A global optimization method for splitless heat exchange networks based on structure enumeration algorithm

Abstract

The present invention relates to a global optimization method for a diverter-free heat exchange network based on a structural enumeration algorithm, comprising the following steps: S1 extracting process logistics and utility engineering logistics data; S2 using a hierarchical superstructure to establish a mathematical model for heat exchange network design, and adding a constraint equation for hot and cold process logistics without diversion restrictions in the model; S3 developing a structural enumeration algorithm for global optimization of the diverter-free heat exchange network; S4 optimizing and solving the superstructure mathematical model for the diverter-free heat exchange network design, obtaining the global optimal solution for the diverter-free heat exchange network design, and recording the optimization solution time and the minimized annual total cost; the present invention establishes a mixed integer nonlinear programming model (MINLP) for the diverter-free heat exchange network design, and by adding a structural elimination constraint, eliminates repetitive heat exchange network structures, reduces the number of feasible network structures, narrows the search space for feasible solution design schemes, and improves the optimization solution efficiency of the diverter-free heat exchange network design.

Description

Technical Field

[0001] The invention relates to the field of industrial heat exchange network design, and in particular to a global optimization method for a non-divided heat exchange network based on a structure enumeration algorithm. Background Art

[0002] Heat exchange networks play an important role in the chemical industry process and are an important means to improve energy efficiency. By reasonably matching the cold and hot process logistics, the heat can be fully transferred between the cold and hot logistics, thereby improving the energy efficiency of the industrial process, reducing the consumption of cold and hot utilities, and saving investment costs. It can not only provide strong support for the energy conservation and emission reduction work of chemical plants, but also minimize the operating investment of the entire plant and maximize the operating income.

[0003] Heat exchange network optimization involves complex mixed integer nonlinear programming (MINLP) problems. Its mathematical model is difficult to solve and easy to fall into local optimality due to its non-convexity and nonlinearity. Commonly used heat exchange network design methods include pinch analysis and mathematical programming. The pinch analysis method is easy to operate and practical, but it is highly dependent on the experience of designers. It cannot simultaneously consider energy recovery and equipment investment, and it is often difficult to achieve the optimal solution for network design. The mathematical programming method optimizes the design of the heat exchange network by establishing a mathematical model and using deterministic algorithms and random optimization algorithms. However, deterministic algorithms have problems such as combinatorial explosion, time-consuming solution, and easy to fall into local optimality when solving. The random optimization algorithm is highly dependent on manual experience, usually requires many parameters to be set manually, and cannot guarantee the design quality.

[0004] At present, the optimization methods of non-dividing heat exchange networks mainly include deterministic algorithms and random optimization algorithms. These two methods have the following two obvious defects:

[0005] (1) The mathematical model of the bypass heat exchange network is a complex mixed integer nonlinear programming (MINLP) problem. Directly using a local solver (deterministic algorithm) can only obtain a local optimal solution, while using a global solver (deterministic algorithm) usually has convergence problems and it is difficult to converge to the global optimal solution within a limited time.

[0006] (2) The mathematical model of the non-divided heat exchange network contains many heat transfer constraints. The development of the random optimization algorithm requires the introduction of many penalty functions, which leads to a long optimization time. It is difficult to obtain a high-quality feasible solution within a limited time, and the global optimality of the feasible solution and the design scheme cannot be guaranteed. Summary of the invention

[0007] In view of the defects of the traditional method for optimizing the diverterless heat exchange network, the technical problem to be solved by the present invention is: to optimize and solve the diverterless heat exchange network through a structural enumeration algorithm to obtain the global optimal network design solution.

[0008] In order to solve the above technical problems, the present invention adopts the following technical solution: a global optimization method for a non-dividing heat exchange network based on a structure enumeration algorithm, comprising the following steps:

[0009] S1: Extract process logistics and utility logistics data, including inlet and outlet temperatures, heat capacity flow rate, convective heat transfer film coefficient, and cost parameters of heat exchangers and utilities of hot and cold process logistics and hot and cold utilities;

[0010] S2: A mathematical model for the design of a non-divided heat exchange network is established using a hierarchical superstructure, and exclusion constraints of a repetitive network structure are added to the mathematical model. The mathematical model is a mixed integer nonlinear programming model MINLP;

[0011] The objective function of MINLP is:

[0012]

[0013] Among them, z i,j,k ,zcu i ,zhu j Binary integer variables representing whether there is a heat exchanger between process streams, a cooler at the end of hot streams, and a heater at the end of cold streams; q i,j,k , i , j They represent the heat loads of the heat exchanger between process streams, the end cooler of hot streams and the end heater of cold streams respectively; and Represent the fixed installation cost and area cost of the heat exchanger, An exponential coefficient representing the area cost; and represent the operating cost coefficients of the cooling and heating utilities respectively; Represents the convective heat transfer film coefficients of process hot stream, process cold stream, cooling utility and heating utility respectively; dt i,j,k represents the heat transfer temperature difference between the k-th process stream heat exchangers, dt i,j,k+1 represents the heat transfer temperature difference between the k+1th process stream heat exchangers; dtcu i and dthu j are the heat transfer temperature differences between the hot end of the cooler and the cold end of the heater in the superstructure; and are the inlet temperatures of the heating and cooling utilities, respectively; HP, CP, and ST represent the set of process hot stream, process cold stream, and heat exchange stages, respectively;

[0014] Energy balance constraint equation for hot and cold process logistics:

[0015]

[0016] in, represent the heat capacity flow rates of the process hot stream and the process cold stream respectively; and Represent the inlet temperatures of the process hot stream and process cold stream respectively; and Represent the outlet temperatures of the process hot stream and process cold stream respectively;

[0017] Energy balance constraint equations for hot and cold process logistics at each level of the superstructure:

[0018]

[0019] Among them, t i,k , t i,k+1 denote the temperature of the process heat flow at the kth stage and the k+1th stage, t j,k , t j,k+1 represent the temperatures of the process cold stream at the kth stage and the k+1th stage respectively;

[0020] Energy balance constraint equations for coolers and heaters:

[0021]

[0022] Among them, t i,NOK+1 Indicates the temperature of the process hot stream at the last stage;

[0023] Logical constraint equation of heat exchange unit:

[0024]

[0025] in, and Represent the total heat load of process hot stream and process cold stream respectively;

[0026] Initial temperature of the process stream when it enters the superstructure:

[0027]

[0028]

[0029] Among them, t i,1 Indicates the temperature of the process hot flow at the first stage; t j,NOK+1It indicates the temperature of the process cold stream at the last stage;

[0030] Temperature feasibility constraint equation:

[0031]

[0032]

[0033] The temperature difference constraint equations for the heat exchangers, heaters and coolers between the cold and hot process streams are:

[0034]

[0035] in, They represent the upper limits of the temperature difference between the heat exchanger, cooler and heater between process streams respectively; and are the outlet temperatures of the hot and cold utilities, respectively; is the minimum heat transfer temperature difference;

[0036] No restriction on diversion of hot and cold process logistics:

[0037]

[0038] S3: Develop a structure enumeration algorithm for global optimization of a non-divided heat exchange network. In the structure enumeration algorithm, a mixed integer linear programming model MILP is used to enumerate the heat exchange network structure. Its mathematical model includes equations (2)-(22) and equations (23)-(27):

[0039] MILP sets the objective function to zero:

[0040] Min pbj=0 (23)

[0041] Number of heat exchangers

[0042]

[0043] Add network structure enumeration constraints:

[0044]

[0045] Wherein, Card(STR) refers to the number of heat exchangers in the current splitless heat exchange network structure; the above MILP can be iterated to enumerate the splitless heat exchange network structure, and the value of the binary integer variable corresponding to each splitless heat exchange network structure, i.e., z i,j,k ,zhu j ,zcu i The value of The network structure enumeration constraints in equation (25) are gradually updated and stored in the parameter network structure set STR, and the repetitive splitless heat exchange network structures are eliminated until no feasible solution is obtained by running MILP, thereby obtaining all feasible splitless heat exchange network structures;

[0046] Add constraints to exclude repetitive network structures:

[0047]

[0048] Where NI represents the number of iterations; B j,j,k,n , Bcu i,n and Bhu j,n Respectively represent the storage of integer variables z at the nth iteration in MILP i,j,k ,zcu i Hezhu j The value of; using the constraint formula (27), the integer variables enumerated by MILP are not repeated, and the repetitive non-divided heat exchange network structure is eliminated, where Ω is a constant:

[0049]

[0050] In the structure enumeration algorithm, the nonlinear programming model NLP includes equations (2)-(7), equations (11)-(16), and equations (28)-(35). The objective function is the annual total cost TAC:

[0051]

[0052] Logical constraint equation of heat exchange unit:

[0053]

[0054] The temperature difference constraint equations for the heat exchangers, heaters and coolers between the cold and hot process streams are:

[0055]

[0056] S4: Use the developed structural enumeration algorithm to optimize the design of the heat exchange network, optimize and solve the super-structural mathematical model of the splitless heat exchange network design, obtain the global optimal solution of the splitless heat exchange network design, record the optimization solution time and minimize the total annual cost.

[0057] Compared with the prior art, the present invention has at least the following advantages:

[0058] (1) The present invention establishes a mixed integer nonlinear programming model (MINLP) for the design of a bypass-free heat exchange network. By adding structural elimination constraints, repetitive heat exchange network structures are eliminated, the number of feasible network structures is reduced, and the search space of feasible solution designs is narrowed, thereby improving the optimization solution efficiency.

[0059] (2) The present invention develops a structure enumeration algorithm for the design of a non-divided heat exchange network. By adding structure enumeration constraints, all feasible network structures are obtained. For each heat exchange network with a fixed structure, a commercial solver is used for optimization and solution, and the annual total costs of different network structures are compared to obtain the global optimal solution and design scheme that minimizes the annual total cost, so as to reduce the production cost of the industrial process and achieve the effect of energy saving and consumption reduction.

[0060] (3) Compared with commercial global solvers, the developed algorithm can reduce the optimization solution time of the bypassless heat exchange network design; compared with commercial local solvers, the developed algorithm can obtain the global optimal solution and design scheme with lower annual total cost, ensuring the design quality. The global optimization method of the bypassless heat exchange network based on the structural enumeration algorithm of the invention can solve the problem of high energy cost of the heat exchange network, thereby significantly improving the efficiency and economy of the entire heat exchange network. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a diagram of the hierarchical superstructure model of the heat exchange network.

[0062] Figure 2 This is a diagram of the global optimization method for a non-diverting heat exchange network based on a structural enumeration algorithm.

[0063] Figure 3 is a block diagram of the method of the present invention.

[0064] Figure 4 It is the optimal design solution for the non-divided heat exchange network.

[0065] Figure 5 It is a graph showing the relationship between the number of heat exchangers (NHE) and the minimum objective function total annual cost (TAC). DETAILED DESCRIPTION

[0066] The present invention is described in further detail below.

[0067] See also Figure 1 , Figure 2 , Figure 3 , Figure 4 and Figure 5 , a global optimization method for a non-dividing heat exchange network based on a structure enumeration algorithm, comprising the following steps:

[0068] S1: Extract process logistics and utility logistics data, including inlet and outlet temperatures, heat capacity flow rate, convective heat transfer film coefficient, and cost parameters of heat exchangers and utilities of hot and cold process logistics and hot and cold utilities;

[0069] S2: A mathematical model for the design of a non-divided heat exchange network is established using a hierarchical superstructure, and exclusion constraints of a repetitive network structure are added to the mathematical model. The mathematical model is a mixed integer nonlinear programming model MINLP;

[0070] The objective function of MINLP is:

[0071]

[0072] Among them, z i,j,k ,zcu i ,zhu j Binary integer variables representing whether there is a heat exchanger between process streams, a cooler at the end of hot streams, and a heater at the end of cold streams; q i,j,k , i , j They represent the heat loads of the heat exchanger between process streams, the end cooler of hot streams and the end heater of cold streams respectively; and Represent the fixed installation cost and area cost of the heat exchanger, An exponential coefficient representing the area cost; and represent the operating cost coefficients of the cooling and heating utilities respectively; Represents the convective heat transfer film coefficients of process hot stream, process cold stream, cooling utility and heating utility respectively; dt i,j,k represents the heat transfer temperature difference between the k-th process stream heat exchangers, dt i,j,k+1 represents the heat transfer temperature difference between the k+1th process stream heat exchangers; dtcu i and dthu j are the heat transfer temperature differences between the hot end of the cooler and the cold end of the heater in the superstructure; and are the inlet temperatures of the heating and cooling utilities, respectively; HP, CP, and ST represent the set of process hot stream, process cold stream, and heat exchange stages, respectively;

[0073] Energy balance constraint equation for hot and cold process logistics:

[0074]

[0075] in, represent the heat capacity flow rates of the process hot stream and the process cold stream respectively; and Represent the inlet temperatures of the process hot stream and process cold stream respectively; and Represent the outlet temperatures of the process hot stream and process cold stream respectively;

[0076] Energy balance constraint equations for hot and cold process logistics at each level of the superstructure:

[0077]

[0078]

[0079] Among them, t i,k , t i,k+1 denote the temperature of the process heat flow at the kth stage and the k+1th stage, t j,k , t j,k+1 represent the temperatures of the process cold stream at the kth stage and the k+1th stage respectively;

[0080] Energy balance constraint equations for coolers and heaters:

[0081]

[0082] Among them, t i,NOK+1 Indicates the temperature of the process hot stream at the last stage;

[0083] Logical constraint equation of heat exchange unit:

[0084]

[0085] in, and Represent the total heat load of process hot stream and process cold stream respectively;

[0086] Initial temperature of the process stream when it enters the superstructure:

[0087]

[0088]

[0089] Among them, t i,1 Indicates the temperature of the process hot flow at the first stage; t j,NOK+1 It indicates the temperature of the process cold stream at the last stage;

[0090] Temperature feasibility constraint equation:

[0091]

[0092]

[0093] The temperature difference constraint equations for the heat exchangers, heaters and coolers between the cold and hot process streams are:

[0094]

[0095] in, They represent the upper limits of the temperature difference between the heat exchanger, cooler and heater between process streams respectively; and are the outlet temperatures of the hot and cold utilities, respectively; is the minimum heat transfer temperature difference;

[0096] No restriction on diversion of hot and cold process logistics:

[0097]

[0098] S3: Develop a structure enumeration algorithm for global optimization of a non-divided heat exchange network. In the structure enumeration algorithm, a mixed integer linear programming model MILP is used to enumerate the heat exchange network structure. Its mathematical model includes equations (2)-(22) and equations (23)-(27):

[0099] MILP sets the objective function to zero:

[0100] Min obj=0 (23)

[0101] Number of heat exchangers

[0102]

[0103] Add network structure enumeration constraints:

[0104]

[0105] Wherein, Card(STR) refers to the number of heat exchangers in the current splitless heat exchange network structure; the above MILP can be iterated to enumerate the splitless heat exchange network structure, and the value of the binary integer variable corresponding to each splitless heat exchange network structure, i.e., z i,j,k ,zhu j ,zcu i The value of The network structure enumeration constraints in equation (25) are gradually updated and stored in the parameter network structure set STR, and the repetitive splitless heat exchange network structures are eliminated until no feasible solution is obtained by running MILP, thereby obtaining all feasible splitless heat exchange network structures;

[0106] Add constraints to exclude repetitive network structures:

[0107]

[0108] Where NI represents the number of iterations; B i,j,k,n, bcu i,n and Bhu j,n Respectively represent the storage of integer variables z at the nth iteration in MILP i,j,k ,zcu i Hezhu j The value of; using the constraint formula (27), the integer variables enumerated by MILP are not repeated, and the repetitive non-divided heat exchange network structure is eliminated, where Ω is a constant:

[0109]

[0110] In the structure enumeration algorithm, the nonlinear programming model NLP includes equations (2)-(7), equations (11)-(16), and equations (28)-(35). The objective function is the annual total cost TAC:

[0111]

[0112] Logical constraint equation of heat exchange unit:

[0113]

[0114] The temperature difference constraint equations for the heat exchangers, heaters and coolers between the cold and hot process streams are:

[0115]

[0116] S4: Use the developed structural enumeration algorithm to optimize the design of the heat exchange network, optimize and solve the super-structural mathematical model of the splitless heat exchange network design, obtain the global optimal solution of the splitless heat exchange network design, record the optimization solution time and minimize the total annual cost.

[0117] Embodiment: A global optimization method for a non-dividing heat exchange network based on a structure enumeration algorithm, the specific steps are as follows:

[0118] Step 1 (S1): Extract process logistics and utility logistics data and related cost parameters. The relevant process parameters and physical property data in this case are shown in Table 1. The minimum heat transfer temperature difference is set to 10°C.

[0119] Table 1 Process parameters and physical properties of the stream

[0120]

[0121] Step 2 (S2): In this case, a mathematical model for the design of a split-free heat exchange network is established using a hierarchical superstructure, and the split-free restriction constraint equations for the hot and cold process streams are added to the model. Figure 1 As shown, its mathematical model is a mixed integer nonlinear programming model (MINLP).

[0122] Step 3 (S3): Develop a structure enumeration algorithm for global optimization of the non-dividing heat exchange network. The algorithm block diagram is as follows: Figure 3 As shown, the super-structure mathematical model of the design of the splitless heat exchange network is optimized and solved to obtain the global optimal solution of the splitless heat exchange network design, and the optimization solution time and the minimized annual total cost are recorded. The mixed integer nonlinear programming model (MINLP) in the developed structural enumeration algorithm is divided into a mixed integer linear programming model (MILP) and a nonlinear programming model (NLP).

[0123] Step 4 (S4): Optimizing and solving the super-structure mathematical model of the splitless heat exchange network design using commercial solvers, including global solvers and local solvers, obtaining the optimal design solution, recording the optimization solution time and minimizing the total annual cost.

[0124] The developed structural enumeration algorithm is used to optimize the case and obtain the design scheme of the splitless heat exchange network with the minimum annual total cost of 154,910.9$ / yr. The optimization results are shown in Table 2. The specific design scheme of the splitless heat exchange network is as follows: Figure 4 Compared with the optimization result of the local solver (DICOPT) (TAC = 160,410.9$ / yr), the TAC was reduced by 3.43% and the optimization time was reduced by 39.31%; compared with the optimization result of the global solver (BARON) (TAC = 154,910.9$ / yr), the structure enumeration algorithm was able to obtain the same TAC (154,910.9$ / yr), but the optimization time was reduced by 85.67%.

[0125] Table 2 Optimization results of the case

[0126]

[0127] From nothing Figure 5 It can be seen that for the global optimization of the non-diverting heat exchange network, when the number of heat exchangers NHE is 4, the corresponding minimum annual total cost TAC is 339,039.437$ / yr; when the number of heat exchangers is 5, the corresponding TAC is 155,413.146$ / yr; when the number of heat exchangers is 6, the corresponding TAC is 154,910.9$ / yr; when the number of heat exchangers is 7, the corresponding TAC is 160,410.9645$ / yr. Therefore, after the optimization solution, the relationship between the number of heat exchangers NHE and the annual total cost TAC is compared and analyzed. When the number of heat exchangers for the global optimization of the non-diverting heat exchange network is 6, the optimal annual total cost corresponding to it is the smallest, that is, the optimal number of heat exchangers is 6.

[0128] Finally, the above embodiments are only used to illustrate the technical solutions 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 solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A global optimization method for a non-dividing heat exchange network based on a structure enumeration algorithm, characterized in that All feasible splitterless heat exchange network structures are obtained through structural enumeration; the global solver is used to optimize and solve each splitterless heat exchange network with a fixed structure, and the annual total costs of all network structures are compared, and the global optimal solution with the lowest annual total cost is selected as the best design solution; The specific steps include: S1: Extract process logistics and utility logistics data, including inlet and outlet temperatures, heat capacity flow rate, convective heat transfer film coefficient, and cost parameters of heat exchangers and utilities of hot and cold process logistics and hot and cold utilities; S2: A mathematical model for the design of a non-divided heat exchange network is established using a hierarchical superstructure, and exclusion constraints of a repetitive network structure are added to the mathematical model. The mathematical model is a mixed integer nonlinear programming model MINLP; The objective function of MINLP is: Among them, z i,j,k ,zcu i ,zhu j Binary integer variables representing whether there is a heat exchanger between process streams, a cooler at the end of hot streams, and a heater at the end of cold streams; q i,j,k , i , j They represent the heat loads of the heat exchanger between process streams, the end cooler of hot streams and the end heater of cold streams respectively; and Represent the fixed installation cost and area cost of the heat exchanger, An exponential coefficient representing the area cost; and represent the operating cost coefficients of the cooling and heating utilities respectively; Represents the convective heat transfer film coefficients of process hot stream, process cold stream, cooling utility and heating utility respectively; dt i,j,k represents the heat transfer temperature difference between the k-th process stream heat exchangers, dt i,j,k+1 represents the heat transfer temperature difference between the k+1th process stream heat exchangers; dtcu i and dthu j are the heat transfer temperature differences between the hot end of the cooler and the cold end of the heater in the superstructure; and are the inlet temperatures of the heating and cooling utilities, respectively; HP, CP, and ST represent the set of process hot stream, process cold stream, and heat exchange stages, respectively; Energy balance constraint equation for hot and cold process logistics: in, represent the heat capacity flow rates of the process hot stream and the process cold stream respectively; and Represent the inlet temperatures of the process hot stream and process cold stream respectively; and Represent the outlet temperatures of the process hot stream and process cold stream respectively; Energy balance constraint equations for hot and cold process logistics at each level of the superstructure: Among them, t i,k , t i,k+1 denote the temperature of the process heat flow at the kth stage and the k+1th stage, t j,k , t j,k+1 represent the temperatures of the process cold stream at the kth stage and the k+1th stage respectively; Energy balance constraint equations for coolers and heaters: Among them, t i,NOK+1 Indicates the temperature of the process hot stream at the last stage; Logical constraint equation of heat exchange unit: in, and Represent the total heat load of process hot stream and process cold stream respectively; Initial temperature of the process stream when it enters the superstructure: Among them, t i,1 Indicates the temperature of the process hot flow at the first stage; t j,NOK+1 It indicates the temperature of the process cold stream at the last stage; Temperature feasibility constraint equation: The temperature difference constraint equations for the heat exchangers, heaters and coolers between the cold and hot process streams are: in, They represent the upper limits of the temperature difference between the heat exchanger, cooler and heater between process streams respectively; and are the outlet temperatures of the hot and cold utilities, respectively; is the minimum heat transfer temperature difference; No restriction on diversion of hot and cold process logistics: S3: Develop a structure enumeration algorithm for global optimization of a non-divided heat exchange network. In the structure enumeration algorithm, a mixed integer linear programming model MILP is used to enumerate the heat exchange network structure. Its mathematical model includes equations (2)-(22) and equations (23)-(27): MILP sets the objective function to zero: Min obj=0 (23) Number of heat exchangers Add network structure enumeration constraints: Wherein, Card(STR) refers to the number of heat exchangers in the current splitless heat exchange network structure; the above MILP can be iterated to enumerate the splitless heat exchange network structure, and the value of the binary integer variable corresponding to each splitless heat exchange network structure, i.e., z i,j,k ,zhu j ,zcu i The value of The network structure enumeration constraints in equation (25) are gradually updated and stored in the parameter network structure set STR, and the repetitive splitless heat exchange network structures are eliminated until no feasible solution is obtained by running MILP, thereby obtaining all feasible splitless heat exchange network structures; Add constraints to exclude repetitive network structures: Where NI represents the number of iterations; B i,j,k,n , Bcu i,n and Bhu j,n Respectively represent the storage of integer variable z at the nth iteration in MILP i,j,k ,zcu i Hezhu j The value of; using the constraint formula (27), the integer variables enumerated by MILP are not repeated, and the repetitive non-divided heat exchange network structure is eliminated, where Ω is a constant: In the structure enumeration algorithm, the nonlinear programming model NLP includes equations (2)-(7), equations (11)-(16), and equations (28)-(35); the objective function is the annual total cost TAC: Logical constraint equation of heat exchange unit: The temperature difference constraint equations for the heat exchangers, heaters and coolers between the cold and hot process streams are: S4: Use the developed structural enumeration algorithm to optimize the design of the heat exchange network, optimize and solve the super-structural mathematical model of the splitless heat exchange network design, obtain the global optimal solution of the splitless heat exchange network design, record the optimization solution time and minimize the total annual cost.

Images