Target gas collection efficiency optimization method based on Robeson upper limit theory

Abstract

The invention provides a target gas collection efficiency optimization method based on a Robeson upper limit theory, belongs to the technical field of gas separation membranes, solves the problem of low target gas collection efficiency of the existing gas separation membrane technology, and comprises the following steps: 1, establishing a mathematical model of a gas mixture, obtaining a relational expression among the permeability coefficient P, the separation factor alpha and the corresponding gas collection efficiency S of different gases; 2, obtaining a membrane material of the target gas with the highest collection efficiency according to the established mathematical model; and 3, performing experimental verification on the membrane material selected in the step 2, and optimizing the established mathematical model according to an experimental result to complete optimization of the target gas collection efficiency. By optimizing the permeability and the separation factor of the gas separation membrane material, the collection efficiency of the target gas is improved, so that the production cost is reduced, and the economic benefit is improved.

Description

Technical Field

[0001] The present invention relates to an optimization method for the collection efficiency of target gas based on Robeson upper bound theory, belonging to the technical field of gas separation membranes. Background Art

[0002] The working principle of gas separation membranes is based on the processes of permeation and diffusion of gas molecules on the membrane. Such membranes are usually made of polymers, inorganic materials or composite materials. Due to differences in factors such as size, shape, and hydrophilicity / hydrophobicity of different gas molecules, different permeation rates will be presented on the separation membrane. When a mixed gas passes through the gas separation membrane under high-pressure drive, gas molecules will enter one side of the membrane through the micropores or porous structure of the membrane, and then pass through the structure of the membrane, and finally be separated into two or more components. The gas with a higher permeation rate will quickly pass through the membrane and be collected on the other side, while the gas with a lower permeation rate will remain on one side of the membrane, achieving gas separation. The separation mechanism of gas separation membranes mainly involves two transport processes: dissolution and diffusion. First, the components in the mixed gas will dissolve on the surface of the membrane. The solubility of different components on the membrane surface is different, resulting in a concentration difference. Then, the gas components will be transferred to the other side at different rates through diffusion in the membrane material. Due to the different diffusion rates of different components, the separation effect is finally achieved. This separation method based on the molecular scale has advantages such as low energy consumption, simple operation, and easy integration compared with traditional methods such as distillation and absorption. With the progress of materials science and the continuous emergence of new high-performance membrane materials, the performance and application scope of gas separation membranes have been significantly improved.

[0003] The Robeson upper bound is an important theoretical benchmark in the field of gas separation membrane performance research, used to describe the trade-off relationship between gas permeability and selectivity of membrane materials. This theory was initially proposed by L.M. Robeson in 1991 through the experimental data analysis of a large number of polymer membranes and was updated in 2008. The core content of the Robeson upper bound is to display the performance of different membrane materials through a double logarithmic coordinate graph, where the upper bound curve limits the performance points of most polymer membranes below an empirical boundary line. This boundary line indicates that gas separation membranes generally face the limitation of the inverse relationship between permeability and selectivity in performance improvement. In specific research, Robeson systematically summarized the performance data of membrane materials in units of gas pairs (such as O2 / N2, H2 / CO2, CO2 / CH4, etc.), and through induction and fitting, proposed the upper bound equations for different gas pairs. This method effectively quantifies the theoretical limits of different gas pairs in separation efficiency and provides a unified standard for the development and performance evaluation of membrane materials. The research on the Robeson upper bound not only has theoretical significance but also promotes the systematic optimization of membrane material performance. In terms of experiments, researchers have explored the key factors affecting permeability and selectivity by regulating the chemical structure, intermolecular interactions, and free volume characteristics of membrane materials. For example, by introducing large side groups or rigid chain segments, the free volume of membrane materials has been increased, thus significantly improving gas permeability; while introducing fluorinated groups or increasing polar groups in membrane materials enhances selectivity. At the same time, methods such as heat treatment, crosslinking, and surface modification have also been widely used to optimize membrane performance and further approach the Robeson upper bound. In recent years, with the development of materials science, the research on the Robeson upper bound has covered a more diverse range of membrane material systems. New polymer materials, metal-organic framework (MOF) composite membranes, and porous polymer membranes have shown superior gas separation performance in experiments. Some MOF composite membranes have achieved efficient screening of gas molecules by regulating pore size and chemical functions, and their performance has approached or even exceeded the traditional Robeson upper bound. In addition, through theoretical modeling and computer simulation, researchers have systematically studied the gas transport behavior of membrane materials at the microscale, further deepening the understanding of the trade-off mechanism between permeability and selectivity. The research on the Robeson upper bound provides a theoretical framework for the performance optimization of gas separation membrane technology and continuously deepens its influence in the field of gas separation by continuously accumulating experimental data and theoretical results. This theory has become an indispensable reference standard for measuring the performance of gas separation membranes and has played an important role in related academic research and industrial applications.

[0004] The Robeson upper bound only studies the relationship between permeability and selectivity and uses this as a criterion for measuring the performance of membrane separation. However, in industrial production, we often need to consider economic efficiency, which is directly related to the amount of target gas collected per unit time. In this regard, there is a lack of relevant theoretical research in the academic community. This study aims to explore the target gas collection efficiency of gas separation membrane technology, that is, the amount of target gas collected per unit time, and proposes an optimization method based on the Robeson upper bound theory. By analyzing the relationship between the permeability coefficient and the separation factor, the present invention establishes a mathematical model for predicting the amount of target gas collected per unit time under specific conditions.

[0005] The working principle of gas separation membranes is based on the process of gas molecules permeating and diffusing through the membrane. These membranes are usually made of polymers, inorganic materials, or composite materials. Due to differences in the size, shape, and hydrophilicity / hydrophobicity of gas molecules, different gas molecules will exhibit different permeation rates and separation effects when passing through the membrane. The Robeson upper bound theory is an important tool for evaluating the performance of gas separation membranes. It plots the performance points of different membrane materials on a double logarithmic coordinate graph and determines an empirical boundary to limit the performance of most polymer membranes. However, there is currently insufficient theoretical research in the academic community on the target gas collection efficiency of gas separation membrane technology. Summary of the Invention

[0006] In order to solve the problem of low target gas collection efficiency of existing gas separation membrane technology, the present invention further proposes an optimization method for target gas collection efficiency based on the Robeson upper bound theory.

[0007] The technical solution adopted by the present invention to solve the above problems is as follows: The present invention includes the following steps:

[0008] Step 1: Establish a mathematical model of the gas mixture to obtain the relationship between the permeability coefficient P, separation factor α, and corresponding gas collection efficiency S of different gases;

[0009] Step 2: Obtain the membrane material with the highest collection efficiency of the target gas according to the established mathematical model;

[0010] Step 3: Conduct experimental verification on the membrane material selected in Step 2 and optimize the established mathematical model according to the experimental results to complete the optimization of the target gas collection efficiency.

[0011] Preferably, Step 1 specifically includes:

[0012] Step 1.1: Set the gas with a high permeability coefficient in the gas mixture as h and the gas with a low permeability coefficient as l;

[0013] Step 1.2: Derive the permeability coefficient P of gas h based on Robeson upper limit theory h and gas permeability coefficient P l , the relationship between the separation factor α and the corresponding gas collection efficiency S;

[0014] Step 1.3: Calculate the derivation result of step 1.2 by mathematical method to obtain the optimal value of the separation factor α when the target gas collection efficiency S reaches the maximum value.

[0015] Preferably, step 1.2 specifically includes:

[0016] Step 1.2.1: Obtain the permeability coefficient P according to Robeson upper limit theory h and the separation factor α;

[0017] Step 1.2.2: Based on the permeability coefficient P h and P l Get the expression of separation factor α;

[0018] Step 1.2.3: Set the volume ratio of gas h and gas l in the mixed gas;

[0019] Step 1.2.4: Calculate the collection efficiency S of the gas l separated per unit time, and combine the expressions of step 1.2.1 and step 1.2.2 to obtain the permeability coefficient P l and the separation factor α;

[0020] Step 1.2.5: Set the permeability coefficient P l Substitute the collection efficiency S of gas l into the relationship between the separation factor α and the permeability coefficient P of gas h. h and gas permeability coefficient P l , the relationship between the separation factor α and the corresponding gas collection efficiency S;

[0021] Permeability coefficient P h The relationship between and separation factor α is:

[0022] P h = kα n * (1);

[0023] In formula (1), α is the separation factor, k is a constant related to the kinetic diameter of gas molecules, which is used to reflect the transport characteristics of gas molecules in the membrane;

[0024] The expression of separation factor α is:

[0025]

[0026] The expression for the volume ratio of gas h to gas l in the mixed gas is:

[0027]

[0028] In formula (3), m is the volume ratio coefficient of the mixed gas;

[0029] The expression for the collection efficiency S of gas l separated per unit time is:

[0030] S = mP h -(1 - m)P l (4);

[0031] The permeability coefficient P l and the relationship with the separation factor α is:

[0032] P l = kα n (5);

[0033] The permeability coefficient P of gas h h and the permeability coefficient P of gas l l 、the separation factor α and the relationship between the corresponding gas collection efficiency S are:

[0034] S = kα n-1 (mα + m - 1) (6).

[0035] Preferably, step 1.3 specifically includes:

[0036] Step 1.3.1: Differentiate the corresponding gas collection efficiency S and set the differential result = 0 to obtain the expression of the separation factor α with respect to the volume ratio coefficients m and n of the mixed gas;

[0037] Step 1.3.2: Obtain the value of n through the Robeson upper limit theory, and on the basis of setting m = 0.5, combine the k value and the activation energy theory to predict and solve the expression obtained in step 1.3.1 to obtain the optimal value of α when S = max(S), where n is the influence of the difference in the kinetic diameters of gas molecules on selectivity;

[0038] The expression for differentiating the corresponding gas collection efficiency S is:

[0039]

[0040] Let The expression of the separation factor α obtained with respect to the volume ratio coefficients m and n of the mixed gas is:

[0041]

[0042] The calculation formula for the optimal value of α is:

[0043]

[0044] In Formulas (9) and (10), d j is the molecular diameter of gas h in the gas pair of the mixed gas, and d i is the molecular diameter of gas l in the gas pair of the mixed gas.

[0045] Preferably, Step 2 specifically includes:

[0046] Step 2.1: According to the target gas pair, select the corresponding membrane material, and measure the permeability coefficient P and separation factor α of the membrane material;

[0047] Step 2.2: Substitute the measured permeability coefficient P and separation factor α into the established mathematical model to calculate the collection efficiency S of the target gas;

[0048] Step 2.3: Replace different membrane materials and compare the collection efficiencies S of the target gas of different membrane materials, and select the membrane material with the highest collection efficiency.

[0049] Preferably, Step 3 specifically includes:

[0050] Step 3.1: Conduct a gas separation experiment on the membrane material selected in Step 2 to verify the accuracy of the optimization of the mathematical model and the permeability coefficient P and separation factor α of the membrane material;

[0051] Step 3.2: Optimize and adjust the mathematical model according to the experimental results to improve the prediction accuracy of the collection efficiency of the target gas.

[0052] The beneficial effects of the present invention are:

[0053] 1. Improve the collection efficiency of the target gas: By optimizing the permeability and separation factor of the gas separation membrane material, the present invention improves the collection efficiency of the target gas, thereby reducing the production cost and improving the economic benefit.

[0054] 2. Broaden the application scope: The method of the present invention can be applied to various gas separation fields, such as natural gas purification, carbon dioxide capture and storage, etc., and has a wide application prospect.

[0055] 3. Promote technological innovation: The proposal and implementation of the present invention will promote the technological innovation and progress of the gas separation membrane technology and provide strong support for the development of related fields. Description of the Drawings

[0056] Figure 1 is a flow chart of an optimization method for the collection efficiency of a target gas based on the Robeson upper bound theory provided by the present invention;

[0057] Figure 2Schematic diagram of the correlation between the gas collection efficiency S and the separation factor α when k = 1,396,000 and n = -5.666 provided by the present invention;

[0058] Figure 3 Schematic diagram of the correlation between the gas collection efficiency S and the separation factor α when k = 5,369,140 and n = -2.636 provided by the present invention. Detailed implementation manners

[0059] Combined with Figures 1-3 to illustrate this implementation manner. As Figure 1 shown, the steps of an optimization method for the target gas collection efficiency based on the Robeson upper bound theory described in this implementation manner include:

[0060] S1: Establish a mathematical model of the gas mixture;

[0061] S101: Set the gas with a high permeability coefficient in the gas mixture as "h" and the gas with a low permeability coefficient as "l";

[0062] S102: Based on the Robeson upper bound theory, derive the relationship between the permeability coefficients P h and P l , the separation factor α, and the target gas collection efficiency S;

[0063] S10201: According to the Robeson upper bound, the following relationship can be obtained:

[0064] P h = kα n * (1);

[0065] In formula (1), k is a constant related to the kinetic diameter of gas molecules, used to reflect the transport characteristics of gas molecules in the membrane, α is the separation factor. At the same time, according to the definition of α, it can be known that:

[0066]

[0067] S10202: Assume that the volume ratio of the two gases in the gas mixture pair is as follows:

[0068]

[0069] In formula (3), m is the volume ratio coefficient of the gas mixture pair;

[0070] The collection efficiency S of l separated per unit time is:

[0071] S = mP h - (1 - m)P l (4);

[0072] According to formulas (1) and (2), it can be obtained that:

[0073] P l = kα n (5);

[0074] Substituting formula (5) into formula (4), it can be obtained that:

[0075] S = kα n- 1(mα + m - 1) (6).

[0076] S103: Through mathematical methods, such as derivation, calculate the derivation result of S102 to obtain the optimal value of the separation factor α when the target gas collection efficiency S reaches the maximum;

[0077] S10301: According to formula (6), when α > 1, S is a concave function with respect to P h To obtain the maximum value of S, take the differential of S:

[0078]

[0079] Let It can be obtained that:

[0080]

[0081] S10302: From the above content, it can be concluded that when k and b are known, the value of α that makes S = max(S) can be obtained according to formula (8), where n can be obtained according to the Robeson upper limit, m is the volume ratio coefficient of the mixed gas pair, and the value of the exponent b is n, which is used to describe the influence of the difference in gas molecular kinetic diameters on selectivity;

[0082] The activation energy theory predicts that the value of -1 / n is related to the gas molecular diameter:

[0083]

[0084] In formula (9), d j is the molecular diameter of gas h in the mixed gas pair, and d i is the molecular diameter of gas l in the mixed gas pair. Particularly, when m = 0.5, it can be obtained that when S = max(S), α is only related to the gas molecular diameter:

[0085]

[0086] S2: Optimize the gas separation membrane material;

[0087] S201: According to the target gas pair, select a suitable membrane material and measure its permeability and separation factor;

[0088] S202: Substitute the measured permeability and separation factor into the mathematical model to calculate the target gas collection efficiency;

[0089] S203: Select the membrane material with the highest collection efficiency by comparing the target gas collection efficiencies of different membrane materials.

[0090] S3: Conduct experimental verification on the selected membrane material, and optimize and adjust the mathematical model according to the experimental results;

[0091] S301: Use the selected membrane material to conduct gas separation experiments to verify the accuracy of the mathematical model and optimization method.

[0092] S302: Optimize and adjust the mathematical model according to the experimental results to improve the prediction accuracy of the target gas collection efficiency.

[0093] Figure 2 The correlation between s(α) and α(O2 / N2) is shown when k = 1,396,000 and n = -5.666. As can be seen from Figure 2 When the separation factor α increases to about 1.18, the collection efficiency S reaches the maximum value of 41,690, which is consistent with the data in the table. Table 1 shows that when m = 0.5, the experimental data points are close to the empirical upper limit of the current O2 / N2 separation. In particular, the Poly[1-phenyl-2-p-(trimethylsilyl)phenylacetylene] polymer exhibits the highest collection efficiency when α is close to 1.18. This indicates that optimizing the separation factor is the key to improving the separation efficiency in the design of gas separation membranes.

[0094] The Robeson upper limit coefficients k = 1,396,000 and n = -5.666 for the gas pair O2 and N2. Substituting them into Equation (6) gives: S = 698000(α - 1)α -6.666 .

[0095] Table 1

[0096]

[0097] Figure 3 The correlation between s*α) and α(CO2 / CH4) is shown when k = 5,369,140 and n = -2.636, as Figure 3As shown, when α increases, S also increases, but the rate of increase gradually slows down, indicating that it is approaching an optimal separation factor; specific experimental data points are provided in Table 2, showing the performance of different polymer materials under this condition. Table 2 shows that when m = 0.5, the experimental data points are close to the empirical upper limit of current CO2 / CH4 separation. Among them, the PTMSP polymer exhibits extremely high collection efficiency, which may be related to its unique chemical structure, emphasizing the influence of material selection on separation efficiency.

[0098] The Robeson upper limit coefficients k = 5,369,140 and n = -2.636 for the gas pair CO2 and CH4. Substituting them into formula (6) gives: S = 2684570(α - 1)α -3.636 。

[0099] Table 2

[0100]

[0101] The above are only the preferred embodiments of the present invention and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments by using the above-disclosed technical content within the scope of the technical solution of the present invention. However, as long as it does not depart from the content of the technical solution of the present invention and is based on the technical essence of the present invention, any simple modification, equivalent replacement, and improvement of the above embodiments still fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for optimizing target gas collection efficiency based on Robeson upper limit theory, characterized in that: The steps of the method for optimizing the target gas collection efficiency based on Robeson upper limit theory include: Step 1: Establish a mathematical model of the gas mixture, obtain the relationship between the permeability coefficient P, separation factor α and the corresponding gas collection efficiency S of different gases; Step 2: Obtain the membrane material with the highest collection efficiency of the target gas according to the established mathematical model; Step 3: Experimentally verify the membrane material selected in step 2 and optimize the established mathematical model based on the experimental results to optimize the target gas collection efficiency.

2. The method for optimizing target gas collection efficiency based on Robeson upper limit theory according to claim 1, characterized in that: Step 1 specifically includes: Step 1.1: Set the gas with high permeability coefficient in the gas mixture as h, and the gas with low permeability coefficient as l; Step 1.2: Derive the permeability coefficient P of gas h based on Robeson upper limit theory h and gas permeability coefficient P l , the relationship between the separation factor α and the corresponding gas collection efficiency S; Step 1.3: Calculate the derivation result of step 1.2 by mathematical method to obtain the optimal value of the separation factor α when the target gas collection efficiency S reaches the maximum value.

3. The method for optimizing target gas collection efficiency based on Robeson upper limit theory according to claim 2, characterized in that: Step 1.2 specifically includes: Step 1.2.1: Obtain the permeability coefficient P according to Robeson upper limit theory h and the separation factor α; Step 1.2.2: Based on the permeability coefficient P h and P l Get the expression of separation factor α; Step 1.2.3: Set the volume ratio of gas h and gas l in the mixed gas; Step 1.2.4: Calculate the collection efficiency S of the gas l separated per unit time, and combine the expressions of step 1.2.1 and step 1.2.2 to obtain the permeability coefficient P l and the separation factor α; Step 1.2.5: Set the permeability coefficient P l Substitute the collection efficiency S of gas l into the relationship between the separation factor α and the permeability coefficient P of gas h. h and gas permeability coefficient P l , the relationship between the separation factor α and the corresponding gas collection efficiency S; Permeability coefficient P h The relationship between and separation factor α is: P h =kα n * (1); In formula (1), α is the separation factor, k is a constant related to the kinetic diameter of gas molecules, which is used to reflect the transport characteristics of gas molecules in the membrane; The expression of separation factor α is: The expression for the volume ratio of gas h and gas l in the mixed gas is: In formula (3), m is the volume ratio coefficient of the mixed gas; The expression of the collection efficiency S of the gas l separated per unit time is: S=mP h -(1-m)P l (4); Permeability coefficient P l The relationship between and separation factor α is: P l =kα n (5); The permeability coefficient P of gas h h and gas permeability coefficient P l , the separation factor α and the corresponding gas collection efficiency S are related as follows: S=ka n-1 (mα+m-1) (6).

4. The method for optimizing target gas collection efficiency based on Robeson upper limit theory according to claim 2, characterized in that: Step 1.3 specifically includes: Step 1.3.1: Differentiate the corresponding gas collection efficiency S and set the differential result = 0 to obtain the expression of the separation factor α with respect to the mixed gas volume ratio coefficients m and n; Step 1.3.2: Obtain the n value through Robeson upper limit theory. On the basis of setting m=0.5, combine the k value and the activation energy theory prediction to solve the expression obtained in step 1.3.1 to obtain the optimal value of α when S=max(S), where n is the effect of the difference in gas molecular kinetic diameter on selectivity; The differential expression corresponding to the gas collection efficiency S is: make The expression of the obtained separation factor α with respect to the mixed gas volume ratio coefficients m and n is: The calculation formula for the optimal value of α is: In formulas (9) and (10), d j is the molecular diameter of the gas h in the mixed gas, d i is the molecular diameter of gas l in the mixed gas.

5. The method for optimizing target gas collection efficiency based on Robeson upper limit theory according to claim 1, characterized in that: Step 2 specifically includes: Step 2.1: According to the target gas pair, select the corresponding membrane material and measure the permeability coefficient P and separation factor α of the membrane material; Step 2.2: Substitute the measured permeability coefficient P and separation factor α into the established mathematical model to calculate the collection efficiency S of the target gas; Step 2.3: Replace different membrane materials and compare the target gas collection efficiency S of different membrane materials, and select the membrane material with the highest collection efficiency.

6. The method for optimizing target gas collection efficiency based on Robeson upper limit theory according to claim 1, characterized in that: Step 3 specifically includes: Step 3.1: Conduct gas separation tests on the membrane material selected in step 2 to verify the accuracy of the mathematical model and the optimization of the permeability coefficient P and separation factor α of the membrane material; Step 3.2: Optimize and adjust the mathematical model based on the experimental results to improve the prediction accuracy of the target gas collection efficiency.

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