Multi-scale fractured porous medium rock physical modeling method and device

Abstract

The invention discloses a multi-scale fractured porous medium rock physical modeling method and device. The method comprises the following steps: determining an elastic modulus of an equivalent rock containing pores and microscopic cracks by utilizing an equivalent medium model based on respective elastic moduli and geometric factors of a mineral matrix, the pores and the microscopic cracks; on the basis of the elastic modulus of the equivalent rock containing the pores and the microscopic cracks, determining the elastic modulus of the equivalent rock containing the extrusion jet effect of the microscopic cracks; based on the elastic modulus of the equivalent rock containing the microcosmic fracture extrusion jet flow effect, the far-field scattering amplitude caused by each group of mesoscopic fractures is determined, the total far-field scattering amplitude caused by all the mesoscopic fractures is obtained, and the total effective longitudinal wave number is determined; and according to the total effective longitudinal wave number, establishing a multi-scale fractured porous medium rock frequency dispersion and attenuation model. According to the method, the frequency dispersion and attenuation model comprehensively considering the crack scale effect and the frequency dispersion characteristic can be established.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of geophysical technology, in particular to a multi-scale fractured porous medium rock physics modeling method and device. BACKGROUND

[0002] Fractures always play an important role in the process of oil and gas accumulation and development. In low-permeability sandstone, carbonate rock, and unconventional reservoirs such as igneous rock and shale, although fractures only account for a small part of the rock volume, they have an important effect on the improvement of reservoir properties and the transport of oil and gas due to their ability to accommodate fluids and serve as fluid migration channels (Zhou Xinguie et al., 2003; Zeng Lianbo et al., 2007). The presence of multi-scale fractures is also related to the brittleness of the rock and the stress field. For example, large-scale fractures are mainly controlled by the regional stress field; medium-scale fractures are mainly affected by the secondary stress field or the regional stress field; and small-scale fractures, which are usually developed inside sand bodies and exhibit high-angle joints, are mainly controlled by the derived stress field (Feng Jianwei et al., 2016). The interlacing and communication of multi-scale fractures not only affect the occurrence and migration of fluids, but also affect the elastic properties of the rock, thereby affecting the rock physics characteristics of rocks containing multi-scale fractures (Rubino et al., 2014; Ba et al., 2016; Guo et al., 2018). Therefore, when studying complex multi-scale heterogeneous rocks underground, it is necessary to study the influence of multi-scale fractures. In this geological background, there is an urgent need for technological innovation in the geophysical characterization of multi-scale fractured reservoirs to describe oil and gas reservoirs and provide important guidance for oil and gas reservoir development adjustment, thereby affecting the understanding of reservoir development patterns and the development effect of oil and gas reservoirs.

[0003] Different frequencies of geophysical measurements can be used to detect different sizes of fractures. Traditional geophysical exploration and measurement covers multiple frequency ranges, including seismic frequencies (Hz), logging frequencies (kHz), and laboratory frequencies (MHz), forming a multi-scale multi-frequency data set. Scale effects significantly affect many reservoir rock properties. Large-scale rocks usually contain more large-scale inhomogeneous fractures and meso and macroscopic fracture characteristics, so the velocity is relatively low. In addition, for rocks of a certain scale, the velocity dispersion and attenuation characteristics of the rock will also be affected by the frequency. Therefore, when establishing a rock physics model that describes the characteristics of multi-scale fractures, the effects of scale and frequency must be considered.

[0004] Current researches on dispersion and attenuation are mainly focused on a specific scale, usually based on laboratory, logging or seismic data, and the dispersion and attenuation characteristics of geophysical data at a specific scale are discussed separately, lacking comprehensive seismic rock physics model considering rock scale effect and dispersion characteristics simultaneously. Multi-scale non-uniform fractures are crucial for quantitatively characterizing fractured reservoirs, and therefore, it is particularly necessary to establish a multi-scale fracture dispersion and attenuation rock physics model including scale effect. SUMMARY

[0005] In order to enrich the process route and increase the selection space, the embodiment of the present application provides a multi-scale fractured porous medium rock physics modeling method and device, which can establish a dispersion and attenuation model considering the scale effect and dispersion characteristics of fractures comprehensively.

[0006] In the first aspect, the embodiment of the present application provides a multi-scale fractured porous medium rock physics modeling method, comprising:

[0007] 1. A multi-scale fractured porous medium rock physics modeling method, comprising:

[0008] Based on the elastic modulus and geometric factor of the mineral matrix, pores and micro-fractures, the elastic modulus of the equivalent rock containing pores and micro-fractures is determined by using the equivalent medium model;

[0009] Based on the elastic modulus of the equivalent rock containing pores and micro-fractures, the elastic modulus of the equivalent rock containing micro-fracture squeeze jet flow effect is determined;

[0010] Based on the elastic modulus of the equivalent rock containing micro-fracture squeeze jet flow effect, the far-field scattering amplitude caused by each group of mesoscopic fractures is determined respectively, the total far-field scattering amplitude caused by all mesoscopic fractures is obtained, and the total effective longitudinal wave number is determined, and one group of mesoscopic fractures contains two perpendicularly intersecting mesoscopic fractures;

[0011] According to the total effective longitudinal wave number, a multi-scale fractured porous medium rock dispersion and attenuation model is established.

[0012] In the second aspect, the embodiment of the present application provides a multi-scale fractured porous medium rock physics modeling device, comprising:

[0013] The equivalent module of pores and micro-fractures is used to determine the elastic modulus of the equivalent rock containing pores and micro-fractures based on the elastic modulus and geometric factor of the mineral matrix, pores and micro-fractures by using the equivalent medium model;

[0014] The equivalent module of micro-fracture squeeze jet flow effect is used to determine the elastic modulus of the equivalent rock containing micro-fracture squeeze jet flow effect based on the elastic modulus of the equivalent rock containing pores and micro-fractures;

[0015] The mesoscopic crack equivalent module is used for determining the far-field scattering amplitude caused by each group of mesoscopic cracks respectively based on the elastic modulus of the equivalent rock containing the micro-crack jet flow effect, obtaining the total far-field scattering amplitude caused by all mesoscopic cracks, and determining the total effective longitudinal wave number, and one group of mesoscopic cracks contains two perpendicularly intersecting mesoscopic cracks.

[0016] The dispersion and attenuation model establishing module is used for establishing the dispersion and attenuation model of the multi-scale cracked porous medium rock according to the total effective longitudinal wave number.

[0017] In a third aspect, an embodiment of the present application provides a computer storage medium, which stores computer executable instructions, and the computer executable instructions are executed by a processor to implement the multi-scale cracked porous medium rock physics modeling method.

[0018] In a fourth aspect, an embodiment of the present application provides a server, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the multi-scale cracked porous medium rock physics modeling method when executing the program.

[0019] The beneficial effects of the above technical solutions provided by the embodiments of the present application at least include:

[0020] The multi-scale cracked porous medium rock physics modeling method provided by the embodiments of the present application comprehensively considers the scale effect and the dispersion characteristics, and establishes a multi-scale crack dispersion and attenuation model containing the random micro-crack jet flow effect and the elastic scattering influence caused by the directional arrangement of the mesoscopic intersecting cracks. Furthermore, the model can be used for quantitative seismic interpretation of laboratory, logging and seismic elastic data, and can be used for cross-scale analysis of reservoir crack characteristics in combination with multi-scale geophysical data.

[0021] Other features and advantages of the present application will be set forth in the following description, and in part will become apparent to those skilled in the art from the description, or can be learned by practice of the present application. The objects and other advantages of the present application will be realized and achieved by means of the structures particularly pointed out in the written description and claims hereof as well as the appended drawings.

[0022] The technical solutions of the present application will be further described in detail below with the drawings and embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0023] The accompanying drawings are included to provide a further understanding of the present application, and constitute a part of the specification, illustrate the present application, and are used to explain the present application together with the embodiments of the present application, and do not constitute a limitation on the present application. In the drawings:

[0024] Figure 1A flow chart of the method for petrophysical modeling of multi-scale fractured porous media in the first embodiment of the present application;

[0025] Figure 2 A flow chart of the method for petrophysical modeling of multi-scale fractured porous media in the first embodiment of the present application; Figure 1 A flow chart of the method for petrophysical modeling of multi-scale fractured porous media in the first embodiment of the present application;

[0026] Figure 3 A flow chart of the method for petrophysical modeling of multi-scale fractured porous media in the first embodiment of the present application;

[0027] Figure 4 A flow chart of the method for petrophysical modeling of multi-scale fractured porous media in the first embodiment of the present application; Figure 2 A flow chart of the method for petrophysical modeling of multi-scale fractured porous media in the first embodiment of the present application;

[0028] Figure 5 A flow chart of the method for petrophysical modeling of multi-scale fractured porous media in the second embodiment of the present application;

[0029] Figure 6 A flow chart of the method for petrophysical modeling of multi-scale fractured porous media in the second embodiment of the present application;

[0030] Figure 7 A flow chart of the method for petrophysical modeling of multi-scale fractured porous media in the second embodiment of the present application;

[0031] Figure 8 A flow chart of the method for petrophysical modeling of multi-scale fractured porous media in the second embodiment of the present application; DETAILED DESCRIPTION

[0032] Exemplary embodiments of the present disclosure will be described more fully hereinafter with reference to the accompanying drawings; however, they are not intended to limit the present disclosure to particular embodiments. Rather, the intention is to convey the concept of the present disclosure to a technical person skilled in the art with the best mode of carrying out the present disclosure.

[0033] It should be understood that the terms used in the present application are merely used to describe particular embodiments and are not intended to limit the present application. In addition, for numerical ranges in the present application, it should be understood that each intermediate value between the upper limit and the lower limit of the range is specifically disclosed. Each smaller range within the range of the stated value or the stated range and any other stated value or intermediate value within the stated range is also included in the present application. The upper limit and the lower limit of these smaller ranges can be included or excluded independently from the range.

[0034] Unless otherwise indicated, all technical and scientific terms used herein have the same meaning as those commonly understood by one of ordinary skill in the art to which this application belongs. Although preferred methods and materials are described herein, any methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present application. All documents mentioned herein are incorporated by reference to disclose and describe in full the methods and / or materials which are described herein. In case of conflict, the content of the present specification will control.

[0035] The embodiment of the present application provides a multi-scale fractured porous medium rock physics modeling method and device, which can establish a dispersion and attenuation model considering the scale effect and dispersion characteristics of fractures.

[0036] Embodiment one

[0037] The embodiment one of the present application provides a multi-scale fractured porous medium rock physics modeling method, the flow thereof is referred to Figure 1 as shown, comprising the following steps:

[0038] Step S11: based on the elastic modulus and geometric factor of the mineral matrix, pores and micro-cracks, respectively, the elastic modulus of the equivalent rock containing pores and micro-cracks is determined by using the equivalent medium model.

[0039] In the embodiment, the mineral matrix is taken as the initial background, and isotropic background pores are added to the mineral matrix; then, micro-cracks with random directions are uniformly distributed and added to the equivalent rock background containing pores to obtain the equivalent rock containing pores and micro-cracks, so as to construct the change relationship of the equivalent elastic properties of the multi-scale fractured rock at the micro-scale with the scale, as the rock background for constructing the rock extrusion and jet flow effect of micro-cracks.

[0040] Specifically, based on the elastic modulus and geometric factor of the mineral matrix, pores and micro-cracks, respectively, the bulk modulus and shear modulus of the equivalent rock containing pores and micro-cracks are obtained by using the equivalent medium model (which can be a differential equivalent medium model DEM) on the background of the mineral matrix, and the pores and micro-cracks are iterated in sequence.

[0041] The specific division standard of the micro-cracks and meso-cracks in the embodiment can be the commonly used crack type division standard in the field, and the embodiment is not additionally limited.

[0042] Further, the pores and micro-cracks are iterated in sequence on the background of the mineral matrix by using the following formulas (1) and (2):

[0043]

[0044]

[0045] In formulas (1) and (2), K2 and μ2 are the bulk modulus and shear modulus of the inclusion; y is the volume percentage of the inclusion; P (*2) and Q (*2) A geometric factor representing the inclusions in the equivalent rock; and are the equivalent bulk modulus and shear modulus, respectively, and the final iteration is the bulk modulus and shear modulus of the equivalent rock containing pores and microcracks.

[0046] It is worth noting that this embodiment assumes that the fracture aspect ratio varies with fracture length. Therefore, the aspect ratio of the microfracture can be determined based on the scale characteristics of the rock microfractures and the relationship between the microfracture aspect ratio and scale. The microfracture geometric factor can then be determined based on the aspect ratio. This allows for different microfracture properties at different fracture lengths (scales).

[0047] Step S12: Based on the elastic modulus of the equivalent rock including pores and micro-cracks, determine the elastic modulus of the equivalent rock including the squirting flow effect of the micro-cracks.

[0048] When seismic waves pass through porous rocks containing softer pore spaces (microcracks or broken particles, etc.), the fluid pressure in these flat or narrow fractures becomes much greater than the fluid pressure in the less compressible main pore space. The fluid exchange between the two is called "squeeze flow," which causes the dispersion and attenuation of seismic waves.

[0049] In some embodiments, see Figure 2 As shown in FIG, the determination of the elastic modulus of the equivalent rock including the squirting flow effect of micro-fractures can include the following steps:

[0050] Step S121: According to the scale characteristics of rock micro-cracks, the density of micro-cracks is determined based on the relationship between the scale and number of micro-cracks, and the aspect ratio of micro-cracks is determined based on the relationship between the aspect ratio of micro-cracks and the scale.

[0051] First, the multi-scale crack distribution law is established to obtain the relationship between the number and length of cracks. Generally, the relationship between the number and length of cracks can be found in Figure 3 As shown in FIG. 3 , in this embodiment, the distribution law of multi-scale cracks is mainly fractal distribution:

[0052] N t (r) = C0·r -D (3)

[0053] Among them, C0 is a constant, r is a parameter representing the crack size, here is the crack radius, N t(r) is the true number of cracks with a size greater than or equal to r. D is the fractal dimension. Assuming that the maximum crack length (2*r) observed and the REV size are consistent, the size in the following is the size of the maximum crack length observed.

[0054] The crack density can be calculated from the number of cracks:

[0055]

[0056] where cr represents the crack density, N represents the number of cracks, and in calculating the crack density at a certain size, this parameter is the total number of cracks in the size range at that time; V represents the volume of the equivalent unit (REV).

[0057] Step S122: determining the elastic modulus of the equivalent rock containing the micro-crack squirt flow effect according to the density and aspect ratio of the micro-crack, the bulk modulus and shear modulus of the mineral matrix and the fluid, and the bulk modulus and shear modulus of the equivalent rock containing pores and micro-cracks.

[0058] Further, referring to Figure 4 As shown in the figure, step S122 specifically includes the following sub-steps:

[0059] Step S1221: determining the equivalent bulk modulus and shear modulus of the fluid-saturated rock at low frequency limit and the shear modulus and Poisson's ratio of the solid rock according to the bulk modulus and shear modulus of the equivalent rock containing pores and micro-cracks.

[0060] Step S1222: determining the contribution degree of the micro-crack squirt flow effect according to the density and aspect ratio of the micro-crack, the shear modulus and Poisson's ratio of the solid rock, the bulk modulus of the mineral matrix and the fluid, and the shear modulus of the equivalent rock containing pores and micro-cracks and the equivalent shear modulus of the fluid-saturated rock at low frequency limit.

[0061]

[0062] In formula (5), S(ω) is the contribution degree of the micro-crack squirt flow effect, cr is the density of the micro-crack, α c is the aspect ratio of the micro-crack, μ0 and v0 are the shear modulus and Poisson's ratio of the solid rock, is the shear modulus of the equivalent rock containing pores and micro-cracks, K G is the equivalent shear modulus of the fluid-saturated rock at low frequency limit, K0 and K f are the bulk modulus of the mineral matrix and the fluid, respectively.

[0063] The frequency-dependent factor f(ζ) and its dimension ζ are expressed as:

[0064]

[0065]

[0066] where J1 and J0 are the first and zero order Bessel functions of the first kind, ω = 2πf represents the angular frequency; η is the fluid viscosity.

[0067] Step S1223: determining the dynamic bulk strain of the fluid pressure diffusion process in the porous medium according to the contribution degree of the micro crack squirt flow effect, the bulk modulus of the equivalent rock containing pores and micro cracks, and the bulk modulus of the mineral matrix and the fluid.

[0068]

[0069] where,

[0070]

[0071]

[0072]

[0073]

[0074] where ε WIFF (f) is the dynamic bulk strain of the fluid pressure diffusion process in the porous medium, dP0 is the pressure disturbance caused by the seismic wave, WIFF (ω), dP0 is the pressure disturbance caused by the seismic wave, is the porosity, is the Biot coefficient.

[0075] Step S1224: determining the bulk modulus and shear modulus of the equivalent rock containing the micro crack squirt flow effect according to the dynamic bulk strain of the fluid pressure diffusion process in the porous medium and the equivalent bulk modulus and shear modulus of the fluid-saturated rock at the low-frequency limit.

[0076] The equivalent bulk modulus and shear modulus of the rock containing the multi-scale complex heterogeneous body and considering the squirt flow effect can be expressed as:

[0077]

[0078] where K * and μ * represent the bulk modulus and shear modulus of the equivalent rock containing the micro crack squirt flow effect, specifically the equivalent bulk modulus and shear modulus of the rock containing the squirt flow effect of all cracks less than or equal to the scale, both of which vary with frequency. K Gand μ are the bulk modulus and shear modulus of the fluid-saturated rock at low frequencies, and can be calculated from the bulk modulus and shear modulus of the equivalent rock containing pores and microcracks based on the Gassmann formula (Gassmann, 1951). ε WIFF (0) represents the dynamic bulk strain at low frequencies.f i represents the volume fraction of the particular inhomogeneous region, subscript i represents a group of inhomogeneous bodies with certain physical characteristics at a certain scale, and satisfies ∑ i f i = 1.

[0079] Step S13: Based on the elastic modulus of the equivalent rock containing the microcrack squirt flow effect, the far-field scattering amplitude caused by the normal oscillation of each microcrack in each group is determined respectively, the total far-field scattering amplitude caused by all the microcracks is obtained, and the total effective longitudinal wave number is determined.

[0080] The group of mesoscopic cracks contains two perpendicularly intersecting mesoscopic cracks.

[0081] The effect of mesoscopic cross cracks at different scales is calculated step by step on the background of the equivalent rock containing all the microcrack squirt flow effects. Guo and Gurevich (2020) show that oblique incidence of longitudinal waves on the crack surface will not only cause forward oscillation of the crack, but also cause shear oscillation. Therefore, the scattering of a single crack can be decomposed into two sub-problems, one is the scattering caused by the normal oscillation of the crack surface (symmetric with respect to the center of the crack), and the other is the scattering caused by the shear oscillation of the crack surface (asymmetric with respect to the center of the crack). The sum of the wave fields of these two sub-scatterings is the total scattering wave field of a single crack in the fluid-saturated background. Since the shear crack surface oscillation does not cause fluid pressure, it is not affected by the fluid connection between intersecting cracks, so the scattering wave field caused by the shear crack surface oscillation is the same as that of the parallel crack case.

[0082] Based on the elastic modulus of the equivalent rock containing the microcrack squirt flow effect, the far-field scattering amplitude caused by the normal oscillation of each microcrack in each group of mesoscopic cracks is determined respectively, and the far-field scattering amplitude caused by the surface shear oscillation of each microcrack is determined. The specific determination process is described in detail later.

[0083] Since the fracture density of each group is assumed to be relatively low, the fracture interaction between parallel fractures should be small. This means that the fracture interaction should mainly occur between intersecting fractures. The interaction between intersecting fractures is complex, depending on the competition between stress shielding and amplification (Grechka and Kachanov, 2006), which is difficult to quantify theoretically. Therefore, we neglect the fracture interaction between intersecting fractures (except for the effect of fluid flow between fractures). Thus, we still use the Foldy approximation to calculate the effective p-wave number.

[0084] The total effective p-wave number caused by all mesoscopic fractures is determined by the following equations (14)-(16) based on the far-field scattering amplitude caused by the normal oscillation of each mesoscopic fracture in each group and the far-field scattering amplitude caused by the surface shear oscillation of each mesoscopic fracture:

[0085]

[0086]

[0087]

[0088] In equations (14)-(16), is the total effective p-wave number, k1 is the equivalent p-wave number of the background rock, i is the serial number of the fracture scale (i.e., the mesoscopic fracture in each group), i = 1, 2, …, N, N is the number of fracture scales, n i is the fracture density under the i-th scale, and are the far-field scattering amplitudes of fracture 1 and fracture 2 under the i-th scale, respectively, u0 represents the displacement amplitude of the incident p-wave, and represent the angles between fracture 1, fracture 2 and the vertical direction, respectively, m represents the m-th component of the scattered wave field or the incident wave field, and are the far-field scattering amplitudes caused by the normal oscillation of fracture 1 and fracture 2, respectively, and are the far-field scattering amplitudes caused by the surface shear oscillation of fracture 1 and fracture 2, respectively.

[0089] Step S14: Establish a multi-scale fractured porous medium rock dispersion and attenuation model based on the total effective p-wave number.

[0090] The multi-scale fractured porous medium rock dispersion and attenuation model based on the total effective p-wave number is respectively the following equations (17) and (18):

[0091]

[0092]

[0093] In formula (17) and (18), v p represents a longitudinal wave phase velocity, represents an effective longitudinal wave number, and ω represents an angular frequency, represents an inverse quality factor, Im(·) represents a real part of a complex number, and Re(·) represents an imaginary part of a complex number.

[0094] The multi-scale fractured porous medium rock physics modeling method provided by the embodiment one of the application comprehensively considers scale effects and dispersion characteristics, and establishes a multi-scale fracture dispersion and attenuation model containing random microscopic fracture extrusion flow effects and elastic scattering effects caused by directionally arranged mesoscopic cross fractures. Furthermore, the model can be used for quantitative seismic interpretation of laboratory, logging and seismic elastic data, and cross-scale analysis of reservoir fracture characteristics is performed in combination with multi-scale geophysical data.

[0095] In some embodiments, the dispersion and attenuation model can also be used to predict dispersion and attenuation curves of multi-scale fractured rocks at different scales; and the relationship between multi-scale fractured rock velocity and scale and the relationship between attenuation and scale in a set frequency band are determined.

[0096] The coefficients of the above scattering wave field general solution The coefficients can be obtained by the following steps:

[0097] (1) far-field scattering amplitude caused by normal oscillation of fracture 1 and fracture 2 and

[0098] A group of two different fractures of mesoscopic cross fractures are respectively marked as fracture 1 and fracture 2, and the boundary conditions of normal oscillation thereof in a cylindrical coordinate system (r, θ, z) can be respectively represented as:

[0099]

[0100]

[0101]

[0102]

[0103]

[0104] and

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] The superscript m denotes the mth component of the scattered or incident wave field. The superscript in denotes the incident wave field. The subscripts 1 and 2 denote the scattered or incident wave field on crack 1 and crack 2 in the cross crack, respectively. zr and σ zθ is the shear stress of the crack, which is zero on the crack central plane; u z and w z denote the solid displacement and relative fluid displacement of the crack in the z direction, respectively; σ zz and p are the normal stress and fluid pressure of the crack, respectively, and p in are the stress and fluid pressure caused by the incident longitudinal wave; Kf is the bulk modulus of the fluid, η represents the viscosity, a and c represent the radius and half-thickness of the crack, respectively. α is a dimensionless parameter that quantifies the degree of crack connectivity. t-time, dispersion is a function of time.

[0111] Using the boundary conditions of crack 1 and crack 2 described above, the coefficients of the general solution of the scattered wave field caused by the normal oscillation of the two cracks can be derived. Taking crack 1 as an example, substituting the general solution into the boundary conditions of crack 1, we can get (Guo et al., 2022):

[0112]

[0113]

[0114]

[0115] where,

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123] where, represents the dynamic permeability, where k0is the static permeability, represents the characteristic frequency of Biot's effect, and a ∞ represents tortuosity.

[0124] Similarly, substituting the general solution into the boundary conditions of crack 2, we have

[0125]

[0126]

[0127]

[0128] where unknowns B and C can be expressed by A, thus, further combining the unused boundary conditions, we have the expressions of and in the full plane:

[0129]

[0130]

[0131] where

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] Solving equations (42) and (43) gives the far-field scattered wave field caused by the normal oscillation of crack 1 and crack 2.

[0138] (2) Far-field scattered amplitude caused by the surface shear oscillation of crack 1 and crack 2 and

[0139] and The scattered wave field is the same as that of the parallel crack case, where can be expressed as:

[0140]

[0141] where can be obtained by solving the following second kind of Fredholm equation:

[0142]

[0143] in,

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151] calculate The formula is the same as formula (49), except that Replace all with

[0152] Example 2

[0153] The second embodiment of the present invention provides a specific application of a multi-scale fracture porous medium rock physics modeling method, the process of which is referred to Figure 5 shown.

[0154] (1) Acquisition of basic rock physical parameters. For multi-scale fracture reservoirs, the main physical parameters affecting the equivalent elastic properties of rocks are extracted, including mineral composition, permeability, porosity, background pore aspect ratio, etc.; multi-scale fracture attributes including fracture aperture, fracture size, geometry, distribution shape, etc. are collected; and fluid properties including fluid bulk modulus, density, viscosity, etc. are determined at the same time.

[0155] Table 1 Modeling parameters of the rock physics model with multi-scale fractures

[0156] Mineral bulk modulus (GPa) 37 Porosity 0.1 Mineral shear modulus (GPa) 44 Pore aspect ratio 0.2 Mineral density (g / cc) 2.65 Total fracture density 0.1 Fluid bulk modulus (GPa) 2.25 Fracture diameter (m) 1e-4～25 Fluid viscosity (cP) 1 Fracture set number 9 Fluid density (g / cc) 1 Fractal dimension 2.5 Background permeability (mD) 100

[0157] (2) The above model parameters are input into a rock physics model that characterizes the dispersion and attenuation characteristics of multi-scale fractures, thereby obtaining parameters such as dispersion, attenuation, and anisotropy of fractured reservoirs at different scales.

[0158] First, the distribution of multi-scale fractures is established to obtain the relationship between fracture density and length; second, the rock physics model describing the squirt flow effect of micro-fractures is used to calculate the dispersion characteristics of each scale step by step, and the dispersion and attenuation model of large scale will take the rock properties calculated by the small scale model as the equivalent background; third, on the basis of the equivalent rock containing the squirt flow effect of all micro-scale fractures, the step-by-step averaging upscaling method is continued to model the dispersion and attenuation of the directional array cross fractures, which includes the wave-induced fluid flow of mesoscopic cross fractures (including FB-WIFF and FF-WIFF), scattering effect and Biot flow influence; thus, the equivalent longitudinal wave number of the rock containing multi-scale fractures is finally obtained, and the longitudinal wave velocity and its attenuation of the rock are calculated.

[0159] (3) The dispersion and attenuation curves of the rock containing multi-scale fractures at different scales are constructed by using the longitudinal wave dispersion and attenuation model of the rock.

[0160] The model can not only predict the dispersion and attenuation curves of the rock containing multi-scale fractures at different scales, but also reveal the relationship between the velocity and attenuation of the multi-scale fracture rock and the scale within a certain frequency band.

[0161] Figure 6 The dispersion and attenuation of the rock containing multi-scale cross fractures under vertical incidence are shown under the condition of including micro-fracture squirt flow, wave-induced fluid flow of mesoscopic fractures (including FB-WIFF and FF-WIFF) and scattering effect. From the results, it can be seen that when the observation scale changes, the characteristics of the rock containing multi-scale fractures change, and more large-scale fractures can be observed in the seismic wavelength range, resulting in changes in the characteristics of the velocity dispersion and attenuation curve. First, Figure 6 The results of medium a show that as the scale increases, the dispersion shows the characteristics that the larger the fracture diameter, the lower the characteristic frequency, which is well understood. The larger the fracture diameter, the longer the time required for pore pressure relaxation, so the characteristic frequency will be reduced as a whole; accordingly, as the scale increases, the dispersion amplitude increases, which is because more large fractures can be observed at large scales, resulting in an increase in the overall equivalent fracture density of the rock, so that the velocity at low frequency is lower. In addition, the larger the scale, the more continuous the overall dispersion characteristics of the rock, which is due to the influence of mesoscopic fractures of each scale on the rock, which couples the wave-induced fluid flow and scattering effect of each scale mesoscopic fracture with different characteristic frequencies.

[0162] Figure 6The middle b shows the modeling results of the attenuation. The overall attenuation is composed of multiple parts, which are meso-fracture wave-induced fluid flow (including FB-WIFF and FF-WIFF), meso-fracture scattering, micro-fracture squirt flow, and Biot flow effect, which may be coupled together. Among them, the micro-fracture squirt flow attenuation is weak and cannot have a very obvious influence on the overall attenuation of the rock; the meso-wave-induced fluid flow and scattering attenuation formed due to the presence of meso-fractures gradually moves to low frequency with the increase of the fracture diameter, and the attenuation amplitude will also increase accordingly.

[0163] Figure 7 The middle b shows the modeling results of the attenuation. The overall attenuation is composed of multiple parts, which are meso-fracture wave-induced fluid flow (including FB-WIFF and FF-WIFF), meso-fracture scattering, micro-fracture squirt flow, and Biot flow effect, which may be coupled together. Among them, the micro-fracture squirt flow attenuation is weak and cannot have a very obvious influence on the overall attenuation of the rock; the meso-wave-induced fluid flow and scattering attenuation formed due to the presence of meso-fractures gradually moves to low frequency with the increase of the fracture diameter, and the attenuation amplitude will also increase accordingly. Figure 7 The results of the middle a can be obviously observed that, with the increase of the scale, the velocity of the rock containing multi-scale cross fractures gradually decreases, which is consistent with the elastic model above, representing that more meso-cross fractures can be observed at a large scale, so that the overall rock fracture density increases and the velocity decreases; in addition, it can be found from the relationship between the velocity and the scale that the velocity dispersion at a large scale will be stronger, which may be related to the larger fracture density and longer fracture radius. Secondly, Figure 7 The middle b shows that the attenuation increases with the increase of the scale, and the distribution of the attenuation is also wider.

[0164] The embodiment of the present application establishes a multi-scale fracture dispersion and attenuation model considering the influence of different scale fractures.

[0165] Firstly, the embodiment of the present application establishes a multi-scale fracture dispersion and attenuation model considering the scale effect and dispersion characteristics based on the existing form of multi-scale fractures. The model includes the effects of random micro-fracture squirt flow and Biot flow, fracture-matrix wave-induced flow (FB-WIFF) and fracture-fracture wave-induced flow (FF-WIFF) caused by the directional arrangement of meso-cross fractures, and the influence of meso-cross fracture elastic scattering, so as to comprehensively describe the seismic dispersion, attenuation and frequency-dependent anisotropy.

[0166] Secondly, at the micro scale, the embodiment of the present application uses the relationship between the aspect ratio of micro-fractures and the scale to construct a rock physics model of multi-scale micro-fracture squirt flow effect in a wide frequency band.

[0167] Thirdly, at the meso scale, the embodiment of the present application establishes a model of the longitudinal wave velocity and attenuation of meso-scale cross fractures under the condition of arbitrary incident angle, and studies the influence of the distribution form and direction of multi-scale fractures on the rock dispersion and attenuation.

[0168] Based on the inventive concept of the present application, the embodiment of the present application further provides a device for multi-scale fractured porous medium rock physics modeling, the structure of the device is shown in Figure 8

[0169] an equivalent module 81 for pores and micro-cracks, configured to determine the elastic modulus of equivalent rock containing pores and micro-cracks based on the elastic modulus and geometric factor of the mineral matrix, pores and micro-cracks respectively by using an equivalent medium model;

[0170] an equivalent module 82 for micro-crack squirt flow effect, configured to determine the elastic modulus of equivalent rock containing micro-crack squirt flow effect based on the elastic modulus of the equivalent rock containing pores and micro-cracks;

[0171] a meso-crack equivalent module 83, configured to determine the far-field scattering amplitude caused by each group of meso-cracks based on the elastic modulus of the equivalent rock containing micro-crack squirt flow effect, obtain the total far-field scattering amplitude caused by all meso-cracks, determine the total effective longitudinal wave number, and a group of meso-cracks contains two perpendicularly intersecting meso-cracks;

[0172] a dispersion and attenuation model establishing module 84, configured to establish the dispersion and attenuation model of multi-scale fractured porous medium rock according to the total effective longitudinal wave number.

[0173] As to the device in the above embodiment, the specific manner in which each module performs the operation has been described in detail in the embodiment related to the method, and thus will not be described in detail here.

[0174] Based on the inventive concept of the present application, the embodiment of the present application further provides a computer storage medium, the computer storage medium stores computer executable instructions, and the computer executable instructions are executed by a processor to implement the multi-scale fractured porous medium rock physics modeling method.

[0175] Based on the inventive concept of the present application, the embodiment of the present application further provides a server, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor executes the program to implement the multi-scale fractured porous medium rock physics modeling method.

[0176] ​Unless specifically stated otherwise, terms such as processing, computing, calculating, determining, displaying, and the like, can refer to an action or process of one or more processing or computing systems, or similar devices, that manipulate or transform data represented as physical (e.g., electronic) quantities within the systems' registers or memories into other data similarly represented as physical quantities within the systems' memories, registers or other such information storage, transmission or display devices. The terms "information," "data," "instructions," “command,” “signal,” “bit,” “symbol,” and the like refer to physical quantities presumed to represent a pertinent physical reality.

[0177] It should be understood that the particular order in which the steps in the disclosed processes have been presented is exemplary. Based on design preferences, it is understood that the particular order of steps in the processes can be rearranged without departing from the scope of the disclosure. The accompanying method claims present elements of the various steps in exemplary order and are not meant to be limited to the specific order or hierarchy presented.

[0178] In the above detailed description, various features are grouped together in single embodiments for the purpose of streamlining the disclosure. This disclosed approach is not to be interpreted as reflecting an intention that the embodiments of the claimed subject matter require more features than are expressly recited in each claim. Rather, as the claims below reflect, inventive subject matter lies in fewer than all features of the disclosed single embodiments. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate preferred embodiment.

[0179] Those skilled in the art will further appreciate that the various illustrative logical blocks, modules, circuits, and algorithm steps described in connection with the embodiments disclosed herein can be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans can implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present disclosure.

[0180] The steps of a method or algorithm described in connection with the embodiments disclosed herein can be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module can reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium can be integral to the processor. The processor and the storage medium can reside in an ASIC. The ASIC can reside in a user terminal. In the alternative, the processor and the storage medium can reside as discrete components in a user terminal.

[0181] For a software implementation, the techniques described herein can be implemented with modules (e.g., procedures, functions, and so on) that perform the functions described herein. The software codes can be stored in memory units and executed by processors. The memory unit can be implemented within the processor or external to the processor, in which case it can be communicatively coupled to the processor via various means as is known in the art.

[0182] The above description includes one or more examples of the embodiments. Of course, not all possible combinations of components or methods described above can be claimed as embodiments. One of ordinary skill in the art can recognize that modifications and variations of the described embodiments can be made without departing from the scope of the present disclosure. It is therefore intended that the embodiments described herein be considered in all respects as illustrative and not restrictive, particularly as numerous modifications and further embodiments can become apparent to those skilled in the art. Accordingly, the scope of the present disclosure is intended to be defined by the following claims rather than the description. Moreover, the use of the terms "first", "second", etc. do not denote any order or importance, but rather the terms are used to distinguish one element from another. Furthermore, the use of the terms "including", "containing", etc. are meant to encompass the terms "consisting of" and / or "consisting essentially of". Moreover, the use of the term "or" is meant to encompass "and / or", unless otherwise indicated.

Claims

1. A method of multi-scale fractured porous media rock physics modeling, characterized in that, The method comprises the following steps: determining the elastic modulus of the equivalent rock containing pores and micro-cracks based on the elastic modulus and geometric factor of the mineral matrix, pores and micro-cracks respectively, and using an equivalent medium model; determining the elastic modulus of the equivalent rock containing micro-crack squirt-flow effect based on the elastic modulus of the equivalent rock containing pores and micro-cracks; determining the far-field scattering amplitude caused by each group of micro-cracks based on the elastic modulus of the equivalent rock containing micro-crack squirt-flow effect, obtaining the total far-field scattering amplitude caused by all micro-cracks, determining the total effective longitudinal wave number, and one group of micro-cracks containing two perpendicularly intersecting micro-cracks; establishing a multi-scale fractured porous medium rock dispersion and attenuation model according to the total effective longitudinal wave number.

2. The method of claim 1, wherein, The micro-crack geometric factor is determined by the following steps: determining the aspect ratio of the micro-cracks according to the scale characteristics of the rock micro-cracks and the relationship between the aspect ratio of the micro-cracks and the scale; determining the micro-crack geometric factor according to the aspect ratio.

3. The method of claim 1, wherein, The method for determining the elastic modulus of the equivalent rock containing pores and micro-cracks based on the elastic modulus and geometric factor of the mineral matrix, pores and micro-cracks respectively, and using an equivalent medium model comprises the following steps: iterating the pores and micro-cracks in turn on the background of the mineral matrix to obtain the bulk modulus and shear modulus of the equivalent rock containing pores and micro-cracks by using a differential equivalent medium model (DEM) based on the elastic modulus and geometric factor of the mineral matrix, pores and micro-cracks respectively.

4. The method of claim 1, wherein, The method for determining the elastic modulus of the equivalent rock containing micro-crack squirt-flow effect based on the elastic modulus of the equivalent rock containing pores and micro-cracks comprises the following steps: determining the density of the micro-cracks based on the relationship between the scale and number of the micro-cracks according to the scale characteristics of the rock micro-cracks, and determining the aspect ratio of the micro-cracks based on the relationship between the aspect ratio of the micro-cracks and the scale; determining the elastic modulus of the equivalent rock containing micro-crack squirt-flow effect according to the density and aspect ratio of the micro-cracks, the bulk modulus and shear modulus of the mineral matrix and fluid, and the bulk modulus and shear modulus of the equivalent rock containing pores and micro-cracks.

5. The method of claim 4, wherein, The method for determining the elastic modulus of the equivalent rock containing micro-crack squirt-flow effect according to the density and aspect ratio of the micro-cracks, the bulk modulus and shear modulus of the mineral matrix and fluid, and the bulk modulus and shear modulus of the equivalent rock containing pores and micro-cracks comprises the following steps: determining the equivalent bulk modulus and shear modulus of the fluid-saturated rock at a low-frequency limit and the shear modulus and Poisson's ratio of the solid rock according to the bulk modulus and shear modulus of the equivalent rock containing pores and micro-cracks; determining the contribution degree of the micro-crack squirt-flow effect according to the density and aspect ratio of the micro-cracks, the shear modulus and Poisson's ratio of the solid rock, the bulk modulus of the mineral matrix and fluid, the shear modulus of the equivalent rock containing pores and micro-cracks, and the equivalent shear modulus of the fluid-saturated rock at a low-frequency limit; determining the dynamic bulk strain of the fluid pressure diffusion process in the porous medium according to the contribution degree of the micro-crack squirt-flow effect, the bulk modulus of the equivalent rock containing pores and micro-cracks, and the bulk modulus of the mineral matrix and fluid. Based on the dynamic volume strain of the fluid pressure diffusion process in porous media and the equivalent bulk modulus and shear modulus of fluid-saturated rock in the low-frequency limit, the bulk modulus and shear modulus of the equivalent rock including the micro-fracture squirting flow effect are determined.

6. The method of claim 1, wherein, The method of determining the far-field scattering amplitude caused by each group of mesoscopic cracks based on the elastic modulus of the equivalent rock including the squirting flow effect of the microscopic cracks comprises: Based on the elastic modulus of the equivalent rock including the squirting effect of the micro-fractures, the far-field scattering amplitude caused by the normal oscillation of each mesoscopic fracture in each group of mesoscopic fractures and the far-field scattering amplitude caused by the surface shear oscillation of each mesoscopic fracture are determined respectively.

7. The method of claim 6, wherein, Determining the total effective longitudinal wave number includes: The total effective longitudinal wave number caused by all mesoscopic cracks is determined by the following formulas (1)-(3): in formulae (1)-(3), is the total effective longitudinal wave number, k1 is the equivalent longitudinal wave number of the background rock, i is the serial number of the fracture scale, i = 1, 2, …, N, N is the number of fracture scales, n i is the fracture density at the i-th scale, and are the far-field scattering amplitudes of the fracture 1 and the fracture 2 at the i-th scale respectively, u0 represents the displacement amplitude of the incident longitudinal wave, and respectively represent the included angles of the fracture 1 and the fracture 2 with the vertical direction, m represents the m-th component of the scattered wave field or the incident wave field, and are the far-field scattering amplitudes caused by the normal oscillation of the fracture 1 and the fracture 2 respectively, and are the far-field scattering amplitudes caused by the surface shear oscillation of the fracture 1 and the fracture 2 respectively.

8. The method of claim 1, wherein, The method of establishing a multi-scale fractured porous medium rock dispersion and attenuation model based on the total effective longitudinal wave number includes: According to the total effective P-wave number, the dispersion and attenuation models of multi-scale fractured porous media rock are established as follows (4) and (5): In formulas (4) and (5), v p represents the longitudinal wave phase velocity, represents the effective longitudinal wave number, ω represents the angular frequency, Represents the inverse quality factor, Im(·) represents the imaginary part of a complex number, and Re(·) represents the real part of a complex number.

9. The method according to any one of claims 1 to 8, characterized in that, Also includes: Using the dispersion and attenuation model to predict the dispersion and attenuation curves of multi-scale fractured rocks at different scales; The relationship between the velocity and scale of multi-scale fracture rocks and the relationship between the attenuation and scale within a set frequency band are determined.

10. A multi-scale fractured porous medium petrophysical modeling apparatus, characterized by, include: The equivalence module for pores and microcracks is used to determine the elastic modulus of the equivalent rock containing pores and microcracks based on the elastic moduli and geometric factors of the mineral matrix, pores and microcracks respectively, using the equivalent medium model; An equivalent module for micro-fracture squirt flow effect, used to determine the elastic modulus of the equivalent rock containing the micro-fracture squirt flow effect based on the elastic modulus of the equivalent rock containing pores and micro-fractures; A mesoscopic fracture equivalent module is used to determine the far-field scattering amplitude caused by each group of mesoscopic fractures based on the elastic modulus of the equivalent rock including the squirting effect of the microscopic fractures, obtain the total far-field scattering amplitude caused by all mesoscopic fractures, and determine the total effective longitudinal wave number. A group of mesoscopic fractures includes two vertically intersecting mesoscopic fractures; The dispersion and attenuation model building module is used to establish a multi-scale fractured porous media rock dispersion and attenuation model based on the total effective longitudinal wave number.

11. A computer storage medium, characterized in that The computer storage medium stores computer executable instructions, which, when executed by a processor, implement the multi-scale fractured porous media rock physics modeling method according to any one of claims 1 to 9.

12. A server, characterized by include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the multi-scale fractured porous media rock physics modeling method according to any one of claims 1 to 9 is implemented.

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