Fractured low-porosity sandstone gas reservoir numerical simulation method and system
By constructing a non-uniform stress-sensitive system of matrix and fracture system, and calculating the permeability correction coefficients of matrix and fracture, the problem of low simulation accuracy of fractured low-porosity sandstone gas reservoirs in existing technologies is solved, and higher-precision numerical simulation and gas reservoir development guidance are achieved.
Patent Information
- Application Number
- CN202410549685.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-05-06
- Publication Date
- 2025-11-07
AI Technical Summary
Existing technologies fail to effectively account for the differences in stress sensitivity characteristics between the matrix and the interior of fractures in numerical simulations of fractured low-porosity sandstone gas reservoirs, resulting in low simulation accuracy.
A non-uniform stress-sensitive system of matrix and fracture system is constructed. By calculating the matrix permeability and fracture permeability correction coefficients, a mathematical model of single-phase gas flow in tight gas reservoir is established and solved by fully implicit iterative solution, taking into account the change of permeability correction coefficient at each time step.
It improves the accuracy of numerical simulation of fractured low-porosity sandstone gas reservoirs, accurately describes the non-uniform stress-sensitive characteristics of the reservoir, and guides the formulation and adjustment of gas reservoir development plans.
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Figure CN120911052A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of gas reservoir numerical simulation, in particular to a fractured low-porosity sandstone gas reservoir numerical simulation method and system. BACKGROUND
[0002] Fractured gas reservoirs have the characteristics of deep burial, abnormally high pressure, fracture development, and strong non-uniformity of the reservoir. In actual production, the internal pore pressure of the reservoir decreases continuously due to natural gas production, the effective stress borne by the rock skeleton increases continuously, the matrix and fracture permeability decreases, and stress sensitivity characteristics are presented. Due to the different particle filling degrees in the matrix and different scale fractures, the physical property distribution is non-uniform, which causes the overall stress sensitivity of the reservoir to also present non-uniform characteristics. In the existing numerical simulation of stress sensitivity of fractured low-porosity sandstone gas reservoirs, only the stress sensitivity characteristics between the matrix and the fractures are distinguished, and the different stress sensitivity characteristics inside the matrix and the fractures are not considered, that is, the non-uniform stress sensitivity system of the fractured low-porosity sandstone gas reservoir is not considered, resulting in low numerical simulation accuracy of the fractured low-porosity sandstone gas reservoir. SUMMARY
[0003] The present application relates to the technical field of gas reservoir numerical simulation, in particular to a fractured low-porosity sandstone gas reservoir numerical simulation method and system.
[0004] To achieve the above-mentioned purpose, the following technical solutions are adopted in the present application:
[0005] In a first aspect, the present application provides a fractured low-porosity sandstone gas reservoir numerical simulation method, comprising:
[0006] Based on the matrix permeability correction coefficient and the fracture permeability correction coefficient, a non-uniform stress sensitivity system of the matrix and the fracture system is constructed;
[0007] A single-phase gas seepage mathematical model of the tight gas reservoir is established;
[0008] The single-phase gas seepage mathematical model of the tight gas reservoir is numerically dispersed and iteratively solved in full implicit mode;
[0009] In the iterative solving process at each time step, the permeability correction coefficient of each matrix grid and fracture grid is calculated using the non-uniform stress sensitivity system of the matrix and the fracture system, and then the iterative calculation of the next time step is entered until the simulation is completed.
[0010] Further, the matrix permeability correction coefficient is derived as follows:
[0011] The constitutive equation for the elastic deformation of the matrix is:
[0012]
[0013] where σ ij represents stress components, Pa; G represents shear modulus, Pa; ε ij represents strain components, dimensionless; v represents Poisson's ratio, dimensionless; ε b represents volumetric strain of rock mass, dimensionless; δ ij represents Kronecker symbol, δ ij = 0 (i = j), δ ij = 1 (i ≠ j); a m represents Biot's coefficient, dimensionless; p represents pore pressure, Pa;
[0014] Expanding and combining equation (1) in three directions, the volumetric strain increment ε b and the pore volume increment ε p are obtained as:
[0015]
[0016] wherein:
[0017]
[0018] wherein the superscript "-" represents the average value; V b and V p represent the rock mass volume and pore volume, m 3 ; K s and K p represent the rock mass volume modulus and pore volume modulus, Pa; E represents Young's modulus, Pa;
[0019] Combining the porosity definition and equation (2), we have:
[0020]
[0021] From the relationship between permeability and porosity, we have:
[0022]
[0023] wherein k m0 represents the initial permeability of rock matrix, m 2 ; φ m0 represents the initial porosity of rock matrix, dimensionless;
[0024] Assuming under uniaxial strain condition, from the constitutive equation (1), we have:
[0025]
[0026] The average stress increment is obtained as:
[0027]
[0028] Substituting equation (7) into equation (5), we obtain the matrix permeability correction coefficient as follows:
[0029]
[0030] Furthermore, the correction coefficient for fracture permeability is derived as follows:
[0031] Assume that the change in fracture permeability is controlled by the mean normal stress, i.e.:
[0032]
[0033] Where, k f0 m is the initial permeability of the fracture. 2 c f The crack compressibility coefficient is 1 / Pa;
[0034] The constitutive equation for the elastic deformation of the crack is written as follows:
[0035]
[0036] Similarly assuming uniaxial strain conditions, we obtain from equation (10):
[0037]
[0038] The mean stress increment was then calculated as follows:
[0039]
[0040] The crack permeability correction coefficient is obtained from equations (9) and (12) as follows:
[0041]
[0042] Furthermore, a non-uniform stress-sensitive system was constructed for the matrix and crack system:
[0043] Matrix permeability correction factor ξ m and the crack permeability correction factor ξ f The calculation formula involves the matrix Biot coefficient α. m and matrix cracking coefficient α f The two values are matrix porosity and fracture porosity, respectively. By assigning different matrix and fracture porosities, different permeability correction coefficients can be obtained, which correspond to the relationship between different reservoir properties and stress sensitivity. This characterizes the different stress sensitivity characteristics inside the matrix and inside the fracture, forming a non-uniform stress-sensitive system.
[0044] Furthermore, a mathematical model for single-phase gas flow in tight gas reservoirs is established:
[0045]
[0046] wherein, p represents gas density, kg / m 3 ; k represents permeability, m 2 ; represents viscosity, Pa·s; q represents volume exchange of source-sink term, m3 / s; t represents time, s.
[0047] Further, the single-phase gas seepage mathematical model of the tight gas reservoir is discretized and solved by full implicit iteration:
[0048]
[0049] wherein, λ represents mobility, 1 / (Pa·s); T represents conductivity, m 3 ; V represents grid volume, m 3 ; the subscripts i and j represent grid numbers; the subscript ij represents a grid interface;
[0050] In the numerical discretization, the fluid exchange between the matrix and the fracture is represented by the embedded discrete fracture model, and the conductivities of different grid connections in the embedded discrete fracture model are calculated; the Newton-Raphson iteration method is used to solve the foregoing discrete numerical model.
[0051] Further, in the iterative solving process at each time step, the permeability correction coefficients of each matrix grid and fracture grid are calculated by using the non-uniform stress-sensitive system of the matrix and the fracture system, and then the iterative calculation of the next time step is entered:
[0052] In each iteration process at each time step, the pressure distribution of the matrix and the fracture grid is calculated, and then the permeability correction coefficients of each matrix grid and fracture grid are calculated by using the matrix and fracture permeability correction coefficients, and on this basis, the pressure value of each grid is recalculated.
[0053] In a second aspect, the present application provides a numerical simulation system for fractured low-porosity sandstone gas reservoirs, comprising:
[0054] The system construction module is configured to construct a non-uniform stress-sensitive system of the matrix and the fracture system based on the matrix permeability correction coefficient and the fracture permeability correction coefficient.
[0055] The mathematical model establishment module is configured to establish a single-phase gas seepage mathematical model of the tight gas reservoir.
[0056] The iterative solving module is configured to discretize the single-phase gas seepage mathematical model of the tight gas reservoir and solve it by full implicit iteration.
[0057] An analog module is used to calculate the permeability correction coefficient of each matrix grid and fracture grid by using the non-uniform stress sensitivity system of the matrix and fracture system at each time step in the iterative solution process, and then enter the next time step of iterative calculation until the simulation ends.
[0058] In a third aspect, the present application provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the numerical simulation method for fractured low-porosity sandstone gas reservoirs when executing the computer program.
[0059] In a fourth aspect, the present application provides a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and the computer program implements the steps of the numerical simulation method for fractured low-porosity sandstone gas reservoirs when executed by a processor.
[0060] Compared with the prior art, the present application has the following technical effects:
[0061] The present application is used to describe the stress sensitivity phenomenon in the production process of fractured low-porosity sandstone gas reservoirs, and by correlating the matrix and fracture permeability correction coefficients with the reservoir properties, the non-uniform stress sensitivity characteristics of the whole reservoir can be characterized, and the accuracy of the numerical simulation of fractured low-porosity sandstone gas reservoirs is further improved.
[0062] The present application can provide a new idea for history matching in the numerical simulation process of fractured low-porosity sandstone gas reservoirs, and provide technical and theoretical support for guiding the development and adjustment of gas reservoir development plans. BRIEF DESCRIPTION OF DRAWINGS
[0063] Figure 1 The flowchart of the present application.
[0064] Figure 2 The numerical simulation calculation flowchart of the present application.
[0065] Figure 3 The matrix and fracture non-uniform stress sensitivity change range diagram in a specific embodiment of the present application.
[0066] Figure 4 The matrix and fracture uniform stress sensitivity change range diagram in a specific embodiment of the present application.
[0067] Figure 5 The gas well daily gas production comparison curve calculated under three conditions of not considering stress sensitivity, considering non-uniform stress sensitivity and considering uniform stress sensitivity in a specific embodiment of the present application.
[0068] Figure 6The cumulative gas production comparison curve of the gas well is obtained by calculation under three conditions of not considering stress sensitivity, considering non-uniform stress sensitivity and considering uniform stress sensitivity in a specific embodiment of the present application. DETAILED DESCRIPTION
[0069] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, but not all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.
[0070] In the description of the present application, it should be understood that the terms “include” and “contain” indicate the existence of described features, whole, steps, operations, elements and / or components, but do not exclude the existence or addition of one or more other features, whole, steps, operations, elements, components and / or sets thereof.
[0071] It should also be understood that the terms used in the present application specification are only for the purpose of describing specific embodiments and are not intended to limit the present application. As used in the present application specification and the appended claims, unless otherwise clear from the context, the singular forms “a”, “an” and “the” are intended to include the plural forms.
[0072] It should be further understood that the term “and / or” used in the present application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes these combinations, for example, A and / or B can represent three cases of A alone, A and B together, and B alone. In addition, the character “ / ” in the present application generally represents an “or” relationship between the front and rear associated objects.
[0073] It should be understood that although the terms first, second, third, etc. may be used in the embodiments of the present application to describe the preset ranges, etc., these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from each other. For example, the first preset range can also be referred to as the second preset range, and similarly, the second preset range can also be referred to as the first preset range without departing from the scope of the embodiments of the present application.
[0074] Depending on the context, the word "if" as used herein can be interpreted to mean "when" or "while" or "in response to determining" or "in response to detecting." Similarly, the phrase "if it is determined" or "if [a stated condition or event] is detected" can be interpreted to mean "when it is determined" or "in response to determining" or "when [the stated condition or event] is detected" or "in response to detecting [the stated condition or event]."
[0075] Various structural diagrams according to the disclosed embodiments of the present application are shown in the drawings. These diagrams are not drawn to scale, in which certain details are exaggerated for clarity and others omitted. The shapes and relative sizes of the various regions, layers, and their relative positions illustrated in the drawings are merely exemplary and may, in actuality, vary depending on the manufacturing process and / or technical level of the art, and regions / layers with different shapes, sizes, and relative positions can be additionally designed by those skilled in the art according to actual needs.
[0076] The present application provides a numerical simulation method for fractured low-porosity sandstone gas reservoirs,
[0077] Please refer to Figure 1 A numerical simulation method for fractured low-porosity sandstone gas reservoirs includes the following steps:
[0078] Based on the matrix permeability correction coefficient and the fracture permeability correction coefficient, a non-uniform stress-sensitive system of the matrix and fracture system is constructed;
[0079] A single-phase gas percolation mathematical model for tight gas reservoirs is established;
[0080] The single-phase gas percolation mathematical model for tight gas reservoirs is numerically discretized and iteratively solved in full implicit mode;
[0081] In the iterative solution process at each time step, the permeability correction coefficient of each matrix grid and fracture grid is calculated using the non-uniform stress-sensitive system of the matrix and fracture system, and then the next iteration calculation at the next time step is entered until the simulation ends.
[0082] Specifically, the following steps are included:
[0083] The matrix permeability correction coefficient is derived as follows.
[0084] The constitutive equation for the elastic deformation of the matrix is:
[0085]
[0086] where σ ij represents a stress component, Pa; G represents a shear modulus, Pa; ε ij represents a strain component, dimensionless; v represents a Poisson's ratio, dimensionless; εb represents the rock bulk volume strain, dimensionless; δ ij represents the Kronecker symbol, δ ij = 0 (i = j), δ ij = 1 (i ≠ j); α m represents the Biot coefficient, dimensionless; p represents the pore pressure, Pa.
[0087] Expanding and combining equation (1) in three directions, the volume strain increment ε b and the pore volume increment ε p are obtained as:
[0088]
[0089] wherein:
[0090]
[0091] wherein the superscript "-" represents the average value; V b and V p represent the rock bulk volume and the pore volume, m 3 ; K s and K p represent the rock bulk volume modulus and the pore volume modulus, Pa; E represents the Young's modulus, Pa.
[0092] Combining the porosity definition and equation (2), we have:
[0093]
[0094] From the relationship between permeability and porosity, we have:
[0095]
[0096] wherein k m0 represents the rock matrix initial permeability, m 2 ; φ m0 represents the rock matrix initial porosity, dimensionless.
[0097] Assuming under uniaxial strain condition, from the constitutive equation (1), we have:
[0098]
[0099] Thus, the average stress increment is:
[0100]
[0101] Substituting equation (7) into equation (5), the matrix permeability correction coefficient is:
[0102]
[0103] The fracture permeability correction coefficient is derived as follows.
[0104] It is assumed that the change of fracture permeability is controlled by the average normal stress, i.e.
[0105]
[0106] where k0 is the initial fracture permeability, m f0 ; c is the fracture compressibility, 1 / Pa. 2 f
[0107] The fracture elastic deformation constitutive equation can be written as,
[0108]
[0109] It is also assumed that under uniaxial strain conditions, from equation (10), we can get:
[0110]
[0111] Further, the average stress increment is calculated as:
[0112]
[0113] From equation (9) and equation (12), the fracture permeability correction coefficient is:
[0114]
[0115] The matrix permeability correction coefficient ξm m and the fracture permeability correction coefficient ξf f involved in the calculation formula are respectively the matrix Biot coefficient αm m and the matrix fracture coefficient αf f , whose values are respectively the matrix porosity and the fracture porosity. By assigning different matrix and fracture porosities, different permeability correction coefficients can be obtained, which can correspond to the correlation between different reservoir physical properties and stress sensitivity strength, and can represent the different stress sensitivity characteristics inside the matrix and inside the fracture (as shown in the attached figure), thereby forming a non-uniform stress sensitivity system. Figure 2
[0116] The mathematical model of single-phase gas seepage in tight gas reservoirs is constructed as follows:
[0117]
[0118] where ρ represents the gas density, kg / m 3 ; k represents the permeability, m 2 ; represents viscosity, Pa s; q represents volumetric exchange of source-sink term, m3 / s; t represents time, s.
[0119] Numerical discretization of the mathematical model is carried out:
[0120]
[0121] wherein, λ represents mobility, 1 / (Pa s); T represents conductivity, m 3 ; V represents grid volume, m 3 ; subscripts i and j represent grid numbers; subscript ij represents a grid interface.
[0122] In the numerical discretization, the fluid exchange between the matrix and the fractures is represented by the embedded discrete fracture model, and the conductivities of different grid connections in the embedded discrete fracture model need to be calculated. Moreover, the matrix and fracture properties (porosity) input before solving need to present the heterogeneous characteristics consistent with the actual. The Newton-Raphson iterative method is used for full implicit solving of the foregoing discrete numerical model.
[0123] Considering that the matrix and fracture permeability correction coefficients change with the change of the internal pressure of the reservoir, the pressure distribution of the matrix and fracture grids needs to be calculated in each iteration process at each time step, and then the matrix and fracture permeability correction coefficients of each matrix grid and fracture grid are calculated by using the matrix and fracture permeability correction coefficients in step S1, and the pressure values of each grid are recalculated on this basis.
[0124] Embodiment:
[0125] The application discloses a numerical simulation method for fractured low-porosity sandstone gas reservoirs. Figure 2 The calculation process is as shown in the accompanying drawings, and comprises the following steps.
[0126] (1) input of numerical simulation basic parameters (geological parameters, fluid parameters, etc.). In the embodiment, the grid scale is 51*51*5, and the grid size is 20m*20m*40m. The matrix porosity is between 4% and 10% (average 6%), and the permeability is between 0.01 and 0.15 mD (average 0.05 mD). Two groups of fractures are set, the porosity of the first group of fractures is between 15% and 30% (average 22%), and the permeability is between 50 and 100 D (average 75 D), the porosity of the second group of fractures is between 30% and 60% (average 53%), and the permeability is between 500 and 1000 D (average 750 D). The gas viscosity is 0.012 mPa s, the gas compressibility factor is 0.12 MPa -1 , the original pressure of the reservoir is 100 MPa, and the bottom hole pressure of the gas well is 80 MPa.
[0127] (2) Based on the input basic parameters, the embedded discrete fracture model pre-processing calculation is performed, that is, the conductivities of different grid connection pairs are calculated.
[0128] (3) The pressure distribution of the matrix grid and the fracture grid is calculated in each iteration step at each time step, and then the permeability correction coefficient of each matrix grid and fracture grid is calculated according to the corresponding matrix and fracture permeability correction coefficient, and the pressure value of each grid is recalculated on this basis.
[0129] (4) When the simulation time reaches the last time step (the simulation period in this embodiment is 10 years), the calculation is stopped, and the results are output.
[0130] In order to illustrate the advantages of the present application, three cases are simulated in this embodiment, that is, without considering stress sensitivity, considering non-uniform stress sensitivity and considering uniform stress sensitivity, the non-uniform stress sensitivity change range is shown in the following table 1, and the uniform stress sensitivity change range is shown in the following table 2. Figure 3 Figure 4
[0131] From the following table 3, it can be seen that the daily gas production calculated by considering the non-uniform stress sensitivity system is lower than that without considering the stress sensitivity, but higher than that considering the uniform stress sensitivity, and from the following table 4, it can also be observed that the total cumulative gas production also presents the same rule. Figure 5 Figure 6 This is because the non-uniform stress sensitivity can reflect the strength of the reservoir stress sensitivity according to the reservoir properties, and can more reasonably describe the decrease of the reservoir permeability. The uniform stress sensitivity cannot reflect the strength of the reservoir stress sensitivity based on the reservoir properties, and will exaggerate the degree of permeability decrease in the area with better properties, thus presenting the above situation.
[0132] The present application can quantitatively describe the correlation between the stress sensitivity of the fractured low porosity sandstone gas reservoir and the reservoir properties in numerical simulation, can accurately characterize the non-uniform stress sensitivity characteristics of the reservoir, has high numerical simulation precision and stability, and further improves the precision of the numerical simulation of the fractured low porosity sandstone gas reservoir.
[0133] In another embodiment of the present application, a numerical simulation system for a fractured low porosity sandstone gas reservoir is provided, which can be used to realize the numerical simulation method for a fractured low porosity sandstone gas reservoir described above. Specifically, the system comprises:
[0134] A system construction module is configured to construct a non-uniform stress sensitivity system of the matrix and the fracture system based on the matrix permeability correction coefficient and the fracture permeability correction coefficient.
[0135] A mathematical model establishment module is configured to establish a single-phase gas seepage mathematical model of the tight gas reservoir.
[0136] An iterative solution module is configured to perform numerical discretization on the single-phase gas seepage mathematical model of the tight gas reservoir and perform full-implicit iterative solution.
[0137] An analog module is configured to calculate the permeability correction coefficient of each matrix grid and fracture grid by using the non-uniform stress sensitive system of the matrix and the fracture system in the iterative solution process at each time step, and then enter the iterative calculation of the next time step until the simulation is completed.
[0138] The division of the modules in the embodiments of the present application is illustrative, and is merely a logical functional division, and another division mode can be used in actual implementation, and each functional module in each embodiment of the present application can be integrated in one processor, or can be physically separated, or two or more modules can be integrated in one module.
[0139] In another embodiment of the present application, a computer device is provided, which comprises a processor and a memory, the memory is configured to store a computer program, the computer program comprises program instructions, and the processor is configured to execute the program instructions stored in the computer storage medium. The processor can be a central processing unit (CPU), and can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and is suitable for implementing one or more instructions, and is specifically suitable for loading and executing one or more instructions in the computer storage medium to implement a corresponding method process or a corresponding function. The processor in the embodiments of the present application can be used for the operation of the numerical simulation method of the fractured low-porosity sandstone gas reservoir.
[0140] In still another embodiment, the present application provides a storage medium, specifically a computer readable storage medium (Memory), which is a memory device in a computer system, for storing programs and data. It should be understood that the computer readable storage medium here can include both built-in storage medium in the computer system, and also can include the extended storage medium supported by the computer system. The computer readable storage medium provides a storage space, which stores an operating system of the terminal. In addition, one or more instructions adapted to be loaded and executed by the processor are also stored in the storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that the computer readable storage medium here can be a high-speed RAM memory, or a non-volatile memory such as at least one disk memory. The one or more instructions stored in the computer readable storage medium can be loaded and executed by the processor to implement the corresponding steps of the method for numerical simulation of fractured low porosity sandstone gas reservoirs in the above embodiments.
[0141] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) containing computer-usable program code.
[0142] The present application is described with reference to the flowcharts and / or block diagrams of the method, device (system), and computer program product according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing apparatus produce a device implemented in the flowcharts and / or block diagrams. Figure 1 The function specified in one or more flows and / or blocks Figure 1 The device that implements the function specified in one or more flows and / or blocks.
[0143] These computer program instructions can also be stored in a computer readable storage medium that can direct the computer or other programmable data processing apparatus to work in a specific manner, so that the instructions stored in the computer readable storage medium produce a manufactured product including instruction devices that implement the flowcharts and / or block diagrams. Figure 1 The function specified in one or more flows and / or blocksFigure 1 the function specified in the one or more blocks.
[0144] These computer program instructions can also be loaded into computer or other programmable data processing devices, so that a series of operation steps are performed on the computer or other programmable data processing devices to generate computer-implemented processes, thus the instructions executed on the computer or other programmable data processing devices provide processes for implementing the flows Figure 1 the flows or the plurality of flows and / or blocks Figure 1 the steps of the function specified in the one or more blocks.
[0145] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application, but not to limit it, although the above embodiments of the present application have been described in detail, those skilled in the art should understand: the specific embodiments of the present application can be modified or replaced by the same, without departing from the spirit and scope of the present application, any modification or equivalent replacement, which should be covered in the protection scope of the claims of the present application.
Claims
1. A numerical simulation method for fractured, low porosity sandstone gas reservoirs, characterized in that, The method comprises the following steps: A non-uniform stress-sensitive system of matrix and fracture is constructed based on a matrix permeability correction coefficient and a fracture permeability correction coefficient; A single-phase gas seepage mathematical model of the tight gas reservoir is established; The single-phase gas seepage mathematical model of the tight gas reservoir is discretized and solved by full implicit iteration; In the iteration solving process at each time step, the permeability correction coefficients of each matrix grid and fracture grid are calculated by using the non-uniform stress-sensitive system of matrix and fracture, and then the iteration calculation at the next time step is entered until the simulation is completed.
2. The method of claim 1, wherein, The matrix permeability correction coefficient is derived as follows: The matrix elastic deformation constitutive equation is as follows: where σ ij represents stress components, Pa; G represents shear modulus, Pa; ε ij represents strain components, dimensionless; v represents Poisson's ratio, dimensionless; ε b represents volumetric strain of rock mass, dimensionless; δ ij represents Kronecker symbol, δ ij = 0 (i = j), δ ij = 1 (i ≠ j); a m represents Biot's coefficient, dimensionless; p represents pore pressure, Pa; Expanding and combining the three directions of equation (1) gives the volumetric strain increment ε b and the pore volume increment ε p as: wherein, where the superscript "-" represents the average value; V b and V p represent the rock volume and the pore volume, respectively, m 3 ; K s and K p represent the rock volume modulus and the pore volume modulus, respectively, Pa; E represents the Young's modulus, Pa; The relationship between the permeability and the porosity is obtained by combining the porosity definition and equation (2): It is assumed that under the uniaxial strain condition, the constitutive equation (1) is as follows: where k m0 represents the initial permeability of the rock matrix, m 2 ; φ m0 represents the initial porosity of the rock matrix, dimensionless The average stress increment is obtained as follows: The matrix permeability correction coefficient is obtained by substituting equation (7) into equation (5): The fracture permeability correction coefficient is derived as follows:
3. The method of claim 1, wherein, It is assumed that the change of the fracture permeability is controlled by the average normal stress, i.e. The fracture elastic deformation constitutive equation is written as, where k f0 is the initial permeability of the fracture, m 2 ; c f is the compressibility of the fracture, 1 / Pa; It is also assumed that under the uniaxial strain condition, equation (10) is as follows: The average stress increment is calculated as follows: The fracture permeability correction coefficient is obtained by substituting equation (9) and equation (12) into equation (11). A non-uniform stress-sensitive system of matrix and fracture is constructed:
4. The method of claim 1, wherein, A single-phase gas seepage mathematical model of the tight gas reservoir is established: Matrix permeability correction coefficient ξ m and fracture permeability correction coefficient ξ f The calculation formula respectively involves matrix Biot coefficient α m and matrix fracture coefficient α f , both of which take matrix porosity and fracture porosity respectively, and different permeability correction coefficients can be obtained by assigning different matrix and fracture porosities, corresponding to the correlation between different reservoir physical properties and stress sensitivity strength, representing the different stress sensitivity characteristics inside the matrix and the fracture, forming a non-uniform stress sensitivity system.
5. The method of claim 1, wherein, The single-phase gas seepage mathematical model of the tight gas reservoir is discretized and solved by full implicit iteration: where p represents the gas density, kg / m 3 ; k represents the permeability, m 2 ; represents the viscosity, Pa-s; q represents the volume exchange of the source-sink term, m3 / s; t represents the time, s.
6. The method of numerical simulation of fractured low porosity sandstone gas reservoirs according to claim 1, characterized in that, In the numerical discretization, the fluid exchange between the matrix and the fracture is represented by an embedded discrete fracture model, the conductivities of different grid connections in the embedded discrete fracture model are calculated, and the Newton-Raphson iteration method is used to solve the full implicit solution for the foregoing discrete numerical model. where λ represents the mobility, 1 / (Pa s); T represents the conductivity, m 3 ; V represents the grid volume, m 3 ; the subscripts i and j represent the grid number; the subscript ij represents the grid interface; In the iteration solving process at each time step, the permeability correction coefficients of each matrix grid and fracture grid are calculated by using the non-uniform stress-sensitive system of matrix and fracture, and then the iteration calculation at the next time step is entered until the simulation is completed.
7. The method of numerical simulation of fractured low porosity sandstone gas reservoirs according to claim 5, characterized in that, In each iteration process at each time step, the pressure distribution of the matrix and fracture grids is calculated, the permeability correction coefficients of each matrix grid and fracture grid are calculated by using the matrix and fracture permeability correction coefficients, and the pressure values of each grid are recalculated on the basis of the permeability correction coefficients. The method comprises the following steps:
8. A numerical simulation system for fractured, low porosity sandstone gas reservoirs, characterized in that, The system construction module is used for constructing a non-uniform stress-sensitive system of matrix and fracture based on a matrix permeability correction coefficient and a fracture permeability correction coefficient; The mathematical model establishment module is used for establishing a single-phase gas seepage mathematical model of the tight gas reservoir; The iteration solving module is used for discretizing the single-phase gas seepage mathematical model of the tight gas reservoir and solving the model by full implicit iteration; The simulation module is used for calculating the permeability correction coefficients of each matrix grid and fracture grid by using the non-uniform stress-sensitive system of matrix and fracture in the iteration solving process at each time step, and then entering the iteration calculation at the next time step until the simulation is completed. The processor executes the computer program to realize the steps of the numerical simulation method of the fractured low-porosity sandstone gas reservoir according to any one of claims 1 to 7.
9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, 10. A computer-readable storage medium storing a computer program, the computer program comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 9. The computer program, when executed by a processor, implements the steps of the numerical simulation method for fractured low-porosity sandstone gas reservoirs according to any one of claims 1 to 7.