A Method for Calculating the Production of Coalbed Methane Fracturing Wells Based on Embedded Flow Exchange

Abstract

The present invention discloses a method for calculating the production of coalbed methane fracturing wells based on embedded flow exchange, belonging to the technical field of geological resource exploration and development, and comprising the following steps: establishing a coalbed methane seepage control equation, using an embedded discrete fracture model to characterize a multi-scale fracture system, and solving the pressure distribution based on the finite volume method; establishing a heterogeneous distribution of coalbed permeability based on the Gaussian distribution, and introducing a multiple seepage mechanism function to characterize the evolution law of coalbed permeability; establishing a coalbed cleat / fracture system based on the Fisher distribution function, considering the evolution of the dynamic fracture width, and combining with the cubic law to establish a self-supporting fracture permeability evolution model; after completing the multi-scale seepage solution of the coalbed methane fracturing well, establishing a basic productivity equation for the coalbed methane fracturing well, discretizing and summing the equation on an orthogonal grid, and substituting the global pressure solution into the productivity equation to obtain the productivity of the coalbed methane fracturing well. The present invention improves the calculation efficiency and accuracy of the productivity of coalbed methane fracturing wells.

Description

Technical Field

[0001] The present invention belongs to the technical field of geological resource exploration and development, and particularly relates to the technical field of production calculation, and specifically relates to a method for calculating the production of a coalbed methane fracturing well based on embedded flow exchange. Background Art

[0002] The technology of closely spaced volume fracturing in horizontal wells has achieved great success in the development of unconventional oil and gas resources. The deep coal rock has a relatively high hardness coefficient, is similar to shale, has a complex pore structure, and the coal rock cleats and fractures are relatively developed. Fracturing is easy to form a complex fracture network with a certain conductivity; the compressive strength of coal rock is much lower than that of the roof limestone and the floor mudstone, the fracture height is controlled, and it has the basis for volume fracturing. Therefore, the technology of closely spaced volume fracturing in horizontal wells can be well used for the efficient development of deep coalbed methane reservoirs. Accurately evaluating the post-fracturing productivity of volume fracturing is of top priority.

[0003] The gas occurrence is mainly adsorbed gas, and the content of free gas is low, and the productivity release is difficult. Due to the relatively soft coal rock formation, during the production process, the proppant is severely embedded under high closure stress conditions, reducing the fracture width and the conductivity. Conventional commercial software and analytical / semi-analytical algorithms cannot couple the multi-scale fracture system after volume fracturing. The existing numerical algorithms reduce the calculation efficiency due to grid encryption, and are limited in the application of calculating the productivity of volume fracturing wells with high-density fracture network characteristics. In recent years, due to its advantage of quickly processing complex fracture systems, the embedded discrete fracture model has been widely used in numerical simulations of shale, sandstone and other fractured unconventional oil and gas reservoirs. Therefore, a numerical model of gas reservoir is established based on the finite volume method, and the embedded fracture model of flow exchange is used to characterize the influence of the multi-scale fracture system (cleat / bedding, natural fracture and hydraulic fracture) on the flow. At the same time, the dynamic evolution of the permeability of the matrix, cleat and hydraulic fracture is coupled. By solving the coal seam pressure distribution and combining with the well model to calculate the single-well production, this method only considers the free gas flowing into the wellbore and ignores the adsorbed gas in the coal seam, resulting in a large error in the productivity calculation. Therefore, it is necessary to fully consider the flow characteristics of the coalbed methane fracturing well, introduce the concept of multiple production, calculate the adsorbed gas in the matrix and the free gas in the fracture system respectively, and establish a new method for calculating the productivity applicable to coalbed methane fracturing wells.

[0004] The multiple production effect is different from the single gas supply mechanism and is also affected by reservoir physical properties, cleat distribution and degree of transformation. Embedded flow exchange is different from the traditional well model. It uses the embedded principle to calculate the flow exchange at different times and in different discrete units respectively, which can accurately capture the matrix desorption, matrix-fracture and fracture-fracture flow exchange, and realize accurate calculation of production capacity. The existing production capacity calculation method also has the following shortcomings: (1) The analytical / semi-analytical calculation method cannot fully consider the heterogeneity of coal seams and the distribution of multi-scale fracture systems; (2) The calculation method using numerical simulation combined with well models cannot reveal the production capacity law under multiple production effects; (3) The single pressure drop (bottom of the well) is used to calculate the global production capacity, which cannot accurately characterize the flux of each flow exchange unit at different times. . Summary of the invention

[0005] In order to solve the above problems, the object of the present invention is to provide a method for calculating the production of coalbed methane fracturing wells based on embedded flow exchange.

[0006] The present invention is achieved through the following technical solutions:

[0007] A method for calculating the production of a coalbed methane fracturing well based on embedded flow exchange comprises the following steps:

[0008] Step 1: The continuity equation, motion equation and state equation of single-phase seepage of coalbed methane are combined to establish the seepage control equation, the multi-scale fracture system is characterized by an embedded discrete fracture model, the coalbed methane seepage control equation is discretized based on the finite volume method, and finally the pressure distribution is solved by the Gauss-Seidel method;

[0009] Step 2: Based on the Gaussian distribution function, the heterogeneous distribution of coal seam permeability is established, and multiple seepage mechanism functions are introduced to characterize the evolution law of coal seam permeability; based on the Fisher distribution function, the coal seam cleat / crack system is established, and the dynamic crack width evolution is considered. Combined with the cubic law, a self-supporting crack permeability evolution model is established, in which the hydraulic fracture conductivity satisfies exponential decrease;

[0010] Step 3. After completing the multi-scale seepage solution of the coalbed methane fracturing well in combination with steps 1 and 2, consider multiple production mechanisms including matrix adsorbed gas, matrix free gas, cleat free gas and main fracture free gas, establish the basic equation for the production capacity of the coalbed methane fracturing well, and perform discretization and summation of the equation on the orthogonal grid, substitute the global pressure solution into the production capacity equation, and finally realize the production capacity calculation of the coalbed methane fracturing well.

[0011] Compared with the prior art, the present invention has the following beneficial effects:

[0012] The present invention fully considers the multi-scale and multi-production characteristics in the process of coalbed methane fracturing development, and couples the dynamic evolution of matrix, fracture and hydraulic fracture permeability under different pressure conditions. The finite volume method is used to discretize the coalbed methane seepage control equation, and the embedded discrete fracture model is used to characterize the seepage characteristics of the multi-scale fracture system. On this basis, by using the flow exchange at different times of the embedded discrete element, a productivity calculation method considering the multi-production conditions of free gas and adsorbed gas in the matrix and fracture systems is established, which greatly improves the productivity calculation efficiency and accuracy of coalbed methane fracturing wells. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the embodiments will be briefly introduced below.

[0014] Figure 1 FIG. is a typical production curve of a fracturing well based on embedded flow exchange;

[0015] Figure 2 FIG. is a comparison chart of contribution rates of different production mechanisms;

[0016] Figure 3 FIG. is a curve graph of the influence of different fracture numbers on productivity;

[0017] Figure 4 FIG. is a curve graph of the influence of different Langmuir pressures on productivity;

[0018] Figure 5 FIG. is a curve graph of the influence of different Langmuir volumes on productivity;

[0019] Figure 6 FIG. is a curve graph of the influence of different cluster spacings on productivity;

[0020] Figure 7 FIG. is a curve graph of the influence of different fracture half lengths on productivity. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0021] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. The described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art without creative efforts based on the embodiments of the present invention fall within the scope of protection of the present invention.

[0022] Example 1

[0023] Step 1: Establish the seepage control equation by combining the continuity equation, motion equation, and state equation of single-phase coalbed methane seepage. Use the embedded discrete fracture model to characterize the multi-scale fracture system, discretize the coalbed methane seepage control equation based on the finite volume method, and finally solve the pressure distribution by the Gauss-Seidel method.

[0024] 1.1. Seepage control equation

[0025] The single-phase seepage continuity equation in the coalbed methane reservoir can be expressed as:

[0026]

[0027] The seepage velocity in the coal reservoir satisfies the generalized Darcy's law, and the relationship between the macroscopic mass transfer of coalbed methane and pressure is described by the Darcy equation, specifically as:

[0028]

[0029] The state equation during the flow of coalbed methane is as follows:

[0030] Z 3 +(A - 2B - 3B 2 )Z - (1 - B)Z 2 -(AB - B 2 - B 3 )=0 (3)

[0031]

[0032] φ m =φ m0 exp[c m (p - p ref )]=φ m0 [1 + c m (p - p ref )] (8)

[0033] Substitute equations 2, 7, and 8 into equation 1 to obtain the coalbed methane seepage pressure diffusion equation as follows:

[0034]

[0035] Among them, ρ g represents the density of coalbed methane, kg / m 3 ; ρ gsc represents the density of coalbed methane under standard conditions, kg / m 3 ; φ m represents the matrix porosity, dimensionless; φ m0 represents the matrix porosity in the initial state, dimensionless; v g represents the seepage velocity of coalbed methane; m / s; q sRepresents the desorption mass source term, kg / s; Q s Represents the desorption volume source term, m 3 / s; p represents the reservoir pressure, MPa; p ref Represents the reservoir reference pressure, MPa; T represents the reservoir temperature, K; k m Represents the matrix permeability, mD; μ g Represents the viscosity of coalbed methane, mPa·s; Z represents the compressibility factor of coalbed methane, dimensionless; p r Represents the critical pressure of coalbed methane, MPa; T r Represents the critical temperature of coalbed methane, K; R represents the gas constant, 8.314, J / mol·K; ω represents the equation of state coefficient, 0.5, dimensionless; B g Represents the volume coefficient of coalbed methane, dimensionless; c m Represents the compressibility coefficient of coal seam, 1 / MPa; t represents time, s.

[0036] 1.2 Embedded Discrete Fracture Model

[0037] For a pair of non - adjacent connection points, the expression of the discrete fracture source - sink intensity is defined as:

[0038] Q f = T NNC Δp NNC (10)

[0039] The fracture - matrix conductivity is defined as follows:

[0040]

[0041] The fracture - fracture conductivity is defined as follows:

[0042]

[0043] Where:

[0044]

[0045] Where, Q f Represents the embedded discrete fracture source - sink intensity, m 3 / s; T NNC Represents the conductivity between a pair of adjacent connection points, m 3 / s·MPa; p NNC Represents the pressure between a pair of adjacent connection points, MPa; d NNC Represents the average distance between a pair of adjacent connection points, m; T m-f and T f-m Represent the conductivities between the matrix and the fracture, and between the fracture and the matrix respectively, m 3 / s·MPa; T f-fDenote the conductivity of fractures, m 3 / s·MPa; T m Denote the conductivity of the matrix, m 3 / s·MPa; T f Denote the conductivity of fractures, m 3 / s·MPa; A m-f =ΔxΔy denotes the contact area between fractures and the matrix, m 2 ; V c =ΔxΔyΔz denotes the volume of the control volume, m 3 ; T f i Denote the conductivity of the i-th fracture, m 3 / s·MPa; n denotes the normal vector of the fracture, dimensionless; x denotes the distance from the fracture to the center of the matrix grid, m.

[0046] 1.3. Numerical Discretization Based on the Finite Volume Method

[0047] After considering the multi-scale fracture system after volume fracturing, Equation (9) can be rewritten as:

[0048]

[0049] Using the finite volume method, numerical discretization is performed on the established multi-scale seepage pressure diffusion equation (Equation (16)). Integrating both ends of Equation (16) within the control volume gives:

[0050]

[0051] The fully implicit discretization format of Equation (17) on an orthogonal grid is:

[0052]

[0053] Further coupling the flow exchange between fractures and the matrix, Equation (18) can be further expressed as:

[0054]

[0055] Where:

[0056]

[0057] Where, Δx = L x / N x , Δy = L y / N y and Δz = L z / N z respectively denote the grid sizes in the x, y, and z directions, m; L x , L x and Lz represent the sizes of the coalbed methane reservoir in the x, y, and z directions, respectively, in m; N x , N x and N z represent the number of grids in the x, y, and z directions, respectively, in number; the superscripts n and n + 1 represent the current and next time steps, respectively; the subscripts i, j represent the grid indices, c represents the grid center; Δt represents the time step length, in days; Ω m represents the matrix domain; Ω HF represents the hydraulic fracture domain; Ω NF represents the natural fracture domain; p L represents the Langmuir pressure, in MPa; V L represents the Langmuir volume, in m 3 / kg.

[0058] 1.4. Numerical Model Solution

[0059] Each grid in the solution domain satisfies the discrete format in Equation 19, and a nonlinear system of equations in the form of AP = B can be obtained as follows:

[0060]

[0061] Using the Gauss - Seidel method to solve, the pressure solution at any iteration step can be expressed as:

[0062]

[0063] The error at each iteration step satisfies:

[0064]

[0065] where, A mm , A mf , A fm and A ff represent the matrix - matrix, matrix - fracture, fracture - matrix, and fracture - fracture coefficient matrices, respectively; P m and P f represent the matrix and fracture pressure vectors, respectively; B m and B f represent the matrix and fracture constant vectors, respectively; δp represents the pressure solution error, in MPa; N represents the total number of grids, in number.

[0066] Step 2: Based on the Gaussian distribution function, establish the heterogeneous distribution of coal seam permeability, introduce the multiple seepage mechanism function to characterize the evolution law of coal seam permeability. Based on the Fisher distribution function, establish the coal seam cleat / fracture system, consider the dynamic evolution of fracture width, and combine with the cubic law to establish the self - supporting fracture permeability evolution model. At the same time, the hydraulic fracture conductivity satisfies exponential decay.

[0067] 2.1. Coal seam heterogeneous permeability

[0068] The reservoir permeability heterogeneity is characterized by a random Gaussian distribution, specifically as follows:

[0069]

[0070] Where:

[0071]

[0072] Fully considering the multiple mechanisms of coalbed methane mass transfer, the evolution equation of coalbed methane matrix permeability is as follows:

[0073]

[0074] Among them, μ represents the standard deviation of the heterogeneous permeability distribution, mD; σ 2 represents the variance of the heterogeneous permeability distribution, mD 2 ; V DP represents the heterogeneity distribution coefficient, 0.05, dimensionless; rand represents a random number between 0 and 1; dimensionless; α and β respectively represent the slip coefficients, 0.5 and 1, dimensionless; Kn = K B T / (2πd m 2 p) / r represents the Knudsen number, dimensionless; K B represents the Boltzmann constant, J / K; d m represents the methane molecule diameter, m; M represents the methane molecule mass, kg / mol; r represents the pore diameter of the coal reservoir matrix, m; r max and r min respectively represent the maximum and minimum pore diameters of the coal reservoir matrix, m; D s represents the surface adsorption coefficient, m 2 / s; C amax represents the maximum adsorption concentration, mol / m 3 ; D f represents the fractal dimension of the coal reservoir matrix pores, dimensionless.

[0075] 2.2. Fracture / natural fracture distribution and its permeability

[0076] The random discrete fracture network model (DFN) is used to quantitatively characterize the self - supporting fracture network after fracturing. The parameter distributions including coordinates, fracture length, fracture width, and dip angle satisfy the following Fisher random function:

[0077]

[0078] During the process of coalbed methane extraction, the aperture of self - supporting fractures will evolve dynamically as the formation pressure drops. Its evolution law can be attributed to three mechanisms: matrix compression, fracture compression, and desorption expansion, specifically as follows:

[0079]

[0080] Using the cubic law, the permeability of a single cleat / natural fracture satisfies the following:

[0081]

[0082] Meanwhile, the conductivity of hydraulic fractures will decrease with production after fracturing, and it satisfies the following exponential decline relationship:

[0083] k HF =216.7t -0.249 (33)

[0084] C HF =w HF k HF =43.21t -0.249 (34)

[0085] where x NF 、y NF ,L NF and w NF represent the coordinates, length, and width of the cleat / natural fracture, in m; ξ represents the distribution exponent, 1, dimensionless; f(θ) represents the Fisher distribution density function; θ represents the dip angle of the cleat / natural fracture, in °; K represents the Fisher distribution coefficient, dimensionless; and represent the increments of fracture width caused by matrix compression, fracture compression, and desorption expansion, in m; w NFini represents the initial fracture width, in m; E represents the Young's modulus of the coal reservoir matrix, in GPa; v represents the Poisson's ratio of the coal reservoir matrix, dimensionless; c fini represents the initial fracture compression coefficient, 1 / MPa; p ini represents the initial pore pressure, in MPa; S L represents the Langmuir strain, dimensionless; k NF represents the permeability of the cleat / natural fracture, in mD; k HF represents the permeability of the hydraulic fracture, in mD; w HF represents the width of the hydraulic fracture, in m; C HF represents the conductivity of the hydraulic fracture, in D·cm.

[0086] Step 3: After completing the multi-scale seepage solution of coalbed methane fracturing wells, considering multiple production mechanisms including matrix adsorbed gas, matrix free gas, fracture free gas, and main fracture free gas, establish the basic productivity equation for coalbed methane fracturing wells, discretize and sum this equation on an orthogonal grid, substitute the global pressure solution into the productivity equation, and finally achieve the productivity calculation of coalbed methane fracturing wells.

[0087] Based on material balance, the gas production of a coalbed methane fracturing well consists of matrix adsorbed gas, matrix free gas, fracture free gas, and main fracture free gas, and its basic productivity calculation equation is defined as follows:

[0088]

[0089] Equation (35) cannot be directly calculated. Therefore, based on the global / local embedded flow exchange principle, on the orthogonal grid in Step 1, Equation (35) can be rewritten as follows:

[0090]

[0091] Substitute the numerically solved pressure distribution into Equation (36), and the productivity calculation formula for coalbed methane fracturing wells considering multi-scale seepage and multiple production mechanisms can be obtained, specifically as follows:

[0092]

[0093] Among them, φ NF and φ HF respectively represent the porosities of natural fractures and hydraulic fractures, dimensionless; Q S , Q Fm , Q FNF and Q FHF respectively represent the gas production rates of matrix adsorbed gas, matrix free gas, fracture free gas, and main fracture free gas, m 3 / s; Q represents the total gas production rate of the coalbed methane fracturing well, m 3 / s.

[0094] The basic parameters of each item are shown in Table 1:

[0095] Table 1 Basic parameters of each item

[0096]

[0097]

[0098] (2) Calculation results

[0099] From Figure 1It can be seen that under the influence of multi-scale and multiple production, the productivity curve of coalbed methane fracturing wells based on embedded flow exchange can be divided into five typical stages, including the initial high-yield stage, the desorption rising stage, the middle-term stable production stage, the late-stage attenuation stage, and the final depletion stage. This indicates that the initial gas production is mainly determined by the transformation range of the main fractures, and the further pressure diffusion is positively promoted by the multi-scale fracture system, enabling a large amount of adsorbed gas to be converted into free gas, forming the co-production of free gas and adsorbed gas. When the free gas is produced to a certain extent, the reservoir pressure decreases significantly, and the adsorbed gas becomes the main gas supply source. With further exploitation, this situation will gradually transition from the stable production stage to the middle and late-stage attenuation and depletion. Therefore, the gas production law of coalbed methane fracturing wells is fully revealed.

[0100] It is known that Figure 2 as the coalbed methane is further produced, the reservoir pressure decreases, and a large amount of adsorbed gas in the matrix desorbs, increasing the contribution rate of adsorbed gas to productivity. On the contrary, as the free gas in the main fractures and cleats / natural fractures is produced, after the initial high yield, the contribution rate to gas production decreases significantly. At about 200 days of production, the contribution rates of adsorbed and free gas are equal. After 1200 days of production, the adsorbed gas is the main gas supply source.

[0101] It is known that Figure 3 by comparing the productivity curves with different numbers of cleats, the results show that as the number of cleats increases from 100 to 300, the initial productivity remains almost unchanged. After the free gas in the main fractures is depleted, as the pressure further diffuses to the cleat area, the more the number of cleats, the faster the pressure drop and the higher the gas production. At the same time, the more the cleats, the more methane stored in the coal reservoir, making the critical time for entering the middle and late-stage attenuation later.

[0102] It is known that Figure 4 by comparing the productivity curves with different Langmuir pressures, the results show that the lower the Langmuir pressure, the faster the gas production growth after entering the desorption rising stage. At the same time, a lower Langmuir pressure means that the coalbed methane is more easily desorbed, resulting in a higher gas production dominated by adsorbed gas in the middle and late stages. When the Langmuir pressure is 3.4 MPa, the coalbed stops producing gas after 3000 days of production, indicating that some methane cannot be desorbed and remains in the reservoir. Therefore, further reducing the Langmuir pressure is an important means to extend the production cycle of coalbed methane fracturing wells.

[0103] It is known that Figure 5 by comparing the productivity curves with different Langmuir volumes, the results show that similar to the Langmuir pressure, increasing the Langmuir volume does not affect the initial gas production. Under the condition of a certain Langmuir pressure, the higher the Langmuir volume, the greater the initial adsorbed gas volume in the coalbed. After entering the desorption rising stage, the gas production is higher. However, due to material balance, the later attenuation rate is faster, but the overall critical depletion gas production is higher.

[0104] It is known thatFigure 6 It can be seen that by comparing the gas production curves with different main fracture cluster spacings, the results show that in the initial stage, the free gas provided by the hydraulic fractures dominates as gas is produced. Narrowing the cluster spacing cuts the coal reservoir into smaller pieces more finely, promoting the conversion of adsorbed gas into free gas and significantly increasing the production capacity during the initial high-production stage. As the adsorbed gas is converted into free gas and produced in advance, after 1000 days of production, there is a positive correlation between the stable gas production volume during the mid-term desorption and the cluster spacing.

[0105] It can be known from Figure 7 It can be seen that by comparing the gas production curves with different main fracture half-lengths, the results show that increasing the fracture half-length leads to more sufficient initial stimulation, a larger control range, a larger pressure-relief area for a single well, and thus more free gas is released, resulting in higher initial production. Similar to the cluster spacing, the principle of material balance leads to high initial production, but during the mid- and late-stages, desorption gas supply dominates, causing a decrease in subsequent production capacity.

[0106] As described above, the above are only the preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the embodiments of the present invention should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A method for calculating the production of a coalbed methane fracturing well based on embedded flow switching, characterized in that, The following steps are involved: Step 1: The continuity equation, motion equation and state equation of single-phase seepage of coalbed methane are combined to establish the seepage control equation, the multi-scale fracture system is characterized by an embedded discrete fracture model, the coalbed methane seepage control equation is discretized based on the finite volume method, and finally the pressure distribution is solved by the Gauss-Seidel method; Step 2: Based on the Gaussian distribution function, the heterogeneous distribution of coal seam permeability is established, and multiple seepage mechanism functions are introduced to characterize the evolution law of coal seam permeability; based on the Fisher distribution function, the coal seam cleat / crack system is established, and the dynamic crack width evolution is considered. Combined with the cubic law, a self-supporting crack permeability evolution model is established, in which the hydraulic fracture conductivity satisfies exponential decrease; Step 3: After completing the multi-scale seepage solution of the coalbed methane fracturing well in combination with steps 1 and 2, multiple production mechanisms including matrix adsorbed gas, matrix free gas, cleat free gas and main fracture free gas are considered to establish a basic equation for the production capacity of the coalbed methane fracturing well, and the equation is discretely summed on an orthogonal grid. The pressure distribution described in step 1 is substituted into the production capacity equation to finally realize the production capacity calculation of the coalbed methane fracturing well.

2. The method for calculating the production of a coalbed methane fracturing well based on embedded flow exchange according to claim 1, wherein In step 1, The seepage control equation includes: Single-phase flow continuity equation in coalbed methane reservoirs: Coalbed methane motion equation: Coalbed methane state equation: Z 3 +(A - 2B - 3B 2 )Z-(1 - B)Z 2 -(AB - B 2 -B 3 ) = 0 (3) φ m = φ m0 [1 + c m (p - p ref )] (8) Coalbed methane seepage pressure diffusion equation: Among them, ρ g represents the density of coalbed methane, kg / m 3 ; ρ gsc represents the density of coalbed methane under standard conditions, kg / m 3 ; φ m represents the matrix porosity, dimensionless; φ m0 represents the matrix porosity in the initial state, dimensionless; v g represents the seepage velocity of coalbed methane; m / s; q s represents the desorption mass source term, kg / s; Q s represents the desorption volume source term, m 3 / s; p represents the reservoir pressure, MPa; p ref represents the reservoir reference pressure, MPa; T represents the reservoir temperature, K; k m represents the matrix permeability, mD; μ g represents the viscosity of coalbed methane, mPa·s; Z represents the compression factor of coalbed methane, dimensionless; p r represents the critical pressure of coalbed methane, MPa; T r represents the critical temperature of coalbed methane, K; R represents the gas constant, 8.314, J / mol·K; ω represents the equation of state coefficient, 0.5, dimensionless; B g represents the volume coefficient of coalbed methane, dimensionless; c m represents the compression coefficient of coal seam, 1 / MPa; t represents time, s; The embedded discrete crack model includes: For a pair of non-adjacent connection points, the calculation formula of discrete crack source and sink strength is: Q f = T NNC Δp NNC (10) The calculation formula of fracture-matrix conductivity is: The calculation formula of crack-crack transmission coefficient is: in: Among them, Q f represents the intensity of the embedded discrete fracture source / sink, m 3 / s; T NNC represents the conductivity between a pair of adjacent connection points, m 3 / s·MPa; p NNC represents the pressure between a pair of adjacent connection points, MPa; d NNC represents the average distance between a pair of adjacent connection points, m; T m-f and T f-m respectively represent the conductivities of the matrix-fracture and fracture-matrix, m 3 / s·MPa; T f-f represents the conductivity between fractures, m 3 / s·MPa; T m represents the conductivity of the matrix, m 3 / s·MPa; T f represents the conductivity of the fracture, m 3 / s·MPa; A m-f =ΔxΔy represents the contact area between the fracture and the matrix, m 2 ; V c =ΔxΔyΔz represents the volume of the control volume, m 3 ; T f i represents the conductivity of the i-th fracture, m 3 / s·MPa; n represents the normal vector of the fracture, dimensionless; x represents the distance from the fracture to the center of the matrix grid, m.

3. The method for calculating the production of a coalbed methane fracturing well based on embedded flow exchange according to claim 2, wherein In step 1, the coalbed methane seepage control equation is discretized based on the finite volume method, and finally the pressure distribution is solved by the Gauss-Seidel method, including: The finite volume method is used to numerically discretize the coalbed methane seepage pressure diffusion equation, and the two ends of the equation are integrated in the control volume to obtain: The fully implicit discretization format of the above equation on an orthogonal grid is: Further coupling the fracture and matrix flow exchange, we get: in: where, Δx = L x / N x , Δy = L y / N y and Δz = L z / N z represent the grid sizes in the x, y, and z directions, respectively, in m; L x , L x and L z represent the sizes of the coalbed methane reservoir in the x, y, and z directions, respectively, in m; N x , N x and N z represent the number of grids in the x, y, and z directions, respectively, in number; the superscripts n and n + 1 represent the current and the next time steps, respectively; the subscripts i, j represent the grid indices, and c represents the grid center; Δt represents the time step, in days; Ω m represents the matrix domain; Ω HF represents the hydraulic fracture domain; Ω NF represents the natural fracture domain; p L represents the Langmuir pressure, in MPa; V L represents the Langmuir volume, in m 3 / kg; During the solution process, each grid in the solution domain satisfies the discrete format in equation (18), and the nonlinear equation system of the form AP = B is obtained as follows: Using the Gauss-Seidel method, the pressure solution at any iteration step is expressed as: The error of each iteration step satisfies: Among them, A mm , A mf , A fm and A ff respectively represent the matrix-matrix, matrix-fracture, fracture-matrix, and fracture-fracture coefficient matrices; P m and P f respectively represent the matrix and fracture pressure vectors; B m and B f respectively represent the matrix and fracture constant vectors; δp represents the pressure solution error, MPa; N represents the total number of grids, units.

4. The method for calculating the production of a coalbed methane fracturing well based on embedded flow switching according to claim 3, wherein Step 2 includes, The reservoir permeability heterogeneity is characterized by a random Gaussian distribution, specifically: in: Coalbed methane matrix permeability evolution equation: Among them, μ represents the standard deviation of the heterogeneous distribution of permeability, mD; σ 2 represents the variance of the heterogeneous distribution of permeability, mD 2 ; V DP represents the heterogeneity distribution coefficient, 0.05, dimensionless; rand represents a random number between 0 and 1; dimensionless; α and β respectively represent the slip coefficients, 0.5 and 1, dimensionless; Kn = K B T / (2πd m 2 p) / r represents the Knudsen number, dimensionless; K B represents the Boltzmann constant, J / K; d m represents the diameter of the methane molecule, m; M represents the mass of the methane molecule, kg / mol; r represents the pore diameter of the coal reservoir matrix pores, m; r max and r min respectively represent the maximum and minimum pore diameters of the coal reservoir matrix pores, m; D s represents the surface adsorption coefficient, m 2 / s; C amax represents the maximum adsorption concentration, mol / m 3 ; D f represents the fractal dimension of the coal reservoir matrix pores, dimensionless; A random discrete fracture network model is used to quantitatively characterize the self-supporting fracture network after compression. The distribution of parameters including coordinates, fracture length, fracture width and inclination angle satisfies the following Fisher random function: The self-supporting fracture permeability evolution model includes: The aperture evolution equation of a self-supporting crack is: Using the cubic law, the permeability of a single cleat / natural fracture satisfies the following: The conductivity of hydraulic fractures satisfies the following exponential decreasing relationship: k HF = 216.7 t -0.249 (32) C HF = w HF k HF = 43.21t -0.249 (33) Among them, x NF , y NF , L NF and w NF respectively represent the coordinates, length, and width of the cleat / natural fracture, in m; ξ represents the distribution exponent, 1, dimensionless; f(θ) represents the Fisher distribution density function; θ represents the dip angle of the cleat / natural fracture, in °; K represents the Fisher distribution coefficient, dimensionless; and respectively represent the increments in fracture width caused by matrix compression, fracture compression, and desorption expansion, in m; w NFini represents the initial fracture width, in m; E represents the Young's modulus of the coal reservoir matrix, in GPa; v represents the Poisson's ratio of the coal reservoir matrix, dimensionless; c fini represents the initial fracture compression coefficient, 1 / MPa; p ini represents the initial pore pressure, in MPa; S L represents the Langmuir strain, dimensionless; k NF represents the cleat / natural fracture permeability, in mD; k HF represents the hydraulic fracture permeability, in mD; w HF represents the hydraulic fracture width, in m; C HF represents the hydraulic fracture conductivity, in D·cm.

5. The method for calculating the production of a coalbed methane fracturing well based on embedded flow switching according to claim 4, wherein Step 3 includes: The basic equation for the production capacity of the coalbed methane fracturing well is: Based on the principle of global / local embedded flow exchange, on the orthogonal grid in step 1, the basic equation of coalbed methane fracturing well productivity is changed to: Substitute the pressure distribution obtained in Step 1 into the rewritten basic productivity equation of coalbed methane fracturing wells to obtain the productivity calculation formula of coalbed methane fracturing wells considering multi-scale seepage and multiple production mechanisms, specifically as follows: where φ NF and φ HF represent the porosities of natural fractures and hydraulic fractures respectively, dimensionless; Q S , Q Fm , Q FNF and Q FHF represent the gas production rates of matrix adsorbed gas, matrix free gas, cleat free gas and main fracture free gas respectively, m 3 / s; Q represents the total gas production rate of a coalbed methane fracturing well, m 3 / s.

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