Method and device for predicting wave propagation characteristics of compact oil and gas reservoir

Abstract

The invention provides a wave propagation characteristic prediction method and prediction device for a compact oil and gas reservoir, and the method comprises the steps: enabling a pore fluid in a compact oil and gas reservoir medium to be equivalent to a power law fluid, and obtaining a dissipation function of a fluid-pore-containing dual-phase medium for a non-Darcy flow seepage mechanism; standard linear body form popularization and fractional order derivative introduction are carried out on the three-dimensional isotropic body constitutive relation, and a system generalized force expression based on a fractional order viscoelastic mechanism is obtained; and finally, according to the combination of a dissipative function, a system generalized force expression and a Biot kinetic energy function with an Euler-Lagrange equation, obtaining a unified wave propagation model which aims at a tight oil and gas reservoir medium and simultaneously contains a non-darcy flow and a fractional order viscoelastic mechanism. According to the method, the propagation rule of the waves in the tight oil and gas reservoir medium can be finely described, and the accuracy of predicting the propagation characteristics of the waves and the accuracy of oil and gas reservoir medium parameter inversion calculation are improved.

Description

Technical Field

[0001] The present application relates to the technical field of oil and gas seismic exploration, and in particular to a method and device for predicting wave propagation characteristics of tight oil and gas reservoirs. Background Art

[0002] The exploration and development of tight oil and gas reservoirs is of great significance to promoting economic and technological progress and energy transformation. Studying the propagation laws of seismic waves in underground porous media and establishing a unified propagation model can effectively promote the understanding of underground media and realize the refined exploration and development of tight oil and gas reservoirs.

[0003] Tight oil and gas reservoirs generally have the characteristics of low porosity (<10%) and low permeability (<1mD), narrow pore throats and poor connectivity, which makes the pore fluid seepage not obey Darcy's law and does not meet the basic assumptions of the conventional wave propagation model (wave propagation characteristics established by Biot theory). The existence of non-Darcy flow seepage mechanism is contrary to the assumption of Darcy flow seepage mechanism of conventional wave propagation model, which will cause the effectiveness of conventional wave propagation model to deteriorate. Many existing experimental results have also confirmed the existence of non-Darcy flow seepage mechanism in tight oil and gas reservoirs. Therefore, it is urgent to establish a wave propagation characteristic prediction method and prediction device for tight oil and gas reservoirs to accurately characterize the propagation law of seismic waves in tight oil and gas reservoir media. Summary of the invention

[0004] The present application aims to solve one of the technical problems in the related art at least to some extent.

[0005] To this end, the first purpose of the present application is to propose a method and device for predicting wave propagation characteristics of tight oil and gas reservoirs, which can provide a unified wave propagation model that simultaneously includes non-Darcy flow seepage mechanism and fractional-order viscoelastic mechanism, so as to finely characterize the propagation law of waves in tight oil and gas reservoir media, improve the accuracy of predicting wave propagation characteristics, and the accuracy of inversion calculation of oil and gas reservoir medium parameters.

[0006] To achieve the above-mentioned purpose, the first embodiment of the present application proposes a method for predicting wave propagation characteristics of tight oil and gas reservoirs, comprising: The pore fluid in the tight oil and gas reservoir medium is equivalent to a power-law fluid, and based on the constitutive relation of the power-law fluid, the dissipation function of the fluid-containing porous two-phase medium for the non-Darcy flow mechanism is obtained. The constitutive relation of three-dimensional isotropic body is generalized into standard linear body form and fractional derivatives are introduced. Combined with the constitutive relation of Biot porous two-phase medium, the generalized force expression of the system based on fractional viscoelastic mechanism is obtained. According to the dissipation function, the system generalized force expression and the Biot kinetic energy function, combined with the Euler-Lagrange equation, a unified wave propagation model expression of tight oil and gas reservoir media including non-Darcy flow and fractional viscoelastic mechanism is obtained.

[0007] Optionally, the step of obtaining the dissipation function of the fluid-containing porous two-phase medium for the non-Darcy flow seepage mechanism according to the power-law fluid constitutive relation comprises: Obtain medium parameters of tight oil and gas reservoir medium; The constitutive relation expression of power-law fluid is combined with the Navier-Stokes equation expression of three-dimensional viscous incompressible fluid to obtain the seepage equation expression of power-law fluid. According to the power-law fluid seepage equation expression, an expression of the friction force of the fluid on a unit volume element is obtained; The dissipation coefficient expression is obtained according to the equivalent relationship between the friction force expression of the fluid per unit volume element and the dissipation coefficient.

[0008] Optionally, the medium parameters of the tight oil and gas reservoir medium include porosity, permeability, pore fluid viscosity coefficient, rock mineral density, solid-fluid two-phase coupling density, pore fluid bulk modulus, rock skeleton bulk modulus and rock mineral bulk modulus.

[0009] Optionally, the dissipation function D satisfy:

[0010] in, is the power-law fluid index, is the fluid viscosity, is the permeability, is the porosity, is the solid phase displacement tensor, is the flow phase displacement tensor.

[0011] Optionally, the step of generalizing the three-dimensional isotropic body constitutive relation in a standard linear body form and introducing fractional derivatives, and combining it with the Biot porous two-phase medium constitutive relation to obtain a system generalized force expression based on a fractional viscoelastic mechanism includes: The three-dimensional isotropic body constitutive relation is generalized to a standard linear body form and fractional derivatives are introduced to obtain a three-dimensional isotropic body constitutive relation based on a fractional viscoelastic mechanism; The three-dimensional isotropic body constitutive relation based on the fractional-order viscoelastic mechanism is combined with the Biot porous two-phase medium constitutive relation to obtain the system generalized force expression based on the fractional-order viscoelastic mechanism.

[0012] Optionally, the three-dimensional isotropic body constitutive relation based on the fractional viscoelastic mechanism satisfies:

[0013] in, Represents the stress tensor of an object The weight, is the stress spherical tensor; Represents the strain tensor of the object The weight, is the strain spherical tensor Represents the stress deviator of an object The amount, Represents the object strain deviator The weight, is the relaxation time of the viscoelastic mechanism, is the bulk modulus of the medium, is the shear modulus of the medium.

[0014] Optionally, the Biot porous two-phase medium constitutive relation includes a solid-phase stress expression and a fluid-phase stress expression, and combining the three-dimensional isotropic body constitutive relation based on the fractional-order viscoelastic mechanism with the Biot porous two-phase medium constitutive relation includes combining the three-dimensional isotropic body constitutive relation based on the fractional-order viscoelastic mechanism with the solid-phase stress expression.

[0015] Optionally, the system generalized force expression based on the fractional-order viscoelastic mechanism satisfies:

[0016] in, is the solid phase stress tensor, is the solid skeleton viscoelastic matrix, is the solid skeleton body strain, is the flow response force tensor, is the fluid body strain, is the pore fluid pressure, I is the second-order unit tensor, is the Biot-Willis coefficient, is the Biot fluid storage coefficient; and is the relaxation function.

[0017] Optionally, the wave propagation model expression satisfies:

[0018] in, is the power-law fluid index, is the fluid viscosity, is the permeability, is the porosity, is the solid phase displacement tensor, is the flow phase displacement tensor, , , Respectively meet:

[0019] in, is the rock mineral density, is the pore fluid density, is the solid-fluid two-phase coupling density.

[0020] To achieve the above-mentioned purpose, the second embodiment of the present application proposes a device for predicting wave propagation characteristics of tight oil and gas reservoirs, comprising: A dissipation function determination module, which is used to equate the pore fluid in the tight oil and gas reservoir medium to a power-law fluid, and obtain a dissipation function of a fluid-containing pore two-phase medium for a non-Darcy flow seepage mechanism based on a constitutive relationship of the power-law fluid; A system generalized force determination module, which is used to generalize the three-dimensional isotropic body constitutive relation to a standard linear body form and introduce fractional derivatives, and combine it with the Biot porous two-phase medium constitutive relation to determine the system generalized force based on the fractional viscoelastic mechanism; A wave propagation model construction module is used to construct a unified wave propagation model of tight oil and gas reservoir media that includes non-Darcy flow and fractional viscoelastic mechanisms based on the dissipation function, the system generalized force and the Biot kinetic energy function, and in combination with the Euler-Lagrange equation.

[0021] The wave propagation characteristics prediction method and prediction device of tight oil and gas reservoirs provided by the present application have at least the following beneficial effects: The present application provides a method and device for predicting wave propagation characteristics of tight oil and gas reservoirs, including treating the pore fluid in the tight oil and gas reservoir medium as equivalent to a power-law fluid, and obtaining the dissipation function of the fluid-containing porous two-phase medium for the non-Darcy flow seepage mechanism; generalizing the three-dimensional isotropic body constitutive relation to the standard linear body form and introducing fractional derivatives, and obtaining the system generalized force expression based on the fractional viscoelastic mechanism; finally, according to the dissipation function, the system generalized force expression and the Biot kinetic energy function combined with the Euler-Lagrange equation, a unified wave propagation model for the tight oil and gas reservoir medium and including both non-Darcy flow and fractional viscoelastic mechanisms is obtained. The present application can accurately characterize the propagation law of waves in tight oil and gas reservoir media, improve the accuracy of predicting wave propagation characteristics, and the accuracy of inversion calculation of oil and gas reservoir medium parameters, realize the effective prediction of wave dispersion and dissipation attenuation of multi-scale frequencies, and provide theoretical guidance for the precise exploration and development of complex oil and gas reservoir media.

[0022] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which: Figure 1 It is a flow chart of a method for predicting wave propagation characteristics of tight oil and gas reservoirs according to an embodiment of the present application.

[0024] Figure 2a It is a schematic diagram of the relationship between the wave propagation model, the Biot wave propagation model and the actually measured S-wave velocity and frequency according to the first core sample in the embodiment of the present application.

[0025] Figure 2b It is a schematic diagram of the relationship between the wave propagation model, the Biot wave propagation model and the actually measured P-wave velocity and frequency according to the first core sample in the embodiment of the present application.

[0026] Figure 3a It is a schematic diagram of the relationship between the wave propagation model, the Biot wave propagation model and the actually measured S-wave velocity and frequency shown in the embodiment of the present application based on the second core sample.

[0027] Figure 3b It is a schematic diagram of the relationship between the wave propagation model, the Biot wave propagation model and the actually measured P-wave velocity and frequency shown in the embodiment of the present application based on the second core sample.

[0028] Figure 4aIt is a schematic diagram of the relationship between the wave propagation model, the Biot wave propagation model and the actually measured S-wave velocity and frequency shown in the embodiment of the present application based on the third core sample.

[0029] Figure 4b It is a schematic diagram of the relationship between the wave propagation model, the Biot wave propagation model and the actually measured P-wave velocity and frequency according to the third core sample in the embodiment of the present application.

[0030] Figure 5a It is a schematic diagram of the relationship between the wave propagation model, the Biot wave propagation model and the actually measured S-wave velocity and frequency according to the fourth core sample in the embodiment of the present application.

[0031] Figure 5b It is a schematic diagram of the relationship between the wave propagation model, the Biot wave propagation model and the actually measured P-wave velocity and frequency according to the fourth core sample in the embodiment of the present application. DETAILED DESCRIPTION

[0032] Embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0033] As one of the most important energy sources for human society, the exploration and development of oil and gas resources has always been a hot topic. It is a common method to use the seismic wave signals received by seismic stations containing underground geological structure information to infer reservoir distribution. Therefore, it is very important to establish a mathematical and physical model that can accurately describe the propagation law of seismic waves in complex oil and gas reservoirs. It is also an important basis for reservoir parameter inversion and oil and gas reservoir structure and distribution prediction. The most common wave propagation model is the elastic wave model, which is based on the assumption that the medium is an ideal elastic body. However, the actual oil and gas reservoir is a multiphase mixture. Its strong heterogeneity and the interaction between the phases of matter lead to complex mechanical mechanisms. Therefore, the single-phase elastic wave model is not suitable for the prediction of oil and gas reservoirs.

[0034] Biot considered the dynamic coupling mechanism of the solid-fluid two-phase in the fluid-containing porous medium, and first established the wave propagation model in the isotropic porous medium, laying the theoretical foundation for the wave propagation model in the multiphase medium. However, the energy dissipation in the Biot theory only considers the friction dissipation caused by the macroscopic relative displacement between the solid and fluid phases, and does not consider the internal dissipation of the solid and fluid phases themselves, which often underestimates the energy attenuation of the wave. On the other hand, for unconventional oil and gas reservoirs, their porosity is usually less than 10%, and their permeability is less than 0.1mD; the pore diameter is generally less than 1 micron, belonging to the micron-nanoscale pores, and the throat is narrow; the connectivity is poor and the heterogeneity is strong. This leads to the assumption that the fluid in the pore of the Biot theory will undergo viscous laminar flow no longer holds. Therefore, it is necessary to modify the traditional Biot theory so that it can accurately describe the propagation law of waves in complex oil and gas reservoirs.

[0035] Existing studies have shown that, in addition to a part of the fluid in the tight oil and gas reservoir medium that satisfies the non-Darcy flow seepage mechanism and can effectively seep, another part of the fluid will be trapped in the solid skeleton with poor connectivity, forming a solid "new skeleton" with the solid skeleton. When the wave passes through this part of the medium, internal friction dissipation will be generated. The viscoelastic mechanism can effectively characterize the energy dissipation caused by the situation of such solid "new skeleton". The applicant believes that further introducing the fractional derivatives defined by Caputo into the viscoelastic mechanism to form a new fractional viscoelastic mechanism can effectively improve the prediction accuracy of the wave propagation model. Therefore, based on the assumption that the seepage of porous fluids obeys the non-Darcy flow seepage mechanism, this application introduces fractional derivatives into the viscoelastic mechanism, and proposes a unified wave propagation model that includes both the non-Darcy flow seepage mechanism and the fractional viscoelastic mechanism, so as to finely characterize the propagation law of waves in the tight oil and gas reservoir medium, improve the accuracy of predicting wave propagation characteristics, and the accuracy of inversion calculation of oil and gas reservoir medium parameters.

[0036] The first embodiment of the present application provides a method for predicting wave propagation characteristics of a tight oil and gas reservoir. The method flow is as follows: Figure 1 As shown, the specific steps include the following steps.

[0037] First, step S1 is performed to treat the pore fluid in the tight oil and gas reservoir medium as equivalent to a power-law fluid, and based on the constitutive relationship of the power-law fluid, a dissipation function of the fluid-containing porous two-phase medium for the non-Darcy flow seepage mechanism is obtained.

[0038] The medium of tight oil and gas reservoirs is a common space occupied by multiphase substances, and is also a combination of multiphase substances coexisting. The part of the space without a solid skeleton is called pores, which are jointly occupied by liquid or gas or gas-liquid phases, and use the solid phase as the solid skeleton. Some of the pores that constitute the pore space are interconnected.

[0039] Before calculating and obtaining the dissipation function of the fluid-containing porous two-phase medium, the method further includes obtaining medium parameters of the tight oil and gas reservoir medium to facilitate the derivation and calculation of the dissipation function. The medium parameters of the tight oil and gas reservoir medium include at least porosity, permeability, rock mineral density, solid-fluid two-phase coupling density, pore fluid viscosity coefficient, pore fluid bulk modulus, rock skeleton bulk modulus, and rock mineral bulk modulus.

[0040] Among them, porosity refers to the ratio of the sum of the volumes of all pore spaces in the rock to the volume of the rock sample, expressed as a percentage. The larger the porosity of the rock, the larger the pore space in the rock. Permeability refers to the ability of rock to allow fluid to pass through under a certain pressure difference. It is a parameter that characterizes the ability of soil or rock itself to conduct liquid. Rock mineral density is the density of mineral particles. The solid-fluid two-phase coupling density refers to the coupling density between the solid phase part (i.e., the rock skeleton) and the fluid phase part (i.e., the pore fluid) in the porous medium. The viscosity coefficient of the pore fluid, also known as the viscosity coefficient, is a physical quantity that describes the viscosity (viscosity) properties of the liquid. Bulk modulus is a type of elastic modulus. It is a physical quantity used to reflect the macroscopic properties of the material, that is, the relationship between the body strain of an object and the average stress (the average of the three principal stresses at a certain point).

[0041] The difference between rock skeleton and rock minerals is that rock skeleton includes not only rock minerals, but also multiple pores, which may contain fluids. Pores refer to the spaces between particles, within particles, and within fillings in rocks. Pore fluids can be water, oil, or Cannon standard viscous fluids. As long as the fluid is located in the pores of the rock skeleton, it can be regarded as pore fluid.

[0042] As an example, the porous medium to be tested may be rock samples collected from different locations of gas fields in different regions, or rock samples collected in water. The rock sample may be a dense sandstone core with a porosity of 9.39%, a permeability of 0.280 mD, and a mineral density of 2664.2 kg / m 3 The rock sample can also be a dense dolomite core with a porosity of 8.55%, a permeability of 0.118mD, and a mineral density of 2894.9kg / m 3 The rock sample can also be Lower-Miocene sandstone collected in water, whose skeleton minerals are mainly quartz, with a porosity of 20.9%, a permeability of 115mD, and a mineral density of 2650kg / m 3 The values ​​of the porosity, permeability and mineral density of the aforementioned rock samples are merely examples of some medium parameters, and the embodiments of the present invention do not specifically limit the various medium parameters of the porous medium.

[0043] Due to the low porosity and low permeability characteristics of tight oil and gas reservoir media, the flow of pore fluids in pores no longer obeys the linear Darcy's law, that is, the fluid shear stress and shear strain rate are nonlinear. Therefore, the pore fluids in tight oil and gas reservoir media can be equivalently regarded as power-law fluids, and based on the stress-strain constitutive relationship of pore fluids in three-dimensional situations and the three-dimensional viscous incompressible fluid Navier-Stokes equation, the power-law fluid seepage equation is obtained using the average volume method under the condition of considering isotropy and ignoring the influence of gravity.

[0044] The stress-strain constitutive relation of pore fluid in three-dimensional situation satisfies: (1) in, is the fluid stress, is the fluid strain rate, is the equivalent viscosity coefficient, which can be approximated as the fluid viscosity , is the power-law fluid index, and the power-law fluid index Used to characterize fluid flowability. It is characterized as a shear-thinning fluid when It is characterized as a shear thickening fluid.

[0045] Fluid strain rate And also satisfied: , (2) in, is the fluid velocity. The Navier-Stokes equations for three-dimensional viscous incompressible fluid are: (3) in, is the fluid pressure gradient, is the fluid density, is the acceleration due to gravity.

[0046] Therefore, under the condition of considering isotropy and ignoring the influence of gravity, the expression (2) is substituted into the expression (1), and then the power-law fluid seepage equation is obtained by using the average volume method, and the power-law fluid seepage equation expression satisfies: (4) in, It represents the average value of the physical quantity in the representative volume element. is the porosity; is the equivalent permeability, which can be approximated as the permeability in this embodiment , is the fluid velocity. In the above expressions, the absolute value of the physical quantity is considered to represent only the size of the physical quantity and has no dimension.

[0047] Therefore, based on expression (4), the friction force expression of the fluid on the representative volume element (RVE) can be obtained: (5) in, is the friction force on the fluid, is the solid phase displacement tensor, is the flow phase displacement tensor.

[0048] The friction force on the fluid can also be expressed by the dissipation function It is derived that the dissipation function Friction force on the fluid The equivalence relationship between them satisfies: (6) Thus, the dissipation function of the fluid-containing porous two-phase medium based on the non-Darcy flow mechanism can be obtained on the representative volume element: The expression is: (7) Then, step S2 is executed to generalize the three-dimensional isotropic body constitutive relation to the standard linear body form and introduce fractional derivatives, and combined with the Biot porous two-phase medium constitutive relation, the system generalized force expression based on the fractional viscoelastic mechanism is obtained.

[0049] In the viscoelastic mechanism, the stress and strain state of an object at the current moment is related to its historical state, which makes the viscoelastic mechanism better describe the energy dissipation caused by the friction mechanism within the solid skeleton. By introducing fractional-order derivatives into the standard linear body model, using the fractional-order viscoelastic mechanism to describe the friction energy dissipation within the solid skeleton, and forming a new fractional-order viscoelastic mechanism, it is more conducive to accurately describe the energy dissipation caused by the friction mechanism within the solid skeleton.

[0050] By generalizing the three-dimensional isotropic body constitutive relation to the standard linear body form and introducing fractional derivatives, the three-dimensional isotropic body constitutive relation based on the fractional viscoelastic mechanism can be obtained. Among them, the fractional derivative is defined by Caputo integral, and the resulting three-dimensional isotropic body stress-strain constitutive relation based on the fractional viscoelastic mechanism satisfies: , (8) in, Represents the stress tensor of an object The weight, is the stress spherical tensor; Represents the strain tensor of the object The weight, is the strain spherical tensor Represents the stress deviator of an object The amount, Represents the object strain deviator The weight, is the relaxation time of the viscoelastic mechanism, is the bulk modulus of the medium, is the shear modulus of the medium.

[0051] In order to conveniently write the three-dimensional isotropic stress-strain constitutive relation based on the fractional viscoelastic mechanism into a vector form, two new relaxation functions can be defined and introduced: , and the equivalent relationship between expression (8) and the relaxation function convolution satisfies: (9) Among them, * represents function convolution.

[0052] Therefore, the relaxation function can be obtained according to expressions (8) and (9): The specific expression in the time domain satisfies: (10) in, , , , All are Mittag-Leffler functions.

[0053] Therefore, according to expression (10), expression (8) can be expressed by a relaxation function, which satisfies: , (11) in, are the components of the stress tensor, are the components of the strain tensor, is the Kronecker Delta function.

[0054] Therefore, by combining the three-dimensional isotropic body constitutive relation based on the fractional viscoelastic mechanism with the Biot porous two-phase medium constitutive relation, the generalized force expression of the system based on the fractional viscoelastic mechanism can be obtained.

[0055] The constitutive relation of Biot porous two-phase medium includes the solid-phase stress expression and the flow-phase stress expression, and the solid-phase stress expression and the flow-phase stress expression satisfy: ,(12) in, is the solid phase stress tensor, is the solid skeleton body strain, is the flow response force tensor, is the fluid body strain, is the pore fluid pressure, is the second-order unit tensor, is the Biot-Willis coefficient, is the Biot fluid storage coefficient, Used to describe the viscoelastic properties of solid skeletons, it satisfies the following after the introduction of fractional viscoelastic mechanism: (13) Therefore, after introducing the fractional viscoelastic mechanism, Substituting into the constitutive relation of the Biot porous two-phase medium and combining it with the generalized force balance equation, the generalized force expression based on the fractional-order viscoelastic mechanism can be obtained. In essence, it is the generalized force expression after the introduction of the fractional-order viscoelastic mechanism. Substitute into the solid phase stress expression.

[0056] Therefore, by substituting expression (13) into expression (12) and combining it with the generalized force balance equation, we can obtain the generalized force expression based on the fractional viscoelastic mechanism, which satisfies: (14) in, is the generalized force on the solid phase, The generalized force acting on the flow phase.

[0057] Finally, step S3 is executed again to obtain the unified wave propagation model expression of tight oil and gas reservoir media including non-Darcy flow and fractional viscoelastic mechanism based on the dissipation function, the system generalized force expression and the Biot kinetic energy function, combined with the Euler-Lagrange equation.

[0058] Biot kinetic energy function T The expression satisfies: (15) This expression uses the Einstein summation convention, where , is the rock mineral density, is the pore fluid density, is the solid-fluid two-phase coupling density.

[0059] The Euler-Lagrange equation with dissipation function satisfies: , (16) in, are generalized coordinates, which can be used to represent the solid phase displacement tensor in this application. and the flow phase displacement tensor is a generalized force, which can be used to represent the generalized force on the solid phase in this application. The generalized force on the flow phase .

[0060] Therefore, by substituting expressions (7) and (15) into expression (16) and combining them with expression (14), we can obtain a unified wave propagation model expression that includes both non-Darcy flow and fractional viscoelastic mechanisms, and the expression satisfies: (17) Therefore, based on expression (17), a unified wave propagation model including non-Darcy flow and fractional viscoelastic mechanism can be constructed. This model can accurately describe the propagation law of waves in tight oil and gas reservoir media, improve the accuracy of predicting wave propagation characteristics, and improve the accuracy of inversion calculation of oil and gas reservoir medium parameters.

[0061] As an example, the solid phase displacement vector is obtained by expression (17): and the flow phase displacement vector After that, the wave dispersion and attenuation characteristics can be analyzed by plane wave analysis. Using the Helmholtz theorem of vector field, the solid phase displacement vector and the flow phase displacement vector Decomposed into the sum of the gradient of the scalar potential and the curl of the vector potential, that is, it satisfies: (18) in, and is the scalar potential function, and is the vector potential function.

[0062] Substituting expression (18) into expression (17), the wave field of the wave propagation model can be decomposed into the compression wave (P wave) wave field and the shear wave (S wave) wave field, and the plane wave solution corresponding to the S wave or P wave can be obtained. The plane wave solution is a variable related to frequency. It can be understood that when the test frequency of the seismic wave changes, the plane wave solution also changes with the test frequency. Then, the plane wave analysis method is used to solve the P wave velocity and the S wave velocity.

[0063] The following figure shows the comparison results between the P-wave velocity and S-wave velocity of the dense core predicted by the wave propagation model provided in this application and the velocity data predicted by the Biot model and the actual data. As shown in Figures 2-5, it can be seen that the wave propagation model provided in this application is more accurate and precise in predicting the actual data, and can effectively realize the quantitative prediction of the wave velocity.

[0064] The second aspect of the present application provides a device for predicting wave propagation characteristics of tight oil and gas reservoirs, which includes a dissipation function determination module, a system generalized force determination module and a wave propagation model construction module.

[0065] The dissipation function determination module is used to equate the pore fluid in the tight oil and gas reservoir medium to a power-law fluid, and obtain the dissipation function of the fluid-containing porous two-phase medium for the non-Darcy flow seepage mechanism based on the constitutive relationship of the power-law fluid.

[0066] The system generalized force determination module is used to generalize the three-dimensional isotropic body constitutive relation to the standard linear body form and introduce fractional derivatives, and combine it with the Biot porous two-phase medium constitutive relation to determine the system generalized force based on the fractional viscoelastic mechanism.

[0067] The wave propagation model construction module is used to construct a unified wave propagation model of tight oil and gas reservoir media that includes non-Darcy flow and fractional viscoelastic mechanisms based on the dissipation function, system generalized force and Biot kinetic energy function, combined with the Euler-Lagrange equation.

[0068] It should be noted that the details shown in the wave propagation characteristics prediction device for tight oil and gas reservoirs provided in this embodiment can refer to the details shown in the wave propagation characteristics prediction method for tight oil and gas reservoirs described in the above embodiments, and will not be described in detail here.

[0069] In summary, this application provides a wave propagation model with a unified multi-physics mechanism that includes both non-Darcy flow and fractional-order viscoelastic mechanisms, targeting the low porosity and low permeability characteristics of tight oil and gas reservoirs. The model can accurately describe the propagation laws of waves in underground porous media, improve the accuracy of predicting wave propagation characteristics, and the accuracy of inversion calculation of oil and gas reservoir medium parameters, realize the effective prediction of wave dispersion and dissipative attenuation of multi-scale frequencies, and provide theoretical guidance for the precise exploration and development of complex oil and gas reservoir media.

[0070] In the description of the aforementioned embodiments, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0071] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of this application, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

Claims

1. A method for predicting wave propagation characteristics of tight oil and gas reservoirs, characterized in that: include: The pore fluid in the tight oil and gas reservoir medium is equivalent to a power-law fluid, and based on the constitutive relation of the power-law fluid, the dissipation function of the fluid-containing porous two-phase medium for the non-Darcy flow mechanism is obtained. The constitutive relation of three-dimensional isotropic body is generalized into standard linear body form and fractional derivatives are introduced. Combined with the constitutive relation of Biot porous two-phase medium, the generalized force expression of the system based on fractional viscoelastic mechanism is obtained. According to the dissipation function, the system generalized force expression and the Biot kinetic energy function, combined with the Euler-Lagrange equation, a unified wave propagation model expression of tight oil and gas reservoir media including non-Darcy flow and fractional viscoelastic mechanism is obtained.

2. The method according to claim 1, characterized in that The step of obtaining the dissipation function of the fluid-containing porous two-phase medium for the non-Darcy flow seepage mechanism according to the power-law fluid constitutive relation comprises: Obtain medium parameters of tight oil and gas reservoir medium; The constitutive relation expression of power-law fluid is combined with the Navier-Stokes equation expression of three-dimensional viscous incompressible fluid to obtain the seepage equation expression of power-law fluid. According to the power-law fluid seepage equation expression, an expression of the friction force of the fluid on a unit volume element is obtained; The dissipation coefficient expression is obtained according to the equivalent relationship between the friction force expression of the fluid on the unit volume element and the dissipation coefficient.

3. The method according to claim 2, characterized in that The medium parameters of the tight oil and gas reservoir medium include porosity, permeability, pore fluid viscosity coefficient, rock mineral density, solid-fluid two-phase coupling density, pore fluid bulk modulus, rock skeleton bulk modulus and rock mineral bulk modulus.

4. The method according to claim 2, characterized in that: The dissipation function satisfy: in, is the power-law fluid index, is the fluid viscosity, is the permeability, is the porosity, Solid phase displacement tensor, is the flow phase displacement tensor.

5. The method according to claim 1, characterized in that The steps of generalizing the three-dimensional isotropic body constitutive relation in a standard linear body form and introducing fractional derivatives, and combining it with the Biot porous two-phase medium constitutive relation to obtain the generalized force expression of the system based on the fractional viscoelastic mechanism include: The three-dimensional isotropic body constitutive relation is generalized to a standard linear body form and fractional derivatives are introduced to obtain a three-dimensional isotropic body constitutive relation based on a fractional viscoelastic mechanism; The three-dimensional isotropic body constitutive relation based on the fractional-order viscoelastic mechanism is combined with the Biot porous two-phase medium constitutive relation to obtain the generalized force expression of the system based on the fractional-order viscoelastic mechanism.

6. The method according to claim 5, characterized in that The three-dimensional isotropic constitutive relation based on the fractional viscoelastic mechanism satisfies: in, Represents the stress tensor of an object The weight, is the stress spherical tensor; Represents the strain tensor of the object The weight, is the strain spherical tensor Represents the stress deviator of an object The amount, Represents the object strain deviator The weight, is the relaxation time of the viscoelastic mechanism, is the bulk modulus of the medium, is the shear modulus of the medium.

7. The method according to claim 5, characterized in that The Biot porous two-phase medium constitutive relation includes a solid-phase stress expression and a fluid-phase stress expression, and the combination of the three-dimensional isotropic body constitutive relation based on the fractional-order viscoelastic mechanism and the Biot porous two-phase medium constitutive relation includes combining the three-dimensional isotropic body constitutive relation based on the fractional-order viscoelastic mechanism with the solid-phase stress expression.

8. The method according to claim 7, characterized in that The generalized force expression of the system based on the fractional viscoelastic mechanism satisfies: in, is the solid phase stress tensor, is the solid skeleton viscoelastic matrix, is the solid skeleton body strain, is the flow response force tensor, is the fluid body strain, is the pore fluid pressure, is the second-order unit tensor, is the Biot-Willis coefficient, is the Biot fluid storage coefficient; and is the relaxation function.

9. The method according to claim 8, characterized in that The wave propagation model expression satisfies: in, is the power-law fluid index, is the fluid viscosity, is the permeability, is the porosity, is the solid phase displacement tensor, is the flow phase displacement tensor, , , Respectively meet: in, is the rock mineral density, is the pore fluid density, is the solid-fluid two-phase coupling density.

10. A device for predicting wave propagation characteristics of tight oil and gas reservoirs, characterized in that: include: A dissipation function determination module, which is used to equate the pore fluid in the tight oil and gas reservoir medium to a power-law fluid, and obtain a dissipation function of a fluid-containing pore two-phase medium for a non-Darcy flow seepage mechanism based on a constitutive relationship of the power-law fluid; A system generalized force determination module, which is used to generalize the three-dimensional isotropic body constitutive relation to a standard linear body form and introduce fractional derivatives, and combine it with the Biot porous two-phase medium constitutive relation to determine the system generalized force based on the fractional viscoelastic mechanism; A wave propagation model construction module is used to construct a unified wave propagation model of tight oil and gas reservoir media that includes non-Darcy flow and fractional viscoelastic mechanisms based on the dissipation function, the system generalized force and the Biot kinetic energy function, and in combination with the Euler-Lagrange equation.

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