Method and program for calculating gas density in nanopores under in-situ conditions of coal seams

Abstract

This invention provides a method and program for calculating gas density within nanopores under in-situ coal seam conditions, belonging to the field of unconventional oil and gas resource development technology. The calculation method obtains the potential energy of gas molecules caused by gas-gas molecule interactions and gas-solid molecule interactions through the intermolecular interaction potential energy equation. Further, it combines these two potential energies to obtain the potential energy function of gas molecules at the solid wall. Considering the combined effect of the upper and lower walls of the nanopore, it further obtains the total potential energy function of gas molecules at different locations within the nanopore. Combining the Boltzmann distribution function, it obtains the functional relationship between the number density of gas molecules near the wall and the total potential energy of gas molecules. Based on function substitution and model simplification, it derives the density distribution function of gas within the nanopore and the method for calculating gas density within the nanopore, applicable to the calculation of gas density within nanoscale pores under in-situ coal seam conditions.

Description

Technical Field

[0001] This invention relates to the field of unconventional oil and gas resource development technology, specifically to a method and program for calculating gas density within nanopores under in-situ coal seam conditions. Background Technology

[0002] Deep coalbed methane resources are a key area for future coalbed methane exploration and development in my country, and have become an important part of the domestic natural gas industry. Coalbed methane is mainly found in nanoscale micropores, and deep coalbed methane is characterized by "high gas content, high saturation, and presence of free gas." However, the extremely low porosity and permeability of deep coal seams mean that they typically lack natural production capacity. Large-scale extreme fracturing is required to create high-permeability flow channels between the matrix, fractures, and wellbore to achieve industrial production. Pilot tests of deep coalbed methane development in the Daning-Jixian block on the eastern edge of the Ordos Basin show that after fracturing, deep coal seams exhibit high initial production followed by rapid decline in output. This is because insufficient methane desorption cannot compensate for the rapid production of free gas. Therefore, understanding the characteristics of methane occurrence within the pores of coal seams is crucial for improving and maintaining high coalbed methane production capacity.

[0003] The invention patent with publication number "CN117630079A" (application number 202410102095.1) provides a dynamic evaluation method for the adsorbed and free states of coalbed methane. This method simulates the adsorption process of coal samples under different pressures and adsorption times using nuclear magnetic resonance (NMR) adsorption experiments. Based on the signal amplitude corresponding to the relaxation time of the NMR spectrum, the NMR spectrum is divided into adsorbed state peaks and free state peaks. The adsorbed state coalbed methane content, free state coalbed methane content, and cumulative coalbed methane content per gram of coal sample are calculated at different pressures. Then, multiple volumetric adsorption experiments are conducted on the coal sample at the same pressures as the NMR experiments to calculate the cumulative coalbed methane content under different pressures. Error analysis is performed on the two experimental methods, and the dynamic evaluation of the changes in the adsorbed and free state contents of coalbed methane over time is achieved through the fitting relationship between the adsorbed and free states and time. The aforementioned patent has certain limitations: First, it uses experimental methods to test and calculate the gas content of adsorbed and free gas in coal samples under different pressure conditions. However, since both nanopores and micropores exist in coal samples, the patent does not provide a method for calculating the gas density in the nanopores of deep coal seams. Second, the patent uses conventional classical thermodynamic equations for gas content calculation, without considering the nano-space confinement effect, making it unsuitable for calculating the gas content within the nanopores of coal seams. Furthermore, the patent achieves dynamic monitoring of the entire process of coalbed methane migration, but does not calculate the density or other physical properties of coalbed methane. It focuses on assessing the adsorbed and free states of coal samples but does not address the scientific problem of calculating gas density within pores.

[0004] Fluids within nanopore throats exhibit unconventional thermodynamic properties due to the confinement effect of nanopores. Professor Strano's team at MIT observed in experiments involving water-filled carbon nanotubes that water exists in a solid state within the nanotubes at 105°C, completely exceeding conventional understanding. The critical temperature values ​​of the fluid within nanochannels measured by differential scanning calorimetry show significant deviations from theoretical calculations, making traditional thermodynamic theories difficult to apply to the development of deep coalbed methane resources. Therefore, accurately understanding the physical properties of gases within nanopores under in-situ coal seam conditions is a crucial issue that needs to be addressed in the development of deep coalbed methane resources. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method and program for calculating the gas density within nanopores under in-situ coal seam conditions. This method is applicable to the calculation of gas density within nanoscale pores under in-situ coal seam conditions and solves the problem of calculating unconventional thermodynamic properties of gas within nanopores under in-situ coal seam conditions.

[0006] The specific technical solution adopted in this invention is as follows:

[0007] A method for calculating the gas density within nanopores under in-situ conditions in coal seams includes the following steps:

[0008] S1. Determine the assumptions: Assume an idealized physical model;

[0009] S2. Establish the total potential energy function of gas molecules in nanopores: Using the intermolecular van der Waals theory, establish the potential energy function of gas molecule interaction and the potential energy function of gas-solid molecule interaction, thereby obtaining the total potential energy function of gas molecules in nanopores.

[0010] S3. Construct a gas density calculation model within nanopores: Based on the Boltzmann distribution theory, obtain the functional relationship between the gas molecule number density near the wall and the total potential energy of the gas molecules, and derive the gas density distribution function within nanopores and the gas density calculation model within nanopores.

[0011] Preferably, step S1 specifically includes:

[0012] Ignore the molecular polarization phenomenon of gases;

[0013] Without considering the influence of the kinetic energy of gas molecules, the kinetic energy includes the translational and rotational kinetic energy of the gas molecules themselves;

[0014] The structural changes of gas molecules under the influence of solid surfaces are ignored;

[0015] We assume that the solid surface is an ideal surface, that is, the surface roughness of the solid surface is ignored.

[0016] Preferably, step S2 includes the following steps:

[0017] Using the van der Waals theory of intermolecular interactions, the pair potential function of intermolecular interactions is:

[0018] ω(r)=-C / r n (1)

[0019] In equation (1), C represents the intermolecular van der Waals interaction constant (J·m). 6 ); r represents the distance (m) between the centers of the interacting atoms or molecules; n represents the bond energy between the interacting atoms or molecules;

[0020] Intermolecular potential energy μ between two adjacent gas molecules g-g for:

[0021]

[0022] In equation (2), A represents the intermolecular interaction parameter; ρ represents the gas molecule number density (1 / m³). 3 C represents the intermolecular van der Waals interaction constant (J·m). 6 ); n represents the number of bond energies between interacting atoms or molecules; σ represents the size of a gas molecule (m); for intermolecular van der Waals interactions, the number of bond energies between interacting atoms or molecules is 6; therefore, equation (2) becomes:

[0023]

[0024] In equation (3), A represents the intermolecular interaction parameter; C represents the intermolecular van der Waals interaction constant (J·m). 6 ); σ represents the size of a gas molecule (m);

[0025] In nanochannels, gas molecules near the solid wall are significantly influenced by solid molecules. Therefore, the thermodynamic properties of the gas within the nanopores depend not only on the interactions between gas molecules but also on the interactions between gas and solid molecules. The potential function for the interactions between gas and solid molecules is characterized by equation (1).

[0026] The potential energy of gas molecules at a distance Z from the solid surface consists of two parts: the potential energy μ generated by the intermolecular interactions between gas molecules. g-g The additional potential energy μ generated by the gas-solid intermolecular interaction g-s , where μ g-g Calculated by equation (3); it should be noted that due to the interaction between gas and solid molecules, the number density of gas molecules is not uniformly distributed near the solid surface, i.e., the number density ρ Z It is a function of position Z;

[0027] For a solid molecule within a ring with a cross-sectional area of ​​dxdz and a radius of x, the number of solid molecules within this ring with a volume of 2πxdxdz is 2πρ. s xdxdz, where ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 Therefore, at a distance Z from the surface, the additional potential energy μ generated by the gas-solid molecular interaction is... g-s We obtain it through the definite integral function:

[0028]

[0029] In equation (4), C' represents the van der Waals interaction constant (J·m⁻¹) between gas molecules and solid molecules. 6 );ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 x and z represent the integration variables; Z represents the distance (m) between the gas and the solid surface; here it is noted that the solid molecule number density per unit volume is related to the solid molecule size d. w The relationship between them is ρ s =6 / π / d w 3 ;

[0030] Therefore, the potential energy of gas molecules near the wall within the nanopore is:

[0031]

[0032] In equation (5), C' represents the van der Waals interaction constant (J·m⁻¹) between gas molecules and solid molecules. 6 );ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 Z represents the distance (m) between the gas and the solid surface.

[0033] Considering the effects of the upper and lower walls, the total potential energy of gas molecules within the nanopore is:

[0034]

[0035] In equation (6), C' represents the van der Waals interaction constant (J·m⁻¹) between gas molecules and solid molecules. 6 );ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 D represents the characteristic size of the pores (m); Z represents the distance between the gas and the solid surface (m); μ g-s (DZ) represents the additional potential energy generated by the interaction of the other wall of the pore with gas molecules.

[0036] Preferably, step S3 includes the following steps:

[0037] According to the Boltzmann distribution theory, the gas molecule number density ρ at a distance Z from the wall is... Z It is obtained by calculation using the following formula:

[0038] ρ Z =ρ0exp[-(μ(Z)-μ0) / kT] (7)

[0039] In equation (7), k represents the Boltzmann constant (J·K). -1 T represents temperature (K); ρ0 represents the number density of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions (1 / m³). 3 μ0 represents the potential energy of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions, and is obtained by the following formula:

[0040]

[0041] In equation (8), C represents the intermolecular van der Waals interaction constant (J·m). 6 ); ρ0 represents the number density of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions (1 / m²). 3 ); σ represents the size of a gas molecule (m);

[0042] Combining equations (6) to (8), the gas molecule number density at position Z is:

[0043] ρ Z =ρ0exp[-(μ g-g (Z)+μ g-s (Z)+μ g-s (DZ)-μ0) / kT] (9)

[0044] Combining equations (3) and (4), equation (9) is transformed into:

[0045]

[0046] Equation (10) is a transcendental function. For ease of solution, the following substitutions and simplifications are made:

[0047]

[0048] In equation (11), the range of x is [0, 1), and equivalent function substitutions are performed within this range:

[0049]

[0050] Error analysis shows that the correlation between the substitution function and the objective function is 0.905, meaning that an equivalent substitution can be performed within the range [0,1). Therefore, equation (10) can be rewritten as:

[0051] (2.5μ0+kT)ln(1-x)-μ g-s =0 (13)

[0052] Solving equation (13) yields:

[0053]

[0054] Therefore, the gas molecule number density at position Z is:

[0055]

[0056] Considering the effects of the upper and lower walls, the gas density distribution function within the nanopores is obtained as follows:

[0057]

[0058] In equation (16), σ represents the gas molecule size (m); D represents the pore characteristic size (m); and C' represents the van der Waals interaction constant between gas molecules and solid molecules (J·m). 6 C represents the intermolecular van der Waals interaction constant (J·m). 6 );ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 ); k represents the Boltzmann constant (J·K). -1 T represents temperature (K); ρ0 represents the number density of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions (1 / m³). 3 ).

[0059] The distribution of gas density within the nanopores can be calculated using equation (16).

[0060] Integrating equation (16), the density of the gas inside the nanopores is obtained as follows:

[0061]

[0062] In equation (17), x, y, and z represent the integral variables of the volume integral, respectively; Δx and Δy represent the dimensions (m) of the gas characterization unit in the pores, respectively; and ξ represents the gas density calculation coefficient in the nanopores.

[0063] In equation (17), σ represents the gas molecule size (m); D represents the pore characteristic size (m); and C' represents the van der Waals interaction constant between gas molecules and solid molecules (J·m). 6C represents the intermolecular van der Waals interaction constant (J·m). 6 );ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 ); k represents the Boltzmann constant (J·K). -1 T represents temperature (K); ρ0 represents the number density of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions (1 / m³). 3 ).

[0064] An electronic device, comprising:

[0065] At least one processor; and

[0066] The memory stores instructions that, when executed by the at least one processor, cause the at least one processor to perform the above-described calculation method.

[0067] A machine-readable storage medium storing executable instructions that, when executed, cause the machine to perform the above-described calculation method.

[0068] A calculation program that performs the above calculation method.

[0069] A method for calculating the gas density distribution within nanopores under in-situ coal seam conditions, using the above formula (16):

[0070]

[0071] In equation (16), C' represents the van der Waals interaction constant between gas molecules and solid molecules (J·m). 6 );ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 σ represents the gas molecule size (m); Z represents the distance from the solid molecule surface (m); D represents the characteristic pore size (m); k represents the Boltzmann constant (J·K). -1 T represents temperature (K); C represents the van der Waals interaction constant between molecules (J·m). 6 ); ρ0 represents the number density of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions (1 / m²). 3 ).

[0072] A method for calculating the gas density within nanopores under in-situ coal seam conditions, using the above formula (17):

[0073]

[0074] In equation (17), σ represents the gas molecule size (m); D represents the characteristic pore size (m); ξ represents the gas density calculation coefficient within the nanopores; and C' represents the van der Waals interaction constant between gas molecules and solid molecules (J·m). 6 C represents the intermolecular van der Waals interaction constant (J·m). 6 );ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 ); k represents the Boltzmann constant (J·K). -1 T represents temperature (K); ρ0 represents the number density of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions (1 / m³). 3 ).

[0075] The beneficial effects of this invention are:

[0076] This invention obtains the potential energy of gas molecules caused by gas-gas molecule interactions and gas-solid molecule interactions through the intermolecular interaction potential energy equation. Furthermore, by combining these two potential energy components, the potential energy function of gas molecules at the solid wall is obtained. Simultaneously, considering the combined effect of the upper and lower walls of the nanopore, the total potential energy function of gas molecules at different locations within the nanopore is further obtained. Combining the Boltzmann distribution function, the functional relationship between the gas molecule number density near the wall and the total potential energy of gas molecules is obtained. Based on function substitution and model simplification, the density distribution function of gas within the nanopore and a method for calculating the gas density within the nanopore are derived. The gas density calculation method provided by this invention considers factors such as the strength of gas-solid molecule interactions and the number density of solid molecules, and is applicable to the calculation of gas density within nanoscale pores under in-situ coal seam conditions. This not only provides a more accurate method for calculating gas properties for assessing recoverable reserves of unconventional natural gas resources, but also facilitates the theoretical development and technological optimization of efficient unconventional natural gas development. Attached Figure Description

[0077] Figure 1 This is a schematic diagram of the gas-solid molecular interaction within nanopores under in-situ coal seam conditions; Figure A shows the effect of the two walls on the gas molecules at position Z within the nanopores; Figure B shows the potential energy of the gas molecules near the wall within the nanopores.

[0078] Figure 2 This is a diagram showing the gas density distribution within nanopores under in-situ coal seam conditions.

[0079] Figure 3 The results are from molecular dynamics simulations of gas density distribution within nanopores.

[0080] Figure 4This is a graph showing the trend of gas density variation in nanopores of different sizes under different strengths of gas-solid intermolecular interactions. Detailed Implementation

[0081] The following description is based on specific embodiments:

[0082] Example 1:

[0083] A method for calculating the gas density within nanopores under in-situ conditions in coal seams, specifically including the following steps:

[0084] S1. Determine the assumptions:

[0085] Ignore the molecular polarization phenomenon of gases;

[0086] The effects of kinetic energy, such as the translation and rotation of gas molecules, are not considered.

[0087] The structural changes of gas molecules under the influence of solid surfaces are ignored;

[0088] We assume that the solid surface is an ideal surface, that is, the surface roughness of the solid surface is ignored.

[0089] S2, Total potential energy function of gas molecules within nanopores:

[0090] Using the van der Waals theory of intermolecular interactions, the pair potential function of intermolecular interactions is:

[0091] ω(r)=-C / r n (1)

[0092] In equation (1), C represents the intermolecular van der Waals interaction constant (J·m). 6 ); r represents the distance (m) between the centers of interacting atoms or molecules; n represents the bond energy between interacting atoms or molecules.

[0093] Intermolecular potential energy μ between two adjacent gas molecules g-g for:

[0094]

[0095] In equation (2), ρ represents the gas molecule number density (1 / m³). 3 C represents the intermolecular van der Waals interaction constant (J·m). 6 ); n represents the number of bond energies between interacting atoms or molecules; σ represents the size of a gas molecule (m); for intermolecular van der Waals interactions, the number of bond energies between interacting atoms or molecules is 6; therefore, equation (2) becomes:

[0096]

[0097] In equation (3), A represents the intermolecular interaction parameter; C represents the intermolecular van der Waals interaction constant (J·m). 6 ) ; σ represents the size of a gas molecule (m).

[0098] In nanochannels, gas molecules near the solid wall are significantly affected by solid molecules. Therefore, the thermodynamic properties of the gas within the nanopores depend not only on the interactions between gas molecules but also on the interactions between gas and solid molecules. The potential function of the gas-solid molecular interactions can be characterized by equation (1).

[0099] The potential energy of gas molecules at a distance Z from the solid surface consists of two parts: the potential energy μ generated by the intermolecular interactions between gas molecules. g-g The additional potential energy μ generated by the gas-solid intermolecular interaction g-s , where μ g-g It can be calculated by equation (3); it should be noted that due to the interaction between gas and solid molecules, the number density of gas molecules is not uniformly distributed near the solid surface, that is, the number density ρ Z It is a function of position Z;

[0100] like Figure 1 As shown, for solid molecules within a ring with a cross-sectional area of ​​dxdz and a radius of x, the number of solid molecules within this ring with a volume of 2πxdxdz is 2πρ. s xdxdz, where ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 Therefore, at a distance Z from the surface, the additional potential energy μ generated by the gas-solid molecular interaction... g-s We obtain it through the definite integral function:

[0101]

[0102] In equation (4), C' represents the van der Waals interaction constant (J·m⁻¹) between gas molecules and solid molecules. 6 );ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 x and z represent the integration variables; Z represents the distance (m) between the gas and the solid surface; here it is noted that the solid molecule number density per unit volume is related to the solid molecule size d. w The relationship between them is ρ s =6 / π / d w 3 .

[0103] Therefore, the potential energy of gas molecules near the wall within the nanopore is:

[0104]

[0105] In equation (5), C' represents the van der Waals interaction constant (J·m⁻¹) between gas molecules and solid molecules. 6 );ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 Z represents the distance (m) between the gas and the solid surface.

[0106] Considering the effects of the upper and lower walls, the total potential energy of gas molecules within the nanopore is:

[0107]

[0108] In equation (6), C' represents the van der Waals interaction constant (J·m⁻¹) between gas molecules and solid molecules. 6 );ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 D represents the characteristic size of the pores (m); Z represents the distance between the gas and the solid surface (m); μ g-s (DZ) represents the additional potential energy generated by the interaction of the other wall of the pore with gas molecules.

[0109] S3. Calculation model for gas density within nanopores:

[0110] According to the Boltzmann distribution theory, the gas molecule number density ρ at a distance Z from the wall is... Z It is obtained by calculation using the following formula:

[0111] ρ Z =ρ0exp[-(μ(Z)-μ0) / kT] (7)

[0112] In equation (7), k represents the Boltzmann constant (J·K). -1 T represents temperature (K); ρ0 represents the number density of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions (1 / m³). 3 μ0 represents the potential energy of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions, and is obtained by the following formula:

[0113]

[0114] In equation (8), C represents the intermolecular van der Waals interaction constant (J·m). 6 ); ρ0 represents the number density of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions (1 / m²). 3 ) ; σ represents the size of a gas molecule (m).

[0115] Combining equations (6) to (8), the gas molecule number density at position Z is:

[0116] ρ Z =ρ0exp[-(μ g-g (Z)+μ g-s (Z)+μ g-s (DZ)-μ0) / kT] (9)

[0117] Combining equations (3) and (4), equation (9) is transformed into:

[0118]

[0119] Equation (10) is a transcendental function. For ease of solution, the following substitutions and simplifications are made:

[0120]

[0121] In equation (11), the range of x is [0, 1), and equivalent function substitutions are performed within this range:

[0122]

[0123] Error analysis shows that the correlation between the substitution function and the objective function is 0.905, meaning that an equivalent substitution can be performed within the range [0,1). Therefore, equation (10) can be rewritten as:

[0124] (2.5μ0+kT)ln(1-x)-μ g-s =0 (13)

[0125] Solving equation (13) yields:

[0126]

[0127] Therefore, the gas molecule number density at position Z is:

[0128]

[0129] Considering the effects of the upper and lower walls, the gas density distribution function within the nanopores is obtained as follows:

[0130]

[0131] In equation (16), σ represents the gas molecule size (m); D represents the pore characteristic size (m); and C' represents the van der Waals interaction constant between gas molecules and solid molecules (J·m). 6 C represents the intermolecular van der Waals interaction constant (J·m). 6 );ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 ); k represents the Boltzmann constant (J·K). -1T represents temperature (K); ρ0 represents the number density of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions (1 / m³). 3 ).

[0132] The distribution of gas density within the nanopores can be calculated using equation (16).

[0133] Integrating equation (16), the density of the gas inside the nanopores is obtained as follows:

[0134]

[0135] In equation (17), x, y, and z represent the integral variables of the volume integral, respectively; Δx and Δy represent the dimensions (m) of the gas characterization unit in the pores, respectively; and ξ represents the gas density calculation coefficient in the nanopores.

[0136] In equation (17), σ represents the gas molecule size (m); D represents the pore characteristic size (m); and C' represents the van der Waals interaction constant between gas molecules and solid molecules (J·m). 6 C represents the intermolecular van der Waals interaction constant (J·m). 6 );ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 ); k represents the Boltzmann constant (J·K). -1 T represents temperature (K); ρ0 represents the number density of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions (1 / m³). 3 ).

[0137] Example 2:

[0138] Taking a coalbed methane field as an example, the coal seam is 1000 meters deep, the pressure is 10.5 MPa, and the temperature is 50℃. Through testing, it can be found that the average pore size in the coal seam is 19 nm, and the gas is methane.

[0139] The parameters required for calculating gas density are obtained through chemical testing methods, as shown in Table 1 below.

[0140] Table 1. Parameter values ​​required for gas density calculation

[0141]

[0142] Substitute the data from Table 1 into the following calculation formula:

[0143]

[0144] The density distribution of methane within nanopores under in-situ coal seam conditions can be plotted, as shown in the following figure. Figure 2As shown in the figure, the vertical axis represents ρ / ρ0, where ρ represents the gas molecule number density (1 / m³). 3 ), ρ0 represents the gas molecule number density (1 / m) far from the solid wall and unaffected by gas-solid intermolecular interactions. 3 ); In the figure, “σ-g” represents the size of a gas molecule (m).

[0145] Depend on Figure 2 The distribution characteristics of methane density within nanoscale pores under in-situ coal seam conditions are as follows: near the pore wall, the gas density increases due to the influence of the solid wall on gas molecules; in the central region of the pores, the gas density is consistent with conventional calculations due to the smaller influence of the solid wall. Furthermore, the smaller the gas molecule size, the more significant the influence of the solid wall on the gas density.

[0146] Accuracy assessment of equation (16): Due to technical limitations, molecular dynamics simulation is commonly used to simulate the gas density distribution in nanopores. The molecular dynamics simulation method described in the literature "Mosher K, He J, Liu Y, et al. Molecular simulation of methane adsorption in micro- and mesoporous carbons with applications tocoal and gas shale systems[J]. International Journal of Coal Geology, 2013, 109-11036-44." was used to simulate methane molecules in nanopores. The density distribution was simulated, and the simulation results are as follows: Figure 3 As shown.

[0147] Depend on Figures 2-3 It can be seen that the gas density distribution law in the nanopores plotted according to Equation (16) is consistent with the molecular dynamics simulation results, which shows that the calculation method provided by the present invention can calculate the density distribution law of gas molecules in nanoscale pores.

[0148] Substitute the data from Table 1 into the following calculation formula:

[0149]

[0150] The density (apparent density) of methane within nanopores under in-situ coal seam conditions can be calculated. Further calculations can be performed on the density of gas within nanopores of different sizes under varying gas-solid molecular interaction strengths, and the trend of gas density variation can be plotted. The results are as follows: Figure 4 As shown.

[0151] Depend on Figure 4It is known that when the strength of gas-solid intermolecular interactions is constant, the methane density within nanopores gradually increases as the pore size decreases, indicating that the influence of gas-solid intermolecular interactions on gas density is enhanced. Within the same nanopore, the methane density gradually increases with the strengthening of gas-solid intermolecular interactions. Therefore, this invention can simulate and calculate the gas density within nanopores under different strengths of gas-solid intermolecular interactions.

Claims

1. A method for calculating the gas density within nanopores under in-situ conditions in coal seams, characterized in that, Includes the following steps: S1. Determine the assumptions: Assume an idealized physical model; S2. Establish the total potential energy function of gas molecules in nanopores: Using the intermolecular van der Waals theory, establish the potential energy function of gas molecule interaction and the potential energy function of gas-solid molecule interaction, thereby obtaining the total potential energy function of gas molecules in nanopores. S3. Constructing a gas density calculation model within nanopores: Based on Boltzmann distribution theory, the functional relationship between the gas molecule number density near the wall and the total potential energy of the gas molecules is obtained. The gas density distribution function within nanopores and the gas density calculation model within nanopores are then derived; where: S1 includes the following steps: Ignore the molecular polarization phenomenon of gases; Without considering the influence of the kinetic energy of gas molecules, the kinetic energy includes the translational and rotational kinetic energy of the gas molecules themselves; The structural changes of gas molecules under the influence of solid surfaces are ignored; Assuming the solid surface is an ideal surface, that is, ignoring the surface roughness of the solid surface; S2 includes the following steps: Using the van der Waals theory of intermolecular interactions, the pair potential function of intermolecular interactions is: (1) In equation (1), C The van der Waals interaction constant (J) represents the intermolecular interaction constant. m 6 ); r Represents the distance (m) between the centers of interacting atoms or molecules; n This represents the bond energy number between interacting atoms or molecules; Intermolecular potential between two adjacent gas molecules μ g-g for: (2) In equation (2), A Indicates parameters of intermolecular interactions; ρ Represents the number density of gas molecules (1 / m 3 ); C The van der Waals interaction constant (J) represents the intermolecular interaction constant. m 6 ); n This represents the bond energy number between interacting atoms or molecules; σ Let m represent the size of the gas molecule; for the van der Waals forces between molecules, the bond energy between the interacting atoms or molecules is 6; therefore, equation (2) becomes: (3) In equation (3), A Indicates parameters of intermolecular interactions; C The van der Waals interaction constant between molecules (J) m 6 ); σ Indicates the size of gas molecules (m); For a cross-sectional area of ​​d x d z , radius is x The solid molecules within the ring have a volume of 2π. x d x d z The number of solid molecules inside the ring is 2π ρ s x d x d z ,in ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 ); at a distance from the surface Z At this point, the additional potential energy generated by the interaction between gas and solid molecules μ g-s We obtain it through the definite integral function: (4) In equation (4), C ' represents the van der Waals interaction constant (J) between gas molecules and solid molecules. m 6 ); ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 ); x and z They represent the integration variables respectively; Z Represents the distance (m) between the gas and the solid surface; the number density of solid molecules per unit volume and the size of solid molecules. d w The relationship is ρ s =6 / π / d w 3 ; The potential energy of gas molecules near the wall within the nanopore is: (5) In equation (5), C ' represents the van der Waals interaction constant (J) between gas molecules and solid molecules. m 6 ); ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 ); Z Indicates the distance (m) between the gas and the solid surface; Considering the effects of the upper and lower walls, the total potential energy of gas molecules within the nanopore is: (6) In equation (6), C ' represents the van der Waals interaction constant (J) between gas molecules and solid molecules. m 6 ); ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 ); D Indicates the characteristic size of the pores (m); Z Indicates the distance (m) between the gas and the solid surface; μ g-s ( D - Z This represents the additional potential energy generated by the interaction between the other wall of the pore and the gas molecules. S3 includes the following steps: According to the Boltzmann distribution theory, the number density of gas molecules at a distance Z from the wall is... ρ Z It is obtained by calculation using the following formula: (7) In equation (7), k Boltzmann constant (J) K -1 ); T Indicates temperature (K); ρ 0 represents the number density of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions (1 / m²). 3 ); μ 0 represents the potential energy of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions. μ 0 is obtained from the following formula: (8) In equation (8), C The van der Waals interaction constant (J) represents the intermolecular interaction constant. m 6 ); ρ 0 represents the number density of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions (1 / m²). 3 ); σ Indicates the size of gas molecules (m); Combining equations (6) to (8), the gas molecule number density at position Z is: (9) Combining equations (3) and (4), equation (9) is transformed into: (10) Equation (10) is modified and simplified as follows: (11) In formula (11), x The value range of is [0, 1), and an equivalent function replacement is made in this range: (12) Equivalent substitution is performed within the range [0,1), and equation (10) is rewritten as: (13) Solving equation (13) yields: (14) Position Z The number density of gas molecules at the location (15) Considering the effects of the upper and lower walls, the gas density distribution function within the nanopores is: (16) In equation (16), σ Indicates the size of gas molecules (m); D Indicates the characteristic size of the pores (m); C ' represents the van der Waals interaction constant (J) between gas molecules and solid molecules. m 6 ); C The van der Waals interaction constant between molecules (J) m 6 ); ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 ); k Boltzmann constant (J) K -1 ); T Indicates temperature (K); ρ 0 represents the number density of gas molecules far from the solid wall and unaffected by gas-solid intermolecular interactions (1 / m²). 3 ); Integrating equation (16), the density of the gas inside the nanopores is obtained as follows: (17) In formula (17), x, y, z respectively represent the volume-integrated integral variable; Δx, Δy respectively represent the size (m) of the gas characterization element within the pore; ξ represents the nanopore gas density calculation coefficient; In equation (17), σ Indicates the size of gas molecules (m); D Indicates the characteristic size of the pores (m); C ' represents the van der Waals interaction constant (J) between gas molecules and solid molecules. m 6 ); C The van der Waals interaction constant between molecules (J) m 6 ); ρ s Represents the number density of solid molecules per unit volume (1 / m³). 3 ); k Boltzmann constant (J) K -1 ); T Indicates temperature (K); ρ 0 represents the gas molecule number density (1 / m³) far from the solid wall and unaffected by gas-solid intermolecular interactions. 3 ).

2. An electronic device, comprising: include: At least one processor; as well as A memory that stores instructions, which, when executed by the at least one processor, cause the at least one processor to perform the computation method of claim 1.

3. A machine-readable storage medium, characterized in that, The machine stores executable instructions that, when executed, cause the machine to perform the computation method of claim 1.

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