Method for predicting surface tension of (h 2+n 2) / h 2o system on basis of linear gradient theory and PR equation of state

Abstract

A method for predicting the surface tension of a (H2+N2) / H2O system on the basis of a linear gradient theory and a PR equation of state (PR-EoS). The method comprises the following steps: on the basis of a PR-EoS, determining an energy parameter and a co-volume parameter of each pure gas, and determining a substance parameter and a co-volume parameter of a mixed gas by using a Waals single-fluid mixing rule and a combination rule; by using a Wertheim molecular association theory, determining a Helmholtz free energy density and a balance density of each pure gas; by using a density mixing rule, determining a Helmholtz free energy and a balance density of a (H2+N2) mixed gas having different components; determining an influence parameter of each pure gas by means of a gradient theory; determining an influence parameter of the mixed gas from the influence parameter of each pure gas and an interaction coefficient; simplifying a gradient theory LGT model; and by combining the LGT model and the PR-EoS, obtaining the surface tension of a (H2+N2) / H2O system at different temperatures. The prediction method can accurately predict the surface tension of a mixed gas at different temperatures.

Description

A method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and PR equation of state Technical Field

[0001] The present invention relates to the field of gas-liquid mixing model prediction, and in particular to a method for predicting the surface tension of a (H2+N2) / H2O system based on linear gradient theory and the PR state equation. Background Art

[0002] The behavior of gas-liquid two-phase flows at microscopic interfaces is a current research hotspot, but the role of surface tension in microstructures is often overlooked in current research. Surface tension is a fundamental thermophysical property that is easily overlooked in applications. In microscopic environments, the effects of surface tension on gas-liquid mixtures cannot be ignored. Experimental measurements of surface tension involving water and various gases have been extensively studied, but corresponding surface tension data for ternary systems with different components are still lacking. Therefore, it is necessary to develop predictive models to calculate the surface tension of ternary systems with different components.

[0003] While there are reports on predictive models for the surface tension of gas-liquid systems, these are typically for binary systems with pure gases, often employing a combined gradient theory (GT) and CPA-EoS approach. For ternary gas mixtures, most rely on experimental methods, with few theoretical predictive models.

[0004] Summary of the Invention

[0005] In view of the shortcomings of the prior art, the present invention provides a method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation. The interaction coefficients of pure gases N2 and H2 are fitted by experimental methods, and the interaction coefficients of mixed gases of different components at different temperatures are calculated by the NRTL equation. mixture , which solves the shortcoming that the interaction coefficient of the mixed gas in the ternary system can only be fitted by experiment; PR-EoS is used to solve the material parameters of the pure gas, which can accurately calculate the material parameters of the ternary system mixture; Wertheim molecular association theory is used to solve the Helmholtz free energy and equilibrium density of the pure gas; the density gradient linearization theory is used to simplify the gradient (GT) theory, so that there is no need to solve the complex density distribution equation inherent in the gradient theory; finally, the simplified gradient theory model LGT is used to combine the PR-EoS method to predict the surface tension of the (H2+N2) / H2O system at different temperatures.

[0006] The present invention achieves the above technical objectives through the following technical means.

[0007] A method for predicting the surface tension of a (H2+N2) / H2O system based on linear gradient theory and the PR equation of state comprises the following steps:

[0008] The energy parameters and co-volume parameters of pure gas are determined according to the PR equation of state, and the material parameters and co-volume parameters of mixed gas are determined using Waals single-fluid mixing rule and combination rule.

[0009] The Helmholtz free energy density and equilibrium density of pure gases are determined using Wertheim molecular association theory; the Helmholtz free energy f of (H2+N2) gas mixtures of different components is determined using the density mixing rule. mixture (ρ) and equilibrium density ρ b,mixture ;

[0010] The pure gas influence parameter κ is determined by gradient theory; the pure gas influence parameter and interaction system mixture Determine the influencing parameters of the gas mixture;

[0011] The gradient theory model is simplified to obtain the simplified gradient theory model LGT;

[0012] By combining the LGT model and PR-EoS, the surface tension of the (H2+N2) / H2O system at different temperatures was obtained.

[0013] Furthermore, the energy parameters and the common volume parameters of the pure gas are determined according to the PR state equation, and the material parameters and the common volume parameters of the mixed gas are determined using the Waals single-fluid mixing rule and the combination rule, including the following steps:

[0014] The energy parameter a and the common volume parameter b of the pure gas are determined according to the thermophysical parameters of the pure gas, as follows:

[0015] Where: T c is the critical temperature of pure gas; p c is the critical pressure of pure gas; R is the gas constant; T is the ambient temperature; m is the coefficient related to the eccentricity factor of pure gas;

[0016] The energy parameters of pure nitrogen can be determined by the thermophysical parameters of pure nitrogen obtained from the above formula. and covolume parameter Thermophysical properties of pure hydrogen determine the energy parameters of pure hydrogen and covolume parameter

[0017] The material parameter a of gas mixtures with different components is determined using Waals' single-fluid mixing rule.mixture and the covolume parameter b mixture , where the mixing rules are:

[0018] Among them: mixture is the interaction coefficient of the mixed gas, and the NRTL equation is used to calculate the interaction coefficient l of the mixed gas of different components. mixture ; is the volume fraction of hydrogen in the mixed gas; is the volume fraction of nitrogen in the mixed gas; k mixture is the binary interaction parameter, the binary interaction parameter k of the (H2+N2) gas mixture mixture The definition is as follows:

[0019] Furthermore, the NRTL equation is used to calculate the interaction coefficient l of mixed gases of different components. mixture , as follows:

[0020] The binary interaction coefficient of pure hydrogen was obtained by fitting the experimental data The binary interaction coefficient with pure nitrogen

[0021] The NRTL equation is used to calculate the interaction coefficient l of mixed gases of different components at different temperatures. mixture , the calculation formula is as follows:

[0022] Among them, G1, G2 and G3 are calculation parameters of the empirical correlation formula.

[0023] Furthermore, the Helmholtz free energy density and equilibrium density of the pure gas are determined using Wertheim's molecular association theory, which includes the following steps:

[0024] Determine the pressure factor P as follows:

[0025] Where: ρ is the molar density; g(ρ) is the HDS radial distribution function, and the simplified form of g(ρ) is:

[0026] X A is an important parameter of the association term in the mixture, specifically:

[0027] Where: Self-association molecules Δ is the association strength (self-association) between gas molecules, which is given by the following formula:

[0028] Where ε represents the association energy of pure gas; β represents the association volume of pure gas, and b is the common volume parameter of pure gas. When calculating pure hydrogen, b is When calculating pure nitrogen, b is

[0029] The equilibrium density of a pure gas is ρ b It is obtained from the following formula:

[0030] The Helmholtz free energy f(ρ) of a pure gas is given by:

[0031] Among them, μ s is the chemical potential of pure gas, its value can be found in the table, p0 is the current ambient atmospheric pressure;

[0032] The equilibrium density of pure hydrogen is obtained Equilibrium density of pure nitrogen Helmholtz free energy of pure hydrogen and the Helmholtz free energy of pure nitrogen

[0033] Furthermore, the density mixing rule is used to determine the Helmholtz free energy f of the (H2+N2) gas mixture with different components. mixture (ρ) and equilibrium density ρ b,mixture , specifically:

[0034] Furthermore, the pure gas influence parameter κ is determined by gradient theory, which specifically includes the following steps:

[0035] By fitting the influencing parameters of known pure gases with respect to the function of temperature, a general expression is obtained, which is expressed as follows:

[0036] Among them: coefficient A = f(ω), coefficient B = f(ω 2 ), ω is the eccentricity factor of pure gas; f(ω) and f(ω 2 ) is determined experimentally based on the influencing parameters of specific known pure gases;

[0037] Calculate the influencing parameters of pure hydrogen and pure nitrogen parameters

[0038] Furthermore, the parameters affected by pure gas and interaction system mixture Determine the influencing parameters of the mixed gas as follows:

[0039] Influencing parameters of mixed gas

[0040] Furthermore, the gradient theory model is simplified. Specifically, the density gradient linearization theory is adopted. By assuming that the density of component i in the mixture is linearly distributed between the equilibrium phases, the density distribution equation inherent in the gradient theory is not solved, and the simplified gradient theory model LGT is obtained.

[0041] Furthermore, by combining the LGT model and PR-EoS, the surface tension of the (H2+N2) / H2O system at different temperatures is obtained as follows:

[0042] The simplified gradient theory model LGT is as follows:

[0043] Where: γ is the surface tension coefficient, P s is the equilibrium pressure, ρ is the bulk molar density, superscripts Ⅰ and Ⅱ represent the mixed gas components H2 and N2 respectively, and ρ b Ⅰ is the hydrogen density under the current composition and temperature conditions; is the nitrogen density under the current composition and temperature conditions;

[0044] Based on the density gradient linearization theory, the influencing parameters of the corrected mixed gas are calculated as follows:

[0045] in, is the difference between the density of component H2 and the equilibrium density of the mixed gas; is the difference between the density of component N2 and the equilibrium density of the mixed gas;

[0046] Ω(ρ) is the total thermodynamic potential energy, defined as follows: Ω(ρ) = f mixture (ρ)-ρ b,mixture *μ s,mixture

[0047] where f mixture (ρ) is the Helmholtz free energy of mixing at a reference density of ρ, ρ b,mixture It represents the equilibrium density of the gas mixture.

[0048] A system for predicting the surface tension of a (H2+N2) / H2O system based on the linear gradient theory and the PR equation of state comprises a storage medium; the storage medium stores a program written using the method for predicting the surface tension of a (H2+N2) / H2O system based on the linear gradient theory and the PR equation of state.

[0049] The beneficial effects of the present invention are:

[0050] 1. The method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation described in the present invention can accurately predict the surface tension of the (H2+N2) / H2O system at different temperatures.

[0051] 2. The method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation described in the present invention is to fit the interaction coefficient of pure gases N2 and H2 by experimental methods, and to calculate the interaction coefficient of mixed gases of different components at different temperatures by the NRTL equation. mixture , which solves the shortcoming that the interaction coefficient of the ternary system mixed gas can only be fitted by experiments;

[0052] 3. The method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR equation of state, described in this invention, uses the PR-EoS equation to solve for the material parameters of pure gases. It can accurately calculate the material parameters of binary and ternary mixtures, and simultaneously uses the Wertheim molecular association theory to solve for the Helmholtz free energy and equilibrium density of pure gases.

[0053] 4. The method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR equation of state described in the present invention uses density gradient linearization theory to simplify the gradient (GT) theory, eliminating the need for complex solutions to the density distribution equation inherent in the gradient theory. Furthermore, the LGT-PR-EoS method is used to predict the surface tension of the (H2+N2) / H2O system at different temperatures. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. The drawings described below are some embodiments of the present invention. For ordinary technicians in this field, it is obvious that other drawings can be obtained based on these drawings without paying any creative work.

[0055] FIG1 is a flow chart of a prediction model for the surface tension of a (H2+N2) / H2O system based on the linear gradient theory and the PR equation of state according to the present invention;

[0056] FIG2 is a calculation flow of the PR-EoS method according to the present invention;

[0057] FIG3 is a calculation flow chart of the Wertheim molecular association theory according to the present invention;

[0058] FIG4 is a diagram showing the equilibrium density calculation results of the present invention;

[0059] FIG5 is a flow chart showing the calculation of the influencing parameters of the gradient theory of the present invention;

[0060] FIG6 is a schematic diagram showing the calculation results of the interaction coefficient of the ternary system of the present invention;

[0061] FIG7 is a diagram showing the predicted results of the surface tension of the (H2+N2) / H2O system of the present invention. DETAILED DESCRIPTION

[0062] The following describes embodiments of the present invention in detail, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and are not to be construed as limiting the present invention.

[0063] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "axial", "radial", "vertical", "horizontal", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first" and "second" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "multiple" means two or more, unless otherwise clearly and specifically defined.

[0064] In the present invention, unless otherwise expressly specified or limited, the terms "mounted," "connected," "connect," "fixed," etc. should be understood broadly. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediary; or internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0065] In order to accurately predict the surface tension of the (H2+N2) / H2O system and calculate the interaction coefficient of the ternary system, the method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation described in the present invention, as shown in Figure 1, includes the following steps:

[0066] S01: Determine the energy parameters and co-volume parameters of the pure gas according to the PR state equation, and use the Waals single-fluid mixing rule and combination rule to determine the material parameters and co-volume parameters of the mixed gas, as shown in Figure 2, including the following steps:

[0067] S1.1: Determine the energy parameters of pure hydrogen based on its thermophysical properties and covolume parameter The details are as follows:

[0068] Where: is the critical temperature of pure hydrogen; is the critical pressure of pure hydrogen; R is the gas constant; T is the ambient temperature; is the coefficient related to the eccentricity factor of pure hydrogen,

[0069] S1.2: Determine the energy parameters of pure nitrogen based on its thermophysical properties and covolume parameter The details are as follows:

[0070] Where: is the critical temperature of pure nitrogen; is the critical pressure of pure nitrogen; R is the gas constant, which is 8.314 J / (mol·K); T is the ambient temperature; is the coefficient related to the eccentricity factor of pure nitrogen,

[0071] S1.3: Determine the material parameters a of gas mixtures of different components using Waals' single-fluid mixing rule mixture and the covolume parameter b mixture , where the mixing rules are:

[0072] Among them: mixture is the interaction coefficient of the mixed gas; is the volume fraction of hydrogen in the mixed gas; is the volume fraction of nitrogen in the mixed gas; k mixture is the binary interaction parameter, which is temperature-dependent. The binary interaction parameter k of the (H2+N2) gas mixture is mixture The definition is as follows:

[0073] The interaction coefficient l of mixed gases with different components is calculated using the NRTL equation mixture , as follows:

[0074] The binary interaction coefficient of pure hydrogen was obtained by fitting the experimental data The binary interaction coefficient with pure nitrogen

[0075] The NRTL equation is used to calculate the interaction coefficient l of mixed gases of different components at different temperatures. mixture , the calculation formula is as follows:

[0076] Wherein, G1, G2 and G3 are calculation parameters of the empirical correlation formula. In the embodiment, G1 = 5.75; G2 = 803.6; G3 = 0.3.

[0077] FIG6 is a schematic diagram showing the results of calculating the interaction coefficient of mixed gases using the NRTL equation according to the present invention.

[0078] S02: Determine the Helmholtz free energy density and equilibrium density of pure gases using Wertheim molecular association theory; determine the Helmholtz free energy f of (H2+N2) gas mixtures of different components using the density mixing rule mixture (ρ) and equilibrium density ρ b,mixture , as shown in Figure 3, includes the following steps:

[0079] S2.1: Determine the pressure factor, P, as follows:

[0080] Where: ρ is the molar density; g(ρ) is the HDS radial distribution function, and the simplified form of g(ρ) is:

[0081] X A is an important parameter of the association term in the mixture, specifically:

[0082] Where: Self-association molecules Δ is the association strength (self-association) between gas molecules, which is given by the following formula:

[0083] Where ε represents the association energy of pure gas; β represents the association volume of pure gas, and b is the common volume parameter of pure gas. When calculating pure hydrogen, b is When calculating pure nitrogen, b is

[0084] S2.2: Equilibrium density ρ of pure gas b It is obtained from the following formula:

[0085] The Helmholtz free energy f(ρ) of a pure gas is given by:

[0086] Among them, μ s is the chemical potential of pure gas, its value can be found in the table, p0 is the current ambient atmospheric pressure;

[0087] Therefore, the equilibrium density of pure hydrogen can be calculated as Equilibrium density of pure nitrogen Helmholtz free energy of pure hydrogen and the Helmholtz free energy of pure nitrogen

[0088] S2.3: Helmholtz free energy f for gas mixtures of different components mixture (ρ) and equilibrium density ρ b,mixture , whose value is solved by the density combination rule, specifically:

[0089] As shown in Figure 4, the liquid and gas-liquid densities theoretically calculated in step S02 are compared with the measured liquid and gas-liquid densities, and the calculated values ​​have a small error compared to the measured values. As can be seen from the figure, the simulation results obtained using the calculation method of the present invention can achieve an accuracy of over 98% compared to the experimental results.

[0090] S03: Determine the pure gas influencing parameter κ by gradient theory: By fitting the values ​​of a large number of known pure gas influencing parameters, establish an empirical correlation formula for the pure gas influencing parameters; for the influencing parameters of mixed gases, their values ​​are determined by the pure gas influencing parameters and interaction system mixture The decision is made through joint action; as shown in Figure 5, it includes the following steps:

[0091] S3.1: By fitting the influencing parameters of a large number of known pure gases as a function of temperature, a general expression is obtained. The general expression is as follows:

[0092] Among them: coefficient A = f(ω), coefficient B = f(ω 2 ), ω is the eccentricity factor of pure gas; f(ω) and f(ω 2 ) is determined experimentally based on the influencing parameters of specific known pure gases.

[0093] Therefore, the influence parameters of pure hydrogen can be calculated and pure nitrogen parameters

[0094] S3.2: Parameters affected by pure gases and the interaction coefficient lmixture Determine the influencing parameters of the mixed gas as follows:

[0095] S04: Using density gradient linearization theory By assuming that the density of component i in the mixture is linearly distributed between the equilibrium phases, it is not necessary to solve the density distribution equation inherent in the gradient theory. That is, the GT theory is simplified to obtain the simplified gradient theory model LGT

[0096] S05: Prediction of surface tension:

[0097] By combining the simplified gradient theory model LGT and PR-EoS, the surface tension of the (H2+N2) / H2O system at different temperatures was calculated.

[0098] The simplified gradient theory model LGT is as follows:

[0099] Where: γ is the surface tension coefficient, P s is the equilibrium pressure, ρ is the bulk molar density, superscripts Ⅰ and Ⅱ represent the mixed gas components H2 and N2 respectively, and ρ b Ⅰ is the hydrogen density under the current composition and temperature conditions; is the nitrogen density under the current composition and temperature conditions;

[0100] Based on the density gradient linearization theory, the influencing parameters of the corrected mixed gas are calculated as follows:

[0101] in, is the difference between the density of component H2 and the equilibrium density of the mixed gas; is the difference between the density of component N2 and the equilibrium density of the mixed gas;

[0102] Ω(ρ) is the total thermodynamic potential energy, defined as follows: Ω(ρ) = f mixture (ρ)-ρ b,mixture *μ s,mixture

[0103] where f mixture (ρ) is the Helmholtz free energy of mixing at a reference density of ρ, ρ b,mixture It represents the equilibrium density of the gas mixture.

[0104] FIG7 is a diagram showing the predicted results of the surface tension of the (H2+N2) / H2O system of the present invention.

[0105] The system for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation described in the present invention includes a storage medium; the storage medium stores a program written using the method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation. The storage medium includes a hard disk, a CD-ROM, an optical storage device, a magnetic storage device, or a combination thereof. Those skilled in the art will appreciate that the various features described herein can be implemented by methods, data processing systems, or computer program products. Therefore, these features can be partially implemented in hardware, entirely implemented in software, or implemented in a combination of hardware and software. In addition, the above features can also be implemented in the form of a computer program product stored on one or more computer-readable storage media, the computer-readable storage medium containing computer-readable program code segments or instructions stored in the storage medium. Any commonly used computer-readable storage medium can be used, including a hard disk, a CD-ROM, an optical storage device, a magnetic storage device, and / or a combination of the above devices.

[0106] It should be understood that although this specification is described according to various embodiments, not every embodiment contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

[0107] The series of detailed descriptions listed above are only specific descriptions of feasible embodiments of the present invention. They are not intended to limit the scope of protection of the present invention. Any equivalent embodiments or changes that do not deviate from the technical spirit of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting the surface tension of a (H2+N2) / H2O system based on linear gradient theory and PR state equation, characterized in that: The steps include: The energy parameters and common volume parameters of pure gas are determined according to the PR state equation, and the material parameters and common volume parameters of mixed gas are determined by using Waals single fluid mixing rule and combination rule. The Helmholtz free energy density and equilibrium density of pure gas are determined using Wertheim molecular association theory; the Helmholtz free energy f of (H2+N2) mixed gas with different components is determined using the density mixing rule. mixture (ρ) and equilibrium density ρ b,mixture ; The pure gas influence parameter κ is determined by gradient theory; and interaction system mixture Determine the influencing parameters of the gas mixture; The gradient theory model is simplified to obtain a simplified gradient theory model LGT; By combining the LGT model and PR-EoS, the surface tension of the (H2+N2) / H2O system at different temperatures was obtained.

2. The method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation according to claim 1, characterized in that: The energy parameters and the common volume parameters of the pure gas are determined according to the PR state equation, and the material parameters and the common volume parameters of the mixed gas are determined by using the Waals single fluid mixing rule and the combination rule, including the following steps: The energy parameter a and the common volume parameter b of the pure gas are determined according to the thermophysical parameters of the pure gas, as follows: Where: T c is the critical temperature of pure gas; p c is the critical pressure of pure gas; R is the gas constant; T is the ambient temperature; m is the coefficient related to the eccentricity factor of pure gas; The energy parameters of pure nitrogen can be determined by the thermophysical parameters of pure nitrogen obtained from the above formula. and the covolume parameter Thermophysical parameters of pure hydrogen determine the energy parameters of pure hydrogen and the covolume parameter The material parameter a of gas mixtures with different components is determined using the Waals single fluid mixing rule. mixture and the common volume parameter b mixture , where the mixing rule is: Where: l mixture is the interaction coefficient of the mixed gas, and the NRTL equation is used to calculate the mixed gas of different components. Interaction coefficient l mixture ; is the volume fraction of hydrogen in the mixed gas; is the volume fraction of nitrogen in the mixed gas; k mixture is the binary interaction parameter, and the binary interaction parameter k of the (H2+N2) gas mixture is mixture The definition is as follows:

3. The method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation according to claim 2, characterized in that: The interaction coefficient l of mixed gases with different components is calculated using the NRTL equation mixture , as follows: The binary interaction coefficient of pure hydrogen was obtained by fitting the experimental data The binary interaction coefficient l with pure nitrogen N2 ; The NRTL equation is used to calculate the interaction coefficient l of mixed gases of different components at different temperatures. mixture , the calculation formula is as follows: Among them, G1, G2 and G3 are calculation parameters of the empirical correlation formula.

4. The method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation according to claim 1, characterized in that: The determination of the Helmholtz free energy density and equilibrium density of a pure gas using Wertheim molecular association theory includes the following steps: Determine the pressure factor P as follows: Where: ρ is the molar density; g(ρ) is the HDS radial distribution function, and the simplified form of g(ρ) is: X A is an important parameter of the association term in the mixture, specifically: Where: Self-association molecules Δ is the association strength (self-association) between gas molecules, which is given by the following formula: Where ε represents the association energy of pure gas; β represents the association volume of pure gas, and b is the common volume parameter of pure gas. When calculating pure hydrogen, b is When calculating pure nitrogen, b is The equilibrium density of a pure gas is ρ b It is obtained from the following formula: The Helmholtz free energy f(ρ) of a pure gas is obtained from the following formula: Among them, μ s is the chemical potential of pure gas, its value can be obtained by looking up the table, p0 is the current ambient atmospheric pressure; The equilibrium density of pure hydrogen is Equilibrium density of pure nitrogen Helmholtz free energy of pure hydrogen and the Helmholtz free energy of pure nitrogen 5. The method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation according to claim 4, characterized in that: Determination of the Helmholtz free energy f of (H2+N2) gas mixtures with different components using the density mixing rule mirture (ρ) and equilibrium density ρ b,mixture , specifically:

6. The method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation according to claim 1, characterized in that: The pure gas influence parameter κ is determined by gradient theory, which specifically includes the following steps: By fitting the influencing parameters of known pure gas with respect to temperature, a general expression is obtained, which is expressed as follows: Among them: coefficient A = f(ω), coefficient B = f(ω 2 ), ω is the eccentricity factor of pure gas; f(ω) and f(ω 2 ) is determined experimentally based on the influencing parameters of specific known pure gases; Calculate the influencing parameters of pure hydrogen and pure nitrogen gas 7. The method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation according to claim 6, characterized in that: Parameters affected by pure gas and interaction system mixture Determine the influencing parameters of the mixed gas as follows:

8. The method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation according to claim 1, characterized in that: The gradient theory model is simplified, specifically: the density gradient linearization theory is adopted, and the density of component i in the mixture is assumed to be linearly distributed between equilibrium phases, so that the density distribution equation inherent in the gradient theory is not solved, and the simplified gradient theory model LGT is obtained.

9. The method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation according to claim 1, characterized in that: By combining the LGT model and PR-EoS, the surface tension of the (H2+N2) / H2O system at different temperatures is obtained. The simplified gradient theory model LGT is as follows: Where: γ is the surface tension coefficient, P s is the phase equilibrium pressure, ρ is the bulk molar density, superscripts Ⅰ and Ⅱ represent the mixed gas components H2 and N2 respectively, and is the hydrogen density under the current composition and temperature conditions; is the nitrogen density under the current composition and temperature conditions; Based on the density gradient linearization theory, the influencing parameters of the corrected mixed gas are calculated as follows: in, is the difference between the density of component H2 and the equilibrium density of the mixed gas; is the difference between the density of component N2 and the equilibrium density of the mixed gas; Ω(ρ) is the total thermodynamic potential energy, defined as follows: Ω(ρ)=f mixture (r)-r b,mixture *m s,mixture where f mixture (ρ) is the Helmholtz free energy of mixing at a reference density of ρ, ρ b,mixture It represents the equilibrium density of the gas mixture.

10. A prediction system for the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation, characterized in that: It comprises a storage medium; the storage medium stores a program written using the method for predicting the surface tension of the (H2+N2) / H2O system based on the linear gradient theory and the PR state equation as described in any one of claims 1 to 9.

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