Complex pore medium longitudinal wave velocity and attenuation prediction method and application thereof

Abstract

The invention discloses a complex pore medium longitudinal wave velocity and attenuation prediction method and application thereof. The method comprises the following steps: step 1, dividing a rock skeleton into a background phase and an embedded body based on rock characteristics; step 2, based on a Pride model, obtaining a dry rock skeleton modulus of a background phase; step 3, based on a Pride model, obtaining a dry rock skeleton modulus of the embedded body; step 4, based on an MFS jet flow model, obtaining a corrected rock dry skeleton modulus of the embedded body; step 5, deriving a Biot-Rayleigh elastic wave propagation equation containing the jet effect; and step 6, obtaining the longitudinal wave velocity and attenuation prediction value of the complex pore medium based on the relationship between the complex wave number and the wave velocity and attenuation. The method can effectively represent the wave propagation characteristics of the complex pore medium containing cracks, and improves the prediction precision of the longitudinal wave velocity of the pore medium.

Description

Technical Field

[0001] The present invention relates to the field of seismic rock technology, and in particular to a method for predicting longitudinal wave velocity and attenuation in a complex porous medium and an application thereof. Background Art

[0002] Reservoir rock is a porous solid medium containing fluid (i.e., a fluid-solid two-phase medium). Theoretical research on the elastic wave propagation characteristics of such media is a key focus of rock physics research. This research can quantitatively establish the relationship between the physical properties of rock minerals, fluids, pores, and other factors and the wave response characteristics. It is generally believed that the primary cause of rock wave propagation velocity dispersion and energy attenuation is the localized fluid flow induced by the heterogeneity of different scales within the rock under elastic wave excitation (Zhang et al., 2003; Carcione et al., 2022; Müller et al., 2010). A number of rock physics theoretical models have been developed to study the propagation and response characteristics of seismic waves through porous media. Among these, research on the theory of elastic wave propagation in fluid-solid two-phase media began in the 1950s, with Biot and Gassmann providing the fundamental framework for this fluid-solid two-phase elastic theory. Under low-frequency conditions, Gassmann derived the theoretical equation for the bulk modulus of rock under saturated fluid conditions (Gassmann, 1951). This equation is the most basic equation in rock physics research, and this rock physics theory is currently the most widely used rock physics model at home and abroad. The Gassmann model assumes that there is no relative movement between the fluid and the solid skeleton in the pores, and treats the entire saturated rock as an elastic body. Therefore, there is no energy attenuation when the wave propagates inside the rock. Biot considered the fluid flow in the pores of a fluid-solid two-phase medium, developed the Gassmann theory, and proposed the Biot theory (Biot 1956a, b, 1962). Assuming that the rock is homogeneous and isotropic, the pore fluid as a whole produces a global flow with relative friction motion relative to the rock skeleton. This can quantitatively describe the elastic wave velocity dispersion and attenuation caused by macroscopic flow. The Biot theory is a classic theory for studying elastic wave attenuation. Because the Biot theory ignores the influence of local flow effects at the mesoscale and microscale, it cannot provide a reasonable explanation for the attenuation and dispersion phenomena actually observed. It can only explain the ultrasonic frequency band of saturated rocks under high pressure and high permeability conditions (Mavko et al., 1998).

[0003] Early theoretical studies assumed that the pores within rocks were homogeneous. However, subsequent research revealed that small-scale heterogeneity within porous media has a significant impact on the propagation and attenuation of elastic waves. Mavko and Nur (1975) proposed that when elastic waves pass through rocks, cracks with relatively small aspect ratios close, causing the fluid within them to flow toward the hard pores, thus proposing the jet flow theory. Dvorkin and Nur (1993) considered both the "Biot" flow of the overall fluid flow and the "jet" flow of microscopic pores and established the BISQ model, which effectively explains the high-frequency dispersion and strong attenuation observed in rocks. However, the fast P-wave velocity estimated by this model is less than that predicted by the Gassmann model at low frequencies, while at higher frequencies it is consistent with the Biot model, which is inconsistent with the actual situation. Mavko and Jizba (1991) proposed a modified rock skeleton to calculate the jet-like relationship (MJ model) for the high-frequency, unrelaxed, wet rock skeleton elastic modulus. The modified rock skeleton effectively treats solid particles containing fractures as a new rock skeleton. The MJ model predicts higher high-frequency P-wave velocities than those calculated by the Biot model, but the model also predicts higher P-wave velocities at lower frequencies than the Gassmann model, and the formula is not applicable to cases where pores contain gas or dry rock. Based on the principles of the BISQ model and combined with a modified rock skeleton jet-like flow theory model, Dvorkin et al. (1995) reestablished a complex modulus model for fluid-saturated rock jets and derived an expression for the complex elastic modulus by considering one-dimensional radial flow. The derived complex modulus predicts P-wave velocities in the low-frequency limit that are consistent with those calculated by Gassmann theory. However, this model does not consider the influence of Biot flow on elastic wave propagation characteristics. Furthermore, the P-wave velocity calculated by this model is greater than the theoretical maximum value at high frequencies (the P-wave velocity calculated using the Biot model when all rock fractures are closed) (Wu et al., 2020). Based on the characteristics of various modified rock skeleton jet flow models, Wu et al. (2020) re-derived a modified rock skeleton jet flow theoretical model, forming an improved modified rock skeleton jet flow model (MFS model).

[0004] In response to the strong heterogeneity of the studied reservoirs, researchers have further investigated dual-porosity media based on Biot theory. Dual-porosity media abstractly represent regions within subsurface rocks with varying compressibility, forming porous media with dual-porosity structures. This structure can be caused by the uneven distribution of multiphase fluids within the rock or by differences in the compressibility of the pores themselves. The concept of dual porosity dates back to the 1960s. The dual-porosity theoretical model (Wang et al., 2012) is a theoretical model based on pore structure heterogeneity. Compared with previous models, it provides a more comprehensive simulation of velocity dispersion and attenuation. Because it simulates the dispersion and attenuation of particles larger than the particle size but much smaller than the seismic wavelength, the dual-porosity model describes mesoscale localized flow. Localized flow is believed to be a key driver of seismic wave velocity dispersion and energy attenuation in fluid-bearing rocks (Ba Jing, 2010; Guo and Gurevich, 2020; Guo et al., 2022). Ba et al. (2011) introduced mesoscale heterogeneity and proposed the Biot-Rayleigh dual-porosity model, a significant development of the dual-porosity theory. However, this model failed to effectively analyze the influence of the jet effect generated by fractures on the propagation characteristics of elastic waves. Therefore, a more accurate prediction method for the propagation characteristics of elastic waves in porous media that reflects the internal characteristics of rocks is needed. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention proposes a method for predicting the longitudinal wave velocity and attenuation of complex porous media, which can effectively characterize the wave propagation characteristics of complex porous media containing cracks and improve the accuracy of longitudinal wave velocity prediction of porous media.

[0006] In order to achieve the above object, the technical solution of the present invention is as follows:

[0007] A method for predicting longitudinal wave velocity and attenuation in complex porous media includes the following steps:

[0008] Step 1: Based on rock characteristics, the rock skeleton is divided into two categories: background phase and embedded body. The background phase is a skeleton containing only hard pores, and the embedded body is a skeleton containing cracks.

[0009] Step 2: Based on the Pride model, obtain the dry rock skeleton modulus of the background phase;

[0010] Step 3, based on the Pride model, obtain the dry rock skeleton modulus of the embedded body;

[0011] Step 4: Based on the MFS jet flow model, the modified rock dry skeleton modulus of the embedded body is obtained;

[0012] Step 5: Based on the dry rock skeleton modulus obtained in steps 2-4, obtain the Biot-Rayleigh elastic wave propagation equation including the jet effect;

[0013] Step 6: Obtain the Christophor equation for longitudinal waves based on the elastic wave propagation equation in step 5, and solve the complex wave number based on the Christophor equation for longitudinal waves; obtain the predicted values ​​of longitudinal wave velocity and attenuation in the complex porous medium based on the relationship between the complex wave number and the wave velocity and attenuation.

[0014] Preferably, the step 2 specifically includes the following steps:

[0015] Based on the formula of the skeleton modulus and matrix modulus of the Pride model, the dry rock skeleton modulus of the background phase is calculated:

[0016] The dry skeleton bulk modulus of the background phase is given by the following formula:

[0017]

[0018] Among them, K d1 is the dry skeleton bulk modulus of the background phase, K0 is the rock matrix bulk modulus, φ 10 is the local porosity of the background phase; α1 is the consolidation coefficient of the background phase;

[0019] The dry skeleton shear modulus of the background phase is as follows:

[0020]

[0021] Among them, G d1 is the dry skeleton shear modulus of the background phase, and G0 is the rock matrix shear modulus.

[0022] Preferably, the step 3 specifically includes the following steps:

[0023] Based on the formula of skeleton modulus and matrix modulus of the Pride model, the dry rock skeleton modulus of the embedded body is calculated:

[0024] The dry skeleton bulk modulus of the embedded body is as follows:

[0025]

[0026] Among them, K d2 is the dry skeleton bulk modulus of the embedded body, φ 20 is the local porosity of the embedment skeleton; α2 is the consolidation coefficient of the embedment;

[0027] The dry skeleton shear modulus of the embedded body is as follows:

[0028]

[0029] Among them, G d2 is the dry skeleton shear modulus of the embedment.

[0030] Preferably, the step 4 specifically includes the following steps:

[0031] The MFS jet flow model is used to obtain the modified rock dry skeleton bulk modulus of the embedded body, which is as follows:

[0032]

[0033] Among them, K md represents the modified rock dry skeleton bulk modulus of the embedded body, G md represents the embedded body modified rock dry skeleton shear modulus, K ms represents the modified solid bulk modulus, K hp It represents the bulk modulus of dry rock when all cracks are closed, that is, the bulk modulus under high pressure.

[0034] Preferably, the step 5 specifically includes the following steps:

[0035] The modified rock dry skeleton bulk modulus with cracks calculated by the MFS jet flow model is used to replace the dry rock skeleton modulus. Therefore, the dry skeleton bulk modulus of the embedded body is K md ; The Biot-Rayleigh elastic wave propagation equation including the jet effect is as follows:

[0036]

[0037] In the formula, u, U (1) 、U (2) are the average particle displacement of the rock skeleton, the displacement of fluid phase 1 (i.e., the fluid in the background phase skeleton), and the displacement of fluid phase 2 (i.e., the fluid in the embedded body skeleton), ε, ζ (1) ,ζ (2) are the corresponding three displacement divergence fields, represents the fluid strain increment caused by the local flow process. Due to the heterogeneity of the pore structure, two different types of pores are developed inside the rock. φ1 and φ2 are the absolute porosities of the background phase and the embedded body skeleton, R0 is the embedded body radius, and ρ f is the density of the fluid, κ is the permeability, ρ 00 , ρ 01 , ρ 02 , ρ 11 and ρ 22 is the density parameter, b1 and b2 are the dissipation coefficients, and A, N, Q1, R1, Q2 and R2 are the elastic parameters, expressed as:

[0038]

[0039] N=Gd (11h)

[0040] Where K f is the bulk modulus of the pore fluid, φ is the total porosity, K d is the rock dry skeleton bulk modulus, G d is the shear modulus of the rock skeleton.

[0041] Preferably, the step 6 specifically includes the following steps:

[0042] The analytical solution of the longitudinal wave i(ωt-kx) Substitute it into the Biot-Rayleigh elastic wave propagation equation with jet effect to obtain the Christopher equation for longitudinal waves. Solve for the complex wave number based on the determinant of the Christopher equation for longitudinal waves being 0. The formula is as follows:

[0043]

[0044] Where k is the complex wave number, a 11 , a 12 , a 13 , a 21 , a 22 , a 23 , a 31 , a 32 , a 33 , b 11 , b 12 , b 13 , b 21 , b 22 , b 23 , b 31 , b 32 , b 33 It is an intermediate parameter, which is related to the rock skeleton and fluid parameters.

[0045] By solving the complex wave number in the matrix equation, the longitudinal wave velocity and attenuation prediction values ​​of the Biot-Rayleigh model with jet effect are calculated as follows:

[0046] The longitudinal wave velocity is:

[0047]

[0048] The decay is:

[0049]

[0050] Where ω is the angular frequency, V p is the longitudinal wave velocity, is the inverse quality factor.

[0051] Based on the above content, the present invention also discloses the application of any of the above-mentioned methods for predicting longitudinal wave velocity and attenuation in complex porous media in reservoir oil and gas exploration and development.

[0052] Based on the above technical solution, the present invention has the following beneficial effects: It divides the rock skeleton into two categories: background phase and embedded phase, taking into account the jet flow effect generated by cracks in the embedded phase. It combines the MFS jet model with the Biot-Rayleigh model to derive the Biot-Rayleigh elastic wave propagation equation including the jet flow effect. This establishes a relationship between the complex wave number and the P-wave velocity and attenuation, deriving expressions for the P-wave velocity and attenuation, and predicting the P-wave velocity and attenuation characteristics in complex porous media. The present method fully considers the influence of cracks on the elastic wave propagation characteristics and effectively predicts the P-wave velocity and attenuation in complex porous media. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a schematic flow chart of a method for predicting longitudinal wave velocity and attenuation in a complex porous medium in an embodiment;

[0054] Figure 2 is a schematic diagram of characterizing the internal microstructural characteristics of a rock in an embodiment;

[0055] Figure 3 1 is a graph showing the relationship between the longitudinal wave velocity (Figure a) and attenuation (Figure b) predicted by the Biot-Rayleigh model with jet effects as a function of frequency;

[0056] Figure 4 The figure shows the prediction of the longitudinal wave velocity and attenuation values ​​of the carbonate rock sample 1 by the Biot-Rayleigh model including the jet effect and the experimental measurement results in one embodiment;

[0057] Figure 5 The figure shows the prediction of the longitudinal wave velocity and attenuation values ​​of carbonate rock sample 2 by the Biot-Rayleigh model including the jet effect and the experimental measurement results in one embodiment;

[0058] Figure 6 The figure shows an embodiment in which the Biot-Rayleigh model including the jet effect is used to predict the longitudinal wave velocity value and attenuation value of the carbonate rock sample 3 and the experimental measurement results. DETAILED DESCRIPTION

[0059] The technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention.

[0060] like Figure 1 As shown, this embodiment provides a method for predicting the longitudinal wave velocity and attenuation of complex porous media. The specific steps are as follows: Figure 1shown.

[0061] Step 1: Based on rock characteristics, the rock skeleton is divided into two categories: background phase and embedded body. The background phase is a skeleton containing only hard pores, and the embedded body is a skeleton containing cracks.

[0062] In this embodiment, considering the internal heterogeneity of the rock, a dual pore structure, namely hard pores and cracks, is adopted to divide the rock skeleton into two categories: background phase and embedded body. The skeleton containing only hard pores is called background phase, and the skeleton containing cracks is embedded body.

[0063] Step 2: Based on the Pride model, obtain the dry rock skeleton modulus of the background phase.

[0064] The dry rock skeleton modulus of the background phase was calculated based on the formula of skeleton modulus and matrix modulus of the Pride model.

[0065] Dry skeletal bulk modulus of the background phase:

[0066]

[0067] Among them, K d1 is the dry skeleton bulk modulus of the background phase, K0 is the rock matrix bulk modulus, φ 10 is the local porosity of the background phase skeleton; α1 is the consolidation coefficient of the background term.

[0068] Coherent skeleton shear modulus of the background phase:

[0069]

[0070] Among them, G d1 is the dry skeleton shear modulus of the background phase, and G0 is the rock matrix shear modulus.

[0071] Step 3: Based on the Pride model, obtain the dry rock skeleton modulus of the embedded body.

[0072] The dry rock skeleton modulus of the embedded body is calculated based on the formula of skeleton modulus and matrix modulus of the Pride model.

[0073] Dry skeleton bulk modulus of the embedment:

[0074]

[0075] Among them, K d2 is the dry skeleton bulk modulus of the embedded body, φ 20 is the local porosity of the embedding skeleton; α2 is the consolidation coefficient of the embedding.

[0076] Dry skeleton shear modulus of the embedded body:

[0077]

[0078] Among them, G d2 is the dry skeleton shear modulus of the embedment.

[0079] Step 4: Based on the jet flow theory, the MFS jet flow model is used to obtain the modified rock dry skeleton modulus of the embedded body.

[0080] Based on the MFS jet flow model, the embedded body-corrected rock dry skeleton bulk modulus is obtained:

[0081]

[0082] Among them, K md represents the embedded body modified rock dry skeleton bulk modulus, G md represents the embedded body modified rock dry skeleton shear modulus, K ms represents the modified solid bulk modulus, K hp It represents the bulk modulus of dry rock when all cracks are closed, that is, the bulk modulus under high pressure.

[0083] Step 5: Based on the dry rock skeleton modulus obtained in steps 2-4, obtain the Biot-Rayleigh elastic wave propagation equation including the jet effect.

[0084] According to the Biot-Rayleigh model, the background phase contains only hard pores, and its dry rock skeleton bulk modulus is K d1 The embedded phase contains cracks. Considering the hardening effect of the liquid in the cracks on the rock skeleton, the modified rock dry skeleton bulk modulus with cracks calculated by the jet flow model is used to replace the dry rock skeleton modulus. Therefore, the embedded coherent skeleton bulk modulus is K md The Biot-Rayleigh elastic wave propagation equation including the jet effect is as follows:

[0085]

[0086]

[0087] In the formula, u, U (1) 、U (2) are the average particle displacement of the rock skeleton, the displacement of fluid phase 1 (fluid in the background phase skeleton), and the displacement of fluid phase 2 (fluid in the embedded body skeleton), ε, ζ (1) ,ζ (2) are the corresponding three displacement divergence fields, represents the fluid strain increment caused by the local flow process. Due to the heterogeneity of the pore structure, two different types of pores are developed inside the rock. φ1 and φ2 are the absolute porosity of the background phase and the embedded body skeleton. R0 is the embedded body radius. ρ fis the density of the fluid, κ is the permeability, A, N, Q1, R1, Q2 and R2 are elastic parameters, ρ 00 , ρ 01 , ρ 02 , ρ 11 and ρ 22 is the density parameter, b1 and b2 are the dissipation coefficients.

[0088] in,

[0089]

[0090] N=G d (11h)

[0091] Where K f is the bulk modulus of the pore fluid. φ is the total porosity, K d is the rock dry skeleton bulk modulus, G d is the shear modulus of the rock skeleton.

[0092] Step 6: Obtain the Christophor equation for longitudinal waves based on the elastic wave propagation equation in step 5, and solve the complex wave number based on the Christophor equation for longitudinal waves; obtain the predicted values ​​of longitudinal wave velocity and attenuation in the complex porous medium based on the relationship between the complex wave number and the wave velocity and attenuation.

[0093] The analytical solution of the longitudinal wave i(ωt-kx) Substitute it into the Biot-Rayleigh elastic wave propagation equation with jet effect to obtain the Christopher equation for longitudinal waves. Solve for the complex wave number based on the determinant of the Christopher equation for longitudinal waves being 0. The formula is as follows:

[0094]

[0095] Where k is the complex wave number, a 11 , a 12 , a 13 , a 21 , a 22 , a 23 , a 31 , a 32 , a 33 , b 11 , b 12 , b 13 , b 21 , b 22 , b 23 , b 31 , b 32 , b 33 It is an intermediate parameter and is related to the rock skeleton and fluid parameters.

[0096] By solving the complex wave number in the matrix equation, the longitudinal wave velocity and attenuation prediction values ​​of the Biot-Rayleigh model with jet effect are calculated as follows:

[0097] The longitudinal wave velocity is:

[0098]

[0099] The decay is:

[0100]

[0101] Where ω is the angular frequency, V p is the longitudinal wave velocity, is the inverse quality factor.

[0102] In an embodiment of the present application, a method for predicting the P-wave velocity and attenuation in complex porous media is provided for application in reservoir oil and gas exploration and development. Specifically, the application includes:

[0103] The characteristics of the Biot-Rayleigh model predicting longitudinal wave velocity and attenuation including the jet effect are analyzed through numerical simulation, and the application effect of the model is verified by combining ultrasonic experimental data.

[0104] Based on the above-mentioned method for predicting longitudinal wave velocity and attenuation in complex porous media, the implementation process of the present invention is described below with specific examples.

[0105] Before carrying out the examples, numerical simulation of the model of the present invention is first performed, and the rock physical parameter values ​​are shown in Table 1:

[0106] Table 1 Simulation parameters of the Biot-Rayleigh model including jet effects

[0107]

[0108]

[0109] The numerical simulation comparison results of the model proposed in this invention and the Biot-Rayleigh model are shown in Figure 3 .Depend on Figure 3 It can be seen from a that when the frequency is low, the longitudinal wave velocities calculated by the two models are consistent. As the frequency increases, the longitudinal wave velocities increase. The longitudinal wave velocity calculated by the Biot-Rayleigh model with jet flow proposed in this invention is greater than the result calculated by the Biot-Rayleigh model, and there is an additional rising step at low frequencies. The main reason is that the jet flow affects the propagation velocity of elastic waves, which makes the dispersion of the Biot-Rayleigh model with jet flow effect larger. Figure 3b It can be seen that at low frequencies, the longitudinal wave attenuation calculated by the model proposed in the present invention has one more attenuation peak than the longitudinal wave attenuation of the Biot-Rayleigh model, but the attenuation caused by the local flow between the cracks and the pores is smaller than that of the Biot-Rayleigh model. The main reason is that part of the fluid pressure is converted into a jet flow between the cracks and the tiny pores of the embedded body, resulting in a microscopic attenuation peak.

[0110] In order to further illustrate the effect of the present invention, this embodiment compares the experimental measured values ​​of the longitudinal wave velocity of three carbonate rock samples with the theoretical predicted values.

[0111] The experimental measurement frequency was 1 MHz, and seven values ​​were measured at effective pressures (15 MPa, 20 MPa, 25 MPa, 30 MPa, 40 MPa, 50 MPa, and 60 MPa). The porosity was 4.26%, 4.44%, and 5.93%, respectively; the permeability was 3.441 mD, 0.214 mD, and 0.963 mD, respectively; the mineral bulk modulus was 60 GPa, 67 GPa, and 62 GPa; the shear modulus was 56 GPa, 55 GPa, and 51 GPa; and the rock dry skeleton density was 2690 kg / m 3 、2714kg / m 3 and 2651kg / m 3 The bulk modulus of the rock matrix is ​​32 GPa and the density of water is 1000 kg / m 3 , the bulk modulus of water is 2.25 GPa, and the viscosity of water is 0.001 Pa·s.

[0112] Figure 4-6 The graphs show the relationship between the actual measured P-wave and attenuation values ​​of three carbonate rock samples and the predictions using the proposed method. The solid lines in the graphs represent the predicted values ​​using the proposed method for effective pressures of 15 MPa, 20 MPa, 25 MPa, 30 MPa, 40 MPa, 50 MPa, and 60 MPa, respectively. The square dots represent the experimentally measured P-wave velocities at the corresponding pressures. Comparing the model-predicted P-wave velocities with the experimental values ​​reveals that the proposed method can effectively predict the P-wave velocities and attenuation values ​​of carbonate rock at different pressures.

[0113] In summary, the present invention divides the rock skeleton into two categories: background phase and embedded body, combining the characteristics of the pore structure. It fully considers the influence of the jet effect generated by the cracks in the embedded body on the elastic wave propagation characteristics of the porous medium, derives the Biot-Rayleigh elastic wave propagation equation including the jet effect, and forms a calculation method for the longitudinal wave velocity and attenuation in complex porous media.

[0114] It should be understood that, although the various steps in the above flow chart are shown in sequence as indicated by the arrows, these steps are not necessarily performed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and these steps can be performed in other orders. Moreover, at least a portion of the steps in the above flow chart may include multiple sub-steps or multiple stages, and these sub-steps or stages are not necessarily performed at the same time, but can be performed at different times, and the execution order of these sub-steps or stages is not necessarily to be performed in sequence, but can be performed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.

[0115] The above is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting longitudinal wave velocity and attenuation in complex porous media, characterized by: The steps include: Step 1: Based on rock characteristics, the rock skeleton is divided into two categories: background phase and embedded body. The background phase is a skeleton containing only hard pores, and the embedded body is a skeleton containing cracks. Step 2: Based on the Pride model, obtain the dry rock skeleton modulus of the background phase; Step 3, based on the Pride model, obtain the dry rock skeleton modulus of the embedded body; Step 4: Based on the MFS jet flow model, the modified rock dry skeleton modulus of the embedded body is obtained; Step 5: Based on the dry rock skeleton modulus obtained in steps 2-4, obtain the Biot-Rayleigh elastic wave propagation equation including the jet effect; Step 6, obtaining the Christoffel equation for longitudinal waves based on the elastic wave propagation equation in step 5, and solving the complex wave number based on the Christoffel equation for longitudinal waves; Based on the relationship between complex wave number, wave velocity and attenuation, the predicted values ​​of longitudinal wave velocity and attenuation in complex porous media are obtained.

2. A method for predicting longitudinal wave velocity and attenuation in complex porous media according to claim 1, characterized in that: The step 2 specifically includes the following steps: Based on the formula of the skeleton modulus and matrix modulus of the Pride model, the dry rock skeleton modulus of the background phase is calculated: The dry skeleton bulk modulus of the background phase is given by the following formula: Among them, K d1 is the dry skeleton bulk modulus of the background phase, K0 is the rock matrix bulk modulus, φ 10 is the local porosity of the background phase; α1 is the consolidation coefficient of the background phase; The dry skeleton shear modulus of the background phase is as follows: Among them, G d1 is the dry skeleton shear modulus of the background phase, and G0 is the rock matrix shear modulus.

3. The method for predicting longitudinal wave velocity and attenuation in complex porous media according to claim 1, characterized in that: The step 3 specifically includes the following steps: Based on the formula of skeleton modulus and matrix modulus of the Pride model, the dry rock skeleton modulus of the embedded body is calculated: The dry skeleton bulk modulus of the embedded body is as follows: Among them, K d2 is the dry skeleton bulk modulus of the embedded body, φ 20 is the local porosity of the embedment skeleton; α2 is the consolidation coefficient of the embedment; The dry skeleton shear modulus of the embedded body is as follows: Among them, G d2 is the dry skeleton shear modulus of the embedment.

4. The method for predicting longitudinal wave velocity and attenuation in complex porous media according to claim 1, characterized in that: The step 4 specifically includes the following steps: The MFS jet flow model is used to obtain the modified rock dry skeleton bulk modulus of the embedded body, which is as follows: Among them, K md represents the modified rock dry skeleton bulk modulus of the embedded body, G md represents the embedded body modified rock dry skeleton shear modulus, K ms represents the modified solid bulk modulus, K hp It represents the bulk modulus of dry rock when all cracks are closed, that is, the bulk modulus under high pressure.

5. The method for predicting longitudinal wave velocity and attenuation in complex porous media according to claim 1, characterized in that: The step 5 specifically includes the following steps: The modified rock dry skeleton bulk modulus with cracks calculated by the MFS jet flow model is used to replace the dry rock skeleton modulus. Therefore, the dry skeleton bulk modulus of the embedded body is K md ; The Biot-Rayleigh elastic wave propagation equation including the jet effect is as follows: In the formula, u, U (1) 、U (2) are the average particle displacement of the rock skeleton, the displacement of fluid phase 1 (i.e., the fluid in the background phase skeleton), and the displacement of fluid phase 2 (i.e., the fluid in the embedded body skeleton), ε, ζ (1) ,ζ (2) are the corresponding three displacement divergence fields, represents the fluid strain increment caused by the local flow process. Due to the heterogeneity of the pore structure, two different types of pores are developed inside the rock. φ1 and φ2 are the absolute porosities of the background phase and the embedded body skeleton, R0 is the embedded body radius, and ρ f is the density of the fluid, κ is the permeability, ρ 00 , ρ 01 , ρ 02 , ρ 11 and ρ 22 is the density parameter, b1 and b2 are the dissipation coefficients, and A, N, Q1, R1, Q2 and R2 are the elastic parameters, expressed as: N=G d (11h) Where K f is the bulk modulus of the pore fluid, φ is the total porosity, K d is the rock dry skeleton bulk modulus, G d is the shear modulus of the rock skeleton.

6. The method for predicting longitudinal wave velocity and attenuation in complex porous media according to claim 1, characterized in that: The step 6 specifically includes the following steps: The analytical solution of the longitudinal wave i(ωt-kx) Substitute it into the Biot-Rayleigh elastic wave propagation equation with jet effect to obtain the Christopher equation for longitudinal waves. Solve for the complex wave number based on the determinant of the Christopher equation for longitudinal waves being 0. The formula is as follows: Where k is the complex wave number, a 11 , a 12 , a 13 , a 21 , a 22 , a 23 , a 31 , a 32 , a 33 , b 11 , b 12 , b 13 , b 21 , b 22 , b 23 , b 31 , b 32 , b 33 It is an intermediate parameter, which is related to the rock skeleton and fluid parameters. By solving the complex wave number in the matrix equation, the longitudinal wave velocity and attenuation prediction values ​​of the Biot-Rayleigh model with jet effect are calculated as follows: The longitudinal wave velocity is: The decay is: Where ω is the angular frequency, V p is the longitudinal wave velocity, is the inverse quality factor.

7. Application of the method for predicting P-wave velocity and attenuation in complex porous media according to any one of claims 1 to 6 in reservoir oil and gas exploration and development.

Images