Press drive fracture network expansion simulation method based on damage mechanics

Through the extended simulation method of pressure-driven seam network based on damage mechanics, combined with the damage-permeability evolution model and finite element calculation, the problem of difficult prediction of the pattern of high-pressure underwater pressure-driven seam network is solved, and the accurate simulation of the dynamic spreading and permeability evolution laws of seam network is achieved, which improves the effect of pressure-drive development.

CN120372992APending Publication Date: 2025-07-25CHINA PETROLEUM & CHEMICAL CORP +1

Patent Information

Application Number
CN202410105559.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-01-25
Publication Date
2025-07-25

AI Technical Summary

Technical Problem

The existing fracture expansion calculation model cannot effectively simulate the complex morphology and evolutionary laws of the pressure-driven seam network under high-pressure water injection conditions, especially the dynamic spread of micro-fractures and the changes in reservoir permeability.

Method used

The compression-driven seam expansion simulation method based on damage mechanics is adopted to construct a three-dimensional ground stress field of the reservoir, combine the core-body model experimental data to establish a damage-permeability evolution model, and perform seepage-deformation-damage coupling finite element calculation, and iteratively correct the correlation coefficient to simulate the expansion and evolution of the fracturing seam.

Benefits of technology

The dynamic spreading of the pressure drive seam network and the evolution law of reservoir permeability are realized, breaking through the limitations of the normal scale model, and improving the prediction accuracy of the pressure drive development effect.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention provides a pressure drive fracture network expansion simulation method based on damage mechanics. The method comprises the steps that 1, a reservoir three-dimensional crustal stress field is constructed through a target block geologic model; 2, obtaining a damage-permeability evolution model through rock core physical model experiment data; 3, the damage-permeability evolution model is embedded into a finite element calculation model in a secondary compiling mode, and a damage field of target well fracturing is calculated; 4, comparing the damage field and the microseismic data when the target well is fractured, and iteratively correcting the correlation coefficient in the permeability evolution model; and 5, seepage-deformation-damage coupling finite element calculation is carried out to obtain the fracture network form of pressure flooding water injection. According to the pressure driving fracture network expansion simulation method based on the damage mechanics, a calculation simulation method for fracture network expansion caused by high-pressure water injection is established, pressure driving fracture network expansion simulation calculation which cannot be processed by a conventional discrete fracture model is achieved, better innovativeness and practicability are achieved, and popularization is facilitated.
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Description

Technical Field

[0001] The present invention relates to the technical field of simulation prediction research on the expansion of injection-induced fracture networks in oil development by pressure drive, and particularly to a method for simulating the expansion of pressure-driven fracture networks based on damage mechanics. Background Art

[0002] Pressure-driven water injection has been widely applied in various types of reservoirs in Shengli Oilfield. Under ultra-high pressure water injection conditions in low-permeability reservoirs, the water injection capacity increases from a few cubic meters to hundreds or thousands of cubic meters, and the injection capacity is greatly improved. It is generally believed that the formation of large-scale underground fracture networks is the fundamental reason for the significant increase in the single-well water injection volume. Laboratory core tests show that the rock permeability will increase slowly with the increase of pore pressure in the initial stage, but when the pore pressure exceeds the formation fracture pressure, fractures appear in the rock and the permeability increases rapidly and significantly.

[0003] The change in the communication situation of the fracture network generated by high-pressure water injection is different from that of the fractures generated by hydraulic fracturing. The fracture network formed by hydraulic fracturing consists of fractures with larger sizes, while the change in the fracture network formed by high-pressure water injection is limited to the microfracture scale. Most of the currently commonly used fracture propagation calculation models perform numerical simulation calculations by embedding one or several discrete fractures into rock blocks, but this method cannot characterize the complex fracture network of pressure drive. Numerous experiments and observations have proven that the failure of rock materials is actually caused by the evolution and aggregation of microfractures at various scales, which is also the reason for the non-linear characteristics of the stress-strain of rocks. Such microfractures leading to the deterioration of rocks are called damage. Continuum damage mechanics can characterize the mechanical properties of rocks and the damage and failure that occur during the deformation process, and the damage variable can be used to describe the influence of the presence of microfractures in the material on the material. The value of the damage variable can represent the degree of fracture initiation in reservoir rocks.

[0004] In the Chinese patent application with the application number: CN202111189832.9, it relates to a method for simulating and characterizing the expansion of complex fracture networks in tight sandstone, including: analyzing the mineral composition of tight sandstone cores; testing the rock mechanical parameters of tight sandstone cores; testing the magnitude and orientation of the maximum horizontal principal stress of tight sandstone cores; using CT technology to scan the distribution law of microfractures in tight sandstone cores; preparing cement-coated tight sandstone core specimens with similar rock mechanical properties and microfracture distribution laws as natural tight sandstone cores; formulating experimental parameters for complex fracture network fracturing construction in the laboratory for tight sandstone; exploring the expansion law of complex fracture networks in tight sandstone under different microfracture distributions; and using the CT technology to establish a three-dimensional data volume before and after the experiment to characterize the complex fracture network. This method for simulating and characterizing the expansion of complex fracture networks in tight sandstone quantitatively analyzes the influence laws of microfractures and mineral components in tight sandstone on the expansion of complex fracture networks, providing an experimental basis for optimizing the on-site tight sandstone fracturing plan.

[0005] In the Chinese patent application with the application number: CN201710689827.1, it involves a multi-scale fracture network modeling and simulation method for tight reservoirs. This multi-scale fracture network modeling and simulation method for tight reservoirs includes: Step 1, dividing the matrix grid by combining the MINC model and SC mapping; Step 2, calculating the flow rate between each node through quasi-steady state flow; Step 3, performing dimensionality reduction processing on the large-scale fracture system through the flow rate equivalence principle; Step 4, simulating the fractures; Step 5, solving and verifying the multi-scale complex fracture network model. This multi-scale fracture network modeling and simulation method for tight reservoirs effectively avoids the detection of complex micro-fractures and the continuous processing of large fractures, and improves the accuracy and efficiency of the fracture description and simulation method within the tight reservoir stimulation volume.

[0006] In the Chinese patent application with the application number: CN201711483019.6, it involves a simulation and characterization method for the propagation of volume fracturing fracture networks in tight reservoirs. First, using the displacement discontinuity method, mechanical mechanism analysis, and fracture initiation and propagation criteria, a calculation model for the combined in-situ stress field of tight reservoirs considering multi-fracture stress interference is established; then, aiming at the stress interference problem existing in the multi-fracture propagation process of volume fracturing, a flow pressure drop distribution model for the flow of fracturing fluid inside the main and secondary fractures is established to form a theoretical model for the propagation of horizontal well fracture networks in tight reservoir volume fracturing; finally, comprehensively analyzing the influence of different factors on the structural morphology of the volume fracturing fracture network, and characterizing the structural morphology and attribute characteristics of the fracture network by defining multiple characteristic parameters. Finally, a set of simulation and characterization methods for the propagation of volume fracturing fracture networks in tight reservoirs is established. The invention has the advantages of comprehensive consideration of model factors, high simulation efficiency, and result visualization, and has certain guiding significance for the fracturing optimization design and efficient development of tight reservoirs.

[0007] The above existing technologies are all quite different from the present invention and fail to solve the technical problems we want to solve. Therefore, we have invented a new simulation method for the propagation of pressure-driven fracture networks based on damage mechanics. Summary of the Invention

[0008] The purpose of the present invention is to provide a simulation method for the dynamic spread of pressure-driven fracture networks and the evolution laws of reservoir permeability and pore pressure, which is a simulation method for the propagation of pressure-driven fracture networks based on damage mechanics.

[0009] The purpose of the present invention can be achieved by the following technical measures: A simulation method for the propagation of pressure-driven fracture networks based on damage mechanics, which includes:

[0010] Step 1, constructing a three-dimensional in-situ stress field of the reservoir through the geological model of the target block;

[0011] Step 2, obtaining a damage-permeability evolution model through core physical simulation experiment data;

[0012] Step 3: Embed the damage-permeability evolution model into the finite element calculation model through secondary compilation to calculate the damage field of the target well during fracturing.

[0013] Step 4: Compare the damage field during the fracturing of the target well with the microseismic data, and iteratively correct the correlation coefficients in the damage-permeability evolution model.

[0014] Step 5: Conduct coupled finite element calculations of seepage-deformation-damage to obtain the fracture network morphology of pressure-driven water injection.

[0015] The object of the present invention can also be achieved by the following technical measures:

[0016] In Step 1, according to the geological model of the target block, establish a three-dimensional finite element fine in-situ stress field model to calculate the magnitudes and directions of the maximum and minimum horizontal principal stresses in the target block.

[0017] In Step 1, on the basis of the geological model of the target area, after adding the top layer and the bottom layer, apply surface force loads and displacement constraints in the vertical and horizontal directions. Apply a uniform surface force load on the top of the model, and its amplitude is equal to the overlying rock pressure. Apply gravity loads and initial in-situ stresses to each element inside the model. Apply zero displacement constraints in the normal direction of the four sides and the bottom surface of the model, and the top of the model is the load boundary; use the finite element method to calculate the three-dimensional fine in-situ stress field of the well group block.

[0018] In Step 2, according to the indoor physical simulation experiment, obtain the variation curve of rock permeability with effective stress, and optimize the damage evolution model according to the physical simulation experiment data to obtain the damage-permeability evolution model dependent on the damage variable.

[0019] In Step 2, take the core of the well group for indoor physical experiments. According to the indoor physical simulation experiment, obtain the variation curve of rock permeability with effective stress, and optimize the damage evolution model according to the physical simulation experiment data to obtain the damage-permeability evolution model dependent on the damage variable.

[0020] In Step 2, the relationship equation of the damage-permeability evolution model is as follows:

[0021]

[0022] Where k D is the permeability of the rock after damage, k0 is the initial permeability of the rock, D is the damage amount, and α, β are the parameters to be fitted.

[0023] In Step 3, introduce the permeability variation model obtained in Step 2 into the finite element calculation model as the connection point for coupling the damage mechanics model and the seepage deformation finite element calculation model, so as to calculate and simulate the fracture propagation morphology of the target well during fracturing, and further obtain the distribution of the damage field of the fracturing fracture.

[0024] In step 3, the damage-permeability evolution model is introduced into the finite element calculation model to perform finite element calculation of coupled seepage and deformation, simulate the fracture propagation pattern of the target well during fracturing, and then obtain the distribution of the fracturing damage field.

[0025] In step 4, the shape of the obtained damage field is compared with the results of fracturing microseismic observations, and the correlation coefficients in the permeability change model dependent on the damage variable are iteratively corrected until the numerical calculation results are consistent with the microseismic observation results, so as to obtain the damage-permeability evolution model for the target block.

[0026] In step 5, finite element calculation is carried out for the coupled seepage-deformation-damage relationship to simulate the expansion of the pressure-driven fracture network caused by pressure-driven water injection, obtain the dynamic evolution law of the pressure-driven fracture network and the law of fluid pressure propagation, analyze the pressure-driven effect, and specifically propose improvement measures for the pressure-driven design to improve the pressure-driven development effect.

[0027] The object of the present invention can also be achieved by the following technical measures: a pressure-driven fracture network expansion simulation method system based on damage mechanics, which uses the pressure-driven fracture network expansion simulation method based on damage mechanics to simulate the dynamic distribution of the pressure-driven fracture network and the evolution laws of reservoir permeability and pore pressure.

[0028] The pressure-driven fracture network expansion simulation method based on damage mechanics in the present invention provides an effective numerical simulation prediction method for the problem that it is difficult to predict the formation effect and dynamic distribution of the complex fracture network caused by high-pressure water injection during the pressure-driven development process. It can accurately simulate the shape and evolution law of the complex fracture network formed by pressure-driven water injection, break through the limitations of the current pressure-driven fracture network simulation method, and can simulate the dynamic distribution of the pressure-driven fracture network and the evolution laws of reservoir permeability and pore pressure. The present invention innovates the method based on the damage mechanics theory, realizes the dynamic simulation of the expansion of the pressure-driven fracture network and the propagation of fluid pressure, couples the evolution of the damage variable and the change of rock permeability and adds them to the fitting process, establishes a calculation simulation method for the expansion of the fracture network caused by high-pressure water injection, and realizes the simulation calculation of the expansion of the pressure-driven fracture network that cannot be handled by the conventional discrete fracture model. Compared with the previous ones, the technical achievements of this time have better innovation and practicability and are conducive to popularization. Description of the Drawings

[0029] Figure 1 It is a flowchart of a specific embodiment of the pressure-driven fracture network expansion simulation method based on damage mechanics of the present invention;

[0030] Figure 2 It is a rock mechanics geological model diagram of a well group block in a specific embodiment of the present invention;

[0031] Figure 3 It is a three-dimensional fine in-situ stress field diagram of a well group block in a specific embodiment of the present invention;

[0032] Figure 4 It is the relationship diagram between rock permeability and effective stress in a specific embodiment of the present invention in the physical model test;

[0033] Figure 5 It is the diagram of permeability change dependent on damage variable in a specific embodiment of the present invention;

[0034] Figure 6 It is the diagram of fitting the results of hydraulic fracturing microseismic monitoring by damage mechanics in a specific embodiment of the present invention;

[0035] Figure 7 It is the permeability distribution map of well group pressure drive in a specific embodiment of the present invention;

[0036] Figure 8 It is the pore pressure distribution map of well group pressure drive in a specific embodiment of the present invention. Specific Embodiment

[0037] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

[0038] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, and / or combinations thereof.

[0039] The present invention provides a dynamic simulation method for the dynamic spread of a pressure-driven fracture network combining seepage-deformation-damage coupling. The method includes: establishing a three-dimensional finite element fine in-situ stress field model according to the geological model of the target block, and calculating the magnitudes and directions of the maximum and minimum horizontal principal stresses of the target block; obtaining the variation curve of rock permeability with effective stress according to indoor physical simulation tests, and optimizing the damage evolution model based on the physical simulation test data to obtain the permeability variation relationship dependent on the damage variable; introducing the permeability evolution model into the finite element calculation model as the connection point between the coupled damage mechanics model and the seepage deformation finite element calculation model, so as to calculate and simulate the propagation pattern of the fracturing cracks of the target well, and further obtain the damage field distribution of the fracturing cracks; comparing the shape of the obtained damage field with the results of fracturing microseismic observations, and iteratively correcting the correlation coefficients in the permeability variation model dependent on the damage variable until the numerical calculation results are consistent with the microseismic observation results, so as to obtain the damage-permeability variation model for the target block; coupling the seepage-deformation-damage relationship for finite element calculation, simulating the expansion of the pressure-driven fracture network caused by pressure-driven water injection, and obtaining the dynamic evolution law of the pressure-driven fracture network and the fluid pressure propagation law.

[0040] The following are several specific embodiments of applying the present invention

[0041] Embodiment 1

[0042] In a specific Embodiment 1 of applying the present invention, as Figure 1 shown Figure 1 is the flow chart of the pressure-driven fracture network expansion simulation method based on damage mechanics of the present invention. The pressure-driven fracture network expansion simulation method based on damage mechanics includes:

[0043] S1. Establish a three-dimensional finite element fine in-situ stress field model according to the geological model of the target block, and calculate the magnitudes and directions of the maximum and minimum horizontal principal stresses of the target block;

[0044] S2. Obtain the variation curve of rock permeability with effective stress according to indoor physical simulation tests, and optimize the damage evolution model based on the physical simulation test data to obtain the damage-permeability evolution model dependent on the damage variable;

[0045] S3. Introduce the permeability variation model obtained in S2 into the finite element calculation model as the connection point between the coupled damage mechanics model and the seepage deformation finite element calculation model, so as to calculate and simulate the propagation pattern of the fracturing cracks of the target well, and further obtain the damage field distribution of the fracturing cracks;

[0046] S4. Compare the shape of the obtained damage field with the results of fracturing microseismic observations, and iteratively correct the correlation coefficients in the permeability variation model dependent on the damage variable until the numerical calculation results are consistent with the microseismic observation results, so as to obtain the damage-permeability evolution model for the target block;

[0047] S5. Perform finite element calculations on the coupled seepage-deformation-damage relationship, simulate the expansion of the pressure-driven fracture network caused by pressure-driven water injection, obtain the dynamic evolution law of the pressure-driven fracture network and the fluid pressure propagation law, analyze the pressure-driven effect, and specifically propose improvement measures for pressure-driven design to improve the pressure-driven development effect.

[0048] Compared with the past, the present invention has better innovation and practicability and is conducive to popularization. This method is applied in the actual development block of the oilfield, successfully simulates the fracture network evolution and pore pressure propagation law during the pressure-driven process, analyzes the pressure-driven development effect based on the simulation results, proposes improved water injection measures, verifies the reliability and practicability of the present invention for simulating the dynamic fracture network of pressure drive, and provides technical support for the simulation and prediction of the fracture network expansion in pressure-driven development.

[0049] Example 2

[0050] In a specific Example 2 of applying the present invention, the method for simulating the expansion of the pressure-driven fracture network based on damage mechanics includes the following steps:

[0051] S1. On the basis of the geological model ( Figure 2 ) of the target area, after adding the top layer and the bottom layer, apply surface force loads and displacement constraints in the vertical and horizontal directions, apply a uniform surface force load on the top of the model, the amplitude of which is equal to the overlying rock pressure, apply gravity loads and initial in-situ stresses to each element inside the model, apply zero displacement constraints in the normal direction on the four sides and the bottom surface of the model, and the top of the model is the load boundary; use the finite element method to calculate the three-dimensional fine in-situ stress field of the well group block (such as Figure 3 );

[0052] S2. Take the core of the well group for indoor physical experiments. According to the indoor physical simulation experiment, obtain the curve of the change of rock permeability with the change of effective stress (such as Figure 4 ), and optimize the damage evolution model according to the physical model experiment data to obtain the damage-permeability evolution model dependent on the damage variable (such as Figure 5 ), and the relationship equation is as follows:

[0053]

[0054] Where k D is the permeability of the rock after damage, k0 is the initial permeability of the rock, D is the damage amount, and α and β are parameters to be fitted.

[0055] S3. Introduce the damage-permeability evolution model into the finite element calculation model, perform finite element calculations of coupled seepage and deformation, simulate the expansion morphology of the fracturing cracks of the target well, and then obtain the distribution of the fracturing damage field;

[0056] S4. Compare the shape of the obtained damage field with the results of hydraulic fracturing microseismic observations, and iteratively correct the correlation coefficients in the damage-permeability evolution model until the numerical calculation results are consistent with the microseismic observation results (such as Figure 6 ). Through fitting, the value of α is obtained as 10.5 and the value of β is 1.65.

[0057] S5. Using the three-dimensional seepage-deformation-damage coupling calculation model, numerically calculate the mechanical behavior of the fracture network expansion during pressure-driven water injection in the pressure-driven model of the well group block. Calculate the distribution and dynamic change law of the fractures around a total of 6 wells, including 1 injection well and 5 production wells, in the Niuxin 21 target well group block during the pressure-driven water injection process, and the permeability distribution of the pressure-driven water injection can be obtained (such as Figure 7 ) and the pore pressure distribution law (such as Figure 8 ).

[0058] Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0059] Except for the technical features described in the specification, the rest are the known technologies of those skilled in the art.

Claims

1. A method for simulating the propagation of a pressure-driven fracture network based on damage mechanics, characterized in that, The simulation method for the extension of pressure-driven fracture network based on damage mechanics includes: Step 1: Construct a three-dimensional in-situ stress field of the reservoir through the geological model of the target block. Step 2: Obtain the damage-permeability evolution model from the experimental data of core physical simulation. Step 3: Embed the damage-permeability evolution model into the finite element calculation model by means of secondary compilation to calculate the damage field of the hydraulic fracturing of the target well. Step 4: Compare the damage field during the hydraulic fracturing of the target well with the microseismic data, and iteratively correct the correlation coefficients in the permeability evolution model. Step 5: Conduct coupled finite element calculations of seepage-deformation-damage to obtain the fracture network morphology of pressure-driven water injection.

2. The method for simulating the extension of a pressure-driven fracture network based on damage mechanics according to claim 1, wherein In Step 1, based on the geological model of the target block, establish a three-dimensional fine in-situ stress field model of finite elements, and calculate the magnitudes and directions of the maximum and minimum horizontal principal stresses in the target block.

3. The method for simulating the extension of the pressure-driven fracture network based on damage mechanics according to claim 2, characterized in that, In Step 1, on the basis of the geological model of the target area, after adding the top layer and the bottom layer, apply surface force loads and displacement constraints in the vertical and horizontal directions. Apply a uniform surface force load on the top of the model, the amplitude of which is equal to the overburden pressure. Apply gravity loads and initial in-situ stresses to each element inside the model. Apply zero displacement constraints to the normal directions of the four sides and the bottom surface of the model. The top of the model is the load boundary. Use the finite element method to calculate the three-dimensional fine in-situ stress field of the well group block.

4. The method for simulating the extension of a pressure-driven fracture network based on damage mechanics according to claim 1, characterized in that, In Step 2, according to the indoor physical simulation test, obtain the curve of the change of rock permeability with the effective stress. Optimize the damage evolution model according to the experimental data of physical simulation to obtain the damage-permeability evolution model dependent on the damage variable.

5. The simulation method for pressure-driven fracture network extension based on damage mechanics according to claim 4, wherein In Step 2, take the cores of the well group for indoor physical experiments. According to the indoor physical simulation test, obtain the curve of the change of rock permeability with the effective stress. Optimize the damage evolution model according to the experimental data of physical simulation to obtain the damage-permeability evolution model dependent on the damage variable.

6. The method for simulating the propagation of the pressure-driven fracture network based on damage mechanics according to claim 5, wherein, In Step 2, the relationship equation of the damage-permeability evolution model is as follows: where k D is the permeability of the rock after damage, k0 is the initial permeability of the rock, D is the damage amount, and α and β are fitting parameters to be determined.

7. The method for simulating the extension of a pressure-driven fracture network based on damage mechanics according to claim 1, characterized in that, In Step 3, introduce the permeability change model obtained in Step 2 into the finite element calculation model as the connection point for coupling the damage mechanics model and the seepage-deformation finite element calculation model, so as to calculate and simulate the propagation morphology of the hydraulic fracturing cracks of the target well, and further obtain the distribution of the damage field of the fracturing cracks.

8. The method for simulating the extension of a pressure-driven fracture network based on damage mechanics according to claim 7, wherein In Step 3, introduce the damage-permeability evolution model into the finite element calculation model, conduct coupled finite element calculations of seepage and deformation, simulate the propagation morphology of the hydraulic fracturing cracks of the target well, and further obtain the distribution of the fracturing damage field.

9. The method for simulating the expansion of a pressure-driven fracture network based on damage mechanics according to claim 1, wherein, In Step 4, compare the shape of the obtained damage field with the observation results of hydraulic fracturing microseismicity, and iteratively correct the correlation coefficients in the permeability change model dependent on the damage variable until the numerical calculation results are consistent with the microseismic observation results, so as to obtain the damage-permeability evolution model for the target block.

10. The method for simulating the propagation of a pressure-driven fracture network based on damage mechanics according to claim 1, characterized in that, In Step 5, conduct finite element calculations of the coupled seepage-deformation-damage relationship, simulate the extension of the pressure-driven fracture network caused by pressure-driven water injection, obtain the dynamic evolution law of the pressure-driven fracture network and the fluid pressure propagation law, analyze the pressure-driven effect, and specifically propose improvement measures for the pressure-driven design to improve the pressure-driven development effect.

11. A simulation method system for the expansion of hydraulic fracturing fracture networks based on damage mechanics, characterized in that, The pressure-driven fracture network extension simulation method system based on damage mechanics uses the pressure-driven fracture network extension simulation method described in any one of claims 1-10 to simulate the dynamic distribution of the pressure-driven fracture network and the evolution laws of reservoir permeability and pore pressure.

Citation Information

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