A method for calculating the adsorbed amount of confined fluid in a nanopore based on a state equation

Abstract

The application discloses a kind of based on state equation's limited fluid adsorption quantity calculation method in nanopore, comprising the following steps: S1: the gravity term of traditional cubic state equation is corrected by critical point movement;S2: the pressure term of state equation is corrected by the interaction between fluid molecules and pore wall in nanopore;S3: according to the adsorption phase equilibrium condition of limited fluid and bulk fluid in nanopore, the iterative calculation method of nonlinear equation set is constructed;S4: using the adsorption isotherm experimental data of pure substance, the model parameters of adsorption fluid under different pore medium conditions are regressed using least square method;S5: using the model parameters fitted by experimental data, the adsorption quantity of limited fluid in shale gas reservoir nanopore under different temperature and pressure conditions is predicted.The application can effectively predict the adsorption quantity of limited fluid in nanopore of shale gas reservoir, with the characteristics of fast calculation speed, high precision, wide application range, etc., providing technical support for efficient development of shale gas reservoir.

Description

Technical Field

[0001] This invention relates to the field of oil and gas field development technology, and in particular to a method for calculating the amount of confined fluid adsorbed in nanopores based on the equation of state. Background Technology

[0002] Shale gas is an important unconventional resource. Shale reservoirs have pores down to the nanoscale, with a high proportion of adsorbed gas within these pores. The phase characteristics of confined fluids within nanopores differ from those of free fluids in the bulk phase; both free and confined fluids may coexist in nanopores. Confined fluids include adsorbed and condensed phases, with the adsorbed phase generated by adsorption on the pore walls and the condensed phase generated by capillary condensation. Therefore, establishing a computational evaluation method to predict the amount of confined fluid adsorbed within nanopores is of great significance for the efficient development of shale gas reservoirs.

[0003] Currently, scholars both domestically and internationally have conducted extensive research on fluid adsorption in shale gas reservoirs, primarily employing experimental testing and molecular simulations. However, experimental measurements are time-consuming and labor-intensive, failing to provide rapid and accurate data on fluid adsorption in shale gas reservoirs. Molecular simulations can only characterize small-scale shale models, making it difficult to calculate fluid adsorption within shale pores larger than 10 nm, and also requiring significant computational time. Furthermore, current methods for calculating and evaluating confined fluid adsorption under nanoconfined conditions cannot describe the adsorption behavior of confined fluids, and conventional models have limited applicability. Therefore, there is an urgent need to establish a new method for calculating and evaluating the adsorption of confined fluids within nanopores of shale gas reservoirs, enabling rapid and accurate calculation of confined fluid adsorption within nanopores, and providing technical support for the efficient development of shale gas reservoirs. Summary of the Invention

[0004] To address the aforementioned problems, this invention aims to provide a method for calculating the amount of confined fluid adsorbed in nanopores based on the equation of state.

[0005] The technical solution of the present invention is as follows:

[0006] A method for calculating the adsorption capacity of confined fluid in nanopores based on the equation of state includes the following steps:

[0007] S1: Using experimental data on the critical point of confined fluid in nanopores of shale gas reservoirs, the gravitational term of the traditional cubic equation of state is modified by shifting the critical point.

[0008] S2: The pressure term of the equation of state is modified by the interaction between fluid molecules and pore walls in nanopores;

[0009] S3: Based on the adsorption phase equilibrium conditions between the confined fluid and the bulk fluid in nanopores, an iterative calculation method for a set of nonlinear equations is constructed.

[0010] S4: Using the adsorption isotherm experimental data of pure substances, the least squares method is used to regress the model parameters of the adsorption fluid under different porous media conditions.

[0011] S5: Using model parameters fitted from experimental data, predict the adsorption amount of confined fluid in nanopores of shale gas reservoirs under different temperature and pressure conditions.

[0012] Preferably, in step S1, the corrected gravitational term is:

[0013]

[0014] In the formula: P ma This is the corrected gravitational pressure, in MPa; α ma It is the gravitational term function of the modified SRK equation of state with respect to temperature; v p m is the reciprocal of the amount of confined fluid adsorbed in the nanopore. 3 / mol; b is the co-volume parameter of the mixture, m 3 / mol.

[0015] Preferably, the gravitational term function α ma The calculation is performed using the following formula:

[0016]

[0017] In the formula: x p,i and x p,j It represents the mole fractions of components i and j in the nanopore; α ma i and N is the gravitational term function of component i and component j; A It is Avogadro's constant, 6.02214076 × 10⁻⁶. 23 ;ε LJ,i and ε LJ,j These are the Lennard-Jones energy parameters for components i and j, J; σ i and σ j These are the Lennard-Jones radius parameters for components i and j.

[0018] Preferably, the gravitational term function α of component i ma i The calculation is performed using the following formula:

[0019]

[0020] In the formula: α 0,i and c 1,i T is the gravitational parameter of component i; T is the temperature of the system, in K. c,iIt is the critical temperature of component i, in K; r p It is the pore radius of the porous medium.

[0021] Preferably, in step S2, the corrected pressure term is:

[0022]

[0023] In the formula: P mw σ is the molecular-pore wall interaction pressure, MPa; σ is the Lennard-Jones radius parameter of the mixture. δ p It is the radius of the square well region of the mixture. R is the universal gas constant, 8.314 J / (mol·K); ε p It is the molecular square well potential energy parameter of the mixture, in J.

[0024] Preferably, the radius of the square well region of the mixture is calculated using the following formula:

[0025]

[0026] Where: δ p,i It is the radius of the square well region of component i.

[0027] The molecular square well potential energy parameter of the mixture is calculated by the following formula:

[0028]

[0029] Where: ε p,i It is the molecular square well potential energy parameter of component i, J;

[0030] The Lennard-Jones radius of the mixture is calculated as follows:

[0031]

[0032] In the formula: σ i It is the Lennard-Jones radius parameter of component i.

[0033] Preferably, step S3 specifically includes the following sub-steps:

[0034] S301: A set of nonlinear equations is constructed based on the adsorption phase equilibrium conditions between the confined fluid and the bulk fluid in nanopores:

[0035]

[0036] In the formula: f iIt is the fugacity of component i in the bulk phase; f p,i x1, x2, ..., x NC-1 It represents the mole fraction of the 1st, 2nd, ..., NC-1th component in the bulk phase; NC is the total number of components.

[0037] S302: The fugacity of the adsorbed phase is calculated using the confined fluid equation of state model with modified gravity and pressure terms, with the density and mole fraction of the adsorbed phase selected as the primary variables.

[0038] The model for the confined fluid state equations with the modified gravity and pressure terms is as follows:

[0039] P = P r +P ma +P mw (9)

[0040] In the formula: P is the total pressure in the modified SRK equation of state, MPa; P r This is the pressure of the repulsive term in the SRK equation of state, in MPa;

[0041] The formula for calculating the fugacity is:

[0042] f p,i =Px p,i φ p,i (10)

[0043] f i =Px i φ i (11)

[0044] In the formula: f p,i It is the fugacity of component i in the nanopore; φ p,i x is the fugacity coefficient of component i in the nanopore; i It is the mole fraction of component i in the bulk phase; φ i f is the fugacity coefficient of component i in the bulk phase; i It is the fugacity of component i in the bulk phase;

[0045] S303: Based on the phase equilibrium between the confined fluid and the bulk fluid in the nanopores, the new mole fraction of the adsorbed phase is calculated using a continuous iterative method. The updated formula for calculating the mole fraction of the nanophase component is as follows:

[0046]

[0047] In the formula: the superscripts n and n+1 represent the nth and n+1th iteration steps;

[0048] S304: The density of the new adsorbed phase is calculated using the secant method. The calculation formula is as follows:

[0049]

[0050] In the formula: the superscript n-1 represents the (n-1)th iteration step; f p,NC f is the fugacity of the NC-th component in the nanopore; NC It is the fugacity of the NCth component in the bulk phase;

[0051] Check whether the adsorption phase equilibrium condition between the confined fluid and the bulk fluid in the nanopore is met based on the new adsorption phase density. If not, return to step S302 to start a new round of calculation; if it is met, stop the calculation.

[0052] Preferably, in step S302, the fugacity coefficient of the adsorbed phase is calculated using the following formula:

[0053]

[0054] In the formula: b i It is the co-volume parameter of component i, m 3 / mol;

[0055] The fugacity coefficient of a volumetric phase is calculated using the following formula:

[0056]

[0057] In the formula: v is the molar volume in the bulk phase, m 3 / mol.

[0058] Preferably, in step S304, the following formula is used to determine whether the adsorption phase equilibrium condition between the confined fluid and the bulk fluid in the nanopore is satisfied:

[0059]

[0060] The beneficial effects of this invention are:

[0061] This invention can accurately calculate the adsorption capacity of pure substances, binary and multi-component mixed systems. It features fast calculation speed, high accuracy and wide applicability. It can effectively predict the adsorption capacity of confined fluids in nanopores of shale gas reservoirs, providing technical support for the efficient development of shale gas reservoirs. Attached Figure Description

[0062] 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. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0063] Figure 1This is a schematic flowchart of the method for calculating the amount of confined fluid adsorbed in nanopores based on the equation of state of the present invention.

[0064] Figure 2 This is a comparison chart of the critical point of pure material in nanopores calculated under different pore radii and experimental data in a specific embodiment.

[0065] Figure 3 This is a diagram of the potential energy function of the internal region of the cylindrical hole and the square well in a specific embodiment.

[0066] Figure 4 This is a comparison chart of the calculated methane and ethane adsorption amounts with experimental measurements from a specific embodiment.

[0067] Figure 5 This is a comparison chart of the calculated adsorption amounts of nitrogen, methane, and hydrogen in a specific embodiment with experimental measurements.

[0068] Figure 6 This is a comparison chart of the calculated adsorption capacity of a mixture of methane and ethane in a specific embodiment with experimental measurements.

[0069] Figure 7 This is a graph comparing the calculated adsorption capacity of a nitrogen, methane, and hydrogen mixture with experimental measurements from a specific embodiment. Detailed Implementation

[0070] The present invention will be further described below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and technical features described in this application can be combined with each other. It should also be pointed out that, unless otherwise indicated, all technical and scientific terms used in this application have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. The terms "comprising" or "including" and similar words used in this invention refer to elements or objects preceding the word that encompass the elements or objects listed following the word and their equivalents, without excluding other elements or objects.

[0071] like Figure 1 As shown, this invention provides a method for calculating the adsorption amount of confined fluid in nanopores based on the equation of state, comprising the following steps:

[0072] S1: Using experimental data on the critical point of confined fluid in nanopores of shale gas reservoirs, the gravitational term of the traditional cubic equation of state is modified by shifting the critical point.

[0073] The traditional cubic equation of state is the SRK equation of state, which consists of repulsion and attraction terms. The SRK equation of state before modification is expressed as follows:

[0074] P SRK =P r +P a (17)

[0075] In the formula: P SRK This is the total pressure in the SRK equation of state before modification, in MPa; P r The pressure of the repulsive term in the SRK equation of state before modification, in MPa; P a It is the gravitational pressure term of the SRK equation of state before modification, in MPa.

[0076] The gravitational term pressure P in the original SRK equation of state a Represented as:

[0077]

[0078] In the formula: v is the molar volume of the fluid, m 3 ·mol -1 b is the co-volume parameter, m 3 ·mol -1 α is the gravitational function of the SRK equation of state with respect to temperature.

[0079] The pure matter gravitational term α in the original SRK equation of state is expressed as:

[0080]

[0081] In the formula: T is the temperature of the system, K; R is the universal gas constant, 8.314 J / (mol·K); T c,i It is the critical temperature (K) in the bulk phase of a pure substance; P c,i ω is the critical pressure in the bulk phase of a pure substance i, in MPa; i It is the eccentricity factor of pure substance i, obtained by looking up a table.

[0082] The original van der Waals mixing rule did not consider the influence of pore radius, Lennard-Jones radius parameter, and Lennard-Jones energy parameter on the equation of state parameters in nanopores. Its expression is as follows:

[0083]

[0084] In the formula: x i and x j These are the mole fractions of components i and j; the subscripts "i" and "j" indicate the i-th and j-th components, respectively.

[0085] The expression for calculating the co-volume parameter of the mixture is:

[0086]

[0087] In the formula: b i It is the co-volume parameter of component i, m 3 ·mol-1 .

[0088] In a specific embodiment, step S1 specifically includes the following sub-steps:

[0089] S101: Using experimental data on the critical points of pure methane, carbon dioxide, nitrogen, oxygen, argon, ethane, and octane in nanopores, we regressed the relationship between critical temperature and molecular radius and pore radius.

[0090] The critical temperature in nanopores is expressed as a function of molecular radius and pore radius. Using experimental data on the critical points of pure methane, carbon dioxide, nitrogen, oxygen, argon, ethane, and octane in nanopores, the adjustable parameters a0 and a1 are fitted using the least squares method.

[0091]

[0092] In the formula: T c,p The critical temperature in nanopores, K; T c σ is the critical temperature in the bulk phase of a pure substance, expressed in K; σ is the Lennard-Jones radius parameter of a molecule in a pure substance. r p It is the pore radius of the porous medium. a0 and a1 are the fitting parameters.

[0093] The Lennard-Jones radii of methane, carbon dioxide, nitrogen, oxygen, argon, ethane, octane, and hydrogen are respectively Their critical temperatures are 190.6K, 304.2K, 126.2K, 154.6K, 150.9K, 305.4K, 296.1K, and 33.15K, respectively. The values ​​of a0 and a1 obtained by least squares fitting are 1.19486 and 1.22543, respectively. Figure 2 The experimental data and fitting results for different pure substances are presented. The fitted parameters can characterize the critical temperature variation of pure substances in nanopores.

[0094] S102: By substituting the critical temperature displacement equation into the gravitational term of the cubic equation of state, an equation of state based on the molecular-molecular interaction of confined fluids is constructed, which can describe the physical properties of fluids under different molecular radii and pore radii.

[0095] In nanopores, the critical point of the confined fluid is lower than that in the bulk state. The critical point shift equation established in S101 is used to replace the critical point, thereby correcting the gravitational term parameters of the equation of state. The corrected gravitational term is expressed as:

[0096]

[0097] In the formula: P ma This is the corrected gravitational pressure, in MPa; α ma It is the gravitational term function of the modified SRK equation of state with respect to temperature; v p m is the reciprocal of the amount of confined fluid adsorbed in the nanopore. 3 / mol; b is the co-volume parameter of the mixture, m 3 / mol.

[0098] The gravitational term α of pure matter in the modified SRK equation of state ma Represented as:

[0099]

[0100] In the formula: α 0,i and c 1,i T is the gravitational parameter of component i; T is the temperature of the system, in K. c,i It is the critical temperature of component i, in K; T c,p,i It is the critical temperature of component i in the nanopore, in K.

[0101] Substituting equation (22) into equation (23), we get:

[0102]

[0103] In the formula: r p It is the pore radius of the porous medium.

[0104] α0 and c1 are related to the saturated vapor pressure and liquid density of the pure substance in the bulk phase. For methane, ethane, nitrogen, and hydrogen, α0 is 232038, 550930, 138063, and 27343, respectively; c1 is 0.4472, 0.5846, 0.5136, and 0.1035, respectively; and b is 2.91 × 10⁻⁶. -5 4.29×10 -5 2.64×10 -5 and 2.05×10 -5 m 3 / mol.

[0105] S103: Calculate the physical parameters of the equation of state for mixtures using the modified van der Waals mixing rule.

[0106] By utilizing the Lennard-Jones potential energy function of confined fluids in nanopores, pore radius, Lennard-Jones radius parameters, and Lennard-Jones energy parameters are introduced into the traditional van der Waals mixing rule, resulting in a modified mixing rule dependent on pore radius and molecular-molecular potential energy. This modified rule is used to calculate the physical terms of the equation of state for mixtures. The modified van der Waals mixing rule is expressed as:

[0107]

[0108] In the formula: x p,i and x p,j It represents the mole fractions of components i and j in the nanopore; α ma i and N is the gravitational term function of component i and component j; A It is Avogadro's constant, 6.02214076 × 10⁻⁶. 23 ;ε LJ,i and ε LJ,j These are the Lennard-Jones energy parameters for components i and j, J; σ i and σ j These are the Lennard-Jones radius parameters for components i and j.

[0109] The ratios of the Lennard-Jones energy parameter to the Boltzmann constant for hydrogen, nitrogen, methane, and ethane are 36.7 K, 364.0 K, 207.0 K, and 155.0 K, respectively.

[0110] S2: The pressure term of the equation of state is modified by the interaction between fluid molecules and pore walls in nanopores.

[0111] In a specific embodiment, step S2 specifically includes the following sub-steps:

[0112] S201. The interaction between fluid molecules and pore walls in nanopores is characterized by the square well potential energy function, and the contribution of molecule-pore wall interaction to pressure is constructed.

[0113] Assuming the nanopores are cylindrical pores, such as Figure 3As shown, there are three regions within the pore: Region I is inaccessible to the center of mass of fluid molecules due to the repulsion of the pore wall, and the square well potential energy in Region I is infinite; Region III is similar to a free fluid region, and its extent is outside the influence range of the pore wall. Therefore, only molecular-molecular interactions exist in this region, represented by the Lennard-Jones potential function; In Region II, fluid molecules are affected by the pore wall, and both molecular-molecular and molecular-pore wall interactions exist. Surface adsorption occurs in this region, δ p It is the radius of the region, ε p This is the molecular square well potential energy parameter. Assuming the interface is continuous and homogeneous, and ignoring the influence of pore boundaries on the molecular-pore wall interaction potential energy, the contribution of the molecular-pore wall interaction to the pressure is constructed using the square well potential energy function as follows:

[0114]

[0115] In the formula: P mw σ is the molecular-pore wall interaction pressure, MPa; σ is the Lennard-Jones radius parameter of the mixture.

[0116] δ p It is the radius of the square well region of the mixture. R is the universal gas constant, 8.314 J / (mol·K); ε p It is the molecular square well potential energy parameter of the mixture, in J.

[0117] S202: Calculate the parameters of the molecular-pore wall interaction term in the equation of state using the linear mixing rule.

[0118] In the modified equation of state, the molecular-pore wall interaction term parameters of the mixture are calculated using a linear mixing rule. The parameter value of the mixture is the sum of the parameter values ​​of all pure substances multiplied by their mole fractions. The expression for calculating the molecular square well potential energy parameter of the mixture is as follows:

[0119]

[0120] Where: ε p,i It is the molecular square well potential energy parameter of component i, J;

[0121] The radius of the trap region of the mixture is calculated using the following formula:

[0122]

[0123] Where: δ p,i It is the radius of the square well region of component i.

[0124] The Lennard-Jones radius of the mixture is calculated as follows:

[0125]

[0126] Where: σ i It is the Lennard-Jones radius parameter of component i.

[0127] S203. The equation of state model is modified by using the attraction term, repulsion term and molecular-pore wall interaction term, so that it can describe the physical property changes of confined fluids in different nanopores due to molecular-molecule and molecular-pore wall interactions.

[0128] The confined fluid in the nanopore is subject to molecular-molecule and molecular-pore wall interactions. Its equation of state includes attractive, repulsive, and molecular-pore wall interaction terms. Using the contributions of the repulsive term from the cubic equation of state, the attractive term based on critical point movement established in S102, and the molecular-pore wall interaction term constructed in S201 to the pressure, the partial pressures of the three terms are summed to obtain the corrected total pressure of the confined fluid in the nanopore:

[0129] P = P r +P ma +P mw (9)

[0130] In the formula: P is the total pressure in the modified SRK equation of state, MPa; P r It is the repulsive term pressure in the SRK equation of state, in MPa.

[0131] S3: Based on the adsorption phase equilibrium conditions between the confined fluid and the bulk fluid in nanopores, an iterative calculation method for a set of nonlinear equations is constructed.

[0132] In a specific embodiment, step S3 specifically includes the following sub-steps:

[0133] S301: Construct a set of nonlinear equations based on the adsorption phase equilibrium conditions between confined fluid and bulk fluid in nanopores;

[0134] In a specific methane and ethane system, the bulk methane phase and the adsorbed phase in the nanopores are in equilibrium, as are the bulk ethane phase and the adsorbed phase in the nanopores. When temperature, pressure, pore radius, and bulk phase composition are known, there are a total of two phase equilibrium equations corresponding to two unknown variables, forming a nonlinear equation system. In a specific nitrogen, methane, and hydrogen system, when temperature, pressure, pore radius, and bulk phase composition are known, there are a total of three phase equilibrium equations corresponding to three unknown variables, forming a nonlinear equation system.

[0135]

[0136] In the formula: f i It is the fugacity of component i in the bulk phase; f p,i x1, x2, ..., x NC-1 It represents the mole fraction of the 1st, 2nd, ..., NC-1th component in the bulk phase; NC is the total number of components.

[0137] S302: The fugacity of the adsorbed phase is calculated using the confined fluid equation of state model with modified gravity and pressure terms, with the density and mole fraction of the adsorbed phase selected as the primary variables.

[0138] Based on the phase equilibrium equations, the density of the adsorbed phase and the mole fraction of the components are designated as primary variables. The parameters of the equation of state for the mixture under nanoconfined conditions are calculated using the van der Waals mixing rule and the linear mixing rule established in S1, S103, and S202. The confined fluid equation of state model established in S203 is solved to calculate the molar volume of the bulk fluid and the reciprocal of the adsorbed fluid's adsorption amount. Then, the fugacity of the adsorbed phase is calculated. The formula for calculating the fugacity is:

[0139] f p,i =Px p,i φ p,i (10)

[0140] f i =Px i φ i (11)

[0141] In the formula: f p,i It is the fugacity of component i in the nanopore; φ p,i x is the fugacity coefficient of component i in the nanopore; i It is the mole fraction of component i in the bulk phase; φ i f is the fugacity coefficient of component i in the bulk phase; i It is the fugacity of component i in the bulk phase.

[0142] The formula for calculating the fugacity coefficient of the adsorbed phase is:

[0143]

[0144] In the formula: b i It is the co-volume parameter of component i, m 3 / mol;

[0145] The formula for calculating the fugacity coefficient of a volumetric phase is:

[0146]

[0147] In the formula: v is the molar volume in the bulk phase, m 3 / mol.

[0148] S303: Based on the phase equilibrium between the confined fluid and the bulk fluid in the nanopores, the new mole fraction of the adsorbed phase is calculated using a continuous iterative method. The updated formula for calculating the mole fraction of the nanophase component is as follows:

[0149]

[0150] In the formula: the superscripts n and n+1 represent the nth and n+1th iteration steps;

[0151] In this step, based on the phase equilibrium criterion between the confined fluid and the bulk fluid in the nanopore, the new mole fraction of the nanophase component is calculated by multiplying the mole fraction of the nanophase component by the fugacity of the bulk component and then dividing by the fugacity of the nanophase component. The fugacity of the nanophase component is then updated using a continuous iterative method until the fugacity of the bulk component is equal to the fugacity of the nanophase component.

[0152] S304: The density of the new adsorbed phase is calculated using the secant method. The calculation formula is as follows:

[0153]

[0154] In the formula: the superscript n-1 represents the (n-1)th iteration step; f p,NC f is the fugacity of the NC-th component in the nanopore; NC It is the fugacity of the NCth component in the bulk phase;

[0155] Check whether the adsorption phase equilibrium condition between the confined fluid and the bulk fluid in the nanopore is met based on the new adsorption phase density. If not, return to step S302 to start a new round of calculation; if it is met, stop the calculation.

[0156] In a specific embodiment, the following formula is used to determine whether the adsorption phase equilibrium condition between the confined fluid and the bulk fluid in the nanopore is satisfied:

[0157]

[0158] S4: Using the adsorption isotherm experimental data of pure substances, the least squares method is used to regress the model parameters of the adsorbed fluid under different porous media conditions.

[0159] Using experimental data of adsorption isotherms of methane and ethane in porous media with a pore radius of 1.72 nm, such as... Figure 4 As shown, the region radii δ of methane and ethane were regressed using the least squares method. p They are respectively and Their square well potential energy ε p The ratios to the Boltzmann constant are 700K and 1100K, respectively. Figure 4The solid line represents the model calculation results. The adsorption amount of pure substances increases with increasing pressure. Under the same conditions, the adsorption amount of ethane is greater than that of methane. The comparison with experimental data shows that the model parameters obtained by regression can accurately calculate the adsorption amounts of methane and ethane in nanopores.

[0160] Using experimental data on adsorption isotherms of nitrogen, methane, and hydrogen in porous media with a pore radius of 0.69 nm, such as... Figure 5 As shown, the region radii δ of nitrogen, methane, and hydrogen were regressed using the least squares method. p They are respectively Their square well potential energy ε p The ratios to the Boltzmann constant are 880K, 1250K, and 180K, respectively. Figure 5 The solid line represents the model calculation results. Under the same conditions, the adsorption capacity of methane is greater than that of nitrogen, and the adsorption capacity of nitrogen is greater than that of hydrogen.

[0161] S5: Using model parameters fitted from experimental data, predict the adsorption amount of confined fluid in nanopores of shale gas reservoirs under different temperature and pressure conditions.

[0162] Using the model parameters of the pure substances in S101 and S4, the adsorption capacity of the binary mixture of methane and ethane in nanopores is predicted as follows: Figure 6 As shown, comparison with experimental values ​​demonstrates that the proposed method for calculating the adsorption amount of confined fluid in shale gas reservoirs under nanopore confinement conditions based on the equation of state can accurately calculate the adsorption amount of confined fluid in nanopores. Figure 6 It can be seen that as the methane content in the bulk phase increases, the ethane content in the adsorbed phase decreases, while the methane content in the adsorbed phase increases. However, the total adsorption of methane and ethane decreases because, under the same conditions, ethane is more easily adsorbed than methane.

[0163] Using the model parameters of the pure substances in S101 and S4, the adsorption capacity of the ternary mixture of nitrogen, methane, and hydrogen in nanopores is predicted as follows: Figure 7 As shown, comparison with experimental values ​​demonstrates that the proposed method for calculating the adsorption amount of confined fluid in shale gas reservoirs under nanopore confinement conditions based on the equation of state can accurately calculate the adsorption amount of confined fluid in nanopores. Figure 7 It can be seen that, under the same conditions, the component with strong adsorption capacity in a pure substance has a stronger adsorption capacity in a mixed system. In the ternary mixed system of nitrogen, methane, and hydrogen, methane has a stronger adsorption capacity than nitrogen, and nitrogen has a stronger adsorption capacity than hydrogen.

[0164] This invention proposes a novel method for calculating and evaluating the adsorption capacity of confined fluids within nanopores of shale gas reservoirs based on equations of state. This method is applicable to the calculation of adsorption capacity in pure substances, binary systems, and multi-component mixed systems. Compared to traditional experimental and molecular simulation methods, the proposed method takes less than 0.1 seconds to calculate, exhibiting advantages such as high speed, high accuracy, and wide applicability. It can effectively predict the adsorption capacity of confined fluids within nanopores of shale gas reservoirs, providing technical support for the efficient development of shale gas reservoirs.

[0165] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for calculating the adsorption capacity of confined fluid in nanopores based on the equation of state, characterized in that, Includes the following steps: S1: Using experimental data on the critical point of confined fluid in nanopores of shale gas reservoirs, the gravitational term of the traditional cubic equation of state is modified by shifting the critical point. S2: The pressure term of the equation of state is modified by the interaction between fluid molecules and pore walls in nanopores; S3: Based on the adsorption phase equilibrium conditions between the confined fluid and the bulk fluid in nanopores, an iterative calculation method for a nonlinear equation system is constructed; specifically, it includes the following sub-steps: S301: A set of nonlinear equations is constructed based on the adsorption phase equilibrium conditions between the confined fluid and the bulk fluid in nanopores: In the formula: f i It is the fugacity of component i in the bulk phase; f p,i It is the fugacity of component i in the nanopore; T is the system temperature in K; P is the bulk pressure in MPa; x1, x2, ..., x NC-1 It represents the mole fraction of the 1st, 2nd, ..., NC-1th components in the bulk phase; NC is the total number of components; v p m is the reciprocal of the amount of confined fluid adsorbed in the nanopore. 3 / mol;r p It is the pore radius of the porous medium, in Å; S302: The fugacity of the adsorbed phase is calculated using the confined fluid equation of state model with modified gravity and pressure terms, with the density and mole fraction of the adsorbed phase selected as the primary variables. The model for the confined fluid state equations with the modified gravity and pressure terms is as follows: In the formula: P is the total pressure in the modified SRK equation of state, MPa; P r The pressure of the repulsive term in the SRK equation of state is MPa; P ma This is the corrected gravitational pressure, in MPa; P mw It is the molecular-pore wall interaction pressure, in MPa; The formula for calculating the fugacity is: In the formula: f p,i ϕ is the fugacity of component i in the nanopore; p,i x is the fugacity coefficient of component i in the nanopore; i It is the mole fraction of component i in the bulk phase; ϕ i It is the fugacity coefficient of component i in the bulk phase; f i It is the fugacity of component i in the bulk phase; S303: Based on the phase equilibrium between the confined fluid and the bulk fluid in the nanopores, the new mole fraction of the adsorbed phase is calculated using a continuous iterative method. The updated formula for calculating the mole fraction of the nanophase component is as follows: In the formula: the superscripts n and n+1 represent the nth and n+1th iteration steps; S304: The density of the new adsorbed phase is calculated using the secant method. The calculation formula is as follows: In the formula: the superscript n-1 represents the (n-1)th iteration step; f p,NC f is the fugacity of the NC-th component in the nanopore; NC It is the fugacity of the NCth component in the bulk phase; Check whether the adsorption phase equilibrium condition between the confined fluid and the bulk fluid in the nanopore is met based on the new adsorption phase density. If not, return to step S302 to start a new round of calculation; if it is met, stop the calculation. S4: Using the adsorption isotherm experimental data of pure substances, the least squares method is used to regress the model parameters of the adsorption fluid under different porous media conditions. S5: Using model parameters fitted from experimental data, predict the adsorption amount of confined fluid in nanopores of shale gas reservoirs under different temperature and pressure conditions.

2. The method for calculating the adsorption amount of confined fluid in nanopores based on the equation of state according to claim 1, characterized in that, In step S1, the corrected gravitational term is: In the formula: α ma It is the gravitational term function of the modified SRK equation of state with respect to temperature; b is the co-volume parameter of the mixture, m 3 / mol.

3. The method for calculating the adsorption amount of confined fluid in nanopores based on the equation of state according to claim 2, characterized in that, The gravitational term function α ma The calculation is performed using the following formula: In the formula: x p,i and x p,j It is the mole fraction of components i and j in the nanopore; α ma i and α ma j N is the gravitational term function of component i and component j; A It is Avogadro's constant, 6.02214076 × 10⁻⁶. 23 ; ε LJ,i and ε LJ,j These are the Lennard-Jones energy parameters for components i and j, in J; σ i and σ j is the Lennard-Jones radius parameter for components i and j, in Å.

4. The method for calculating the adsorption amount of confined fluid in nanopores based on the equation of state according to claim 3, characterized in that, The gravitational term function α of component i ma i The calculation is performed using the following formula: In the formula: α 0,i and c 1,i It is the gravitational term parameter of component i; T c,i It is the critical temperature of component i, in K.

5. The method for calculating the adsorption amount of confined fluid in nanopores based on the equation of state according to claim 4, characterized in that, In step S2, the corrected pressure term is: In the formula: σ is the Lennard-Jones radius parameter of the mixture, in Å; δ p ε is the radius of the square well region of the mixture, Å; R is the universal gas constant, 8.314 J / (mol·K); ε p It is the molecular square well potential energy parameter of the mixture, in J.

6. The method for calculating the adsorption amount of confined fluid in nanopores based on the equation of state according to claim 5, characterized in that, The radius of the trap region of the mixture is calculated using the following formula: Where: δ p,i The radius of the square well region of component i is Å; The molecular square well potential energy parameter of the mixture is calculated by the following formula: Where: ε p,i It is the molecular square well potential energy parameter of component i, J; The Lennard-Jones radius of the mixture is calculated as follows: In the formula: σ i is the Lennard-Jones radius parameter of component i, in Å.

7. The method for calculating the adsorption amount of confined fluid in nanopores based on the equation of state according to claim 1, characterized in that, In step S302, the fugacity coefficient of the adsorbed phase is calculated using the following formula: In the formula: b is the co-volume parameter of the mixture, m 3 / mol; b i It is the co-volume parameter of component i, m 3 / mol; α ma It is the gravitational term function of the modified SRK equation of state with respect to temperature; α ma i and α ma j N is the gravitational term function of component i and component j; A It is Avogadro's constant, 6.02214076 × 10⁻⁶. 23 ; ε LJ,i and ε LJ,j These are the Lennard-Jones energy parameters for components i and j, in J; σ i and σ j These are the Lennard-Jones radius parameters for components i and j, in Å; δ p It is the radius of the square well region of the mixture, in Å; ε p,i It is the molecular square well potential energy parameter of component i, J; The fugacity coefficient of a volumetric phase is calculated using the following formula: In the formula: v is the molar volume in the bulk phase, m 3 / mol.

8. The method for calculating the adsorption amount of confined fluid in nanopores based on the equation of state according to claim 1, characterized in that, In step S304, the following formula is used to determine whether the adsorption phase equilibrium condition between the confined fluid and the bulk fluid in the nanopore is satisfied: (16)。

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