Method for constructing fractal model of rough fractures and irregular pores of shale under multi-field coupling

Abstract

The invention discloses a shale rough fracture and irregular pore fractal model construction method under multi-field coupling, and the method comprises the following steps: S1, constructing a fractal theoretical model based on a rough fracture system; s2, constructing a fractal theoretical model based on a pore system; S3, constructing a solid mechanical control equation; and S5, determining the flow mechanism of shale methane gas between fractures and pores. According to the method, a fractal flow model coupling gas migration, shale deformation and fracture-matrix interaction is established so as to realize quantitative analysis of a shale gas seepage mechanism, and four fractal parameters including tortuosity, roughness, fracture number and fracture length are introduced and evaluated so as to quantify the influence of the fractal parameters on permeability and gas pressure. Through numerical simulation, the interaction between a fracture network and a pore structure under different structure parameters is quantified, and the change rule of the pore fractal dimension and the gas pressure caused by the interaction is emphatically revealed.

Description

Technical Field

[0001] This invention belongs to the field of shale gas technology, specifically relating to a method for constructing a fractal model of rough fractures and irregular pores in shale under multi-field coupling. Background Technology

[0002] Shale gas, as a clean energy source, is receiving increasing attention in modern exploration and development due to its enormous development potential. For example... Figure 1 As shown, in shale gas extraction, the complex fracture-pore network within shale reservoirs serves as the primary pathway for gas migration. Furthermore, the structural characteristics of fracture networks within the rock mass typically encompass multiple dimensions, including orientation, size, and morphology. The pores within the reservoir rock exhibit a complex, interconnected structure across multiple scales and dimensions. The interaction between coarse fractures and irregular pores plays a crucial role in the multi-field coupled gas extraction process. Therefore, a comprehensive and quantitative analysis of the reservoir microstructure (especially coarse fractures) considering various factors is essential for understanding the migration, enrichment, and extraction mechanisms of methane.

[0003] Current research on shale gas extraction characteristics typically combines factors such as matrix deformation, thermal-fluid-solid coupling, and gas injection, and generally employs coupled models for analysis. These models often integrate Darcy's law, heat transfer equations, and fractal geometry theory. Throughout the extraction process, temperature plays a crucial role in matrix deformation and gas migration. Noorishad assessed the thermal-fluid-solid coupling behavior of rocks and explored how thermal stress affects permeability through fracture deformation. Yan et al. proposed a coupled model aimed at simultaneously evaluating adsorption-desorption processes, pore pressure, and matrix stress. Mitra et al. studied observed gas pressure changes and examined the impact of the interaction between effective stress and deformation caused by adsorption-induced expansion on reservoir permeability. Zhu et al. used a systematic approach to analyze heat transfer within the reservoir, considering the combined effects of gas and solid components. These simulation and experimental studies clearly demonstrate that multiphysics processes have a significant impact on shale gas extraction. Furthermore, the fracture network within shale is highly complex, with fractures exhibiting randomness and disorder in spatial distribution, length, aperture, and arrangement. Fractal geometry theory has been successfully applied to study fluid flow, thermal conduction, and electrical conductivity in porous media, as well as physical properties related to porous surface roughness, pool boiling, nanofluid behavior, and dendritic branching modes. However, these studies have failed to fully consider the interaction between rough fractures and their pore microstructure in shale, thus making it difficult to comprehensively reveal the mechanism by which fracture structure affects pore structure under the coupling of multiple factors.

[0004] Furthermore, existing studies rarely integrate fracture-pore characteristics into multi-field coupling analysis, nor do they systematically evaluate how their quantitative evolution affects shale methane extraction.

[0005] Therefore, to address the aforementioned technical issues, it is necessary to provide a method for constructing fractal models of rough fractures and irregular pores in shale under multi-field coupling.

[0006] The information disclosed in this background section is intended only to enhance the understanding of the overall background of the invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0007] The purpose of this invention is to provide a method for constructing a fractal model of rough fractures and irregular pores in shale under multi-field coupling, which can solve the above-mentioned technical problems.

[0008] To achieve the above objectives, a specific embodiment of the present invention provides the following technical solution:

[0009] A method for constructing a fractal model of rough fractures and irregular pores in shale under multi-field coupling includes the following steps:

[0010] S1. Construction of a fractal theory model based on a rough fracture system;

[0011] The true length of the bending fracture in the rock mass Relative to the length of the character unit It exhibits fractal characteristics;

[0012]

[0013] In the formula, The fractal dimension related to the tortuosity of the roughness crack;

[0014] The length and number of rough fractures in the rock mass satisfy the following fractal relationship:

[0015]

[0016] as well as

[0017]

[0018] In the formula, Represents the fracture length. The fractal dimension associated with rough fracture;

[0019] Based on the fractal theory of porous media, the fractal porosity of the matrix and the fractal parameters characterizing the fracture scale can be expressed as follows:

[0020]

[0021]

[0022] Therefore, the average effective height of irregular elements on the crack surface can be defined as:

[0023]

[0024] In the formula, The aperture of the rough crack; The height of the irregular unit; It is the ratio of the sum of the base areas within a shale fractal unit to the total area of ​​the entire fractal unit;

[0025] S2. Construction of a fractal theory model based on porous systems;

[0026] The fractal power law relationship can be expressed as follows:

[0027]

[0028] in, Let represent the equivalent radius of the pores, and satisfy . ; This represents the fractal dimension of the pore size, while Represents the number of pores in two-dimensional space. ;

[0029] Furthermore, equation (15) can be restated as:

[0030]

[0031] In the formula, is a proportionality constant; the differential expression is derived from equation (15);

[0032] equivalent radius at The number of pores within the range is:

[0033]

[0034] A negative sign indicates that, under the condition of constant porosity, an increase in the size of a single pore will lead to a decrease in the number of pores;

[0035] S3. Construct the governing equations for solid mechanics;

[0036] The relationship between displacement and strain is expressed as:

[0037]

[0038] in, and Represents the displacement components, while Let represent the total strain components in all directions. Therefore, the deformation equilibrium equation can be expressed as:

[0039]

[0040] In the formula, Represents the stress tensor components. The deformation caused by adsorption, representing the force component, can be expressed by the following formula:

[0041]

[0042] The bulk modulus of the shale reservoir is given by the formula. Give; Indicates shear modulus; and The strain represents the gas adsorption-induced stress, based on the force analysis of the micro-element. ,here, The Biot coefficient is defined as follows: , It is the bulk modulus of shale particles. Represents the Kronecker function;

[0043] S4. Construct the governing equations for the porosity evolution model;

[0044] The deformation of the pores is described by the Langmuir equation:

[0045]

[0046] Langmuir volumetric strain is due to This indicates that, assuming the strain in shale caused by desorption is equivalent to the pore strain, we can obtain:

[0047]

[0048] The total volume of porous shale consists of shale volume and pore volume, and its volumetric strain is defined as:

[0049]

[0050]

[0051] Represents the average stress. Represents pore volume, Indicates the volume of shale;

[0052] S5. The flow mechanism of methane gas in shale between fractures and pores;

[0053] The coupling function describing mass transfer between the fractured system and the porous structure is shown below:

[0054]

[0055] in , Permeability of a porous system is expressed as fluid viscosity. express, Represents the volume of gas, while Represents the shape factor. It is the pressure inside the cracked structure, and This represents the pressure of the pore structure.

[0056] In one or more embodiments of the present invention, S1 further includes;

[0057] The surface roughness of shale fractures is defined as follows:

[0058]

[0059] Gas flowing through a smooth-surfaced crack can be described as:

[0060] Attached Figure Description

[0061] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0062] Figure 1 A schematic diagram illustrating the impact of irregular pore and coarse fracture networks on energy extraction;

[0063] Figure 2 This is a schematic diagram of a unit representing the fractal characteristics of rough cracks.

[0064] Figure 3 This is a schematic diagram of the coupling relationship in a fractal model;

[0065] Figure 4 A schematic diagram of the model for on-site data verification;

[0066] Figure 5 This is a schematic diagram comparing numerical simulation and field observation results;

[0067] Figure 6 A schematic diagram of the initial conditions and boundaries;

[0068] Figure 7 This is a schematic diagram illustrating the evolution of stress distribution in shale.

[0069] Figure 8 This is a schematic diagram illustrating the evolution of pore gas pressure.

[0070] Figure 9 This is a schematic diagram illustrating the evolution of fracture gas pressure.

[0071] Figure 10 This is a schematic diagram illustrating the evolution of overall penetration rate;

[0072] Figure 11 This is a schematic diagram illustrating the evolution of permeability in a mid-plane pore system.

[0073] Figure 12 This is a schematic diagram illustrating the evolution of permeability in a mid-plane fracture system.

[0074] Figure 13 This is a schematic diagram illustrating the effect of crack roughness on the fractal dimension of pores.

[0075] Figure 14 A schematic diagram illustrating the effect of the fractal dimension of fracture tortuosity on the fractal dimension of pores;

[0076] Figure 15 This is a schematic diagram illustrating the effect of the fractal dimension of roughness cracks on the fractal dimension of pores.

[0077] Figure 16 This is a schematic diagram illustrating the effect of fracture roughness on fracture gas pressure.

[0078] Figure 17 A schematic diagram illustrating the effect of pore fractal dimension on fracture gas pressure;

[0079] Figure 18 A schematic diagram illustrating the effect of fracture tortuosity and fractal dimension on fracture gas pressure;

[0080] Figure 19 This is a schematic diagram illustrating the effect of the fractal dimension of a rough fracture on the fracture gas pressure. Detailed Implementation

[0081] To enable those skilled in the art to better understand the technical solutions in this disclosure, the technical solutions in the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this disclosure.

[0082] like Figure 1 As shown in one embodiment of the present invention, the fractal model construction method for shale rough fractures and irregular pores under multi-field coupling constructs a fractal flow model that integrates gas migration, shale deformation and fracture-matrix interaction, and introduces four fractal parameters, namely tortuosity, roughness, number of fractures and length, to quantify structural effects.

[0083] S1. Construction of a fractal theory model based on a rough fracture system;

[0084] Similar to coal and rock structures, based on the well-established fractal theory in porous media, fractures in shale reservoirs often exhibit varying degrees of tortuosity. The true length of these tortuous fractures within the rock mass... Relative to the length of the character unit It exhibits fractal characteristics (such as) Figure 2 (As shown).

[0085]

[0086] In the formula, The fractal dimension is related to the tortuosity of the roughness crack.

[0087] The length and number of rough fractures in the rock mass satisfy the following fractal relationship:

[0088]

[0089] as well as

[0090]

[0091] In the formula, Represents the fracture length. The fractal dimension is related to rough fracture.

[0092] Based on the fractal theory of porous media, the fractal porosity of the matrix and the fractal parameters characterizing the fracture scale can be expressed as follows:

[0093]

[0094]

[0095] Therefore, the average effective height of irregular elements on the crack surface can be defined as:

[0096]

[0097] In the formula, The aperture of the rough crack; The height of the irregular unit; It is the ratio of the sum of the base areas within a shale fractal unit to the total area of ​​the entire fractal unit.

[0098] Therefore, the surface roughness of shale fractures is defined as follows:

[0099]

[0100] Gas flowing through a smooth-surfaced crack can be described as:

[0101]

[0102] Furthermore, the effective fluid flow resistance within the fissure can be expressed as:

[0103]

[0104] in Indicates gas viscosity. This represents the fractal power law exponent.

[0105] Figure 2 The complete cross-sectional area of ​​all cracks within the fractal unit shown is:

[0106]

[0107] Therefore, by combining equation (8) with the basic principles of fluid dynamics, the fluid pressure gradient can be obtained as follows:

[0108]

[0109] By combining equations (7) and (11) and considering the crack roughness, the fluid flow equation in a single pipe can be obtained as follows:

[0110]

[0111] Therefore, the pressure gradient within the rough crack can be expressed as:

[0112]

[0113] Combining Darcy's law with the above equations, we can establish a fractal model of shale permeability that considers fracture roughness, as shown in the following expression:

[0114]

[0115] Clearly, equation (14) provides a comprehensive analysis of the microscopic behavior of rough fractures (such as their number, tortuosity, length, and roughness), thus defining a model to describe the dynamic permeability of shale rough fractures. Furthermore, macroscopic parameters are directly influenced by the microscopic parameters that quantitatively describe the behavior of rough fractures, which is closely related to the interaction effects of multi-field coupling during the mining process. Considering the interaction between complex fracture networks and irregular pore structures, and examining the structural evolution under the influence of multi-physics field effects, this application will delve into the dynamic characteristics of shale gas migration under the combined effects of multiple factors.

[0116] S2. Construction of a fractal theory model based on porous systems;

[0117] Considering the similar gas production mechanisms of shale and coal seams, the study of fracture-pore coupling effects in coal seams provides valuable insights into the evolution of shale gas reservoir permeability. Based on fractal geometry theory, a shale permeability model is established by introducing microstructural parameters to explore how pore microstructure affects macroscopic permeability. First, the microscopic characterization units of shale samples are extracted and simplified into a structure composed of channels and pores when constructing the fractal flow model. Subsequently, a fractal permeability model is established, which includes parameters such as pore size fractal dimension, tortuosity fractal dimension, and maximum pore size. In the two-dimensional analysis, the fractal dimension ranges between 1 and 2; a higher value indicates greater structural complexity.

[0118] Based on the fractal model, its fractal power law relationship can be expressed as follows:

[0119]

[0120] in, Let represent the equivalent radius of the pores, and satisfy . . This represents the fractal dimension of the pore size, while This represents the number of pores. In two-dimensional space, Furthermore, equation (15) can be restated as:

[0121]

[0122] In the formula, It is a proportionality constant. The differential expression is derived from equation (15). The equivalent radius is in The number of pores within the range is:

[0123]

[0124] The negative sign indicates that, under the condition of constant porosity, an increase in the size of a single pore leads to a decrease in the number of pores. According to equation (17), the probability density function of pore size can be expressed as:

[0125]

[0126] In the formula, Let be the total number of pores. Its normalized probability density function is given by the following equation:

[0127]

[0128] therefore:

[0129]

[0130] like Equation (20) can be simplified to:

[0131]

[0132] Natural porous networks typically satisfy This condition. Based on the fractal distribution principle of porous materials, the number of pores can be expressed as:

[0133]

[0134] Combining equations (21) and (22), we get:

[0135] .

[0136] Substituting equation (23) into equation (17), we get:

[0137]

[0138] Equation (24) gives the fractal power law relationship. The relationship between fractal dimension and porosity is established:

[0139] =

[0140] The length of the meandering pipe follows a fractal distribution:

[0141]

[0142] In the formula, This is the length of the pipe in the flow direction; Let be the fractal dimension of the pipe's tortuosity, and satisfy . ; This is the actual length of the pipe. When... This indicates that the pipe is straight. Based on the classic Hagen-Poiseuille equation, the flow rate through a single throat can be determined as follows:

[0143]

[0144] in This represents the pressure difference between the inlet and outlet of a single pipe. Solving equations (26) and (27), the total flow rate through all pipes within the Weiyuan infinitesimal element can be derived:

[0145] Given and Then there is .therefore and Therefore, equation (28) can be simplified to:

[0146] in This represents the cross-sectional area of ​​the infinitesimal element. According to Darcy's law,

[0147]

[0148] By combining equations (29) and (30), the expression obtained is:

[0149]

[0150] S3. Construct the governing equations for solid mechanics;

[0151] In this section, the relationship between displacement and strain is expressed as:

[0152]

[0153] in, and Represents the displacement components, while This represents the total strain components in all directions. Therefore, the deformation equilibrium equation can be expressed as:

[0154]

[0155] In the formula, Represents the stress tensor components. This represents the force component. The deformation caused by adsorption can be expressed by the following formula:

[0156]

[0157] in, The bulk modulus of the shale reservoir is given by the formula. Give; Indicates shear modulus; and This represents the strain caused by gas adsorption. Based on the force analysis of the infinitesimal element, .here, The Biot coefficient is defined as follows: , It is the bulk modulus of shale particles. This represents the Kronecker function.

[0158] By solving equations (32) and (33) simultaneously, and simplifying equation (34), the following relation can be derived:

[0159]

[0160] Equation (35) is the governing equation for the deformation of shale reservoirs.

[0161] S4. Construct the governing equations for the porosity evolution model;

[0162] According to previous studies, the deformation of pores is described by the Langmuir equation:

[0163]

[0164] Langmuir volumetric strain is due to It is stated that, assuming the strain generated by desorption in shale is equivalent to the pore strain, we can obtain:

[0165]

[0166] The total volume of porous shale consists of shale volume and pore volume, and its volumetric strain is defined as:

[0167]

[0168]

[0169] in, Represents the average stress. Represents pore volume, This represents the volume of shale. Based on the definition of porosity, we can infer that:

[0170]

[0171]

[0172] Solving equations (38), (39), (40), and (41) simultaneously, we obtain:

[0173]

[0174] The volumetric strain is 0 under initial conditions, and the porosity is defined as:

[0175]

[0176] in and .exist and Under the given conditions, equation (43) can be simplified to:

[0177]

[0178] According to equation (35), we can express the equation controlling shale deformation as follows:

[0179]

[0180] Under initial pressure, the deformation is 0, and the change in porosity is expressed as:

[0181]

[0182] In the formula, The volumetric strain of the shale. As the source term, and let The volumetric strain of the particles is represented by the equation for shale gas flow that takes into account the adsorption deformation effect.

[0183]

[0184] In the formula, Represents the Langmuir pressure coefficient. Indicates shale density, This represents the Langmuir volume coefficient. In the formula... For shale pore pressure, Represents atmospheric pressure, and satisfies Using the fractal permeability model described above, the permeability in this equation can be calculated. .

[0185] S5. The flow mechanism of methane gas in shale between fractures and pores;

[0186] The coupling function describing mass transfer between the fractured system and the porous structure is shown below:

[0187]

[0188] in , Permeability of a porous system is expressed as fluid viscosity. express, Represents the volume of gas, while Represents the shape factor. It is the pressure inside the cracked structure, and This represents the pressure of the pore structure.

[0189] The coupling and integration between various physical fields are achieved through the following parameters: roughness, tortuosity, stress, pressure, etc. Figure 3 The coupling relationships in this fractal model are illustrated. The above equations are solved synchronously in COMSOL using a multiphysics coupling module, which dynamically captures the interactions between gas migration, matrix deformation, porosity evolution, and fracture-pore permeability: gas flow provides pressure input to the solid mechanics model, which in turn updates stress and deformation, thereby altering the pore structure and fracture geometry. The evolution of porosity then updates permeability through the fractal permeability equation and feeds back to the gas flow model, thus forming a closed coupling loop.

[0190] Model Validation

[0191] To verify the accuracy of the proposed fractal permeability model, it was used to fit and interpret field experimental data on shale gas production. Figure 4The numerical model configuration is shown: rolling constraints were applied to the left and bottom boundaries of the reservoir domain, while horizontal in-situ stresses of 42 MPa and 37.2 MPa were applied to the top and right sides, respectively. The initial reservoir pressure was set to 34.6 MPa, and the wellbore pressure was maintained at 2.4 MPa throughout the simulation. Apart from gas migration between the horizontal well and the reservoir, there was no mass or energy exchange between the model boundaries and adjacent non-simulated regions. Due to the strong nonlinearity of the governing equations, all simulations were performed using COMSOL Multiphysics, a software capable of systematically analyzing the influence of microstructure on multi-field gas migration, quantitatively assessing difficult-to-measure parameters, and studying complex multiphysics interactions. The relevant input parameters are listed in Table 1.

[0192]

[0193] Table 1 Parameters of the simulation model

[0194] The above equations are solved simultaneously in COMSOL using a multiphysics coupling module. This module can dynamically capture the interaction between gas migration, matrix deformation, porosity evolution, and fracture-pore permeability: gas flow provides pressure input to the solid mechanics model, which then updates the stress and deformation fields accordingly, thereby changing the porosity and fracture geometry; the evolution of porosity then updates the permeability parameters through the fractal permeability equation and feeds back to the gas flow model, thus forming a closed coupling loop.

[0195] like Figure 5 As shown, the blue curve represents the gas production rate predicted by the model in this application, while the purple markers represent the corresponding field-measured data. It can be observed that the numerical model proposed in this application predicts a relatively fast early gas production rate, which may be due to the neglect of temperature effects. Overall, the calculated coefficient of determination (R² = 0.866) indicates a high degree of agreement between the simulation results and the observed data. The coefficient of determination is used to quantitatively evaluate the consistency between model predictions and observed data; R² = 1 indicates perfect agreement, while R² close to 0 indicates poor predictive ability. This result verifies the effectiveness of the established structure-gas fractal coupling model.

[0196] To evaluate the behavior of the new model under multi-process coupling effects, it was applied to a typical case with constant confining pressure. The computational model is a rectangular region with dimensions of 0.1 m × 0.05 m. The initial pore pressure was set to 6.2 MPa, with no gas flow constraint at the bottom boundary and the pressure at the other three boundaries maintained at 0.1 atm. Displacement constraints were applied to the bottom boundary, while the other boundaries were subjected to a pressure of 100 psia. Detailed physical properties of shale and gas are listed in Table 2. Figure 6 The initial conditions and boundary settings of the model are shown.

[0197]

[0198] Table 2. Property parameters of shale and natural gas

[0199] After fully verifying the accuracy and computational advantages of the proposed model, this application systematically explores the coupling behavior of complex fracture networks and irregular pore structures in shale gas extraction, and their impact on permeability and production capacity. Figures 7 to 19 The analysis results of the influence of fracture-pore micro-behavior on shale gas extraction under multi-physics field coupling conditions are explained from the following five dimensions: (1) evolution of shale stress and deformation; (2) evolution of pore gas pressure; (3) evolution of fracture gas pressure; (4) evolution law of permeability; and (5) influence of the evolution of rough fracture behavior on irregular pores. The research results of this application are compared with important research results at home and abroad. The fractal model established in this application is further deepened on the existing basis. By directly quantifying the influence of pore structure on pressure and considering fracture-pore interaction at the same time, a more comprehensive understanding of shale gas transport behavior is provided.

[0200] Unlike previous studies that often neglected local stress changes and boundary effects, this application quantitatively characterizes the spatial evolution of stress and pressure distribution within a coupled multiphysics framework, providing a new perspective for understanding the mechanical response of shale during gas extraction.

[0201] Based on the defined parameters and coupled control equations, the deformation and stress distribution of shale at 1 day, 50 days, 100 days and 200 days were simulated. Figure 7 The results show that shale deformation gradually increases over time, while the stress in the gas-bearing zone generally decreases, with a stress reduction of about 40% at the bottom boundary. The bottom boundary constraint leads to the highest stress concentration near this area, while the stress in the upper part of the shale body remains at a low level. In addition, due to expansion deformation, the stress at the other three boundaries is also significantly lower than that at the bottom boundary, with the lowest stress values ​​at the two corners of the upper boundary.

[0202] exist Figure 8 Based on the aforementioned parameters and the equations established in this application, the variation of pore pressure at 0, 50, 100, and 200 days was analyzed. The pore pressure of the shale mass generally decreased gradually over time, reaching its maximum value on day 0. Due to the pressure difference, gas flow occurred at the right, left, and upper boundaries, maintaining a constant external force; conversely, because the bottom was fixed and no gas flowed out, the high-pressure zone was concentrated at the bottom center. Over time, the low-pressure zone at the edges gradually expanded towards the center. Simulation results show that the pore pressure gradually decreased from the right, left, and top sides towards the center, with the stress in the central region decreasing by up to 17%.

[0203] Based on the aforementioned parameters and the equations established in this application, the changes in fracture pressure at 0, 50, 100, and 200 days were analyzed. Figure 9 The evolution of fracture pressure distribution, as shown by the simulation results, is presented.

[0204] like Figure 9 As shown, similar to the aforementioned evolution of pore gas pressure, the fracture pressure in the shale mass continuously decreases over time. Since the bottom is a fixed constraint with no gas outflow, the high-pressure zone is concentrated at the bottom center; conversely, gas flows along the right, left, and upper boundaries due to pressure differences, maintaining a constant external force. Simulation results show that the fracture pressure gradually decreases from the right, left, and top sides towards the center, with the stress in the central region decreasing by approximately 33%. Meanwhile, with... Figure 8 As can be seen from the comparison, the low-pressure zone at the edge of the fissure pressure distribution map is larger.

[0205] COMSOL Multiphysics was used to simulate shale gas seepage under multi-field coupling. The results showed that due to stress concentration, fracture permeability decreases from the edge to the center, leading to a corresponding decrease in overall structural permeability, a trend consistent with our simulation results. However, their studies were mainly limited to qualitative trend descriptions, while this application establishes quantitative relationships. Furthermore, unlike previous studies that focused on average permeability trends, this application achieves spatiotemporal evolution analysis of pore and fracture permeability, thus revealing the distinct evolutionary patterns of rough fractures and pore networks during mining.

[0206] Based on the aforementioned parameters and coupled control equations, the overall structural permeability of shale at 0, 50, 100, and 200 days was simulated, and the results are as follows: Figure 10 As shown, the overall permeability gradually decreases as mining progresses. The lowest permeability area appears at the mining edge, especially near the bottom boundary. The results indicate that the structural permeability gradually decreases from the top and bottom corners, but the overall permeability value changes relatively little.

[0207] Based on this model, the pore and fracture system at cross-sections within a shale mass is analyzed to assess permeability variations. Under the same model parameters, Figure 11 and Figure 12 The evolution of permeability in porous and rough fracture systems over space and time is presented separately. It can be observed that pore permeability generally decreases over time, while rough fracture permeability exhibits the opposite trend. Furthermore, it can be inferred that pore permeability is lower at the edges and higher at the center over time; conversely, rough fracture permeability shows a distribution characteristic of low permeability at the center and high permeability at the edges.

[0208] Furthermore, the analysis of pore structure evolution in this application is consistent with previous research findings using digital core technology and fractal reconstruction methods. Existing studies have shown that multi-point statistics and fractal algorithms can effectively characterize three-dimensional pore connectivity and reveal the crucial role of microstructural complexity in transport processes. It indicates that pore characteristics have a decisive influence on permeability and flow behavior, which is consistent with our observations that complex pore networks hinder gas escape but simultaneously enhance adsorption capacity.

[0209] Compared with the above studies, this application quantitatively evaluates the interaction between complex fracture networks and irregular pore networks, and focuses on exploring the influence of rough fracture structure parameters on pore fractal dimension and its mechanism of action on shale methane extraction, specifically including: (1) fracture roughness (2) Pore fractal dimension (3) Tortuousness and fractal dimension (4) Fractal dimension of rough cracks Unlike previous studies that only considered a single factor or average attribute, this application analyzes and captures the coupled effects of multiple fractal parameters.

[0210] Existing fractal pore models based on nitrogen adsorption data show that adsorption capacity increases significantly with increasing pore fractal dimension. This application verifies this trend in detail. In contrast, based on the aforementioned models, this application systematically investigates the effect of fracture roughness on pore fractal dimension while keeping other fracture parameters constant. Three typical roughness values ​​of 0.04, 0.06, and 0.08 are selected as the analysis objects, and the simulation results are as follows: Figure 13 As shown.

[0211] Crack roughness This reflects the irregularity of the fracture surface. When the mining duration is constant, the fractal dimension of the pore structure gradually increases with increasing fracture roughness. During gas extraction, higher fracture roughness hinders gas flow, leading to more complex seepage paths and ultimately affecting overall permeability. This mechanism is reflected in changes in the pore structure. Furthermore, increased fracture roughness also alters the connectivity between pores. Simulation results show that when the roughness... As the pore fractal dimension increases from 0.04 to 0.08, It increased from 1.1835 to 1.1854. The increase in fracture roughness usually means that the pore structure is more complex and diverse, which is manifested by an increase in the fractal dimension of the pores, thereby affecting the occurrence and extraction efficiency of gas.

[0212] The dual-porosity model used to simulate shale gas migration emphasizes the influence of fracture aperture and stress sensitivity. In comparison, the fractal model used in this application further introduces fracture roughness and tortuosity parameters, thereby enabling a more quantitative description of the microstructure evolution. Figure 14 The study demonstrates the variation of the pore fractal dimension under different tortuosity fractal dimensions, showing that in the dual-scale fractal model, the pore fractal dimension gradually increases with the increase of the tortuosity fractal dimension.

[0213] In this application, the fractal dimension of fracture tortuosity is between 1 and 2. The closer the value is to 2, the higher the degree of pipe tortuosity, the greater the gas flow resistance, and thus the more permeability is affected. Such changes in flow characteristics cause the reorganization of pore structure and affect its fractal dimension. During gas extraction, tortuous fractures form more tortuous seepage paths. This increased complexity may lead to more complex pore morphologies (such as branched or annular structures), resulting in diverse characteristics of multi-scale pores. Simulation results show that when the tortuosity fractal dimension... When the pore fractal dimension increases from 1.2 to 1.6, The value increased from 1.1827 to 1.1855. The increase in tortuosity fractal dimension usually means that the pore structure is more complex and diverse, and this change has an important impact on gas occurrence and extraction efficiency.

[0214] like Figure 15 As shown, the fractal dimension of the rough crack was analyzed under the same conditions. The correlation between the fractal dimension of roughness and pore size: The increase in the fractal dimension of roughness corresponds to a gradual increase in the fractal dimension of pore size.

[0215] In gas extraction, an increase in the fractal dimension of rough fractures signifies an increase in the number of fractures, which alters key factors such as seepage paths and gas permeability. This impact is partly reflected in the distribution and structural characteristics of pores, including pore morphology, size, and uniformity of distribution. Simulation data shows that when the fractal dimension of rough fractures increases... When the pore fractal dimension increases from 1.2 to 1.6, It increased slightly from 1.1841 to 1.1848. The results indicate that an increase in the fractal dimension of roughness fractures usually leads to a corresponding increase in the fractal dimension of pores.

[0216] The model in this application further elucidates the fracture-pore coupling mechanism through explicit fractal parameters, providing a more direct measurement of how structural complexity affects permeability and gas pressure. Figures 16 to 19 The study demonstrated the influence of fracture and pore structure parameters on fracture gas pressure under the same conditions, and further analyzed the mechanism by which these parameters affect fluid flow in porous media.

[0217] In the gas extraction process, increasing the roughness from 0.04 to 0.08 and simultaneously increasing the tortuosity and fracture fractal dimension from 1.2 to 1.6 resulted in a 23%, 40%, and 32% decrease in fracture gas pressure, respectively. This complex fracture network expands gas diffusion paths, enhances fracture connectivity, and increases permeability, thereby promoting smoother gas flow and improving extraction efficiency. Furthermore, the rough fracture surface reduces gas adsorption and enhances desorption, leading to a decrease in gas pressure. In contrast, existing technologies have proposed fractal models of shale pore networks, indicating that the pore fractal dimension directly affects gas adsorption and diffusion capacity. Studies have shown that increasing the pore fractal dimension from 1.2 to 1.6 can increase adsorption by approximately 15%. This application verifies this trend; when the pore fractal dimension... When the pressure increases from 1.2 to 1.6, the fracture gas pressure From 1.6×10 6 Pa increased to 1.9 × 10 6 Pa. The complex pore structure provides more adsorption sites, enhancing gas adsorption capacity and releasing more gas during desorption; at the same time, it forms a more tortuous seepage path, hindering gas escape and thus leading to an increase in fissure gas pressure.

[0218] This application incorporates multiple factors into coupled multiphysics analysis using a fractal model, systematically examining the interaction between rough fractures and irregular pores. Based on a comprehensive consideration of the interactive effects of multiple factors, it reveals in depth the mechanism of the fracture network's influence on the pore network and effectively assesses the impact of its quantitative evolution on shale methane extraction.

[0219] Based on the model research results, the main conclusions are as follows:

[0220] 1) The effects of three key parameters—torsional fractal dimension, roughness fracture fractal dimension, and fracture roughness—on pore fractal dimension were investigated, and the combined effect of these parameters and pore fractal dimension on gas extraction was analyzed. The results show that all three parameters have a positive impact on pore fractal dimension: when the roughness increases from 0.04 to 0.08, and the two fractal dimensions increase from 1.2 to 1.6, the pore fractal dimension increases by 0.0019, 0.0028, and 0.0007, respectively. Increased fracture complexity reduces fracture gas pressure by 23%–40% and enhances connectivity and permeability; however, increased pore complexity leads to an increase in gas pressure of approximately 20% due to enhanced adsorption capacity and more tortuous flow channels.

[0221] 2) During the 200-day simulation period, shale deformation continued to increase, while the stress in the gas-bearing zone showed a decreasing trend, with the stress at the bottom boundary decreasing by 40%. The stress at other boundaries was relatively low, with the lowest stress at the two corners of the upper boundary. The fracture pressure and pore pressure gradually decreased from the boundary to the center, with the stress at the center decreasing by 33% and 17% respectively, and the low-pressure zone gradually expanded inward over time.

[0222] 3) Permeability exhibits distinct spatiotemporal variation characteristics: overall permeability gradually decreases from the bottom boundary and top corners. Over time, pore permeability is high in the center and low at the edges, while fracture permeability shows a distribution pattern of low in the center and high at the edges. These results fully reveal the distinct yet closely coupled mechanisms by which fracture and pore evolution control shale gas flow and recovery efficiency.

[0223] It will be apparent to those skilled in the art that this disclosure is not limited to the details of the exemplary embodiments described above, and that this disclosure can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of this disclosure is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within this disclosure. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0224] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for constructing a fractal model of rough fractures and irregular pores in shale under multi-field coupling, characterized in that, Includes the following steps: S1. Construction of a fractal theory model based on a rough fracture system; The true length of the bending fracture in the rock mass Relative to the length of the character unit It exhibits fractal characteristics; ； In the formula, The fractal dimension related to the tortuosity of the roughness crack; The length and number of rough fractures in the rock mass satisfy the following fractal relationship: ； as well as ； In the formula, Represents the fracture length. The fractal dimension associated with rough fracture; Based on the fractal theory of porous media, the fractal porosity of the matrix and the fractal parameters characterizing the fracture scale can be expressed as follows: ； ； Therefore, the average effective height of irregular elements on the crack surface can be defined as: ； In the formula, The aperture of the rough crack; The height of the irregular unit; It is the ratio of the sum of the base areas within a shale fractal unit to the total area of ​​the entire fractal unit; S2. Construction of a fractal theory model based on porous systems; The fractal power law relationship can be expressed as follows: ； in, Let represent the equivalent radius of the pores, and satisfy . ; This represents the fractal dimension of the pore size, while Represents the number of pores in two-dimensional space. ; Furthermore, equation (15) can be restated as: ； In the formula, is a proportionality constant; the differential expression is derived from equation (15); equivalent radius at The number of pores within the range is: ； A negative sign indicates that, under the condition of constant porosity, an increase in the size of a single pore will lead to a decrease in the number of pores; S3. Construct the governing equations for solid mechanics; The relationship between displacement and strain is expressed as: ； in, and Represents the displacement components, while Let represent the total strain components in all directions. Therefore, the deformation equilibrium equation can be expressed as: ； In the formula, Represents the stress tensor components. The deformation caused by adsorption, representing the force component, can be expressed by the following formula: ； The bulk modulus of the shale reservoir is given by the formula. Give; Indicates shear modulus; and The strain represents the gas adsorption-induced stress, based on the force analysis of the micro-element. ,here, The Biot coefficient is defined as follows: , It is the bulk modulus of shale particles. Represents the Kronecker function; S4. Construct the governing equations for the porosity evolution model; The deformation of the pores is described by the Langmuir equation: ； Langmuir volumetric strain is due to This indicates that, assuming the strain in shale caused by desorption is equivalent to the pore strain, we can obtain: ； The total volume of porous shale consists of shale volume and pore volume, and its volumetric strain is defined as: ； ； Represents the average stress. Represents pore volume, Indicates the volume of shale; S5. The flow mechanism of methane gas in shale between fractures and pores; The coupling function describing mass transfer between the fractured system and the porous structure is shown below: ； in , Permeability of a porous system is expressed as fluid viscosity. express, Represents the volume of gas, while Represents the shape factor. It is the pressure inside the cracked structure, and This represents the pressure of the pore structure.

2. The method for constructing a fractal model of shale rough fractures and irregular pores under multi-field coupling according to claim 1, characterized in that, S1 also includes; The surface roughness of shale fractures is defined as follows: ； Gas flowing through a smooth-surfaced crack can be described as: 。 3. The method for constructing a fractal model of shale rough fractures and irregular pores under multi-field coupling according to claim 2, characterized in that, The effective fluid flow resistance within the fissure can be expressed as: ； in Indicates gas viscosity. Represents the fractal power law exponent; The complete cross-sectional area of ​​all cracks within the fractal unit is: ； Therefore, by combining equation (8) with the basic principles of fluid dynamics, the fluid pressure gradient can be obtained as follows: ； By combining equations (7) and (11) and considering the crack roughness, the fluid flow equation in a single pipe can be obtained as follows: ； Therefore, the pressure gradient within the rough crack can be expressed as: ； Combining Darcy's law with the above equations, a fractal model of shale permeability considering fracture roughness is established, and its expression is as follows: 。 4. The method for constructing a fractal model of shale rough fractures and irregular pores under multi-field coupling according to claim 1 or 3, characterized in that, S2 also includes; According to equation (17), the probability density function of the aperture can be expressed as: ； In the formula, The normalized probability density function of the total number of pores is given by the following equation: ； therefore: ；； like Equation (20) can be simplified to: ； Natural porous networks typically satisfy This condition, based on the fractal distribution principle of porous materials, can be expressed as follows: 。 5. The method for constructing a fractal model of shale rough fractures and irregular pores under multi-field coupling according to claim 4, characterized in that, Combining equations (21) and (22), we get: ； Substituting equation (23) into equation (17), we get: ； Yu established the relationship between fractal dimension and porosity: ； The length of the meandering pipe follows a fractal distribution: ； In the formula, This is the length of the pipe in the flow direction; Let be the fractal dimension of the pipe's tortuosity, and satisfy . ; This refers to the actual length of the pipe; when When this indicates that the pipe is straight, based on the classic Hagen-Poiseuille equation, the flow rate through a single throat can be determined as follows: ； in This indicates the pressure difference between the inlet and outlet of a single pipe.

6. The method for constructing a fractal model of shale rough fractures and irregular pores under multi-field coupling according to claim 5, characterized in that, By combining equations (26) and (27), the total flow rate through all pipes within the Wei Yuan micro-element can be derived: Given and Then there is ,therefore and ; ； in Represent the cross-sectional area of ​​the infinitesimal element; according to Darcy's law; ； By combining equations (29) and (30), the expression obtained is: 。 7. The method for constructing a fractal model of shale rough fractures and irregular pores under multi-field coupling according to claim 1, characterized in that, S3 also includes; By solving equations (32) and (33) simultaneously, and simplifying equation (34), the following relation can be derived: 。 8. The method for constructing a fractal model of shale rough fractures and irregular pores under multi-field coupling according to claim 7, characterized in that, S4 also includes; Based on the definition of porosity, it can be inferred that: ； ； Solving equations (38), (39), (40), and (41) simultaneously, we obtain: ； The volumetric strain is 0 under initial conditions, and the porosity is defined as: 。 9. The method for constructing a fractal model of shale rough fractures and irregular pores under multi-field coupling according to claim 8, characterized in that, in and ,exist and Under the given conditions, equation (43) can be simplified to: ； According to equation (35), we can express the equation controlling shale deformation as follows: ； Under initial pressure, the deformation is 0, and the change in porosity is expressed as: ； In the formula, This represents the volumetric strain of the shale.

10. The method for constructing a fractal model of shale rough fractures and irregular pores under multi-field coupling according to claim 9, characterized in that, Will As the source term, and let The volumetric strain of the particles is represented by the equation for shale gas flow that takes into account the adsorption deformation effect. ； In the formula, Represents the Langmuir pressure coefficient. Indicates shale density, This represents the Langmuir volume coefficient; where For shale pore pressure, Represents atmospheric pressure, and satisfies Using the fractal permeability model described above, the permeability in this equation can be calculated. .

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