CO2 flooding simulation method based on dual-grid system

Abstract

The present invention provides a CO2 flooding simulation method based on a dual-grid system. The method comprises the following steps: 1. establishing a CO2 flooding geological model and dividing the dual-grid system; 2. upscaling parameters on fine grid cells and further calculating parameters on a coarse grid; 3. solving a pressure equation on the coarse grid system to obtain a pressure field; 4. solving a velocity field on the fine grid system based on the pressure solution; and 5. solving a transport equation on the fine grid system. The dual-grid system-based CO2 flooding simulation method solves the pressure equation on the coarse grid system while simultaneously solving the transport equation and performing flash calculations on the fine grid. This method improves calculation speed while reflecting the impact of fine grid heterogeneity on CO2 flooding flow.

Description

Technical Field

[0001] The present invention relates to the technical field of CO2 flooding simulation, and in particular to a CO2 flooding simulation method based on a dual-grid system. Background Art

[0002] Since the industrial era, the massive emission of greenhouse gases, primarily carbon dioxide, along with industrial development, has caused a series of environmental and ecological problems. According to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC), atmospheric carbon dioxide concentrations have risen from 280 ppm before the Industrial Revolution to 379 ppm in 2005, exceeding the natural range of variation over the past 650,000 years. Recently, measurements have shown that atmospheric carbon dioxide concentrations have exceeded 415 ppm, setting an all-time high. CO2 emission reduction has become a global research hotspot, with CO2 flooding and CO2 storage being among the most effective and practical methods of reducing emissions.

[0003] CO2 injection for oil recovery is a relatively ideal method. CO2 is a superior oil displacement agent and has been proven to be an effective method for enhancing oil recovery. CO2 has low viscosity and is easy to inject. Furthermore, upon contact with crude oil after injection into the formation, it causes the oil to expand, reducing viscosity, extracting light components, lowering oil-water interfacial tension, and improving mobility, effectively enhancing oil recovery. Once miscible with crude oil, CO2 eliminates interfacial tension, significantly increasing oil recovery. Carbon dioxide capture and storage for oil recovery (CCS-EOR) permanently stores CO2 underground through CO2 capture, injection into formations for oil recovery, and recycling and reuse. This effectively reduces greenhouse gas levels, achieving a win-win situation of increasing oil production and storing CO2. It is currently the most realistic approach to carbon emission reduction and utilization. The application of CO2 for oil recovery is a key tool for large oil companies to implement carbon emission reduction efforts and implement the national green and low-carbon development concept. Therefore, the development of CO2 flooding technology is in line with the national low-carbon development strategy.

[0004] Numerical simulation technology is crucial for understanding CO2 flooding dynamics and formulating CO2 enhanced oil recovery measures, among other decisions. CO2 flooding numerical simulations rely on component models, which incorporate the mechanisms of extraction, miscibility, and miscibility between CO2 and crude oil. Simple black oil models cannot accurately simulate the CO2 flooding process. While component models can accurately describe the CO2 flooding process, they often require simulating numerous components, resulting in high computational complexity and long computation times. In oilfield-level simulations, the geological model is sophisticated, the grid count is enormous, and the computational complexity is even greater, making effective simulation difficult.

[0005] The upscaling method is a traditional method to reduce the amount of calculation and is also widely used in reservoir numerical simulation. However, the traditional upscaling method averages the heterogeneity and artificially smoothes the heterogeneity. Although it reduces the amount of calculation, it will lead to low calculation accuracy and fail to fully reflect the heterogeneity. For this reason, domestic and foreign experts and scholars have also proposed dual-grid methods to reduce the amount of calculation. The dual-grid method was first used to solve two-phase flow problems, that is, solving the pressure field and saturation field on two sets of grid systems, and upscaling the pressure equation during the solution process. Since then, this idea has attracted the attention of scholars, has been widely developed, and has gradually been extended to component models, including component models involving chemical reactions. However, it has not yet been extended to CO2 flooding single-phase flow simulation.

[0006] Chinese patent application number CN201610867559.3 describes a method for describing CO2-flooded reservoir heterogeneity. The method includes the following steps: 1. Calculating permeability differentials within a block and determining reasonable permeability differential boundaries based on the permeability differentials within the study area; 2. Processing the permeability interpretation results within a study area to calculate the permeability differentials for a grid model; 3. Using numerical simulations to investigate the impact of different methods on CO2 flooding gas appearance time; 4. Analyzing the impact of crude oil physicochemical properties on the gas-to-oil ratio during CO2 flooding; 5. Using numerical simulations to analyze flow rate differences between models with different permeability values; and 6. Correcting the average permeability using CO2 flooding gas-to-oil ratio fitting and comparison of the actual model. This method establishes a permeability curve discretization method based on the parameters available in the numerical simulation, providing a numerical simulation basis for improving the accuracy of CO2 flooding simulations and quantitatively characterizing the displacement mechanism.

[0007] Chinese patent application number CN201910561096.1 describes a mathematical simulation method for two-dimensional CO2 immiscible flooding in low-permeability reservoirs. The method includes establishing a two-dimensional CO2 immiscible flooding mathematical model for low-permeability reservoirs; processing the parameters and boundary conditions required for solving the two-dimensional CO2 immiscible flooding process; solving the two-dimensional CO2 immiscible flooding mathematical model for low-permeability reservoirs using a numerical method, namely, the implicit pressure explicit saturation method; selecting a low-permeability reservoir and obtaining its geological parameters, performing calculations using the two-dimensional CO2 immiscible flooding mathematical simulation method, and analyzing the results. This method considers changes in crude oil viscosity and fluid starting pressure gradient during CO2 immiscible flooding, establishing a mathematical model for CO2 immiscible flooding in low-permeability reservoirs that more closely matches the actual reservoir properties. The method also provides a solution method and results analysis methods, resulting in more reliable calculation results that can be used to guide CO2 immiscible flooding development in low-permeability reservoirs.

[0008] Chinese patent application number CN201910645227.4 discloses a numerical simulation method for calculating the minimum miscibility pressure of CO2 flooding, encompassing CO2 flooding enhanced oil recovery technology. The method includes the following steps: establishing a general model for long and thin tubular components; inputting crude oil component parameters, flash separation, and differential separation experimental data of the target reservoir into the PVTi module of the numerical simulation software; batching the crude oil components and performing regression calculations on the flash separation and differential separation experimental data of the crude oil components in the batching results using a three-parameter state equation; selecting the regression parameters as fitting parameters, and setting fitting parameter weights to achieve rapid component fitting; deriving state equation parameters from the fitting data in the PVTi module to obtain a numerical model for the long and thin tubular components; running the numerical model under different reservoir pressure conditions to output the corresponding full-field recovery; and using the model to simulate and calculate the minimum miscibility pressure of CO2 flooding in the target reservoir.

[0009] The above existing technologies are significantly different from the present invention and fail to solve the technical problem we want to solve. Therefore, we have invented a new CO2 flooding simulation method based on a dual-grid system. Summary of the Invention

[0010] The object of the present invention is to provide a CO2 flooding simulation method based on a dual-grid system, which improves the calculation speed while reflecting the influence of fine grid heterogeneity on CO2 flooding flow.

[0011] The object of the present invention can be achieved by the following technical measures: a CO2 flooding simulation method based on a dual-grid system, the CO2 flooding simulation method based on a dual-grid system comprising:

[0012] Step 1: Establish a CO2 flooding geological model and divide the double grid system;

[0013] Step 2: Upscale the parameters on the fine grid cells and further calculate the parameters on the coarse grid;

[0014] Step 3, solving the pressure equation on the coarse grid system to obtain the pressure field;

[0015] Step 4: Solve the velocity field on the fine grid system based on the pressure solution;

[0016] Step 5: Solve the transport equations on the fine grid system.

[0017] The purpose of the present invention can also be achieved by the following technical measures:

[0018] In step 1, a geometric model is established based on the actual situation of the model, and model parameters, including permeability and porosity, are collected; then a dual-grid system is divided, including a set of fine grids and a set of coarse grids, and a coarse grid unit contains several connected fine grid units.

[0019] In step 1, the fine grid size is determined according to the computational requirements, and the fine grid system is divided. Then, a coarse grid system is formed based on the fine grid system. Each coarse grid cell contains several interconnected fine grid cells; the permeability is contained in each fine grid cell. At the same time, the grid cell affiliation of the dual-grid system is calculated, that is, the relationship between the coarse grid cells and the fine grid cells.

[0020] In step 2, the permeability values are averaged within the coarse grid according to the permeability values of the fine grid, and the conductivity coefficient is further calculated based on this:

[0021]

[0022] in k i is the permeability, S ij is the unit connection length, n ij is the normal vector, d i d j Represents the vector connecting the cell center and the cell boundary center.

[0023] In step 3, by deforming the control equation to a certain extent, the pressure equation is solved on the coarse grid to obtain the coarse grid pressure field and velocity field. The pressure values are distributed in the grid cells, and the velocity values are distributed on the grid boundaries.

[0024] In step 3, considering single-phase flow, the expression of porosity is introduced:

[0025] φ=φ 0 (1+c t (pp 0 ))

[0026] where φ 0 is the initial porosity, p 0 is the initial pressure, c t is the rock compression coefficient, p is the pressure; bring the porosity into the governing equation and deform

[0027]

[0028] The pressure equation is

[0029]

[0030] Where ρ is the density, D eff，i represents the diffusion coefficient, q is the source and sink term, t is time, v is velocity, k is permeability, φ is porosity, t is time, x i is the i-th component, q iis the source and sink term, μ is the viscosity; solving this pressure equation can obtain the pressure field on the coarse grid. After obtaining the pressure field, the velocity field on the coarse grid is obtained through Darcy's law in the above formula.

[0031] In step 4, based on step 3, the coarse grid boundary conditions are constructed, and then the pressure value is solved to further obtain the fine grid velocity field.

[0032] In step 4, the velocity on the coarse grid in step 3 is used as the boundary condition of the local coarse grid. In order to better reflect the heterogeneity and maintain the conservation of the calculation, the coarse grid velocity is weighted by the fine grid conduction coefficient as the boundary condition of the local problem of the coarse grid.

[0033]

[0034] At the same time, the source and sink items are also weighted

[0035]

[0036] where t i represents the small-scale conduction coefficient, Q c is the coarse grid flow, is the fine grid flow, Γ is the boundary, is the fine grid source and sink term, Q J,well is the coarse grid source and sink term, t i,well The small-scale conductivity coefficient, well, represents all source and sink terms. In the coarse-grid system solution, the local pressure solution is obtained by solving the pressure equation. Darcy's law and the local pressure solution are then combined to calculate the velocity on the fine grid. The flow in the coarse grid is assumed to be steady-state.

[0037] In step 5, after obtaining the fine grid solution through the above steps, the transmission equation is solved on the fine grid; for the transmission equation

[0038]

[0039] Where ρ is the density, D eff,i represents the diffusion coefficient, q is the source and sink term, t is time, v is velocity, k is permeability, φ is porosity, t is time, x i is the i-th component, q i Source-sink term

[0040] The discrete form of each term can be written as

[0041]

[0042]

[0043] After discretization, the solution can be obtained. Δt is the time step, Vi represents the volume of unit i, φ i represents the porosity of unit i, represents the density ρ, φ of unit i at the nth time step n is the porosity at the nth time step, v n+1 is the velocity at the n+1th time step, x n represents the component x at the nth time step, n is a vector, Γ is the boundary, Γ i is the boundary of grid cell i, is the i-th component x at the n-th time step, and V is the solution region. Solving this pressure equation yields the pressure field on the coarse grid. Once the pressure field is obtained, the velocity field on the coarse grid is obtained using Darcy's law in the above equation.

[0044] For component models, heterogeneity has a greater impact on the final component concentration results, so the impact of heterogeneity needs to be captured in the calculation. The present invention takes single-phase flow into consideration, constructs a dual-grid system, solves the pressure equation on the coarse grid, and solves the transmission equation on the fine grid, while taking into account the heterogeneity of the fine grid, reducing the amount of calculation. This invention can provide new ideas for CO2 flooding and CO2 storage numerical simulation technology, and is of great significance. The CO2 flooding simulation method based on the dual-grid system in the present invention solves the pressure equation on the coarse grid system, and solves the transmission equation on the fine grid and performs flash calculations, while improving the calculation speed, reflecting the influence of fine grid heterogeneity on CO2 flooding flow. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 This is a flow chart of a specific embodiment of the CO2 flooding simulation method based on a dual-grid system of the present invention;

[0046] Figure 2 A schematic diagram of a double grid in a specific embodiment of the present invention;

[0047] Figure 3 Schematic diagram of coarse grid pressure solution of a CO2 flooding simulation method based on a dual-grid system in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0048] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0049] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations and / or combinations thereof.

[0050] like Figure 1 As shown, the CO2 flooding simulation method based on the dual-grid system of the present invention includes the following steps:

[0051] S1. Build a CO2 flooding geological model and create a dual-grid system. Based on the actual model conditions, establish a geometric model and collect model parameters, including permeability, porosity, and other parameters. Then, create a dual-grid system consisting of a fine grid and a coarse grid. Each coarse grid cell contains several connected fine grid cells.

[0052] S2. Upscaling the fine grid parameters and calculating the coarse grid parameters; Upscaling the parameters on the fine grid cells and further calculating the parameters on the coarse grid;

[0053] S3. Solve the pressure equation on the coarse grid system to obtain the pressure field; by performing a certain deformation on the control equation, solve the pressure equation on the coarse grid to obtain the coarse grid pressure field and velocity field, with the pressure values distributed in the grid cells and the velocity values distributed on the grid boundaries;

[0054] S4. Solve the velocity field on the fine grid system based on the pressure solution;

[0055] On the basis of S3, the coarse grid boundary conditions are constructed, and then the pressure value is solved to further obtain the fine grid velocity field;

[0056] S5. Solve the transport equation on the fine grid system; Combining the above steps, solve the transport equation on the fine grid.

[0057] The following are several specific embodiments of the present invention.

[0058] Example 1

[0059] In a specific embodiment 1 of the present invention, the CO2 flooding simulation method based on the dual-grid system includes the following steps:

[0060] Step 1: Establish a CO2 flooding geological model and divide the double grid system;

[0061] The required geometric model is established based on the requirements, and the geological parameters required for the simulation, including permeability and porosity, are collected. The fine grid size is determined based on the computational requirements, and the fine grid system is then divided. A coarse grid system is then formed based on the fine grid system. Each coarse grid cell contains several interconnected fine grid cells. Properties such as permeability are contained within each fine grid cell. Furthermore, the grid cell dependency relationships of the dual grid system are calculated, that is, the relationship between the coarse grid cells and the fine grid cells.

[0062] like Figure 2 As shown, Figure 2 This is a schematic diagram of a dual grid in a specific embodiment of the present invention. Thicker lines form a 6×4 coarse grid, and thinner lines form a 24×16 fine grid. Each coarse grid is composed of 4×4 fine grids.

[0063] Step 2: Upscale the fine grid parameters and calculate the coarse grid parameters;

[0064] In the coarse grid, the permeability value is averaged according to the permeability value of the fine grid, and the conductivity coefficient is further calculated based on this.

[0065]

[0066] in k i is the permeability, S ij is the unit connection length, n ij is the normal vector, d i Represents the vector connecting the cell center and the cell boundary center.

[0067] Step 3, solving the pressure equation on the coarse grid system to obtain the pressure field;

[0068] Considering single-phase flow, the expression of porosity is introduced

[0069] φ=φ 0 (1+c t (pp 0 ))

[0070] where φ 0 is the initial porosity, p 0 is the initial pressure, c t is the rock compressibility coefficient, and p is the pressure. Substitute the porosity into the governing equation and transform

[0071]

[0072] The pressure equation is

[0073]

[0074] Where ρ is the density, Deff,i represents the diffusion coefficient, q is the source and sink term, t is time, v is velocity, expressed by Darcy's law, and μ is viscosity. Solving this pressure equation yields the pressure field on the coarse mesh. Once the pressure field is obtained, the velocity field on the coarse mesh is obtained using Darcy's law in the above equation.

[0075] like Figure 3 As shown, Figure 3 This is a schematic diagram of a coarse grid pressure solution for a CO2 flooding simulation method based on a dual-grid system in a specific embodiment of the present invention. During the solution, the pressure is solved on the coarse grid, and the flow rate on the coarse grid boundary is also solved.

[0076] Step 4: Solve the velocity field on the fine grid system based on the pressure solution;

[0077] The velocity on the coarse grid in the previous step is used as the boundary condition of the local coarse grid. In order to better reflect the heterogeneity and maintain the conservation of the calculation, the coarse grid velocity is weighted with the fine grid conduction coefficient as the boundary condition of the local problem of the coarse grid.

[0078]

[0079] At the same time, the source and sink items are also weighted

[0080]

[0081] where t i represents the small-scale conduction coefficient, Q c is the coarse grid flow, is the fine grid flow, Γ is the boundary, is the fine grid source and sink term, Q J,well is the coarse grid source and sink term, t i,well The small-scale conductivity coefficient, well, represents all source and sink terms. In the coarse-grid system solution, the local pressure solution is obtained by solving the pressure equation. Darcy's law and the local pressure solution are then combined to calculate the velocity on the fine grid. The flow in the coarse grid is assumed to be steady-state.

[0082] Step 5: Solve the transmission equation on the fine grid system; After obtaining the fine grid solution through the above steps, solve the transmission equation on the fine grid.

[0083]

[0084] The discrete form of each term can be written as

[0085]

[0086] After discretization, the solution can be obtained. Where Δt is the time step, V i represents the volume of unit i, φi represents the porosity of unit i, represents the density ρ, φ of unit i at the nth time step n is the porosity at the nth time step, v n+1 is the velocity at the n+1th time step, x n represents the component x at the nth time step, n is a vector, Γ is the boundary, Γ i is the boundary of grid cell i, is the i-th component x at the n-th time step, and V is the solution region. Solving this pressure equation yields the pressure field on the coarse grid. Once the pressure field is obtained, the velocity field on the coarse grid is obtained using Darcy's law in the above equation.

[0087] Example 2:

[0088] In Specific Example 2, a permeability field with a permeability between 5 and 25 was randomly generated. This permeability field was then used as the basis for a dual-grid model. Numerical simulations using this method demonstrated that, compared to traditional precise calculation methods, the proposed method achieved a computational error within 15% and a two-fold increase in computational speed.

[0089] Example 3:

[0090] In Specific Example 3, which applies the present invention, numerical simulations were conducted based on an actual block, and the results were compared with those from commercial software. The results showed that the crude oil yields calculated by the present invention were essentially consistent with the reference solution calculated using commercial software, with an error of less than 10.

[0091] This paper provides a CO2 flooding simulation method based on a dual-grid system. The pressure equation is solved on a coarse grid, and the transport equation is solved on a fine grid. This method minimizes the impact of reaction heterogeneity while minimizing the computational effort. Compared with traditional upscaling methods that artificially average geological heterogeneity, this method offers higher computational accuracy and lower computational effort compared to traditional methods that solve the overall control equation on a fine grid. This technology can expand upon technical concepts such as CO2 miscible numerical simulation and CO2 storage. With the development of CO2 capture and oil recovery technologies, this technology has broad application prospects.

[0092] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art may modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features therein. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

[0093] Except for the technical features described in the specification, all other technical features are known technologies to those skilled in the art.

Claims

1. A CO2 flooding simulation method based on a dual-grid system is characterized by: The CO2 flooding simulation method based on the dual-grid system includes: Step 1: Establish a CO2 flooding geological model and divide the double grid system; Step 2: Upscale the parameters on the fine grid cells and further calculate the parameters on the coarse grid; Step 3, solving the pressure equation on the coarse grid system to obtain the pressure field; Step 4: Solve the velocity field on the fine grid system based on the pressure solution; Step 5, solve the transport equation on the fine grid system; The pressure equation is Where ρ is the density, D eff,i represents the diffusion coefficient, q is the source and sink term, φ 0 is the initial porosity, c t is the rock compression coefficient, t is time, υ is velocity, k is permeability, x i is the i-th component, μ is the viscosity; solving this pressure equation can obtain the pressure field on the coarse grid. After obtaining the pressure field, the velocity field on the coarse grid is obtained by Darcy's law in the above formula; In step 4, the velocity on the coarse grid in step 3 is used as the boundary condition of the local coarse grid. In order to better reflect the heterogeneity and maintain the conservation of the calculation, the coarse grid velocity is weighted by the fine grid conduction coefficient as the boundary condition of the local problem of the coarse grid. At the same time, the source and sink items are also weighted where t i represents the small-scale conduction coefficient, Q c is the coarse grid flow, is the fine grid flow, Γ is the boundary, is the fine grid source and sink term, Q J,well is the coarse grid source and sink term, t i,well The small-scale conductivity coefficient, well, represents all source and sink terms. In the coarse-grid system solution, the local pressure solution is obtained by solving the pressure equation, and the velocity of the fine grid is further calculated by combining Darcy's law and the local pressure solution. The flow in the coarse grid is assumed to be steady-state flow. In step 5, after obtaining the fine grid solution through the above steps, the transmission equation is solved on the fine grid; for the transmission equation Where φ is the porosity, q i is the source and sink term of the i-th component, and the discrete form of each term can be written as After discretization, the solution can be obtained; where Δt is the time step, V i represents the volume of unit i, φ i represents the porosity of unit i, represents the density ρ, φ of unit i at the nth time step n is the porosity at the nth time step, v n+1 is the velocity at the n+1th time step, x n represents the component x at the nth time step, n is a vector, Γ is the boundary, Γ i is the boundary of grid cell i, is the i-th component x at the n-th time step, and V is the solution area; by solving this pressure equation, the pressure field on the coarse grid can be obtained. After obtaining the pressure field, the velocity field on the coarse grid is obtained through Darcy's law in the above formula.

2. The CO2 flooding simulation method based on the dual-grid system according to claim 1, characterized in that: In step 1, a geometric model is established based on the actual situation of the model, and model parameters, including permeability and porosity, are collected; then a dual-grid system is divided, including a set of fine grids and a set of coarse grids, and a coarse grid unit contains several connected fine grid units.

3. The CO2 flooding simulation method based on the dual-grid system according to claim 2, characterized in that: In step 1, the fine grid size is determined according to the computational requirements, and the fine grid system is divided. Then, a coarse grid system is formed based on the fine grid system. Each coarse grid cell contains several interconnected fine grid cells; the permeability is contained in each fine grid cell. At the same time, the grid cell affiliation of the dual-grid system is calculated, that is, the relationship between the coarse grid cells and the fine grid cells.

4. The CO2 flooding simulation method based on a dual-grid system according to claim 1, characterized in that: In step 2, the permeability values are averaged within the coarse grid according to the permeability values of the fine grid, and the conductivity coefficient is further calculated based on this: in k i is the permeability, S ij is the unit connection length, n ij is the normal vector, d i d j Represents the vector connecting the cell center and the cell boundary center.

5. The CO2 flooding simulation method based on a dual-grid system according to claim 1, characterized in that: In step 3, considering single-phase flow, the expression of porosity is introduced: f=f 0 (1+c t (pp. 0 )) where p 0 is the initial pressure, p is the pressure, the porosity is brought into the governing equation, and the deformation

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