Optimal design method of variable heat capacity heat exchange network considering both economic and environmental impacts

Abstract

The present invention relates to a variable heat capacity heat exchange network optimization design method that takes both economic and environmental impacts into consideration. The method extracts the physical property data of the stream temperature, convective heat transfer film coefficient and variable heat capacity. The genetic algorithm is used to generate a binary variable z indicating whether a stream heat exchanger exists. i,j,k ; Establish a multi-objective optimization model for variable heat capacity heat exchange network that minimizes both annual total cost and environmental impact; Use simple linear weighting method to decompose the model into several single-objective optimization sub-models; Solve the sub-models to obtain the optimal z of each sub-model i,j,k ; The ε-constraint method is used to solve the newly created single-objective optimization problem under different weights to obtain the Pareto frontier solution; the Pareto frontier solution is non-dominated sorted to obtain the final Pareto frontier solution of the model; the TOPSIS method is used to obtain the optimal solution of the model from the final Pareto frontier solution of the model, and the optimal solution is used as the trade-off solution of the variable heat capacity heat exchange network that considers both economic and environmental impacts.

Description

Technical Field

[0001] The invention relates to the field of industrial heat exchange network design, and in particular to a variable heat capacity heat exchange network optimization design method that takes both economic and environmental impacts into consideration. Background Art

[0002] Energy shortage, as one of the major global issues, has attracted increasing attention from industry and academia in recent years. Heat exchange network synthesis (HENS), as an efficient and economical heat recovery system design method, has been deeply studied in the field of chemical engineering. After decades of research and development, HENS methods can be divided into two categories: pinch analysis and mathematical programming. Pinch analysis is a step-by-step design method with simple principles and easy operation, but it is highly dependent on manual experience and it is difficult to obtain the global optimal solution. Mathematical programming is to optimize and solve by establishing a rigorous mathematical model using commercial solvers or developing algorithms, but for large-scale cases, there will be problems such as combinatorial explosion, long solution time, and easy to fall into local optimality. The mathematical model of HENS is a complex mixed integer nonlinear programming (MINLP) problem, especially nonlinearity, nonconvexity and binary variables may cause the solution process to fall into local optimality. These characteristics of HENS make it necessary to develop efficient solution strategies.

[0003] HENS faces challenges such as non-isothermal mixing and variable heat capacity of fluids, and it is also necessary to improve the optimization efficiency of HENS models. In addition, previous HENS research mainly focused on minimizing the total annual cost, usually ignoring the impact of the environment. Considering non-isothermal mixing and variable heat capacity, two shortcomings of current HENS research are summarized: (1) The HENS mathematical model considering variable heat capacity is a very complex MINLP problem. In particular, when considering large-scale non-isothermal mixing heat exchange networks, there are a large number of local optimal solutions. Existing solution algorithms and commercial solvers are difficult to obtain high-quality feasible solutions, and even cannot obtain feasible solutions for large-scale problems. (2) Existing multi-objective optimization methods for heat exchange networks are mainly based on the fact that process logistics have constant heat capacity, but ignore the situation of variable heat capacity encountered in some industrial cases, so they cannot solve the multi-objective optimization problem of variable heat capacity heat exchange networks. Summary of the invention

[0004] In view of the above problems existing in the existing research technology, the technical problem to be solved by the present invention is: how to solve the multi-objective optimization problem of variable heat capacity heat exchange network taking into account both economic and environmental impacts.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solution: a variable heat capacity heat exchange network optimization design method considering both economic and environmental impacts, comprising the following steps:

[0006] S1: Extract physical property data such as flow temperature, convective heat transfer film coefficient and variable heat capacity.

[0007] S2: Genetic algorithm GA is used to generate a binary variable z indicating whether the logistics heat exchanger HE exists i,j,k .

[0008] S3: z generated by S2 i,j,k , a variable heat capacity heat exchange network HEN multi-objective optimization model is established to simultaneously minimize the total annual cost TAC and the environmental impact EI. The variable heat capacity heat exchange network HEN multi-objective optimization model is a mixed integer nonlinear programming MINLP model, which contains the following binary variables: a binary variable zcu indicating whether a cooler exists, and a binary variable zhu indicating whether a heater exists; the variable heat capacity heat exchange network HEN multi-objective optimization model also contains the following objectives: minimizing TAC and minimizing EI; the variable heat capacity heat exchange network HEN multi-objective optimization model also contains the following constraints: variable heat capacity constraints, process logistics energy balance constraints, superstructure energy balance constraints at all levels, utility energy balance constraints, non-isothermal mixing constraints, heat exchange unit logic constraints, heat transfer temperature difference constraints and temperature feasibility constraints.

[0009] S4: Assign parameters to the HEN multi-objective optimization model of the variable heat capacity heat exchange network: the parameters include the minimum heat transfer temperature difference and the HEN superstructure level.

[0010] S5: By setting 6 different weights, the variable heat capacity heat exchange network HEN multi-objective optimization model established in S3 is decomposed into 6 single-objective optimization sub-models A1, A2, A3, A4, A5, and A6 using the linear weighted method.

[0011] S6: Use GA to solve A1, A2, A3, A4, A5, and A6 in turn to obtain the optimal z for each single-objective optimization sub-model. i,j,k .

[0012] S7: Optimal z obtained according to S6 i,j,k , under the 6 different weights defined by S5, EI constraints are added, and only TAC minimization is taken as the goal. 6 new single-objective optimization sub-models B1, B2, B3, B4, B5, and B6 are re-established, and the ε-constraint method is used to solve them. The Pareto frontier solution of each new single-objective optimization sub-model is obtained, where each new single-objective optimization sub-model corresponds one-to-one to the single-objective optimization sub-model.

[0013] S8: Integrate all Pareto front solutions obtained in S7 and perform non-dominated sorting to obtain the final Pareto front solution of the HEN multi-objective optimization model of the variable heat capacity heat exchange network.

[0014] S9: The TOPSIS method is used to obtain the optimal solution of the HEN multi-objective optimization model of the variable heat capacity heat exchange network from the final Pareto front solution obtained in S8, and the optimal solution is used as the trade-off solution of the variable heat capacity heat exchange network that considers both economic efficiency and environmental impact.

[0015] Furthermore, in step S3, minimizing TAC and minimizing EI are achieved through the objective function min(x,y) with the aim of simultaneously minimizing the annual total cost TAC and the environmental impact EI.

[0016]

[0017] In the formula, x and y represent binary variables and continuous variables respectively.

[0018] The calculation formulas of the objective functions TAC and EI are as follows:

[0019]

[0020]

[0021] In the formula, HP, CP, and ST represent the collection of hot flow, cold flow, and superstructure series, respectively; q i,j,k ,qcu i ,qhu j Represent the heat load of HE, cooler and heater respectively; i,j,k ,zcu i ,zhu j Binary variables indicating whether HE, cooler, and heater exist; C f , C a Respectively represent the fixed installation cost and purchase cost of the heat exchanger; C cu , C hu Represent the unit operating cost of the cooler and heater respectively; h i 、h j , hcu i ,hhu j Respectively represent the convective heat transfer film coefficients of hot logistics, cold logistics, cooling utilities, and heating utilities; Tout i 、Tout j Represent the outlet temperature of hot and cold logistics respectively; Tcuin i , Thuin j represent the inlet temperatures of the cooling utility and the heating utility respectively; Represents the heat transfer temperature difference between the hot end and the cold end of HE; dtcu i 、dthu j They represent the heat transfer temperature difference between cooling utilities and heating utilities respectively; β is an economic parameter to measure the size of the above heat transfer unit.

[0022]

[0023] Where, EP ss ,EP cu ,EP hu They are the ecological points of stainless steel, cold utility engineering and hot utility engineering respectively; m i,j,k 、mcu i 、mhu j are the weights of stainless steel in HE, cooler and heater respectively, and they satisfy the following relationship:

[0024] m=Aδρ

[0025] Where A is the heat exchanger area (m 2 ); δ and ρ represent the thickness (m) and density (kg / m 3 ).

[0026] Furthermore, in step S3, the relationship between heat capacity and temperature in the variable heat capacity constraint is:

[0027] Cp=a 0 +a 1 T+a 2 T 2 +a 3 T 3

[0028] In the formula, a 0 、a 1 、a 2 、a 3 is the coefficient of the heat capacity relationship.

[0029] The heat capacity flow rate constraint in the variable heat capacity constraint is as follows:

[0030] F = f(a 0 +a 1 T+α 2 T 2 +a 3 T 3 )

[0031] Where f is the mass flow rate of the material flow.

[0032] Furthermore, in step S3, in the process logistics energy balance constraint, the energy balance constraint of the thermal logistics is:

[0033]

[0034] In the formula, Tin i represents the inlet temperature of the hot flow; f i represents the flow rate of the heat flow; a i,0、a i,1 、a i,2 、a i,3 is the coefficient of the heat capacity relation for heat flow i.

[0035] Among the process logistics energy balance constraints, the energy balance constraint of cold logistics is:

[0036]

[0037] In the formula, Tin j represents the inlet temperature of the cold stream; f j represents the flow rate of cold stream; a j,0 、a j,1 、a j,2 、a j,3 is the heat capacity relationship coefficient of the cold stream j.

[0038] Furthermore, in step S3, in the energy balance constraints at each level of the superstructure, the energy balance constraints at each level of the heat flow are:

[0039]

[0040] Where, T i,k 、T i,k+1 They represent the kth and k+1th stage temperatures of the heat flow respectively.

[0041] Among the energy balance constraints at each level of the superstructure, the heat balance constraints at each level of the cold logistics are:

[0042]

[0043] Where, T j,k 、T j,k+1 They represent the kth and k+1th stage temperatures of the cold logistics respectively.

[0044] Furthermore, in step S3, in the utility energy balance constraint, the energy balance constraint of the cooling utility is:

[0045]

[0046] In the formula, It is the temperature of the hot flow at the last stage of the heat exchange network.

[0047] Among the utility energy balance constraints, the energy balance constraint for heating utilities is:

[0048]

[0049] Where, T j,1 It is the temperature of the cold stream at the first stage in the heat exchange network.

[0050] Furthermore, in step S3, the non-isothermal mixing constraint is:

[0051]

[0052] In the formula, is the temperature of the heat flow at the hot end of the HE; is the temperature of the cold flow at the cold end of the HE; hr i,j,k 、cr i,j,k are the split ratios of hot and cold streams, respectively; Y i,k , Y j,k The parameters that indicate whether the hot and cold streams are split or not, and they satisfy the following constraints:

[0053]

[0054] Furthermore, in step S3, the heat exchange unit logic constraint is:

[0055]

[0056] In the formula, Q i and Q j Represents the total heat load of hot and cold streams respectively.

[0057] Furthermore, in step S3, the temperature feasibility constraint is:

[0058]

[0059] Where, T i,1 is the temperature of the hot stream at the first stage in the heat exchange network; It is the temperature of the cold stream at the last stage of the heat exchange network.

[0060] Further, in step S6, the optimal z is obtained i,j,k The formula is as follows:

[0061]

[0062] In the formula, x ut It is a binary variable that only represents whether the cooler and heater exist, and OBJ is the overall objective function.

[0063] Compared with the prior art, the present invention has at least the following advantages:

[0064] 1) Aiming at the multi-objective optimization problem of HENS, the non-isothermal mixing and variable heat capacity of process streams are considered simultaneously, which is suitable for handling actual industrial cases.

[0065] 2) A variable heat capacity heat exchange network optimization design method that considers both economic and environmental impacts is proposed to help decision makers better balance TAC and EI.

[0066] 3) It can not only provide decision makers with a series of Pareto solutions, but also provide them with trade-off solutions and design plans that take into account both optimal cost and minimal environmental impact. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 Schematic diagram of the superstructure model of the heat exchange network.

[0068] Figure 2 Pareto front solution for the case.

[0069] Figure 3 Provide the optimal network design solution for the case. DETAILED DESCRIPTION

[0070] The present invention is described in further detail below.

[0071] See also Figure 1 , Figure 2 and Figure 3 , a variable heat capacity heat exchange network optimization design method considering both economic and environmental impacts, comprising the following steps:

[0072] S1: Extract physical property data such as flow temperature, convective heat transfer film coefficient and variable heat capacity.

[0073] S2: Genetic algorithm GA is used to generate a binary variable z indicating whether the logistics heat exchanger HE exists i,j,k .

[0074] S3: z generated by S2 i,j,k , a variable heat capacity heat exchange network HEN multi-objective optimization model is established to simultaneously minimize the total annual cost TAC and the environmental impact EI. The variable heat capacity heat exchange network HEN multi-objective optimization model is a mixed integer nonlinear programming MINLP model, which contains the following binary variables: a binary variable zcu indicating whether a cooler exists, and a binary variable zhu indicating whether a heater exists; the variable heat capacity heat exchange network HEN multi-objective optimization model also contains the following objectives: minimizing TAC and minimizing EI; the variable heat capacity heat exchange network HEN multi-objective optimization model also contains the following constraints: variable heat capacity constraints, process logistics energy balance constraints, superstructure energy balance constraints at all levels, utility energy balance constraints, non-isothermal mixing constraints, heat exchange unit logic constraints, heat transfer temperature difference constraints and temperature feasibility constraints.

[0075] S4: Assign parameters to the HEN multi-objective optimization model of the variable heat capacity heat exchange network: the parameters include the minimum heat transfer temperature difference and the HEN superstructure level.

[0076] S5: By setting 6 different weights, the variable heat capacity heat exchange network HEN multi-objective optimization model established in S3 is decomposed into 6 single-objective optimization sub-models A1, A2, A3, A4, A5, and A6 using the linear weighted method.

[0077] S6: Use GA to solve A1, A2, A3, A4, A5, and A6 in turn to obtain the optimal z for each single-objective optimization sub-model. i,j,k .

[0078] S7: Optimal z obtained according to S6 i,j,k , under the 6 different weights defined by S5, EI constraints are added, and only TAC minimization is taken as the goal. 6 new single-objective optimization sub-models B1, B2, B3, B4, B5, and B6 are re-established, and the ε-constraint method is used to solve them. The Pareto frontier solution of each new single-objective optimization sub-model is obtained, where each new single-objective optimization sub-model corresponds one-to-one to the single-objective optimization sub-model.

[0079] S8: Integrate all Pareto front solutions obtained in S7 and perform non-dominated sorting to obtain the final Pareto front solution of the HEN multi-objective optimization model of the variable heat capacity heat exchange network.

[0080] S9: The TOPSIS method is used to obtain the optimal solution of the HEN multi-objective optimization model of the variable heat capacity heat exchange network from the final Pareto front solution obtained in S8, and the optimal solution is used as the trade-off solution of the variable heat capacity heat exchange network that considers both economic efficiency and environmental impact.

[0081] Specifically, in step S3, minimizing TAC and minimizing EI are achieved through the objective function min(x, y) with the aim of simultaneously minimizing the annual total cost TAC and the environmental impact EI.

[0082]

[0083] In the formula, x and y represent binary variables and continuous variables respectively.

[0084] The calculation formulas of the objective functions TAC and EI are as follows:

[0085]

[0086]

[0087] In the formula, HP, CP, and ST represent the collection of hot flow, cold flow, and superstructure series, respectively; q i,j,k ,qcu i ,qhu j Represent the heat load of HE, cooler and heater respectively; i,j,k ,zcui ,zhu j Binary variables indicating whether HE, cooler, and heater exist; C f , C a Respectively represent the fixed installation cost and purchase cost of the heat exchanger; C cu , C hu Represent the unit operating cost of the cooler and heater respectively; h i 、h j , hcu i ,hhu j Respectively represent the convective heat transfer film coefficients of hot logistics, cold logistics, cooling utilities, and heating utilities; Tout i 、Tout j Represent the outlet temperature of hot and cold logistics respectively; Tcuin i , Thuin j represent the inlet temperatures of the cooling utility and the heating utility respectively; Represents the heat transfer temperature difference between the hot end and the cold end of HE; dtcu i 、dthu j They represent the heat transfer temperature difference between cooling utilities and heating utilities respectively; β is an economic parameter to measure the size of the above heat transfer unit.

[0088]

[0089] Where, EP ss ,EP cu ,EP hu They are the ecological points of stainless steel, cold utility engineering and hot utility engineering respectively; m i,j,k 、mcu i 、mhu j are the weights of stainless steel in HE, cooler and heater respectively, and they satisfy the following relationship:

[0090] m=Aδρ

[0091] Where A is the heat exchanger area (m 2 ); δ and ρ represent the thickness (m) and density (kg / m 3 ).

[0092] Specifically, in step S3, the relationship between heat capacity and temperature in the variable heat capacity constraint is:

[0093] Cp=a 0 +a 1 T+a 2 T 2 +a 3 T 3

[0094] In the formula, a 0 、a 1 、a 2 、a 3 is the coefficient of the heat capacity relationship.

[0095] The heat capacity flow rate constraint in the variable heat capacity constraint is as follows:

[0096] F = f(a 0 +a 1 T+a 2 T 2 +a 3 T 3 )

[0097] Where f is the mass flow rate of the material flow.

[0098] Specifically, in step S3, in the process logistics energy balance constraint, the energy balance constraint of the heat logistics is:

[0099]

[0100] In the formula, Tin i represents the inlet temperature of the hot flow; f i represents the flow rate of the heat flow; a i,0 、a i,1 、a i,2 、a i,3 is the coefficient of the heat capacity relation for heat flow i.

[0101] Among the process logistics energy balance constraints, the energy balance constraint of cold logistics is:

[0102]

[0103] In the formula, Tin j represents the inlet temperature of the cold stream; f j represents the flow rate of cold stream; a j,0 、a j,1 、a j,2 、a j,3 is the heat capacity relationship coefficient of the cold stream j.

[0104] Specifically, in step S3, in the energy balance constraints at each level of the superstructure, the energy balance constraints at each level of the heat flow are:

[0105]

[0106] Where, T i,k 、T i,k+1 They represent the kth and k+1th stage temperatures of the heat flow respectively.

[0107] Among the energy balance constraints at each level of the superstructure, the heat balance constraints at each level of the cold logistics are:

[0108]

[0109] Where, T j,k 、T j,k+1 They represent the kth and k+1th stage temperatures of the cold logistics respectively.

[0110] Specifically, in step S3, in the utility energy balance constraint, the energy balance constraint of the cooling utility is:

[0111]

[0112] In the formula, It is the temperature of the hot flow at the last stage of the heat exchange network.

[0113] Among the utility energy balance constraints, the energy balance constraint for heating utilities is:

[0114]

[0115] Where, T j,1 It is the temperature of the cold stream at the first stage in the heat exchange network.

[0116] Specifically, in step S3, the non-isothermal mixing constraint is:

[0117]

[0118]

[0119] In the formula, is the temperature of the heat flow at the hot end of the HE; is the temperature of the cold flow at the cold end of the HE; hr i,j,k 、cr i,j,k are the split ratios of hot and cold streams, respectively; Y i,k , Y j,k The parameters that indicate whether the hot and cold streams are split or not, and they satisfy the following constraints:

[0120]

[0121] Specifically, in step S3, the heat exchange unit logic constraint is:

[0122]

[0123] In the formula, Q i and Q j Represents the total heat load of hot and cold streams respectively.

[0124] Specifically, in step S3, the temperature feasibility constraint is:

[0125]

[0126] Where, T i,1 is the temperature of the hot stream at the first stage in the heat exchange network; It is the temperature of the cold stream at the last stage of the heat exchange network.

[0127] Specifically, in step S6, the optimal z is obtained i,j,k The formula is as follows:

[0128]

[0129] In the formula, x ut It is a binary variable that only represents whether the cooler and heater exist, and OBJ is the overall objective function.

[0130] Specifically, in step S5, the multi-objective optimization problem established in S3 is decomposed into a single-objective problem using the following linear weighting method:

[0131]

[0132] Where ω is the weight, and its values ​​are 0, 0.2, 0.4, 0.6, 0.8 and 1 respectively.

[0133] Specifically, the formula for solving the newly created single-objective optimization submodel using the ε-constraint method in step S7 is as follows:

[0134]

[0135] st min EI j ≤ε j , j = 1, 2, ..., k;

[0136] In the formula, ε j is the parameter constraining EI.

[0137] Embodiment: The specific steps are as follows:

[0138] Step 1: Extract the process parameters, physical property data, economic parameters, and environmental impact values ​​(Eco-points) of the process logistics as shown in Table 1, and the variable heat capacity related parameters as shown in Table 2.

[0139] Table 1 Process parameters, physical properties, environmental impact values ​​and related economic parameters of process logistics

[0140]

[0141] Table 2 Variable heat capacity parameters

[0142]

[0143] Step 2: In this embodiment, GA is used to generate a binary variable z indicating whether the logistics heat exchanger HE exists. i,j,k .

[0144] Step 3, z generated by step 2 i,j,k , a multi-objective optimization model for a variable heat exchange network is established to minimize both the total annual cost and the environmental impact. Examples of superstructure models for heat exchange networks include Figure 1 shown.

[0145] Step 4, assign values ​​to the parameters in the variable heat capacity heat exchange network HEN multi-objective optimization model established in step 3: the minimum heat transfer temperature difference and the HEN superstructure order are set to 1K and 3 respectively.

[0146] Step 5, by setting 6 different weights, the variable heat capacity heat exchange network HEN multi-objective optimization model established in step 3 is decomposed into 6 single-objective optimization sub-models A1, A2, A3, A4, A5, and A6 using a linear weighted method.

[0147] Step 6: Use GA to solve the six single-objective optimization sub-models in step 5 in turn to obtain the optimal z for each sub-model. i ,j, k .

[0148] Step 7, based on the optimal z obtained in step 6 i,j,k , under the 6 different weights defined in step 5, add EI constraints, and only take TAC minimization as the goal, re-establish 6 new single-objective optimization sub-models as B1, B2, B3, B4, B5, B6, and use the ε-constraint method to solve them, and obtain the Pareto frontier solution of each newly created single-objective optimization sub-model, where each new single-objective optimization sub-model corresponds one-to-one to the single-objective optimization sub-model.

[0149] Step 8, integrating all the Pareto front solutions obtained in step 7 and performing non-dominated sorting to obtain the final Pareto front solution of the HEN multi-objective optimization model of the variable heat capacity heat exchange network.

[0150] Step 9, using the TOPSIS method to obtain the optimal solution of the HEN multi-objective optimization model of the variable heat capacity heat exchange network from the final Pareto front solution obtained in S8, and using the optimal solution as the trade-off solution of the variable heat capacity heat exchange network that considers both economic and environmental impacts.

[0151] Step 10: According to the above steps, the model of solving the optimization problem is used to obtain the Pareto frontier of the heat exchange network. Figure 2 As shown in the figure, the trade-off solution that takes both economic and environmental impacts into consideration is as follows: Figure 3As shown in the figure, its TAC is 1,741,193$ / year and EI is 2,286,580$ / year, which is 2.38% lower than the optimal TAC (1,783,727$ / year) reported in the literature, and EI is significantly reduced by 16.44%.

[0152] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A variable heat capacity heat exchange network optimization design method that takes both economic and environmental impacts into consideration, characterized in that: The following steps are involved: S1: Extract the temperature, convective heat transfer film coefficient and heat capacity of the stream; S2: Genetic algorithm GA is used to generate a binary variable z indicating whether the logistics heat exchanger HE exists i,j,k ; S3: z generated by S2 i,j,k , a variable heat capacity heat exchange network HEN multi-objective optimization model is established to minimize the total annual cost TAC and the environmental impact EI at the same time. The variable heat capacity heat exchange network HEN multi-objective optimization model is a mixed integer nonlinear programming MINLP model, which contains the following binary variables: binary variable zcu indicating whether a cooler exists, binary variable zhu indicating whether a heater exists; the variable heat capacity heat exchange network HEN multi-objective optimization model also contains the following objectives: minimizing TAC and minimizing EI; the variable heat capacity heat exchange network HEN multi-objective optimization model also contains the following constraints: variable heat capacity constraints, process logistics energy balance constraints, superstructure energy balance constraints at all levels, public works energy balance constraints, non-isothermal mixing constraints, heat exchange unit logic constraints, heat transfer temperature difference constraints and temperature feasibility constraints; In step S3, minimizing TAC and minimizing EI are achieved by the objective function min(x,y) In the formula, x and y represent binary variables and continuous variables respectively; The calculation formulas of the objective functions TAC and EI are as follows: In the formula, HP, CP, and ST represent the collection of hot flow, cold flow, and superstructure series, respectively; q i,j,k ,qcu i ,qhu j Represent the heat load of HE, cooler and heater respectively; i,j,k ,zcu i ,zhu j Binary variables indicating whether HE, cooler, and heater exist; C f , C a Respectively represent the fixed installation cost and purchase cost of the heat exchanger; C cu , C hu Represent the unit operating cost of the cooler and heater respectively; h i 、h j , hcu i ,hhu j Respectively represent the convective heat transfer film coefficients of hot logistics, cold logistics, cooling utilities, and heating utilities; Tout i 、Tout j Represent the outlet temperature of hot and cold logistics respectively; Tcuin i , Thuin j represent the inlet temperatures of the cooling utility and the heating utility respectively; Represents the heat transfer temperature difference between the hot end and the cold end of HE; dtcu i 、dthu j represent the heat transfer temperature difference between the cooling utility and the heating utility respectively; β is an economic parameter to measure the size of the above heat transfer unit; Where, EP ss ,EP cu ,EP hu They are the ecological points of stainless steel, cold utility engineering and hot utility engineering respectively; m i,j,k 、mcu i 、mhu j are the weights of stainless steel in HE, cooler and heater respectively, and they satisfy the following relationship: m=Aδρ Where A is the heat exchanger area; δ and ρ represent the thickness and density of stainless steel respectively; In step S3, the relationship between heat capacity and temperature in the variable heat capacity constraint is: Cp=a0+a1T+a2T 2 +a3T 3 In the formula, a0, a1, a2, and a3 are coefficients of the heat capacity relationship; The heat capacity flow rate constraint in the variable heat capacity constraint is as follows: F=f(a0+a1T+a2T 2 +a3T 3 ) Where f is the mass flow rate of the logistics; In step S3, in the process logistics energy balance constraint, the energy balance constraint of the heat logistics is: In the formula, Tin i represents the inlet temperature of the hot flow; f i represents the flow rate of the heat flow; a i,0 、a i,1 、a i,2 、a i,3 is the coefficient of the heat capacity relation of heat flow i; Among the process logistics energy balance constraints, the energy balance constraint of cold logistics is: In the formula, Tin j represents the inlet temperature of the cold stream; f j represents the flow rate of cold stream; a j,0 、a j,1 、a j,2 、a j,3 is the coefficient of the heat capacity relation of cold stream j; In step S3, among the energy balance constraints at each level of the superstructure, the energy balance constraints at each level of the heat flow are: Where, T i,k , T i,k+1 represent the kth and k+1th stage temperatures of the heat flow respectively; Among the energy balance constraints at each level of the superstructure, the heat balance constraints at each level of the cold logistics are: Where, T j,k , T j,k+1 represent the kth and k+1th stage temperatures of the cold stream respectively; In step S3, among the utility energy balance constraints, the energy balance constraint of the cooling utility is: In the formula, is the temperature of the hot stream at the last stage of the heat exchange network; Among the utility energy balance constraints, the energy balance constraint for heating utilities is: Where, T j,1 is the temperature of the cold stream at the first stage in the heat exchange network; In step S3, the non-isothermal mixing constraint is: In the formula, is the temperature of the heat flow at the hot end of the HE; is the temperature of the cold flow at the cold end of the HE; hr i,j,k 、cr i,j,k are the split ratios of hot and cold streams, respectively; Y i,k , Y j,k The parameters that indicate whether the hot and cold streams are split or not, and they satisfy the following constraints: In step S3, the heat exchange unit logic constraint is: In the formula, Q i and Q j Represent the total heat load of hot and cold streams respectively; In step S3, the temperature feasibility constraint is: Where, T i,1 is the temperature of the hot stream at the first stage in the heat exchange network; It is the temperature of the cold stream at the last stage of the heat exchange network; S4: Assigning parameters of the HEN multi-objective optimization model for the variable heat capacity heat exchange network: the parameters include the minimum heat transfer temperature difference and the HEN superstructure level; S5: By setting 6 different weights, the variable heat capacity heat exchange network HEN multi-objective optimization model established in S3 is decomposed into 6 single-objective optimization sub-models A1, A2, A3, A4, A5, and A6 using a linear weighted method; S6: Use GA to solve A1, A2, A3, A4, A5, and A6 in turn to obtain the optimal z for each single-objective optimization sub-model. i,j,k ; S7: Optimal z obtained according to S6 i,j,k , under the 6 different weights defined by S5, add EI constraints, and only take TAC minimization as the goal, re-establish 6 new single-objective optimization sub-models B1, B2, B3, B4, B5, B6, and use the ε-constraint method to solve them, and obtain the Pareto frontier solution of each new single-objective optimization sub-model, where each new single-objective optimization sub-model corresponds to the single-objective optimization sub-model one by one; S8: Integrate all Pareto front solutions obtained in S7 and perform non-dominated sorting to obtain the final Pareto front solution of the HEN multi-objective optimization model of the variable heat capacity heat exchange network; S9: The TOPSIS method is used to obtain the optimal solution of the HEN multi-objective optimization model of the variable heat capacity heat exchange network from the final Pareto front solution obtained in S8, and the optimal solution is used as the trade-off solution of the variable heat capacity heat exchange network that considers both economic efficiency and environmental impact.

2. A variable heat capacity heat exchange network optimization design method considering both economic and environmental impacts as claimed in claim 1, characterized in that: In step S6, the optimal z is obtained. i,j,k The formula is as follows: In the formula, x ut Binary variables representing the presence of coolers and heaters, and OBJ is the overall objective function.

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