where BZ r and HA r are the reaction rates of BZ and HA, BZ c is the concentration of BZ, and TR is the reaction temperature. At 298 K and 5 MPa, the reaction heat for reaction 1 and 2 are −95,000 J·mol −1 and −120,000 J·mol −1 , respectively. To simplify the calculation, the molar heat capacity of each component is taken as constant, and the reaction heat for reaction 1 and 2 in reaction temperature can be obtained by Equations (25) and (26).
The reaction system can be taken as a quasi-homogeneous system and the reactor can be taken as PFR. On the basis of Equations (23)-(26), the reactor volume can be adjusted to maximize the target product HE; the flowrate of BZ, HE and HA can be calculated according to the mass and energy balances, as shown by Equations (19) and (20) in Section 4. With the reactor outlet temperature keeping to be 473 K and the inlet temperature (T0) changing from 303 K to 353 K in the step of 10 K, the product composition is calculated and plotted in Figure 6. It can be seen from this figure that, along with the variation of the reactor's inlet temperature, the flowrate of desired product (HE) decreases slowly, while its yield increases first and then decreases. When the inlet temperature is 313 K, the maximum yield of HE, 0.298, is obtained. It can be seen from this figure that, along with the variation of the reactor's inlet temperature, the flowrate of desired product (HE) decreases slowly, while its yield increases first and then decreases. When the inlet temperature is 313 K, the maximum yield of HE, 0.298, is obtained.
In the reactor's effluent, HA, HE and BZ form three binary azeotropes, and extractive distillation is used to separate them. In the presence of solvent, the decreasing order of components' volatility is HA > HE > BZ. The candidate solvents include N,N-Dimethylacetamide (DMAC), N-Methylpyrrolidone (NMP) and N-Formylmorpholine (NFM), and the prices of the three candidate solvents are shown in Table 2. Based on the method introduced in Section 2.2, when different solvents are employed and SF = 3, the relative volatility (α) versus reactor inlet temperature (T 0 ) curve is calculated for every pair of adjacent components and plotted in Figure 7. As the inlet temperature of reactor increases, the relative volatilities between components increase accordingly. When NFM is employed, the relative volatilities are much greater than those when the other two solvents are used. When the solvent DMAC is employed, components have the minimum relative volatility. volatility (α) versus reactor inlet temperature (T0) curve is calculated for every pair of adjacent components and plotted in Figure 7. As the inlet temperature of reactor increases, the relative volatilities between components increase accordingly. When NFM is employed, the relative volatilities are much greater than those when the other two solvents are used. When the solvent DMAC is employed, components have the minimum relative volatility.  For each solvent, the relative volatility of components changes along the solvent-tofeed ratio. For example, when the feed temperature is 323 K, the molar composition of the reactor effluent is 18% HA, 30% HE and 52% BZ. For three candidate solvents, the variation of relative volatility along the solvent-to-feed ratio is plotted in Figure 8. It can be seen that the relative volatility increases along the solvent-to-feed ratio or flowrate of solvent, no matter which solvent is used. However, increasing solvent's flowrate will increase duty of separation and cost of solvent, and hence will cause an increment of the system's TAC.  For each solvent, the relative volatility of components changes along the solvent-tofeed ratio. For example, when the feed temperature is 323 K, the molar composition of the reactor effluent is 18% HA, 30% HE and 52% BZ. For three candidate solvents, the variation of relative volatility along the solvent-to-feed ratio is plotted in Figure 8. It can be seen that the relative volatility increases along the solvent-to-feed ratio or flowrate of solvent, no matter which solvent is used. However, increasing solvent's flowrate will increase duty of separation and cost of solvent, and hence will cause an increment of the system's TAC. volatility (α) versus reactor inlet temperature (T0) curve is calculated for every pair of adjacent components and plotted in Figure 7. As the inlet temperature of reactor increases, the relative volatilities between components increase accordingly. When NFM is employed, the relative volatilities are much greater than those when the other two solvents are used. When the solvent DMAC is employed, components have the minimum relative volatility.  For each solvent, the relative volatility of components changes along the solvent-tofeed ratio. For example, when the feed temperature is 323 K, the molar composition of the reactor effluent is 18% HA, 30% HE and 52% BZ. For three candidate solvents, the variation of relative volatility along the solvent-to-feed ratio is plotted in Figure 8. It can be seen that the relative volatility increases along the solvent-to-feed ratio or flowrate of solvent, no matter which solvent is used. However, increasing solvent's flowrate will increase duty of separation and cost of solvent, and hence will cause an increment of the system's TAC. The feed of the extractive distillation system includes three components (excludes the solvent), the corresponding non-key component matrix shown by Equation (14) can represent the possible extractive distillation sequences. Herein, A1, A2, A3 represent HA, HE and BZ, respectively. Based on this and with the solvent considered, sequence 1 (S1) and sequence 2 (S2) are identified, and their flowsheets are the same as those shown in Figure   Figure 8. Variation of relative volatilities with different solvent-to-feed ratios.
The feed of the extractive distillation system includes three components (excludes the solvent), the corresponding non-key component matrix shown by Equation (14) can represent the possible extractive distillation sequences. Herein, A 1 , A 2 , A 3 represent HA, HE and BZ, respectively. Based on this and with the solvent considered, sequence 1 (S1) and sequence 2 (S2) are identified, and their flowsheets are the same as those shown in Figure 1. Since the solvents of two extractive distillation columns are the same, the first solvent recovery column of S1 is taken out. For sequences S1 and S2, the TACs and TACs of unit desired product of the system are calculated according to the procedure introduced in Section 4, and are plotted in Figure 9. When the solvent-to-feed ratio increases, the TAC and TAC of unit desired product decrease first and then increase, no matter which solvent is used. For S1, when DMAC is used and the reactor's inlet temperature lies in 303~343 K, the minimum TAC is obtained when the solvent-to-feed ratio equals 2, while the solventto-feed ratio corresponding to the minimum TAC is 3 when the feed inlet into the reactor is at 353 K. When NMP is used, the solvent-to-feed ratio with minimum TAC is equal to 2, while it is 3 when NFM is the solvent. For S2, the solvent-to-feed ratio with minimum TAC is equal to 3 when DMAC and NMP are used at all of the reactor's inlet temperatures, while it is 4 when NFM is used.
To sum up, the minimum TAC of the system can be achieved when the solvent is NFM, the solvent-to-feed ratio is 4 and S2 is applied. As shown in Figure 9b(3), for S2, when the reactor's inlet temperature increases, the TACs of unit desired product wavelike rise. The minimum TAC of unit desired product, 4.01 $·kmol −1 , is achieved when the reaction inlet temperature is 333 K.

Conclusions
A method was proposed to integrate the reaction and the extractive distillation, and identify the optimal solvent and solvent-to-feed ratio. The two-step procedure can identify the extractive distillation sequences efficiently and automatically. The variation trend curves of the TAC of the reaction and the extractive distillation system indicate the variation of total cost along key parameters, and can be used to analyze the effect of reactor operating conditions, solvents and solvent-to-feed ratio, and compare different distillation sequences efficiently. The proposed method also can be used to identify the optimal extractive distillation sequence and optimize the reactor operating conditions. Case study shows that for the ethylbenzene process, the minimum TAC of unit desired product, 4.01 $·kmol −1 , is achieved when the reaction inlet temperature is 333 K, solvent NFM and sequence S2 are employed, and the solvent-to-feed ratio is 4.
In this work, the reactor's inlet temperature and solvent-to-feed ratio were analyzed and optimized. Other reactor conditions, such as reactant concentration, operation pressure, reflux ratio in extractive distillation system and the recycle of unreacted reactant also affect the reaction and extractive distillation system. Besides, columns with side stream or those performing non-sharp split can also be used in the extractive distillation. The proposed method will be extended to take these factors into consideration.   Heavy key component lk Light key component

The Totally Annualized Cost
The totally annualized cost (TAC) includes the annualized capital costs of the equipment and the annualized operating costs.
The capital cost of the reactor C react is calculated by Equation (A1) [30].
C react = 937.6D r 1.066 H r 0.802 (2.18 + 2F c1 ) where D r and H r are the diameter and the height of the reactor, F c1 is the correction factor for the reactor and distillation column, F c1 = F p F m1 . F p and F m1 are the correction factors associated with pressure and material, as shown in Table A1. where D c and H c are the diameter and the height of the distillation column, and calculated by Equations (A3) and (A4) [31]. F c2 is the correction factor for column plate, F c2 = F s + F t + F m2 , F s , F t and F m2 are the correction factor associated with plate spacing, type and plate material, as shown by Table A2. where T D is the temperature of distillate; H T is the plate spacing, is the plate efficiency, N p is the number of manholes, V v is the average vapor velocity in the column. The capital cost of the heat exchanger, C exc , is calculated by Equation (A5) [30]. A exc is its heat transfer area and calculated by Equation (A6), Q exc is the heat duty of the heat exchanger and calculated by Equation (A7).
C exc = 474.7A exc 0.65 (2.29 + 2F c3 ) (A5) where F c3 is the correction factor for heat exchanger, it is associated with type, as shown in Table A3 [30]; U is the heat transfer coefficient, and is set as 1500 J·m −2 ·s −1 ·K −1 ; ∆T is the temperature difference; F exc is the flowrate of the stream being cooled or heated, and the ∆H v is the latent heat of stream. The capital cost introduced above is calculated based on that in 1968, and it can be updated according to the Chemical Engineering Plant Cost Index (CI) [32] by Equation (A8). The annualized operating cost is calculated by Equation (A9). In this equation, t OP denotes the annual operating time and is set as 8500 h; and C U represent the prices of utilities, and is shown in Table A4.