A method for constructing a thermoelastic AVO response model for high-temperature media and the medium

Abstract

The present invention belongs to the field of seismic wave simulation, and specifically provides a method and medium for constructing a thermoelastic AVO response model of a high-temperature medium. The present invention aims to solve the problem that the simulation results of the traditional seismic wave AVO response model are inaccurate due to the normal temperature medium. The construction method includes the following steps: establishing a thermoelastic equation based on the hyperbolic LS thermoelastic theory; performing a plane wave analysis in the thermoelastic medium; establishing thermoelastic boundary conditions to obtain the Zoplitz equation in the thermoelastic medium; assuming that the medium parameters of the adjacent medium change slightly, expanding each term of the Zoplitz equation for thermoelastic AVO approximation; simulating the thermoelastic AVO seismic response; and analyzing the influence of formation parameters on the thermoelastic AVO seismic response. The present invention can accurately examine the influence of high temperature on the AVO seismic response, provide a theoretical basis for the expansion of deep and ultra-deep oil and gas exploration, and provide a reasonable explanation for the abnormal phenomenon of deep earth observation data.

Description

Technical Field

[0001] The invention belongs to the field of geophysical seismic exploration research, and specifically provides a method for constructing a high-temperature medium thermoelastic AVO response model and a medium. Background Art

[0002] AVO (Amplitude Versus Offset) technology occupies an important position in seismic exploration. This method is based on the law of variation of seismic reflection amplitude with offset distance, and then determines the lithological characteristics and physical parameters of the overlying and underlying media of the reflection interface. It is a powerful tool for oil and gas reservoir identification and reservoir parameter prediction.

[0003] With the gradual deepening of seismic exploration technology research, seismic exploration has gradually shifted from shallow normal temperature oil and gas reservoir exploration to deep high temperature oil and gas reservoir exploration. However, the traditional AVO response model is usually simplified based on the classical elastic wave theory, which does not consider the influence of deep reservoir high temperature conditions and thermophysical parameters on the model, and cannot fully describe and effectively utilize high temperature and thermophysical characteristic information.

[0004] The density, elastic modulus, wave velocity and other parameters of rocks are seriously affected by temperature, especially the thermoelastic parameters and deep complex fracture structures. Therefore, in actual deep and ultra-deep seismic exploration, the influence of temperature must be taken into account in order to more accurately obtain reservoir elasticity and physical property parameters. Summary of the invention

[0005] In order to solve the above problems in the prior art, that is, to solve the problem that the traditional AVO response model does not consider the temperature effect, resulting in inaccurate inversion of reservoir elasticity and physical property parameters, the present invention provides a method for constructing a high-temperature medium thermoelastic AVO response model and a storage medium.

[0006] The technical solution of the present invention provides a method for constructing a thermoelastic AVO response model of a high-temperature medium, comprising the following steps:

[0007] Establish the hyperbolic thermoelastic equation;

[0008] The hyperbolic thermoelastic equation is used to analyze the plane wave in the thermoelastic medium to obtain the propagation speed and attenuation of the wave in the thermoelastic medium;

[0009] Establish thermoelastic boundary conditions, accurately solve the reflection and transmission coefficient of the thermoelastic interface, and obtain the accurate expression of the reflection and transmission coefficient in the thermoelastic medium;

[0010] Assuming that the dielectric parameters of the adjacent media change little, the exact expression of the reflection and transmission coefficient is expanded and the thermoelastic AVO approximation is performed;

[0011] Thermoelastic AVO seismic response simulation;

[0012] Analyze the influence of formation parameters on the thermoelastic AVO seismic response.

[0013] Furthermore, the hyperbolic thermoelastic equation is formula (1):

[0014]

[0015] In the formula, u i (or u j )(i,j=x,y,z) represents the displacement component, T 0 is the reference temperature under stress-free and strain-free conditions, and T is relative to T 0 The temperature increment, ρ represents the volume density, λ and μ are the Lame coefficients, represents thermal conductivity, c represents specific heat under constant strain, thermal modulus in represents the coefficient of thermal expansion, τ represents the relaxation time, the dot above the symbol represents the time derivative, the number of dots represents the number of times the time derivative is taken, the subscripts (,i), (,j), (,ji), (,jj) (i,j=x,z) represent the partial derivative with respect to space, and the equation follows the Einstein summation convention.

[0016] Furthermore, the plane wave analysis in the thermoelastic medium using the hyperbolic thermoelastic equation is specifically based on Helmholtz decomposition, and the plane wave analysis in the thermoelastic medium using the hyperbolic thermoelastic equation is performed to obtain the propagation speed and attenuation of the wave in the thermoelastic medium.

[0017] Furthermore, the establishment of thermoelastic boundary conditions includes:

[0018] Considering a two-dimensional thermoelastic interface, the boundary conditions are set as radial displacement and stress continuity, tangential displacement and stress continuity, and temperature and heat flow continuity, as shown in formula (2):

[0019]

[0020] In the formula, u z and σ z denote radial displacement and stress respectively, u x and σ x denote tangential displacement and stress respectively, T denotes temperature, represents thermal conductivity, It represents the partial derivative of temperature with respect to z. The one without superscript represents medium I on the upper side of the thermoelastic interface, and the one with superscript ' represents medium II on the lower side. There is an angle between the propagation direction and the attenuation direction, which is the attenuation angle. When the attenuation angle is 0°, it is a uniform wave, otherwise it is a non-uniform wave.

[0021] Furthermore, the reflection transmission coefficient of the thermoelastic interface is accurately solved to obtain an accurate expression of the reflection transmission coefficient in the thermoelastic medium, which includes the following steps:

[0022] Based on the Helmholtz decomposition, consider the generalized Snell's law;

[0023] Assuming that the incident wave potential function has a general solution, the hyperbolic thermoelastic equation is used to establish the boundary equation according to the boundary conditions. The boundary equation is used to obtain the exact expression of the reflection and transmission coefficient in the thermoelastic medium, as shown in formula (3):

[0024] B·R=D (3)

[0025] In formula (3), B, R and D represent 6×6, 6×1 and 6×1 matrices respectively.

[0026] Furthermore, in step 4), a high-temperature medium thermoelastic AVO response model is constructed by approximating the precise reflection and transmission coefficient equation in the thermoelastic medium with a small elastic assumption, that is, the difference in parameters between the upper and lower layers of the medium is small.

[0027] Furthermore, assuming that the elastic parameters of the adjacent media change little, the exact expression of the reflection and transmission coefficient in the thermoelastic medium is expanded and ΔV is taken P , ΔV S The first-order approximation of Δρ and the thermoelastic AVO approximation formula (4) is obtained:

[0028]

[0029] In formula (4), R PP and T PP They represent the reflection and transmission coefficients of the fast longitudinal wave when the fast longitudinal wave is incident, sin 2 θ and cos 2 θ represents the sine and cosine square of the incident angle, V P and V S Respectively represent the average values ​​of the fast longitudinal and transverse wave velocities in the upper and lower layers, ρ represents the volume density, ΔV P , ΔV S and Δρ represent the fast longitudinal wave velocity difference, shear wave velocity difference and density difference between the upper and lower media, respectively.

[0030] Furthermore, the thermoelastic AVO seismic response simulation includes the following steps:

[0031] The AVO response model in thermoelastic medium is established by using the AVO approximate formula and the frequency domain convolution method of the source function.

[0032] The AVO response model parameters are set and the AVO simulated seismogram of the thermoelastic medium is obtained through Fourier transform.

[0033] Further, the influence of formation parameters on the thermoelastic AVO seismic response is analyzed, including:

[0034] By changing the formation medium parameters, the influence on the AVO simulated seismic map is analyzed.

[0035] Another aspect of the technical solution of the present invention further provides a computer-readable storage medium storing computer instructions, wherein the computer instructions are used to implement the method for constructing the high-temperature medium thermoelastic AVO response model when executed by a processor.

[0036] The present invention adopts the above technical solution, which has the following advantages:

[0037] By taking into account the thermal parameters of the formation and adding the influence of temperature, the effect of high temperature on the propagation of seismic waves can be accurately examined; the thermoelastic AVO approximation simplifies the exact solution, making its application more extensive; and a more accurate seismic response is obtained; compared with the traditional elastic AVO response, it is not only applicable to normal temperature formations, but also to high-temperature reservoirs (such as deep-ultra-deep formations, geothermal, etc.), providing a theoretical basis for the expansion of deep and ultra-deep oil and gas exploration, and providing a reasonable explanation for the abnormal phenomena in deep earth observation data. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A flowchart of the main steps of a method for constructing a thermoelastic AVO response model of a high-temperature medium according to the present invention;

[0039] Figure 2 It is the relationship diagram of phase velocity and attenuation coefficient and frequency of the present invention;

[0040] Figure 3 A schematic diagram of the present invention for performing inhomogeneous plane wave analysis in a thermoelastic medium;

[0041] Figure 4 A comparison diagram of the precise and approximate reflection and transmission coefficients in the thermoelastic medium of the present invention;

[0042] Figure 5 This is an AVO simulated seismogram in a thermoelastic medium of the present invention;

[0043] Figure 6 A comparison of simulated earthquakes in a thermoelastic medium at different temperatures. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0045] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only used to explain the technical principles of the present invention and are not intended to limit the protection scope of the present invention.

[0046] The heat conduction equation of thermoelastic materials derived from the basic laws of thermodynamics, constitutive relations and Helmholtz free energy expression contains strain rate in addition to the temperature field function to be determined. It shows that the temperature field on the object depends not only on the heat source and related thermodynamic physical parameters, but also on the elastic deformation strain rate. In other words, the volume strain rate of elastic deformation will change the heat transfer on the object to a certain extent. Therefore, the heat conduction equation and the thermoelastic motion equation need to be solved in a coupled manner.

[0047] like Figure 1 As shown, the implementation of the present invention provides a method for constructing a thermoelastic AVO response model of a high-temperature medium. Constructing the model requires the following steps:

[0048] 1) Based on the modified Fourier law of heat conduction, the hyperbolic LS (Lord-Shulman) thermoelastic equation is established by considering the coupling relationship between temperature and stress-strain;

[0049] 2) Based on the Helmholtz decomposition, the hyperbolic thermoelastic equation is used to perform plane wave analysis in thermoelastic media (elastic media that considers temperature and thermal parameters);

[0050] 3) Establish thermoelastic boundary conditions, accurately solve the reflection-transmission coefficient of the thermoelastic interface, and obtain the exact expression of the reflection-transmission coefficient in the thermoelastic medium, namely the Zoeppritz equation;

[0051] 4) Assuming that the medium parameters of the adjacent medium change little, the Zoplitz equation is expanded to perform the thermoelastic AVO approximation;

[0052] 5) Thermoelastic AVO seismic response simulation;

[0053] 6) Analyze the influence of formation parameters on the thermoelastic AVO seismic response.

[0054] In step 1), based on the modified Fourier heat conduction law, the coupling relationship between temperature and stress-strain is considered (Formula (1)):

[0055] σ ij =2μ∈ ij +δ ij (λ∈-γT) (1)

[0056] Where σ ij (i,j=x,y,z) and ∈ ij (i, j = x, y, z) are stress and strain components respectively, ∈ represents volume strain, and T is relative to T 0 Temperature increment, T 0 is the reference temperature under stress-free and strain-free conditions, λ and μ are Lame coefficients, γ represents thermal conductivity, and δ ij represents the Kronecker function, following the Einstein summation convention. Using the strain-displacement relationship (Formula (2)) and the momentum conservation equation (Formula (3)):

[0057] 2∈ ij =u i,j +u j,i (2)

[0058] In the formula, u i (or u j )(i,j=x,y,z) represents the displacement component, and the subscript (,j)((,i)) represents u i (or u j ) in the j (or i) direction, ∈ ij (i, j = x, y, z) are strain components, following the Einstein summation convention;

[0059] σ ij,j =ρü i +f i (3)

[0060] In the formula, σ ij (i, j = x, y, z) are stress components, and the subscript (, j) represents σ ij The partial derivative in the j direction, ρ represents the density, f i represents the body force component, (··) on the displacement component represents the second-order derivative with time, and the equation follows the Einstein summation convention;

[0061] Substituting the stress-strain relationship (Formula (1)) into the momentum conservation equation (Formula (3)), and using the strain-displacement relationship (Formula (2)), we can obtain the thermoelastic dynamic equation that characterizes the relationship between displacement and temperature: Establish the hyperbolic LS thermoelastic equation:

[0062]

[0063] In formula (4), u i (or u j )(i,j=x,y,z) represents the displacement component, T 0 is the reference temperature under stress-free and strain-free conditions, and T is relative to T 0 The temperature increment, ρ represents the volume density, λ and μ are the Lame coefficients, represents thermal conductivity, c represents specific heat under constant strain, thermal modulus in represents the thermal expansion coefficient, τ represents the relaxation time, the dot above the symbol represents the time derivative, the number of dots represents the number of times the time derivative is calculated, and the subscript (,i), (, j ),(, ji ),(, jj )(i,j=x,z) represents the partial derivative with respect to space, and the equation follows the Einstein summation convention.

[0064] In step 2), based on the Helmholtz decomposition, the LS thermoelastic equation is used to perform plane wave analysis, and the displacement vector u and the change of temperature T are expressed in the form of plane waves:

[0065]

[0066] Where ω is the angular frequency, t is the time, k is the complex wave number vector, x is the position vector, T 0 and U represents the amplitude, If the plane wave is a longitudinal wave, the direction of its displacement vector is consistent with the propagation direction, and the matrix about the complex wave number k is obtained:

[0067]

[0068] In the formula, the determinant of matrix A is 0, and then the phase velocity v is used ph The relationship between the complex wave number and the dispersion relation is obtained, such as Figure 2 As shown, using the plane wave analysis method, the phase velocity and attenuation of waves in thermoelastic media are obtained.

[0069] In the above preferred technical solution for accurately solving the reflection and transmission coefficient of the thermoelastic interface, the step 3) further comprises:

[0070] (a) Considering a two-dimensional thermoelastic interface, the boundary conditions are set as radial displacement and stress continuity, tangential displacement and stress continuity, and temperature and heat flow continuity, as shown in formula (7):

[0071]

[0072] In the formula, u z and σ zdenote radial displacement and stress respectively, u x and σ x denote tangential displacement and stress respectively, T denotes temperature, represents thermal conductivity, represents the partial derivative of temperature with respect to z. The one without superscript represents medium I on the upper side of the thermoelastic interface, and the one with superscript ′ represents medium II on the lower side, such as Figure 3 As shown, there is an angle between the propagation direction and the attenuation direction, which is the attenuation angle. When the attenuation angle is 0°, it is a uniform wave, otherwise it is a non-uniform wave.

[0073] (b) Based on the Helmholtz decomposition, consider the generalized Snell's law:

[0074]

[0075] In the formula, θ 0 represents the angle of incidence, angle θ m , phase velocity (v ph ) m (m=1,2,3 represent reflected fast longitudinal wave, thermal wave and shear wave respectively), angle θ′ m , phase velocity (V′ ph ) m (m=1, 2, 3 represent the transmission of fast longitudinal wave, thermal wave and transverse wave respectively).

[0076] (c) Assuming that the incident wave potential function has a general solution, the thermoelastic equation (Formula (4)) is used to establish the equation according to the boundary conditions (Formula (7)) to obtain the exact expression of the reflection transmission coefficient in the thermoelastic medium:

[0077]

[0078] In the formula, the specific expression is:

[0079]

[0080] Where p and q represent the horizontal and vertical wave numbers, respectively. The superscript ' represents the parameters in medium II, otherwise it represents the parameters in medium I. The subscripts 0, 1, 2, and 3 correspond to the incident wave, fast longitudinal wave, thermal wave, and transverse wave, respectively.

[0081]

[0082] The six values ​​represent the reflection coefficients of reflected longitudinal waves, thermal waves, transverse waves, transmitted longitudinal waves, thermal waves and transverse waves. Figure 4 As shown, using formula (9), the relationship between the incident angle and the exact reflection and transmission coefficients is obtained by programming. The parameters in the upper medium are: absolute temperature T 0 =330K, volume density ρ = 2425Kg / m3 , reference speed V 0 =3757m / s, shear wave velocity V S =2390m / s, specific heat c = 0.9kJ / (kg·K), thermal conductivity κ = 2.9W / (m·K), thermal expansion coefficient α = 3.3×10 -16 K -1 , the parameters in the lower medium are: T 0 =350K,ρ=2475Kg / m 3 , V 0 =3898m / s, V S =2666m / s, c=0.92kJ / (kg·K), κ=3.0W / (m·K), α=3.28×10 -16 K -1 ;

[0083] Step 4) By approximating the precise reflection and transmission coefficient equation in the thermoelastic medium with the small elastic assumption, that is, the difference in the parameters of the upper and lower layers of the medium is small, a thermoelastic AVO response model for high-temperature medium is constructed. Further comprising:

[0084] Assuming that the elastic parameters of the adjacent media change little, expand the thermoelastic Zoplitz equation obtained in the previous step and take ΔV P , ΔV S The first-order approximation of Δρ gives the thermoelastic AVO approximation formula:

[0085]

[0086] In the formula, R PP and T PP They represent the reflection and transmission coefficients of the fast longitudinal wave when the fast longitudinal wave is incident, sin 2 θ and cos 2 θ represents the sine and cosine square of the incident angle, V P and V S Respectively represent the average values ​​of the fast longitudinal and transverse wave velocities in the upper and lower layers, ρ represents the volume density, ΔV P , ΔV S and Δρ represent the fast P-wave velocity difference, S-wave velocity difference and density difference between the upper and lower layers, respectively. Figure 4 As shown, using formula (12), the relationship between the incident angle and the approximate reflection and transmission coefficients is obtained by programming, where the parameters used in the example are consistent with the parameters mentioned in step 3).

[0087] like Figure 5 As shown, the reflection and transmission coefficients of the thermoelastic approximation in formula (12) are convolved with the Ricker wavelet to obtain a synthetic seismic record. The step 5) includes:

[0088] (a) The AVO response model in thermoelastic media is established by using the AVO approximate formula and the frequency domain convolution method of the source function;

[0089] (b) Set the AVO response model parameters, use the Ricker wavelet with a main frequency of 75 Hz as the source, and the distance between the interface and the receiver is 100 m. The AVO simulated seismogram of the thermoelastic medium is obtained by Fourier transform. The physical parameters used are the same as Figure 4 Consistent.

[0090] like Figure 6 As shown in the figure, the temperature of the lower layer medium is changed to 350K, 400K and 450K respectively, and the synthetic seismic record is obtained by convolution with Ricker wavelet using formula (4). The other parameters are Figure 4 Consistent, step 6) includes:

[0091] By changing the formation medium parameters, the influence on the AVO simulated seismic map is analyzed.

[0092] So far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. A method for constructing a thermoelastic AVO response model of a high-temperature medium, characterized in that: The following steps are involved: Establish the hyperbolic thermoelastic equation; The hyperbolic thermoelastic equation is used to analyze the plane wave in the thermoelastic medium, and the phase velocity and attenuation of the wave in the thermoelastic medium are obtained; Establishing thermoelastic boundary conditions, and using the hyperbolic thermoelastic equation to obtain an accurate expression of the reflection and transmission coefficient in the thermoelastic medium according to the boundary conditions and the phase velocity and attenuation; Assuming that the dielectric parameters of the adjacent media change little, the exact expression of the reflection and transmission coefficient is expanded and the thermoelastic AVO approximation is performed; Thermoelastic AVO seismic response simulation; Analyze the influence of formation parameters on the thermoelastic AVO seismic response; The hyperbolic thermoelastic equation is formula (1): In the formula, u i or j represents the displacement component, i, j = x, y, z, T0 is the reference temperature under stress-free and strain-free state, T is the temperature increment relative to T0, ρ represents the volume density, λ, μ are the Lame coefficients, represents thermal conductivity, c represents specific heat under constant strain, thermal modulus in represents the thermal expansion coefficient, τ represents the relaxation time, the dot above the symbol represents the time derivative, the number of dots represents the number of times the time derivative is calculated, and the subscript (, i ),(, j ),(, ji ),(, jj )(i, j = x, z) represents the partial derivative with respect to space, and the equation follows the Einstein summation convention; The plane wave analysis in the thermoelastic medium is performed by using the hyperbolic thermoelastic equation based on Helmholtz decomposition, and the propagation speed and attenuation of the wave in the thermoelastic medium are obtained; Establishing thermoelastic boundary conditions includes: Considering a two-dimensional thermoelastic interface, the boundary conditions are set as radial displacement and stress continuity, tangential displacement and stress continuity, and temperature and heat flow continuity, as shown in formula (2): In the formula, u z and σ z denote radial displacement and stress respectively, u x and σ x denote tangential displacement and stress respectively, T denotes temperature, represents thermal conductivity, represents the partial derivative of temperature with respect to z. The one without superscript represents medium I on the upper side of the thermoelastic interface, and the one with superscript ' represents medium II on the lower side. There is an angle between the propagation direction and the attenuation direction, which is the attenuation angle. When the attenuation angle is 0°, it is a uniform wave, otherwise it is a non-uniform wave. The precise solution of the reflection transmission coefficient of the thermoelastic interface and the accurate expression of the reflection transmission coefficient in the thermoelastic medium include the following steps: Based on the Helmholtz decomposition, consider the generalized Snell's law; Assuming that the incident wave potential function has a general solution, the hyperbolic thermoelastic equation is used to establish a boundary equation according to the boundary conditions, and the boundary equation is used to obtain the exact expression of the reflection and transmission coefficient in the thermoelastic medium, as shown in formula (3): B·R=D (3) In formula (3), B, R and D represent 6×6, 6×1 and 6×1 matrices respectively; Analysis of the influence of formation parameters on the thermoelastic AVO seismic response includes: By changing the formation medium parameters, the influence on the AVO simulated seismic map is analyzed.

2. The method for constructing the high temperature medium thermoelastic AVO response model according to claim 1, characterized in that: The step of performing thermoelastic AVO approximation by expanding the precise expression of the reflection transmission coefficient under the assumption that the medium parameters of the adjacent medium change little constructs a thermoelastic AVO response model for high-temperature media by making a small elastic assumption approximation to the precise reflection transmission coefficient equation in the thermoelastic medium, that is, the difference in the parameters of the upper and lower layers of the medium is small.

3. The method for constructing the high temperature medium thermoelastic AVO response model according to claim 2, characterized in that: Assuming that the elastic parameters of the adjacent media change little, the exact expression of the reflection and transmission coefficient in the thermoelastic medium is expanded, and ΔV is taken P , ΔV S The first-order approximation of Δρ and the thermoelastic AVO approximation formula (4) is obtained: In formula (4), R PP and T PP They represent the reflection and transmission coefficients of the fast longitudinal wave when the fast longitudinal wave is incident, sin 2 θ and cos 2 θ represents the sine and cosine square of the incident angle, V P and V S Respectively represent the average values ​​of the fast longitudinal and transverse wave velocities in the upper and lower layers, ρ represents the volume density, ΔV P , ΔV S and Δρ represent the fast longitudinal wave velocity difference, shear wave velocity difference and density difference between the upper and lower media, respectively.

4. The method for constructing a thermoelastic AVO response model of a high temperature medium according to claim 1, characterized in that: Thermoelastic AVO seismic response simulation includes the following steps: The AVO response model in thermoelastic medium is established by using the AVO approximate formula and the frequency domain convolution method of the source function. The AVO response model parameters are set, and the AVO response model in the thermoelastic medium is transformed by Fourier transform to obtain the AVO simulated seismic map of the thermoelastic medium.

5. A computer-readable storage medium, characterized in that: Computer instructions are stored, and the computer instructions are used to implement the method for constructing the high-temperature medium thermoelastic AVO response model according to any one of claims 1 to 4 when executed by a processor.

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