A method for characterizing carbon dioxide migration in deep reservoirs based on compressional wave velocity calculation

Abstract

The application discloses a deep oil reservoir carbon dioxide migration characterization method based on longitudinal wave velocity calculation and belongs to the technical field of reservoir rock physical property research. The application establishes a rock pore three-phase fluid thermal fluid-solid coupling constitutive equation, couples potential energy, kinetic energy and dissipation energy equations of the three-phase fluid by Lagrange energy density to form a wave equation, and combines with LS thermal elasticity theory to construct a wave equation group under the influence of temperature. The fluid properties of the three-phase fluid are updated by considering the dissolution characteristics of CO2, oil and water. The longitudinal wave velocity characteristics under the full frequency band are solved through plane wave analysis. Finally, longitudinal wave velocity and fluid bulk modulus are used as objective functions to invert three-phase fluid saturation by using a multi-objective particle swarm optimization algorithm. The application improves the CO2-oil-water three-phase fluid migration characterization precision through longitudinal wave velocity calculation, and can accurately characterize the CO2-oil-water three-phase fluid saturation change and the longitudinal wave velocity change rule in deep high-temperature reservoirs.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of reservoir petrophysical property research, and particularly relates to a deep reservoir carbon dioxide migration characterization method based on longitudinal wave velocity calculation. BACKGROUND

[0002] With the continuous deepening of exploration and development, deep high-temperature reservoirs have become an important resource for increasing reserves and production. As a typical deep resource, tight sandstone reservoirs generally have the characteristics of small rock skeleton particles, large specific surface area, poor pore development, strong heterogeneity, and high reservoir temperature. The pores of tight sandstone are micron-sized, and the fluid is unevenly distributed in the micron-sized pores, and there is a complex interfacial effect between the pore media. Under supercritical conditions, the mutual solubility of CO2, oil and water causes the phase state and properties of the fluid to change dramatically. By analyzing the change of acoustic wave signal velocity, necessary information can be provided for monitoring the CO2-oil-water migration in deep high-temperature reservoirs. Therefore, clarifying the relationship between rock properties, multiphase flow properties and temperature on wave velocity has become an important issue in this technical research field.

[0003] Acoustic wave monitoring is a non-polluting monitoring technology that collects acoustic wave propagation signals in the reservoir to invert the petrophysical properties of the reservoir. There are multiple-phase fluids in the rock pores, and the differences in fluid properties have a significant impact on acoustic wave propagation velocity. The influence of temperature on fluid properties further exacerbates the differences in acoustic monitoring signals. Acoustic and elastic wave theory equates the underground structure to a single-phase fluid or solid medium, which is not accurate in describing the actual reservoir flow field. The Gassmann model for calculating acoustic wave propagation velocity is limited to the middle and low frequency bands and simplifies the distribution of multi-phase fluids, and cannot characterize the wave velocity dispersion caused by phenomena such as jet flow. The poroelastic medium theory can more accurately characterize the influence of fluid and rock matrix interaction on wave velocity, but existing poroelastic medium theory models are limited to monitoring two-phase fluid saturation at a specific frequency, while the fluid in the reservoir is in a three-phase flow distribution. For CO2, oil and water three-phase fluid, due to its mutual solubility characteristics, the properties of CO2-oil-water fluid in deep high-temperature reservoirs will change dramatically. In addition, the poroelastic medium theory ignores the influence of temperature and jet flow on wave velocity. Therefore, it is urgent to establish a Biot-Reyleigh (BR) poroelastic medium theory considering the micro jet flow effect, and combine it with Lord-Shulman (LS) thermoelastic theory to construct a thermal poroelastic medium model containing three-phase fluid. For CO2-oil-water three-phase fluid, the solubility characteristics of CO2, oil and water need to be considered to improve the accuracy of longitudinal wave characterization of CO2-oil-water migration in deep reservoirs. SUMMARY

[0004] In order to solve the above problems, the application provides a deep reservoir carbon dioxide migration characterization method based on longitudinal wave velocity calculation, a BR hole elastic medium theory considering micro jet flow effect is combined with an LS thermal elastic theory to establish a thermal fluid-solid coupling constitutive equation and a potential energy equation of a CO2-oil-water three-phase fluid, and a thermal hole elastic medium model containing the three-phase fluid is established based on the coupling of potential energy, kinetic energy and dissipation equation of the Lagrange equation. The solubility characteristics of CO2, oil and water are considered, the fluid properties of CO2-oil-water after mutual solubility are updated, the longitudinal wave velocity in the full frequency band is accurately characterized through plane wave analysis, and finally the longitudinal wave velocity and the fluid bulk modulus are used as the objective function to invert the three-phase fluid saturation by using a multi-objective particle swarm optimization algorithm, so that the three-phase fluid migration characterization of the deep reservoir is realized.

[0005] The technical scheme of the application is as follows:

[0006] A deep reservoir carbon dioxide migration characterization method based on longitudinal wave velocity calculation, comprising the following steps:

[0007] Step 1, a thermal fluid-solid coupling constitutive equation and a potential energy equation of a CO2-oil-water three-phase fluid are established based on the BR hole elastic medium theory;

[0008] Step 2, a total kinetic energy equation and a total dissipation equation of the CO2-oil-water three-phase fluid are established;

[0009] Step 3, the potential energy, the total kinetic energy and the total dissipation equation are combined based on the Lagrange equation, and a wave equation and a heat transfer equation of the three-phase fluid of the double-pore thermal elastic medium are established in combination with the LS thermal elastic theory;

[0010] Step 4, the three-phase saturation and the bulk modulus of CO2 after dissolution in oil and water are calculated;

[0011] Step 5, the longitudinal wave velocity in the full frequency band is solved through plane wave analysis;

[0012] Step 6, the migration process of the three-phase fluid in the rock is characterized based on the longitudinal wave velocity calculation and the multi-objective particle swarm inversion method.

[0013] Further, the specific process of step 1 is as follows:

[0014] Step 1.1, a thermal fluid-solid coupling constitutive equation of a CO2-oil-water three-phase fluid in a double-pore medium is established based on the BR hole elastic medium theory:

[0015] (1);

[0016] wherein, , , all represent three different directions in three-dimensional space; is the three-dimensional space solid stress in direction x, when solid normal stress, when solid shear stress; represents the solid skeleton elastic modulus coefficient; is the solid strain; represents the six different regions of the three-phase fluid inside the dual-porosity rock; is the region skeleton and fluid coupling stiffness coefficient; is the fluid strain after fluid migration in the region ; is the thermal elastic coefficient of the solid; is the thermal elastic coefficient of the fluid; is the temperature; is the Kronecker operator in three-dimensional space in direction x, when is 1, is 0; is the solid skeleton shear modulus coefficient; is the solid strain in three-dimensional space in direction x, when is the solid normal strain, is the solid shear strain; is the fluid stress in the region ; is the fluid flow stiffness coefficient in the region ;

[0017] Step 1.2, relationship between stress, strain and potential energy, as follows:

[0018] (2);

[0019] where, is the potential energy; is the fluid strain in the region ;

[0020] Step 1.3, combining equation (1) and equation (2), finally get the potential energy equation of CO2-oil-water three-phase fluid under dual-porosity medium:

[0021] (3);

[0022] where, is the invariant of the strain tensor; , , , , , ​​Fluid bulk strain of region 1, region 2, region 3, region 4, region 5, region 6, respectively; Bulk strain increment of fluid flow between region 1 and region 2; Bulk strain increment of fluid flow between region 1 and region 3; Bulk strain increment of fluid flow between region 2 and region 4; Bulk strain increment of fluid flow between region 3 and region 5; Bulk strain increment of fluid flow between region 4 and region 6; 、 、 、 、 、 Rock porosity of region 1, region 2, region 3, region 4, region 5, region 6, respectively.

[0023] Further, the specific process of step 2 is as follows:

[0024] Step 2.1, establishing the total kinetic energy equation considering global flow and local flow; the specific process is as follows:

[0025] Step 2.1.1, the kinetic energy equation considering global flow is expressed as:

[0026] (4);

[0027] Wherein, is the kinetic energy of global flow; is the rock porosity; is the rock skeleton density; is the rock porosity of region ; is the fluid density of region ; is the rock skeleton solid displacement; is the first derivative of ; is the fluid saturation of region ; is the fluid displacement of region ; is the first derivative of ;

[0028] Step 2.1.2, the kinetic energy equation considering local flow is expressed as:

[0029] (5);

[0030] Wherein, is the kinetic energy of local flow; , 、 、 are the fluid densities in region 1, region 2, region 3, and region 4, respectively; 、 、 、 、 They are 、 、 、 、 The first derivative of ; is the dynamic radius of the fluid after migration in regions 1 and 2; is the dynamic radius of the fluid after migration in regions 1 and 3; is the dynamic radius of the fluid after migration in regions 2 and 4; is the dynamic radius of the fluid after migration in regions 3 and 5; is the dynamic radius of the fluid after migration in regions 4 and 6; 、 、 、 are the local porosity of region 1, region 2, region 2, and region 4, respectively;

[0031] Step 2.1.3: The total kinetic energy equation for the three-phase fluid is expressed as:

[0032] (6);

[0033] in, is the total kinetic energy;

[0034] Step 2.2: Based on the friction dissipation mechanism between the three-phase fluid and the rock skeleton, establish a total dissipation equation that takes into account global and local flows.

[0035] Furthermore, the specific process of step 2.2 is as follows:

[0036] Step 2.2.1: The dissipation equation considering the global flow is expressed as:

[0037] (7);

[0038] in, is the dissipation function of the global flow; For the region Dissipation coefficient of the internal fluid;

[0039] Step 2.2.2: The dissipation equation considering the local flow is expressed as:

[0040] (8);

[0041] where, is the dissipation function of local flow; , , , are the fluid viscosities of region 1, region 2, region 2, region 4, respectively; , are the different permeabilities of the dual-porosity structure;

[0042] Step 2.2.3. The total dissipation equation with three-phase fluid is expressed as:

[0043] (9);

[0044] where, is the total flow dissipation function.

[0045] Further, the specific process of the step 3 is:

[0046] Step 3.1. The Lagrangian equation with dissipation form is expressed as:

[0047] (10);

[0048] where, is the symbol of partial derivative; is time; is the partial derivative of ; is the partial derivative of ; is the variable for substituting the body strain increment of fluid displacement, solid displacement or fluid flow; is the first derivative of ;

[0049] Step 3.2. The body strain increment of fluid displacement, solid displacement and fluid flow is substituted into respectively, to obtain the wave equation group of CO2-oil-water three-phase fluid in the dual-porosity thermoelastic medium:

[0050] (11);

[0051] (12);

[0052] (13);

[0053] where, is the gradient operator; , , , , , 、 They are 、 、 、 、 、 、 The second derivative of 、 、 、 、 、 are the fluid volume strains after fluid migration in regions 1, 2, 3, 4, 5, and 6, respectively; 、 、 、 、 、 are the coupling stiffness coefficients between the skeleton and the fluid in regions 1, 2, 3, 4, 5, and 6 respectively; 、 、 、 、 、 are the fluid flow stiffness coefficients of region 1, region 2, region 3, region 4, region 5, and region 6 respectively;

[0054] Step 3.3: The heat transfer equation for the dual-porosity thermoelastic medium is:

[0055] (14);

[0056] in, is the thermal conductivity coefficient; is the total density of the fluid-saturated rock; is the specific heat capacity; 、 They are The first and second derivatives of ; is the relaxation time; is the absolute temperature.

[0057] Furthermore, the specific process of step 4 is as follows:

[0058] Step 4.1: Calculate the amount, mass, and dissolved volume of CO2 dissolved in the water and oil phases. The specific process is as follows:

[0059] Step 4.1.1: The amount of CO2 dissolved in the water phase and the oil phase is expressed as:

[0060] (15);

[0061] wherein, is the mass of the water phase; is the mass of the oil phase; is the solubility of CO2 in the water phase; is the solubility of CO2 in the oil phase; is the amount of substance dissolved in the water phase; is the amount of substance dissolved in the oil phase;

[0062] Step 4.1.2, the mass of CO2 dissolved in the water and oil phases is expressed as:

[0063] (16);

[0064] wherein, is the mass of CO2 dissolved in the water phase; is the mass of CO2 dissolved in the oil phase; is the molar mass of CO2;

[0065] Step 4.1.3, the mixed density and the dissolved volume of CO2 dissolved in the water and oil phases are expressed as:

[0066] (17);

[0067] (18);

[0068] wherein, is the volume of the water phase; is the volume of the oil phase; is the volume of CO2 dissolved in the water phase; is the volume of CO2 dissolved in the oil phase; is the mixed density of CO2 dissolved in the water phase; is the mixed density of CO2 dissolved in the oil phase; is the density of the water phase; is the density of the oil phase; is the density of CO2;

[0069] Step 4.2, calculating the viscosity, fluid saturation, and fluid bulk modulus of the oil and water phases after CO2 dissolution;

[0070] Step 4.3, updating the calculated CO2-oil-water property parameters.

[0071] Further, the specific process of the step 4.2 is:

[0072] Step 4.2.1, the viscosity of the water and oil phases after CO2 dissolution in water and oil is expressed as:

[0073] (19);

[0074] wherein, is a logarithmic operator; is the viscosity of the water phase after CO2 dissolution; is the viscosity of the water phase; is the ion concentration in the water phase; is a temperature correction term for the linear variation of the water phase viscosity with ion concentration; is a temperature correction term for the square variation of the water phase viscosity with ion concentration; is a temperature correction term for the cubic variation of the water phase viscosity with ion concentration; is the viscosity of the oil phase after CO2 dissolution; is the viscosity of the crude oil; is the viscosity of CO2; is a correlation coefficient;

[0075] Step 4.2.2, the saturations of CO2, oil phase and water phase after CO2 dissolution in water and oil are expressed as:

[0076] (20);

[0077] wherein, is the rock volume; is the CO2 saturation after CO2 dissolution in oil and water; is the water phase saturation after CO2 dissolution in water; is the oil phase saturation after CO2 dissolution in oil; is the CO2 volume;

[0078] Step 4.2.3, the bulk modulus of CO2 after dissolution in water and oil is calculated based on the Wood model as:

[0079] (21);

[0080] wherein, is the water phase saturation; is the oil phase saturation; is the mixed saturation after CO2 dissolution in water; is the mixed saturation after CO2 dissolution in oil; is the bulk modulus of water; is the bulk modulus of oil; is the bulk modulus of the water phase after CO2 dissolution in water; is the bulk modulus of the oil phase after CO2 dissolution in oil; is the mixed bulk modulus after CO2 dissolution in water; is the mixed bulk modulus after CO2 dissolution in oil;

[0081] The specific process of step 4.3 is as follows: the mixed density of CO2 dissolved in the water phase and the oil phase, the viscosity of the oil phase and the water phase after CO2 is dissolved, the saturation of the oil phase after CO2 is dissolved in the oil, and the saturation of the water phase after CO2 is dissolved in the water calculated in steps 4.1 and 4.2 are substituted into equations (11) to (14) for solution.

[0082] Furthermore, the specific process of step 5 is as follows:

[0083] Step 5.1: Substitute the one-dimensional plane wave kernel function into equations (11) to (14) to calculate the wave number. The plane wave kernel function is:

[0084] (twenty two);

[0085] in, is an exponential function with base e; is an imaginary number; is the angular frequency; is the wave number;

[0086] Step 5.2: The full-band longitudinal wave propagation velocity is related to the wave number and angular frequency as follows:

[0087] (twenty three);

[0088] in, is the longitudinal wave velocity; represents the real part.

[0089] Furthermore, the specific process of step 6 is as follows:

[0090] Step 6.1: Calculate the updated particle swarm velocity and position; the specific process is:

[0091] The speed update formula is as follows:

[0092] (twenty four);

[0093] in, For particles In the The velocity vector at the iteration; For particles In the The velocity vector at the iteration; is the inertia weight; is the individual learning factor; Learn random numbers for individuals; is the group learning factor; Learn random numbers for the group; particle The best historical position; global optimal position of the population; for the particle the position vector at the first iteration; the position vector at the first iteration;

[0094] The position update formula is:

[0095] (25);

[0096] wherein, for the particle the position vector at the first iteration; the position vector at the first iteration, which is a 1 × 3 dimensional row vector, i.e. wherein the three position vector elements correspond to the oil phase saturation after CO2 is dissolved in oil, the CO2 saturation after CO2 is dissolved in oil and water, and the water phase saturation after CO2 is dissolved in water, in turn;

[0097] The updated position vector is mapped to the oil phase saturation after CO2 is dissolved in oil, the CO2 saturation after CO2 is dissolved in oil and water, and the water phase saturation after CO2 is dissolved in water;

[0098] Step 6.2, define the constraint condition and the objective function and solve the optimal CO2-oil-water saturation in the Pareto front.

[0099] Further, the specific process of the step 6.2 is as follows:

[0100] Step 6.2.1, define the constraint condition as:

[0101] (26);

[0102] wherein, for the CO2 saturation;

[0103] Step 6.2.2, define the objective function as:

[0104] (27);

[0105] wherein, for the longitudinal wave velocity calculated according to formula (23); for the fluid bulk modulus calculated according to formula (21); for the longitudinal wave velocity actually tested in the experiment; for the fluid bulk modulus actually tested in the experiment; for the objective function value of the longitudinal wave velocity; for the objective function value of the fluid bulk modulus;

[0106] Step 6.2.3, solving the optimal CO2-oil-water saturation solution in the Pareto front:

[0107] (28);

[0108] wherein, is the objective function value, is the particle position vector , subscript , represents the objective function value of the longitudinal wave velocity, subscript , represents the objective function value of the fluid bulk modulus; is the target minimum value; is the target maximum value; is the larger value of the two normalized objectives; is the minimum value of the Pareto front, is the particle position vector set; is the optimal recommended solution in the Pareto front;

[0109] By calculating , the best , and can be mapped.

[0110] The beneficial technical effects brought by the present application: the present application combines the BR poroelastic medium theory and the LS thermal elastic theory to construct a thermal fluid-solid coupling constitutive equation, which couples stress, fluid flow and heat conduction, improves the accuracy of the strain and thermodynamic response of the rock; the present application extends two-phase flow to three-phase flow, recharacterizes the distribution law of three-phase fluid in double-porosity medium, constructs a wave equation containing three-phase fluid by considering the global flow, mesoscopic flow and local flow of three-phase fluid in the rock skeleton and combining potential energy function; the present application considers the miscibility characteristics of CO2-oil-water, updates key fluid parameters such as saturation and bulk modulus of three-phase fluid required for double-porosity thermal elastic medium theory calculation; the present application obtains the propagation velocity of longitudinal wave in three-phase fluid by substituting the plane wave solution form into the wave equation; the present application takes the longitudinal wave velocity and the fluid bulk modulus as the objective function by using the multi-objective particle swarm optimization algorithm, and inverses the CO2-oil-water three-phase fluid migration process. BRIEF DESCRIPTION OF DRAWINGS

[0111] Figure 1 is the flowchart of the deep reservoir carbon dioxide migration characterization method based on the longitudinal wave velocity calculation of the present application.

[0112] Figure 2 is the velocity distribution result diagram of longitudinal wave in rock saturated with different three-phase fluids at full frequency in embodiment 1 of the present application.

[0113] Figure 3 Schematic diagram of the thermoelastic effect on longitudinal wave velocity distribution at all frequencies in Example 2 of the present invention.

[0114] Figure 4 Schematic diagram of the results of the CO2-oil-water saturation change inversion during the CO2 displacement process using the thermoporoelastic medium model and the multi-objective particle swarm optimization algorithm in Example 3 of the present invention. DETAILED DESCRIPTION

[0115] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0116] like Figure 1 As shown, a method for characterizing carbon dioxide migration in deep reservoirs based on P-wave velocity calculation specifically includes the following steps:

[0117] Step 1: Based on the BR poroelastic medium theory, the thermal-fluid-solid coupling constitutive equation and potential energy equation of the CO2-oil-water three-phase fluid are established. The specific steps are as follows:

[0118] Step 1.1: Based on the BR poroelastic medium theory, the thermal-fluid-solid coupling constitutive equation of the CO2-oil-water three-phase fluid in the dual-porosity medium is established, as shown in Equation (1):

[0119] (1);

[0120] in, , , all represent three different directions in three-dimensional space; In three-dimensional space The solid stress in the direction is the solid normal stress, When is the solid shear stress; represents the elastic modulus coefficient of the solid skeleton; is the solid strain; , indicating the six different regions where three-phase fluids exist in dual-porosity rocks; For the region The stiffness coefficient of the coupling between the skeleton and the fluid; For the region Fluid volume strain after internal fluid migration; is the thermoelastic coefficient of the solid, kg / (m·s 2 °K); is the thermoelastic coefficient of the fluid, kg / (m·s 2 °K); is the temperature, °C; In three-dimensional space The Kronecker operator in the direction t = 1, t = 0; G is the solid skeleton shear modulus coefficient; is the solid strain in the direction of when t = 1; is the solid normal strain when t = 0, is the solid shear strain when t = 0; is the fluid stress in region ; is the fluid stress in region ;

[0121] Step 1.2, the relationship between stress, strain and potential energy, as shown below, as shown in equation (2):

[0122] (2);

[0123] where, is the potential energy; is the fluid bulk strain in region ;

[0124] Step 1.3, combining equation (1) and equation (2), finally get the potential energy equation of CO2-oil-water three-phase fluid under dual-porosity medium, as shown in equation (3):

[0125] (3);

[0126] where, is the invariant of strain tensor; , , , , , are the fluid bulk strain of region 1, region 2, region 3, region 4, region 5, region 6 respectively; is the bulk strain increment of fluid flow between region 1 and region 2; is the bulk strain increment of fluid flow between region 1 and region 3; is the bulk strain increment of fluid flow between region 2 and region 4; is the bulk strain increment of fluid flow between region 3 and region 5; is the bulk strain increment of fluid flow between region 4 and region 6; , , , , , are the rock porosities of region 1, region 2, region 3, region 4, region 5, region 6 respectively.

[0127] Step 2: Establish the total kinetic energy equation and total dissipation equation for the CO2-oil-water three-phase fluid. The specific process is as follows:

[0128] Step 2.1: Establish the total kinetic energy equation considering global and local flows. The specific process is as follows:

[0129] Step 2.1.1: The kinetic energy equation considering the global flow is expressed as Equation (4):

[0130] (4);

[0131] in, is the kinetic energy of the global flow, kg·m 2 / s 2 ; is the rock porosity; is the rock skeleton density, kg / m 3 ; For the region rock porosity; For the region Fluid density, kg / m 3 ; is the solid displacement of the rock skeleton, m; for The first derivative of , m; For the region Fluid saturation; For the region Fluid displacement, m; for The first derivative of , m;

[0132] Step 2.1.2: Consider the kinetic energy equation of local flow as shown in (5):

[0133] (5);

[0134] in, is the kinetic energy of the local flow, kg·m 2 / s 2 ; 、 、 、 The fluid densities of region 1, region 2, region 3, and region 4, kg / m 3 ; 、 、 、 、 They are 、 、 、 、 The first derivative of ; is the dynamic radius of the fluid after migration in regions 1 and 2, m; is the dynamic radius of the fluid after migration in regions 1 and 3, m; is the dynamic radius of the fluid after migration in regions 2 and 4, m; is the dynamic radius of the fluid after migration in regions 3 and 5, m; is the dynamic radius of the fluid after migration in regions 4 and 6, m; 、 、 、 The local porosity of region 1, region 2, region 2, and region 4, respectively.

[0135] Step 2.1.3: The total kinetic energy equation of the three-phase fluid is expressed as (6):

[0136] (6);

[0137] in, is the total kinetic energy.

[0138] Step 2.2: Based on the friction dissipation mechanism between the three-phase fluid and the rock skeleton, establish a total dissipation equation that considers both global and local flows. The specific steps are as follows:

[0139] Step 2.2.1. Consider the dissipation equation of global flow as shown in (7):

[0140] (7);

[0141] in, is the dissipation function of the global flow, kg·m 2 / s 2 ; For the region Dissipation coefficient of internal fluid, Pa·s / m 2 .

[0142] Step 2.2.2: Consider the dissipation equation of local flow as shown in (8):

[0143] (8);

[0144] in, is the dissipation function of the local flow; 、 、 、 are the fluid viscosities in regions 1, 2, 2, and 4, respectively, in Pa·s; 、 different permeability for dual-porosity structure;

[0145] Step 2.2.3, the total dissipation equation of the three-phase fluid is expressed as shown in equation (9):

[0146] (9);

[0147] wherein, is the total flow dissipation function, kg·m 2 / s 2 .

[0148] Step 3, based on the Lagrangian equation combined with potential energy, total kinetic energy and total dissipation equation, and combined with the LS thermal elastic theory, the wave equation and heat transfer equation of the three-phase fluid of the dual-porosity thermal elastic medium are established, and the specific process is as follows:

[0149] Step 3.1, the Lagrangian equation with dissipation form is expressed as shown in equation (10):

[0150] (10);

[0151] wherein, is the symbol of partial derivative; is time; is the partial derivative of ; is the partial derivative of ; is a variable used for substituting the body strain increment of fluid displacement, solid displacement or fluid flow; is the first-order derivative of ;

[0152] Step 3.2, the body strain increment of fluid displacement, solid displacement and fluid flow is substituted into respectively, to obtain the wave equation group of CO2-oil-water three-phase fluid under the dual-porosity thermal elastic medium, as shown in equations (11)-(13):

[0153] (11);

[0154] (12);

[0155] (13);

[0156] wherein, is the gradient operator; , , , , , , respectively , , , , , , second derivative of the function f(x) = x , , , , , are the fluid bulk strains after fluid migration in region 1, region 2, region 3, region 4, region 5, region 6, respectively; , , , , , are the skeleton and fluid coupled stiffness coefficients in region 1, region 2, region 3, region 4, region 5, region 6, respectively. , , , , , are the fluid flow stiffness coefficients in region 1, region 2, region 3, region 4, region 5, region 6, respectively.

[0157] Step 3.3, the heat transfer equation of the double-porosity thermoelastic medium is shown in formula (14):

[0158] (14);

[0159] wherein, is the thermal conductivity, m·kg / (s 3 ·°K); is the total density of saturated fluid rock, kg / m 3 ; is the specific heat capacity, m 2 / (s 2 ·°K); , are the first derivative, second derivative of the function f(x) = x , °K; is the relaxation time, s; is the absolute temperature, °K.

[0160] Step 4, calculate the three-phase saturation and bulk modulus of CO2 after dissolving in oil and water two-phase, the specific steps are as follows:

[0161] Step 4.1, calculate the amount of substance, mass and dissolution volume of CO2 dissolved in water phase and oil phase, the specific steps are as follows:

[0162] Step 4.1.1, the amount of substance of CO2 dissolved in the water phase and the oil phase is expressed as shown in equation (15):

[0163] (15);

[0164] wherein, is the mass of the water phase, Kg; is the mass of the oil phase, Kg; is the solubility of CO2 in the water phase, mol / kg; is the solubility of CO2 in the oil phase, mol / kg; is the amount of substance dissolved in the water phase, mol; is the amount of substance dissolved in the oil phase, mol.

[0165] Step 4.1.2, the mass of CO2 dissolved in the water phase and the oil phase is expressed as shown in equation (16):

[0166] (16);

[0167] wherein, is the mass of CO2 dissolved in the water phase, Kg; is the mass of CO2 dissolved in the oil phase, Kg; is the molar mass of CO2, Kg / mol.

[0168] Step 4.1.3, the mixed density and the dissolved volume of CO2 dissolved in the water phase and the oil phase are respectively expressed as shown in equations (17)-(18):

[0169] (17);

[0170] (18);

[0171] wherein, is the volume of the water phase, m 3 ; is the volume of the oil phase, m 3 ; is the volume of CO2 dissolved in the water phase, m 3 ; is the volume of CO2 dissolved in the oil phase, m 3 ; is the mixed density of CO2 dissolved in the water phase, Kg / m 3 ; is the mixed density of CO2 dissolved in the oil phase, Kg / m 3 ; is the density of the water phase, Kg / m 3 ; is the density of the oil phase, Kg / m3 ; is the CO2 density, Kg / m 3 .

[0172] Step 4.2: Calculate the viscosity, fluid saturation, and fluid bulk modulus of the oil and water phases after CO2 dissolution. The specific process is as follows:

[0173] Step 4.2.1: The viscosity of the water phase and oil phase after CO2 is dissolved in water and oil is expressed as shown in formula (19):

[0174] (19);

[0175] in, is the logarithm operator; is the viscosity of the aqueous phase after CO2 dissolution, Pa·s; is the viscosity of the water phase, Pa·s; is the ion concentration in the aqueous phase, mol / kg; The temperature correction term for the linear change of aqueous phase viscosity with ion concentration is obtained by experimentally testing the viscosity of aqueous phase with low ion concentration and fitting a temperature-dependent quadratic function; The temperature correction term for the change of aqueous phase viscosity with the square of ion concentration is obtained by experimentally testing the aqueous phase viscosity with medium ion concentration and fitting the temperature-dependent quadratic function; The temperature correction term for the change of aqueous phase viscosity with the cubic change of ion concentration is obtained by experimentally testing the viscosity of aqueous phase with high ion concentration and fitting a temperature-dependent linear function; is the viscosity of the oil phase after CO2 dissolution, Pa·s; is the crude oil viscosity, Pa·s; is the viscosity of CO2, Pa·s; is the correlation coefficient.

[0176] Step 4.2.2: After CO2 is dissolved in water and oil, the saturation of CO2, oil phase, and water phase is expressed as shown in formula (20):

[0177] (20);

[0178] in, is the rock volume, m 3 ; It is the CO2 saturation after CO2 is dissolved in oil and water; is the saturation of the water phase after CO2 is dissolved in water; is the oil phase saturation after CO2 is dissolved in oil; is the volume of CO2, m 3 .

[0179] Step 4.2.3, the volume modulus of CO2 dissolved in water and oil is calculated based on the Wood model, which is shown in formula (21):

[0180] (21);

[0181] wherein, is the water phase saturation; is the oil phase saturation; is the mixed saturation of CO2 dissolved in water; is the mixed saturation of CO2 dissolved in oil; is the volume modulus of water, Pa; is the volume modulus of oil, Pa; is the water phase volume modulus of CO2 dissolved in water, Pa; is the oil phase volume modulus of CO2 dissolved in oil, Pa; is the mixed volume modulus of CO2 dissolved in water, Pa; is the mixed volume modulus of CO2 dissolved in oil, Pa.

[0182] Step 4.3, update the calculation of CO2-oil-water property parameters; the specific process is: the mixed density of CO2 dissolved in water and oil phase, the viscosity of oil and water phase after CO2 is dissolved, and the fluid saturation (the fluid saturation includes the oil phase saturation after CO2 is dissolved in oil and the water phase saturation after CO2 is dissolved in water) calculated by step 4.1 and step 4.2 are substituted into formula (11)-(14) to solve, which provides fluid parameters for subsequent longitudinal wave velocity solving; when, the range of is 1-6; when , the mixed density of CO2 dissolved in oil phase, the viscosity of oil phase after CO2 is dissolved, and the oil phase saturation after CO2 is dissolved are substituted to solve, that is, , , , , , ; when , the density, viscosity of CO2, and CO2 saturation after CO2 is dissolved in oil and water are substituted to solve, that is, , , , , , ; when , the mixed density of CO2 dissolved in water phase, the viscosity of water phase after CO2 is dissolved, and the water phase saturation after CO2 is dissolved are substituted to solve, that is, , , , 、 、 .

[0183] Step 5: Solve the longitudinal wave velocity in the full frequency band through plane wave analysis. The specific process is as follows:

[0184] Step 5.1: Substitute the one-dimensional plane wave kernel function into equations (11) to (14) to calculate the wave number. The plane wave kernel function is:

[0185] (twenty two);

[0186] in, is an exponential function with base e; is an imaginary number; is the angular frequency; is the wave number;

[0187] Step 5.2: The full-band longitudinal wave propagation velocity is related to the wave number and angular frequency as shown in formula (23):

[0188] (twenty three);

[0189] in, is the longitudinal wave velocity; represents the real part.

[0190] Step 6: Characterize the migration process of three-phase fluid in rock based on the calculation of longitudinal wave velocity and multi-objective particle swarm inversion method. The specific process is as follows:

[0191] Step 6.1: Calculate the updated particle swarm velocity and position. The specific process is as follows:

[0192] Step 6.1.1. Each particle has two characteristics: position and velocity. Assuming that the current population consists of N particles, the search range of the particle is n-dimensional hyperspace. The updated velocity formula is as follows:

[0193] (twenty four);

[0194] in, For particles In the The velocity vector at the iteration; For particles In the The velocity vector at the iteration; is the inertia weight; is the individual learning factor; Learn random numbers for individuals; is the group learning factor; Learn random numbers for the group; particle history optimal position; population global optimal position; for particle position vector at the first iteration.

[0195] Step 6.1.2, the position update formula is shown in equation (25):

[0196] (25);

[0197] wherein, for particle position vector at the first iteration, which is a 1x3 dimensional row vector, i.e. wherein the three position vector elements correspond to the oil phase saturation after CO2 dissolves in oil, the CO2 saturation after CO2 dissolves in oil and water, and the water phase saturation after CO2 dissolves in water in turn.

[0198] Step 6.1.3, map the updated position vector to the oil phase saturation after CO2 dissolves in oil, the CO2 saturation after CO2 dissolves in oil and water, and the water phase saturation after CO2 dissolves in water, i.e. .

[0199] Step 6.2, define the constraint condition and the objective function and solve the optimal CO2-oil-water saturation in the Pareto front, the specific process is as follows:

[0200] Step 6.2.1, the constraint condition is defined as shown in equation (26):

[0201] (26);

[0202] wherein, is the CO2 saturation.

[0203] Step 6.2.2, the objective function is defined as shown in equation (27):

[0204] (27);

[0205] wherein, is the longitudinal wave velocity calculated according to equation (23), m / s; is the fluid bulk modulus calculated according to equation (21), Pa; is the longitudinal wave velocity actually tested in the experiment, m / s; is the fluid bulk modulus actually tested in the experiment, Pa; is the objective function value of the longitudinal wave velocity; Objective function value of fluid bulk modulus.

[0206] Step 6.2.3, solving the optimal CO2-oil-water saturation solution in the Pareto front:

[0207] (28);

[0208] wherein, is the objective function value, is the particle position vector , subscript , represents the objective function value of the longitudinal wave velocity, subscript , represents the objective function value of the fluid bulk modulus; is the target minimum value; is the target maximum value; is the larger value of the two normalized objectives; is the minimum value of the Pareto front, is the particle position vector set; is the optimal recommended solution in the Pareto front. By calculating , the best , and can be mapped.

[0209] In order to prove the feasibility and superiority of the present application, the following examples are given.

[0210] Example 1: The full-band wave velocity change caused by the change of fluid saturation in the present application is compared. In this example 1, the preferred specific heat capacity is 0.38 m 2 / (s 2 ·°K), the permeability is 0.05 mD, the rock skeleton bulk modulus is 1.65×10 10 Pa, the rock matrix bulk modulus is 4.94×10 10 Pa, the shear modulus of the rock matrix is 2.97×10 10 Pa, the shear modulus of the rock skeleton is 6.32×10 9 Pa, the porosity is 0.03, the total density of the rock is 2.58×10 3 kg / m 3 , and the densities and viscosities of oil, CO2 and water are 812.66, 662.66, 955.56 kg / m 3 and 1.4×10 -1 , 1.5×10 -3 , 2.4×10 -4Pa / s. The bulk moduli of oil, CO2, and water are 1.32×10 9 , 8×10 7 , 2.5×10 9 Pa. The temperature is 130 °C. The two preferred saturation comparison schemes are: ① oil, CO2, and water saturation are 70%, 20%, and 10% respectively; ② oil, CO2, and water saturation are 50%, 40%, and 10% respectively. The final calculation comparison results of this Example 1 are shown in Figure 2 As shown, Figure 2 The velocity distribution results of the longitudinal wave in the rock saturated with different three-phase fluids at all frequencies are shown in Figure 2. Figure 2 It can be seen that when the liquid phase saturation in the rock pores increases, the propagation speed of the longitudinal wave in the rock increases. The present invention can achieve the saturation characterization of the three-phase fluid during migration by calculating the longitudinal wave velocity.

[0211] Example 2: The full-band wave velocity changes caused by the change of the thermoelastic effect in the present invention are compared. In this example 2, the preferred specific heat capacity is 0.38 m 2 / (s 2 °K), the permeability is 0.05 mD, and the rock skeleton bulk modulus is 1.65×10 10 Pa, the rock matrix bulk modulus is 4.94×10 10 Pa, the shear modulus of the rock matrix is ​​2.97×10 10 Pa, the shear modulus of the rock skeleton is 6.32×10 9 Pa, porosity is 0.03, and the total density of rock is 2.58×10 3 kg / m 3 The density and viscosity of oil, CO2 and water are 812.66, 662.66 and 955.56 kg / m respectively. 3 With 1.4×10 -1 , 1.5×10 -3 , 2.4×10 -4 Pa / s. The bulk moduli of oil, CO2, and water are 1.32×10 9 , 8×10 7 , 2.5×10 9 Pa. The temperature is 130℃. The preferred saturation scheme is: oil, CO2, water saturation are 70%, 20% and 10% respectively. The influence of pore thermoelastic effect on wave velocity is compared with or without considering it. The final calculation comparison results of this Example 2 are shown in Figure 3 As shown, Figure 3 The results of the thermoelastic effect on the longitudinal wave velocity distribution at all frequencies are shown in Table 1. Figure 3It can be seen that the longitudinal wave velocity considering the thermoelastic effect is significantly increased, and the thermoelastic effect cannot be ignored for deep high-temperature reservoirs.

[0212] Example 3: The thermo-poroelastic medium model of the present application is applied to a core-scale CO2 displacement process, and in this example 3, a dense sandstone core with a permeability of 0.05 mD and a porosity of 0.03 is preferred, and the core is subjected to water flooding and oil flooding in sequence, and the core is fully saturated with oil. The CO2 displacement is carried out at a temperature of 130℃ and a confining pressure of 40 MP, the acoustic wave velocity and the fluid bulk modulus are tested by an acoustic wave transducer, and the thermo-poroelastic medium model of the present application is used to jointly invert the CO2-oil-water saturation change results in the CO2 displacement process by using a multi-objective particle swarm optimization algorithm, and the results are shown in Figure 4 Figure 4 Figure 6 is a CO2-oil-water three-phase fluid saturation change graph in the core during the CO2 displacement process, and the results are shown in Figure 4 It can be seen that as the CO2 displacement time increases, the CO2 saturation in the core gradually increases, and the oil and water saturations gradually decrease, which is consistent with the experimental law.

[0213] Of course, the above description is not a limitation on the present application, and the present application is not limited to the above examples, and changes, modifications, additions or replacements made by those skilled in the art within the essential scope of the present application should also belong to the protection scope of the present application.​

Claims

1. A method for characterizing carbon dioxide migration in deep oil reservoirs based on longitudinal wave velocity calculation, characterized in that: The steps include: Step 1: Based on the BR poroelastic medium theory, the thermal-fluid-solid coupling constitutive equation and potential energy equation of the CO2-oil-water three-phase fluid are established; Step 2: Establish the total kinetic energy equation and total dissipation equation of the CO2-oil-water three-phase fluid; Step 3: Based on the Lagrange equation, combined with the potential energy, total kinetic energy and total dissipation equations, and combined with the LS thermoelasticity theory, the wave equation and heat transfer equation of the three-phase fluid in the dual-porosity thermoelastic medium are established; Step 4: Calculate the three-phase saturation and bulk modulus of CO2 after it is dissolved in the oil and water phases; Step 5: Determine the longitudinal wave velocity in the full frequency band through plane wave analysis; Step 6: Characterize the migration process of three-phase fluid in rock based on the calculation of longitudinal wave velocity and multi-objective particle swarm inversion method; the specific process is as follows: Step 6.1: Calculate the updated particle swarm velocity and position; the specific process is: The speed update formula is as follows: （24）； in, For particles In the The velocity vector at the iteration; For particles In the The velocity vector at the iteration; is the inertia weight; is the individual learning factor; Learn random numbers for individuals; is the group learning factor; Learn random numbers for the group; For particles The best historical position; is the global optimal position of the group; For particles In the The position vector at the iteration; The position update formula is: （25）； in, For particles In the The position vector at the iteration is a 1×3 dimensional row vector, that is, ,in The three position vector elements correspond to the oil phase saturation after CO2 dissolves in oil, the CO2 saturation after CO2 dissolves in oil and water, and the water phase saturation after CO2 dissolves in water; The updated position vector Mapped to the oil phase saturation after CO2 dissolves in oil, the CO2 saturation after CO2 dissolves in oil and water, and the water phase saturation after CO2 dissolves in water; Step 6.2: Define the constraints and objective function and solve for the optimal CO2-oil-water saturation on the Pareto front. The specific process is as follows: Step 6.2.

1. Define the constraints as follows: （26）； in, is CO2 saturation; Step 6.2.2, define the objective function as: （27）； in, is the longitudinal wave velocity calculated according to formula (23); is the bulk modulus of the fluid calculated according to formula (21); is the longitudinal wave velocity actually tested in the experiment; is the bulk modulus of the fluid actually tested in the experiment; is the objective function value of the longitudinal wave velocity; is the objective function value of the fluid bulk modulus; Formula (21) is: （21）； in, is the water phase saturation; is the oil phase saturation; is the mixed saturation after CO2 is dissolved in water; is the mixed saturation after CO2 is dissolved in oil; is the bulk modulus of water; is the bulk modulus of oil; is the bulk modulus of the aqueous phase after CO2 is dissolved in water; is the bulk modulus of the oil phase after CO2 is dissolved in oil; is the mixed bulk modulus of CO2 dissolved in water; is the mixed bulk modulus of CO2 dissolved in oil; is the saturation of the water phase after CO2 is dissolved in water; is the oil phase saturation after CO2 is dissolved in oil; Formula (23) is: （23）； in, is the longitudinal wave velocity; represents the real part; is the angular frequency; is the wave number; Step 6.2.

3. Find the optimal CO2-oil-water saturation solution in the Pareto front: （28）； in, is the objective function value, is the particle position vector Function, subscript hour, represents the objective function value of the longitudinal wave velocity, subscript hour, represents the objective function value of the fluid bulk modulus; is the target minimum value; is the target maximum value; is the larger of the two normalized targets; is the minimum value of the Pareto front, is the particle position vector set; is the optimal recommended solution in the Pareto frontier; By calculation You can map the best 、 and .

2. The method for characterizing carbon dioxide migration in deep oil reservoirs based on longitudinal wave velocity calculation according to claim 1, characterized in that: The specific process of step 1 is: Step 1.1: Based on the BR poroelastic medium theory, establish the thermal-fluid-solid coupling constitutive equation of the CO2-oil-water three-phase fluid in dual-porosity medium: (1)； in, , , all represent three different directions in three-dimensional space; In three-dimensional space The solid stress in the direction is the solid normal stress, When is the solid shear stress; represents the elastic modulus coefficient of the solid skeleton; is the solid strain; , indicating the six different regions where three-phase fluids exist in dual-porosity rocks; For the region The stiffness coefficient of the coupling between the skeleton and the fluid; For the region Fluid volume strain after internal fluid migration; is the thermoelastic coefficient of the solid; is the thermoelastic coefficient of the fluid; is temperature; In three-dimensional space The Kronecker operator in the direction When is 1, Time is 0; is the shear modulus coefficient of the solid skeleton; In three-dimensional space The solid strain in the direction When is the solid normal strain, When is the solid shear strain; For the region Fluid stress; For the region Fluid flow stiffness coefficient; Step 1.2: The relationship between stress, strain and potential energy is as follows: （2）； in, is potential energy; For the region The fluid volume strain; Step 1.3: Combine equations (1) and (2) to obtain the potential energy equation for the CO2-oil-water three-phase fluid in dual-porosity media: （3）； in, is the invariant of the strain tensor; 、 、 、 、 、 are the fluid volume strains in regions 1, 2, 3, 4, 5, and 6, respectively; is the volume strain increment of the fluid flow between region 1 and region 2; is the volume strain increment of the fluid flow between region 1 and region 3; is the volume strain increment of the fluid flow between regions 2 and 4; is the volume strain increment of the fluid flow between regions 3 and 5; is the volume strain increment of the fluid flow between regions 4 and 6; 、 、 、 、 、 The rock porosity of Area 1, Area 2, Area 3, Area 4, Area 5, and Area 6 are shown in order.

3. The method for characterizing carbon dioxide migration in deep oil reservoirs based on longitudinal wave velocity calculation according to claim 2, characterized in that: The specific process of step 2 is: Step 2.1: Establish the total kinetic energy equation considering global and local flows. The specific process is as follows: Step 2.1.1: The kinetic energy equation considering the global flow is expressed as: （4）； in, is the kinetic energy of the global flow; is the rock porosity; is the rock skeleton density; For the region rock porosity; For the region The density of the fluid; is the solid displacement of the rock skeleton; for The first derivative of ; For the region Fluid saturation; For the region Fluid displacement; for The first derivative of ; Step 2.1.2: Consider the kinetic energy equation of local flow and express it as: （5）； in, is the kinetic energy of the local flow; 、 、 、 are the fluid densities in region 1, region 2, region 3, and region 4, respectively; 、 、 、 、 They are 、 、 、 、 The first derivative of ; is the dynamic radius of the fluid after migration in regions 1 and 2; is the dynamic radius of the fluid after migration in regions 1 and 3; is the dynamic radius of the fluid after migration in regions 2 and 4; is the dynamic radius of the fluid after migration in regions 3 and 5; is the dynamic radius of the fluid after migration in regions 4 and 6; 、 、 、 are the local porosity of region 1, region 2, region 2, and region 4, respectively; Step 2.1.3: The total kinetic energy equation for the three-phase fluid is expressed as: （6）； in, is the total kinetic energy; Step 2.2: Based on the friction dissipation mechanism between the three-phase fluid and the rock skeleton, establish a total dissipation equation that takes into account global and local flows.

4. The method for characterizing carbon dioxide migration in deep oil reservoirs based on longitudinal wave velocity calculation according to claim 3, characterized in that: The specific process of step 2.2 is as follows: Step 2.2.1: The dissipation equation considering the global flow is expressed as: （7）； in, is the dissipation function of the global flow; For the region Dissipation coefficient of the internal fluid; Step 2.2.2: The dissipation equation considering the local flow is expressed as: （8）； in, is the dissipation function of the local flow; 、 、 、 are the fluid viscosities in region 1, region 2, region 2, and region 4, respectively; 、 Different permeabilities for dual pore structures; Step 2.2.3: The total dissipation equation for the three-phase fluid is expressed as: （9）； in, is the total flow dissipation function.

5. The method for characterizing carbon dioxide migration in deep oil reservoirs based on longitudinal wave velocity calculation according to claim 4, characterized in that: The specific process of step 3 is: Step 3.1: The Lagrange equation with dissipative form is expressed as: （10）； in, To find the sign of partial derivative; For time; For Find partial derivatives; For Find partial derivatives; is a variable used to substitute for the fluid displacement, solid displacement, or volume strain increment of fluid flow; for The first derivative of ; Step 3.2: Substitute the fluid displacement, solid displacement, and volumetric strain increment of fluid flow into The wave equations for the CO2-oil-water three-phase fluid in a dual-porosity thermoelastic medium are obtained: （11）； （12）； （13）； in, is the gradient operator; 、 、 、 、 、 、 They are 、 、 、 、 、 、 The second derivative of 、 、 、 、 、 are the fluid volume strains after fluid migration in regions 1, 2, 3, 4, 5, and 6, respectively; 、 、 、 、 、 are the coupling stiffness coefficients between the skeleton and the fluid in regions 1, 2, 3, 4, 5, and 6 respectively; 、 、 、 、 、 are the fluid flow stiffness coefficients of region 1, region 2, region 3, region 4, region 5, and region 6 respectively; Step 3.3: The heat transfer equation for the dual-porosity thermoelastic medium is: （14）； in, is the thermal conductivity coefficient; is the total density of the fluid-saturated rock; is the specific heat capacity; 、 They are The first and second derivatives of ; is the relaxation time; is the absolute temperature.

6. The method for characterizing carbon dioxide migration in deep oil reservoirs based on longitudinal wave velocity calculation according to claim 5, characterized in that: The specific process of step 4 is as follows: Step 4.1: Calculate the amount, mass, and dissolved volume of CO2 dissolved in the water and oil phases. The specific process is as follows: Step 4.1.1: The amount of CO2 dissolved in the water phase and the oil phase is expressed as: （15）； in, is the mass of the aqueous phase; is the mass of the oil phase; is the solubility of CO2 in the aqueous phase; is the solubility of CO2 in the oil phase; is the amount of substance dissolved in the water phase; is the amount of substance dissolved in the oil phase; Step 4.1.2: The mass of CO2 dissolved in the water phase and the oil phase is expressed as: （16）； in, is the mass of CO2 dissolved in the water phase; is the mass of CO2 dissolved in the oil phase; is the molar mass of CO2; Step 4.1.3: The mixed density and dissolved volume of CO2 dissolved in the water phase and oil phase are expressed as: （17）； （18）； in, is the volume of the aqueous phase; is the volume of the oil phase; is the volume of CO2 dissolved in the water phase; is the volume of CO2 dissolved in the oil phase; is the mixed density of CO2 dissolved in water phase; is the mixed density of CO2 dissolved in the oil phase; is the density of the water phase; is the density of the oil phase; is the CO2 density; Step 4.2, calculate the viscosity, fluid saturation, and fluid bulk modulus of the oil and water phases after CO2 dissolution; Step 4.3: Update and calculate the CO2-oil-water property parameters.

7. The method for characterizing carbon dioxide migration in deep oil reservoirs based on longitudinal wave velocity calculation according to claim 6, characterized in that: The specific process of step 4.2 is as follows: Step 4.2.1: The viscosity of the water phase and oil phase after CO2 is dissolved in water and oil is expressed as: （19）； in, is the logarithm operator; is the viscosity of the water phase after CO2 dissolution; is the viscosity of the water phase; is the ion concentration in the aqueous phase; is the temperature correction term for the linear change of aqueous phase viscosity with ion concentration; is the temperature correction term for the change of aqueous phase viscosity with the square of ion concentration; is the temperature correction term for the change of aqueous phase viscosity with the cube of ion concentration; is the viscosity of the oil phase after CO2 dissolution; is the crude oil viscosity; is the viscosity of CO2; is the correlation coefficient; Step 4.2.2: After CO2 is dissolved in water and oil, the saturation of CO2, oil phase, and water phase is expressed as: （20）； in, is the rock volume; It is the CO2 saturation after CO2 is dissolved in oil and water; is the volume of CO2; Step 4.2.3: Calculate the bulk modulus of CO2 dissolved in water and oil based on the Wood model using formula (21). The specific process of step 4.3 is as follows: the mixed density of CO2 dissolved in the water phase and the oil phase, the viscosity of the oil phase and the water phase after CO2 is dissolved, the saturation of the oil phase after CO2 is dissolved in the oil, and the saturation of the water phase after CO2 is dissolved in the water calculated in steps 4.1 and 4.2 are substituted into equations (11) to (14) for solution.

8. The method for characterizing carbon dioxide migration in deep oil reservoirs based on longitudinal wave velocity calculation according to claim 7, characterized in that: The specific process of step 5 is as follows: Step 5.1: Substitute the one-dimensional plane wave kernel function into equations (11) to (14) to calculate the wave number. The plane wave kernel function is: （22）； in, is an exponential function with a natural constant as its base; is an imaginary number; Step 5.2: The full-band longitudinal wave propagation velocity is related to the wave number and angular frequency, and is calculated using formula (23).

Images