Method and device for predicting elasticity modulus dispersion of rock sample under dead volume boundary condition

Abstract

The invention provides a method and a device for predicting the elastic modulus dispersion of a rock sample under a dead volume boundary condition. According to the method, the influence of a dead volume boundary condition is simulated on the basis of a Biot pore elasticity theory, and three-dimensional experimental simulation is carried out by fully considering the flowing characteristics of rock fluid inside rock and in a dead volume. According to the method, the assumption that the dead volume condition is one-dimensional in a traditional Zimmerman hole elasticity method is effectively overcome, and the elasticity modulus frequency dispersion characteristics under the three-dimensional dead volume boundary condition are directly predicted. The prediction result precision of the method is higher than the prediction precision of a traditional method.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic rock physics, and more particularly, to a method and apparatus for predicting the elastic modulus dispersion of a rock sample with dead volume boundary conditions. Background Art

[0002] The elastic wave velocity dispersion and attenuation of fully saturated rocks are closely related to frequency. The essential reason is that seismic waves cause fluid flow through rock formations, resulting in energy dissipation. This process is called wave-induced fluid flow (White et al., 2015; 1975; Dutta & Ode 1979; Mavko & Nur 1979; Mavko & Mukerji 1998; Pride et al., 2004; Muller et al., 2010). To accurately measure the seismic wave dispersion and attenuation of rocks, it is necessary to drill samples in the rock formation and simulate in-situ conditions for measurement. However, since the rock leaves the in-situ rock formation, its environment, especially the boundary conditions, changes significantly. Therefore, according to the fluid flow state, two experimental boundary conditions are determined: drained and undrained. In the drained state, the fluid freely flows out of the rock sample boundary, and the flow process will affect the dispersion and attenuation characteristics of the elastic parameters (Dunn 1986, 1987; Xu 2007; Vogelaret al. 2015); in the undrained state, the fluid cannot flow out of the rock sample boundary, so it has little effect on the elastic dispersion of the rock. In actual experiments, rock samples are usually wrapped with heat shrink tubes, epoxy resins or rubber sleeves to achieve undrained boundary conditions. However, existing experiments must leave pipelines for injecting fluid into the rock sample, and the pipelines connecting the pipelines to the fluid pressure pump will inevitably increase the additional fluid volume (Pimienta et al. 2015a), that is, the so-called "dead volume" (for example Figure 1 ). The flow of the dead volume, as an additional boundary condition, has a significant impact on elastic dispersion and attenuation (Pimienta et al. 2015a, 2016b). Therefore, successfully predicting the influence of dead volume boundary conditions on the actual measurement results is very important for the quantitative analysis of elastic wave velocity dispersion and attenuation in a wide frequency range. To solve this problem, Pimienta et al. (2016) studied the influence of dead volume boundary conditions based on Zimmerman's poroelastic theory. However, their research results did not fully consider the actual situation of the boundary conditions. Therefore, it is very necessary to provide a method that can correctly predict the elastic modulus dispersion under dead volume boundary conditions in the field of rock physics. Summary of the Invention

[0003] In view of this, the present invention aims to provide a method that can accurately predict the elastic modulus dispersion under dead volume boundary conditions in an experiment, and this method can effectively overcome the incorrect prediction results in traditional methods.

[0004] According to one aspect of the present invention, a method for predicting the elastic modulus dispersion of a rock sample with dead volume boundary conditions is proposed, including the following steps:

[0005] Step 1, construct a digital rock sample based on the actual sample size and physical property parameters;

[0006] Step 2, obtain the elastic parameters of the gripper according to the sample gripper in the actual experiment, and construct a numerical model, wherein the elastic parameters of the injected fluid are used for the fluid pipeline part of the gripper;

[0007] Step 3, based on the numerical model, solve the distribution characteristics of the fluid in the gripper and the sample;

[0008] Step 4, simulate the actual experimental process, and apply a periodic oscillating stress along the top of the gripper as a boundary condition;

[0009] Step 5, apply a fixed boundary condition at the bottom of the gripper;

[0010] Step 6, solve the displacement tensor and fluid pressure under the boundary conditions set in Step 4 and Step 5;

[0011] Step 7, simulate the experimental acquisition process, set an acquisition area corresponding to the strain gauge in the middle of the sample, and calculate the strain of this acquisition area;

[0012] Step 8, calculate the Young's modulus of the rock sample according to the applied stress and the calculated strain.

[0013] In some embodiments, Step 2 further includes using tetrahedral mesh division for the numerical model.

[0014] In some embodiments, Step 3 specifically includes:

[0015] Based on the numerical model, use the poroelastic equation as the control equation for the gripper and the control equation for the rock sample and the pipeline embedded in the gripper, and solve the distribution characteristics of the fluid in the gripper and the sample by the finite element method.

[0016] In some embodiments, use the following poroelastic equation as the control equation for the gripper and the control equation for the rock sample and the pipeline embedded in the gripper:

[0017]

[0018]

[0019] wherein, Equation 1 is used as the control equation for the gripper, Equation 2 is used as the control equation for the rock sample and the pipeline embedded in the gripper, ω is the angular frequency, ρ bis the density of the saturated sample, ρ c (ω) is the intermediate variable complex density, ρ f is the fluid density, u s is the displacement tensor of the rock sample, is the gradient operator, σ is the stress tensor, M is the bulk modulus of the pore space, and α is the Biot coefficient.

[0020] In some embodiments, step 6 specifically includes:

[0021] Using the finite element method to solve for the displacement tensor and fluid pressure under the boundary conditions set in steps 4 and 5.

[0022] In some embodiments, in step 8, the Young's modulus E of the rock sample is calculated based on the following formula:

[0023]

[0024] where S 0 is the amplitude of the applied periodic oscillatory stress, and ε is the strain of the acquisition area calculated in step 7.

[0025] According to another aspect of the present invention, there is also provided a device for predicting the dispersion of the elastic modulus of a rock sample with dead volume boundary conditions, including:

[0026] A digital rock sample unit for constructing a digital rock sample based on the actual sample size and physical property parameters;

[0027] A numerical model construction unit for obtaining the elastic parameters of the gripper according to the gripper in the actual experiment, constructing a numerical model, and using the elastic parameters of the injection fluid for the fluid pipeline part of the gripper;

[0028] A distribution characteristic solving unit for solving the distribution characteristics of the fluid in the gripper and the sample based on the numerical model;

[0029] A first boundary condition setting unit for simulating the actual experimental process and loading a periodic oscillatory stress along the top of the gripper as the boundary condition;

[0030] A second boundary condition setting unit for loading a fixed boundary condition at the bottom of the gripper;

[0031] A displacement and fluid pressure calculation unit for solving the displacement tensor and fluid pressure under the boundary conditions set by the first boundary condition setting unit and the second boundary condition setting unit;

[0032] A strain calculation unit for simulating the experimental acquisition process, setting an acquisition area corresponding to the strain gauge in the middle of the sample, and calculating the strain of the acquisition area;

[0033] A prediction unit, configured to calculate the Young's modulus of a rock sample according to the loaded stress and the calculated strain.

[0034] In some embodiments, in the numerical model construction unit 2, the numerical model adopts tetrahedral mesh division.

[0035] In some embodiments, the distribution characteristic solving unit is specifically configured to:

[0036] Based on the numerical model, using the poroelastic equation as the control equation of the holder and the control equation of the rock sample and the pipeline embedded inside the holder, solve the distribution characteristics of the fluid in the holder and the sample by the finite element method.

[0037] In some embodiments, the following poroelastic equation is used as the control equation of the holder and the control equation of the rock sample and the pipeline embedded inside the holder:

[0038]

[0039]

[0040] Among them, Equation 1 is used as the control equation of the holder, Equation 2 is used as the control equation of the rock sample and the pipeline embedded inside the holder, ω is the angular frequency, and ρ b is the density of the saturated sample, and ρ c (ω) is the intermediate variable complex density, and ρ f is the fluid density, u s is the displacement tensor of the rock sample, is the gradient operator, σ is the stress tensor, M is the bulk modulus of the pore space, and α is the Biot coefficient.

[0041] In some embodiments, the displacement and fluid pressure calculation unit is specifically configured to:

[0042] Solve the displacement tensor and the fluid pressure under the boundary conditions set by the first boundary condition setting unit and the first boundary condition setting unit by the finite element method.

[0043] In some embodiments, in the prediction unit, the Young's modulus E of the rock sample is calculated based on the following formula:

[0044]

[0045] Among them, S 0 is the amplitude of the loaded periodic oscillating stress, and ε is the strain of the acquisition area calculated in step 7.

[0046] According to another aspect of the present invention, an electronic device is further provided, and the electronic device includes:

[0047] A memory storing executable instructions;

[0048] A processor runs the executable instructions in the memory to implement the method for predicting the elastic modulus dispersion of rock samples under dead volume boundary conditions as described above.

[0049] According to another aspect of the present invention, a computer-readable storage medium is also proposed, which stores a computer program. When the computer program is executed by a processor, it implements the method for predicting the elastic modulus dispersion of rock samples under dead volume boundary conditions as described above.

[0050] The present invention has at least the following beneficial effects.

[0051] 1. Improved prediction accuracy. Compared with the traditional method based on 1D Zimmerman model, the present invention fully considers the three-dimensional effect of the sample and dead volume by establishing a 3D numerical model, which is closer to the conditions of the actual sample, so the prediction results will be more accurate and reliable.

[0052] Second, the theoretical basis is more rigorous. Compared with the simple Zimmerman model, the present invention is based on the Biot poroelasticity theory, simulates the influence of dead volume boundary conditions, and can simultaneously describe the displacement of the solid phase and fluid in the sample, and has a more rigorous theoretical basis.

[0053] 3. Expand the scope of application. The traditional method is only applicable to samples that are assumed to be uniform and symmetrical, while this solution can handle a variety of non-uniform and asymmetrical samples, greatly broadening the scope of application.

[0054] 4. Provide a basis for parameter measurement. This scheme can predict the dead volume effect with high accuracy, which provides a reliable basis for the subsequent experimental determination of sample parameters such as wave velocity dispersion curves.

[0055] 5. It is helpful for optimizing sample design. By predicting the dead volume effect through this scheme, the design of the sample clamping system can be optimized to reduce the influence of dead volume on the test results.

[0056] 6. Promote theoretical research on wave-induced flow. The effects considered in this method are more in line with actual sample conditions, which helps theoretical research to obtain more realistic and reliable results.

[0057] In summary, the present invention can improve the prediction accuracy of elastic modulus dispersion under dead volume boundary conditions in experiments, expand the scope of application, provide strong support for parameter measurement and sample optimization design, and play an important role in promoting the theoretical research on wave-induced flow.

[0058] The methods and apparatuses of the present invention have other characteristics and advantages, which will be apparent in the accompanying drawings incorporated herein and the following detailed description, or will be described in detail in the accompanying drawings incorporated herein and the following detailed description. These accompanying drawings and detailed description are used together to explain the specific principles of the present invention. Description of the Drawings

[0059] The above and other objects, features, and advantages of the present invention will become more apparent by describing the exemplary embodiments of the present invention in more detail in conjunction with the accompanying drawings, in which, in the exemplary embodiments of the present invention, the same reference numerals generally represent the same components.

[0060] Figure 1 The flowchart of a method for predicting the dispersion of the elastic modulus of a rock sample according to an embodiment of the present invention is shown.

[0061] Figure 2 The schematic diagram of the numerical model constructed and the schematic diagram of the numerical model after grid division according to an exemplary embodiment of the present invention are shown.

[0062] Figure 3 The schematic diagram of the distribution of the control equation according to an exemplary embodiment of the present invention is shown.

[0063] Figure 4 The schematic diagram of the fluid pressure and fluid distribution according to an exemplary embodiment of the present invention is shown.

[0064] Figure 5 The comparison diagram of the prediction results and experimental results obtained according to an exemplary embodiment of the present invention is shown. Detailed Description of the Embodiments

[0065] The preferred embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the preferred embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to make the present invention more thorough and complete, and to fully convey the scope of the present invention to those skilled in the art.

[0066] Example 1

[0067] Figure 1 The flowchart of a method for predicting the dispersion of the elastic modulus of a rock sample according to an embodiment of the present invention is shown. As shown, the method includes Step 1 to Step 8.

[0068] Step 1, construct a digital rock sample according to the actual sample size and physical property parameters.

[0069] A digital rock sample with corresponding dimensions can be constructed according to the actual sample dimensions. Its physical property parameters can be obtained through experimental measurements, including the density of the rock, geometric parameters, the bulk modulus of the rock sample, the bulk modulus of the particles, etc.

[0070] Step 2: Obtain the elastic parameters of the sample holder in the actual experiment and construct a numerical model, where the elastic parameters of the injected fluid are used for the fluid pipeline part of the sample holder.

[0071] In some embodiments, Step 2 further includes using tetrahedral mesh generation for the numerical model.

[0072] Using tetrahedral mesh generation for the numerical model has the following beneficial effects: It can improve the accuracy of numerical calculations. After tetrahedral mesh generation, complex geometric shapes are approximated by discrete tetrahedral elements, which is conducive to accurately describing complex boundaries; it is convenient for calculating complex fluid flows. The tetrahedral mesh divides the inside of the model into connected small elements, which is conducive to capturing the complex flow of the fluid between the elements; it lays the foundation for complex models. The tetrahedral mesh lays a computational framework for subsequent calculations and simulations such as loading complex control equations, solving multidisciplinary coupling fields, and analyzing complex flow characteristics; it ensures numerical stability. Compared with other meshes, the number of tetrahedral meshes is small, avoiding cumulative errors in the numerical calculation process.

[0073] According to this embodiment, using tetrahedral mesh generation for the numerical model plays a key role in constructing an accurate and reliable numerical model, ensuring the accuracy and stability of numerical calculations, and exploring the complex physical mechanisms inside the model.

[0074] Step 3: Based on the numerical model, solve the distribution characteristics of the fluid in the sample holder and the sample.

[0075] In some embodiments, specifically solving the distribution characteristics of the fluid in the sample holder and the sample may include: Based on the numerical model, using the poroelastic equation as the control equation for the sample holder and the control equations for the rock sample and the pipelines embedded inside the sample holder, and solving the distribution characteristics of the fluid in the sample holder and the sample through the finite element method.

[0076] In some embodiments, the following poroelastic equations are used as the control equation for the sample holder and the control equations for the rock sample and the pipelines embedded inside the sample holder:

[0077]

[0078]

[0079] Among them, Equation 1 is used as the control equation for the sample holder, and Equation 2 is used as the control equations for the rock sample and the pipelines embedded inside the sample holder.

[0080] The physical meanings of the parameters and operators in Equations 1 and 2 are described below. is the gradient operator, ω is the angular frequency, α is the Biot coefficient, K d is the bulk modulus of the dry sample, which can also be defined as the drained bulk modulus, K g is the bulk modulus of the rock grains. The density of the saturated sample is ρ b , and the intermediate variable complex density ρ c (ω) is closely related to the pore curvature τ of the rock sample, the fluid density ρ f , the porosity φ, the fluid viscosity η, and the permeability κ of the rock sample. Specifically, u s is the displacement tensor of the rock sample, σ is the stress tensor, which is closely related to the displacement of the rock sample skeleton and the fluid pressure P f . Specifically, where i and j represent three directions, namely the x, y, and z directions. is the first constant in the Lamé constants, μ is the second constant (also called the shear modulus), is the Kronecker tensor, M is the bulk modulus of the pore space, and its specific definition is where φ is the porosity, K f is the bulk modulus of the fluid.

[0081] Step 4: Simulate the actual experimental process and apply a periodic oscillatory stress at the top of the holder as the boundary condition.

[0082] The actual experimental process can be simulated by applying a periodic oscillatory stress boundary condition along the top of the holder. Let the stress amplitude be S 0 , usually with a frequency not exceeding 1 MHz and a phase of 0.

[0083] Step 5: Apply a fixed boundary condition at the bottom of the holder.

[0084] A fixed boundary condition can be applied at the bottom of the holder, making the displacement u s = 0.

[0085] Step 6: Solve for the displacement tensor and fluid pressure under the boundary conditions set in Step 4 and Step 5.

[0086] In some embodiments, the finite element method can be used to solve the governing equations under the above specific boundary conditions to obtain the displacement tensor u s , the fluid pressure P f .

[0087] Solving the boundary condition equation using the finite element method can handle complex geometries. For the complex boundary conditions of this method, the finite element method can provide high-precision numerical solutions and can also conveniently handle boundary conditions. Various boundary conditions such as pressure and displacement can be easily loaded into the finite element framework. The mathematical framework of the finite element method also allows for coupling solutions of different physical fields such as the mechanical field and the fluid field, and the computational cost is relatively low.

[0088] Step 7: Simulate the experimental acquisition process. Set an acquisition area corresponding to the strain gauge in the middle of the sample, and calculate the strain of this acquisition area.

[0089] In the simulation experiment, an acquisition area with the size of a strain gauge can be set in the middle of the sample. The size and shape of this area are the same as those of the actual strain gauge, so that the strain value can be accurately measured during the simulation process.

[0090] After setting the acquisition area, the strain of this acquisition area can be calculated based on the displacement tensor and fluid pressure calculated in Step 6.

[0091] Step 8: Calculate the Young's modulus of the rock sample based on the applied stress and the calculated strain.

[0092] In some embodiments, the Young's modulus E of the rock sample can be calculated based on the following formula:

[0093]

[0094] where S 0 is the amplitude of the applied periodic oscillating stress, and ε is the strain of the acquisition area calculated in Step 7.

[0095] Each embodiment of this example has some or all of the following beneficial effects.

[0096] First, the prediction accuracy is improved. Compared with the traditional method based on the 1D Zimmerman model, by establishing a 3D numerical model, the present invention fully considers the three-dimensional effects of the sample and the dead volume, which is closer to the actual sample conditions. Therefore, the prediction results will be more accurate and reliable.

[0097] Second, the theoretical basis is more rigorous. Compared with the simple Zimmerman model, the present invention is based on the Biot poroelastic theory, simulates the influence of the dead volume boundary conditions, and can simultaneously describe the solid and fluid displacements in the sample. The theoretical basis is more rigorous.

[0098] Third, the applicable range is expanded. The traditional method is only applicable to samples assumed to be uniform and symmetric, while this solution can handle various non-uniform and asymmetric samples, greatly expanding the applicable range.

[0099] IV. Provide a basis for parameter measurement. This solution can accurately predict the dead volume effect, which provides a reliable foundation for subsequent experimental determination of sample parameters such as wave velocity dispersion curves.

[0100] V. Contribute to the optimization of sample design. By predicting the dead volume effect with this solution, the design of the sample clamping system can be optimized to reduce the influence of the dead volume on the test results.

[0101] VI. Facilitate the theoretical research on wave-induced flow. The effects considered in this method are more in line with the actual sample conditions, which helps to obtain more realistic and reliable results in theoretical research.

[0102] Example 2

[0103] According to an embodiment of the present invention, a device for predicting the dispersion of the elastic modulus of a rock sample with dead volume boundary conditions includes:

[0104] A digital rock sample unit for constructing a digital rock sample based on the actual sample size and physical property parameters;

[0105] A numerical model construction unit for obtaining the elastic parameters of the gripper according to the sample gripper in the actual experiment, constructing a numerical model, and using the elastic parameters of the injected fluid for the fluid pipeline part of the gripper;

[0106] A distribution characteristic solving unit for solving the distribution characteristics of the fluid in the gripper and the sample based on the numerical model;

[0107] A first boundary condition setting unit for simulating the actual experimental process and loading a periodic oscillating stress along the top of the gripper as the boundary condition;

[0108] A second boundary condition setting unit for loading a fixed boundary condition at the bottom of the gripper;

[0109] A displacement and fluid pressure calculation unit for solving the displacement tensor and fluid pressure under the boundary conditions set by the first boundary condition setting unit and the second boundary condition setting unit;

[0110] A strain calculation unit for simulating the experimental acquisition process, setting an acquisition area corresponding to the strain gauge in the middle of the sample, and calculating the strain of the acquisition area;

[0111] A prediction unit for calculating the Young's modulus of the rock sample according to the loaded stress and the calculated strain.

[0112] In some embodiments, in the numerical model construction unit 2, the numerical model uses tetrahedral mesh division.

[0113] In some embodiments, the distribution characteristic solving unit is specifically used for:

[0114] Based on the numerical model, the poroelastic equation is used as the control equation for the holder and the control equation for the rock sample and the pipeline embedded inside the holder, and the distribution characteristics of the fluid in the holder and the sample are solved by the finite element method.

[0115] In some embodiments, the following poroelastic equation is used as the control equation for the holder and the control equation for the rock sample and the pipeline embedded inside the holder:

[0116]

[0117]

[0118] Among them, Equation 1 is used as the control equation for the holder, Equation 2 is used as the control equation for the rock sample and the pipeline embedded inside the holder, ω is the angular frequency, ρ b is the density of the saturated sample, ρ c (ω) is the intermediate variable complex density, ρ f is the fluid density, u s is the displacement tensor of the rock sample, is the gradient operator, σ is the stress tensor, M is the bulk modulus of the pore space, and α is the Biot coefficient.

[0119] In some embodiments, the displacement and fluid pressure calculation unit is specifically configured to:

[0120] Use the finite element method to solve the displacement tensor and fluid pressure under the boundary conditions set by the first boundary condition setting unit and the first boundary condition setting unit.

[0121] In some embodiments, in the prediction unit, the Young's modulus E of the rock sample is calculated based on the following formula:

[0122]

[0123] Among them, S 0 is the amplitude of the applied periodic oscillatory stress, and ε is the strain of the acquisition area calculated in step 7.

[0124] Each embodiment of this example has some or all of the following beneficial effects.

[0125] First, the prediction accuracy is improved. Compared with the traditional method based on the 1D Zimmerman model, the present invention establishes a 3D numerical model, fully considering the three-dimensional effects of the sample and the dead volume, which is closer to the actual sample conditions, so the prediction results will be more accurate and reliable.

[0126] II. The theoretical basis is more rigorous. Compared with the simple Zimmerman model, the present invention is based on the Biot poroelastic theory, simulates the influence of the dead volume boundary conditions, and can simultaneously describe the solid phase and fluid displacements in the sample, with a more rigorous theoretical basis.

[0127] III. Expand the applicable scope. Traditional methods are only applicable to samples assumed to be uniform and symmetric, while the present solution can handle various non-uniform and asymmetric samples, greatly broadening the applicable scope.

[0128] IV. Provide a basis for parameter measurement. The present solution can predict the dead volume effect with high precision, which provides a reliable basis for subsequent experimental determination of sample parameters such as the wave velocity dispersion curve.

[0129] V. Contribute to the optimization of sample design. By predicting the dead volume effect through the present solution, the design of the sample clamping system can be optimized to reduce the influence of the dead volume on the test results.

[0130] VI. Promote the research on the wave-induced flow theory. The effects considered by the present method are more in line with the actual sample conditions, which helps to obtain more realistic and reliable results in theoretical research.

[0131] For other detailed descriptions and advantages of this embodiment, reference can be made to the corresponding descriptions in the foregoing embodiments, which will not be elaborated herein.

[0132] Example 3

[0133] According to another aspect of the present invention, an electronic device is further provided. The electronic device includes:

[0134] A memory storing executable instructions:

[0135] A processor that runs the executable instructions in the memory to implement the method for predicting the dispersion of the elastic modulus of a rock sample with dead volume boundary conditions according to the present invention.

[0136] Specifically, the memory may include one or more computer program products, and the computer program products may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may include, for example, random access memory (RAM) and / or cache memory, etc. The non-volatile memory may include, for example, read-only memory (ROM), hard disk, flash memory, etc.

[0137] The processor may be a central processing unit (CPU) or other forms of processing units with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In an embodiment of the present invention, the processor is used to run the computer-readable instructions stored in the memory.

[0138] The method for predicting the dead volume boundary condition and the elastic modulus dispersion of rock samples includes the following steps:

[0139] Step 1, construct a digital rock sample according to the actual sample size and physical property parameters;

[0140] Step 2, obtain the elastic parameters of the holder according to the sample holder in the actual experiment, and construct a numerical model, where the elastic parameters of the injected fluid are used for the fluid pipeline part of the holder;

[0141] Step 3, based on the numerical model, solve the distribution characteristics of the fluid in the holder and the sample;

[0142] Step 4, simulate the actual experimental process, and apply a periodic oscillating stress along the top of the holder as the boundary condition;

[0143] Step 5, apply a fixed boundary condition at the bottom of the holder;

[0144] Step 6, solve the displacement tensor and fluid pressure under the boundary conditions set in Step 4 and Step 5;

[0145] Step 7, simulate the experimental acquisition process, set an acquisition area corresponding to the strain gauge in the middle of the sample, and calculate the strain of this acquisition area;

[0146] Step 8, calculate the Young's modulus of the rock sample according to the applied stress and the calculated strain.

[0147] In some embodiments, Step 2 further includes tetrahedral mesh generation for the numerical model.

[0148] In some embodiments, Step 3 specifically includes:

[0149] Based on the numerical model, use the poroelastic equation as the control equation for the holder and the control equation for the rock sample and the pipeline embedded in the holder, and solve the distribution characteristics of the fluid in the holder and the sample by the finite element method.

[0150] In some embodiments, use the following poroelastic equation as the control equation for the holder and the control equation for the rock sample and the pipeline embedded in the holder:

[0151]

[0152]

[0153] Among them, Equation 1 is used as the control equation for the holder, Equation 2 is used as the control equation for the rock sample and the pipeline embedded in the holder, ω is the angular frequency, ρ b is the density of the saturated sample, ρc (ω) is the complex density of the intermediate variable, ρ f is the fluid density, u s is the displacement tensor of the rock sample, is the gradient operator, σ is the stress tensor, M is the bulk modulus of the pore space, and α is the Biot coefficient.

[0154] In some embodiments, step 6 specifically includes:

[0155] Using the finite element method to solve for the displacement tensor and fluid pressure under the boundary conditions set in steps 4 and 5.

[0156] In some embodiments, in step 8, the Young's modulus E of the rock sample is calculated based on the following formula:

[0157]

[0158] where S 0 is the amplitude of the applied periodic oscillatory stress, and ε is the strain of the acquisition area calculated in step 7.

[0159] Each embodiment of this example has some or all of the following beneficial effects.

[0160] First, the prediction accuracy is improved. Compared with the traditional method based on the 1D Zimmerman model, the present invention establishes a 3D numerical model, fully considering the three-dimensional effects of the sample and the dead volume, which is closer to the conditions of the actual sample. Therefore, the prediction results will be more accurate and reliable.

[0161] Second, the theoretical basis is more rigorous. Compared with the simple Zimmerman model, the present invention is based on the Biot poroelastic theory, simulates the influence of the dead volume boundary conditions, and can simultaneously describe the solid and fluid displacements in the sample, with a more rigorous theoretical basis.

[0162] Third, the applicable range is expanded. The traditional method is only applicable to samples assumed to be uniform and symmetric, while this solution can handle various non-uniform and asymmetric samples, greatly broadening the applicable range.

[0163] Fourth, it provides a basis for parameter measurement. This solution can accurately predict the dead volume effect, which provides a reliable basis for subsequent experimental determination of sample parameters such as the wave velocity dispersion curve.

[0164] Fifth, it helps optimize the sample design. By predicting the dead volume effect with this solution, the design of the sample clamping system can be optimized to reduce the influence of the dead volume on the test results.

[0165] Sixth, it promotes the research on the wave-induced flow theory. The effects considered by this method are more in line with the conditions of the actual sample, which helps to obtain more realistic and reliable results in theoretical research.

[0166] For a detailed description of this embodiment, reference may be made to the corresponding descriptions in the foregoing embodiments, which will not be elaborated herein.

[0167] Example 4

[0168] According to another aspect of the present invention, there is also provided a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the method for predicting the elastic modulus dispersion of a rock sample with dead volume boundary conditions according to the present invention.

[0169] The computer-readable storage medium according to an embodiment of the present invention stores non-transitory computer-readable instructions. When the non-transitory computer-readable instructions are run by a processor, all or part of the steps of the methods of the foregoing embodiments of the present invention are executed.

[0170] The above computer-readable storage medium includes but is not limited to: optical storage media (e.g., CD-ROMs and DVDs), magneto-optical storage media (e.g., MOs), magnetic storage media (e.g., magnetic tapes or external hard drives), media with built-in rewritable non-volatile memories (e.g., memory cards), and media with built-in ROMs (e.g., ROM cartridges).

[0171] Those skilled in the art should understand that, in order to solve the technical problem of how to obtain good user experience effects, this embodiment may also include well-known structures such as communication buses and interfaces, and these well-known structures should also be included in the protection scope of the present invention.

[0172] The method for predicting the elastic modulus dispersion of a rock sample with dead volume boundary conditions includes the following steps:

[0173] Step 1, constructing a digital rock sample according to the actual sample size and physical property parameters;

[0174] Step 2, obtaining the elastic parameters of the holder according to the sample holder in the actual experiment, and constructing a numerical model, wherein the elastic parameters of the injected fluid are used for the fluid pipeline part of the holder;

[0175] Step 3, solving the distribution characteristics of the fluid in the holder and the sample based on the numerical model;

[0176] Step 4, simulating the actual experimental process, and loading a periodic oscillating stress along the top of the holder as a boundary condition;

[0177] Step 5, loading a fixed boundary condition at the bottom of the holder;

[0178] Step 6, solving the displacement tensor and fluid pressure under the boundary conditions set in Step 4 and Step 5;

[0179] Step 7: Simulate the experimental acquisition process, set an acquisition area corresponding to the strain gauge in the middle of the sample, and calculate the strain of this acquisition area.

[0180] Step 8: Calculate the Young's modulus of the rock sample based on the applied stress and the calculated strain.

[0181] In some embodiments, step 2 further includes tetrahedral mesh generation for the numerical model.

[0182] In some embodiments, step 3 specifically includes:

[0183] Based on the numerical model, use the poroelastic equation as the control equation for the gripper and the control equation for the rock sample and the pipelines embedded inside the gripper, and solve for the distribution characteristics of the fluid in the gripper and the sample by the finite element method.

[0184] In some embodiments, use the following poroelastic equation as the control equation for the gripper and the control equation for the rock sample and the pipelines embedded inside the gripper:

[0185]

[0186]

[0187] Among them, Equation 1 is used as the control equation for the gripper, Equation 2 is used as the control equation for the rock sample and the pipelines embedded inside the gripper, ω is the angular frequency, ρ b is the density of the saturated sample, ρ c (ω) is the intermediate variable complex density, ρ f is the fluid density, u s is the displacement tensor of the rock sample, is the gradient operator, σ is the stress tensor, M is the bulk modulus of the pore space, and α is the Biot coefficient.

[0188] In some embodiments, step 6 specifically includes:

[0189] Use the finite element method to solve for the displacement tensor and the fluid pressure under the boundary conditions set in steps 4 and 5.

[0190] In some embodiments, in step 8, calculate the Young's modulus E of the rock sample based on the following formula:

[0191]

[0192] Among them, S 0 is the amplitude of the applied periodic oscillating stress, and ε is the strain of the acquisition area calculated in step 7.

[0193] Each implementation of this embodiment has some or all of the following beneficial effects.

[0194] 1. Improved prediction accuracy. Compared with the traditional method based on 1D Zimmerman model, the present invention fully considers the three-dimensional effect of the sample and dead volume by establishing a 3D numerical model, which is closer to the conditions of the actual sample, so the prediction results will be more accurate and reliable.

[0195] Second, the theoretical basis is more rigorous. Compared with the simple Zimmerman model, the present invention is based on the Biot poroelasticity theory, simulates the influence of dead volume boundary conditions, and can simultaneously describe the displacement of the solid phase and fluid in the sample, and has a more rigorous theoretical basis.

[0196] 3. Expand the scope of application. The traditional method is only applicable to samples that are assumed to be uniform and symmetrical, while this solution can handle a variety of non-uniform and asymmetrical samples, greatly broadening the scope of application.

[0197] 4. Provide a basis for parameter measurement. This scheme can predict the dead volume effect with high accuracy, which provides a reliable basis for the subsequent experimental determination of sample parameters such as wave velocity dispersion curves.

[0198] 5. It is helpful for optimizing sample design. By predicting the dead volume effect through this scheme, the design of the sample clamping system can be optimized to reduce the influence of dead volume on the test results.

[0199] 6. Promote theoretical research on wave-induced flow. The effects considered in this method are more in line with actual sample conditions, which helps theoretical research to obtain more realistic and reliable results.

[0200] For detailed description of this embodiment, reference may be made to the corresponding descriptions in the aforementioned embodiments, which will not be repeated here.

[0201] Example 5

[0202] In order to make the purpose, technical solutions and advantages of the present invention more clearly described, embodiments are presented below based on the solutions to exemplify the beneficial effects of the present invention.

[0203] Figure 2 A schematic diagram of a constructed numerical model according to an exemplary embodiment of the present invention and a schematic diagram of a numerical model after meshing are shown.

[0204] Figure 3 A schematic diagram of the distribution of control equations according to an exemplary embodiment of the present invention is shown.

[0205] Figure 4 A schematic diagram of fluid pressure and fluid distribution according to an exemplary embodiment of the present invention is shown.

[0206] Figure 5 The figure shows a comparison chart of the predicted results and experimental results obtained according to an exemplary embodiment of the present invention.

[0207] Rock samples with a diameter of 50 mm and a length of 100 mm can be constructed according to the actual sample size, and their physical property parameters are obtained through experiments, as shown in Table 1.

[0208] Table 1 Physical property parameters of rock samples

[0209]

[0210]

[0211] Clamps can be designed according to the upper and lower ends of the samples in the actual experiment, a numerical model can be constructed, and mesh generation can be carried out. The implementation effect is as Figure 2 shown. Figure 2 The left side in the figure is a schematic diagram of the constructed numerical model, and the right side is a schematic diagram of the numerical model after mesh generation.

[0212] The control equations and boundary conditions can be loaded. Equation 2 is loaded into the space shown in the sample and the fluid pipeline to analyze the fluid flow position. The implementation effect is as Figure 3 shown.

[0213] After that, the fluid pressure and displacement can be calculated. The fluid pressure is as Figure 4 shown. It can be seen the fluid flow process from the pipeline into the sample, indicating the influence of the boundary conditions.

[0214] The Young's modulus can be calculated and compared with the test results. Figure 5 The figure shows a comparison chart of the predicted results and experimental results obtained according to an exemplary embodiment of the present invention. As Figure 5 shown, the measurement results of the present invention are highly consistent with the experimental measurement results.

[0215] It can be understood that the above-mentioned embodiments mentioned in the present disclosure can be combined with each other to form a combined embodiment without violating the principle logic. Due to space limitations, the present disclosure will not elaborate further. Those skilled in the art can understand that in the above method of the specific implementation manner, the specific execution order of each step should be determined according to its function and possible internal logic.

[0216] Note that, unless otherwise directly stated, all features disclosed in this specification (including any appended claims, abstract, and drawings) may be replaced by alternative features serving the same, equivalent, or similar purpose. Therefore, unless otherwise explicitly specified, each feature disclosed is only an example of a group of equivalent or similar features. Where used, "furthermore", "preferably", "moreover", and "even more preferably" are simply the starting points for elaborating another embodiment based on the foregoing embodiments. The content following such "furthermore", "preferably", "moreover", or "even more preferably" in combination with the foregoing embodiments constitutes a complete composition of another embodiment. Combinations can be arbitrarily made among several "furthermore", "preferably", "moreover", or "even more preferably" settings following the same embodiment to form yet another embodiment.

[0217] Those skilled in the art should understand that the embodiments of the present invention described above and shown in the drawings are only examples and do not limit the present invention. The objectives of the present invention have been fully and effectively achieved. The functions and structural principles of the present invention have been demonstrated and explained in the embodiments. Without departing from the said principles, the embodiments of the present invention may be subject to any deformation or modification.

[0218] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present disclosure, not to limit them; although the present disclosure has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present disclosure.

Claims

1. A method for predicting the elastic modulus dispersion of a rock sample with dead volume boundary conditions, characterized in that, it includes the following steps: Step 1, construct a digital rock sample according to the actual sample size and physical property parameters; Step 2, obtain the elastic parameters of the sample holder according to the sample holder in the actual experiment, and construct a numerical model, wherein the elastic parameters of the injected fluid are used for the fluid pipeline part of the sample holder; Step 3, based on the numerical model, solve the distribution characteristics of the fluid in the sample holder and the sample; Step 4, simulate the actual experimental process, and apply a periodic oscillating stress along the top of the sample holder as a boundary condition; Step 5, apply a fixed boundary condition at the bottom of the sample holder; Step 6, solve the displacement tensor and fluid pressure under the boundary conditions set in Step 4 and Step 5; Step 7, simulate the experimental acquisition process, set an acquisition area corresponding to the strain gauge in the middle of the sample, and calculate the strain of this acquisition area; Step 8, calculate the Young's modulus of the rock sample according to the applied stress and the calculated strain.

2. The method according to claim 1, characterized in that, Step 2 further includes: Using tetrahedral mesh division for the numerical model.

3. The method according to claim 3, characterized in that, Step 3 specifically includes: Based on the numerical model, use the poroelastic equation as the control equation for the sample holder and the control equation for the rock sample and the pipeline embedded inside the sample holder, and solve the distribution characteristics of the fluid in the sample holder and the sample by the finite element method.

4. The method according to claim 3, characterized in that, Use the following poroelastic equation as the control equation for the sample holder and the control equation for the rock sample and the pipeline embedded inside the sample holder: Among them, Equation 1 serves as the control equation for the gripper, and Equation 2 serves as the control equation for the rock sample and the pipeline embedded inside the gripper. ω is the angular frequency, ρ b is the density of the saturated sample, ρ c (ω) is the intermediate variable complex density, ρ f is the fluid density, u s is the displacement tensor of the rock sample, is the gradient operator, σ is the stress tensor, M is the bulk modulus of the pore space, and α is the Biot coefficient.

5. The method according to claim 1, characterized in that, Step 6 specifically includes: Use the finite element method to solve the displacement tensor and fluid pressure under the boundary conditions set in Step 4 and Step 5.

6. The method according to claim 1, characterized in that, In Step 8, calculate the Young's modulus E of the rock sample based on the following formula: where S 0 is the amplitude of the applied cyclic oscillatory stress, and ε is the strain of the acquisition area calculated in step 7.

7. A device for predicting the elastic modulus dispersion of a rock sample with dead volume boundary conditions, characterized in that, it includes: A digital rock sample unit for constructing a digital rock sample according to the actual sample size and physical property parameters; A numerical model construction unit for obtaining the elastic parameters of the sample holder according to the sample holder in the actual experiment, and constructing a numerical model, wherein the elastic parameters of the injected fluid are used for the fluid pipeline part of the sample holder; A distribution characteristic solving unit for solving the distribution characteristics of the fluid in the sample holder and the sample based on the numerical model; A first boundary condition setting unit for simulating the actual experimental process and applying a periodic oscillating stress along the top of the sample holder as a boundary condition; A second boundary condition setting unit for applying a fixed boundary condition at the bottom of the sample holder; A displacement and fluid pressure calculation unit for solving the displacement tensor and fluid pressure under the boundary conditions set by the first boundary condition setting unit and the second boundary condition setting unit; A strain calculation unit for simulating the experimental acquisition process, setting an acquisition area corresponding to the strain gauge in the middle of the sample, and calculating the strain of this acquisition area; A prediction unit, configured to calculate the Young's modulus of a rock sample according to the loaded stress and the calculated strain.

8. The apparatus according to claim 7, wherein, in the numerical model construction unit 2, the numerical model uses tetrahedral mesh division.

9. The apparatus according to claim 7, wherein, the distribution characteristic solving unit is specifically configured to: Based on the numerical model, using the poroelastic equation as the control equation of the holder and the control equations of the rock sample and the pipelines embedded inside the holder, solve the distribution characteristics of the fluid in the holder and the sample by the finite element method.

10. The apparatus according to claim 9, wherein, using the following poroelastic equation as the control equation of the holder and the control equations of the rock sample and the pipelines embedded inside the holder: Among them, Equation 1 serves as the control equation of the gripper, and Equation 2 serves as the control equation of the rock sample and the pipeline embedded inside the gripper. ω is the angular frequency, ρ b is the density of the saturated sample, ρ c (ω) is the intermediate variable complex density, ρ f is the fluid density, u s is the displacement tensor of the rock sample, is the gradient operator, σ is the stress tensor, M is the bulk modulus of the pore space, and α is the Biot coefficient.

11. An electronic device, wherein, the electronic device includes: a memory storing executable instructions; a processor, the processor running the executable instructions in the memory to implement the method according to any one of claims 1-6.

12. A computer-readable storage medium storing a computer program, which when executed by a processor implements the method according to any one of claims 1-6.

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