CN111695308B - Method for predicting change characteristics of longitudinal wave speed along with temperature change - Google Patents

Abstract

The invention discloses a method for predicting the change characteristic of longitudinal wave velocity along with temperature change, which considers the influence of temperature on the micro-fracture void degree by using David and Zimmerman models, considers the influence of temperature on different fluid parameters by using Batzle and Wang models, respectively considers the influence of temperature on fluid and micro-fracture in a Biot-Rayleigh double-hole medium model, and analyzes the relation of temperature on the longitudinal wave velocity by using plane waves so as to further research the influence of temperature on the longitudinal wave velocity. The method has high prediction precision and strong applicability, and provides a powerful reference for predicting the influence of the temperature on the longitudinal wave velocity in actual work.

Description

Method for predicting change characteristics of longitudinal wave speed along with temperature change

Technical Field

The invention relates to analysis of temperature on rock physical characteristics, in particular to a method for predicting change characteristics of longitudinal wave velocity along with temperature change.

Background

In recent years, with the increasing consumption of resources, the exploitation depth of oil and gas reservoirs is increased, and the influence of thermodynamic environment (pressure and temperature) on rock properties is more and more prominent. The thermodynamic environment is also an important factor in the exploitation and drilling of geothermal reservoirs. Therefore, the influence of pressure and temperature on the physical and mechanical properties of rock is always an important subject of rock physics research. The research on the influence of the temperature on various physical and mechanical parameters of the rock, particularly on wave response characteristics, has very important significance on engineering such as geothermal exploration and the like.

Since temperature changes are a major component of reservoir changes during production, it is important to understand the effects of temperature on seismic velocity. To relate changes in seismic attributes to reservoir conditions, the effect of temperature on petrophysical properties must be thoroughly understood. At present, a great number of analysis methods for the change of longitudinal and transverse wave speeds along with temperature are direct analysis obtained by fitting experimental data. And the influence of pore fluid is not considered in the research, so that the influence of temperature on the response characteristic of the saturated fluid rock wave cannot be intuitively described.

Disclosure of Invention

The purpose of the invention is as follows: the application aims to provide a method for predicting the change characteristic of longitudinal wave velocity along with temperature change, which is used for solving the defects that the existing method is low in prediction accuracy, incomplete in consideration and incapable of describing the response characteristic of temperature to saturated fluid rock wave.

The technical scheme is as follows: the invention provides a method for predicting the change characteristics of longitudinal wave velocity along with temperature change, which comprises the following steps:

(1) acquiring ultrasonic velocity experimental data which changes along with temperature, wherein the experimental data comprises the porosity, permeability, rock density, fluid property, longitudinal and transverse wave velocity and pressure of rock;

(2) establishing a relationship between the elastic modulus of the rock and the micro-pore structure based on David and Zimmerman models, and calculating the micro-fracture density and the micro-fracture aspect ratio under the same temperature and different pressures so as to obtain a differential pressure relationship of the micro-fracture porosity;

(3) according to the longitudinal and transverse wave speed changing with the temperature, based on the differential pressure relation of the microcrack porosity, establishing the relation of the microcrack porosity changing with the temperature under the same pressure;

(4) establishing a relation between temperature, pressure and fluid properties based on a Batzle model and a Wang model according to experimental data to obtain different fluid parameters under different temperature conditions;

(5) a temperature-dependent double-hole medium model is obtained by utilizing a Biot-Rayleigh equation;

(6) and solving the double-hole medium model, establishing a relation between the longitudinal wave speed and the temperature change by utilizing plane wave analysis, and predicting the longitudinal wave change characteristics.

Further, the step (2) comprises:

(21) establishing a relationship between the rock elastic modulus and the micro-pore structure based on David and Zimmerman models, and determining the microcrack densities corresponding to different pressures by adopting an effective elastic modulus expression of Mori-Tanaka theory, wherein the relationship is specifically represented as follows:

in the formula, C_eff＝1/K_dry，S_eff＝1/G_dryRespectively representing the effective volume compressibility and shear compliance of the rock, K_dryAnd G_dryRespectively representing the bulk modulus and the shear modulus of the dry rock; v. of_stiff＝(3K_stiff-2G_stiff)/(6K_stiff+2G_stiff) Denotes the substrate Poisson's ratio, C_stiffAnd S_stiffRespectively, the equivalent compressibility and shear compliance of the stone containing only intergranular porosity, C₀And S₀Respectively the compressibility and shear compliance of the rock particles, phi_stiffΓ is the microcrack density (total number of microcracks embedded in the unit cell) of the hard pores in the rock, P, Q is the shape factor of the hard pores, respectively, in relation to the aspect ratio α of the ellipsoidal pores, and the poisson's ratio v of the rock particles, the specific expression:

wherein:

v＝(3K₀-2G₀)/(6K₀+2G₀)；

(22) based on the obtained microcrack densities at the same temperature and different effective pressures p, fitting the microcrack density gamma under each pressure by using least square regression_p；

The quantitative relationship between the microcrack aspect ratio and effective pressure can be expressed as:

wherein E is_stiffIs the equivalent Young's modulus under effective pressure, defined as E_stiff＝3K_stiff[1-2ν_stiff]；

(23) According to the relationship between the microcrack porosity and the microcrack density in the David and Zimmerman models, the microcrack porosity at different pressures and at the same temperature is calculated:

wherein phi is₂And (p) is the microcrack porosity at the same temperature and under different pressures p.

Further, the step (3) comprises:

(31) longitudinal and transverse wave velocity (V) of rock sample changing along with temperature based on ultrasonic experiment_p，V_s) Respectively calculating the corresponding variation ranges at different temperaturesEquivalent bulk modulus K of press saturated rock_satAnd shear modulus G_satThe expression is as follows:

G_sat＝ρV_s ² (7)

wherein ρ is the density of the rock;

(32) according to equivalent bulk modulus K_satAnd shear modulus G_satCalculating the bulk modulus K of the dry skeleton of the rock sample based on the Gassmann equation_drAnd shear modulus G_drThe expression is as follows:

G_dr＝G_sat (9)

wherein, K_mIs the bulk modulus, K, of the minerals that make up the rock_fThe bulk modulus of the fluid at the corresponding temperature, phi, the total porosity of the rock;

(33) and (3) fitting according to the microcrack porosity under the same pressure to obtain the distribution of the rock elastic modulus and the microcrack porosity at different temperatures based on the relationship between the rock elastic modulus and the microcrack structure and the differential pressure relationship of the microcrack porosity established in the step (2).

Further, the fluid comprises water and oil, and step (4) comprises:

empirical equations between different fluid properties and temperature (T), pressure (P) were developed using the Batzle and Wang models, with different fluids including water and oil, as follows:

density of water ρ_wIs composed of

Acoustic velocity V of water_wIs composed of

Wherein, ω is_ijConstant in the Batzle and Wang models;

viscosity of water eta of

Density of oil ρ_oilIs composed of

Where ρ is₀Describing the reference density of the petroleum, i.e. the density at a temperature of 15.6 ℃ and one atmosphere;

acoustic velocity V of oil_oilIs composed of

Viscosity η of oil_oilIs composed of

Further, the step (5) comprises:

based on a Biot-Rayleigh equation, a wave control equation is derived by utilizing a Hamilton principle, strain energy and kinetic energy are introduced through local fluid flow and interaction among different pore areas, then corresponding potential energy functions, kinetic energy functions and dissipation functions are established, and a temperature-related double-pore medium model is derived, wherein the wave propagation control equation is as follows:

wherein U, U⁽¹⁾,U⁽²⁾The average particle displacement of the solid matrix, the displacement of the first phase fluid (i.e., the fluid in the host matrix), and the displacement of the second phase fluid (i.e., the fluid in the microfractures), respectively; superscripts (1) and (2) represent two types of porosity; epsilon, zeta⁽¹⁾,ζ⁽²⁾Respectively representing the corresponding 3 displacement divergence fields;

the fluid strain increment caused in the local flow process is expressed, and the physical meaning of the expression is the volume of fluid exchange between interparticle pores and microcracks in the fluid flow; due to the heterogeneity of the pore structure within the rock, the rock develops into two different types of pores, hard and soft, respectively₁₀And phi₂₀Local porosity representing intergranular porosity and microcracking; r₁₂Radius of the microcracks; phi is a₁,φ₂Is the absolute porosity of two types of pores, b₁,b₂Is the Biot dissipation factor, p_f,η,κ₁Density, viscosity and permeability of the fluid, respectively, p₁₁,ρ₁₂,ρ₁₃,ρ₂₂,ρ₃₃As density parameter, A, Q₁,Q₂,R₁,R₂And N is an elasticity parameter.

Further, the step (6) comprises:

(61) according to the microcracked porosity (phi) in dependence on temperature₂(p)) and different fluid parameters under different temperature conditions to obtain corresponding elastic parameters, dissipation coefficients and density parameters;

(62) bringing the obtained elastic parameters, dissipation coefficients and density parameters into the double-hole medium models of (17a) - (17d) to obtain a temperature-related equation of motion;

(63) and solving a temperature-related motion equation by using a plane wave analysis method to obtain a temperature-related longitudinal wave velocity prediction result.

Further, the step (63) includes:

solving the longitudinal wave^i(ωt-k·x)Substituting into the Biot-Rayleigh equation to obtain the complex wave number square k²The complex unitary cubic equation set of (2) solves the equation set:

wherein k represents the wave number, and other parameters are as follows:

wherein:

x₁＝i(Q₁φ₂-Q₂φ₁)/Z,x₂＝iR₁φ₂/Z,x₃＝iR₂φ₁/Z

square k of complex wave number²The three solutions respectively correspond to a fast longitudinal wave and two types of slow longitudinal waves, wherein the fast longitudinal wave with the highest speed corresponds to the solved longitudinal wave, and the longitudinal wave speed of the saturated rock mass related to the temperature is predicted by a prediction formula of the longitudinal wave speed:

where ω is 2 pi f and f is the frequency.

Has the advantages that: compared with the prior art, the micro-fracture structure in the rock physical model matrix is fully considered, the relation of micro-fracture changing along with temperature is established based on MT theory and test data, the relation of temperature, pressure and fluid property is established through BW theory, a temperature-micro-fracture related double-hole medium model is established by combining BR theory, the relation of longitudinal wave velocity and temperature is established, and the change rule of seismic wave velocity at different temperatures is further analyzed by utilizing the model. The method has high accuracy of the prediction result, and can provide reference for seismic wave velocity prediction.

Drawings

FIG. 1 is a schematic flow chart of a prediction method of the present application;

FIG. 2 is a graph of the effect of temperature on density (a) viscosity (b) bulk modulus (c) of water and oil at a pore fluid pressure of 10 MPa;

FIG. 3 is a plot of microcracked porosity versus temperature for 10 samples of carbonate under water (a) and oil (b) saturated conditions;

FIG. 4 shows the trend of longitudinal wave velocity with temperature for carbonate samples 1(a), 2(b) and 4(c) with different fluids (water, oil);

FIG. 5 is a comparison of modified Gassmann equation (dashed line) for the rate of change of pore fluid (water) at different temperatures for sample 3 under 50bar pore fluid pressure;

FIG. 6 is a comparison of experimental data and theoretical results of 10 samples of water (a) and oil (b) saturated carbonate with changes in longitudinal wave velocity with porosity at different temperatures;

FIG. 7 is a histogram of the velocity change of 10 samples of water (a) saturated and oil (b) saturated carbonates at different temperatures.

Detailed Description

The invention is further described below with reference to the following figures and examples:

the invention provides a method for predicting the change characteristic of longitudinal wave velocity along with temperature change, which comprises the following steps as shown in figure 1:

s101, ultrasonic velocity experimental data which change along with temperature are obtained, and the experimental data comprise the porosity, permeability, rock density, fluid property, longitudinal and transverse wave velocity and pressure of rock.

S102, establishing a relationship between the elastic modulus of the rock and the micro-pore structure based on the David and Zimmerman models, and calculating the density and the aspect ratio of the micro-fractures under the same temperature and different pressures so as to obtain a differential pressure relationship of the micro-fracture porosity. The method comprises the following specific steps:

(21) establishing a relation between the elastic modulus of the rock and the micro-pore structure based on David and Zimmerman models, wherein the models assume that the microcracks are slender oblate spheroids, and in order to determine the density of the microcracks, an effective elastic modulus expression of Mori-Tanaka theory is adopted and specifically expressed as follows:

in the formula, C_eff＝1/K_dry，S_eff＝1/G_dryRespectively representing the effective volume compressibility and shear compliance of the rock, K_dryAnd G_dryRespectively representing the bulk modulus and the shear modulus of the dry rock; v. of_stiff＝(3K_stiff-2G_stiff)/(6K_stiff+2G_stiff) Denotes the substrate Poisson's ratio, C_stiffAnd S_stiffRespectively, the equivalent compressibility and shear compliance of the stone containing only intergranular pores (i.e. hard pores), C₀And S₀Respectively the compressibility of the rock particles andshear compliance, phi_stiffΓ is the microcrack density (total number of microcracks embedded in the unit cell) of the hard pores in the rock, P, Q is the shape factor of the hard pores, respectively, in relation to the aspect ratio α of the ellipsoidal pores, and the poisson's ratio v of the rock particles, the specific expression:

wherein:

v＝(3K₀-2G₀)/(6K₀+2G₀)；

(22) based on the obtained microcrack densities at the same temperature and different effective pressures p, fitting the microcrack density gamma under each pressure by using least square regression_p；

Meanwhile, the quantitative relationship between the aspect ratio of the microcracks and the effective pressure can be expressed as:

wherein E is_stiffIs the equivalent Young's modulus under effective pressure, defined as E_stiff＝3K_stiff[1-2ν_stiff]；

(23) According to the relationship between the microcrack porosity and the microcrack density in the David and Zimmerman models, the microcrack porosity at different pressures and at the same temperature is calculated:

wherein phi is₂(p) is phaseMicrocracked porosity at the same temperature and different pressures p.

As shown in fig. 3, the microcrack porosity gradually increases with increasing temperature.

S103, establishing a relationship that the microcracked porosity changes with the temperature under the same pressure based on the differential pressure relationship of the microcracked porosity according to the longitudinal and transverse wave speeds changing with the temperature. The method specifically comprises the following steps:

(31) longitudinal and transverse wave velocity (V) of rock sample changing along with temperature based on ultrasonic experiment_p，V_s) Respectively calculating the equivalent bulk modulus K of the saturated rock with variable confining pressure corresponding to different temperatures_satAnd shear modulus G_satThe expression is as follows:

G_sat＝ρV_s ² (7)

wherein ρ is the density of the rock;

(32) according to equivalent bulk modulus K_satAnd shear modulus G_satCalculating the bulk modulus K of the dry skeleton of the rock sample based on the Gassmann equation_drAnd shear modulus G_drThe expression is as follows:

G_dr＝G_sat (9)

wherein, K_mIs the bulk modulus, K, of the minerals that make up the rock_fThe bulk modulus of the fluid at the corresponding temperature, phi, the total porosity of the rock;

(33) and (3) fitting according to the microcrack porosity under the same pressure to obtain the distribution of the rock elastic modulus and the microcrack porosity at different temperatures based on the relationship between the rock elastic modulus and the microcrack structure and the differential pressure relationship of the microcrack porosity established in the step (2).

S104, establishing a relation between temperature, pressure and fluid properties based on the Batzle and Wang models according to experimental data to obtain different fluid parameters under different temperature conditions. The method specifically comprises the following steps:

in embodiments of the present application, the fluid comprises water and oil.

Empirical equations between different fluid (pure water, oil) properties and temperature (T), pressure (P) using the Batzle and Wang models are shown below:

density of water ρ_wIs composed of

Acoustic velocity V of water_wIs composed of

Wherein, ω is_ijConstant in the Batzle and Wang models;

viscosity of water eta of

Density of oil ρ_oilIs composed of

Where ρ is₀The reference density of petroleum is described, i.e. the density at a temperature of 15.6 ℃ and one atmosphere.

Acoustic velocity V of oil_oilIs composed of

Viscosity η of oil_oilIs composed of

For a constant fluid pressure, the density, viscosity, and bulk modulus of different fluids vary significantly with temperature. As shown in FIG. 2, the density of water decreases steadily between 0 and 300 ℃. However, at 75 ℃, the viscosity of water rapidly drops to around 0.002Pa · s and then drops more slowly with increasing temperature. The bulk modulus of water is slightly increased between 0 and 75 ℃, and is rapidly reduced within the range of 0 to 300 ℃, and the bulk modulus is from 820 to 630kg/m³. On the other hand, the oil density also decreases with increasing temperature, but has a different tendency from the water density. Compared with the viscosity of water, the viscosity of oil is reduced more quickly at 0-75 ℃, and is reduced more slowly at the temperature of more than 250 ℃. In addition, there is also a significant difference in the bulk modulus-temperature curves for water and oil. From 0 ℃ to 300 ℃, the bulk modulus of the oil decreases rapidly. We have observed that temperature has a large effect on the thermophysical properties of the fluid. Therefore, the effect of temperature on longitudinal wave velocity is closely related to the thermophysical properties of the fluid.

S105, a temperature-dependent double-hole medium model is deduced by using a Biot-Rayleigh equation.

In particular, the invention utilizes the Biot-Rayleigh (BR) dual pore media model for analysis, taking into account the heterogeneity of the rock. The BR model is a model approximately describing heterogeneous porous rock and is closer to the internal structure of a real rock, a wave control equation is derived by utilizing the Hamilton principle, strain energy and kinetic energy are introduced through local fluid flow and interaction among different pore areas, and then corresponding potential energy function, kinetic energy function and dissipation function are established, so that a corresponding double-pore medium model can be derived, wherein the wave propagation control equation is as follows:

wherein U, U⁽¹⁾,U⁽²⁾The average particle displacement of the solid matrix, the displacement of the first phase fluid (i.e., the fluid in the host matrix), and the displacement of the second phase fluid (i.e., the fluid in the microfractures), respectively; superscripts (1) and (2) represent two types of porosity; epsilon, zeta⁽¹⁾,ζ⁽²⁾Respectively representing the corresponding 3 displacement divergence fields;

representing the increase in fluid strain induced during local flow, the physical meaning of the expression being the volume of fluid exchange between the interparticle pores (hard pores) and the microfractures (soft pores) in the fluid flow; due to the heterogeneity of the pore structure within the rock, the rock develops into two different types of pores, hard and soft, respectively₁₀And phi₂₀Local porosity representing intergranular pores and fissures; r₁₂Radius of the microcracks; phi is a₁,φ₂Is the absolute porosity of two types of pores, b₁,b₂Is the Biot dissipation factor, p_f,η,κ₁Density, viscosity and permeability of the fluid, respectively, p₁₁,ρ₁₂,ρ₁₃,ρ₂₂,ρ₃₃As density parameter, A, Q₁,Q₂,R₁,R₂And N is an elasticity parameter.

Wherein, the expression of the density parameter is specifically as follows:

the expression of the elasticity parameter is specifically:

N＝μ_b

s106, solving the double-hole medium model, establishing the relation between the longitudinal wave speed and the temperature change by utilizing plane wave analysis, and predicting the longitudinal wave change characteristics. The method specifically comprises the following steps:

(61) according to the microcracked porosity (phi) in dependence on temperature₂(p)) and different fluid parameters under different temperature conditions to obtain corresponding elastic parameters, dissipation coefficients and density parameters;

(62) bringing the obtained elastic parameters, dissipation coefficients and density parameters into the double-hole medium models of (17a) - (17d) to obtain a temperature-related equation of motion;

(63) and solving a temperature-related motion equation by using a plane wave analysis method to obtain a temperature-related longitudinal wave velocity prediction result.

Specifically, the step (63) includes:

solving the longitudinal wave^i(ωt-k·x)Substituting into the Biot-Rayleigh equation to obtain the complex wave number square k²The complex unitary cubic equation set of (2) solves the equation set:

wherein k represents the wave number, and other parameters are as follows:

wherein:

x₁＝i(Q₁φ₂-Q₂φ₁)/Z,x₂＝iR₁φ₂/Z,x₃＝iR₂φ₁/Z

square k of complex wave number²The three solutions respectively correspond to a fast longitudinal wave and two types of slow longitudinal waves, wherein the fast longitudinal wave with the highest speed corresponds to the solved longitudinal wave, and the longitudinal wave speed of the saturated rock mass related to the temperature is predicted by a prediction formula of the longitudinal wave speed:

where ω is 2 pi f and f is the frequency.

The effect of the simulation method of the present application is illustrated by the following relevant experiments:

as can be seen from fig. 4, the variable microcracks are not dominant in the effect of temperature on the saturated fluid rock p-wave velocity. The longitudinal wave velocity prediction of the model is well matched with experimental data. For each carbonate rock, the p-wave velocity of the water-saturated sample tends to increase and then decrease with increasing temperature, while the p-wave velocity of the oil-saturated sample gradually decreases with increasing temperature.

While compared to the modified Gassmann equation (MG) proposed by Jaya et al (2010). As shown in fig. 5, the two models did not differ significantly below 125. But with increasing temperature the consistency of the MG results (dashed line) is lower. The transparent rock is hard, so the pore structure of the rock is complex. As the temperature increases, the soft pores within the rock open up gradually, causing a change in the pore structure of the rock, which in turn changes the fluid flow path. Thus, compared to our model, the MG method ignores changes in complex pore structures at high temperatures.

On the basis of the velocity-temperature model, 10 pieces of carbonate rock were simulated. We measured the velocity of longitudinal waves at both temperatures of 20 ℃ and 140 ℃. The results shown in fig. 6 were obtained. At the same temperature, the longitudinal wave velocity of saturated rock decreases with increasing porosity. In general, the velocity of longitudinal waves decreases with increasing temperature. The results of comparing the velocity variations under the two simulation assumptions are shown in fig. 7. As the porosity increases, the change in microcrack porosity also has some effect on the longitudinal wave velocity as the temperature induced velocity decreases. It is clear that in the velocity-temperature relationship of saturated rocks, the effect of temperature on the fluid is the main cause of velocity variation. The temperature-induced variation in microcrack porosity is not a critical factor in the reduction of longitudinal wave velocity. As the temperature increases from 20 ℃ to 140 ℃, the effect of oil saturation on the velocity of longitudinal waves is much greater than water saturation. These changes are related to the speed of sound of the fluid. As porosity increases, the p-wave velocity of some saturated rocks varies less.

As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.

The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

Claims (6)

1. A method for predicting the change characteristic of longitudinal wave velocity along with temperature change is characterized by comprising the following steps:

(1) acquiring ultrasonic velocity experimental data which changes along with temperature, wherein the experimental data comprises the porosity, permeability, rock density, longitudinal and transverse wave velocity and pressure of rock;

(2) establishing a relationship between the elastic modulus of the rock and the micro-pore structure based on David and Zimmerman models, and calculating the micro-fracture density and the micro-fracture aspect ratio under the same temperature and different pressures so as to obtain the relationship between the micro-fracture porosity and the differential pressure;

(3) according to the longitudinal and transverse wave speeds of the measured rock along with the temperature change, establishing the relationship of the microcrack porosity along with the temperature change under the same pressure based on the pressure difference relationship of the microcrack porosity;

(4) establishing a relation between temperature, pressure and fluid properties based on a Batzle model and a Wang model according to experimental data to obtain different fluid parameters under different temperature conditions;

(5) a temperature-dependent double-hole medium model is obtained by utilizing a Biot-Rayleigh equation;

(6) solving a double-hole medium model, establishing a relation between the velocity of longitudinal waves and the temperature change by utilizing plane wave analysis, and predicting the change characteristics of the longitudinal waves, wherein the method specifically comprises the following steps:

(61) obtaining corresponding elastic parameters, dissipation coefficients and density parameters according to the microcrack porosity related to the temperature and different fluid parameters under different temperature conditions;

(62) the obtained elastic parameters, dissipation coefficients and density parameters are introduced into a double-hole medium model to obtain a temperature-related motion equation;

(63) and solving a temperature-related motion equation by using a plane wave analysis method to obtain a temperature-related longitudinal wave velocity prediction result.

2. The method of claim 1, wherein step (2) comprises:

(21) establishing a relationship between the rock elastic modulus and the micro-pore structure based on David and Zimmerman models, and determining the microcrack densities corresponding to different pressures by adopting an effective elastic modulus expression of Mori-Tanaka theory, wherein the relationship is specifically represented as follows:

in the formula, C_eff＝1/K_dry，S_eff＝1/G_dryRespectively representing the effective volume compressibility and shear compliance of the rock, K_dryAnd G_dryRespectively representing the bulk modulus and the shear modulus of the dry rock; v. of_stiff＝(3K_stiff-2G_stiff)/(6K_stiff+2G_stiff) Denotes the substrate Poisson's ratio, C_stiffAnd S_stiffRespectively, the equivalent compressibility and shear compliance of the stone containing only intergranular porosity, C₀And S₀Respectively the compressibility and shear compliance of the rock particles, phi_stiffFor the porosity of hard pores in rock, Γ is the microcrack density, i.e. the total number of microcracks embedded in the unit cell, P, Q is the shape factor of the hard pores, respectively, related to the aspect ratio α of the ellipsoidal pores, and the poisson's ratio v of the rock particles, the specific expression:

wherein:

v＝(3K₀-2G₀)/(6K₀+2G₀)；

(22) based on the obtained microcrack densities at the same temperature and different effective pressures p, fitting the microcrack density gamma under each pressure by using least square regression_p；

The quantitative relationship between the microcrack aspect ratio and effective pressure can be expressed as:

wherein E is_stiffIs the equivalent Young's modulus under effective pressure, defined as E_stiff＝3K_stiff[1-2ν_stiff]；

(23) According to the relationship between the microcrack porosity and the microcrack density in the David and Zimmerman models, the microcrack porosity at different pressures and at the same temperature is calculated:

wherein phi is₂And (p) is the microcrack porosity at the same temperature and under different pressures p.

3. The method of claim 2, wherein step (3) comprises:

(31) longitudinal and transverse wave velocity (V) of rock sample changing along with temperature based on ultrasonic experiment_p，V_s) Separately determining the corresponding temperatureEquivalent volume modulus K of variable confining pressure saturated rock_satAnd shear modulus G_satThe expression is as follows:

G_sat＝ρV_s ² (7)

wherein ρ is the density of the rock;

(32) according to equivalent bulk modulus K_satAnd shear modulus G_satCalculating the bulk modulus K of the dry skeleton of the rock sample based on the Gassmann equation_drAnd shear modulus G_drThe expression is as follows:

G_dr＝G_sat (9)

wherein, K_mIs the bulk modulus, K, of the minerals that make up the rock_fThe bulk modulus of the fluid at the corresponding temperature, phi, the total porosity of the rock;

(33) and (3) fitting according to the microcrack porosity under the same pressure to obtain the distribution of the rock elastic modulus and the microcrack porosity at different temperatures based on the relationship between the rock elastic modulus and the microcrack structure and the differential pressure relationship of the microcrack porosity established in the step (2).

4. The method of claim 3, wherein the fluid comprises water and oil, and step (4) comprises:

empirical equations between different fluid properties and temperature (T), pressure (P) using the Batzle and Wang models, including water and oil, are shown below:

density of water ρ_wIs composed of

ρ_w＝1+10^-6×(-80T-3.3T²+0.00175T³+489P (10)

-2TP+0.016T²P-1.3×10^-5T³P-0.333P²-0.002TP²)

Acoustic velocity V of water_wIs composed of

Wherein, ω is_ijConstant in the Batzle and Wang models;

viscosity of water eta of

Density of oil ρ_oilIs composed of

Where ρ is₀Describing the reference density of the petroleum, i.e. the density at a temperature of 15.6 ℃ and one atmosphere;

acoustic velocity V of oil_oilIs composed of

Viscosity η of oil_oilIs composed of

5. The method of claim 4, wherein step (5) comprises:

based on a Biot-Rayleigh equation, a wave control equation is derived by utilizing a Hamilton principle, strain energy and kinetic energy are introduced through local fluid flow and interaction among different pore areas, then corresponding potential energy functions, kinetic energy functions and dissipation functions are established, and a temperature-related double-pore medium model is derived, wherein the wave propagation control equation is as follows:

wherein the content of the first and second substances,_u,U⁽¹⁾,U⁽²⁾respectively the average particle displacement of the solid skeleton, the displacement of the fluid in the first-phase main skeleton and the displacement of the fluid in the second-phase microcracks; superscripts (1) and (2) represent two types of porosity; epsilon, zeta⁽¹⁾,ζ⁽²⁾Respectively representing the corresponding 3 displacement divergence fields;

the fluid strain increment caused in the local flow process is expressed, and the physical meaning of the expression is the volume of fluid exchange between interparticle pores and microcracks in the fluid flow; due to the heterogeneity of the pore structure within the rock, the rock develops into two different types of pores, hard and soft, respectively₁₀And phi₂₀Local porosity representing intergranular porosity and microcracking; r₁₂Radius of the microcracks; phi is a₁,φ₂Is of two types of poresAbsolute porosity, b₁,b₂Is the Biot dissipation factor, p_f,η,κ₁Density, viscosity and permeability of the fluid, respectively, p₁₁,ρ₁₂,ρ₁₃,ρ₂₂,ρ₃₃As density parameter, A, Q₁,Q₂,R₁,R₂And N is an elasticity parameter.

6. The method of claim 1, wherein step (63) comprises:

solving the longitudinal wave^i(ωt-k·x)Substituting into the Biot-Rayleigh equation to obtain the complex wave number square k²The complex unitary cubic equation set of (2) solves the equation set:

wherein k represents the wave number, and other parameters are as follows:

wherein:

x₁＝i(Q₁φ₂-Q₂φ₁)/Z,x₂＝iR₁φ₂/Z,x₃＝iR₂φ₁/Z

square k of complex wave number²The three solutions respectively correspond to a fast longitudinal wave and two types of slow longitudinal waves, wherein the fast longitudinal wave with the highest speed corresponds to the solved longitudinal wave, and the longitudinal wave speed of the saturated rock mass related to the temperature is predicted by a prediction formula of the longitudinal wave speed:

where ω is 2 pi f and f is the frequency.

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