Estimation method of microfracture porosity and nonlinear characteristic index of rocks at different temperatures

Abstract

The present invention discloses a method for estimating the porosity and nonlinear characteristic index of rock microfractures at different temperatures, relating to the field of seismic rock physics. The method comprises the following steps: obtaining experimental data on the dispersion and attenuation of the elastic modulus of saturated porous rock as a function of frequency at different temperatures; constructing a frequency-domain characteristic equation based on a nonlinear viscoelastic dual-porosity rock physics model; substituting known physical property parameters into the characteristic equation and setting initial values ​​for the parameters to be inverted; solving the characteristic equation to obtain elastic wave dispersion and attenuation curves; constructing an error function between the elastic wave dispersion curve, attenuation curve, and predicted values ​​to invert the rock microfracture porosity and nonlinear characteristic index; and substituting known physical property parameters and inversion parameters into the characteristic equation to obtain broadband P- and S-wave dispersion and attenuation characteristics. The method of the present invention clearly describes the seismic wave attenuation dispersion mechanism and relates to the inversion of rock microfracture porosity and nonlinear characteristic index under different temperature conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic rock physics, and in particular to a method for estimating porosity and nonlinear characteristic index of rock microcracks at different temperatures. Background Art

[0002] Reservoir microcracks and the nonlinear characteristics of reservoir fluids greatly affect the seismic wave response characteristics. Predicting the porosity, nonlinear characteristic index and temperature-dependent characteristics of reservoir rock microcracks is crucial for reservoir identification and describing the reservoir's oil and gas migration capacity, especially for unconventional reservoirs containing high-viscosity fluids.

[0003] Traditional data analysis and interpretation of broadband seismic wave attenuation and dispersion in fluid-bearing porous media relies on generalized linear viscoelastic representation models with multiple relaxation times or linear wave-induced flow models. These models are complex, with the attenuation mechanism poorly understood. Microscopic parameters of the pore structure and the nonlinear characteristics of the rock are also difficult to infer from rock physics experimental data. Therefore, constructing a concise and more physically meaningful rock physics model to describe the seismic wave response characteristics of complex porous media is a core issue in inverting and predicting reservoir rock microfracture porosity, nonlinear characteristic indices, and their temperature-dependent characteristics, thereby characterizing the reservoir's oil and gas migration capacity. Summary of the Invention

[0004] To solve the above technical problems, the present invention discloses a method for estimating the porosity and nonlinear characteristic index of rock microfractures at different temperatures, obtaining experimental data on the dispersion and attenuation of the elastic modulus of fluid-containing porous rocks that changes with frequency at different temperatures; using a nonlinear attenuated viscoelastic double-poroelastic model that takes temperature changes into account, multi-parameter inversion is performed on the experimental data to solve the physical properties such as the rock microfracture porosity and nonlinear characteristic index under different temperature conditions.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] The method for estimating the porosity and nonlinear characteristic index of rock microfractures at different temperatures includes the following steps:

[0007] Step S1. Acquire experimental data on the dispersion and attenuation of elastic modulus of saturated porous rock as a function of frequency at different temperatures;

[0008] Step S2. constructing a frequency domain characteristic equation based on a nonlinear viscoelastic dual-poroelastic rock physics model;

[0009] Step S3. Substitute the known physical property parameters into the characteristic equation and set initial values ​​for the parameters to be inverted;

[0010] Step S4. Solving the characteristic equation to obtain theoretical prediction results of the elastic wave dispersion curve and attenuation curve;

[0011] Step S5. construct an error function between the elastic wave dispersion curve, attenuation curve experimental data and theoretical prediction results, perform iterative optimization step by step, and invert to obtain the rock microcrack porosity and nonlinear characteristic index;

[0012] Step S6. Substitute the known physical parameters and the rock microcrack porosity and nonlinear characteristic index obtained in step S5 into the frequency domain characteristic equation to obtain the broadband longitudinal and transverse wave dispersion and attenuation characteristics.

[0013] Optionally, in step S2, the steps of constructing the nonlinear viscoelastic dual-poroelastic rock physics model are as follows:

[0014] The expressions of the bulk modulus matrix K and the shear modulus matrix μ of the cracked skeleton are constructed. The dimensionless coefficient α3 is introduced in this process, which is analogous to the Biot-Willis parameter. Among them, K d is the bulk modulus of dry rock skeleton, K s is the bulk modulus of rock particles, as shown in formula (1):

[0015]

[0016] Among them, the stiffness coefficient φ c is the microcrack porosity, K f is the bulk modulus of the fluid; μ3 is the shear modulus of the high-viscosity fluid; the coupling terms δK and δμ are the differences between the high-frequency and low-frequency limits of the rock skeleton modulus. δμ=μ3, representing the difference between undrained and drained elastic moduli; μ d is the shear modulus of the drainage rock skeleton; dimensionless coefficient K d is the bulk modulus of the drained rock skeleton, K h bulk modulus of drained rock skeleton under high pressure conditions;

[0017] The volume matrix η of the rock skeleton K and the shear viscosity matrix η μ , as shown in formula (2):

[0018]

[0019] Among them, η K3 and η μ3 is the volume of the solid skeleton containing cracks and the shear solid viscosity coefficient.

[0020] In the framework of generalized linear solid model, the nonlinear attenuation characteristics of strong viscous fluid V are considered. Δ、V ε , construct the Lagrangian energy density L and attenuation density function D, as shown in formula (3):

[0021]

[0022] in, u i is the deformation of the medium, Δ is the volume strain of the medium, is pure shear strain, the superscript T is the transpose symbol, and the other matrices are defined as follows:

[0023]

[0024] Where ρ is the density of the rock mass, ρ f is the pore fluid density, φ is the Biot porosity, a is the pore tortuosity, κ is the permeability, η f is the fluid viscosity coefficient, and M is the Biot modulus.

[0025] The Euler-Lagrange formula is used to transform Equation (3) to obtain the stress-strain constitutive equation, that is, the constitutive equation and frequency domain characteristic equation of the nonlinear viscoporous elastic medium. Assuming V Δ =V ε =V, then:

[0026]

[0027] In a homogeneous isotropic medium, after Fourier transform, the frequency domain characteristic equation (6) is obtained:

[0028] ρ * υ (n) =γ (n) M * υ (n) (6)

[0029] Among them, (n) Complex wave (n) , γ (n) is the corresponding eigenvalue, For P waves, For S waves,

[0030] Optionally, in step S4, the characteristic equation is solved to obtain the elastic wave dispersion curve V phase and attenuation curve Q -1 The predicted value is shown in formula (7):

[0031]

[0032] Optionally, in step S5, construct the measured value V of the elastic wave dispersion curve observe, measured value of attenuation curve and elastic wave dispersion curve predicted value V phase , attenuation curve prediction value Q -1 The error function between them is shown in formula (8):

[0033]

[0034] The beneficial effects of the present invention are:

[0035] 1. The invented method is based on standard and strict continuum mechanics principles and utilizes the fundamental inherent properties of rocks that do not change with time or frequency, resulting in great simplicity.

[0036] 2. The parameters involved in the model (including the inverted microfracture physical parameters) are all measurable macro-equivalent medium characteristics, compatible with arbitrary pore microstructures, and can describe seismic wave attenuation mechanisms at various scales, conforming to the characteristics of seismic wave exploration;

[0037] 3. This method has clear physical significance, describing a clear and explicit mechanism for seismic wave attenuation and dispersion. It also involves the inversion of rock microfracture porosity and nonlinear characteristic indices under varying temperature conditions. This method can be used to interpret broadband experimental observations of multi-pore seismic rock physics and can also be extended to reservoir pore structure prediction and the inversion of nonlinear characteristic indices. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Schematic diagram of the process of estimating the porosity and nonlinear characteristic index of rock microfractures at different temperatures according to the present invention;

[0039] Figure 2 This embodiment of the present invention provides a comparison of the Young's modulus dispersion and attenuation (points) measured in the laboratory for glycerol-saturated sandstone at different temperatures and the theoretical model prediction results (line); a) and d) are the attenuation curve and dispersion curve at 23°, respectively; b) and e) are the attenuation curve and dispersion curve at 31°, respectively; c) and f) are the attenuation curve and dispersion curve at 37.5°, respectively;

[0040] Figure 3 These are the curves of broadband P- and S-wave velocities and attenuation versus temperature for the glycerol-saturated sandstone predicted by the present invention; a) and d) are the broadband fast P-wave attenuation and dispersion diagrams calculated based on known and predicted model parameters, b) and e) are the slow P-wave attenuation and dispersion diagrams, and c) and f) are the shear wave attenuation and dispersion diagrams, respectively. DETAILED DESCRIPTION

[0041] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0042] A method for estimating the porosity and nonlinear characteristic index of rock microfractures at different temperatures, such as Figure 1 As shown, the following steps are included:

[0043] Step S1. Based on the rock physics experimental data of the seismic frequency band, the experimental data of Young's modulus dispersion and attenuation of sandstone saturated with glycerol at different temperatures are obtained as follows: Figure 2 Black dots in a)-f);

[0044] Step S2. constructing a frequency domain characteristic equation based on a nonlinear viscoelastic dual-poroelastic rock physics model;

[0045] In this optional embodiment, the secondary pores and viscous fluid fillings in the reservoir rock are taken into account, and a nonlinear index is introduced to describe the complex coupling behavior between the rock skeleton and the filling fluid, thereby constructing a porous medium that is more suitable for containing viscous fluids;

[0046] Optionally, the nonlinear viscoelastic dual-poroelastic rock physics model is constructed in the following steps:

[0047] In step S2, the nonlinear viscoelastic rock physics model is constructed in the following steps:

[0048] Construct expressions for the bulk modulus matrix K and shear modulus matrix μ of the cracked skeleton, analogous to the Biot-Willis parameters Among them, K d is the bulk modulus of dry rock skeleton, K s is the bulk modulus of rock particles, as shown in formula (1):

[0049]

[0050] Among them, the stiffness coefficient φ c is the microcrack porosity, K f is the bulk modulus of the fluid; μ3 is the shear modulus of the high-viscosity fluid; the coupling terms δK and δμ are the differences between the high-frequency and low-frequency limits of the rock skeleton modulus. δμ=μ3, representing the difference between undrained and drained elastic moduli; μ d is the shear modulus of the drainage rock skeleton; dimensionless coefficient K dis the bulk modulus of the drained rock skeleton, K h bulk modulus of drained rock skeleton under high pressure conditions;

[0051] The volume matrix η of the rock skeleton K and the shear viscosity matrix η μ , as shown in formula (2):

[0052]

[0053] Among them, η K3 and η μ3 is the volume of the solid skeleton containing cracks and the shear solid viscosity coefficient.

[0054] In the framework of generalized linear solid model, the nonlinear attenuation characteristics of strong viscous fluid V are considered. Δ 、V ε , construct the Lagrangian energy density L and attenuation density function D, as shown in formula (3):

[0055]

[0056] in, u i is the deformation of the medium, Δ is the volume strain of the medium, is pure shear strain, with the superscript T is the transpose symbol, and the other matrices are defined as follows:

[0057]

[0058] Where ρ is the density of the rock mass, ρ f is the pore fluid density, φ is the Biot porosity, a is the pore tortuosity, κ is the permeability, η f is the fluid viscosity coefficient, and M is the Biot modulus.

[0059] In formula (4), the method of this embodiment involves a total of 14 independent model parameters. The key parameters can be measured in standard experiments on porous rocks, reasonably estimated according to the Gassmann equation, or determined by empirical relationships. Under general experimental conditions, the model ultimately contains only five unknowns, namely, the microcrack porosity φ c , nonlinear index V, solid viscosity coefficient η K and shear viscosity η μ , and the difference between the high- and low-frequency limits of the rock skeleton shear modulus μ3. If the dispersion and attenuation specifically for the shear modulus are added, the number of unknown parameters can be reduced to four; similarly, continuing to add reasonable experimental data can further shorten the number of unknowns and improve the reliability of the inversion.

[0060] The Euler-Lagrange formula is used to transform Equation (3) to obtain the stress-strain constitutive equation, that is, the constitutive equation and frequency domain characteristic equation of the nonlinear viscoporous elastic medium. Assuming V Δ =V ε =V, then:

[0061]

[0062] In a homogeneous isotropic medium, after Fourier transform, the frequency domain characteristic equation (6) is obtained:

[0063] ρ * υ (n) =γ (n) M * v (n) (6)

[0064] Among them, v (n) Complex wave (n) , γ (n) is the corresponding eigenvalue, For P waves, For S waves,

[0065] Step S3. Substitute the known physical property parameters into the characteristic equation and set initial values ​​for the parameters to be inverted;

[0066] In this optional embodiment, the physical property parameters are inherent properties of the medium and have strict physical meanings. The present invention realizes for the first time the inversion of micro-cracks and nonlinear characteristic indices inside rocks using seismic bands;

[0067] Step S4. Solve the characteristic equation to obtain the elastic wave dispersion curve and attenuation curve, see Figure 2 a)-f) in black solid line;

[0068] In this optional embodiment, the characteristic equation is solved to obtain the elastic wave dispersion curve V phase and attenuation curve Q -1 The predicted value is shown in formula (7):

[0069]

[0070] Step S5. construct an error function between the elastic wave dispersion curve, the attenuation curve and the predicted value, and use a nonlinear optimization algorithm to invert and obtain the rock microcrack porosity and nonlinear characteristic index;

[0071] In this optional embodiment, the elastic wave dispersion curve measured value V is constructed observe , measured value of attenuation curve and elastic wave dispersion curve predicted value V phase , attenuation curve prediction value Q -1The error function between them is shown in formula (8):

[0072]

[0073] Step S6. Substitute the known physical parameters and inversion parameters into the frequency domain characteristic equation to broaden the simulation frequency range and obtain the wide-band P- and S-wave dispersion attenuation characteristics, which can further guide the exploration and development of ultra-deep high-temperature reservoir oil and gas. Figure 3 It can be seen that when the temperature is low (23°, Figure 3 Black line), the longitudinal and shear waves show a more complex attenuation dispersion feature in the seismic frequency band, which is related to the higher temperature (31°, 37.5°, Figure 3 This feature has positive significance in detecting heavy oil thermal recovery and geothermal recovery processes.

[0074] By using the frequency domain characteristic equation obtained in step S4 and the physical property parameter values ​​predicted in step S5, combined with known parameters, formula (6) or the broadband elastic wave velocity dispersion and attenuation characteristics are solved again in a wider frequency range to provide a theoretical tool for broadband field data.

[0075] In view of the complex pore structure and soft material filling in the pores under different temperature conditions, the present invention utilizes a newly established nonlinear attenuation viscoelastic model based on Lagrangian continuum mechanics to invert the temperature-dependent variation characteristics of microfracture porosity, nonlinear index, and other temperature-sensitive physical parameters from the stress-strain rock physics experimental data of variable-temperature saturated fluid in the seismic frequency band.

[0076] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A method for estimating the porosity and nonlinear characteristic index of rock microfractures at different temperatures, characterized by: The steps include: Step S1. Acquire experimental data on the dispersion and attenuation of elastic modulus of saturated porous rock as a function of frequency at different temperatures; Step S2. constructing a frequency domain characteristic equation based on a nonlinear viscoelastic dual-poroelastic rock physics model; Step S3. Substitute the known physical property parameters into the characteristic equation and set initial values ​​for the parameters to be inverted; Step S4. Solving the characteristic equation to obtain theoretical prediction results of the elastic wave dispersion curve and attenuation curve; Step S5. construct an error function between the elastic wave dispersion curve, attenuation curve experimental data and theoretical prediction results, perform iterative optimization step by step, and invert to obtain the rock microcrack porosity and nonlinear characteristic index; Step S6. Substitute the known physical parameters and the rock microcrack porosity and nonlinear characteristic index obtained in step S5 into the frequency domain characteristic equation to obtain the broadband longitudinal and transverse wave dispersion and attenuation characteristics.

2. The method for estimating the porosity and nonlinear characteristic index of rock microfractures at different temperatures according to claim 1, characterized in that: In step S2, the nonlinear viscoelastic rock physics model is constructed by the following steps: The expressions of the bulk modulus matrix K and the shear modulus matrix μ of the cracked skeleton are constructed as shown in formula (1): Among them, the stiffness coefficient φ c is the microcrack porosity, K f is the bulk modulus of the fluid; μ3 is the shear modulus of the high-viscosity fluid; the coupling terms δK and δμ are the differences between the high-frequency and low-frequency limits of the rock skeleton modulus. δμ=μ3, representing the difference between undrained and drained elastic moduli; μ d is the shear modulus of the drainage rock skeleton; dimensionless coefficient K d is the bulk modulus of the drained rock skeleton, K h bulk modulus of drained rock skeleton under high pressure conditions; The volume matrix η of the rock skeleton K and the shear viscosity matrix η μ , as shown in formula (2): Among them, η K3 and η μ3 is the volume of the solid skeleton containing cracks and the shear solid viscosity coefficient; In the framework of generalized linear solid model, the nonlinear attenuation characteristics of strong viscous fluid V are considered. Δ 、V ε , construct the Lagrangian energy density L and attenuation density function D, as shown in formula (3): in, u i is the deformation of the medium, Δ is the volume strain of the medium, is pure shear strain, with the superscript T is the transpose symbol, and the other matrices are defined as follows: Where ρ is the density of the rock mass, ρ f is the pore fluid density, φ is the Biot porosity, a is the pore tortuosity, κ is the permeability, η f is the fluid viscosity coefficient, and M is the Biot modulus.

3. The method for estimating the porosity and nonlinear characteristic index of rock microfractures at different temperatures according to claim 2, characterized in that: The Euler-Lagrange formula is used to transform Equation (3) to obtain the stress-strain constitutive equation. Assuming V Δ =V ε =V, then: In a homogeneous isotropic medium, after Fourier transform, the frequency domain characteristic equation (6) is obtained: r * u (n) =c (n) M * u (n) (6) Among them, (n) Complex wave (n) , γ (n) is the corresponding eigenvalue, For P waves, For S waves, 4. The method for estimating the porosity and nonlinear characteristic index of rock microfractures at different temperatures according to claim 1, characterized in that: In step S4, the characteristic equation is solved to obtain the elastic wave dispersion curve V phase and attenuation curve Q -1 The predicted value is shown in formula (7):

5. The method for estimating the porosity and nonlinear characteristic index of rock microfractures at different temperatures according to claim 1, characterized in that: In step S5, the elastic wave dispersion curve measured value V is constructed observe , measured value of attenuation curve and elastic wave dispersion curve predicted value V phase , attenuation curve prediction value Q -1 The error function between them is shown in formula (8):

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