A method of predicting macro-micro double-scale flow dispersion and attenuation

Abstract

The present application belongs to the technical field of flow seismic wave prediction, and particularly relates to a method for predicting macro-micro double-scale flow dispersion and attenuation, which comprises the following steps: S1: geometric model construction: constructing a digital model according to the size of a rock sample; S2: grid division: a. fine grid at positions representing fluid pipelines; b. coarse grid at other positions; S3: control equation: combining the pore elasticity theory of Zimmerman with the equivalent medium model of micro-scale to construct a control equation for describing macro-micro scale flow; S4: boundary condition: the side boundary and the cross-section position except the pipeline of the entire rock sample are free of fluid outflow, and the cross-section of the fluid pipeline at the upper and lower boundaries of the rock has fluid outflow. The present application can overcome the shortcoming that the low-frequency limit of the traditional method BISQ does not satisfy the Gassmann equation, directly couples the micro mechanism in the macro mechanism, and provides a simple method for describing the double-scale flow dispersion mechanism.

Description

Technical Field

[0001] This invention belongs to the field of flow seismic wave prediction technology, specifically relating to a method for predicting macroscopic-microscopic dual-scale flow dispersion and attenuation. Background Technology

[0002] The propagation of flowing seismic waves can lead to internal fluid flow at different scales, namely macroscopic flow at the wavelength scale or local flow within a representative element (REV) (Dutta and Odé, 1979; Mavko and Mukerji, 1998; Mavko and Nur, 1979; Müller et al., 2010; Pride et al., 2004; White et al., 1975). Macroscopic flow balances pressure by connecting all REVs, while local flow or jet flow balances fluid pressure between soft microcracks and circular pores within each REV (Mavko and Jizba, 1991).

[0003] Fluid flow can be divided into three stages: drained, undrained, and unreleased (Pimienta et al., 2016a). In the drained stage, the fluid has time to flow through all REVs via both local and macroscopic flow (Borgomano J.VM et al., 2017). Therefore, the fluid pressure within the REVs is almost zero, resulting in elastic properties of the porous media similar to those under dry conditions (ignoring chemical interactions). In the undrained stage, the fluid pressure has no time to escape from the REVs (Pimienta et al., 2016a). In this stage, the REVs remain isobaric (O'Connell and Budiansky, 1977), leading to a higher stiffness of the porous media compared to the drained stage. Finally, in the unreleased stage, the fluid pressure has no time to reach equilibrium within each REV through local flow. In this case, the fluid is almost stationary, thus creating a pressure gradient within the pores.

[0004] Pressure gradients reduce the compressibility of saturated media. Therefore, fluid flow at these stages is often considered the primary controlling factor for the dispersion and attenuation of the modulus of saturated rocks (e.g., Muller et al., 2010). To study these fluid flows, numerous models have been developed: Pimenta et al. (2016) investigated the dispersion and attenuation characteristics of 1D macroscopic flow using a porosity elasticity model (utilizing fluid flow at the boundary); O'Connell and Budiansky (1977) developed a model to describe the influence of fracture geometry.

[0005] Recently, Gurevich et al. (2010) proposed a jet model, a correction to the method of Murphy et al. (1986), which allows for (i) low-frequency constraints consistent with Gassmann's (1951) predictions and (ii) high-frequency constraints consistent with Mavko and Jizba's (1991) predictions. Jet flow can also be viewed as an additional acoustic energy loss mechanism. Bourbié et al. (1987) validated this by comparing different loss mechanisms in porous media with experimental observations.

[0006] Building upon previous research, Dvorkin and Nur (1993; 1994) proposed the two-scale model, or BISQ model, which combines dynamic Biot theory and jet flow mechanisms for more refined analysis. However, the low-frequency predictions of this model do not align with those of Gassmann theory, thus limiting its widespread application. Therefore, providing a method to overcome the shortcomings of the BISQ model and accurately predict macroscopic-microscopic two-scale dispersion mechanisms is not only significant but also necessary. Summary of the Invention

[0007] The purpose of this invention is to provide a method for predicting macro-micro dual-scale flow dispersion and attenuation, which overcomes the shortcoming of the low-frequency limit in the traditional method BISQ that does not satisfy the Gassmann equation. It directly couples the micro mechanism to the macro mechanism, providing a simple method for describing the dual-scale flow dispersion mechanism.

[0008] The specific technical solution adopted by this invention is as follows:

[0009] A method for predicting dispersion and attenuation of macro- and micro dual-scale currents, the method comprising the following steps:

[0010] S1: Geometric model construction: Constructing a digital model based on the dimensions of the rock sample;

[0011] S2: Mesh generation:

[0012] a. Fine grid is used at locations representing fluid pipelines;

[0013] b. Coarse grid in other locations;

[0014] S3: Governing equations: By combining Zimmerman's porosity theory with the equivalent medium model at the microscale, governing equations describing macro-microscale flow are constructed.

[0015] S4: Boundary conditions: No fluid flows out at the lateral boundaries of the entire rock sample and at the cross-sectional locations other than the pipelines; fluid flows out at the cross-sections of the fluid pipelines at the upper and lower boundaries of the rock.

[0016] S5: Solution: Use MUMPS to solve for the physical field variable fluid pressure.

[0017] In step S1, the construction of the digital model of the rock sample size includes the following steps:

[0018] S11: Collect rock samples from the study area and ensure the representativeness and diversity of the sample rocks to simulate the actual site;

[0019] S12: Prepare samples of specified dimensions from rocks by cutting and grinding.

[0020] S13: Use a 3D scanner to scan and measure the rock sample to obtain accurate data of the rock sample, and import the measurement data into a computer program for data processing;

[0021] S14: Use 3D modeling software to convert the geometric model into a discrete mesh model, and divide a single rock sample model into a discrete unit for numerical simulation;

[0022] S15: Assign corresponding rock material properties based on the physical and mechanical characteristics of the discrete unit;

[0023] S16: Import the mesh model using numerical simulation software and set the corresponding boundary conditions to obtain a digital model of the rock sample size.

[0024] In S3, the macroscopic scale control equation is:

[0025]

[0026] Where P f (z, r, ω) is the frequency domain form of pore pressure, P c (ω) is the confining pressure of the periodic oscillation, and its frequency domain form is (ΔP0e iωt Its amplitude is ΔP0, where ω is the angular frequency, t is time, i is the imaginary unit, κ is the sample permeability, B is the Skempton coefficient, and K mf Let η be the bulk modulus of the rock skeleton, η be the fluid viscosity, and α be the Biot coefficient. Its physical meaning is the diffusion coefficient;

[0027] K mf K is the skeletal modulus of the rock; when there is no fluid in the rock, K... mf =K d .

[0028] The simplified equation of the macroscopic scale control equation is:

[0029]

[0030] At the microscale, when fluid fills a rock, the stiffness of the rock's microfractures changes, K mf It becomes:

[0031]

[0032] Where P is the fluid pressure, ω is the angular frequency, and K... h It is the bulk modulus when there are no cracks, K d (P) is the bulk modulus of drainage under a specific pressure, φ c η is the soft porosity in the rock, r is the aspect ratio of the fracture, and η is the fluid viscosity.

[0033] In S4, the relevant boundary conditions are:

[0034]

[0035]

[0036]

[0037] A0 is the cross-sectional area of ​​the rock pipeline, S 1，2 =V 1，2 / K f It is the fluid storage capacity, where V 1，2 It is the pipeline volume, K f It is the bulk modulus of the fluid, P f is the fluid pressure, and n· is the dot product of the normal operator.

[0038] In step S5, based on the obtained fluid pressure, the load on the rock is calculated as the volume stress, and the bulk modulus of the rock is obtained as follows:

[0039]

[0040] Among them, P c It is the amplitude of the periodic oscillation consolidation.

[0041] ε v It is the volumetric strain of the sample, and its formula is:

[0042]

[0043] The technical effects achieved by this invention are as follows:

[0044] Compared to existing techniques for predicting dispersion and attenuation, this invention provides a more comprehensive prediction of the dispersion and attenuation characteristics caused by fluid flow during actual experiments. Its predicted two-scale flow dispersion characteristics are consistent with rock physics theory and actual measurement results. To illustrate the effectiveness of the invention, it will be explained from two aspects:

[0045] 1. The method for predicting dispersion and attenuation of macro- and micro-scale flows according to this invention addresses the shortcomings of traditional methods. Specifically, the low-frequency limit predicted by the BISQ method does not match the prediction results of the Gassmann equation, violating the most widely accepted rock physics model and contradicting experimental results. This invention addresses these shortcomings by proposing the following approach: obtaining the dynamic framework of the rock at the micro-scale using effective medium theory, and coupling it to the governing equations of the macro-flow to calculate the dispersion and attenuation laws induced by the dual-scale flow.

[0046] 2. Regarding the prediction results, the high and low frequency limits of the present invention for predicting macro-micro dual-scale current dispersion and attenuation satisfy the basic theory and are consistent with the experimental prediction results. Attached Figure Description

[0047] Figure 1 This is a technical circuit diagram of an embodiment of the present invention;

[0048] Figure 2 This is a grid-based diagram of digital lithology from an embodiment of the present invention;

[0049] Figure 3 This is a boundary condition loading diagram according to an embodiment of the present invention;

[0050] Figure 4 This is a fluid pressure distribution diagram and fluid flow curve at 100Hz in an embodiment of the present invention;

[0051] Figure 5 This is a comparison between the predicted bulk modulus and the actual modulus in the embodiments of the present invention. Detailed Implementation

[0052] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0053] like Figure 1-5 As shown, a method for predicting the dispersion and attenuation of a macro-micro dual-scale flow is presented, comprising the following steps:

[0054] S1: Geometric model construction: Constructing a digital model based on the dimensions of the rock sample;

[0055] S2: Mesh generation:

[0056] a. Fine grid is used at locations representing fluid pipelines;

[0057] b. Coarse grid in other locations;

[0058] Specifically, based on S1 and S2, a numerical model is constructed and a mesh is generated, as shown below. Figure 2 As shown;

[0059] S3: Governing equations: By combining Zimmerman's porosity theory with the equivalent medium model at the microscale, governing equations describing macro-microscale flow are constructed.

[0060] Zimmerman porosimetry, also known as porosimetry mechanics, is a theoretical model used to describe the elastic behavior of porous media. This theory is based on the following assumptions: the pores in the porous medium are spherical, and the elastic material is isotropic. It treats pore distribution as a characteristic of the medium and introduces parameters such as porosity and energy-equivalent porosity to describe the influence of pore distribution. Zimmerman porosimetry modifies traditional linear elasticity by introducing a correction factor to account for the porosity effect present in porous media. This correction factor is used to adjust Young's modulus and Poisson's ratio to be correlated with porosity and energy-equivalent porosity.

[0061] Specifically, according to S3, the overall loading control equation for the sample is 5, and the loading equations for the top and bottom are 1. The implementation effect of the case is as follows: Figure 3 As shown in the figure; the required elastic parameters are shown in the table below:

[0062] Parameters required for execution of the example

[0063] Sample length (L [mm]) 72 Sample diameter (d [mm]) 38 Sample porosity (φ [%)) 24.4 Discharge bulk modulus (Kd [GPa]) 4.32 Shear modulus (μ[GPa]) 3.73 Sample permeability (κ[m2]) 65e-15 Confining pressure amplitude (ΔP0 [MPa]) 0.02 Lower space (V1[ml]) 3.3 Upper space (V2[ml]) 3.3 Kfluid bulk modulus (GPa) 1.8 Fluid viscosity (η[Pa*s]) 3E-3 <![CDATA[V1 storage capacity (S1 [m 4 ·s 2 / kg])]]> 1.83e-15 <![CDATA[V2 storage capacity (S2 [m 4 ·s 2 / kg])]]> 1.8Se-15 Upper surface area of ​​the fluid pipeline (A0) [m2] 7.854e-7 Sample volume (V [m3]) 8.17e-5 Sample cross-sectional area (A [m2]) 1.13e-3 Particle bulk modulus (K0 [GPa]) 45

[0064] S4: Boundary conditions: No fluid flows out at the lateral boundaries of the entire rock sample and at the cross-sectional locations other than the pipelines; fluid flows out at the cross-sections of the fluid pipelines at the upper and lower boundaries of the rock.

[0065] In S4, the relevant boundary conditions are:

[0066]

[0067]

[0068] A0 is the cross-sectional area of ​​the rock pipeline, S 1，2 =V 1，2 / K f It is the fluid storage capacity, where V 1，2 It is the pipeline volume, K f It is the bulk modulus of the fluid, P f is the fluid pressure, and n· is the dot product of the normal operator.

[0069] S5: Solution: Use MUMPS to solve for the physical field variable fluid pressure.

[0070] In S5, based on the obtained fluid pressure, the load on the rock is calculated as the body stress, and the bulk modulus of the rock is obtained as follows:

[0071]

[0072] Among them, P c It is the amplitude of the periodic oscillation consolidation.

[0073] ε v It is the volumetric strain of the sample, and its formula is:

[0074]

[0075] Specifically, according to S5, calculate the fluid pressure and rock bulk modulus.

[0076] Result: Fluid pressure at 100Hz is as follows Figure 4 As shown, the overall fluid pressure distribution is basically uniform, and the fluid pressure rapidly decreases to 0 MPa at the point where the fluid pipeline contacts the rock sample.

[0077] Bulk modulus calculated based on fluid pressure, such as Figure 5 As shown, the bulk modulus gradually increases with increasing frequency, with a second step appearing around 100Hz. As the frequency further increases to around 1000Hz, the bulk modulus increases to 20.5GPa.

[0078] The entire dispersion curve exhibits two dispersion segments: 0.1Hz-100Hz and 100Hz-1000Hz. Comparing the prediction results of this invention with experimental measurements, it can be seen that the two coincide well, proving the effectiveness of this invention. Furthermore, the low-frequency predictions conform to Gassmann theory, and the high-frequency predictions conform to effective medium theory, demonstrating that this invention has overcome the shortcomings of traditional methods.

[0079] In S1, the construction of the digital model of rock sample size includes the following steps:

[0080] S11: Collect rock samples from the study area and ensure the representativeness and diversity of the sample rocks to simulate the actual site;

[0081] S12: Prepare samples of specified dimensions from rocks by cutting and grinding.

[0082] S13: Use a 3D scanner to scan and measure the rock sample to obtain accurate data of the rock sample, and import the measurement data into a computer program for data processing;

[0083] S14: Use 3D modeling software to convert the geometric model into a discrete mesh model, and divide a single rock sample model into a discrete unit for numerical simulation;

[0084] S15: Assign corresponding rock material properties based on the physical and mechanical characteristics of the discrete unit;

[0085] S16: Import the mesh model using numerical simulation software and set the corresponding boundary conditions to obtain a digital model of the rock sample size.

[0086] In S3, the macroscopic scale governing equation is:

[0087]

[0088] Where P f (z, r, ω) is the frequency domain form of pore pressure, P c (ω) is the confining pressure of the periodic oscillation, and its frequency domain form is (ΔP0e iωt Its amplitude is ΔP0, where ω is the angular frequency, t is time, i is the imaginary unit, κ is the sample permeability, B is the Skempton coefficient, and K mf Let η be the bulk modulus of the rock skeleton, η be the fluid viscosity, and α be the Biot coefficient. Its physical meaning is the diffusion coefficient;

[0089] K mf K is the skeletal modulus of the rock; when there is no fluid in the rock, K... mf =K d .

[0090] The simplified equation for the macroscopic scale governing equation is:

[0091]

[0092] At the microscale, when fluid fills a rock, the stiffness of the rock's microfractures changes, K mf It becomes:

[0093]

[0094] Where P is the fluid pressure, ω is the angular frequency, and K... h It is the bulk modulus when there are no cracks, K d (P) is the bulk modulus of drainage under a specific pressure, φ c η is the soft porosity in the rock, r is the aspect ratio of the fracture, and η is the fluid viscosity.

[0095] The above description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained in this invention are implemented according to conventional methods in the art unless otherwise specified or limited.

Claims

1. A method for predicting dispersion and attenuation of a macro-micro dual-scale current, characterized in that: The method includes the following steps: S1: Geometric model construction: Constructing a digital model based on the dimensions of the rock sample; S2: Mesh generation: a. Fine grid is used at locations representing fluid pipelines; b. Coarse grid in other locations; S3: Governing equations: By combining Zimmerman's porosity theory with the equivalent medium model at the microscale, governing equations describing macro-microscale flow are constructed. The macroscopic scale governing equation is: ； in It is the frequency domain form of pore pressure. It is the confining pressure of periodic oscillations, and its frequency domain form is as follows: Its amplitude is , middle It is angular frequency. It is time. It is the imaginary unit. It is the sample permeability. It is the Skempton coefficient. It is the bulk modulus of the rock skeleton. It is fluid viscosity. It is the Biot coefficient, let Its physical meaning is the diffusion coefficient; It is the skeletal modulus of the rock, which is present when there is no fluid in the rock. ; S4: Boundary conditions: No fluid flows out at the lateral boundaries of the entire rock sample and at the cross-sectional locations other than the pipelines; fluid flows out at the cross-sections of the fluid pipelines at the upper and lower boundaries of the rock. S5: Solution: Use MUMPS to solve for the physical field variable fluid pressure.

2. The method for predicting macro-micro dual-scale flow dispersion and attenuation according to claim 1, characterized in that: In step S1, the construction of the digital model of the rock sample size includes the following steps: S11: Collect rock samples from the study area and ensure the representativeness and diversity of the sample rocks to simulate the actual site; S12: Prepare samples of specified dimensions from rocks by cutting and grinding. S13: Use a 3D scanner to scan and measure the rock sample to obtain accurate data of the rock sample, and import the measurement data into a computer program for data processing; S14: Use 3D modeling software to convert the geometric model into a discrete mesh model, and divide a single rock sample model into a discrete unit for numerical simulation; S15: Assign corresponding rock material properties based on the physical and mechanical characteristics of the discrete unit; S16: Import the mesh model using numerical simulation software and set the corresponding boundary conditions to obtain a digital model of the rock sample size.

3. The method for predicting macro-micro dual-scale flow dispersion and attenuation according to claim 1, characterized in that: The simplified equation of the macroscopic scale control equation is: 。 4. The method for predicting macro-micro dual-scale flow dispersion and attenuation according to claim 1, characterized in that: At the microscopic scale, when fluid fills a rock, the stiffness of the rock's microfractures changes. It becomes: ； Where P is the fluid pressure. It is angular frequency. It is the bulk modulus when there are no cracks. The bulk modulus of drainage under a specific pressure. It refers to the soft porosity in rocks. It is the aspect ratio of the crack. It refers to fluid viscosity.

5. The method for predicting macro-micro dual-scale flow dispersion and attenuation according to claim 1, characterized in that: In S4, the relevant boundary conditions are: ； It is the cross-sectional area of ​​the rock pipeline. It is fluid storage capacity, of which It is the pipeline volume. It is the bulk modulus of the fluid. It is fluid pressure. It is the dot product of the normal operators.

6. The method for predicting macro-micro dual-scale flow dispersion and attenuation according to claim 1, characterized in that: In step S5, based on the obtained fluid pressure, the load on the rock is calculated as the volume stress, and the bulk modulus of the rock is obtained as follows: ； in, It is the amplitude of the periodic oscillation consolidation.

7. The method for predicting macro-micro dual-scale flow dispersion and attenuation according to claim 6, characterized in that: It is the volumetric strain of the sample, and its formula is: 。

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