An analysis method for apparent permeability considering the coupling of multiple mass transfer mechanisms in coal and rock

Abstract

The present invention discloses an analysis method for apparent permeability considering the coupling of multiple mass transfer mechanisms in coal and rock, which relates to a calculation method for the permeability of coal and rock, and solves the problem that the traditional coalbed methane permeability model ignores the influence of adsorption on the flow of coalbed methane and the inaccurate characterization of the flow law of coalbed methane. The key points of the technical solution are as follows: The nano-pores of coal and rock are equivalently divided into an adsorption layer region and an internal region, an apparent permeability equation for the adsorption layer region is established, and the apparent permeability equation for the adsorption layer region is corrected by the proportion of the adsorption layer region to obtain a first apparent permeability equation; an apparent permeability equation for the internal region is established, and the apparent permeability equation for the internal region is corrected by the proportion of the internal region to obtain a second apparent permeability equation; the first and second apparent permeability equations are superimposed to obtain a calculation model for the apparent permeability of gas in the nano-pores of coal and rock; the contribution of surface diffusion of gas in the adsorption layer to the flow flux and the influence of the coupling of multiple mass transfer mechanisms are considered.

Description

Technical Field

[0001] The present invention relates to a method for calculating the permeability of coal and rock, and more specifically, to an analysis method for apparent permeability considering the coupling of various mass transfer mechanisms in coal and rock. Background Art

[0002] Coal and rock are typical porous media with a pore throat system in the micro-nano scale. Generally, a large amount of coalbed methane is stored in underground coal seams. Coalbed methane refers to the natural gas generated and self-stored in coal seams during the coalification process. The flow of coalbed methane in coal pores is mainly diffusion-based. The permeability of coalbed methane refers to the resistance characteristics of coal seams to the flow of coalbed methane and is a key parameter for the flow of coalbed methane in coal and rock. The flow behavior of coalbed methane is usually the result of the coupling of multiple flow mechanisms, such as viscous flow, slip flow, Knudsen diffusion, and surface diffusion.

[0003] Currently, the main apparent permeability models of coalbed methane formed based on seepage mechanics methods are the Beskok-Karniadakis, Javadpour, and Klinkenberg models. The models such as Jones-Owens, Florence, Ertekin, Michel, Sakhaee-Bryant, and Civan are based on the Klinkenberg model, and the main difference lies in the calculation method of the slip coefficient b k being different. The above three types of models all assume that coalbed methane is an ideal gas and do not consider the size of coalbed methane molecules and the intermolecular interaction forces. In addition, in a medium where adsorbed gas and free gas coexist, the gas migration mechanisms mainly include the viscous flow and Knudsen diffusion of free gas and the surface diffusion of adsorbed gas. Knudsen diffusion describes the gas migration phenomenon caused by the collision of gas molecules with the pore wall, and the root cause of the slip effect is also the collision of gas molecules with the pore wall. Therefore, the two are essentially the same mechanism. The existing models only consider the viscous flow and Knudsen diffusion of free gas and do not consider the surface diffusion phenomenon of adsorbed gas, and cannot accurately characterize the flow law of coalbed methane under micro-nano scale conditions. Therefore, it is urgent to establish a coalbed methane permeability model applicable to the micro-nano scale of coal and rock to characterize the flow capacity of coalbed methane under different flow mechanisms in coal micropores. Summary of the Invention

[0004] The purpose of this application is to provide an analysis method for apparent permeability considering the coupling of various mass transfer mechanisms in coal and rock, considering the influence of adsorption on the flow of coalbed methane, equivalently dividing the nano-pores of coal and rock into two regions, respectively constructing an apparent permeability calculation model, and correcting the model through the ratio of the adsorption layer to the non-adsorption layer to improve the accuracy of permeability calculation.

[0005] The above technical objectives of the present application are achieved through the following technical solutions: including

[0006] A. Equivalently divide the nano-pores of coal and rock into two regions: the adsorption layer region and the internal region;

[0007] B. Establish the apparent permeability equation of the adsorption layer region, and correct the apparent permeability equation of the adsorption layer region through the proportion of the adsorption layer region to obtain the first apparent permeability equation;

[0008] Consider Knudsen diffusion and viscous flow to establish the apparent permeability equation of the internal region, and correct the apparent permeability equation of the internal region through the proportion of the internal region to obtain the second apparent permeability equation;

[0009] C. Superimpose the first apparent permeability equation and the second apparent permeability equation to obtain the calculation model of the apparent permeability of gas in the nano-pores of coal and rock.

[0010] Compared with the prior art, the present application equivalently divides the nano-pores of coal and rock into two regions, namely the adsorption layer region and the internal region, and respectively considers the influencing factors of the two regions on gas molecules. For the adsorption layer region, the movement of gas molecules is mainly surface diffusion based on the interaction between gas molecules and the pore wall. Therefore, on the basis of the Fick diffusion equation, the apparent permeability equation of the adsorption layer region is constructed, and it is corrected through the proportion of the adsorption layer region to obtain the first apparent permeability equation. For the internal region of the non-adsorption layer, the apparent permeability equation of the internal region can be expressed as the absolute permeability multiplied by the correction factor. At the same time, considering the influence of Knudsen diffusion and viscous flow, the apparent permeability equation of the internal region is constructed, and it is corrected through the proportion of the internal region to obtain the second apparent permeability equation. Finally, combining the first and second apparent permeability equations, the calculation model of the apparent permeability of gas in the nano-pores of coal and rock is obtained. This model comprehensively considers three flow mechanisms: viscous flow, Knudsen diffusion, and surface diffusion, and considers the proportions of the adsorption layer region and the internal region, which can effectively improve the calculation accuracy of gas permeability.

[0011] Further, in the above step B, the apparent permeability equation of the adsorption layer region is as follows:

[0012]

[0013] Where: D s is the surface diffusion coefficient, m 2 / s; μ is the fluid viscosity, μPa·s; M is the gas molecule mass, g / mol; C smax is the adsorption phase concentration under the limit pressure, mmol / g; P Lis the Langmuir pressure, MPa; P is the gas pressure, MPa.

[0014] Further, in the above step B, the first apparent permeability equation is as follows:

[0015]

[0016] where: r in is the radius of the internal region, nm; r is the pore radius, nm.

[0017] Further, in the above step B, the apparent permeability equation of the internal region is as follows:

[0018]

[0019] where: K ab is the absolute permeability; Kn is the Knudsen coefficient; α is the rarefaction coefficient for viscosity correction; b is the slip coefficient, usually taken as -1 for circular pores.

[0020] Further, in the above step B, the second apparent permeability equation is as follows:

[0021]

[0022] Further, in the above step C, the calculation model of the apparent permeability of coal-rock nano-pore gas is as follows:

[0023]

[0024] Further, it also includes D. Construct a coal-rock nano-pore structure model through molecular dynamics simulation, obtain key parameters and simulated apparent permeability results, substitute the key parameters into the apparent permeability calculation model to obtain the model apparent permeability results, and compare the model apparent permeability results with the simulated apparent permeability results to verify the accuracy of the calculation model of the apparent permeability of coal-rock nano-pore gas.

[0025] Adopting the above technical solution, a coal-rock nano-pore structure model is constructed through molecular dynamics simulation, key parameters and simulated apparent permeability results are obtained, the key parameters are substituted into the apparent permeability calculation model to calculate the model apparent permeability results, and the model apparent permeability results are compared with the simulated apparent permeability results to verify the accuracy of the model. This verification method has stronger adaptability and smaller errors, and is not limited by factors such as experimental conditions, parameter ranges, and experimental media.

[0026] Further, in the above step D, it includes:

[0027] D1. Construct a coal-rock nano-pore structure model, conduct isothermal adsorption simulation, and obtain key parameters, where the key parameters include: the adsorption-phase concentration C under the limit pressure smax and the Langmuir pressure P L ;

[0028] D2. Substitute the key parameters into the calculation formula for the apparent permeability of gas in coal-rock nano-pores to obtain the apparent permeability curve of coal-rock nano-pores;

[0029] D3. Calculate the permeability through the coal-rock nano-pore structure model to obtain the simulated apparent permeability; compare the apparent permeability curve of coal-rock nano-pores with the simulated apparent permeability to verify the calculation accuracy of the calculation formula for the apparent permeability of gas in coal-rock nano-pores.

[0030] Further, in the above step D1, it includes:

[0031] D11. Use molecular models of high, medium, and low coal ranks to establish an initial coal-rock nano-pore structure configuration;

[0032] D12. Relax the initial coal-rock nano-pore structure model to obtain a constant-energy coal-rock nano-pore structure model;

[0033] D13. Conduct isothermal adsorption simulation through the constant-energy coal-rock nano-pore structure model, calculate the adsorption amount, fit the adsorption amount with the adsorption isotherm curve in the Langmuir form to obtain key parameters.

[0034] Further, in the above step D1, it also includes: D14. Calculate the adsorption amount through the constant-energy coal-rock nano-pore structure model, compare the adsorption amount with the excess adsorption amount obtained experimentally, and verify the reliability of the constant-energy coal-rock nano-pore structure model.

[0035] Compared with the prior art, the present application has the following beneficial effects:

[0036] 1. The present application provides a calculation model for the apparent permeability of gas in coal-rock nano-pores, which considers the contribution of surface diffusion of gas in the adsorption layer to the flow flux, and considers three flow mechanisms of viscous flow, Knudsen diffusion, and surface diffusion existing in gas mass transfer in coal-rock nano-pores. When calculating the apparent permeability, the coal-rock nano-pores are equivalently divided into two regions, namely the adsorption layer region and the internal region, and the influencing factors of gas molecules in the two regions are considered separately, and the model is corrected by combining the proportion of the adsorption layer region and the non-adsorption layer region, thereby improving the accuracy of the model.

[0037] 2. This application provides a method for verifying the reliability of a computational model. Traditional model verification mostly uses the method of comparing with the experimental result data of predecessors. Limited by factors such as experimental conditions, parameter ranges, and experimental media, the analysis of experimental results cannot well adapt to the model calculation results, resulting in a very low coverage rate of the model calculation results and experimental data. In this paper, molecular dynamics simulation is used to construct a coal-rock nano-pore structure model, simulate the flow of gas in the coal-rock nano-pores, and verify the established computational model. When verifying the model, it has stronger adaptability, is more convenient for comparison, and has smaller errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, form a part of this application, and do not limit the embodiments of the present invention. In the drawings:

[0039] Figure 1 It is a method for constructing a computational model for the apparent permeability of coal-rock nano-pore gas provided by an embodiment of the present invention;

[0040] Figure 2 It is a method for verifying the apparent permeability computational model provided by an embodiment of the present invention;

[0041] Figure 3 It is a schematic diagram of coal-rock nano-pores based on the distribution of the adsorption layer region and the internal region provided by an embodiment of the present invention;

[0042] Figure 4 It is the verification of the low-rank coal model result and the molecular dynamics result provided by an embodiment of the present invention;

[0043] Figure 5 It is the verification of the medium-rank coal model result and the molecular dynamics result provided by an embodiment of the present invention;

[0044] Figure 6 It is the verification of the high-rank coal model result and the molecular dynamics result provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0045] Here, the exemplary embodiments will be described in detail, and the examples are shown in the drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. On the contrary, they are merely examples of devices and methods consistent with some aspects of this application as detailed in the appended claims.

[0046] Embodiment: An analysis method for apparent permeability considering the coupling of multiple mass transfer mechanisms in coal-rock nano-pores

[0047] This embodiment aims to provide an analysis method for apparent permeability considering the coupling of multiple mass transfer mechanisms in coal-rock nano-pores, including two parts: constructing an apparent permeability calculation model and verifying the apparent permeability calculation model. The following will be combined with the attached Figure 1-6 , to describe the embodiments of the present application.

[0048] As Figure 1 shown, constructing an apparent permeability calculation model includes the following processes:

[0049] A. Equivalently divide the coal-rock nano-pores into two regions: the adsorption layer region and the internal region;

[0050] B. Establish an apparent permeability equation for the adsorption layer region, and modify the apparent permeability equation of the adsorption layer region through the proportion of the adsorption layer region to obtain the first apparent permeability equation;

[0051] Consider Knudsen diffusion and viscous flow to establish an apparent permeability equation for the internal region, and modify the apparent permeability equation of the internal region through the proportion of the internal region to obtain the second apparent permeability equation;

[0052] C. Superimpose the first apparent permeability equation and the second apparent permeability equation to obtain an apparent permeability calculation model for the gas in the coal-rock nano-pores.

[0053] In addition to considering viscous flow and Knudsen diffusion in the flow within the coal-rock nano-pores, the surface diffusion of adsorbed gas also needs to be characterized. The applicant found through research that due to density fluctuations, the density distribution of fluid molecules has a multi-layer characteristic under high pressure, but it has no obvious effect on the velocity distribution in the central region. There is still only a single layer of adsorbed molecules that has a significant impact on gas flow.

[0054] Therefore, in step A, the coal-rock nano-pores are equivalently divided into two regions, namely the adsorption layer region and the internal region of the non-adsorption layer region. As Figure 3 shown, r is the pore radius, r in is the radius of the internal region, and (r - r in ) is the width of the adsorption layer region;

[0055] In step B, for the adsorption layer region within the pores, the flow mechanism is surface diffusion based on the interaction between gas molecules and the pore wall, where the adsorbed gas molecules can be regarded as sliding along the surface under the action of a concentration gradient. It can be expressed in the form of the Fick diffusion equation as:

[0056]

[0057] In the formula, J s is the molar flux, mol / m 2 ·s; Ds is the surface diffusion coefficient, m 2 / s; C s is the adsorbed-phase concentration, mol / m 3 .

[0058] Considering that gas molecules mainly undergo monolayer adsorption in the nano-pores of coal and rock, the gas adsorption amount on the pore surface can be expressed by the Langmuir isothermal adsorption law:

[0059]

[0060] where C smax is the adsorbed-phase concentration at the limit pressure, mmol / g; P L is the Langmuir pressure, MPa; P is the gas pressure, MPa.

[0061] The surface diffusion mass flux equation can be obtained through formulas (1) and (2) as:

[0062]

[0063] where M is the mass of gas molecules, g / mol.

[0064] For the determination of the surface diffusion coefficient D s , it can be determined by fitting experimental data or calculated through a theoretical model. Considering applicability and experimental conditions, the theoretical model calculation is selected to obtain the D s value. When calculating the D s value, considering the influence of monolayer adsorption and pressure, the calculation formula is:

[0065]

[0066]

[0067]

[0068]

[0069] where is the surface diffusion coefficient when the surface coverage is equal to 0, m 2 / s; θ is the surface coverage of the gas in the equilibrium state, which can be defined by the Langmuir isotherm: θ = P / (P + P L ); κ is the surface gas molecule blocking coefficient; κ b is the blocking rate constant, m / s; κ m is the moving rate constant, m / s; ΔH is the isosteric heat of adsorption, kJ / mol; T is the temperature, K.

[0070] It should be noted that for Equation (5), only considering it as a function of the equivalent adsorption heat and not considering the influence of gas molecular weight, simplification is carried out. Thus, the apparent permeability equation in the adsorption layer region is derived, and the expression is:

[0071]

[0072] In the formula, μ is the fluid viscosity, in μPa·s.

[0073] In step B, taking into account the proportion of the adsorption layer region, Equation (8) is corrected to obtain the first apparent permeability equation, and the expression is as follows:

[0074]

[0075] In the formula, r in is the radius of the internal region, in nm; r is the pore radius, in nm.

[0076] In step B, for the internal region of the non-adsorption layer in the coal-rock pores, it can be expressed as the absolute permeability multiplied by a correction factor. The absolute permeability is an inherent property of the porous medium, and the absolute permeability of a viscous fluid in a circular pore can be expressed as:

[0077]

[0078] Considering the influence of Knudsen diffusion on the flow, the absolute permeability can be corrected with reference to the B-K model, where the expression of the B-K theoretical model:

[0079]

[0080] In the formula can be replaced by the bulk-phase fluid density, in g / cm 3 ; R is the gas constant, 8.314 J / (mol·K); r is the pore radius, in nm; μ is the fluid viscosity, in μPa·s; dp / dz is the pressure gradient along the flow direction, in Pa / nm; α is the rarefaction coefficient for viscosity correction; b is the slip coefficient, usually taken as -1 for circular pores; Kn is the Knudsen coefficient.

[0081] The B-K model is corrected by multiplying a correction factor function:

[0082]

[0083] Among them, f(Kn) is a correction factor function containing the Knudsen number, and its expression is as follows:

[0084]

[0085] For accuracy, the sparsity coefficient α for viscosity correction can be obtained from the following formula:

[0086]

[0087] Then, considering the influence of Knudsen diffusion, the apparent permeability equation for the internal region can be expressed as:

[0088]

[0089] In step B, taking into account the proportion of the internal region, formula (15) is corrected to obtain the second apparent permeability equation, and the expression is as follows:

[0090]

[0091] In step C, the first apparent permeability equation (9) and the second apparent permeability equation (16) are superimposed to obtain the calculation model for the apparent permeability of gas in coal-rock nano-pores as:

[0092]

[0093] In this embodiment, the coal-rock nano-pores are equivalently divided into two regions, namely the adsorption layer region and the internal region, and the influencing factors of gas molecules in the two regions are considered separately. For the adsorption layer region, the diffusion flow of gas molecules is mainly surface diffusion based on the interaction between gas molecules and the pore wall. Therefore, an apparent permeability equation for the adsorption layer region is constructed based on the Fick diffusion equation and corrected by the proportion of the adsorption layer region to obtain the first apparent permeability equation. For the internal region of the non-adsorption layer, the apparent permeability equation of the internal region can be expressed as the absolute permeability multiplied by a correction factor. Considering the influence of Knudsen diffusion and viscous flow, an apparent permeability equation for the internal region is constructed and corrected by the proportion of the internal region to obtain the second apparent permeability equation. Finally, combining the first and second apparent permeability equations, a calculation model for the apparent permeability of gas in coal-rock nano-pores is obtained. This model comprehensively considers three flow mechanisms: viscous flow, Knudsen diffusion, and surface diffusion, and considers the proportions of the adsorption layer region and the internal region, which can effectively improve the calculation accuracy of gas permeability.

[0094] Verify the apparent permeability calculation model, specifically including: constructing a coal-rock nano-pore structure model through molecular dynamics simulation to obtain key parameters and simulated apparent permeability results, substituting the key parameters into the apparent permeability calculation model to obtain the model apparent permeability results, and comparing the model apparent permeability results with the simulated apparent permeability results to verify the accuracy of the apparent permeability calculation formula for gas in coal-rock nano-pores.

[0095] In a possible embodiment, verifying the apparent permeability calculation model can be divided into the following steps, as Figure 2 shown:

[0096] D1. Construct a coal-rock nano-pore structure model, conduct isothermal adsorption simulation, and obtain key parameters. The key parameters include: the adsorbed-phase concentration C under the limit pressure smax and the Langmuir pressure P L ;

[0097] D2. Substitute the key parameters into the formula for calculating the apparent permeability of coal-rock nano-pore gas to obtain the apparent permeability curve of coal-rock nano-pores;

[0098] D3. Simulate and calculate the permeability through the coal-rock nano-pore structure model to obtain the simulated apparent permeability; compare the apparent permeability curve of coal-rock nano-pores with the simulated apparent permeability to verify the calculation accuracy of the formula for calculating the apparent permeability of coal-rock nano-pore gas.

[0099] In D1, molecular models of high, medium, and low coal ranks are used to obtain the initial coal-rock nano-pore structure model;

[0100] Specifically, to establish the initial coal-rock nano-pore structure model, molecular models of three different coal ranks are used, representing low-rank coal (C 39 H 37 NO 10 S), medium-rank coal (C 100 H 82 N 2 O 5 S 2 ), and high-rank coal (C 199 H 146 N 2 O 9 ). First, to establish the coal-rock single-pore structure model, it is necessary to determine the number of macromolecules of coal required for different models. For cylindrical pores, the variable is the target pore radius, r tar , and two parameters are involved, the solid density ρ of coal-rock s and the minimum distance, d b,min , between the expected formed pore and the simulation boundary after completing the relaxation process under the isothermal and isobaric ensemble. Assuming that the cylindrical pore finally occupies the center of the cubic simulation unit, according to the definition of d b,min , the minimum side length, l min , of the cubic unit must be greater than:

[0101] l min = 2(r tar + d b,min )(18)

[0102] Therefore, the minimum volume of the solid part of the coal-rock model, V s,min , should be:

[0103]

[0104] Once the macromolecular model of coal is determined, the average mass M of each molecule can be calculated coal , g / mol. Therefore, the number of macromolecules of coal required, N coal,min , is at least:

[0105]

[0106] where N A is the Avogadro constant, 6.02×10 23 ; ρ s is the solid density of coal-rock with different coal ranks, g / cm 3 .

[0107] To ensure that the distance between gas molecules and the solid outer surface and the distance between gas molecules along the periodic direction are greater than the cut-off distance d of atoms in the LJ interaction, b,min d is selected as 1.3 nm.

[0108] After determining the number of macromolecules of coal, the macromolecules of coal are randomly placed into the simulation unit with the "clipped atoms" fixed. The "clipped atoms" are composed of carbon atoms, which form a clipped area and are located at the center of the simulation unit. The density of the coal-rock skeleton in the initial state is maintained at 0.05 g / cm 3 . Then, a series of molecular dynamics simulations are performed on the entire system to relax the configuration. During the relaxation process, the "clipped atoms" remain fixed, and the macromolecules of coal are continuously compressed and cannot enter the clipped area. Therefore, a nanopore surrounded by coal molecules can be formed.

[0109] Finally, the "clipped atoms" are removed, and the coal-rock solid nanopore with the required pore size and coal-rock type is constructed through the above process. The size of the pore size can be controlled by adjusting the volume of the clipped area formed by the "clipped atoms".

[0110] Molecular simulation uses the large-scale atomic / molecular parallel simulator LAMMPS of the US Sandia National Laboratory to perform molecular dynamics simulations. The force field selects the all-atom pcff+ force field developed by the Materials Design team.

[0111] Then, the Smart minimization algorithm is used to minimize the energy of these units to obtain the initial configuration of the coal-rock nanopore structure.

[0112] In D1, the initial coal-rock nano-pore structure model was relaxed to obtain a constant-energy coal-rock nano-pore structure model;

[0113] Specifically, to ensure that the density and energy of the structural units fluctuate around fixed values, i.e., reach an equilibrium state, the molecular dynamics simulation under the isothermal and isobaric ensemble was run for a long enough simulation time with a time step of 1 fs. Finally, the molecular dynamics simulation under the canonical ensemble was performed again for 3 ns on the structural configuration to obtain the constant-energy coal-rock nano-pore structure configuration for data statistics and result analysis.

[0114] During the grand canonical Monte Carlo simulation, only the interaction between the gas and the solid was considered, so the coal-rock structure remained fixed all the time, which could save a large amount of computing time and improve the simulation efficiency at the same time. The Nosé-Hoover constant-temperature method was selected during the molecular dynamics simulation to keep the system temperature constant, and the Andersen constant-pressure method was selected to keep the system pressure stable.

[0115] In D1, isothermal adsorption simulation was carried out through the constant-energy coal-rock nano-pore structure model, the adsorption amount was calculated, and the adsorption amount was fitted with the adsorption isotherm curve in the form of Langmuir to obtain the key parameters.

[0116] Specifically, during the isothermal adsorption simulation with the constant-energy coal-rock nano-pore structure model, the calculated adsorption amount was the absolute adsorption amount, and the absolute adsorption amount was converted into the excess adsorption amount through formula (21) so as to be fitted with the adsorption isotherm curve in the form of Langmuir.

[0117] N e =N a -V p ρ(21)

[0118] In the formula, N e is the excess adsorption amount, g; N a is the absolute adsorption amount, g; V p is the free pore volume of the adsorbent, cm 3 ; ρ is the density of the gas at a certain temperature and pressure, g / cm 3 .

[0119] The free pore volume V p can be obtained by the Atom Volumes&Surface tool in the MS software. It should be noted that the unit of the adsorption amount simulated and calculated by the Sorption module in the MS software is moleculars / u.c, while the unit used in ordinary calculations is mmol / g, so formula (22) needs to be used for conversion.

[0120]

[0121] Where N A is the Avogadro constant, 6.02×10 23 ; M is the mass of the unit cell, g.

[0122] The excess adsorption amount is fitted with the adsorption isotherm curve in the Langmuir form to determine the key parameters, which are the parameters in formula (17), including: the maximum adsorption amount C smax and the Langmuir pressure P L , as shown in Table 1 for details.

[0123] Table 1 CH in different coal rock pores 4 Maximum adsorption amount and Langmuir pressure

[0124]

[0125] For the surface gas molecule blocking coefficient, the value is κ = 0.5; the isosteric heat of adsorption ΔH-CH 4 when the surface coverage of gas molecules is 0 is 14.92 kJ / mol; the viscosity value is obtained from the NIST database, and the surface diffusion coefficient is calculated by formula (4), and the specific parameters are shown in Table 2.

[0126] Table 2 CH in different coal rock pores under different pressures 4 Surface diffusion coefficient and viscosity parameters

[0127]

[0128]

[0129]

[0130] It should be noted that in the step of D1 above, the molecular dynamics is used to construct the coal rock nano-pore structure model, and the isothermal adsorption simulation is carried out to obtain the key parameters. In the actual experiment process, a verification step can also be added to verify the reliability of the apparent permeability calculation model by using the molecular dynamics to construct the coal rock nano-pore structure model. Specifically, the excess adsorption amount can be obtained by experimental methods and compared with the excess adsorption amount obtained by converting the constant energy coal rock nano-pore structure model through formula (21) for verification.

[0131] In D2, the width of the CH 4 adsorption layer region is set to 0.38 nm, the temperature is set to 298 K, and then the key parameters are corresponding from Table 1 to Table 2 and substituted into formula (17) respectively, so as to obtain the model apparent permeability results, that is, the apparent permeability curves of coal rock nano-pores under different pressure conditions.

[0132] In D3, the permeability is simulated through the coal-rock nano-pore structure model to obtain the simulated apparent permeability. The calculation formula for the simulated apparent permeability is as follows:

[0133]

[0134] In the formula, μ is the fluid viscosity, in μPa·s; is the average density of the gas in the pores, in g / cm 3 ; f MD is the mass flux obtained by MD calculation, in g / s; is the pressure gradient along the flow direction, in MPa / m; A is the cross-sectional area of the flow in the pores,

[0135] To obtain the gas mass flux f in formula (23) MD , it is necessary to simulate the flow of coalbed methane in the coal-rock nano-pores, which can be specifically obtained through the following method:

[0136] Through the equilibrium molecular dynamics simulation method, the equilibrium state occurrence configurations of CH 4 molecules in different coal-rock nano-pores are obtained. To study its flow law in the nano-pores, we use the non-equilibrium molecular dynamics simulation method to deviate the occurrence system from equilibrium. The specific process is as follows. Based on the equilibrium state configuration obtained by the equilibrium molecular dynamics simulation, a constant force is applied to the CH 4 molecules in the pores, so as to carry out the non-equilibrium molecular dynamics simulation and make the system enter the steady state. When setting the magnitude of the force, the acceleration of each molecule is kept at 10 -4 ~10 -3 nm / ps 2 to ensure linear response. Since the gas is subjected to an additional force, a certain pressure difference will be generated in the flow direction, which can be calculated by formula (24):

[0137]

[0138] In the formula, N G is the number of molecules to which the external force is applied; F E is the applied external force, A cross is the cross-sectional area of the pores,

[0139] When calculating the fluid temperature, only the degrees of freedom perpendicular to the driving force direction are considered, and this constant temperature method is more reasonable. When the flow system in the coal-rock nano-pores reaches the steady state, the fluid flux can be obtained by measuring the average density and average flow velocity of the system in the steady state. When calculating the density distribution of the system, the simulation system is divided into N along the flow direction (z direction)b equal secondary units, each with a width of 0.05 nm, by the number of fluid molecules N occupying the secondary units i and the volume V of the secondary unit i The ratio is used to calculate the average molar density within the i-th secondary unit

[0140]

[0141] where N T is the total number of steps output during the steady-state operation statistics; f is the number of the time step

[0142] Similarly, calculate the average fluid velocity within the i-th secondary unit as follows

[0143]

[0144] where l b is the width of each secondary unit N is the total number of particles within the secondary unit i during the steady-state time; v jz is the velocity of the j-th particle within the i-th secondary unit along the z-direction (flow direction)

[0145] Thus, the average molar flux J along the z-direction (flow direction) can be calculated from equations (25) and (26) z as follows

[0146]

[0147] where A eff is the effective cross-sectional area of the nanochannel

[0148] Then, convert the average molar flux J z to the mass flux f of equation (23) MD , and the simulated apparent permeability can be obtained

[0149] To obtain accurate simulation results with high computational efficiency, in the simulation work, the simulation duration of non-equilibrium molecular dynamics simulation is longer than that of equilibrium molecular dynamics simulation, approximately between 18 and 30 ns. This is because the moving speed needs to overcome the thermal motion speed in the flow direction to reach a steady state. By monitoring the fluctuations of the system temperature and potential energy and the density gradient of the fluid within the entire coal-rock, the convergence of parameters to the steady state during the simulation is evaluated. The last 10 ns of each non-equilibrium molecular dynamics simulation is used as the statistical stage, during which measurement data is collected. For certain specific parameter conditions, longer simulations are also carried out, such as an equilibrium duration of 50 ns and a statistical simulation duration of 15 ns to confirm that the system enters the steady state stage.

[0150] In D3, the simulated apparent permeability obtained from molecular dynamics simulation is compared with the model apparent permeability results (coal-rock nano-pore apparent permeability curve) calculated by the calculation model of the apparent permeability of gas in coal-rock nano-pores to verify the calculation accuracy of the model. The verification results are as Figure 4-6 shown.

[0151] As Figure 4-6 shown, the coal-rock nano-pore apparent permeability calculated by the calculation model of the apparent permeability of gas in coal-rock nano-pores is in good agreement with the permeability results obtained from molecular dynamics simulation, indicating that the theoretical model proposed in the embodiments of the present application can accurately characterize the apparent permeability of coalbed methane in coal-rock nano-pores. From the results in the figure, it can be seen that the apparent permeability of coalbed methane in nano-pores is extremely low (<1.0×10-16 m 2 ), and the apparent permeability of coalbed methane in coal-rock nano-pores is greatly affected by pressure and pore size, decreasing with the decrease of pore size and the increase of pressure, and the difference between different coal rank types is not obvious.

[0152] After considering the specification and the invention disclosed herein, those skilled in the art will readily conceive of other embodiments of the present application. The present application is intended to cover any variations, uses, or adaptations of the present application, which follow the general principles of the present application and include the common general knowledge or conventional technical means in the technical field not disclosed in the present application. The specification and the embodiments are only regarded as exemplary, and the true scope and spirit of the present application are pointed out by the following claims.

Claims

1. An analysis method for apparent permeability considering the coupling of multiple mass transfer mechanisms in coal and rock, characterized in that: It includes A. Equivalently divide the nano-pores of coal and rock into two regions: the adsorption layer region and the internal region; B. Establish an apparent permeability equation for the adsorption layer region, and correct the apparent permeability equation of the adsorption layer region through the proportion of the adsorption layer region to obtain the first apparent permeability equation; Consider Knudsen diffusion and viscous flow to establish an apparent permeability equation for the internal region, and correct the apparent permeability equation of the internal region through the proportion of the internal region to obtain the second apparent permeability equation; C. Superimpose the first apparent permeability equation and the second apparent permeability equation to obtain a calculation model for the apparent permeability of gas in the nano-pores of coal and rock; The apparent permeability equation of the adsorption layer region is as follows: Where: D s is the surface diffusion coefficient, m 2 / s; μ is the fluid viscosity, μPa·s; M is the gas molecular mass, g / mol; C smax is the adsorbed-phase concentration under the limiting pressure, mmol / g; P L is the Langmuir pressure, MPa; P is the gas pressure, MPa; The first apparent permeability equation is as follows: Where: r in is the radius of the internal region, nm; r is the pore radius, nm; The apparent permeability equation of the internal region is as follows: Where: K ab is the absolute permeability; Kn is the Knudsen coefficient; α is the rarefaction coefficient for viscosity correction; b is the slip coefficient; The second apparent permeability equation is as follows:

2. The analysis method for apparent permeability considering the coupling of multiple mass transfer mechanisms in coal and rock according to claim 1, characterized in that: In the above step C, the calculation model for the apparent permeability of gas in the nano-pores of coal and rock is as follows:

3. The analysis method for apparent permeability considering the coupling of multiple mass transfer mechanisms in coal and rock according to any one of claims 1-2, characterized in that: It further includes Step D. Construct a nano-pore structure model of coal and rock through molecular dynamics simulation, obtain key parameters and simulation apparent permeability results, substitute the key parameters into the apparent permeability calculation model to obtain the model apparent permeability result, and compare the model apparent permeability result with the simulation apparent permeability result to verify the accuracy of the calculation formula for the apparent permeability of gas in the nano-pores of coal and rock.

4. The analysis method for apparent permeability considering the coupling of multiple mass transfer mechanisms in coal and rock according to claim 3, characterized in that: In the above step D, it includes: D1. Construct a coal-rock nano-pore structure model, conduct isothermal adsorption simulation, and obtain key parameters, where the key parameters include: the adsorption-phase concentration C under the limiting pressure smax and the Langmuir pressure P L ; D2. Substitute the key parameters into the calculation formula for the apparent permeability of gas in the nano-pores of coal and rock to obtain the apparent permeability curve of the nano-pores of coal and rock; D3. Simulate and calculate the permeability through the nano-pore structure model of coal and rock to obtain the simulated apparent permeability; compare the apparent permeability curve of the nano-pores of coal and rock with the simulated apparent permeability to verify the calculation accuracy of the calculation formula for the apparent permeability of gas in the nano-pores of coal and rock.

5. The analysis method for apparent permeability considering the coupling of multiple mass transfer mechanisms in coal and rock according to claim 4, characterized in that: In the above step D1, it includes: D11. Use molecular models of high, medium, and low coal ranks to establish an initial nano-pore structure configuration of coal and rock; D12. Relax the initial nano-pore structure configuration of coal and rock to obtain a constant energy nano-pore structure model of coal and rock; D13. Perform isothermal adsorption simulation through the constant energy nano-pore structure configuration of coal and rock, calculate the adsorption amount, and fit the adsorption amount with the adsorption isotherm curve in the form of Langmuir to obtain key parameters.

6. The analysis method for apparent permeability considering the coupling of multiple mass transfer mechanisms in coal and rock according to claim 5, characterized in that: In the above step D1, it further includes: D14. Calculate the adsorption amount through the constant-energy coal-rock nano-pore structure configuration, compare the adsorption amount with the excess adsorption amount obtained from experiments, and verify the reliability of the constant-energy coal-rock nano-pore structure configuration.

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