Method for calculating adsorption quantity of limited fluid in nanopore based on state equation

Abstract

The invention discloses a method for calculating the adsorption capacity of limited fluid in a nanopore based on a state equation. The method comprises the following steps: S1, correcting a gravitational term of a traditional cubic state equation through critical point movement; s2, correcting a pressure term of the state equation through interaction between fluid molecules in the nanopores and pore walls; s3, constructing an iterative calculation method of a nonlinear equation set according to adsorption phase equilibrium conditions of the limited fluid and the volume phase fluid in the nanopores; s4, regression model parameters of the adsorption fluid under different pore medium conditions by adopting a least square method according to adsorption isotherm experimental data of a pure substance; and S5, predicting the adsorption capacity of the limited fluid in the shale gas reservoir nanopores under different temperature and pressure conditions by utilizing model parameters fitted by experimental data. The method can effectively predict the adsorption capacity of the limited fluid in the shale gas reservoir nanopores, has the characteristics of high calculation speed, high precision, wide application range and the like, and provides technical support for efficient development of shale gas reservoirs.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of oil and gas field development, and particularly relates to a calculation method of adsorption amount of confined fluid in nano-pore based on state equation. BACKGROUND

[0002] Shale gas is one of the important unconventional resources. The pore of shale reservoir reaches nanometer level, and the adsorbed gas in the pore accounts for a high proportion. The phase state characteristics of confined fluid in nano-pore are different from those of free fluid in bulk phase. In the nano-pore, free fluid and confined fluid may exist simultaneously. The confined fluid includes adsorbed phase and condensate phase, wherein the adsorbed phase is generated by adsorption of the pore wall, and the condensate phase is generated by capillary condensation. Therefore, it is of great significance to establish a calculation and evaluation method for predicting the adsorption amount of confined fluid in nano-pore for efficient development of shale gas reservoirs.

[0003] At present, domestic and foreign scholars have carried out a large amount of research on fluid adsorption of shale gas reservoirs, mainly by experimental test and molecular simulation. The experimental measurement is time-consuming and laborious, and cannot quickly and accurately obtain the adsorption amount of shale gas reservoir fluid. The molecular simulation can only characterize small-scale shale models, and it is difficult to calculate the fluid adsorption amount in shale pores above 10 nm, and a large amount of calculation time is required. In addition, the current calculation and evaluation method of adsorption amount of confined fluid under nano-limiting conditions cannot be used to describe the adsorption behavior of confined fluid, and the application range of the conventional model is limited. Therefore, it is urgent to establish a new calculation and evaluation method of adsorption amount of confined fluid in nano-pore of shale gas reservoir, so as to realize the rapid and accurate calculation of the adsorption amount of confined fluid in nano-pore, and provide technical support for efficient development of shale gas reservoirs. SUMMARY

[0004] In view of the above problems, the present application aims to provide a calculation method of adsorption amount of confined fluid in nano-pore based on state equation.

[0005] The technical scheme of the present application is as follows:

[0006] A calculation method of adsorption amount of confined fluid in nano-pore based on state equation, comprising the following steps:

[0007] S1: using the experimental data of critical point of confined fluid in nano-pore of shale gas reservoir, modifying the gravity term of traditional cubic state equation by critical point movement;

[0008] S2: modifying the pressure term of state equation by the interaction between fluid molecules and pore wall in nano-pore;

[0009] S3: constructing an iterative calculation method of nonlinear equation set according to the adsorption phase equilibrium condition of confined fluid in nano-pore and bulk phase fluid;

[0010] S4: Using the adsorption isotherm experimental data of pure substances, the model parameters of adsorbed fluid under different pore medium conditions are regressed by least square method;

[0011] S5: Using the model parameters fitted by experimental data, the adsorption amount of confined fluid in shale gas reservoir nanometer pores under different temperature and pressure conditions is predicted.

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

[0013]

[0014] In the formula: P ma is the corrected gravitational term pressure, MPa; α ma is the corrected SRK state equation gravitational term function about temperature; v p is the reciprocal of the adsorption amount of confined fluid in nanometer pores, m 3 / mol; b is the common volume parameter of the mixture, m 3 / mol.

[0015] As preferred, the gravitational term function α ma is calculated by the following formula:

[0016]

[0017] In the formula: x p,i and x p,j are the mole fractions of components i and j in the nanometer pores; α ma i and are the gravitational term functions of component i and component j; N A is the Avogadro constant, 6.02214076×10 23 ; ε LJ,i and ε LJ,j are the Lennard-Jones energy parameters of components i and j, J; σ i and σ j are the Lennard-Jones radius parameters of components i and j,

[0018] As preferred, the gravitational term function α ma i of component i is calculated by the following formula:

[0019]

[0020] In the formula: α 0,i and c 1,i are the gravitational term parameters of component i; T is the temperature of the system, K; T c,iis the critical temperature of component i, K; r p is the pore radius of the porous medium,

[0021] As preferred, in step S2, the revised pressure term is:

[0022]

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

[0024] As preferred, the square-well region radius of the mixture is calculated by the following formula:

[0025]

[0026] wherein: δ p,i is the square-well region radius of component i,

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

[0028]

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

[0030] The Lennard-Jones radius calculation expression of the mixture is:

[0031]

[0032] wherein: σ i is the Lennard-Jones radius parameter of component i,

[0033] As preferred, step S3 specifically comprises the following sub-steps:

[0034] S301: constructing a nonlinear equation set according to the adsorption phase equilibrium condition of the confined fluid in the nanopore and the bulk fluid:

[0035]

[0036] wherein: f iis the fugacity of component i in the bulk phase; f p,i is the fugacity of component i in the nanopore; P is the pressure of the bulk phase, MPa; x1, x2, …, x NC-1 are the mole fractions of the 1st, 2nd, …, NC-1 components in the bulk phase; NC is the total number of components;

[0037] S302: The adsorption phase density and mole fraction are selected as the primary variables, and the fugacity of the adsorption phase is calculated by using a restricted fluid equation of state model with a modified attractive term and a pressure term;

[0038] The restricted fluid equation of state model with a modified attractive term and a pressure term is as follows:

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

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

[0041] The calculation formula of the fugacity is as follows:

[0042] f p,i = P x p,i φ p,i (10)

[0043] f i = P x i φ i (11)

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

[0045] S303: According to the phase equilibrium of the restricted fluid in the nanopore and the bulk fluid, a continuous iteration method is used to calculate the new adsorption phase mole fraction, and the updated nanopore component mole fraction calculation formula is as follows:

[0046]

[0047] In the formula, the superscripts n and n+1 are the n th and (n+1) th iteration steps;

[0048] S304: The secant method is used to calculate the new adsorption phase density, and the calculation formula is as follows:

[0049]

[0050] wherein: subscript n-1 is the (n-1)th iteration step number; f p,NC is the fugacity of the NCth component in the nanopore; f NC is the fugacity of the NCth component in the bulk phase;

[0051] According to the new adsorption phase density, it is checked whether the adsorption phase equilibrium condition of the confined fluid in the nanopore and the bulk fluid is met, and if not, the calculation is returned to step S302 to start a new round of calculation; if yes, the calculation is stopped.

[0052] As a preference, in step S302, the fugacity coefficient of the adsorption phase is calculated by the following formula:

[0053]

[0054] wherein: b i is the common volume parameter of component i, m 3 / mol;

[0055] The fugacity coefficient of the bulk phase is calculated by the following formula:

[0056]

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

[0058] As a preference, in step S304, it is judged whether the adsorption phase equilibrium condition of the confined fluid in the nanopore and the bulk fluid is met by the following formula:

[0059]

[0060] The present application has the following beneficial effects:

[0061] The present application can accurately calculate the adsorption amount of pure substances, binary and multi-component mixed systems, has the characteristics of fast calculation speed, high precision, wide application range, etc., and can effectively predict the adsorption amount of the confined fluid in the nanopore of the shale gas reservoir, thereby providing technical support for efficient development of the shale gas reservoir. BRIEF DESCRIPTION OF DRAWINGS

[0062] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0063] Figure 1is a flowchart of a method for calculating the adsorption amount of a confined fluid in a nanopore based on a state equation according to an embodiment of the present application;

[0064] Figure 2 is a comparison graph of the critical point of a pure substance in a nanopore calculated by a specific embodiment at different pore radii and experimental data;

[0065] Figure 3 is a graph of the potential function in the internal region of a cylindrical pore and a square well potential function according to a specific embodiment;

[0066] Figure 4 is a comparison graph of the adsorption amount of methane and ethane calculated by a specific embodiment and experimental measurement values;

[0067] Figure 5 is a comparison graph of the adsorption amount of nitrogen, methane, and hydrogen calculated by a specific embodiment and experimental measurement values;

[0068] Figure 6 is a comparison graph of the adsorption amount of a mixture of methane and ethane calculated by a specific embodiment and experimental measurement values;

[0069] Figure 7 is a comparison graph of the adsorption amount of a mixture of nitrogen, methane, and hydrogen calculated by a specific embodiment and experimental measurement values. DETAILED DESCRIPTION

[0070] The present application will be further described below in conjunction with the accompanying drawings and embodiments. It should be noted that the embodiments in the present application and the technical features in the embodiments can be combined with each other without conflict. It should be noted that all the technical and scientific terms used in the present application have the same meaning as that generally understood by the ordinary skilled in the art to which the present application belongs, unless otherwise specified. The similar words such as “comprise” or “include” and the like used in the present application mean that the elements or objects before the words cover the elements or objects listed after the words and their equivalents, and do not exclude other elements or objects.

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

[0072] S1: using the experimental data of the critical point of a confined fluid in a shale gas reservoir nanopore, the gravity term of a traditional cubic state equation is modified by moving the critical point.

[0073] The traditional cubic state equation is the SRK state equation, which is composed of a repulsion term and a gravity term. The SRK state equation before modification is represented as:

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

[0075] P is the total pressure of the SRK equation of state before correction, MPa; P SRK P is the repulsion item pressure of the SRK equation of state before correction, MPa; P r P is the repulsion item pressure of the SRK equation of state before correction, MPa; P a P is the gravity item pressure of the SRK equation of state before correction, MPa.

[0076] The gravity item pressure P of the SRK equation of state before correction a is expressed as:

[0077]

[0078] 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 gravity item function of the SRK equation of state with respect to temperature.

[0079] The pure substance gravity item function α of the SRK equation of state before correction is expressed as:

[0080]

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

[0082] The van der Waals mixing rule before correction does not consider the influence of the pore radius, the Lennard-Jones radius parameter and the Lennard-Jones energy parameter on the equation of state parameters in the nanopore, and its expression is as follows:

[0083]

[0084] x i and x j are the molar fractions of components i and j; the subscripts “i” and “j” represent the i th and j th components.

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

[0086]

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

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

[0089] S101: Regression of the critical temperature with the molecular radius and the pore radius by using the critical point experimental data of pure methane, carbon dioxide, nitrogen, oxygen, argon, ethane, octane in nanopores.

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

[0091]

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

[0093] The Lennard-Jones radius of methane, carbon dioxide, nitrogen, oxygen, argon, ethane, octane, hydrogen is respectively Their critical temperatures are respectively 190.6K, 304.2K, 126.2K, 154.6K, 150.9K, 305.4K, 296.1K, 33.15K, and the a0 and a1 fitted by the least square method are respectively 1.19486 and 1.22543. Figure 2 The experimental data and fitting results of different pure substances are shown in Table 1, and the fitted parameters can characterize the critical temperature variation characteristics of pure substances in nanopores.

[0094] S102: The critical temperature displacement equation is brought into the gravitational term of the cubic equation of state to construct the equation of state based on the restricted fluid molecule-molecule interaction, so that it can describe the physical property characteristics of fluids under different molecular radii and pore radii.

[0095] In nanopores, the critical point of the restricted fluid is less than that in the bulk phase state, and the critical point displacement equation established by S101 is used to replace the critical point, so as to modify the gravitational term parameters of the equation of state. The modified gravitational term is expressed as:

[0096]

[0097] wherein: P ma is the corrected gravitational term pressure, MPa; a ma is the corrected SRK equation of state gravitational term function with respect to temperature; v p is the inverse of the adsorbed amount of the confined fluid in the nanopore, m 3 / mol; b is the mixture's co-volume parameter, m 3 / mol.

[0098] The pure substance gravitational term function a ma of the corrected SRK equation of state is expressed as:

[0099]

[0100] wherein: a 0,i and c 1,i are the gravitational term parameters of component i; T is the temperature of the system, K; T c,i is the critical temperature of component i, K; T c,p,i is the critical temperature of component i in the nanopore, K.

[0101] Substituting equation (22) into equation (23) gives:

[0102]

[0103] wherein: r p is the pore radius of the porous medium,

[0104] a0and c1are related to the saturated vapor pressure and liquid density of the pure substance in the bulk phase, a0of methane, ethane, nitrogen and hydrogen is respectively taken as 232038, 550930, 138063, 27343, c1of them is respectively taken as 0.4472, 0.5846, 0.5136 and 0.1035, b of them is respectively taken as 2.91×10 -5 , 4.29×10 -5 , 2.64×10 -5 and 2.05×10 -5 m 3 / mol.

[0105] S103: Calculate the physical term parameters of the mixture's equation of state by using the corrected van der Waals mixing rule.

[0106] The Lennard-Jones potential function of the limited fluid molecule-molecule interaction in the nanopore is used, the pore radius, the Lennard-Jones radius parameter and the Lennard-Jones energy parameter are introduced into the traditional van der Waals mixing rule, the modified mixing rule depending on the pore radius and the molecule-molecule potential energy is obtained, and the state equation physical item parameters of the mixture are calculated. The modified van der Waals mixing rule is expressed as:

[0107]

[0108] In the formula, x p,i and x p,j are the mole fractions of components i and j in the nanopore; α ma i and are the attractive item functions of components i and j; N A is the Avogadro constant, 6.02214076×10 23 ; ε LJ,i and ε LJ,j are the Lennard-Jones energy parameters of components i and j, J; σ i and σ j are the Lennard-Jones radius parameters of components i and j,

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

[0110] S2: The pressure item of the state equation is modified by the interaction between the fluid molecules in the nanopore and the pore wall.

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

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

[0113] It is assumed that the nanopore is a cylindrical pore, such as Figure 3As shown, there are three regions in the hole: region I is a region where the mass center of fluid molecules cannot reach due to the repulsion of the hole wall, the square well potential in region I is infinite; region III is a free fluid region, the range of region III is not within the influence range of the hole wall, therefore, only molecule-molecule interaction exists in this region, which is represented by the Lennard-Jones potential function; region II is a region where fluid molecules are affected by the hole wall, and there are molecule-molecule and molecule-hole wall interactions, surface adsorption occurs in this region, δ p is the radius of the region, ε p is the molecular square well potential energy parameter, it is assumed that the interface is continuous and uniform, and the influence of the pore boundary on the molecule-hole wall interaction potential is ignored, the contribution of the molecule-hole wall interaction to the pressure is constructed by using the square well potential function as follows:

[0114]

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

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

[0117] S202: Calculate the state equation molecule-hole wall interaction term parameter by using the linear mixing rule.

[0118] The molecule-hole wall interaction term parameter of the mixture in the modified state equation adopts the 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, and the calculation expression of the molecular square well potential energy parameter of the mixture is:

[0119]

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

[0121] The square well region radius of the mixture is calculated by the following formula:

[0122]

[0123] In the formula: δ p,i is the square well region radius of component i,

[0124] The Lennard-Jones radius calculation expression of the mixture is:

[0125]

[0126] In the formula, σ i is the Lennard-Jones radius parameter of component i,

[0127] S203, the state equation model is corrected by using the attractive term, the repulsive term and the molecule-pore wall interaction term, so that it can describe the property change characteristics of the confined fluid in different nanopores subjected to molecule-molecule and molecule-pore wall interactions.

[0128] The confined fluid in the nanopore is subjected to molecule-molecule and molecule-pore wall interactions, and the state equation thereof includes an attractive term, a repulsive term and a molecule-pore wall interaction term. The partial pressures of the three terms are summed to obtain the total pressure of the confined fluid in the nanopore after correction by using the contribution of the repulsive term of the cubic state equation, the attractive term established based on the critical point movement in S102 and the contribution of the molecule-pore wall interaction term constructed in S201 to the pressure.

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

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

[0131] S3: According to the adsorption phase equilibrium condition of the confined fluid in the nanopore and the bulk phase fluid, an iterative calculation method of a nonlinear equation set is constructed.

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

[0133] S301: According to the adsorption phase equilibrium condition of the confined fluid in the nanopore and the bulk phase fluid, a nonlinear equation set is constructed.

[0134] In a specific methane and ethane system, the methane bulk phase and the adsorption phase in the nanopore are in equilibrium, and at the same time, the ethane bulk phase and the adsorption phase in the nanopore are in equilibrium. When the temperature, pressure, pore radius and bulk phase composition are known, a total of two phase equilibrium equations correspond to two unknown variables, forming a nonlinear equation set. In a specific nitrogen, methane and hydrogen system, when the temperature, pressure, pore radius and bulk phase composition are known, a total of three phase equilibrium equations correspond to three unknown variables, forming a nonlinear equation set:

[0135]

[0136] f = P x φ i is the fugacity of component i in the bulk phase; f p,i is the fugacity of component i in the nanopore; P is the pressure of the bulk phase, MPa; x1, x2, …, x NC-1 are the mole fractions of the 1st, 2nd, …, NC-1 components in the bulk phase; NC is the total number of components;

[0137] S302: Selecting the adsorption phase density and the mole fraction as the primary variables, the fugacity of the adsorption phase is calculated by using the restricted fluid equation of state model with the corrected attractive and pressure terms;

[0138] According to the phase equilibrium equation set, the adsorption phase density and the component mole fraction are specified as the primary variables, the state equation parameters of the mixture under the nanopore confinement condition are calculated by using the van der Waals mixing rule and the linear mixing rule established by S1, S103 and S202, the restricted fluid equation of state model established by S203 is solved, the molar volume of the bulk phase fluid and the reciprocal of the adsorption amount of the adsorption phase fluid are calculated, and then the fugacity of the adsorption phase is calculated. The calculation formula of the fugacity is:

[0139] f = P x φ p,i = P x x1 p,i φ1 p,i (10)

[0140] f = P x φ i = P x x1 i φ1 i (11)

[0141] f = P x φ p,i is the fugacity of component i in the nanopore; φ p,i is the fugacity coefficient of component i in the nanopore; x i is the mole fraction of component i in the bulk phase; φ i is the fugacity coefficient of component i in the bulk phase; f i is the fugacity of component i in the bulk phase.

[0142] The calculation formula of the fugacity coefficient of the adsorption phase is:

[0143]

[0144] wherein b i is the co-volume parameter of component i, m 3 / mol;

[0145] The calculation formula of the fugacity coefficient of the bulk phase is:

[0146]

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

[0148] S303: According to the phase equilibrium of the confined fluid in the nanopore and the bulk fluid, a new adsorption phase molar fraction is calculated by using a continuous iteration method, and the updated nanopore phase component molar fraction calculation formula is as follows:

[0149]

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

[0151] In this step, according to the phase equilibrium criterion of the confined fluid in the nanopore and the bulk fluid, the new nanopore phase component molar fraction is calculated by multiplying the nanopore phase component molar fraction by the bulk phase component fugacity and dividing by the nanopore phase component fugacity, and the nanopore phase component fugacity is updated by using a continuous iteration method until the bulk phase component fugacity is equal to the nanopore phase component fugacity.

[0152] S304: The new adsorption phase density is calculated by using a secant method, and the calculation formula is as follows:

[0153]

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

[0155] According to the new adsorption phase density, it is checked whether the adsorption phase equilibrium condition of the confined fluid in the nanopore and the bulk fluid is met, if not, it returns to step S302 to start a new round of calculation; if yes, the calculation is stopped.

[0156] In a specific embodiment, whether the adsorption phase equilibrium condition of the confined fluid in the nanopore and the bulk fluid is met is judged by the following formula:

[0157]

[0158] S4: Using the adsorption isotherm experimental data of pure substances, the model parameters of adsorbed fluids under different pore media conditions are regressed by using a least squares method.

[0159] Using the adsorption isotherm experimental data of methane and ethane in a porous medium with a pore radius of 1.72 nm, as shown in Figure 4 , the pore radii δ p of methane and ethane are regressed by using a least squares method and respectively. The ratio of their square well potential energy ε p to the Boltzmann constant is 700 K and 1100 K respectively. Figure 4The middle solid line is the model calculation result, the adsorption capacity of pure substance increases with the increase of pressure, and the adsorption capacity of ethane is greater than that of methane under the same conditions. Compared with the experimental data, it is shown that the model parameters obtained by regression can accurately calculate the adsorption capacity of methane and ethane in nanopores.

[0160] Using the experimental data of adsorption isotherms of nitrogen, methane and hydrogen in porous media with a pore radius of 0.69 nm, as shown in Figure 5 The regional radius δ p of nitrogen, methane and hydrogen is obtained by regression using the least square method as The ratio of their square well potential energy ε p to the Boltzmann constant is 880 K, 1250 K and 180 K, respectively. Figure 5 The middle solid line is the model calculation result, the adsorption capacity of methane is greater than that of nitrogen under the same conditions, and the adsorption capacity of nitrogen is greater than that of hydrogen.

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

[0162] Using the model parameters of pure substances in S101 and S4, predict the adsorption capacity of methane and ethane binary mixture in nanopores as shown in Figure 6 By comparing with the experimental values, it is shown that the proposed calculation method of adsorption capacity of confined fluids under the condition of nano-limitation of shale gas reservoir based on state equation can accurately calculate the adsorption capacity of confined fluids in nanopores. From Figure 6 It can be seen that with the increase of methane content in the bulk phase, the ethane content in the adsorption phase decreases, the methane content in the adsorption phase increases, but the total adsorption capacity of methane and ethane decreases, because under the same conditions, ethane is more easily adsorbed than methane.

[0163] Using the model parameters of pure substances in S101 and S4, predict the adsorption capacity of nitrogen, methane and hydrogen ternary mixture in nanopores as shown in Figure 7 By comparing with the experimental values, it is shown that the proposed calculation method of adsorption capacity of confined fluids under the condition of nano-limitation of shale gas reservoir based on state equation can accurately calculate the adsorption capacity of confined fluids in nanopores. From Figure 7 It can be seen that under the same conditions, the component with strong adsorption capacity in the pure substance has stronger adsorption capacity in the mixed system. The adsorption capacity of methane in the ternary mixture of nitrogen, methane and hydrogen is stronger than that of nitrogen, and the adsorption capacity of nitrogen is stronger than that of hydrogen.

[0164] The application provides a new calculation and evaluation method of adsorption amount of limited fluid in shale gas reservoir nanometer pores based on a state equation, which is suitable for adsorption amount calculation of pure substances, binary and multi-component mixed systems, and compared with traditional experimental methods and molecular simulation methods, the method has the characteristics of fast speed, high precision and wide application range, and can effectively predict the adsorption amount of limited fluid in shale gas reservoir nanometer pores, thereby providing technical support for efficient development of shale gas reservoirs.

[0165] The above is only a preferred embodiment of the present application, and does not limit the present application in any form. Although the present application has been disclosed as above with a preferred embodiment, it is not intended to limit the present application. Any person skilled in the art can make some changes or modifications to the above disclosed technical content without departing from the technical solution of the present application, and any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present application still belong to the scope of the technical solution of the present application.

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 set of nonlinear equations is constructed. 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: 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.

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 These are the Lennard-Jones radius parameters for components i and j.

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 is the system temperature, in K; T c,i It is the critical temperature of component i, in K; r p It is the pore radius of the porous medium.

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: 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.

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 It is the radius of the square well region of component i. 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: Where: σ i It is the Lennard-Jones radius parameter of component i.

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, Step S3 specifically 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 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. 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: P=P r +P ma +P mw (9) 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; The formula for calculating the fugacity is: f p,i =Px p,i φ p,i (10) f i =Px i φ i (11) 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 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.

8. The method for calculating the adsorption amount of confined fluid in nanopores based on the equation of state according to claim 7, characterized in that, In step S302, the fugacity coefficient of the adsorbed phase is calculated using the following formula: In the formula: b i It is the co-volume parameter of component i, m 3 / mol; 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.

9. The method for calculating the adsorption amount of confined fluid in nanopores based on the equation of state according to claim 7, 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:

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