A multi-stage membrane separation optimization design method for enumerating separation sequences

Abstract

The application discloses a kind of multistage membrane separation optimization design methods of enumeration separation sequence, comprising the following steps: S1, draw the superstructure diagram of multistage membrane separation, then establish integer programming model to it;S2, add enumeration method in the integer programming model of step S1, calculate all the multistage membrane separation sequence meeting model constraint;S3, the separation sequence obtained in step S2 is substituted into membrane separation process model one by one;S4, finally calculate and obtain the separation sequence meeting separation target, output optimal solution.The application uses the above-mentioned multistage membrane separation optimization design method of enumeration separation sequence, optimizes multistage membrane separation technology with intelligent enumeration method, divides step by step simplification of mixed integer programming (MINLP) model to optimize the scheme of multistage membrane separation method for purification and capture of post-combustion CO2, split the superstructure model of membrane separation and the membrane separation process model, to simplify the model, shorten the purpose of solving time, and then reduce the difficulty of existing model solution, optimize membrane separation technology.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of gas membrane separation, and particularly relates to a multi-stage membrane separation optimization design method of enumeration separation sequence. BACKGROUND

[0002] Global warming is one of the important challenges faced by human society, and responding to climate change has become a global consensus. More and more scientific researches show that the increase of CO2 concentration in the atmosphere is the main cause of global warming, glacier melting, species reduction and other environmental problems, which seriously affects the sustainable development of human civilization. At present, the commonly used CO2 separation technologies mainly include chemical absorption method, physical adsorption method, low-temperature separation method and membrane separation method. Among them, the membrane separation method mainly utilizes the difference in permeation rate of different gases through the separation membrane to separate the gases. The gas with high permeation rate is enriched on the permeation side, and the gas with low permeation rate is enriched on the retention side, so as to achieve the purpose of separating each component. The membrane separation has the advantages of low energy consumption, no pollution and simple operation, and has broad application prospect.

[0003] For the multi-stage membrane separation system for separating multi-component gas mixture, due to the large number of feasible separation structures and the complexity of multi-component membrane separation problem. Most studies have proposed mixed integer nonlinear programming (MINLP) model to solve the multi-component gas mixture multi-stage membrane separation problem, but because the MINLP model itself is difficult to solve, and the complexity of multi-component permeation separation makes the model calculation amount very large. Therefore, an enumeration separation sequence multi-stage membrane separation optimization design method is urgently needed. SUMMARY

[0004] The purpose of the application is to provide an enumeration separation sequence multi-stage membrane separation optimization design method, which optimizes multi-stage membrane separation technology by intelligent enumeration method, simplifies the mixed integer programming (MINLP) model step by step, optimizes the multi-stage membrane separation method for purifying and capturing CO2 after combustion, splits the superstructure model and the membrane separation process model of membrane separation, so as to achieve the purpose of simplifying the model and shortening the solving time, and further reduce the solving difficulty of the existing model and optimize the membrane separation technology.

[0005] To achieve the above purpose, the application provides an enumeration separation sequence multi-stage membrane separation optimization design method, which comprises the following steps:

[0006] S1, a superstructure diagram of multi-stage membrane separation is drawn, and an integer programming model is established thereon;

[0007] S2, the enumeration method is added to the integer programming model of step S1, and all multi-stage membrane separation sequences meeting the model constraints are calculated;

[0008] S3, the separation sequence obtained in step S2 is substituted into the membrane separation process model one by one;

[0009] S4, the separation sequence meeting the separation target is finally calculated to obtain an optimal solution.

[0010] Preferably, in step S1, a binary variable Z representing whether the n-stage membrane exists and a binary variable W representing whether the stream exists are obtained;

[0011]

[0012]

[0013] wherein RP represents the stream flowing out as the retentate product stream; PP represents the stream flowing out as the permeate product stream; RS represents the stream flowing to other membranes on the retentate side; PS represents the stream flowing to other membranes on the permeate side; n, n' represent the n-stage membrane to the n' stage membrane.

[0014] Preferably, the basic framework of the constraints constituting the superstructure is,

[0015]

[0016] Preferably, the constraints make the multi-stage membrane always in a series state and avoid the retentate side and the permeate side stream flowing to the same stage membrane to remove unreasonable structures and narrow the enumeration range; the constraints are specifically,

[0017] Z n ≥Z n+1 n∈N\{|N|}

[0018]

[0019] Preferably, in step S2, the integer programming model is added with the enumeration method, and the specific constraints are,

[0020]

[0021] wherein y represents the five binary variables in step one; Y 1 represents the set of binary variables taking 1; Y 0 represents the set of binary variables taking 0.

[0022] Preferably, in step S3, the membrane separation process model has the specific constraints,

[0023]

[0024] wherein, represents the average pressure of component i on the feed side and the retentate side in the n-stage membrane; J i,n represents the permeation flux of component i in the n-stage membrane; πi represents the permeation coefficient of component i in the separation membrane; represents the feed flow rate, the retentate flow rate, and the permeate flow rate of the nth stage membrane, respectively.

[0025] Preferably, the objective function is,

[0026]

[0027] where F fc represents the fixed capital cost, f mh / f cp / f cc / f wk / f mr / f mt / f sg / f hv / t m / t wk represents the price of the unit area membrane, the price of the compressor, the annual capital expenditure ratio, the operating capital ratio, the membrane replacement cost, the maintenance rate, the initial stream unit price, the total heating value of the fuel gas, the working life, and the working days per year, respectively; η represents the compressor efficiency. represents the work of the compressor, RF represents the initial feed flow rate, and R i represents the product flow rate in the product stream, y i represents the product concentration.

[0028] Therefore, the present application adopts the above-mentioned multi-stage membrane separation optimization design method of enumerating separation sequences, optimizes the multi-stage membrane separation technology by using the intelligent enumeration method, divides the mixed integer programming (MINLP) model step by step to simplify the optimization scheme of the multi-stage membrane separation method for purifying and capturing CO2 after combustion, splits the superstructure model of the membrane separation and the membrane separation process model to achieve the purpose of simplifying the model and shortening the solving time, and further reduces the solving difficulty of the existing model and optimizes the membrane separation technology.

[0029] The technical scheme of the present application will be further described in detail below with reference to the drawings and embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 FIG. 1 is a superstructure diagram of multi-stage membrane separation of step S1 of the embodiment of the multi-stage membrane separation optimization design method of enumerating separation sequences of the present application;

[0031] Figure 2 FIG. 2 is an optimal three-stage membrane separation structure diagram of the embodiment of the multi-stage membrane separation optimization design method of enumerating separation sequences of the present application. DETAILED DESCRIPTION

[0032] The technical scheme of the present application will be further described in detail below with reference to the drawings and embodiments. The technical scheme of the present application will be further described in detail below with reference to the drawings and embodiments.

[0033] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0034] Example 1

[0035] like Figure 1 As shown, a multi-stage membrane separation optimization design method for enumerating separation sequences includes the following steps:

[0036] S1. Draw a superstructure diagram of multi-stage membrane separation and then establish an integer programming model for it.

[0037] Determine the binary variable Z indicating whether the n-stage membrane exists and the binary variable W indicating whether the stream exists.

[0038]

[0039] Where RP represents the stream flowing out as the retentate product. PP represents the stream flowing out as the permeate product. RS represents the stream flowing from the retentate side to other membranes. PS represents the stream flowing from the permeate side to other membranes. n,n' represents the stream from the nth stage membrane to the n'th stage membrane.

[0040] The basic framework of the superstructure is composed of constraints.

[0041]

[0042] Constraints are used to keep multi-stage membranes in series and to prevent the rejection and permeate streams from flowing into the same membrane stage, thereby eliminating unreasonable structures and narrowing the enumeration range. The specific constraints are:

[0043]

[0044] S2. Adding enumeration method to the integer programming model of step S1 to calculate all multi-stage membrane separation sequences that meet the model constraints.

[0045] Add enumeration method to the integer programming model, the specific constraints are:

[0046]

[0047] Where y represents the five binary variables in step 1. 1 represents a set of binary variables that take the value 1. 0 represents the set of binary variables that take the value 0.

[0048] S3. Substitute the separation sequences obtained in step S2 into the membrane separation process model one by one.

[0049] The specific constraints of the membrane separation process model are:

[0050]

[0051] in, represents the average pressure of component i on the feed side and the cutoff side in the nth stage membrane, J i,n represents the permeation flux of component i in the nth-level membrane, π i represents the permeability coefficient of component i in the separation membrane, They represent the feed flow, rejection side flow, and permeate side flow of the nth stage membrane respectively.

[0052] The objective function is,

[0053]

[0054] Among them, F fc represents the fixed capital cost, f mh / f cp / f cc / f wk / f mr / f mt / f sg / f hv / t m / t wk They represent the membrane price per unit area, compressor price, annual capital expenditure ratio, working capital ratio, membrane replacement cost, maintenance ratio, initial stream price, total calorific value of gas, service life, and annual working days. η represents the compressor efficiency. represents the work done by the compressor, RF represents the initial feed flow rate, R i represents the product flow rate in the product stream, y i Indicates the product concentration.

[0055] S4. Finally, the separation sequence that meets the separation target is calculated and the optimal solution is output.

[0056] Example 2

[0057] This embodiment desulfurizes natural gas and reduces the CO2 concentration to 2%.

[0058] The composition is 73% CH4, 19% CO2, 7% C 2+ The model uses a natural gas mixture with 1% H2S and 0.1% H2S to separate CO2 and reduce it to within the specified 2%. The process parameters required for the model are shown in Table 1.

[0059] Table 1 Various process parameters required for the model

[0060]

[0061]

[0062] The specific implementation steps of this embodiment are:

[0063] S1. First, draw the superstructure diagram of multi-stage membrane separation, and then establish an integer programming model for it.

[0064] S2. Then, an enumeration method is added to the integer programming model of step S1. According to the model calculation, a total of 50 membrane separation sequences that meet the requirements are enumerated in the three-stage membrane separation system.

[0065] S3. Substitute the separation sequence in step S2 into the membrane separation process model one by one. The target equation is as follows:

[0066]

[0067] Among them, F fc represents the fixed capital cost, f mh / f cp / f cc / f wk / f mr / f mt / f sg / f hv / t m / t wk They represent the price of membrane per unit area, compressor price, annual capital expenditure ratio, working capital ratio, membrane replacement cost, maintenance rate, initial stream unit price, total calorific value of gas, working years, and annual working days respectively; η represents the compressor efficiency. Indicates the work done by the compressor, RF indicates the initial feed flow rate, represents the product flow rate in the product stream, y CH4 Indicates the product concentration.

[0068] S4. Finally, the separation sequence that meets the separation target is calculated and the optimal solution is output.

[0069] The optimal structure finally calculated in this embodiment is as follows Figure 2 As shown, the model took 543.78 seconds to solve, and the minimum value of the target equation was calculated to be 7.538$ / 1000m 3 .

[0070] Therefore, the present invention adopts the above-mentioned multi-stage membrane separation optimization design method of enumerating separation sequences, uses the intelligent enumeration method to optimize the multi-stage membrane separation technology, simplifies the mixed integer programming (MINLP) model step by step to optimize the multi-stage membrane separation method for purifying and capturing post-combustion CO2, and splits the superstructure model and membrane separation process model of membrane separation to achieve the purpose of simplifying the model and shortening the solution time, thereby reducing the difficulty of solving the existing model and optimizing the membrane separation technology.

[0071] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A multi-stage membrane separation optimization design method for enumerating separation sequences, characterized in that: The following steps are involved: S1. Draw a superstructure diagram of multi-stage membrane separation and then establish an integer programming model for it; Find the binary variable Z indicating whether the n-stage membrane exists and the binary variable W indicating whether the stream exists; ； Wherein, RP represents the stream flowing out as the retentate product; PP represents the stream flowing out as the permeate product; RS represents the stream flowing to other membranes on the retentate side; PS represents the stream flowing to other membranes on the permeate side; Indicates the transition from the nth level membrane to the Grade membrane; S2, adding an enumeration method to the integer programming model of step S1 to calculate all multi-stage membrane separation sequences that meet the model constraints; Add enumeration method to the integer programming model, the specific constraints are: ； Where y represents the five binary variables in step S1; Y 1 represents a set of binary variables that take the value 1; Y 0 represents the set of binary variables that take the value 0; S3, substituting the separation sequences obtained in step S2 into the membrane separation process model one by one; S4. Finally, the separation sequence that meets the separation target is calculated and the optimal solution is output.

2. The multi-stage membrane separation optimization design method of enumerating separation sequences according to claim 1, characterized in that: The basic framework of the superstructure is composed of constraints. 。 3. The multi-stage membrane separation optimization design method of enumerating separation sequences according to claim 2, characterized in that: Constraints are set to keep the multi-stage membranes in series and to prevent the interception side and permeation side streams from flowing to the same stage of membrane, thereby eliminating unreasonable structures and narrowing the enumeration range. The specific constraints are: 。 4. The multi-stage membrane separation optimization design method of enumerating separation sequences according to claim 1, characterized in that: In step S3, the specific constraints of the membrane separation process model are: ； in, It represents the average pressure of component i on the feed side and the cut-off side in the n-stage membrane; represents the permeation flux of component i in the n-th level membrane; represents the permeability coefficient of component i in the separation membrane; They represent the feed flow, rejection side flow, and permeate side flow of the nth stage membrane respectively.

5. The multi-stage membrane separation optimization design method of enumerating separation sequences according to claim 4, characterized in that: The objective function is, ； in, represents the fixed capital cost, They represent the price of membrane per unit area, compressor price, annual capital expenditure ratio, working capital ratio, membrane replacement cost, maintenance ratio, initial stream unit price, total calorific value of gas, working years, and annual working days respectively; Indicates compressor efficiency; represents the work done by the compressor in the nth stage membrane, RF represents the initial feed flow rate, represents the product flow rate in the product stream, Indicates the product concentration.

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