A Cross-Scale Numerical Method for Wavefield Forward Modeling in Complex Fracture Systems

Abstract

The present invention relates to a cross-scale numerical method for forward wavefield simulation of complex fracture systems, comprising the following steps: 1) generating and obtaining input parameters of RVE lattice nodes; 2) obtaining the elastic modulus of RVE and quantifying the scale characteristic parameters of RVE; 3) simulating the wavefield of complex fracture systems; 4) exploring the correlation mechanism of scale effects by comparing with ultrasonic experiments. The present invention can realize a cross-scale numerical method that can account for the abnormal wavefield characteristics induced by microfractures at smaller sample scales, which has important theoretical significance for clarifying the correlation mechanism and superposition effect of wavefield characteristics of fracture systems at different sample scales, and has wide practical application value for promoting the exploration and development of unconventional oil and gas reservoirs.

Description

Technical Field

[0001] The invention belongs to the technical field of seismic wave propagation and anisotropy analysis in oil and gas-bearing fractured reservoirs. Specifically, it relates to a cross-scale numerical method for forward wavefield simulation of complex fracture systems. Background Art

[0002] In fractured reservoirs, natural fractures developed in multiple tectonic periods and newly induced fractures in later stages form a multi-genetic and multi-scale complex fracture system. A typical complex fracture system represented by shale gas reservoirs mainly includes nano-micron intergranular pores, micron-millimeter natural fractures, and larger-scale hydraulic fractures, with scales spanning multiple orders of magnitude from nanometers to kilometers. However, actual measurements can only be carried out for the sample scales where they are located. How to comprehensively integrate the measurement results of different sample scales to obtain more comprehensive wavefield information of complex fracture systems is a key basic scientific problem urgently to be solved in the industry. Therefore, if research can be carried out from the pore scale, a bridge can be established across multiple sample scales from micro to macro, and a cross-scale research method can be proposed, which has important theoretical significance and wide practical application value.

[0003] However, the related traditional research has the following limitations: (1) Fracture simulation is mostly based on equivalent fracture media such as VTI (Vertical Transverse Isotropy), HTI (Horizontal Transverse Isotropy), and TTI (Tilted Transverse Isotropy) or ideal regular-shaped fracture structures, which overly simplifies the complex heterogeneity and multi-scale nature of actual fracture systems; (2) The correlation mechanism and superposition effect of wavefield characteristics of fracture systems at different sample scales are ignored, and there is a lack of an ideal cross-scale numerical method. Summary of the Invention

[0004] Aiming at the above problems, the purpose of the present invention is to provide a cross-scale numerical method to deeply explore the correlation mechanism and superposition effect of wavefield characteristics of fracture systems at different sample scales, develop relevant frontier theories, and provide necessary theoretical basis and technical support for practical engineering applications.

[0005] To achieve the above purpose, the present invention adopts the following technical solutions: A cross-scale numerical method for forward wavefield simulation of complex fracture systems, comprising the following steps:

[0006] 1) Generate and obtain the input parameters of the lattice nodes of the Representative Volume Element (RVE): Select a millimeter-scale cylindrical shale sample to conduct in-situ uniaxial compression-tension experiments using micro-CT, obtain the internal microstructure snapshots and mechanical characteristic response curves of the millimeter-scale cylindrical shale sample, discretize the millimeter-scale cylindrical shale sample into micron-scale RVEs, extract microstructure information based on the internal microstructure snapshots, establish a corresponding modified Lattice Spring Model (LSM)-Discrete Fracture Network (DFN) numerical model, simulate the uniaxial compression-tension experiment, and construct an objective function for the numerical simulation data and the in-situ uniaxial compression-tension experiment data based on the least squares method to obtain the input parameters of the RVE lattice nodes;

[0007] 2) Obtain the elastic modulus of the RVE and quantify the scale characteristic parameters of the RVE: Establish a modified lattice spring-discrete fracture network model for each micron-scale Representative Volume Element (RVE), and conduct triaxial compression and biaxial compression numerical simulations to stepwise identify and quantify the elastic modulus and scale characteristic parameters of the RVE;

[0008] 3) Simulate the wave field of the complex fracture system: Select a centimeter-scale cylindrical shale specimen as the research object for the ultrasonic experiment, extract the fracture structure to generate a DFN, and accordingly establish a modified lattice spring-discrete fracture network model (LSM-DFN model) for this rock sample. Inverse solve the lattice nodes in the equivalent lattice unit cell of the RVE, that is, the input parameters of the lattice nodes in the cross-scale model in step 1. Use the Ricker wavelet as the source function to simulate the ultrasonic signal, and obtain the wave field information of the entire research area by solving the local generalized forces and generalized displacements of the lattice nodes, thereby simulating the wave field of the complex fracture system;

[0009] 4) Explore the scale effect correlation mechanism by comparing with the ultrasonic experiment: Take centimeter-scale cylindrical shale specimens to conduct ultrasonic experiments at different frequencies, compare with the numerical simulation data, and comprehensively record the wave field. Based on the signal processing and analysis methods in the mechanical engineering discipline, deeply explore the scale effect and correlation mechanism of the wave field anomalies induced by fractures.

[0010] Among them, the specific process of step 1) is as follows:

[0011] 11) Select a millimeter-scale cylindrical shale sample to conduct in-situ uniaxial compression-tension experiments using micro-CT, and obtain the internal microstructure snapshots and mechanical characteristic response curves of the millimeter-scale sample;

[0012] 12) Discretize the millimeter-scale cylindrical shale sample into micron-scale representative volume elements, extract microstructure information based on the internal microstructure snapshots, and establish a modified lattice spring-discrete fracture network (LSM-DFN) numerical model at the micron-scale representative volume element scale;

[0013] 13) A modified lattice spring-discrete fracture network (LSM-DFN) numerical model corresponding to millimeter-scale cylindrical shale is established to simulate uniaxial compression-tension experiments. Based on the least squares method, the objective function for the numerical simulation data and the in-situ uniaxial compression-tension experiment data of micro-CT is constructed as shown in the following formula:

[0014]

[0015] where x is the set of input parameters of the lattice nodes to be calibrated, N is the number of existing experimental data used for calibration, d i is the i-th data point, w i is the weight factor corresponding to the i-th data point, s i (x) is the simulation result obtained by taking the data set x corresponding to the i-th data point as the input parameter, r i is the residual between the simulation result and the experimental data corresponding to the i-th data point;

[0016] 14) The NL2SOL algorithm is used to minimize the objective function, and the optimal input parameter data set x is obtained through multiple iterative calibrations.

[0017] Among them, the specific process of step 2) is as follows:

[0018] 21) Establish a modified LSM-DFN model for each RVE;

[0019] 22) Conduct triaxial compression numerical simulations, and obtain the traditional elastic parameters such as λ, μ, etc. of each RVE through the following formula etc.,

[0020]

[0021]

[0022] where σ is the stress tensor, is the symmetric part of the strain tensor, I is the identity matrix, is the critical volume strain, is the maximum proportion of the lattice node volume during the RVE loading process, is the proportion of the lattice node volume of the initial RVE, ε V is the volume strain;

[0023] 23) Conduct biaxial compression numerical simulations to identify the material scale characteristic parameters through the following formula

[0024]

[0025] where the subscript i represents the i-th data point, N σ represents the number of loading data, σ0 is the reference stress value used to non-dimensionalize the objective function, σ11i (s) and are the simulated value and experimental data value of the axial stress of the i-th data point respectively; N H represents the number of shear band data values, H0 is the shear band thickness, H i (s) and are the simulated value and experimental data value of the shear band thickness of the i-th data point respectively.

[0026] Among them, the specific process of the said step 3) is as follows:

[0027] 31) Select a centimeter-scale cylindrical shale specimen as the research object for carrying out ultrasonic experiments, generate DFN based on the fracture structure, and accordingly establish a modified LSM-DFN model of this rock sample. The crystal bond length of LSM and the RVE size need to satisfy a certain proportional relationship to ensure that the lattice unit cell is equal to the RVE volume;

[0028] 32) Based on the principle of energy conservation and the couple stress theory of generalized continuum mechanics including material scale characteristic parameters, establish a quantitative relationship between the input parameters of the modified LSM lattice nodes and the corresponding equivalent lattice unit cell material scale characteristic parameters. The specific formula is as follows,

[0029] U cell = U continuum (5)

[0030]

[0031]

[0032]

[0033] m = 2l 2 γχ (9)

[0034]

[0035]

[0036] In the formula, U cell 、U continuum are the elastic energies of the equivalent unit cell of the modified lattice model (LSM) and the corresponding couple stress theory of generalized continuum mechanics respectively; σ and ε are the Cauchy stress tensor and strain tensor respectively; m and χ are the skew-symmetric part in the couple stress tensor and the symmetric part of the curvature tensor respectively; K n and K s are the tensile-compressive and shear spring stiffnesses of the modified lattice spring model (LSM) respectively; and are as Figure 2The normal and tangential displacements of the $i$-th lattice node among the 6 lattice nodes in the modified lattice spring model (LSM) lattice unit cell as shown in -c), where $\lambda$ and $\mu$ are elastic constants in classical continuum mechanics, and $l$ is the characteristic parameter of the material scale;

[0037] 33) Inversely solve the lattice nodes in the centimeter-scale RVE equivalent lattice unit cell, that is, the input parameters of the lattice nodes in the cross-scale model;

[0038] 34) Use the Ricker wavelet as the source function to simulate ultrasonic signals. By solving the local generalized forces and generalized displacements of the lattice nodes, the wave field information of the entire research area can be obtained.

[0039] Among them, the input parameters in step 33) and step 32) include spring stiffness, particle density, crystal bond length, and micro-moment of inertia.

[0040] Among them, the specific process of step 4) is as follows:

[0041] 41) Take centimeter-scale cylindrical shale specimens to conduct ultrasonic experiments at different frequencies;

[0042] 42) Compare with the numerical simulation data, comprehensively analyze the wave field records, and deeply explore the scale effect and correlation mechanism of the wave field anomalies induced by fractures based on the signal processing and analysis methods in the discipline of mechanical engineering.

[0043] Among them, the signals in step 42) include time domain, frequency domain, wavelet, and VMD.

[0044] 1) Among them, the rock sample is a millimeter-scale cylindrical shale specimen.

[0045] Due to the above technical solutions, the present invention has the following advantages: adopting a research method that combines multidisciplinary cross (geophysics, mechanics, computational science, and mechanical engineering, etc.), numerical simulation, theoretical derivation, and experimental measurement, following an overall research idea that gradually progresses from a simple model to an actual complex fracture system, starting from the pore scale, introducing the representative volume element (RVE), comprehensively applying basic theories such as generalized continuum mechanics, computational dynamics, and composite material mechanics, quantitatively characterizing the scale characteristic parameters of the RVE as correlation factors, and thereby establishing a bridge between different sample scales, developing a cross-scale numerical method that can account for the wave field anomalies induced by micro-fractures at smaller sample scales, which has important theoretical significance for clarifying the correlation mechanism and superposition effect of the wave field characteristics of fracture systems at different sample scales, and has broad practical application value for promoting the exploration and development of unconventional oil and gas reservoirs. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Flow chart for obtaining the input parameters of the lattice nodes of the representative volume element (RVE);

[0047] Figure 2 For the lattice spring model (LSM) unit and the corresponding lattice unit cell: (a) triangular lattice; (b) square lattice; (c) hexagonal lattice;

[0048] Figure 3 It is the flow chart of the modified lattice spring-discrete fracture network (LSM-DFN) modeling for complex fracture systems across sample scales. Detailed implementation manners

[0049] The present invention will be described in detail below with reference to the accompanying drawings and embodiments. However, it should be understood that the provided drawings are only for better understanding of the present invention, and they should not be construed as limitations on the present invention.

[0050] The cross-scale numerical method for forward wavefield simulation of complex fracture systems proposed by the present invention includes the following steps:

[0051] 1) Generate an RVE and obtain the input parameters of the RVE lattice nodes. The specific process is as follows:

[0052] 11) Select a millimeter-scale cylindrical shale sample to conduct a micron CT in-situ uniaxial compression-tension experiment to obtain the internal microstructure snapshot and mechanical characteristic response curve of the millimeter-scale sample;

[0053] 12) Discretize the millimeter-scale cylindrical shale sample into micron-scale representative volume elements (RVEs), extract microstructure information according to the internal microstructure snapshot, and establish a modified lattice spring-discrete fracture network model for the millimeter-scale cylindrical shale sample (hereinafter, the lattice spring-discrete fracture network model is simply referred to as the LSM-DFN numerical model)

[0054] 13) Based on the modified LSM-DFN numerical model of the millimeter-scale cylindrical shale, simulate the uniaxial compression-tension experiment, and construct the objective function of the numerical simulation data and the micron CT in-situ uniaxial compression-tension experiment data based on the least square method as shown in the following formula,

[0055]

[0056] In the formula, x is the set of input parameters of the lattice nodes to be calibrated (such as spring stiffness, particle density, crystal bond length, micro moment of inertia, etc.), N is the number of existing experimental data for calibration, d i is the i-th data point, w i is the weight factor corresponding to the i-th data point, s i (x) is the simulation result obtained by taking the data set x corresponding to the i-th data point as the input parameter, r i is the residual between the simulation result and the experimental data corresponding to the i-th data point;

[0057] 14) Minimize the objective function using the NL2SOL algorithm. According to the calibration process as shown in Figure 1 , first give the initial value of the input parameter dataset x. Based on the modified LSM program, obtain the simulation results, calculate the residuals according to formula (1), and judge whether the calibration criteria are met (the square of the residuals approaches 0). If not, adjust the input parameter dataset x. After multiple iterative calibrations, obtain the optimal input parameter dataset x (the optimal input parameter dataset x is the optimal input parameter dataset x of the modified LSM-DFN model of millimeter-scale cylindrical shale and the modified LSM-DFN model of the representative volume element (RVE) at the micron-scale RVE).

[0058] 2) Obtain the elastic modulus of the RVE and quantify the characteristic parameters of the RVE scale. The specific process is as follows:

[0059] 21) Based on the micron-scale representative volume element (RVE) in step 12), establish a modified LSM-DFN model for each micron-scale representative

[0060] volume element (RVE) scale;

[0061] 22) Conduct triaxial hydrostatic compression numerical simulations. Obtain λ, μ, etc. of each micron-scale representative volume element (RVE) through the following formulas (2) and (3), conventional elastic parameters,

[0062]

[0063]

[0064] where σ is the stress tensor, is the symmetric part of the strain tensor, I is the identity matrix, is the critical volume strain, is the maximum proportion of the lattice node volume during the RVE loading process, is the proportion of the lattice node volume of the initial RVE, ε V is the volume strain;

[0065] 23) Conduct biaxial compression numerical simulations. Identify the characteristic parameters of the material scale through the following formula (4),

[0066]

[0067] where the subscript i represents the i-th data point, N σ represents the number of loading data, σ0 is the reference stress value used to dimensionless the objective function, σ 11i (s) and are the simulated value and experimental data value of the axial stress at the i-th data point respectively; N HIndicates the number of shear band data values, H0 is the shear band thickness, H i (s) and are the simulated value and experimental data value of the shear band thickness at the i-th data point, respectively.

[0068] 3) Simulate the wave field of a complex fracture system, and the specific process is as follows:

[0069] 31) Select a centimeter-scale cylindrical shale specimen as the research object for ultrasonic experiments. Based on the fracture structure, generate a DFN, and accordingly establish a modified LSM-DFN model at the centimeter-scale rock sample. The crystal bond length d of the modified lattice model (LSM) at the centimeter-scale rock sample and the RVE size need to satisfy a certain proportional relationship. Taking the two-dimensional problem Figure 2 -c) as an example, if the side length of the RVE is a square with side length L, then to ensure that the lattice unit cell has the same area as the RVE. For the three-dimensional problem, the volume needs to be equal;

[0070] 32) Based on the principle of energy conservation and the couple stress theory of generalized continuum mechanics including material scale characteristic parameters, establish the quantization relationship between the input parameters of the modified LSM lattice nodes (such as spring stiffness, particle density, crystal bond length, micro-inertia moment, etc.) and the corresponding equivalent lattice unit cell material scale characteristic parameters (i.e., cross-scale characterization parameters) as shown Figure 2 -c) as an example, the specific formula is as follows: Figure 2 -c) as an example, the specific formula is as follows:

[0071] U cell =U continuum (5)

[0072]

[0073]

[0074]

[0075] m=2l 2 μχ (9)

[0076]

[0077]

[0078] In the formula, U cell 、U continuum are the elastic energies of the equivalent unit cell of the modified lattice model (LSM) and the corresponding couple stress theory of generalized continuum mechanics, respectively; σ and ε are the Cauchy stress tensor and strain tensor, respectively; m and χ are the skew-symmetric part of the couple stress tensor and the symmetric part of the curvature tensor, respectively; K n and Ks They are the tension, compression and shear spring stiffness of the modified lattice spring model (LSM); and Yes Figure 2 -c) The normal and tangential displacements of the i-th lattice node among the six lattice nodes in the modified lattice spring model (LSM) lattice unit cell shown in FIG. 1 ; λ and μ are elastic constants in classical continuum mechanics, and l is a material scale characteristic parameter;

[0079] 33) Inversely solve the lattice nodes in the equivalent lattice unit cell of the centimeter-scale RVE, that is, the input parameters of the lattice nodes in the cross-(up-) scale model (such as spring stiffness, mass point density, crystal bond length, micro-moment of inertia, etc.);

[0080] 34) The ultrasonic signal is simulated using Ricker wavelet as the source function, and the wave field information of the entire study area is obtained by solving the local generalized forces and generalized displacements of the lattice nodes.

[0081] 4) The ultrasonic experiment was used to further verify the effectiveness of the wave field forward modeling method for complex fracture systems across sample scales and to explore the scale effect of elastic wave propagation in complex fracture systems. The specific process is as follows:

[0082] 41) Take centimeter-sized cylindrical shale samples to carry out ultrasonic experiments at different frequencies;

[0083] 42) By comparing the numerical simulation data and integrating the wave field records, the effectiveness of the wave field forward modeling method for the complex fracture system across sample scales is further verified, and based on the time domain, frequency domain, wavelet, VMD and other signal processing analysis methods in the mechanical engineering discipline, the scale effect and correlation mechanism of the abnormal characteristics of the fracture-induced wave field are deeply explored.

[0084] The above embodiments are only used to illustrate the present invention, wherein the structure, connection mode and manufacturing process of each component may be changed. Any equivalent transformations and improvements based on the technical solution of the present invention should not be excluded from the protection scope of the present invention.

Claims

1. A cross-scale numerical method for forward wavefield simulation of complex fracture systems, characterized in that, Including the following steps: 1) Generate and obtain the input parameters of the RVE lattice nodes: Select a cylindrical shale sample at the millimeter scale, obtain the internal microstructure snapshot and mechanical characteristic response curve of the cylindrical shale sample at the millimeter scale, discretize the cylindrical shale sample at the millimeter scale into a representative volume element at the micron scale, extract microstructure information based on the internal microstructure snapshot, and establish a modified lattice spring-discrete fracture network numerical model at the millimeter scale, so as to obtain the input parameters of the RVE lattice nodes; 2) Obtain the RVE elastic modulus and quantify the RVE scale characteristic parameters: Based on the representative volume element at the micron scale in step 1), establish a modified lattice spring-discrete fracture network model at the scale of each representative volume element at the micron scale, and carry out triaxial compression and biaxial compression numerical simulations to identify and quantify the RVE elastic modulus and scale characteristic parameters step by step; 3) Simulate the wave field of the complex fracture system: Select a cylindrical shale specimen at the centimeter scale as the research object for ultrasonic experiments, establish a modified lattice spring-discrete fracture network model at the centimeter scale accordingly, inversely solve the lattice nodes in the equivalent lattice unit cell of the centimeter-scale RVE, that is, the input parameters of the lattice nodes in the cross-scale model, use the Ricker wavelet as the source function to simulate ultrasonic signals, and obtain the wave field information of the entire research area by solving the local generalized force and generalized displacement of the lattice nodes, and simulate the wave field of the complex fracture system; 4) Further verify the effectiveness of the wave field forward simulation method for the complex fracture system across sample scales by comparing with ultrasonic experiments. The specific process is as follows: 41) Conduct ultrasonic experiments with different frequencies on a cylindrical shale specimen at the centimeter scale; 42) Compare with the numerical simulation data and comprehensively record the wave field to further verify the effectiveness of the wave field forward simulation method for the complex fracture system across sample scales; The specific process of step 1) is as follows: 11) Select a cylindrical shale sample at the millimeter scale to conduct an in-situ uniaxial compression-tension experiment using micro-CT to obtain the internal microstructure snapshot and mechanical characteristic response curve of the sample at the millimeter scale; 12) Discretize the cylindrical shale sample at the millimeter scale into a representative volume element at the micron scale, extract microstructure information based on the internal microstructure snapshot, and establish a modified lattice spring-discrete fracture numerical model at the scale of the representative volume element at the micron scale; 13) Establish a modified lattice spring-discrete fracture network numerical model corresponding to the cylindrical shale at the millimeter scale, simulate the uniaxial compression-tension experiment, and construct an objective function for the numerical simulation data and the in-situ uniaxial compression-tension experiment data of micro-CT based on the least square method as shown in the following formula (1) wherein, is the input parameter set of the lattice nodes to be calibrated, is the number of existing experimental data for calibration, is the th data point, is the weight factor corresponding to the ith data point, is the data set corresponding to the ith data point is the simulation result obtained with the input parameters, is the residual between the simulation result and the experimental data corresponding to the ith data point; 14) The NL2SOL algorithm is used to minimize the objective function, and the optimal input parameter dataset is obtained through multiple iterations of calibration. .

2. The cross-scale numerical method for forward wavefield simulation of complex fracture systems according to claim 1, characterized in that The specific process of step 2) is as follows: 21) Establish a modified LSM-DFN model for each RVE; 22) Conduct triaxial compression numerical simulation, and obtain the traditional elastic parameters of each RVE through the following formula (2) (3) In the formula, is the stress tensor, is the symmetric part of the strain tensor, is the identity matrix, is the critical volume strain, is the maximum proportion of the lattice node volume during the RVE loading process, is the proportion of the lattice node volume of the initial RVE, is the volume strain; 23) Conduct biaxial compression numerical simulation, and identify the material scale characteristic parameters through the following formula (4) In the formula, the subscript represents the th data point, represents the number of loaded data, is the reference stress value, which is used to nondimensionalize the objective function, and are respectively the simulated value and the experimental data value of the axial stress at the th data point; represents the number of data values of the shear band appearance, is the shear band thickness, and are respectively the simulated value and the experimental data value of the shear band thickness at the th data point.

3. The cross-scale numerical method for forward wavefield simulation of complex fracture systems according to claim 1, wherein The specific process of step 3) is as follows: 31) Select a centimeter-scale cylindrical shale specimen as the research object for ultrasonic experiments. Generate a DFN based on the fracture structure, and accordingly establish a modified LSM-DFN model for this rock sample. The bond length of the LSM and the size of the RVE need to satisfy a certain proportional relationship to ensure that the lattice unit cell is equal in volume to the RVE; 32) Based on the principle of energy conservation and the couple stress theory of generalized continuum mechanics containing material scale characteristic parameters, establish a quantitative relationship between the input parameters of the modified LSM lattice nodes and the corresponding equivalent lattice unit cell material scale characteristic parameters. The specific formula is as follows: (5) (6) (7) (8) (9) (10) (11) wherein, and are the equivalent unit cell of the modified lattice model and the elastic energy of the corresponding generalized couple stress theory of continuum mechanics, respectively; and are the Cauchy stress tensor and the strain tensor, respectively; and are the deviatoric part in the couple stress tensor and the symmetric part of the curvature tensor, respectively; and are the tensile / compressive and shear spring stiffnesses of the modified lattice spring model, respectively; and are the normal and tangential displacements of the i-th lattice node among the 6 lattice nodes in the lattice unit cell of the modified lattice spring model shown in Equation 6; and are the elastic constants in classical continuum mechanics; is the material scale characteristic parameter; 33) Inversely solve the lattice nodes in the centimeter-scale RVE equivalent lattice unit cell, that is, the input parameters of the lattice nodes in the cross-scale model; 34) Use the Ricker wavelet as the source function to simulate ultrasonic signals. By solving the local generalized forces and generalized displacements of the lattice nodes, the wave field information of the entire research area can be obtained.

4. The cross-scale numerical method for forward wavefield simulation of a complex fracture system according to claim 3, characterized in that, The input parameters in steps 33) and 32) include spring stiffness, particle density, bond length, and micro moment of inertia.

5. The cross-scale numerical method for forward wavefield simulation of complex fracture systems according to any one of claims 1-4, characterized in that, The shale sample is a millimeter-scale cylindrical shale specimen.

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