Anisotropic shale matrix apparent permeability calculation method

Abstract

The invention relates to an anisotropic shale matrix apparent permeability calculation method, which comprises the following steps: directionally sampling a rock core sample in parallel bedding / vertical bedding directions, and obtaining anisotropic characteristic parameters such as TOC, aperture, surface diffusion coefficient, stress sensitivity coefficient and the like through experiments; according to the method, high-pressure mercury injection and nuclear magnetic resonance experiments are combined to represent multi-scale pore distribution and connectivity, an atomic force microscope is adopted to measure pore surface roughness, and a cone roughness element is taken as a physical model to represent roughness fractal dimension; on the basis of a three-dimensional fractal theory, factors such as multi-scale pore size distribution, connectivity, roughness, a water film, stress sensitivity and a real gas effect are integrated, transmission mechanisms such as viscous flow, Knudsen diffusion, surface diffusion and a desorption effect are coupled, and the anisotropic multi-scale micro-nano pore mass transfer model of the shale is established. Compared with a prediction model in the prior art, the anisotropic shale matrix apparent permeability calculation method provided by the invention is higher in accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of petroleum engineering, and in particular to a method for calculating the apparent permeability of anisotropic shale matrix. Background Art

[0002] The anisotropy of shale matrix permeability (i.e., significant differences in permeability in different directions) is an important factor affecting shale gas migration, storage, and production capacity. Shale matrix is ​​usually composed of micro-nanoscale pores and bedding structures. The difference in permeability between the parallel bedding direction and the perpendicular bedding direction can reach 1 to 2 orders of magnitude. This anisotropy directly determines the dominant channel direction of gas flow after fracturing and the long-term stable production capacity. Therefore, establishing an anisotropic matrix permeability calculation model that takes into account comprehensive factors is of great significance for accurately predicting shale gas well production capacity, optimizing reservoir transformation plans, and formulating development strategies.

[0003] Existing technologies have comprehensively studied viscous flow, slip flow, Knudsen diffusion, surface diffusion mechanisms, and stress sensitivity in shale pores. However, these studies fail to fully consider the influence of matrix pore roughness, connectivity, and adsorbed water films on capillary pore diameters, leading to inflated permeability results. Furthermore, differences in pore roughness and connectivity parallel to and perpendicular to bedding can also lead to anisotropy in shale matrix permeability. Summary of the Invention

[0004] Based on the consideration of multiple action mechanisms of single capillary slip viscous flow, Knudsen flow and surface diffusion in the shale matrix, the present invention corrects the gas flow integral of a single capillary within the pore size range and combines it with Darcy's law to provide a calculation model for the apparent permeability of anisotropic shale matrix that comprehensively considers matrix pore roughness, connectivity, stress sensitivity, real gas effect and adsorbed water film.

[0005] The present invention achieves the above-mentioned purpose through the following technical solutions:

[0006] A method for calculating the apparent permeability of anisotropic shale matrix comprises the following steps:

[0007] S1. Obtain roughness fractal dimension, pore connectivity coefficient, porosity stress sensitivity coefficient and permeability stress sensitivity coefficient through experimental testing;

[0008] S2. Based on the three-dimensional capillary bundle fractal model of shale matrix, a calculation model for the fractal dimension of the aperture and tortuosity of a single capillary was constructed;

[0009] S3. Considering the slip viscous flow, Knudsen flow, and surface diffusion of a single capillary, a single capillary volume flow calculation model is constructed;

[0010] S4. Considering the inorganic capillary adsorption water film, the thickness of the organic capillary adsorption layer, the stress sensitivity effect and the pore surface roughness, a shale capillary pore size correction model is constructed;

[0011] S5. Integrate the gas flow rate of a single capillary within the corrected pore size range to construct a calculation model for the total volume flow rate of organic and inorganic matter. Combined with Darcy's law and TOC coefficient weighting, a calculation model for the apparent permeability of the anisotropic shale matrix is ​​constructed.

[0012] S6. Substitute the measured parameters in step S1 into the anisotropic shale matrix apparent permeability calculation model to obtain the permeability.

[0013] Furthermore, in step S1, the shale surface morphology is scanned by atomic force microscopy to obtain the roughness fractal dimension; the connected pore volume and total pore volume are obtained by nuclear magnetic resonance and mercury intrusion experiments, and the pore connectivity coefficient is calculated; the porosity stress sensitivity coefficient and permeability stress sensitivity coefficient are obtained by fitting the overburden porosity and permeability experiments.

[0014] Furthermore, the steps include:

[0015] Considering the influence of real gas effect, the gas deviation factor is introduced to construct the real gas viscosity correction model.

[0016] Furthermore, in step S4, for the shale organic capillary pores, a modified capillary pore size model is constructed by taking into account the wall roughness, stress sensitivity effect, and capillary adsorption layer thickness.

[0017] Furthermore, in step S4, for the inorganic capillary pores in shale, a modified capillary pore size model is constructed by taking into account the wall roughness, capillary adsorbed water film, and stress sensitivity effect.

[0018] Furthermore, the organic matter volume flow calculation model in step S5 is:

[0019] Q o =Q o,v +Q o,k +Q o,s

[0020] Among them, Q o is the total volume flow rate of organic pores, m 3 / s;Q o,v is the volume flow rate of organic pore slip viscous flow, m 3 / s;Q o,k is the volume flow rate of organic pore Knudsen flow, m 3 / s;Q o,s is the diffusion volume flow rate of organic pore surface, m 3 / s.

[0021] Furthermore, the inorganic matter volume flow calculation model in step S5 is:

[0022] Q io =Q io,v +Q io,k

[0023] Where Q io is the total volume flow rate without matrix pores, m 3 / s;Q io,v is the volume flow rate of viscous flow without matrix pore slip, m 3 / s;Q io,k is the volume flow rate of Knudsen flow without matrix pore, m 3 / s.

[0024] Furthermore, the calculation model of the anisotropic shale matrix apparent permeability in step S5 is:

[0025]

[0026] Among them, k m is the shale matrix permeability, mD; α is the pore connectivity coefficient; TOC is the shale organic matter content, dimensionless; μ r is the real gas viscosity, Pa·s; L 0,o L is the linear length of the capillary with matrix pores, nm; 0,io is the linear length of the capillary without matrix pores, nm; Δp is the mass transfer pressure difference, MPa.

[0027] The present invention also provides a computer-readable storage medium comprising instructions, which, when executed on a computer, enable the computer to execute the method for calculating the apparent permeability of anisotropic shale matrix provided by the above technical solution.

[0028] The present invention also provides a computing device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method for calculating the apparent permeability of anisotropic shale matrix as provided in the above technical solution is implemented.

[0029] The beneficial effects of the present invention are as follows: the present invention obtains anisotropic characteristic parameters such as TOC, pore size, surface diffusion coefficient, stress sensitivity coefficient, etc. through experiments, and based on three-dimensional fractal theory, integrates factors such as multi-scale pore size distribution, connectivity, roughness, water film, stress sensitivity and real gas effect, couples transmission mechanisms such as viscous flow, Knudsen diffusion, surface diffusion and desorption effect, and establishes an anisotropic shale matrix apparent permeability model, which is more accurate than the prediction models in the existing technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1Schematic diagram of the method flow of the present invention;

[0031] Figure 2 Schematic diagram of a conical rough element in a specific embodiment of the present invention;

[0032] Figure 3 is a fractal diagram of shale matrix pores in a specific embodiment of the present invention;

[0033] Figure 4 A schematic diagram of the core sampling direction in a specific embodiment of the present invention;

[0034] Figure 5 is a pore connectivity test result in a specific embodiment of the present invention;

[0035] Figure 6 A fitting diagram of the porosity and permeability of the parallel bedding planes and the effective stress in a specific embodiment of the present invention;

[0036] Figure 7 A fitting diagram of vertical bedding surface porosity and permeability and effective stress in a specific embodiment of the present invention;

[0037] Figure 8 A diagram comparing model calculation results and experimental results in a specific embodiment of the present invention;

[0038] Figure 9 This is a comparison chart of different model results in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0039] The storage and migration of shale gas in the reservoir matrix pores involve multiple mass transfer mechanisms such as viscous flow, slip flow, Knudsen diffusion, desorption, and surface diffusion. The anisotropy of permeability is affected by the coupling of multiple factors such as pore structure characteristics, stress sensitivity effects, and fluid occurrence status.

[0040] In addition, factors such as the rough surface morphology of microscopic pores, disconnected pores, and water film adsorbed on inorganic pores will significantly reduce the permeability of the matrix, while the increase in effective stress will compress the matrix pores and produce stress sensitivity, further reducing the matrix porosity and permeability.

[0041] Prior art models for shale pore permeability lack consideration of these factors, resulting in inflated permeability calculations. This paper investigates key characteristic parameters, such as the fractal dimension of pore roughness, connectivity coefficient, and stress sensitivity coefficient, through experimental testing. Based on three-dimensional capillary bundle fractal theory, this paper constructs calculation models for single capillary slip viscous flow, Knudsen flow, and surface diffusion flow in a shale matrix. By modifying the integral of the gas flow within the pore size range and combining this with Darcy's law, this paper provides a theoretical model for calculating the apparent permeability of anisotropic shale matrices that comprehensively considers matrix pore roughness, connectivity, stress sensitivity, real gas effect, and adsorbed water film.

[0042] Figure 1 The method for calculating the apparent permeability of anisotropic shale matrix provided in the embodiment of the present invention is as follows: Figure 1 As shown, the method includes:

[0043] S1. Obtain roughness fractal dimension, pore connectivity coefficient, porosity stress sensitivity coefficient and permeability stress sensitivity coefficient through experimental testing;

[0044] S2. Based on the three-dimensional capillary bundle fractal model of shale matrix, a calculation model for the fractal dimension of the aperture and tortuosity of a single capillary was constructed;

[0045] S3. Considering the slip viscous flow, Knudsen flow, and surface diffusion of a single capillary, a single capillary volume flow calculation model is constructed;

[0046] S4. Considering the inorganic capillary adsorption water film, the thickness of the organic capillary adsorption layer, the stress sensitivity effect and the pore surface roughness, a shale capillary pore size correction model is constructed;

[0047] S5. Integrate the gas flow rate of a single capillary within the corrected pore size range to construct a calculation model for the total volume flow rate of organic and inorganic matter. Combined with Darcy's law and TOC coefficient weighting, a calculation model for the apparent permeability of the anisotropic shale matrix is ​​constructed.

[0048] S6. Substitute the measured parameters in step S1 into the anisotropic shale matrix apparent permeability calculation model to obtain the permeability.

[0049] Specifically, in step S1, an atomic force microscope shale surface morphology scanning experiment can be used to calculate the roughness fractal dimension in combination with fractal theory; nuclear magnetic resonance and mercury intrusion experiments can be used to obtain the connected pore volume and total pore volume, thereby calculating the pore connectivity coefficient; and an overburden porosity and permeability experiment can be used to fit and obtain the stress sensitivity coefficients of porosity and permeability.

[0050] The surface of shale pores is not smooth, but rough and has fractal characteristics. Its surface roughness actually reflects static heterogeneity. Therefore, an atomic force microscope is used to scan and 3D reconstruct the surface of the shale sample. The roughness element of the rough surface is approximately a cone, such as Figure 2 As shown in the figure, h min 、h max 、h av The longitudinal minimum, maximum and average heights are determined by the bottom diameter, while the longitudinal height affects the pipe diameter.

[0051] The cone rough element satisfies the statistical self-similar fractal, and the surface roughness fractal dimension is:

[0052]

[0053] Where D r is the roughness fractal dimension, which is between 2.0 and 3.0; σ is the ratio of the total area of ​​the base of all cones to the total area of ​​the entire fractal unit; d min d max are the minimum and maximum diameters of the bottom surface of the rough element, nm.

[0054] There are connected pores and unconnected pores in porous media. Pore connectivity is a key feature of anisotropic mass transfer, and the mass transfer process is controlled by both pore structure and connectivity. In this paper, nuclear magnetic resonance experiments are used to measure the intensity and attenuation law of the hydrogen nuclear magnetic resonance signal of the fluid-saturated core to inversely calculate the fluid volume in the pores. This volume is the total pore volume of the core. In mercury injection experiments, mercury only enters the connected pores, thereby obtaining the connected pore volume. The connectivity coefficient is used to quantify the connectivity of the matrix pores:

[0055]

[0056] Where α is the pore connectivity coefficient, V connect is the volume of connected pores, m 3 ; V total is the total pore volume, m 3 .

[0057] As the matrix pores are compressed, the porosity and permeability of shale decrease with the increase of effective stress, which is the porosity stress sensitivity effect and permeability stress sensitivity effect, which can be expressed as:

[0058] p e =p ob -p (3)

[0059]

[0060] Where p eis the effective stress, MPa; p ob is the confining pressure, MPa; p is the pore pressure; k i is the permeability at a certain pressure, mD; k0 is the permeability when the effective stress is 0, mD; s is the permeability stress sensitivity coefficient, MPa -1 ;φ i is the porosity under a certain pressure, %; φ0 is the porosity when the effective stress is 0, %; q is the porosity stress sensitivity coefficient, MPa -1 .

[0061] Through the overburden porosity experiment, the changes of shale core permeability and porosity with effective stress were measured under constant flow pressure and variable confining pressure conditions. The permeability stress sensitivity effect and porosity stress sensitivity coefficient were obtained by fitting according to Equations (4) and (5).

[0062] Through the above experiments, relevant characteristic parameters describing the anisotropy of shale matrix can be obtained.

[0063] In step S2, based on the three-dimensional capillary bundle fractal model of the shale matrix, a calculation model for the fractal dimension of the aperture and tortuosity of a single capillary is constructed.

[0064] like Figure 3 As shown in Figure 2, in the cross section of a shale reservoir, the number N of pores with a pore size greater than or equal to λ follows the fractal law.

[0065] The calculation formula of the pore size fractal dimension of the matrix pores is:

[0066]

[0067] Where λ is the pore size of any shale matrix, nm; min ,λ max are the minimum and maximum pore sizes of shale matrix, nm; D f is the aperture fractal dimension, dimensionless.

[0068] Differentiating Equation (6) with respect to λ yields:

[0069]

[0070] The fractal dimension of three-dimensional space is:

[0071]

[0072] Where φ is the porosity and β is the ratio of the minimum pore size to the maximum pore size of the matrix.

[0073] The pore tortuosity distribution also conforms to the fractal theory. The tortuosity fractal dimension is used to describe the distribution characteristics of the true pore throat tortuosity length:

[0074]

[0075] Where, L t (λ) is the capillary tortuosity length, nm; L0 is the capillary straight length, nm; D T is the fractal dimension of tortuosity, dimensionless.

[0076] Tortuosity fractal dimension and average tortuosity τ of porous media av , average pore size λ av The relationship is:

[0077]

[0078] Where, τ av is the average tortuosity of the porous medium, dimensionless; λ av is the average capillary diameter, nm.

[0079] The straight length L0 of the capillary in three-dimensional space is:

[0080]

[0081] Average tortuosity τ av for:

[0082]

[0083] Capillary average diameter λ av for:

[0084]

[0085] Specifically, when determining the fractal dimension of tortuosity, set D T An initial value D T,0 , calculate L0 by formula (11), and calculate D by combining formula (10) and formula (13) T,i , if |D T,0 -D T,i |≤10 -5 , then output D T,i Otherwise, a search is performed in the region [1, 3] with a step size of 0.01 until the accuracy is met. In step S3, for the specific transmission mechanism, the present invention constructs a single capillary slip viscous flow volume flow calculation model based on the Hagen-Poiseuille equation; considers the capillary surface roughness to construct a single capillary Knudsen flow volume flow calculation model; and constructs a single capillary surface diffusion volume flow calculation model based on Fick's first diffusion law.

[0086] The rock matrix gas transport mechanism includes viscous flow, slip flow, Knudsen flow, and surface diffusion. Based on the Hagen-Poiseuille equation, a single capillary slip viscous flow volume flow calculation model is constructed:

[0087]

[0088] Where, J v (λ) is the volume flow rate of the slip viscous flow of a single capillary tube, m 3 / s; μ is the gas viscosity, Pa·s; Kn is the Knudsen number, dimensionless; Δp is the mass transfer pressure difference, MPa.

[0089] The calculation formula of Kn is:

[0090]

[0091] Where R is the gas constant, which is 8.314 J / (mol·K); T is the temperature, in K; and M is the molar mass of the gas, in g / mol.

[0092] The Knudsen flow volume flow calculation model is:

[0093]

[0094] Surface roughness has a significant effect on Knudsen diffusion. The roughness elements on the capillary wall are similar to a series of "fjords". The roughness fractal dimension is introduced to characterize the effect of matrix pore surface roughness on gas transmission:

[0095]

[0096] Where, J k (λ) is the Knudsen flow volume flow rate considering the pore surface roughness, m 3 / s;d m is the diameter of gas molecules, nm.

[0097] Fick's first diffusion law is used to quantify the surface diffusion mechanism of absorbed gas transport. Assuming that the adsorption / desorption process can reach equilibrium immediately, the surface diffusion volume flow rate calculation model is:

[0098]

[0099] Where, J s (λ) is the surface diffusion volume flow rate, m 3 / s; θ is the coverage of the gas on the wall in equilibrium state, dimensionless; D s is the surface diffusion coefficient, m 2 / s;C L is the maximum adsorption capacity of gas, mol / m 3;p L is the Langmuir pressure, Pa; ρ is the gas density, kg / m 3 .

[0100] In formula (18):

[0101]

[0102] Where Z is the gas deviation factor, dimensionless.

[0103]

[0104] Where, is the surface diffusion coefficient when the gas coverage is 0, m 2 / s; ω is the ratio of the adsorbed gas congestion rate to the mobility, dimensionless; H(1-ω) is the Heaviside function, which is:

[0105]

[0106] A Heaviside function value of 1 means that surface diffusion will occur, while a value of 0 means that surface diffusion will cease because the gas molecules are blocked.

[0107]

[0108] Where, ρ s is the density of shale, kg / m 3 ; V L is the Langmuir volume, m 3 / kg; TOC is organic carbon content, dimensionless; V s is the molar volume of the gas under standard conditions, taking 0.0224m 3 / mol.

[0109] In step S4, a shale capillary pore size correction model is constructed by considering the thickness of the inorganic capillary adsorption water film, the organic capillary adsorption layer, the stress sensitivity effect, and the pore surface roughness.

[0110] The geometry of the flow path in shale matrix pores varies irregularly, with the cross-sectional area exhibiting a distinct alternating expansion-contraction phenomenon along the flow direction. For gas flow within capillaries, surface roughness reduces the gas flow velocity. Because shale pores are self-similar, the ratio of any corresponding roughness to the tube diameter is equal to the ratio of the average roughness to the average tube diameter:

[0111]

[0112] For shale organic matter capillary pores, the corrected capillary pore diameter considering the wall roughness, stress sensitivity effect, and capillary adsorption layer thickness is:

[0113] λ o,e =(λ o,0 -2h)(p e / p0) 0.5(q-s) -2d m ·θ (24)

[0114] Where λ o,e is the capillary corrected pore size of shale organic matter, nm; λ o,0 is the initial pore size of the organic capillary, nm; p0 is the initial pressure, MPa.

[0115] For inorganic capillary pores, the modified capillary pore diameter considering the wall roughness, capillary adsorption water film, and stress sensitivity effect is:

[0116]

[0117] Where λ io,e is the corrected pore size of the inorganic capillary, nm; λ io,0 is the initial pore size of the inorganic capillary, nm; s w is the water saturation, dimensionless.

[0118] In addition, in order to consider the influence of real gas effect, the gas deviation factor is introduced to construct the real gas viscosity correction model.

[0119] The gas deviation factor is introduced to characterize the difference between real gas and ideal gas. The calculation formula is:

[0120]

[0121] p r =p / p c (27)

[0122] T r =T / T c (28)

[0123] Where p r is the comparative pressure, dimensionless; T r is the comparison temperature, dimensionless; p c is the critical pressure, Pa; T c is the critical temperature, K.

[0124] The viscosity of real gas changes with pressure and temperature, and the calculation formula is:

[0125]

[0126] in:

[0127]

[0128] Where μ r is the real gas viscosity, Pa·s.

[0129] In step S5, the gas flow integral of a single capillary within the pore size range is corrected to construct a calculation model for the total volume flow of organic and inorganic matter. The Darcy's law and the TOC coefficient weighting are further combined to construct a calculation model for the anisotropic shale matrix apparent permeability.

[0130] Specifically, by integrating the individual gas flow rates within the entire capillary pore size range within the unit cell, the total volume flow rate can be calculated:

[0131]

[0132] For organic pores, the total volume flow rate of slip viscous flow, Knudsen flow and surface diffusion is:

[0133] Q o =Q o,v +Q o,k +Q o,s (32)

[0134] Where Q o is the total volume flow rate of organic pores, m 3 / s;Q o,v is the volume flow rate of organic pore slip viscous flow, m 3 / s;Q o,k is the volume flow rate of organic pore Knudsen flow, m 3 / s;Q o,s is the diffusion volume flow rate of organic pore surface, m 3 / s.

[0135] in:

[0136]

[0137] Among them, λ o，e，min is the minimum inorganic pore size; λ o，e，max is the maximum organic pore size; λ is the micro-nanopore diameter, nm; μ is the gas viscosity, Pa·s; Kn is the Knudsen number, dimensionless; Δp is the mass transfer pressure difference, MPa; L t (λ)—capillary tortuosity length, nm; D f is the aperture fractal dimension; L 0,o is the linear length of the organic pore capillary, nm; D T is the fractal dimension of tortuosity, dimensionless; d m is the diameter of gas molecules, m; D ris the roughness fractal dimension, dimensionless; p is pressure, Pa; R is the gas constant, J / (mol·K); T is temperature, K; M is the gas molar mass, g / mol; θ is the gas coverage; C L is the maximum adsorption capacity of gas, mol / m 3 ; ρ is the gas density, kg / m 3 ;p L is the Langmuir pressure, Pa; D s is the surface diffusion coefficient, m 2 / s.

[0138] For inorganic pores, the total volume flow rate of the integrated slip viscous flow and Knudsen flow is:

[0139] Q io =Q io,v +Q io,k (36)

[0140] Where Q io is the total volume flow rate without matrix pores, m 3 / s;Q io,v is the volume flow rate of viscous flow without matrix pore slip, m 3 / s;Q io,k is the volume flow rate of Knudsen flow without matrix pore, m 3 / s.

[0141] in:

[0142]

[0143] Where λ io，e，min is the minimum inorganic pore size; λ io，e，max is the maximum inorganic pore size; L 0,io is the straight length of the capillary without matrix pores, nm.

[0144] Substituting Equations (32) and (36) into Darcy's law, weighting the apparent permeability of organic matter and the apparent permeability of inorganic matter by the TOC coefficient, and considering the connectivity of the shale matrix, the apparent permeability of the shale matrix is:

[0145] k m ={αμ r ×[TOC×Q o / L 0,o +(1-TOC)×Q io / L 0,io ]} / Δp (39)

[0146] It can also be written as:

[0147]

[0148] Where k m is the shale matrix permeability, mD; TOC is the shale organic matter content, dimensionless; μ r is the real gas viscosity, Pa·s.

[0149] In step S6, the measured parameters in step S1 are substituted into the anisotropic shale matrix apparent permeability calculation model to calculate the permeability.

[0150] Application Examples

[0151] In this embodiment, relevant experiments and anisotropic permeability calculations are carried out using the core of the shale gas pilot well J1 in a certain block.

[0152] (1) Roughness and connectivity experimental test

[0153] The anisotropy of shale is transversely isotropic, so the permeability difference between the parallel and perpendicular bedding directions was studied. The core sampling direction is as follows: Figure 4 As shown, the x / y plane is a plane parallel to the bedding, and the z plane is a plane perpendicular to the bedding, and the radial standard core J1-x / y and the axial standard core J1-z are taken respectively.

[0154] Atomic force microscope scanning was performed on the cores parallel to the bedding and perpendicular to the bedding, and the roughness fractal dimension was calculated according to formula (1). The experimental results are shown in Table 1. The average roughness of the parallel bedding is 0.8 nm, and the average roughness of the perpendicular bedding is 2.16 nm.

[0155] Table 1 Core surface roughness test results

[0156]

[0157] Nuclear magnetic resonance and mercury injection experiments were carried out on two cores respectively, and the pore connectivity coefficients parallel to and perpendicular to the bedding were calculated using formula (2). The experimental results are shown in the figure below. Figure 5 As shown in the figure, the connectivity coefficient in the direction parallel to the bedding is calculated to be 0.4, and the connectivity coefficient in the direction perpendicular to the bedding is 0.024.

[0158] Overburden porosity tests were carried out on two cores to measure the permeability and porosity of the target cores at confining pressures of 10 MPa to 50 MPa. The experimental results are shown in Table 2.

[0159] Table 2 Results of overburden pressure permeability test

[0160]

[0161] According to equations (4) and (5), the relationship between permeability, porosity and effective stress is fitted, and the results are as follows: Figure 6 and Figure 7As shown, the stress sensitivity coefficient of J1-x / y permeability is 0.075MPa -1 , the porosity stress sensitivity coefficient is 0.04MPa -1 , J1-z permeability stress sensitivity coefficient is 0.079MPa -1 , the porosity stress sensitivity coefficient is 0.036MPa -1 .

[0162] (2) Calculation of anisotropic permeability

[0163] The anisotropic permeability calculation was carried out by combining the roughness, pore connectivity coefficient, stress sensitivity coefficient and the core parameters in Table 3. The basic parameters of the model are shown in Table 4.

[0164] Table 3 Core foundation parameters

[0165]

[0166] Table 4 Basic parameters of the model

[0167] parameter unit Numerical parameter unit Numerical Temperature / T K 298 Gas molecular mass / M g / mol 16.0425 <![CDATA[Gas molecular diameter / d m > nm 0.38 <![CDATA[Critical pressure / p c > MPa 4.6 Ratio of adsorbed gas congestion rate to mobility / ω \ 0.5 <![CDATA[Critical temperature / T c > K 190.6

[0168] The comparison between the model calculation results and the experimental results is shown in Figure 8 As shown, the average relative error is between 3.24% and 5.12%, and the permeability in the direction parallel to the bedding is on average 17 times that in the direction perpendicular to the bedding, indicating that permeability anisotropy has an important influence on the calculation of gas transport.

[0169] The comparison between the calculation results of the model of the present invention and the calculation results of the model in the literature is as follows: Figure 9 As shown in the figure, the existing model does not consider the influence of matrix pore roughness and connectivity, so the calculated results are greater than the experimental results. After comprehensively considering the real gas effect, stress sensitivity, pore wall roughness, adsorbed water film thickness and pore connectivity, the permeability calculation results of the proposed model are more accurate.

[0170] It can be seen that the method proposed in the present invention can quantify the influence of parameters such as pore roughness and connectivity on the permeability of shale matrix, realize the calculation of the apparent permeability of anisotropic shale matrix, and lay the foundation for shale gas production capacity simulation.

[0171] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating the apparent permeability of anisotropic shale matrix, comprising the following steps: S1. Obtain roughness fractal dimension, pore connectivity coefficient, porosity stress sensitivity coefficient and permeability stress sensitivity coefficient through experimental testing; S2. Based on the three-dimensional capillary bundle fractal model of shale matrix, a calculation model for the fractal dimension of the aperture and tortuosity of a single capillary was constructed; S3. Considering the slip viscous flow, Knudsen flow, and surface diffusion of a single capillary, a single capillary volume flow calculation model is constructed; S4. Considering the inorganic capillary adsorption water film, the thickness of the organic capillary adsorption layer, the stress sensitivity effect and the pore surface roughness, a shale capillary pore size correction model is constructed; S5. Integrate the gas flow rate of a single capillary within the corrected pore size range to construct a calculation model for the total volume flow rate of organic and inorganic matter. Combined with Darcy's law and TOC coefficient weighting, a calculation model for the apparent permeability of the anisotropic shale matrix is ​​constructed. S6. Substitute the measured parameters in step S1 into the anisotropic shale matrix apparent permeability calculation model to obtain the permeability.

2. The method for calculating the apparent permeability of an anisotropic shale matrix according to claim 1, wherein in step S1, the surface morphology of the shale is scanned using an atomic force microscope to obtain a roughness fractal dimension; the connected pore volume and total pore volume are obtained by nuclear magnetic resonance and mercury intrusion experiments, and the pore connectivity coefficient is calculated; and the porosity stress sensitivity coefficient and the permeability stress sensitivity coefficient are obtained by fitting the overburden porosity and permeability experiments.

3. The method for calculating the anisotropic shale matrix apparent permeability according to claim 1, further comprising the steps of: Considering the influence of real gas effect, the gas deviation factor is introduced to construct the real gas viscosity correction model.

4. The method for calculating the apparent permeability of anisotropic shale matrix according to claim 1, wherein in step S4, a modified capillary pore size model is constructed for the organic capillary pores in the shale, taking into account wall roughness, stress sensitivity effect, and capillary adsorption layer thickness.

5. The method for calculating the apparent permeability of anisotropic shale matrix according to claim 1, wherein in step S4, a modified capillary pore size model is constructed for the inorganic capillary pores in the shale, taking into account wall roughness, capillary adsorbed water film, and stress sensitivity effects.

6. The method for calculating the anisotropic shale matrix apparent permeability according to claim 1, wherein the organic matter volume flow calculation model in step S5 is: Q o =Q o,v +Q o,k +Q o,s in, Q o is the total volume flow rate of organic pores, m 3 / s;Q o,v is the volume flow rate of organic pore slip viscous flow, m 3 / s;Q o,k is the volume flow rate of organic pore Knudsen flow, m 3 / s;Q o,s is the diffusion volume flow rate of organic pore surface, m 3 / s.

7. The method for calculating the anisotropic shale matrix apparent permeability according to claim 1, wherein the inorganic matter volume flow calculation model in step S5 is: Q io =Q io,v +Q io,k Where Q io is the total volume flow rate without matrix pores, m 3 / s;Q io,v is the volume flow rate of viscous flow without matrix pore slip, m 3 / s;Q io,k is the volume flow rate of Knudsen flow without matrix pore, m 3 / s.

8. The method for calculating the anisotropic shale matrix apparent permeability according to claim 1, wherein the anisotropic shale matrix apparent permeability calculation model in step S5 is: in, k m is the shale matrix permeability, mD; α is the pore connectivity coefficient; TOC is the shale organic matter content, dimensionless; μ r is the real gas viscosity, Pa·s; L 0,o L is the linear length of the capillary with matrix pores, nm; 0,io is the linear length of the capillary without matrix pores, nm; Δp is the mass transfer pressure difference, MPa.

9. A computer-readable storage medium comprising instructions, which, when executed on a computer, enable the computer to execute the method for calculating the anisotropic shale matrix apparent permeability according to any one of claims 1 to 8.

10. A computing device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method for calculating the anisotropic shale matrix apparent permeability according to any one of claims 1 to 8 is implemented.

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