Simulation-Based Multiobjective Optimization of the Product

Article Cite This: Ind. Eng. Chem. Res. 2019, 58, 12166−12178

pubs.acs.org/IECR

Simulation-Based Multiobjective Optimization of the Product Separation Process within an MTP Plant Li Zhou,† Zuwei Liao,*,‡ Lin Wang,¶ Lingling Zhang,‡ Xu Ji,† Hongqiao Jiao,¶ Jingdai Wang,‡ Yongrong Yang,‡ and Yagu Dang† †

School of Chemical Engineering, Sichuan University, Chengdu 610065, PR China State Key Laboratory of Chemical Engineering, Department of Chemical and Biological Engineering, Zhejiang University, Hangzhou, Zhejiang 310027, PR China ¶ Coal to Liquids Chemical R&D Center, Shenhua Ningxia Coal Industry Group, Yinchuan 750001, PR China Downloaded via GUILFORD COLG on July 28, 2019 at 08:23:04 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

S Supporting Information *

ABSTRACT: This work proposes a simulation-based multiobjective optimization model for the operation of the product separation process in a methanol to propylene (MTP) plant, striving to enhance the system energy utilization efficiency. The formation of byproducts including an oxygenated hydrocarbon, dimethyl ether (DME), makes the product refining process highly energy-intensive, not only because that the various hydrocarbon byproducts require a long train of distillation columns but also owing to the fact that DME forms azeotrope with product propylene. Furthermore, the formation of oxygenated DME byproduct varies with the catalyst activity, which makes the system more complex. The contribution of this paper is 2-fold. First, it proposes a novel way of DME removal with responsive consumption of extractant methanol according to the DME concentration during one production period. In this way, the energy consumption of the condenser and reboiler of the methanol recovery unit can be expected to decrease by 61.5% and 37.6%, respectively. Second, a simulation-based multiobjective optimizaton framework is introduced to minimize the total heating and cooling costs and maximize the product purity, by integrating a rigorous process simulation model with an intelligent optimization algorithm. Given the characteristics of the MTP production process, three different operation scenarios, namely, the start of run, the designed operation condition, and the end of run, which correspond to different DME concentrations in the system, are covered. The approach is illustrated by its application to a real MTP plant, in which numerical results indicate that the proposed method is capable of identifying appealing operation options, and it can be utilized to support decision-making of the product separation of MTP plants.

1. INTRODUCTION

the separation of various byproducts including hydrogen and carbon monoxide as well as hydrocarbons ranging from C1 to C10 requires a long train of distillation columns and heat exchangers, in order to produce valuable products, such as propylene, gasoline, and ethylene, and recover methanol and light ends for possible recycling. Second, the formation of oxygenated hydrocarbon dimethyl ether (DME) forms azeotrope with the product propylene, which demands extractive distillation for separation. This further makes the separating process more energy-intensive. It contributes to more than 45% of the overall system energy consumption. Furthermore, due to the decay of the catalyst activity, the DME content changes from the start of run to the end of run.

The methanol to propylene (MTP) reaction plays an important role in linking alternative feed stocks such as biomass and carbon dioxide to high-demand petrochemical commodity propylene, of which the annual market demand is estimated to surpass 140 million metric tons by 2025.1 Much attention from both academia2,3 and industry4 has been paid to the MTP processes, concerning the catalyst preparation and modification,5 element reactions of deactivation,6 process kinetic study,7 reactor simulation,8,9 and so on. These studies have helped in gaining better insight into the process and identifying the scope for modifications at both design and operation stages. However, most of the studies mainly focused on the MTP reaction process, while not much attention has been paid to the product separation and refinement, which is of equal importance to the reaction. Obtaining propylene from methanol is much more energyintensive than steam cracking of saturated hydrocarbons. First, © 2019 American Chemical Society

Received: Revised: Accepted: Published: 12166

April 15, 2019 May 29, 2019 June 12, 2019 June 12, 2019 DOI: 10.1021/acs.iecr.9b02033 Ind. Eng. Chem. Res. 2019, 58, 12166−12178

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Industrial & Engineering Chemistry Research

Figure 1. A typical flow sheet of the methanol-to-propylene (MTP) process.

frameworks for the optimal design of energy-integrated separation systems by integrating genetic algorithm (GA) with short-cut mathematical models which proved to be viable and robust. Subsequently, Pandey and Rangaiah27 proposed a multiobjective optimization model for the cold-end separation process of an ethylene plant, via the integration of a commercial software package and the elitist nondominated sorting genetic algorithm (NAGA-II). Most recently, Yang and Ward28 introduced an optimization framework for continuous extractive distillation processes by combining simulated annealing (SA) algorithm with process simulation. Ibrahim et al.29 addressed the design of a complex crude oil distillation unit by integrating rigorous column simulation using commercial process simulation software with GA. In their work, both structural variables and operational variables were ́ taken into consideration. Briones-Ramirez and Gutiérrez30 Antonio presented a procedure to integrate MATLAB and Aspen Plus processes simulation for chemical process optimization.

Therefore, energy saving is critical to this process, and it requires particular attention. Process synthesis and optimization is an effective tool for process efficiency enhancement. Numerous methodologies have been proposed,10−16 and there has developed a popularity of solving the problem by integrating rigorous or short-cut simulation models with intelligent algorithms. Wang et al.17 developed an optimal separation process scheme for the MTP process, by comparing several demethanizer exhaust gas recovery technologies. Strategies for selecting the suitable separation technologies18 as well as the optimal design of separation process19,20 for effluent gas recovery of petrochemical plants were also reported. Simulation-based process synthesis and optimization methods were reported in the separation of petrochemical processes.21 Brunet et al.22−24 proposed unified frameworks that combine process simulation, multiobjective optimization, and life cycle assessment (LCA) to identify the optimal design and operating conditions of process systems which fully account for economic and environmental concerns. Smith et al.25,26 proposed synthesis 12167

DOI: 10.1021/acs.iecr.9b02033 Ind. Eng. Chem. Res. 2019, 58, 12166−12178

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depropanizer (DP), along with the gaseous hydrocarbon stream from the previous section and a methanol stream which serves as extractant for DME removal. In this case, DP fulfills two tasks: a) separation of the C4 component from lighter hydrocarbons C3− and b) extraction of DME. The bottom stream from the DP is then stratified into two layers in a subsequent separation tank. The top layer contains C4, while the bottom layer is methanol with the extracted DME. A large portion of the C4 component is recycled to the DME reactor, and the remaining is sent to a methanol extractor. DP’s overhead vapor stream which comprises C3− (light hydrocarbons up to C3) is fed into a de-ethanizer (DE) to separate C2− and C3. C2− exits from the top and then goes through a CO2 scrubber, followed by a demethanizer (DM) and a C2 separator, to separate methanol and ethane and produce polymer grade ethylene. Methanol from the top of DM and ethane from the bottom of the C2 separator are mixed to produce fuel gas. The bottom product of DE is sent to a C3 separator to produce propane and a polymer grade propylene product. Propane is mixed with the top gas from the methanol extractor to produce LPG. The DB bottoms comprising C5+ (hydrocarbons C5 and above) is fed to a dehexanizer (DH), whose overhead stream consists of C5 and C6 hydrocarbons. It is split into two streams. One is sent to a gasoline stabilizer (GS) to further separate the C5 and C6 components. The vapor from the GS is recycled back to the reaction section, together with the other split stream of DH overheads. The liquid exiting GS is mixed with the bottoms from DH to produce byproduct gasoline.

The complex nature of the product separation of MTP processes distinguishes itself from other ordinary petrochemical separation processes. Special attention should be paid to the design and operation of the DME removal process as well as the product refining. This study strives to enhance the energy-efficiency of the DME removal process and the hydrocarbon refinement process of an MTP plant. Given that the formation of DME varies along with the catalyst activity, a new way of DME removal with responsive consumption of extractant methanol is proposed. For the operation of the long distillation column train for hydrocarbon refinement, a multiobjective optimization framework is established by integrating the nondominated sorting genetic algorithm (NSGA-II) with a process simulation automation server. Selected optimization objectives include quality of the two main products, namely propylene and ethylene, and the total consumption of heating and cooling utilities. The optimization under three operation conditions in a practical production process is covered. For each considered case, the method provides a set of optimal solutions in the form of a Pareto-optimal front, which illuminates the trade-off between the considered objectives. The rest of this paper is organized as follows. Section 2 briefly introduces an MTP process. Section 3 presents the modeling of the product separation process of an MTP plant. Section 4 presents an alternative operation of the extractive distillation process for DME removal. Section 5 introduces the establishment of the proposed multiobjective optimization framework, covering the selection of objectives, decision variables, and constraints as well as the detailed implementation steps of the NSGA-II algorithm. Results and discussion on the different combinations of objectives under different operation conditions are given in Section 6. Finally, conclusions are drawn in Section 7.

3. SIMULATION OF THE MTP PRODUCT SEPARATION PROCESS AND RESULT VALIDATION The product separation process of the considered case comprises 7 distillation columns, 1 extractor, 1 stabilizer, 1 CO2 absorption tower, and 22 heat exchangers (including the reboilers and condensers of the distillation columns), which is shown in Figure 1. The process is simulated using Aspen Plus. Selection of a suitable property package is important for the simulation procedure, because the accuracy of simulation relies on accurate estimation of the thermodynamic and transport properties. Two property models, SRK (Soave−RedlichKwoong) and PR (Peng−Robinson), are selected by considering the following factors, nature of the properties of interest, composition of the involved mixture, pressure and temperature ranges, and availability of parameters required by the property model. The simulation result is validated by industrial operation data. Details of the Product Separation Process. The product separation process used in this study is based on a real process flow diagram, which is part of an MTP plant. The feed for the refining process includes a liquid hydrocarbon stream, a gaseous hydrocarbon stream, and a methanol stream. The feed streams comprise hydrogen, carbon monoxide, methane, methanol, DME, and hydrocarbons from C2 to C10. Compositions of the liquid and gaseous streams under designed operation conditions are given in the Supporting Information. The output of the process includes polymer grade propylene, gasoline, polymer grade ethylene, LPG, and fuel gas. The distillation columns are simulated by a rigorous stageby-stage calculation model. The operating pressure and tray number take reference values from an operating plant. The number of ideal trays is estimated by using overall efficiency of the column calculated by the following equation32

2. MTP PROCESS DESCRIPTION For a typical MTP process, the reaction effluent contains olefin, alkane, aromatics, cycloalkanes, and some light components (H2, CO, CO2), of which the contents are approximately 85%, 9%, 3%, 2%, and 1% in weight, respectively. It is first cooled down from 480 to 190 °C in heat exchangers by preheating reactant methanol. This is followed by a coarse gas separation process to recover unreacted methanol and heavy components (C7 hydrocarbons and above, C7+) as well as heat from the effluent. As is shown in Figure 1, the reaction effluent is sequentially fed into the bottom of two quench towers, where the unreacted methanol and the heavy components as well as the carried heat are shifted to the counter-current contacting chilled water stream. The scouring water from the bottom of the quench tower is pumped for methanol recovery, while the quench gas exit from the top is further separated, compressed, and dehydrated in a series of 4−5 separator-compressor-cooler stages. This fractionates the quench gas into two streams, namely, a gaseous and a liquid hydrocarbon stream, which is the starting point of the product separation process that is of interest to this study. For more detailed information about the parameters of the apparatus, the readers are referred to ref 31. The product separation process studied in this work is highlighted by a rectangle with blue outlines in Figure 1. In this process, the liquid hydrocarbon from the previous section is fed into a debutanizer (DB), whose overhead stream containing lighter hydrocarbons up to C4 (C4−) is sent to a 12168


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grades of the olefin products, namely propylene and ethylene. Traces of DME exist in both the gaseous and liquid hydrocarbon streams, and it is a contaminant to the products. In a typical MTP process, methanol is applied in DP to extract DME from the hydrocarbons. Extractant methanol and the extracted DME are then separated from the hydrocarbons in a subsequent separation tank. A small portion of DME is sent back to the MTP reaction section along with the C4 recycling stream, while the main body of the DME component stays in the methanol aqueous solution and goes through a methanol extractor, a methanol recovery column, and then back to the DME reactor. The flow track of DME in this case is marked with bolded green lines in Figure 1, which is also briefly illustrated in Figure 2(a). In order to ensure the removal of DME, the current operation consumes a fixed amount of extractant methanol input of 936.2 kmol/h. This amount of methanol will be recovered from the methanol recovery tower, which is energy intensive. In this case, 1.19 × 108 kJ/h of heat duty and 6.25 × 107 kJ/h of cooling duty are required by the methanol recovery tower. It should also be noted that due to the aging of catalyst inside the fixed bed reactor, the DME concentration increases from the start of run (0 ppm) to the end of run (20000 ppm) during one operating period. It can be easily concluded that different DME concentration requires different amount of extractant. Hence, the load of the methanol recovery tower can be alleviated by adjusting the methanol input accordingly. Let us consider the condition of methanol not feeding into DP as extractant, namely the nonextractive distillation condition. In this case, the DME flow direction is not the one shown in Figure 2(a), but the one shown in Figure 2(b). In this case, the DME component exits DP from the overhead, then goes to DE, and exits from the bottom, after which, it is sent to the C3 separation tower and leaves it from the bottom. After the C3 separation tower, the DME component is sent to the methanol extractor and then back to the main MTP reaction process. The existing and alternative way of DME removal is marked in Figure 1 and Figure 3 with green and light green lines, respectively. In order to minimize the energy consumption while ensuring the removal of DME, the operation parameters of the relative units should be adjusted according to the inlet concentration of DME. In this work, Aspen simulation is performed to obtain operation values under certain operation conditions. Table 3 gives a series of inlet DME concentration as well as its corresponding operation parameters of DP, methanol recovery tower, and C3 separation column. As is shown, when the DME concentration achieves 5000 ppm, DP’s overheads flow rate starts to increase, so does the energy consumption of methanol recovery tower. In the meanwhile, the temperature at the bottom of the C3 separator reaches 67.9 °C. This temperature approaches the limiting temperature difference of the reboiler, which is heated by the process waste heat. In other words, 67.9 °C is the upper bound of the bottom temperature of the C3 separator under the given heating conditions. As a result, when DME concentration exceeds 5000 ppm, the extractant methanol should be applied in DP. It is suggested to apply methanol with a gradually increasing amount to shift a portion of DME from the vapor stream to the liquid stream, thus to alleviate the operation load of the relevant units, when DME concentration exceeds 5000 ppm. The amount of methanol utilized defines the DME distribution profile in DP’s overheads and bottoms, thus determining the

(1)

This overall efficiency is calculated based on viscosity (μ) of the liquid feed and the relative volatility (α) of light-heavy key components at the column average conditions. The number of ideal trays can thus be calculated by the following equation. As is suggested by Kaes,33 the calculated number of ideal trays is used in Aspen simulation of the distillation columns, in order to make the model more realistic. Nideal = E0Nactual

(2)

Validation of the Simulation. All the input data of the simulation are extracted from the existing flow sheet of a certain MTP plant. To validate the predictions obtained by Aspen plus software, Table 1 presents the comparison between Table 1. Comparison of Predicted Temperature with the Designed Data column DB DP DE C3 separator DM C2 separator

output stream

designed value (°C)

predicted value (°C)

overheads bottoms overheads bottoms overheads bottoms overheads bottoms overheads bottoms overheads bottoms

83.4 175.7 39.2 103.9 −35.0 47 53.3 63.0 −66.6 −8.6 −33.6 −33.6

79.1 172.4 37.6 102.6 −35.9 47 53.3 62.7 −71.8 −8.7 −33.6 −10.9

absolute error 4.3 3.3 1.6 1.3 0.9 0 0 0.3 5.2 0.1 0 1.3

(5.1%) (1.9%) (4.1%) (1.3%) (2.6%)

(0.5%) (7.8%) (1.2%) (13.5%)

Table 2. Comparison of Predicted Flow Rate with the Designed Data output stream DB overheads DP bottoms DE overheads C3 separator overheads DM overheads C2 separator bottoms

designed value (kmol/h)

predicted value (kmol/h)

absolute error

2457 1700.8 1185.5 1458.3

2493 1726.9 1186.0 1458.3

36 (1.47%) 26.1 (1.53%) 0.5 (0.04%) 0

53.7

53.1

16.2

16.2

0.6 (1.12%) 0

predicted flow temperature and the designed value for the concerned columns in the current study, while Table 2 gives a comparison between the predicted flow rate and the designed value. The calculation of absolute error and percentage error shows that prediction by the simulation model remains in an acceptable range. As is shown, most of the average error for temperature prediction remains less than 5 °C, while the average percentage error for flow rate prediction remains less than 2%.

4. ALTERNATIVE OPERATION OF THE EXTRACTIVE DISTILLATION PROCESS FOR DME REMOVAL The depropanizer (DP) is a key column in the gas refining section. Its separation efficiency directly affects the quality 12169


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Figure 2. Two different ways of DME removal for methanol-to-propylene (MTP) product separation.

Figure 3. Proposed process flow sheet for DME removal.

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Industrial & Engineering Chemistry Research Table 3. Operation Parameters of Certain Columns Correspond to Certain DME Concentrationsa methanol recovery tower CDME (ppm)

FDP−Overheads (kmol/h)

FDP−Bottoms (kmol/h)

reflux ratio

FDP−Overheads (kmol/h)

QCondenser (107 kJ/h)

QReboiler (107 kJ/h)

Fmethanol (kmol/h)

C3 sep Tbot (°C)

1500 3000 4000 4100 4300 5000 7000 9000 20000

2635.0 2641.5 2647.0 2647.0 2647.0 2650.0 2658.0 2667.0 2716.0

759.2 759.3 757.8 758.1 759.1 759.1 759.7 759.3 759.4

0.80 0.80 0.80 0.80 0.80 0.80 0.82 0.86 1.13

242.2 243.0 243.2 243.1 243.1 243.1 243.2 243.3 244.4

1.66 1.67 1.68 1.68 1.68 1.68 1.71 1.74 1.85

6.62 6.62 6.61 6.61 6.61 6.60 6.60 6.61 6.65

3.407 3.348 3.455 3.471 3.497 3.588 3.677 3.601 3.486

64.7 66.4 66.9 67.1 67.4 67.9 69.4 70.4 73.8

Abbreviations: C - concentration, F - flow rate, Q - heating/cooling duty, T - temperature.

a

Table 4. Operation Parameters of the Columns for the Proposed DME Removal Process DP DME

Methanol

methanol recovery column

C (ppm)

F (t/h)

overhead (kmol/h)

bottom (kmol/h)

reflux ratio

overhead (kmol/h)

QCondenser (107 kJ/h)

QReboiler (107 kJ/h)

FMethanol (kmol/h)

C3 sep Tbot (°C)

1500 3000 4000 4100 4300 5000 7000 9000 10000 12000 15000 18000 20000

0 0 0 0 0 2.08 4.96 6.40 7.04 7.84 8.64 9.12 9.44

2635 2642 2647 2647 2647 2647 2647 2647 2647 2647 2647 2647 2647

759.16 759.30 757.80 758.10 759.10 826.98 925.47 979.10 1003.44 1037.21 1075.53 1104.07 1123.23

0.80 0.80 0.80 0.80 0.80 0.64 0.64 0.64 0.64 0.64 0.64 0.64 0.64

242.21 243.00 243.17 243.14 243.09 306.25 392.07 409.63 451.36 472.43 491.43 500.34 506.28

1.66 1.67 1.68 1.68 1.68 1.87 2.32 2.53 2.63 2.75 2.85 2.90 2.93

6.62 6.62 6.61 6.61 6.61 6.85 7.35 7.58 7.68 7.79 7.88 7.90 7.92

3.41 3.35 3.46 3.47 3.50 1.62 0.37 0.20 0.16 0.13 0.11 0.10 0.10

64.7 66.4 66.9 67.1 67.4 67.3 67.3 67.4 67.3 67.3 67.3 67.4 67.4

operation load of the relevant units. Therefore, it is an optimization variable, which is subject to DME concentration and preferable operation condition of the concerned units. A series of reference operation parameters for a whole operation period are obtained via Aspen plus simulation, which are presented in Table 4. As is shown, DP starts to consume methanol at the flow rate of 2.08 t/h when DME concentration reaches 5000 ppm, which keeps the overheads at 2647 kmol/h and increases the bottoms to 827 kmol/h. The temperature requirement at the bottom of the C3 separator decreases to a preferable 67.3 °C. As DME concentration increases, the consumption of methanol increases accordingly. The optimized methanol consumption during one operation period is shown in Figure 4, and the corresponding heating/cooling duty required by the methanol recovery column is given in Figure 5. Comparison of the energy consumption by the methanol recovery column between the proposed DME removal process and the original process is carried out, which is demonstrated in Figure 5. As is shown, the energy consumption of the condenser decreases by 61.5% after the optimization, and the energy consumption of the reboiler decreases by 37.6%.

Figure 4. Consumption of extractant methanol under different DME concentrations in the product.

exchanger network of the MTP process are rather complicated, which are composed of 8 distillation columns and 22 heat exchangers (including the reboiler and condenser of the distillation columns). Normally, the most commonly considered objective for process optimization is profit, namely, the difference of revenue and system cost. However, in the considered plant, propylene and ethylene are not the final products. They are further processed for the production of high-value-added polypropylene and polyethylene. The poly-

5. FORMULATION OF THE MULTIOBJECTIVE OPTIMIZATION MODELS For a large-scale complex process, there are many factors that need to be considered while formulating objective functions. The product separation process and the accompanying heat 12171


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Industrial & Engineering Chemistry Research min (UC , −yk ) k∈K

s.t.

UC = f (X ) yk = gk (X )

k ∈ K = {1, 2}

T

X = [N , R i ] yk ≥ Lpk

N ∈ * , R ∈ , i ∈ I = {1, 2, 3, 4, 5, 6}

k ∈ K = {1, 2}

LN ≤ N ≤ UN LR i ≤ R i ≤ UR i

(3)

where UC stands for utility cost, yk represents the purity of product k, X is the vector for the decision variables, in this case, N and Ri, which are the feeding tray number and reflux ratio of the concerned distillation columns, Lpk denotes the lower bounds for the purity requirement of product k, and LN, LRi, UN, and URi are the lower and upper bounds of the feeding tray number and reflux ratio determined based on practical experiences.

Figure 5. Comparison of the heat/cooling duty of the methanol recovery column between the proposed and the original DME removal process.

6. RESULTS AND DISCUSSION The multiobjective optimization problems under different operation conditions are solved by using a nondominated sorting algorithm (NSGA-II). A detailed description of the implementation of the algorithm can be found in the Supporting Information. This section gives the results and discussions of the cases. Case a: Maximization of Propylene Purity and Minimization of Utility Cost. After 10 generations of evolution calculation, the Pareto-optimal front is depicted. NSGA-II gives 60 optimal solutions which provide engineers insights for the process and facilitate decision making. Tradeoffs between the two objectives can be clearly depicted by the Pareto-optimal front. As is shown in Figure 6, the propylene purity first experiences a rapid increase from 0.99607 to 0.99723 with the corresponding utility cost slowly growing from 6106 to 6289 $/h. As we continue moving from one optimal solution to another toward the right of the Pareto front, utility cost continues to grow (from 6289 $/h to 6796 $/h), yet propylene purity improves with a negligible rate (from 0.99723 to 0.99729). In other words, improvement of propylene purity can only be achieved at a larger cost in the second half of the front. Note that each solution on the Pareto front is considered as an optimal solution. Since the propylene purity increases steeply initially, a good trade-off solution is 0.99723 of propylene purity with utility cost of 6289 $/h. Solutions scattered on the left side of the front before the inflection point, i.e. (6289, 0.99723), are preferable for production compared to the solutions on the right side. The calculated feeding tray and reflux ratio of DB corresponding to the preferable solution is 17 and 0.915, respectively. The optimal values of the 7 considered decision variables are distributed within their respective upper and lower bounds, which are illustrated in Figure 6(b)−(h). Two of the selected decision variables, namely DB reflux ratio and DP reflux ratio, affect the two objectives in opposite directions. The correlations between utility cost and the reflux ratio of DB and DP are shown in Figures 6(c) and 6(d), respectively. Take the DP reflux ratio as an example, as it increases from 1.5 to 2, utility cost increases by 690 $/h, while the improvement of propylene purity in this case can be derived from Figure 6(a) that it increases from 0.99607 to 0.99729. This is due to the fact that increasing the DP reflux ratio improves the separation

merization reaction requires the reactant to be of high purity. The higher the purity of reactant, the better the product quality. Hence, in the current study, the purity of products (propylene and ethylene) and utility cost (UC) is used as the optimization objectives. Improvement in product purity is usually achieved at the price of growing utility cost. It is therefore important to study the trade-off between the required heating and cooling duty and the purity of products in order to draw comprehensive conclusions for better system operation. Optimization Objectives and Decision Variables. The optimization is carried out premised on assurance of steady yields and satisfying quality of the products. Objectives considered for the multiobjective optimization for the current study are as follows: case a, maximization of propylene product purity and minimization of utility cost; case b, maximization of ethylene product purity and minimization of utility cost; and case c, maximization of propylene product purity, maximization of ethylene product purity, and minimization of utility cost. For the distillation columns, reflux ratio and position of the feeding tray are often the manipulated variables that affect the column performance. In this study, the reflux ratio of the columns and the position of feeding tray for DB are selected as decision variables. Bounds are set for the reflux ratios to avoid flooding or dry trays in the columns, which are listed in Table 5. Product specifications for propylene and ethylene are set to be no lower than 99.6% and 99.9%, respectively. The optimization model is formulated as follows Table 5. Type and Feasible Region of the Decision Variables operation parameter

type

N (DB feeding tray)

*      

R1 R2 R3 R4 R5 R6

(DB reflux ratio) (DP reflux ratio) (DE reflux ratio) (C3 reflux ratio) (DM reflux ratio) (C2 reflux ratio)

lower bound 5 0.90 1.50 0.89 13.40 2.00 3.87

upper bound 53 1.50 2.00 1.00 15.40 2.50 4.84 12172


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Figure 6. (a) Optimal-Pareto front for maximization of propylene purity and minimization of utility cost and (b)−(h) optimal values of the considered decision variables corresponding to the Pareto-optimal front.

Case b: Maximization of Ethylene Purity and Minimization of Utility Cost. In this case, ethylene purity is maximized and utility cost is minimized. Noted that utility cost is calculated on an hourly basis. The same as propylene,

efficiency between C3− (light hydrocarbon up to C3) and C4, leading to a higher propylene and ethylene content in the DP’s overheads, which further affects the specification of the products. 12173


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Figure 7. (a), Optimal-Pareto front for maximization of ethylene purity and minimization of utility cost and (b)−(h) optimal values of the considered decision variables corresponding to the Pareto-optimal front.

replaced by its reflux flow rate. The lower and upper bounds of

ethylene is an important byproduct of the MTP product separation process, and it is directly fed to the following polymerization unit. Considered decision variables are the same as listed in Table 5, except that the reflux ratio of DP is

the reflux flow rate for DP is 3800 and 4800 kmol/h, respectively. 12174


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Figure 8. (a) Optimal-Pareto front for maximization of propylene purity and ethylene purity and minimization of utility cost and (b)−(h) optimal values of the considered decision variables corresponding to the Pareto-optimal front.

Thirty optimal results are obtained by NSGA-II, which is shown in Figure 7(a). Correlation between ethylene purity and the system utility cost shows similar characteristic as in the previous case. The optimal solutions on the first half of the

front, namely solutions before the point (6268, 0.99919), represent a relatively notable increase in ethylene purity, compared to the solutions on the second half of the front. As we move from the left most point to the identified point, 12175


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Figure 9. (a) Optimal solutions for the process operates at the start of run (when the system DME concentration is very low) and (b) optimal solutions for the process approaching the end of run (when the system DME concentration is relatively high).

frontier of the covered area, along with the improvement in ethylene purity, utility cost grows slowly at the beginning and then grows steeply. The same pattern applies for the changes in propylene purity, which is consistent with the conclusion drawn from the previous two cases. A collection of appealing operation solutions with reasonable utility costs (6300 to 6350 $/h) and relatively high purity of both the products is highlighted by an oval dotted line. When lower utility cost is preferred, the optimal solutions distributed in the left bottom area are preferred. In this case, operation with the lowest utility cost is 6199 $/h with the feedstock entering DB from the 11th theoretical tray, and the corresponding reflux ratios for DB, DP, DE, C3 separator, DM, and C2 separator are 0.900, 1.574, 0.906, 13.572, 2.000, and 4.072, respectively. When a slightly higher product purity is inclined, the identified optimal solutions appear to be good choices of suggestion, as it corresponds to relatively high purity for both propylene and ethylene with a slight increment in utility cost. The optimal values of the decision variables to the Pareto front are given in Figure 8(b)−(h). As is shown, all the decision variables are distributed within the constraint range.

ethylene purity increases by 0.00015, while with the same amount of increase in utility cost afterward, ethylene purity only increases by 0.00002. From an economic perspective, the preferable solution for practical operation is the one with the lowest utility cost (6097.47, 0.99904). The corresponding optimal values of the decision variables to the Pareto front are given in Figure 7(b)−(h). Case c: Maximization of Propylene Purity, Ethylene Purity, and Minimization of Utility Cost. Figure 8(a) gives the Pareto optimal solutions obtained by NSGA-II for this case. A clear correlation between the three objectives can be concluded from the diamonds and empty circles paired via color coding. As is shown, on the left bottom of the figure, the paired diamonds and circles lay rather closely, which indicates that when the products’ purity are both kept to their lower bounds, the corresponding utility cost can be controlled to the lowest. While on the right side of the figure, the distances between the paired diamonds and circles are much bigger, implying that improvement in the quality of one product can only be realized by decreasing that of the other. Furthermore, it can be seen from the trend depicted by the circles on the left 12176


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Industrial & Engineering Chemistry Research Multiobjective Optimization under Different Operation Conditions. In the previous sections, the product separation process of the MTP production process under the designed operation condition is optimized. However, the MTP process in real practice is not static but rather dynamic due to the declining of the catalyst activity. At the beginning of an operation period when the catalyst is of high activity, the intermediate product DME can be fully converted in the MTP reactor. Thus, the DME concentration in the hydrocarbon streams is very low, which can be assumed to be 0 ppm. When the catalyst is deactivated and requires regeneration, the corresponding DME concentration is at a very high level, approximately 20000 ppm, which is almost 7 times higher than that of the designed operation condition. In order to take such a dynamic factor into consideration, optimization efforts are also carried out for these two operation conditions. The Pareto-optimal solutions obtained for the two scenarios are shown in Figures 9(a) and 9(b), respectively. Different from the case with designed operation condition, high purity of ethylene/propylene can be obtained at a low utility cost at the start of run, which is highlighted by an oval dotted line in Figure 9(a). When the process approaches the end of run, maintaining product quality is realized at the price of increasing the utility consumption. It can be concluded by comparing the results of the two cases that, during the later stage of an operation period, to produce products with comparable purity to that of the beginning, the utility cost is likely to increase from around 6225 to 6450 $/h. In this case, low utility cost can be maintained by lowering the requirement for product purity. From an economic perspective, solutions with lower utility costs are more preferable. At the beginning of an operation period, the suggested cost-effective operation parameters are as follows. The feeding tray of DB is the 23th theoretical tray, and the reflux ratios for DB, DP, DE, C3 separator, DM, and C2 separator are 0.929, 1.500, 0.908, 14.767, 2.483, and 4.452, respectively. This corresponds to the utility cost of 6181.05 $/h. While at the end of an operation period, the suggested values for the decision variables for a cost-effective operation are 10, 0.910, 1.500, 0.966, 13.959, 2.113, and 3.970, with the utility cost at 6146.96 $/h.

which the Aspen plus software package is integrated via the Excel-Aspen plus interface for data exchange. Operation optimization of the studied process is then carried out for two cases of two objectives (propylene/ethylene purity and utility cost) and three cases of three objectives (propylene purity, ethylene purity, and utility cost) under different operation conditions. The Pareto-optimal solutions for maximizing propylene purity and minimizing utility cost suggest that propylene purity can be notably improved over the range (0.99607, 0.99723) at relatively low utility cost. While for the ethylene product, the cost-efficient improvement for the purity occurs over the range of (0.99904, 0.99919). The Paretooptimal fronts for maximizing propylene and ethylene purity and minimizing utility cost under different operation conditions showed similar trends. The best operating point can be identified from the Pareto-optimal solutions, based on different decision-making inclinations. The proposed simulation and optimization approach can be applied to other schemes of product separation processes.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.9b02033. Design of algorithm: detailed description of steps of implementing NSGA-II algorithm to solve multiobjective optimization problems formulated in this study (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Zuwei Liao: 0000-0001-9063-1049 Jingdai Wang: 0000-0001-8594-4286 Yongrong Yang: 0000-0002-5598-6925 Yagu Dang: 0000-0003-1715-3153 Notes

The authors declare no competing financial interest.

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7. CONCLUSIONS The product composition of an MTP reaction is rather complicated, which consists of hydrocarbons ranging from C1 to C10 and oxygenated byproduct DME. The boiling point of DME is close to that of the main product propylene, leading to the formation of azeotrope in this system. Extractive distillation is thus employed for DME removal. Additionally, the DME concentration varies with the activity of the catalyst. As a result, the complexity of the MTP product separation is much higher than a general separation process in the petrochemical processes, and it is more energy-intensive. In this work, the gas separation process of an MTP plant is simulated using the Aspen plus software package. The simulation model is validated based on the design data of a real MTP plant. Based on the model, an alternative operation of the extractive distillation process for DME removal is proposed, which can reduce the system energy consumption remarkably. Multiobjective optimization models are formulated with the objectives being the products (propylene and ethylene) purity and the system utility cost. The nondominated sorting algorithm (NSGA-II) is applied to solve the multiobjective optimization problem. It is implemented in MATLAB, through

ACKNOWLEDGMENTS The financial support from the project of National Natural Science Foundation of China (21822809 and 61590925), the National Science Fund for Distinguished Young Scholars (21525627), and the Fundamental Research Funds for the Central Universities (YJ201838) are gratefully acknowledged.

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REFERENCES

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Simulation-Based Multiobjective Optimization of the Product

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