CN116130015B - Carbon dioxide flooding and sealing numerical simulation method under pore scale - Google Patents
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Abstract
The invention discloses a carbon dioxide flooding and sealing numerical simulation method under pore scale, which comprises the steps of constructing a basic calculation domain by collecting data images of a real oil reservoir, performing binarization processing and converting the data images into matrix data according to the distribution characteristics of residual oil of a high-water-content oil reservoir in the rock of the reservoir, then establishing a corresponding microscopic equation of different phase fluids, starting to inject CO 2 into the calculation domain after initial and boundary conditions are determined so as to realize simulation of CO 2 -oil-water three-phase fluid displacement or sealing process, and judging whether a mixed phase condition is reached so as to realize displacement or sealing behavior of mixed phases and non-mixed phases of CO 2; and outputting a CO 2 -oil-water three-phase fluid migration image and an oil recovery ratio change curve after stable flow is achieved. The pore structure of the method facing the true oil reservoir is suitable for realizing a stable migration process aiming at CO 2 -oil-water three-phase fluid with different densities and viscosities under different oil reservoir temperature and pressure conditions.
Description
Technical Field
The invention belongs to the field of carbon dioxide flooding oil sealing and storage, and relates to a carbon dioxide flooding oil sealing and storage numerical simulation method under a pore scale.
Background
Capturing and storing CO 2 in depleted hydrocarbon reservoirs and salt-containing aquifers is considered to be the most effective and feasible method to reduce CO 2 emissions and to suppress the greenhouse effect. CO 2 gas-drive enhanced oil recovery (CO 2 -EOR) technology is to inject CO 2 into an oil reservoir, increase oil yield by utilizing the interaction of CO 2 and reservoir fluid, and realize effective sequestration of CO 2 in the reservoir, and has been widely applied to the oil exploitation industry. In recent years, the CO 2 -EOR direction of high water reservoirs has become the mainstream in the CCUS project.
Most of the current simulation methods of the CO 2 -EOR process are developed under the core scale and the site scale, and few simulation methods for researching the displacement behavior of the CO 2 -oil-water three-phase fluid aiming at the pore scale of the high-water-content oil reservoir are provided. The core or field scale is mainly aimed at the change of macroscopic parameters (such as injection speed, injection pressure difference, heterogeneity of porous medium, fluid viscosity and density difference), the overall displacement efficiency is changed, then parameters are continuously regulated to find rules so as to determine a reasonable CO 2 -EOR project scheme, and the method is mostly influenced by experience in the determination of the scheme because the coupling effect of the CO 2 -oil-water three-phase fluid and the complex pore structure is not deeply known. Because CO 2 -oil-water three-phase fluid has very complex flowing process and coupling relation in the displacement process of porous medium, the phenomenon that interfacial tension between CO 2 -oil changes along with the pressure change of flowing process is also considered when mixed phase flowing between CO 2 and oil is involved, and the problems make the research on the coupling effect between the CO 2 -oil-water three-phase fluid mixed phase and non-mixed phase displacement process and complex pore structure under the pore scale very difficult.
At present, only a simulation method for CO 2 -oil-water three-phase non-miscible displacement under the pore scale is adopted, and the following technical difficulties are caused: (1) The method for dissolving and transferring dilute substances at the pore size by using the core or the site size is used for representing that a great error exists between the miscible process of CO 2 -oil and the actual result. (2) In a real high-water-content oil reservoir environment, along with the progress of a CO 2 displacement and sealing process, the conditions such as ambient temperature, pressure and the like are changed in real time, the physical properties of three-phase fluid such as CO 2, oil and water and the types of mixed-phase and non-mixed-phase displacement are also changed in real time, and the method has great inapplicability only by using a numerical method. (3) The complex flow channel structure of the true oil reservoir has the complexity of non-uniformity, randomness and geometric topological structure, and is difficult to be generated by simulation of the existing four-parameter method, expansion sphere algorithm and the like. Therefore, a simulation method applicable to both CO 2 -oil-water three-phase fluid mixed phase and non-mixed phase displacement and sequestration under the pore scale of a high-water-content oil reservoir is needed in the present stage.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention constructs a carbon dioxide flooding oil-displacement and sequestration numerical simulation method under a pore scale according to the distribution characteristics of residual oil of a high-water-content oil reservoir in reservoir rock, and the method is applicable to realizing a stable migration process aiming at CO 2 -oil-water three-phase fluids with different densities and viscosities under the conditions of temperature and pressure of different oil reservoirs, and specifically comprises the following steps:
Step 1: binarizing a porous medium RGB vector image of a real oil reservoir into a binary matrix of corresponding pixel points, and setting an iteration step length to convert the same proportion of the pixel points into corresponding grid points as a basic calculation domain;
Step 2: in a basic calculation domain, according to initial distribution of CO 2 -oil-water three-phase fluid and macroscopic parameters A, determining an initial discrete distribution function of CO 2 -oil-water three-phase fluid under a target working condition, and calculating and traversing all lattice points through a distribution function evolution equation in a migration collision process to obtain a new discrete distribution function of each lattice point;
Step 3: calculating macroscopic parameters B of the CO 2 -oil-water three-phase fluid at the moment through the new discrete distribution function of each lattice point calculated in the step 2;
Step 4: and (3) repeating the steps (2) and (3) to perform a new round of iterative computation, and judging that the migration process of the CO 2 -oil-water three-phase fluid in the porous medium reaches a stable state when the macroscopic parameter value change of the CO 2 -oil-water three-phase fluid does not exceed a set threshold value, and ending the loop iteration.
Further, the macro-parameters B include macro-density and macro-velocity of the CO 2 -oil-water three-phase fluid.
Further, the specific steps of the step 1 are as follows:
(1) Collecting a porous medium slice in an actual high-water-content oil reservoir, and performing image scanning on the porous medium slice to generate an RGB vector image;
(2) Converting the RGB vector image into a binary image;
(3) Converting the binary image into corresponding matrix arrays of 0 and 1 according to the arrangement positions of the pixel points, setting iteration step length to convert the same proportion of the pixel points into corresponding grid points, and taking the corresponding grid points as a basic calculation domain of the method, wherein each grid point serves as a basic calculation unit.
Further, the specific steps of the step 2 are as follows:
(1) Determining an initial distribution state of three-phase fluid of CO 2, oil and water in a basic calculation domain, wherein the initial distribution state is specifically expressed as: initially setting the porous medium to be in an oil saturated state, and injecting water at an inlet to perform water-oil two-phase displacement; when stable flow is achieved, the porous medium forms a water-oil two-phase distributed high water content state which is an initial state of CO 2 for driving a high water content oil reservoir;
(2) Setting macroscopic parameters of the selected CO 2 -oil-water three-phase fluid, wherein the macroscopic parameters A comprise: macroscopic density, macroscopic viscosity, macroscopic velocity, and contact angle between different fluids;
(3) Determining an initial discrete distribution function of CO 2 -oil-water three-phase fluid under a target working condition; since each lattice point serves as a basic calculation unit, the total fluid distribution in the calculation domain is obtained by calculating the particle distribution of all lattice points in the whole basic calculation domain once, and the particle distribution of different lattice points at this time is represented by a distribution function, which is called an equilibrium distribution function when the particle distribution of a lattice point somewhere is in an equilibrium state; since the microscopic particles are not in random thermal motion at any moment, the velocity of the microscopic particles is continuous, the velocity is infinite in phase space, however, the motion details of the particles do not significantly determine the macroscopic motion of the fluid, and therefore, the velocity of the particles is reduced to a finite-dimensional velocity space in phase space, then the continuous distribution function is also discretized into discrete distribution functions of the same number as discrete velocities The equilibrium distribution function of each lattice point is also discretized into a discrete equilibrium distribution function/>, which is the same as the number of discrete velocitiesWherein the initial discrete distribution function/>, of the CO 2 -oil-water three-phase fluidBringing the macroscopic density and velocity of the different phase fluids in step (2) into an equilibrium state distribution function/>The formula is found:
Where k represents a discrete number of serial numbers (e.g., if the number is 9, k represents 0 to 8), and a represents a number of different phase fluids (since the model study is a three-phase fluid of CO 2 -oil-water, a ranges from 0 to 2); w k is a weight factor of different discrete amounts, specific values are different according to the different discrete amounts, but the weight factors of all the discrete amounts are added to be equal to 1; c represents the lattice speed, the value needs to be converted with the actual sound speed, and when the actual sound speed is 332.532m/s, c=1; /(I) Representing the spatial distribution of discrete quantities, expressed in the form of vector coordinates, with the difference/>, of discrete quantitiesThe coordinate values of (2) are also different, but the/>, is required to be satisfiedIs equal to 1, ρ a and/>Respectively representing the macroscopic density and macroscopic velocity of the different phase fluids;
(4) Setting boundary conditions of CO 2 miscible and non-miscible flooding high-water-content oil reservoir processes according to different working conditions; most simulation studies use pressure boundary conditions or speed boundary conditions, and the values of different discrete amounts of particles need to be correspondingly modified according to different boundary conditions. The situation is slightly different at the boundary of the inlet and the outlet, and the CO 2 fluid is injected at the inlet, only the pressure boundary condition or the speed boundary condition is required to be set for CO 2. At the outlet there will be outflow of three phase fluids CO 2, oil, water, so it is necessary to set corresponding pressure boundary conditions or velocity boundary conditions for all three phase fluids CO 2, oil, water. For boundary processing of the porous medium in the simulation area, the invention adopts specular reflection without sliding boundary, namely, a cell at a certain position is determined as a boundary entity, so that the normal collision process is omitted, and the density of the fluid is rebounded.
(5) Traversing all lattice points through calculation according to an evolution equation in the migration collision process to obtain a new discrete distribution function of each lattice point; since the temporal and spatial dispersion in the model is not independent, it is linked by the discrete velocity of the particles. The movement of the particles is divided into two links of migration and collision, namely, the particles move from one lattice node to the corresponding adjacent lattice node between two time steps and collide with other particles on the lattice node, so that an evolution equation of the distribution function in the migration collision process is formed, namely:
in the formula, the adjacent points of x are obtained by solving the formulas of the distribution function and the equilibrium distribution function at the time t of the point x A distribution function at a position t+Δt time; [ (M a)-1ΛaMa ] represents relaxation time, i.e. the time required for fluid to transition from the current state to the equilibrium state, the method meets the stable migration of CO 2 -oil-water three-phase fluid under different working conditions and corresponding to different density and different viscosity fluid parameters by setting the parameter of lambda a;)The force term representing the fluid, where M a is represented as a matrix of specific values:
Λ a is a diagonal relaxation matrix, expressed as:
Is a force term related to interfacial tension of CO 2 -oil-water three-phase fluid, expressed as:
Wherein the method comprises the steps of The potential function dependent on local density and interaction strength is used to express the interaction force between CO 2 -oil-water three-phase molecules, and is specifically formed from three parts, the first is CO 2 -oil-water three-phase flow interaction forceThe second is the acting force/>, among different particles in the CO 2 -oil-water three-phase flowThirdly, the acting force between the CO 2 -oil-water three-phase flow and the wall surface/>The formula is as follows:
further, in one embodiment of the present invention, parameters in the present study Take the value of/>
Relaxation timeHas the following relationship with the fluid viscosity v a:
Balance speed Expressed as:
The stable migration of CO 2 -oil-water three-phase fluid under different working conditions and different density and viscosity fluid parameters is met by setting the parameters of the diagonal relaxation matrix of the lambda a.
The interaction force between fluids is expressed in the last term in the evolution equation of the discrete distribution function, and by constructing the interaction force between multiphase fluid particles, the flow forms of CO 2 -oil miscible phase and non-miscible phase are realized, which is specifically expressed asThe fluid is automatically separated into different phases by adding an appropriate potential function, also known as the interparticle potential energy ψ a (x, t), to the force term equation.
The interaction force between the CO 2 -oil-water three-phase flow in the step 2 (5)The solving process is as follows:
Wherein ψ a (x, t) is the potential energy between particles, the potential function value at this point is related to the pressure P a, density ρ a of the phase fluid and the force coefficient G aa between the phase fluid, and the specific formula is:
Wherein the constant c 0 =6.0, the value of the pressure P a is calculated by a state mode, and the specific calculation process is as follows:
In the calculation process of the state equation, the critical temperature, critical pressure, eccentric factor, molar mass and other basic fluid parameters of CO 2, oil and water are determined, the determined pressure value changes are obtained by using the parameters, and then the determined pressure value changes are brought into a calculation formula of a potential function ψ a (x, T) to carry out specific calculation, and the density ratio under different working conditions is realized by changing the parameter T a, which is set as T Oil (oil) ＝385、TCO2＝21、T Water and its preparation method =331 in one embodiment of the invention.
Parameters related to the equation of state
The specific values of the acting force parameters between different phase fluids are tested and finally determined by the research according to the surface tension parameter change of specific CO 2 -oil-water three-phase fluid under different working conditions and the contact angle change of different phase fluids when the different phase fluids are contacted, wherein G co2- oil=0.085, G co2- water=0.115 and G Oil (oil) - water=0.095;
In the process of selecting the parameters of G co2- Oil (oil) , it is necessary to determine the value of P a at this time, if the value of the pressure P a is higher than the miscible pressure, at this time, G co2- oil=0.001, the interfacial tension between the CO 2 -oil at this time disappears and a miscible band is formed, and the continuity, flow and convection diffusion equations of the miscible band region are expressed as:
D is the diffusion coefficient (m 2/s) of CO 2 solute in the miscible solution fluid density ρ (c), viscosity of the miscible phase band is expressed as:
c is the saturation of CO 2 in the mixed phase band, c inj is the saturation of CO 2 in the injected solution, c 0 is the initial saturation of CO 2 in the porous medium, and the calculation formula of the saturation is determined by the fluid density ρ a of the phase, specifically expressed as:
By using the method, the flow condition of the mixed phase and non-mixed phase displacement process between CO 2 -oil-water three-phase fluid is constructed.
The action force between different particles in the CO 2 -oil-water three-phase flow in the step 2 (5)The solving process is as follows:
Wherein the potential function psi a (x, t) is specifically expressed as
Wherein G aa represents the force coefficient between in-phase fluids, the value of which is determined by the present study from the determination of the basic physical properties of CO 2 -oil-water three-phase fluids and through multiple tests, wherein G co2＝-0.11,G Water and its preparation method ＝-0.25,G Oil (oil) = -0.18.
The action force between the CO 2 -oil-water three-phase flow and the wall surface in the step 2 (5)The solving process is as follows:
The forces acting on the porous media walls of fluid phase a and solid phase s are expressed as:
In the middle of Represents the strength of interaction between fluid phase a and solid phase s, when/>When expressed as a non-wetting phase; /(I)When expressed as a wet phase. s (x) is an indicator function, s (x) =1 represents a solid, and s (x) =0 represents a fluid. According to the wettability relation of CO 2 -oil-water three-phase fluid,/>The method comprises the following steps: /(I)
Further, the specific steps of the step3 are as follows:
the CO 2 -oil-water three-phase fluid evolution at each lattice point is iterated to obtain a discrete distribution function Is brought into the following formula, combining the spatial distribution of discrete quantities/>Obtaining the macroscopic density rho a and macroscopic speed/>, of the CO 2 -oil-water different-phase fluid in the porous medium
Further, the specific steps of the step 4 are as follows:
Traversing all lattice points as the process proceeds to the nth iteration, when the equation is satisfied:
Wherein ε 1 is the steady state threshold of macroscopic density and ε 2 is the steady state threshold of macroscopic speed; at this time, the migration process of the CO 2 -oil-water three-phase fluid in the porous medium reaches a stable state, and the loop iteration is ended; the output content at this time includes: the saturation values of the CO 2 -oil-water three-phase fluid at all lattice points in the effective area at different time steps, and the velocity gradient values of the fluid at different spatial directions. And (3) by counting the result values, an oil recovery rate change curve, a three-phase fluid migration change image and the like of the CO 2 mixed-phase and non-mixed-phase flooding high-water-content oil reservoir and the sealing process are made.
The beneficial effects of the invention are as follows:
1. The method is oriented to simulation research in a real high-water-content oil reservoir environment, and the constructed simulation domain has non-uniformity with characteristics consistent with those of a real oil reservoir, so that CO 2 -oil-water three-phase fluid mixed phase and non-mixed phase displacement or CO 2 sealing simulation is carried out in a real complex flow channel structure.
2. The microscopic equation constructed by the method is suitable for the mechanism research of the CO 2 mixed phase and non-mixed phase displacement process of the high-water-content oil reservoir, and solves the macroscopic parameters (speed, density, pressure and the like) of the fluid, so that the microscopic mechanism of the CO 2 -oil-water three-phase fluid displacement is researched, and the macroscopic migration behavior of the CO 2 -oil-water three-phase fluid is represented.
3. The method determines a plurality of key parameters, such as diagonal relaxation matrix The nine parameters realize normal displacement processes of different viscosity ratios of CO 2 -oil-water three-phase fluid under different working conditions; determining a parameter P a in a state equation to realize normal displacement processes of different density ratios of CO 2 -oil-water three-phase fluid under different working conditions; determining an interaction force parameter G co2- Oil (oil) 、Gco2- Water and its preparation method 、G Oil (oil) - Water and its preparation method of the CO 2 -oil-water three-phase fluid, and realizing that the three-phase fluid has a phase interface with the same property as the actual three-phase flow in the migration process; determining an acting force parameter G co2、G Water and its preparation method 、G Oil (oil) in the CO 2 -oil-water three-phase fluid to realize interaction force expression among particles of the same-phase fluid; determination of force parameter/>, of CO 2 -oil-water three-phase fluid and wall surfaceThe wettability relation between the three-phase fluid and the real oil reservoir wall surface is realized.
Drawings
FIG. 1 is a flow chart of a pore size simulation method of CO 2 miscible and immiscible flooding high water reservoir processes.
Fig. 2 is an image of a porous medium used in the design of the solution.
FIG. 3 is a discrete velocity model of each grid point in the example.
Fig. 4 is a boundary condition setting in an example. a entrance boundary, b exit boundary.
Fig. 5 is a phase diagram change of CO 2 -oil-water three-phase fluid for mixed and non-mixed phase displacement processes.
Fig. 6 is a velocity gradient image of CO 2 -oil-water three-phase fluid for both miscible and immiscible displacement processes.
Fig. 7 is a plot of oil recovery trend for miscible and immiscible displacement processes.
Detailed Description
The technical scheme of the invention is further described in detail according to the accompanying drawings in the specification.
The invention is described in detail below with reference to the accompanying drawings and examples.
As shown in fig. 1, a flow chart of a pore size simulation method of CO 2 miscible and immiscible flooding high water-bearing oil reservoir processes is shown, and specific steps are as follows:
Step 1: the method comprises the steps of binarizing a porous medium RGB vector image of a real oil reservoir into a binary matrix of corresponding pixel points, setting iteration step length to convert the same proportion of the pixel points into corresponding lattice points, and taking the lattice points as a basic calculation domain, wherein the method mainly comprises the following steps:
(1) And acquiring a two-dimensional porous medium slice of the real oil reservoir and extracting RGB vector images of the pore flow channel by means of an instrument.
(2) The RGB vector image is converted into a binary image by imageJ, openCv, matlab or other software, as shown in fig. 2, wherein white represents particles, black represents flow channels, and specific parameters of the porous medium are shown in the following table:
Main parameters of the porous medium
(3) Converting the flow channel image shown in fig. 2 into corresponding 0, 1 matrix arrays according to the arrangement positions of the pixel points, setting iteration step length to convert the pixel points into corresponding grid points in equal proportion, and taking each grid point as a basic calculation unit as a basic calculation domain of the method, wherein the number of grid points of an effective area of the example is as follows: 1000 x 1000.
Step 2: in a basic calculation domain, according to initial distribution and macroscopic parameters of CO 2-oil-water three-phase fluid, determining an initial discrete distribution function of CO 2 -oil-water three-phase fluid under a target working condition, and calculating and traversing all lattice points through an evolution equation in a migration collision process to obtain a new discrete distribution function of each lattice point, wherein the method mainly comprises the following steps of:
(1) Setting macroscopic density, viscosity and speed values of the selected CO 2 -oil-water three-phase fluid and contact angles among different fluids;
The density and viscosity between different fluids are shown
Contact angles between different fluids
(2) Determining an initial distribution state of three-phase fluid of CO 2, oil and water in a basic calculation domain; the method is characterized in that a porous medium is initially set to be in an oil saturated state, water is injected into an inlet to perform water-oil two-phase displacement, and the injection speed is 0.10mL/min; when stable flow is achieved, the porous medium forms a water-oil two-phase distributed high water content state which is an initial state of CO 2 for driving a high water content oil reservoir; CO 2 was then injected at the inlet for CO 2 -oil-water three-phase displacement at a rate of 0.10mL/min.
(3) An initial discrete distribution function of the CO 2-oil-water three-phase fluid under the target working condition is determined. This example employs a CO 2 -oil-water three-phase fluid mixed-phase and non-mixed-phase displacement process in a two-dimensional porous medium, wherein the initial discrete distribution function of the CO 2-oil-water three-phase fluidIs to bring the macroscopic density and velocity of the different phase fluids in (1) into the equilibrium state distribution function/>The formula finds that the velocity at each lattice point is discrete into 9 components, namely the center point of the lattice is one velocity component, the center lines of four sides of the lattice are four velocity components, the four diagonals of the lattice are four velocity components, and at the moment, 9 discrete velocity vectors/>Expressed as:
the continuous distribution function is also discretized into 9 discrete distribution functions Wherein k=0 to 9; the equilibrium distribution function of each lattice point is also discretized into 9 discrete equilibrium distribution functions/>Wherein k=0 to 9:
a represents the serial number of the CO 2 -oil-water three-phase fluid (i.e., a=0 to 2);
w k is a weight factor of different discrete amounts, and since each lattice point is discrete into nine amounts, the weight factor is expressed as:
c represents the lattice velocity, in this example c=1.
(4) And setting boundary conditions of the CO 2 miscible and non-miscible flooding high-water-content oil reservoir processes according to working conditions of different research backgrounds.
For the boundary treatment of the porous medium in this example, the injection mode of CO 2 adopts dirichlet (pressure) boundary, and is constant pressure difference injection. By assuming that the velocity tangential to the boundary is zero, and finding the velocity component perpendicular to the boundary. As shown in fig. 4, setting the left side as the entrance boundary, the corresponding formula can be deduced as:
This example uses specular reflection of slip-free sidewalls for boundary setup where the fluid contacts porous media walls. I.e. a cell at a certain position is determined as a boundary entity, the normal collision process is omitted, and the density will be bounced, which can be expressed specifically as:
(5) And traversing all lattice points through calculation according to an evolution equation in the migration collision process, and obtaining a new discrete distribution function of each lattice point.
Since the temporal and spatial dispersion in the model is not independent, but is linked by the discrete velocity of the particles. The movement of the particles is divided into two links of migration and collision, namely, the particles move from one lattice node to the corresponding adjacent lattice node exactly between two time steps, and collide with other particles on the lattice node, so that an evolution equation of a distribution function in the migration collision process is formed, namely:
obtaining an adjacent point x by solving a formula of a distribution function and a balance state distribution function at the point x and the point t A distribution function at t+Δt time; [ (M a)-1ΛaMa ] represents relaxation time, namely the time required by the fluid to transit from the current state to the equilibrium state, the method meets the stable migration of CO 2 -oil-water three-phase fluid under different working conditions and corresponding to different density and different viscosity fluid parameters through setting the parameter of lambda a Representing the forces between the different phase fluids and between the phase fluids.
For the [ (M a)-1ΛaMa ] term, M a is represented as a matrix of specific values:
Λ a is a diagonal relaxation matrix, expressed as:
In the present embodiment, parameters Take the value of/> Relaxation time/>Has the following relationship with the fluid viscosity v a:
Balance speed Expressed as:
The stable migration of the CO 2 -oil-water three-phase fluid under the working condition of the embodiment is met by setting the parameters of the diagonal relaxation matrix of the lambda a.
Then constructing interaction force among multiphase fluid particles to realize mixed phase and non-mixed phase flow forms among CO 2 -oil-water three-phase fluid, which mainly comprises the following steps:
the interaction force between fluids is expressed in the last term in the evolution equation of the discrete distribution function, and is specifically expressed as Wherein/>Is a force term related to interfacial tension of the CO 2 -oil-water three-phase fluid. The expression is as follows:
Wherein the method comprises the steps of For the basic concept, a potential function which depends on local density and interaction strength is used for representing the interaction between CO 2 -oil-water three-phase molecules, and the potential function is specifically composed of three parts, namely the interaction force/>, between CO 2 -oil-water three-phase flowThe second is the acting force/>, among different particles in the CO 2 -oil-water three-phase flowThirdly, the acting force between the CO 2 -oil-water three-phase flow and the wall surface/>The formula is as follows:
the automatic separation of the fluid into different phases is achieved by adding an appropriate potential function, also known as the interparticle potential energy ψ a (x, t), to the force term.
1. The force function between the different phase fluids at this time is expressed as:
Wherein ψ a (x, t) is the potential energy between particles, the potential function value at this point is related to the pressure P a, the density P a of the phase fluid and the force coefficient G aa between the phase fluid, and the specific formula is:
Wherein the constant c 0 =6.0, the value of the pressure P a is calculated by a state mode, and the specific calculation process is as follows:
In the calculation process of the state equation, the critical temperature, critical pressure, eccentric factor, molar mass and other basic fluid parameters of CO 2, oil and water are determined, the determined pressure value change is obtained by utilizing the parameters, then the determined pressure value change is brought into a calculation formula of a potential function psi a (x, T) to carry out specific calculation, the density ratio under different working conditions is realized by changing the T a parameter, and the method is set as T Oil (oil) ＝385、TCO2＝21、T Water and its preparation method =331 aiming at the parameter.
Parameters involved in table state equations
/>
The specific value of the acting force coefficient between different phase fluids is finally determined by carrying out multiple tests according to the surface tension parameter change of specific CO 2 -oil-water three-phase fluid under different working conditions and the contact angle change of different phase fluids when the different phase fluids are contacted, wherein G co2- oil=0.085, G co2- water=0.115 and G Oil (oil) - water=0.095;
In the process of selecting the parameters of G co2- Oil (oil) , it is necessary to determine the value of P a at this time, if the value of the pressure P a is higher than the miscible pressure, at this time, G co2- oil=0.001, the interfacial tension between the CO 2 -oil at this time disappears and a miscible band is formed, and the continuity, flow and convection diffusion equations of the miscible band region are expressed as:
D is the diffusion coefficient (m 2/s) of CO 2 solute in the miscible solution fluid density ρ (c), viscosity of the miscible phase band is expressed as:
c is the saturation of CO 2 in the mixed phase band, c inj is the saturation of CO 2 in the injected solution, c 0 is the initial saturation of CO 2 in the porous medium, and the calculation formula of the saturation is determined by the fluid density ρ a of the phase, specifically expressed as:
By using the method, the flow condition of the mixed phase and non-mixed phase displacement process between CO 2 -oil-water three-phase fluid is constructed.
2. The force function between in-phase fluids is expressed as:
Wherein the potential function psi a (x, t) is specifically expressed as
Wherein G aa represents the force coefficient between in-phase fluids, the value of which is determined by the present study from the determination of the basic physical properties of CO 2 -oil-water three-phase fluids and through multiple tests, wherein G co2＝-0.11,G Water and its preparation method ＝-0.25,G Oil (oil) = -0.18.
3. Force between CO 2 -oil-water three-phase fluid and wall:
The forces acting on the porous media walls of fluid phase a and solid phase s are expressed as:
represents the strength of interaction between fluid phase a and solid phase s, when/> When expressed as a non-wetting phase; /(I)When expressed as a wet phase. s (x) is an indicator function, s (x) =1 represents a solid, and s (x) =0 represents a fluid.
According to the wettability relation of CO 2 -oil-water three-phase fluid,The method comprises the following steps: /(I)
Step 3: the macro parameters of the CO 2 -oil-water three-phase fluid at the moment are calculated through the new discrete distribution function of each lattice point calculated in the step 2, and the macro parameters mainly comprise:
v a Representing macroscopic density and macroscopic velocity, respectively, of different phase fluids, determination of these two parameters requiring the combination of discrete distribution functions/>Spatial distribution with discrete quantities/>Is determined by iterating the evolution of the CO 2 -oil-water three-phase fluid at each lattice point into a discrete distribution function/>Is carried into the following formula to obtain the macroscopic velocity distribution and macroscopic density distribution of CO 2 -oil-water in the porous medium.
Step 4: repeating the steps 2 and 3, performing a new round of iterative computation, and when the macroscopic parameter value change of the CO 2 -oil-water three-phase fluid does not exceed a set threshold value, judging that the migration process of the CO 2 -oil-water three-phase fluid in the porous medium reaches a stable state, and ending the loop iteration.
In the step, the iteration process of the steps 2 and 3 is continuously repeated, new discrete distribution function values of all lattice points in the basic calculation domain are obtained after each iteration is completed, and new macroscopic parameters (namely macroscopic density and macroscopic speed of CO 2 -oil-water three-phase fluid) of each lattice point are obtained according to the numerical value of the discrete distribution function. Traversing all lattice points as the process proceeds to the nth iteration, when the equation is satisfied:
At this time, the migration process of the CO 2 -oil-water three-phase fluid in the porous medium reaches a stable state, and the loop iteration is ended. The output content at this time includes: the saturation values of the CO 2 -oil-water three-phase fluid at all lattice points in the effective area at different time steps, and the velocity gradient values of the fluid at different spatial directions. By counting the numerical values of the results, oil recovery rate change curves, three-phase fluid migration change images and the like (fig. 5, 6 and 7) of the CO 2 mixed-phase and non-mixed-phase flooding high-water-content oil reservoir and the sealing process are made, and the oil recovery rate simulation results and experimental verification results under different injection modes are shown in the following table.
Table results of oil recovery simulation and experimental verification under different injection modes
/>
Claims (8)
1. The carbon dioxide flooding and sealing numerical simulation method under the pore size is characterized by comprising the following steps of:
Step 1: binarizing a porous medium RGB vector image of a real oil reservoir into a binary matrix of corresponding pixel points, and setting an iteration step length to convert the same proportion of the pixel points into corresponding grid points as a basic calculation domain;
Step 2: in a basic calculation domain, according to initial distribution of CO 2 -oil-water three-phase fluid and macroscopic parameters A, determining an initial discrete distribution function of CO 2 -oil-water three-phase fluid under a target working condition, and calculating and traversing all lattice points through a distribution function evolution equation in a migration collision process to obtain a new discrete distribution function of each lattice point; the method comprises the following specific steps:
(1) Determining an initial distribution state of three-phase fluid of CO 2, oil and water in a basic calculation domain, wherein the initial distribution state is specifically expressed as: initially setting the porous medium to be in an oil saturated state, and injecting water at an inlet to perform water-oil two-phase displacement; when stable flow is achieved, the porous medium forms a water-oil two-phase distributed high water content state which is an initial state of CO 2 for driving a high water content oil reservoir;
(2) Setting macroscopic parameters of the selected CO 2 -oil-water three-phase fluid, wherein the macroscopic parameters A comprise: macroscopic density, macroscopic viscosity, macroscopic velocity, and contact angle between different fluids;
(3) Determining an initial discrete distribution function of a CO 2 -oil-water three-phase fluid under a target working condition Bringing the macroscopic density and velocity of the different phase fluids in step (2) into an equilibrium state distribution function/>The formula is found:
Where k represents the serial number of the discrete quantity and a represents the serial number of the different phase fluid; w k is the weight factor of different discrete quantities; c represents the lattice velocity; /(I) Representing the spatial distribution of discrete quantities ρ a and/>Respectively representing the macroscopic density and macroscopic velocity of the different phase fluids;
(4) Setting boundary conditions of CO 2 miscible and non-miscible flooding high-water-content oil reservoir processes according to different working conditions;
(5) Traversing all lattice points through calculation according to an evolution equation in the migration collision process to obtain a new discrete distribution function of each lattice point; the evolution equation of the distribution function is as follows:
in the formula, the adjacent points of x are obtained by solving the formulas of the distribution function and the equilibrium distribution function at the time t of the point x A distribution function at a position t+Δt time; [ (M a)-1ΛaMa ] represents relaxation time; The force term representing the fluid, where M a is represented as a matrix of specific values:
Λ a is a diagonal relaxation matrix, expressed as:
Is a force term related to interfacial tension of CO 2 -oil-water three-phase fluid, expressed as:
Wherein the method comprises the steps of The potential function dependent on local density and interaction strength is used to express the interaction force between CO 2 -oil-water three-phase molecules, and is specifically formed from three parts, the first is CO 2 -oil-water three-phase flow interaction forceThe second is the acting force/>, among different particles in the CO 2 -oil-water three-phase flowThirdly, the acting force between the CO 2 -oil-water three-phase flow and the wall surface/>The formula is as follows:
Step 3: calculating macroscopic parameters B of the CO 2 -oil-water three-phase fluid at the moment through the new discrete distribution function of each lattice point calculated in the step 2; the method comprises the following specific steps:
the CO 2 -oil-water three-phase fluid evolution at each lattice point is iterated to obtain a discrete distribution function Is brought into the following formula, combining the spatial distribution of discrete quantities/>Obtaining the macroscopic density rho a and macroscopic speed/>, of the CO 2 -oil-water different-phase fluid in the porous medium
Step 4: and (3) repeating the steps (2) and (3) to perform a new round of iterative computation, and judging that the migration process of the CO 2 -oil-water three-phase fluid in the porous medium reaches a stable state when the macroscopic parameter value change of the CO 2 -oil-water three-phase fluid does not exceed a set threshold value, and ending the loop iteration.
2. The method for modeling carbon dioxide flooding seal-up values at pore scale of claim 1, wherein the macro-parameter B comprises macro-density and macro-velocity of CO 2 -oil-water three-phase fluid.
3. The method for simulating the carbon dioxide flooding sequestration numerical simulation under the pore scale according to claim 1, wherein the specific steps of the step 1 are as follows:
(1) Collecting a porous medium slice in an actual high-water-content oil reservoir, and performing image scanning on the porous medium slice to generate an RGB vector image;
(2) Converting the RGB vector image into a binary image;
(3) Converting the binary image into corresponding matrix arrays of 0 and 1 according to the arrangement positions of the pixel points, setting iteration step length to convert the same proportion of the pixel points into corresponding grid points, and taking the corresponding grid points as a basic calculation domain of the method, wherein each grid point serves as a basic calculation unit.
4. The method for simulating the carbon dioxide flooding sequestration numerical simulation at the pore scale according to claim 1, wherein in the process of setting the boundary conditions in the step 2 (4): and carrying out boundary treatment on the porous medium in the simulation area by adopting a specular reflection method without a sliding boundary.
5. The method for simulating carbon dioxide flooding sequestration numerical simulation under pore scale according to claim 1, wherein the interaction force between the CO 2 -oil-water three-phase flow in the step 2 (5)The solving process is as follows:
Wherein ψ a (x, t) is the potential energy between particles, the potential function value at this point is related to the pressure P a, density ρ a of the phase fluid and the force coefficient G aa between the phase fluid, and the specific formula is:
Where c 0 is a constant.
6. The method for simulating carbon dioxide flooding sequestration numerical simulation under pore scale according to claim 1, wherein the forces between different particles in the three-phase flow of CO 2 -oil-water in step 2 (5)The solving process is as follows:
7. The method for simulating a carbon dioxide flooding seal under pore size according to claim 1, wherein the force between the CO 2 -oil-water three-phase flow and the wall in step 2 (5) The solving process is as follows:
In the middle of Represents the strength of interaction between fluid phase a and solid phase s, when/>When expressed as a non-wetting phase; /(I)When expressed as a wet phase; s (x) is an indicator function, s (x) =1 represents a solid, and s (x) =0 represents a fluid.
8. The method for simulating the carbon dioxide flooding sequestration numerical simulation under the pore scale according to claim 1, wherein the specific steps of the step 4 are as follows:
Traversing all lattice points as the process proceeds to the nth iteration, when the equation is satisfied:
Wherein ε 1 is the steady state threshold of macroscopic density and ε 2 is the steady state threshold of macroscopic speed; at this time, the migration process of the CO 2 -oil-water three-phase fluid in the porous medium reaches a stable state, and the loop iteration is ended; the output content at this time includes: the saturation values of the CO 2 -oil-water three-phase fluid at all lattice points in the effective area at different time steps, and the velocity gradient values of the fluid at different spatial directions.
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