A method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state.
Patent Information
- Application Number
- CN202311158102.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-09-08
- Publication Date
- 2026-09-08
- Estimated Expiration
- 2043-09-08
AI Technical Summary
对于三元体系混合气体的情况，大部分采用实验研究的方法，鲜有理论预测模型
[0064] 1. The method for predicting the surface tension of the (H2+N2)/H2O system based on linear gradient theory and PR equation of state described in this invention can accurately predict the surface tension of the (H2+N2)/H2O system at different temperatures.
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Figure CN117191648B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of gas-liquid mixing model prediction, and in particular to a method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state. Background Technology
[0002] The behavior of gas-liquid two-phase flows at microscopic interfaces is currently a hot research topic. However, current research often neglects the role of surface tension in microstructures. Surface tension is a fundamental thermophysical property that is easily overlooked in applications. In microscopic environments, the effect of surface tension on gas-liquid mixtures cannot be ignored. While experimental measurements of surface tension in water and various gases have been extensively studied, corresponding surface tension data for ternary systems with different components are still lacking. Therefore, it is essential to develop predictive models to calculate the surface tension of ternary systems with different components.
[0003] While predictive models for surface tension in gas-liquid systems have been reported, they typically address the case of binary pure gases. For this, a combination of gradient theory (GT) and CPA-EoS models is usually employed. For ternary gas mixtures, most studies rely on experimental methods, with few theoretical predictive models available. Summary of the Invention
[0004] To address the shortcomings of existing technologies, this invention provides a method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state. The method experimentally fits the interaction coefficients of pure gases N2 and H2, and calculates the interaction coefficients l of different component mixtures at different temperatures using the NRTL equation. mixture This method overcomes the limitation that the interaction coefficients of ternary gas mixtures can only be fitted experimentally; it uses PR-EoS to solve for the material parameters of pure gases, enabling accurate calculation of the material parameters of ternary mixtures; it uses Wertheim molecular association theory to solve for the Helmholtz free energy and equilibrium density of pure gases; it uses density gradient linearization theory to simplify the gradient (GT) theory, thus eliminating the need for complex solutions to the inherent density distribution equations in the gradient theory; and finally, it uses the simplified gradient theory model LGT in conjunction with the PR-EoS method to predict the surface tension of the (H2+N2) / H2O system at different temperatures.
[0005] The present invention achieves the above-mentioned technical objectives through the following technical means.
[0006] A method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state includes the following steps:
[0007] The energy parameters and co-volume parameters of the pure gas are determined based on the PR equation of state, and the material parameters and co-volume parameters of the mixed gas are determined using the Waals single-fluid mixing rule and the combination rule.
[0008] The Helmholtz free energy density and equilibrium density of a pure gas were determined using Wertheim's molecular association theory; the Helmholtz free energy f of a (H2+N2) gas mixture with different components was determined using the density mixing rule. mixture (ρ) and equilibrium density ρ b,mixture ;
[0009] The influence parameter κ of pure gas was determined using gradient theory; the influence parameter of pure gas was then used to determine the influence parameter. and interaction system l mixture Determine the parameters affecting the mixed gas;
[0010] The gradient theory model is simplified to obtain the simplified gradient theory model LGT.
[0011] By combining the LGT model and PR-EoS, the surface tension of the (H2+N2) / H2O system at different temperatures was obtained.
[0012] Furthermore, the energy parameters and co-volume parameters of the pure gas are determined according to the PR equation of state, and the material parameters and co-volume parameters of the mixed gas are determined using Waals' single-fluid mixing rule and combination rule, including the following steps:
[0013] The energy parameter 'a' and the co-volume parameter 'b' of the pure gas are determined based on its thermophysical properties, as follows:
[0014]
[0015]
[0016]
[0017] In the formula: T c p is the critical temperature of a pure gas. c R is the critical pressure of the pure gas; T is the ambient temperature; m is a coefficient related to the eccentricity factor of the pure gas.
[0018] The energy parameters of pure nitrogen can be determined from the thermophysical properties obtained from the above formula. and co-volume parameters The thermophysical properties of pure hydrogen determine its energy parameters. and co-volume parameters
[0019] The material parameters a of gas mixtures with different components were determined using Waals' one-fluid mixing rule.mixture and co-volume parameter b mixture The mixing rules are as follows:
[0020]
[0021] Where: l mixture The interaction coefficients of the gas mixtures are calculated using the NRTL equations, where l represents the interaction coefficients of different component gas mixtures. mixture ; This represents the volume fraction of hydrogen in the gas mixture. k represents the volume fraction of nitrogen in the gas mixture. mixture Let k be the binary interaction parameter for the (H2+N2) gas mixture. mixtyre The definition is as follows:
[0022] Furthermore, the interaction coefficients l of different component gas mixtures were calculated using the NRTL equation. mixture The details are as follows:
[0023] The binary interaction coefficient of pure hydrogen gas was obtained by fitting experimental data. The binary interaction coefficient with pure nitrogen gas
[0024] The interaction coefficients l of different component gas mixtures at different temperatures were calculated using the NRTL equation. mixture The calculation formula is as follows:
[0025]
[0026] Among them, G1, G2 and G3 are the calculation parameters of the empirical correlation formula.
[0027] Furthermore, the Helmholtz free energy density and equilibrium density of a pure gas were determined using Wertheim's molecular association theory, including the following steps:
[0028] The pressure factor P is determined as follows:
[0029]
[0030] Where: ρ is the molar density; g(ρ) is the radial distribution function of HDS, and the simplified form of g(ρ) is:
[0031]
[0032] X A Important parameters for association terms in mixtures, specifically:
[0033]
[0034] In the formula: Δ, representing the association strength (self-association) between gas molecules, is given by the following formula:
[0035]
[0036] Where ε represents the association energy of the pure gas; β represents the association volume of the pure gas; and b is the co-volume parameter of the pure gas. When calculating pure hydrogen, b is... When calculating pure nitrogen gas, b is...
[0037] The equilibrium density ρ of a pure gas b We obtain it from the following formula:
[0038] The Helmholtz free energy f(ρ) of a pure gas is obtained by the following equation:
[0039] Where, μ s p0 is the chemical potential of a pure gas, the value of which can be obtained from a table, and p0 is the current ambient atmospheric pressure.
[0040] The equilibrium density of pure hydrogen gas was obtained. equilibrium density of pure nitrogen Helmholtz free energy of pure hydrogen Helmholtz free energy of pure nitrogen
[0041] Furthermore, the Helmholtz free energy f of (H2+N2) gas mixtures with different components was determined using the density mixing rule. mixture (ρ) and equilibrium density ρ b,mixture Specifically:
[0042]
[0043]
[0044] Furthermore, the influence parameter κ of pure gas is determined using gradient theory, specifically including the following steps:
[0045] By fitting a function of temperature to the influence parameters of a known pure gas, a general expression is obtained, which is expressed as follows:
[0046]
[0047] Where: coefficient A = f(ω), coefficient B = f(ω) 2 ), where ω is the eccentricity factor for a pure gas; f(ω) and f(ω) 2 The influence parameters of a specific known pure gas are determined experimentally.
[0048] The influence parameters of pure hydrogen were calculated. Influence parameters of pure nitrogen
[0049] Furthermore, the parameters affected by pure gas and interaction system l mixture The parameters affecting the gas mixture are determined as follows:
[0050] Influence parameters of mixed gas
[0051] Furthermore, the gradient theory model is simplified by adopting the density gradient linearization theory. By assuming that the density of component i in the mixture is linearly distributed between equilibrium phases, the inherent density distribution equation in the gradient theory is not solved, thus obtaining the simplified gradient theory model LGT.
[0052] Furthermore, by combining the LGT model and PR-EoS, the surface tension of the (H2+N2) / H2O system at different temperatures was obtained, as follows:
[0053] The simplified gradient theory model LGT is as follows:
[0054]
[0055] Where: γ is the surface tension coefficient, P s It is the pressure at phase equilibrium, ρ is the bulk molar density, and the superscripts I and II represent the mixed gas components H2 and N2, respectively. This represents the hydrogen density under the current composition and temperature conditions. This represents the nitrogen density under the current composition and temperature conditions.
[0056] Based on the density gradient linearization theory, the corrected influence parameters of the mixed gas are calculated as follows:
[0057]
[0058] in, This is the difference between the density of component H2 and the equilibrium density of the mixed gas; This is the difference between the density of component N2 and the equilibrium density of the mixed gas;
[0059] Ω(ρ) is the total thermodynamic potential energy, defined as follows:
[0060] Ω(ρ)=f mixture (ρ)-ρ b,mixture *μ s,mixture
[0061] Where f mixture(ρ) is the Helmholtz free energy of the mixture at a reference density of ρ, where ρ b,mixture This represents the equilibrium density of the gas mixture.
[0062] A system for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state includes a storage medium; the storage medium stores a program written using the aforementioned method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state.
[0063] The beneficial effects of this invention are as follows:
[0064] 1. The method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and PR equation of state described in this invention can accurately predict the surface tension of the (H2+N2) / H2O system at different temperatures.
[0065] 2. The method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state described in this invention uses experimental methods to fit the interaction coefficients of pure gases N2 and H2, and calculates the interaction coefficients l of different component gas mixtures at different temperatures using the NRTL equation. mixture This solves the problem that the interaction coefficients of ternary gas mixtures can only be fitted experimentally;
[0066] 3. The method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and PR equation of state described in this invention uses PR-EoS to solve for the material parameters of pure gases, which can accurately calculate the material parameters of binary and ternary mixtures. At the same time, Wertheim molecular association theory is used to solve for the Helmholtz free energy and equilibrium density of pure gases.
[0067] 4. The method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and PR equation of state described in this invention simplifies the gradient (GT) theory by using density gradient linearization theory, thus eliminating the need for complex solutions to the inherent density distribution equation in the gradient theory; and uses the LGT combined with PR-EoS method to predict the surface tension of the (H2+N2) / H2O system at different temperatures. Attached Figure Description
[0068] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. The drawings described below are some embodiments of the present invention. For those skilled in the art, it is obvious that other drawings can be obtained from these drawings without creative effort.
[0069] Figure 1 This is a flowchart of the prediction model for the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state as described in this invention.
[0070] Figure 2 The calculation process of the PR-EoS method described in this invention;
[0071] Figure 3 This is the calculation process of the Wertheim molecular association theory described in this invention;
[0072] Figure 4 This is a graph showing the calculated equilibrium density results of this invention;
[0073] Figure 5 This is the calculation process for the gradient theory influence parameters of this invention;
[0074] Figure 6 This is a schematic diagram showing the calculation results of the interaction coefficients of the ternary system of the present invention;
[0075] Figure 7 The figure shows the predicted surface tension of the (H2+N2) / H2O system of this invention. Detailed Implementation
[0076] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.
[0077] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "axial," "radial," "vertical," "horizontal," "inner," and "outer," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.
[0078] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.
[0079] To accurately predict the surface tension of the (H2+N2) / H2O system and calculate the interaction coefficient of this ternary system, the present invention provides a method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state, such as... Figure 1 As shown, it includes the following steps:
[0080] S01: Determine the energy parameters and co-volume parameters of the pure gas according to the PR equation of state. Use Waals' single-fluid mixing rule and combination rule to determine the material parameters and co-volume parameters of the mixed gas, such as... Figure 2 As shown, it includes the following steps:
[0081] S1.1: Determine the energy parameters of pure hydrogen based on its thermophysical properties. and co-volume parameters Specifically as follows:
[0082]
[0083]
[0084]
[0085] In the formula: This is the critical temperature of pure hydrogen. R is the critical pressure of pure hydrogen; T is the gas constant; and T is the ambient temperature. The coefficient is related to the eccentricity factor of pure hydrogen.
[0086] S1.2: Determine the energy parameters of pure nitrogen based on its thermophysical properties. and co-volume parameters Specifically as follows:
[0087]
[0088]
[0089]
[0090] In the formula: This is the critical temperature of pure nitrogen. R is the critical pressure of pure nitrogen; R is the gas constant, with a value of 8.314 J / (mol·K); T is the ambient temperature. The coefficient is related to the eccentricity factor of pure nitrogen.
[0091] S1.3: Determine the material parameters a of gas mixtures with different components using Waals' single-fluid mixing rules. mixture and co-volume parameter b mixture The mixing rules are as follows:
[0092]
[0093] Where: l mixture The interaction coefficient of the gas mixture; This represents the volume fraction of hydrogen in the gas mixture. k represents the volume fraction of nitrogen in the gas mixture. mixture The binary interaction parameter k is a temperature-dependent parameter for a (H2+N2) gas mixture. mixture The definition is as follows:
[0094]
[0095] The interaction coefficient l of different component gas mixtures was calculated using the NRTL equation. mixture The details are as follows:
[0096] The binary interaction coefficient of pure hydrogen gas was obtained by fitting experimental data. The binary interaction coefficient with pure nitrogen gas
[0097] The interaction coefficients l of different component gas mixtures at different temperatures were calculated using the NRTL equation. mixture The calculation formula is as follows:
[0098]
[0099] Wherein, G1, G2, and G3 are the calculation parameters of the empirical correlation formula. In the example, G1 = 5.75; G2 = 803.6; G3 = 0.3.
[0100] Figure 6 This is a schematic diagram showing the results of calculating the interaction coefficient of the mixed gas using the NRTL equation in this invention.
[0101] S02: The Helmholtz free energy density and equilibrium density of a pure gas were determined using Wertheim's molecular association theory; the Helmholtz free energy f of a (H2+N2) gas mixture with different components was determined using the density mixing rule. mixture (ρ) and equilibrium density ρ b,mixture ,like Figure 3 As shown, it includes the following steps:
[0102] S2.1: Determine the pressure factor P, as follows:
[0103]
[0104] Where: ρ is the molar density; g(ρ) is the radial distribution function of HDS, and the simplified form of g(ρ) is:
[0105]
[0106] X A Important parameters for association terms in mixtures, specifically:
[0107]
[0108] In the formula: Δ, representing the association strength (self-association) between gas molecules, is given by the following formula:
[0109]
[0110] Where ε represents the association energy of the pure gas; β represents the association volume of the pure gas; and b is the co-volume parameter of the pure gas. When calculating pure hydrogen, b is... When calculating pure nitrogen gas, b is...
[0111] S2.2: Equilibrium density ρ of pure gas b We obtain it from the following formula:
[0112] The Helmholtz free energy f(ρ) of a pure gas is obtained by the following equation:
[0113] Where, μ s p0 is the chemical potential of a pure gas, the value of which can be obtained from a table, and p0 is the current ambient atmospheric pressure.
[0114] Therefore, the equilibrium density of pure hydrogen can be calculated. equilibrium density of pure nitrogen Helmholtz free energy of pure hydrogen Helmholtz free energy of pure nitrogen
[0115] S2.3: Helmholtz free energy f for gas mixtures with different components mixture (ρ) and equilibrium density ρ b,mixture Its value is solved by the density combination rule, specifically:
[0116]
[0117]
[0118] like Figure 4 As shown in the figure, the liquid density and gas-liquid density calculated theoretically through step S02 are compared with the measured liquid density and gas-liquid density, and the calculated values have small errors compared with the measured values. It can be seen from the figure that the simulation results obtained using the calculation method of this invention have an accuracy of over 98% compared with the experiments.
[0119] S03: Determine the pure gas influence parameter k using gradient theory: Establish an empirical correlation for the pure gas influence parameter by fitting a large number of known pure gas influence parameter values; for the influence parameter of mixed gases, its value is determined by the pure gas influence parameter. and interaction system l mixture The combined effect determines; such as Figure 5 As shown, it includes the following steps:
[0120] S3.1: By fitting a function of temperature to a large number of known pure gas influence parameters, a general expression is obtained, which is expressed as follows:
[0121]
[0122] Where: coefficient A = f(ω), coefficient B = f(ω) 2 ), where ω is the eccentricity factor for a pure gas; f(ω) and f(ω) 2 The influence parameters of the specific known pure gas are determined experimentally.
[0123] Therefore, the influence parameters of pure hydrogen can be calculated. Influence parameters of pure nitrogen
[0124] S3.2: Parameters affected by pure gas and interaction coefficient l mixture The parameters affecting the gas mixture are determined as follows:
[0125]
[0126] S04: Employing density gradient linearization theory By assuming that the density of component i in the mixture is linearly distributed between equilibrium phases, it is unnecessary to solve the inherent density distribution equation in gradient theory. In other words, the gradient theory is simplified to obtain the simplified gradient theory model LGT.
[0127] S05: Prediction of surface tension:
[0128] The surface tension of the (H2+N2) / H2O system at different temperatures was calculated by combining the simplified gradient theory models LGT and PR-EoS.
[0129] The simplified gradient theory model LGT is as follows:
[0130]
[0131] Where: γ is the surface tension coefficient, P s It is the pressure at phase equilibrium, ρ is the bulk molar density, and the superscripts I and II represent the mixed gas components H2 and N2, respectively. This represents the hydrogen density under the current composition and temperature conditions. This represents the nitrogen density under the current composition and temperature conditions.
[0132] Based on the density gradient linearization theory, the corrected influence parameters of the mixed gas are calculated as follows:
[0133]
[0134] in, This is the difference between the density of component H2 and the equilibrium density of the mixed gas; This is the difference between the density of component N2 and the equilibrium density of the mixed gas;
[0135] Ω(ρ) is the total thermodynamic potential energy, defined as follows:
[0136] Ω(ρ)=f mixture (ρ)-ρ b,mixture *μ s,mixture
[0137] Where f mixture (ρ) is the Helmholtz free energy of the mixture at a reference density of ρ, where ρ b,mixture This represents the equilibrium density of the gas mixture.
[0138] Figure 7 The figure shows the predicted surface tension of the (H2+N2) / H2O system of this invention.
[0139] The surface tension prediction system for the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state, as described in this invention, includes a storage medium. The storage medium stores a program written using the aforementioned method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state. The storage medium may include a hard disk, CD-ROM, optical storage device, magnetic storage device, or a combination thereof. Those skilled in the art will understand that the various features described herein can be implemented by methods, data processing systems, or computer program products. Therefore, these features can be implemented entirely in hardware, entirely in software, or a combination of hardware and software. Furthermore, the above features can also be implemented as a computer program product stored on one or more computer-readable storage media, which contains computer-readable program code segments or instructions stored in the storage medium. Any commonly used computer-readable storage medium can be used, including hard disks, CD-ROMs, optical storage devices, magnetic storage devices, and / or combinations thereof.
[0140] It should be understood that although this specification is described according to various embodiments, not every embodiment contains only one independent technical solution. This way of describing the specification is only for 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.
[0141] The detailed descriptions listed above are merely specific illustrations of feasible embodiments of the present invention and are not intended to limit the scope of protection of the present invention. All equivalent embodiments or modifications made without departing from the spirit of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state, characterized in that, Includes the following steps: The energy parameters and co-volume parameters of the pure gas are determined based on the PR equation of state, and the material parameters and co-volume parameters of the mixed gas are determined using the Waals single-fluid mixing rule and the combination rule. The Helmholtz free energy density and equilibrium density of pure gases were determined using Wertheim's molecular association theory; the Helmholtz free energy of (H2+N2) gas mixtures with different components was determined using density mixing rules. and equilibrium density ; Determining the influence parameters of pure gas using gradient theory The pure gas influence parameters Including the influence parameters of pure hydrogen Influence parameters of pure nitrogen ; Influence parameters of pure hydrogen gas Parameters affecting pure nitrogen and interaction system Determine the parameters affecting the mixed gas; The gradient theory model is simplified to obtain the 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; The energy parameters and co-volume parameters of the pure gas are determined based on the PR equation of state. The material parameters and co-volume parameters of the mixed gas are determined using Waals' single-fluid mixing rule and combination rule, including the following steps: Determine the energy parameters of a pure gas based on its thermophysical properties. and co-volume parameters The details are as follows: ， ， ， In the formula: It is the critical temperature of a pure gas; R is the critical pressure of the pure gas; T is the gas constant; and T is the ambient temperature. This is a coefficient related to the eccentricity factor of the pure gas; The energy parameters of pure nitrogen can be determined from the thermophysical properties obtained from the above formula. and co-volume parameters ; The thermophysical properties of pure hydrogen determine its energy parameters. and co-volume parameters ; Material parameters of gas mixtures with different components were determined using Waals' one-fluid mixing rules. and co-volume parameters The mixing rules are as follows: ， in: The interaction coefficients of the gas mixtures are calculated using the NRTL equations for different component gas mixtures. ; This represents the volume fraction of hydrogen in the gas mixture. This represents the volume fraction of nitrogen in the gas mixture. The binary interaction parameter is the binary interaction parameter of the (H2+N2) gas mixture. The definition is as follows: ; The interaction coefficients of different component gas mixtures were calculated using the NRTL equation. The details are as follows: The binary interaction coefficient of pure hydrogen gas was obtained by fitting experimental data. The binary interaction coefficient with pure nitrogen gas ; The interaction coefficients of different component gas mixtures at different temperatures were calculated using the NRTL equation. The calculation formula is as follows: ， in, , and These are the calculation parameters for the empirical correlation.
2. The method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state as described in claim 1, characterized in that, The Helmholtz free energy density and equilibrium density of a pure gas are determined using Wertheim's molecular association theory, including the following steps: The pressure factor P is determined as follows: ， in: Molar density; Let be the radial distribution function of HDS. The simplified form is: ， Important parameters for association terms in mixtures, specifically: ， In the formula: self-associating molecules The association strength (self-association) between gas molecules is given by the following formula: ， in Represents the association energy of a pure gas; Let represent the association volume of the pure gas, and b be the co-volume parameter of the pure gas. When calculating pure hydrogen, b is... When calculating pure nitrogen, b is... ; equilibrium density of pure gas We obtain it from the following formula: ; Helmholtz free energy of pure gases We obtain it from the following formula: ; in, The chemical potential of a pure gas can be found in a table. The current atmospheric pressure; The equilibrium density of pure hydrogen gas was obtained. The equilibrium density of pure nitrogen Helmholtz free energy of pure hydrogen Helmholtz free energy of pure nitrogen .
3. The method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state as described in claim 2, is characterized in that... The Helmholtz free energy of (H2+N2) gas mixtures with different components was determined using the density mixing rule. and equilibrium density Specifically: ， 。 4. The method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state as described in claim 1, characterized in that, Determining the influence parameters of pure gas using gradient theory Specifically, it includes the following steps: By fitting a function of temperature to the influence parameters of a known pure gas, a general expression is obtained, which is expressed as follows: ， Where: coefficient A = f( ), coefficient B = f( ), For pure gases, the eccentricity factor is f( ) and f( The influence parameters of a specific known pure gas are determined experimentally. The influence parameters of pure hydrogen were calculated. Influence parameters of pure nitrogen .
5. The method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state according to claim 4, characterized in that, Influence parameters of pure hydrogen Parameters affecting pure nitrogen and interaction system The parameters affecting the gas mixture are determined as follows: Influence parameters of mixed gas .
6. The method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state according to claim 1, characterized in that, The gradient theory model is simplified by adopting the density gradient linearization theory. By assuming that the density of component i in the mixture is linearly distributed between equilibrium phases, the inherent density distribution equation in the gradient theory is not solved, thus obtaining the simplified gradient theory model LGT.
7. The method for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state 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 was obtained. The simplified gradient theory model LGT is as follows: ， in: The surface tension coefficient, It is the pressure in a phase equilibrium state. Bulk molar density, superscript and These represent the components of the mixed gas, H2 and N2, respectively. This represents the hydrogen density under the current composition and temperature conditions. This represents the nitrogen density under the current composition and temperature conditions. Based on the density gradient linearization theory, the corrected influence parameters of the mixed gas are calculated as follows: ， in, ; This is the difference between the density of component H2 and the equilibrium density of the mixed gas; This is the difference between the density of component N2 and the equilibrium density of the mixed gas; It is the total thermodynamic potential energy, defined as follows: ， in The reference density is The Helmholtz free energy of the mixture over time, This represents the equilibrium density of the gas mixture.
8. A system for predicting the surface tension of the (H2+N2) / H2O system based on linear gradient theory and the PR equation of state, characterized in that, 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 linear gradient theory and PR equation of state as described in any one of claims 1-7.