A numerical well test analysis method for fractured horizontal wells based on the complex flow mechanism of shale gas

Abstract

The present invention relates to the technical field of shale gas reservoir production and development, and specifically relates to a numerical well test analysis method for fractured horizontal wells based on the complex flow mechanism of shale gas: establishing a gas-phase seepage model for the matrix system of the shale reservoir; establishing a gas-phase and water-phase seepage model for the fracture system of the shale reservoir; establishing a gas-water two-phase seepage model for the shale gas reservoir according to the seepage models of the matrix system and the fracture system; using the Galerkin meshless method to solve the gas-water two-phase seepage model of the shale gas well, constructing a meshless node system according to the proximity averaging method, compressing the matrix using the COO organization and storing it in the CSR format, and substituting it into the PARDISO solver for solution to ensure the accuracy of the numerical well test analysis method, and dividing different flow characteristic segments to form a numerical well test analysis method for fractured horizontal wells in the shale gas reservoir. Compared with the calculation methods in the prior art, the accuracy of the numerical well test analysis of fractured horizontal wells in the shale gas reservoir is higher using the above method.

Description

Technical Field

[0001] The present invention relates to the technical field of shale gas reservoir production and development, and particularly relates to a numerical well test analysis method for fractured horizontal wells based on the complex flow mechanism of shale gas. Background Art

[0002] Shale reservoirs have a significant ultra-dense, extra-low porosity, and extra-low permeability nano-porous structure, and their pore-permeability structure is extremely complex. Therefore, their development requires reservoir modification through means such as large-scale sand fracturing, so that the induced fractures formed after fracturing can communicate with the natural fractures of the reservoir, thereby forming a crisscross fracture network to obtain effective production capacity. In addition, due to the desorption of matrix adsorbed gas and the mass transfer and diffusion mechanism in nano-scale reservoir pores in shale reservoirs, the fluid flow process therein is extremely complex, and the seepage mathematical models established by these complex factors are also very complex and often cannot be solved using conventional methods. Therefore, conventional well test analysis methods cannot be directly applied to the numerical interpretation of shale gas reservoirs. Through numerical solution methods, the complex well test mathematical models of shale gas reservoirs can be directly solved to obtain more accurate shale reservoir parameters.

[0003] In current numerical well test research, the finite difference method and the finite element method are the most widely used numerical calculation methods. However, these methods are all based on grids in numerical calculations, and the final calculation accuracy will be affected by grid division. For grids that do not meet the requirements, they need to be reconstructed, and the grids need to be continuously re-divided when solving the fracture propagation problem, which greatly increases the calculation amount, and the process before and after is very complex, resulting in insufficient accuracy in the numerical well test analysis of existing shale gas reservoir fractured horizontal wells. Summary of the Invention

[0004] The purpose of the present invention is to provide a numerical well test analysis method for fractured horizontal wells based on the complex flow mechanism of shale gas, so as to solve the problem in the prior art that the calculation amount of the numerical calculation method used for the numerical well test analysis of shale gas reservoir fractured horizontal wells is too large, resulting in poor analysis accuracy.

[0005] To achieve the above purpose, the present invention provides a numerical well test analysis method for fractured horizontal wells based on the complex flow mechanism of shale gas. The numerical well test analysis method for fractured horizontal wells based on the complex flow mechanism of shale gas includes the following steps:

[0006] S1: Establish a gas-phase seepage model for the matrix system of the shale reservoir considering the complex flow mechanism;

[0007] S2: Establish a gas-phase and water-phase seepage model for the fracture system of the shale reservoir considering the complex flow mechanism;

[0008] S3: Establish a gas-water two-phase seepage model for the shale gas reservoir according to the seepage models of the matrix system and the fracture system;

[0009] S4: Use the Galerkin meshless method to solve the gas-water two-phase seepage model of shale gas wells and give the corresponding numerical integration method;

[0010] S5: Determine the support domain of the meshless method according to the proximity averaging method, thereby constructing a meshless node system;

[0011] When constructing the meshless node system, considering the complex seepage characteristics near the fractured horizontal well, determine the size of the support domain of the meshless method by the proximity averaging method, and the calculation formula is:

[0012]

[0013] In the formula: A ns is the sum of the areas of all triangular elements in the neighborhood; is the number of field nodes; d c is the average spacing of field nodes;

[0014] Adopt a node encryption method based on the isoparametric transformation of the integral grid to encrypt the fractures of the fractured horizontal well, and add a transition zone with a density between the encrypted area and the non-encrypted area between the encrypted area and the non-encrypted area. The encryption formula is:

[0015]

[0016] In the formula: x i , y i are the global coordinates of the i-th corner point of the triangular element; L i,k is the i-th local coordinate of the k-th new node;

[0017] Based on the generation and encryption methods of the meshless method nodes and background grids studied above, compile a node layout and background grid generation program through Matlab language and display it to complete the construction of the meshless node system;

[0018] S6: Adopt COO organization matrix compression according to the characteristics of the constructed meshless node system and store it in CSR format, and finally bring it into the PARDISO solver for solution to ensure the accuracy of this numerical well test analysis method;

[0019] S7: Divide different flow characteristic segments to form a numerical well test analysis method for fractured horizontal wells in shale gas reservoirs;

[0020] S8: Fit the measured data of shale gas wells based on this method to obtain the typical curve of well test analysis for fractured horizontal wells in shale gas reservoirs.

[0021] Among them, in step S1, the complex flow mechanism includes desorption mechanism, pseudo-steady-state diffusion, unsteady-state diffusion and seepage mechanism.

[0022] Among them, in step S1, the process of establishing the gas seepage model of the shale reservoir matrix system is as follows:

[0023] S11: Establish an isothermal adsorption model for shale gas, and obtain:

[0024]

[0025] In the formula: V is the adsorbed gas volume, with the unit of cm 3 / g; V L is the Langmuir volume, with the unit of cm 3 / g; p L is the Langmuir pressure, with the unit of MPa;

[0026] S12: Establish a gas seepage model for the shale reservoir matrix system, and the established formula is:

[0027]

[0028] Among them, the gas flow rate from the matrix to the fracture system is expressed as:

[0029]

[0030] Among them, the shape factor is expressed as:

[0031]

[0032] Among them, the matrix rock compressibility is expressed as:

[0033]

[0034] Among them, the formation gas compressibility is:

[0035]

[0036] In the formula: L x , L y , L z are the lengths of the matrix rock block in the x, y, and z directions, with the unit of m; α is the dimensional factor, dimensionless; K m is the matrix effective permeability, with the unit of μm 2 ; μ mg is the matrix gas viscosity, with the unit of mPa·s; B g is the gas volume coefficient, with the unit of m 3 / m 3 ; P m is the matrix pore pressure, with the unit of MPa; φ m is the matrix porosity; P fg is the gas phase pressure in the fracture system, with the unit of MPa.

[0037] Among them, in step S2, the establishment process of the gas-phase and water-phase seepage models for the shale reservoir fracture system is as follows:

[0038] S21: Considering the influence of stress sensitivity, an exponential stress-sensitivity corrected fracture system permeability is established:

[0039]

[0040] Among them:

[0041]

[0042] In the formula: K0 is the initial permeability of the fracture system, with the unit of μm 2 ; is the rock compressibility, with the unit of MPa -1 ; σ is the effective stress of the rock, with the unit of MPa; A is the cross-sectional area through which the fluid flows, with the unit of m 2 ; N is the number of fractures; l is the fracture length, with the unit of m; ξ is the effective width of the fracture, with the unit of m;

[0043] S22: Establish a gas-phase and water-phase seepage model for the shale reservoir fracture system considering complex flow mechanisms, and obtain:

[0044] Gas phase:

[0045]

[0046] Water phase:

[0047]

[0048] In the formula: α is the dimensionality factor, dimensionless; λ fg 、λ fw are the mobilities of the gas phase and water phase in the fracture system; B g 、B w are the volume coefficients of gas and water in the fracture system, with the unit of m 3 / m 3 ; P fg is the pressure of the gas phase in the fracture system, with the unit of MPa; q smfg is the gas leakage flow rate from the matrix to the fracture system; q sg 、q sw are the wellbore production rates of gas and water in the fracture system, with the unit of kg / s; φ f is the porosity of the fracture system; S fw is the water saturation in the fracture system.

[0049] Among them, in step S3, the establishment process of the gas-water two-phase seepage model for the shale gas well is as follows:

[0050] S31: In a period of time after the well is switched on and off, since the surface production affected by the wellbore reservoir is not equal to the bottom hole production, the numerical well test production model of the fractured horizontal well is derived, including the pressure drop production model of the fractured horizontal well and the pressure recovery production model of the fractured horizontal well, and the result is:

[0051] Fracturing horizontal well pressure drop production model:

[0052]

[0053] Fracturing horizontal well pressure recovery production model:

[0054]

[0055] in:

[0056]

[0057] Where: is the formation gas flow rate of the ith node in the mth fracture; C is the wellbore storage coefficient; f m,i is the production fraction of the i-th node in the m-th fracture; P fm,i is the formation pressure; N is the number of fractures;

[0058] S32: The gas phase continuity equation established in the matrix system and the gas and water continuity equations established in the fracture system are combined to obtain the basic seepage equation of shale gas considering the complex flow mechanism:

[0059]

[0060] Where: α is the dimension factor, dimensionless; φ m is the matrix porosity; C m is the matrix rock compression coefficient, C g Formation gas compressibility factor; P L is the Langmuir pressure constant, in MPa; V L is the Langmuir volume constant, in cm 3 / g;P m is the matrix pore pressure, in MPa; q smfg is the gas flow from the matrix to the fracture system; P fg is the gas phase pressure of the fracture system, in MPa; B g , B w is the volume coefficient of gas and water in the fracture system, in m 3 / m 3 ;q sg ,q sw is the wellbore production of gas and water in the fracture system, in kg / s; φ f is the porosity of the fracture system; Sfw is the saturation of the aqueous phase in the fracture system;

[0061] S33: Before numerically simulating and solving the basic seepage equation of shale gas, it is necessary to define the initial conditions and boundary conditions. The definite solution conditions of the model include the boundary conditions and initial conditions of the fracture and matrix systems. The initial conditions need to give the pressure and saturation parameter distributions at the initial moment. Assuming that the initial pressures of the fracture and matrix systems are the same, the initial pressure condition is obtained as:

[0062]

[0063] S34: Since the research object is a closed unit, the outer boundary of the mathematical model is closed, and the inner boundary is for production with a fixed bottom-hole flowing pressure. Then the inner boundary condition of the model is:

[0064] P fg (x, y, t) = P wf (t)

[0065] The outer boundary condition is:

[0066]

[0067] Among them, in step S4, before using the numerical solution method of alternately solving implicit pressure and explicit saturation to solve, the corresponding equations are first discretized:

[0068] EFGM numerical model of the gas-phase flow equation in the matrix system:

[0069]

[0070] EFGM numerical model of the gas-phase flow equation in the fracture system:

[0071]

[0072] EFGM numerical model of the aqueous-phase flow equation in the fracture system:

[0073]

[0074] Since the above EFGM numerical model has an integral function, it is necessary to give an integration method for solving this numerical model to obtain:

[0075]

[0076] In the formula: n c is the number of background cells; G is the integrand; Ω k is the domain of the k-th background cell.

[0077] Among them, in step S6, the specific steps to solve the problem of complex calculation of the node system constructed by the Galerkin meshless method are:

[0078] Construct a stiffness matrix for the linear equations of numerical well testing of fractured horizontal wells in shale gas reservoirs with large scale, symmetry and sparsity, and assemble the stiffness matrix using the COO compression storage strategy;

[0079] Store the linear equations of the system to be solved in CSR format;

[0080] Based on the node system matrix in CSR storage form, substitute the converted CSR format system equations of the numerical well testing global weak form meshless method into the PARDISO solver for solution.

[0081] A numerical well testing analysis method for fractured horizontal wells based on the complex flow mechanism of shale gas in the present invention establishes a gas-phase seepage model for the matrix system of shale reservoirs considering complex flow mechanisms such as desorption mechanism, diffusion mechanism and seepage mechanism; establishes a gas-phase and water-phase seepage model for the fracture system of shale reservoirs considering complex flow mechanisms; establishes a gas-water two-phase seepage model for shale gas reservoirs according to the seepage models of the matrix system and the fracture system; uses the Galerkin meshless method to solve the gas-water two-phase seepage model of shale gas wells and gives the corresponding numerical integration method; determines the support domain of the meshless method according to the adjacent averaging method, designs a set of node arrangement and encryption methods considering the complex seepage characteristics of fractured horizontal wells and generates meshless method nodes and background grids, so as to construct a meshless node system; compresses and organizes the matrix in COO according to the characteristics of the constructed meshless node system and stores it in CSR format, and finally substitutes it into the PARDISO solver for solution to ensure the accuracy of the numerical well testing analysis method, divides different flow characteristic segments to form a numerical well testing analysis method for fractured horizontal wells in shale gas reservoirs, fits the measured data of shale gas wells based on this method, obtains the typical curve of well testing analysis for fractured horizontal wells in shale gas reservoirs, and forms a set of typical numerical well testing analysis methods for fractured horizontal wells in shale gas reservoirs suitable for actual oil fields. Compared with the calculation methods in the prior art, the accuracy of the numerical well testing analysis of fractured horizontal wells in shale gas reservoirs using the above method is higher. Description of the Drawings

[0082] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0083] Figure 1 It is a flowchart of the steps of the numerical well testing analysis method for fractured horizontal wells based on the complex flow mechanism of shale gas in the present invention.

[0084] Figure 2It is the background grid of the meshless global weak form method of the present invention.

[0085] Figure 3 It is the method for determining the support domain of the present invention.

[0086] Figure 4 It is the double logarithmic curve comparison chart of the numerical solution of the meshless method simulator and the Zerzar analytical solution of the present invention.

[0087] Figure 5 It is the flow stage of the well test curve of the fractured horizontal well in the shale gas reservoir of the present invention.

[0088] Figure 6 It is the influence of the langmuir volume and langmuir pressure on the typical curve of the numerical well test in the parameter sensitivity analysis of the present invention. Detailed implementation manners

[0089] The embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the drawings, where the same or similar reference numerals indicate the same or similar elements or elements with the same or similar functions from beginning to end. The embodiments described below with reference to the drawings are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0090] Please refer to Figures 1 to 6 , the present invention provides a numerical well test analysis method for fractured horizontal wells based on the complex flow mechanism of shale gas. The numerical well test analysis method for fractured horizontal wells based on the complex flow mechanism of shale gas includes the following steps:

[0091] S1: Establish a gas-phase seepage model for the matrix system of the shale reservoir considering the complex flow mechanism;

[0092] S2: Establish a gas-phase and water-phase seepage model for the fracture system of the shale reservoir considering the complex flow mechanism;

[0093] S3: According to the seepage models of the matrix system and the fracture system, establish a gas-water two-phase seepage model for the shale gas reservoir;

[0094] S4: Use the Galerkin meshless method to solve the gas-water two-phase seepage model of the shale gas well and give the corresponding numerical integration method;

[0095] S5: Determine the support domain of the meshless method according to the proximity averaging method, so as to construct a meshless node system;

[0096] S6: Compress the matrix according to the characteristics of the constructed meshless node system by using the COO organization and store it in the CSR format, and finally bring it into the PARDISO solver for solution to ensure the accuracy of the numerical well test analysis method;

[0097] S7: Divide different flow characteristic segments to form a numerical well test analysis method for fractured horizontal wells in shale gas reservoirs;

[0098] S8: Fit the measured data of shale gas wells based on this method to obtain the typical curve of well test analysis for fractured horizontal wells in shale gas reservoirs.

[0099] In this embodiment, a gas-phase seepage model for the matrix system of shale reservoirs considering complex flow mechanisms such as desorption mechanism, diffusion mechanism, and seepage mechanism is established; a gas-phase and water-phase seepage model for the fracture system of shale reservoirs considering complex flow mechanisms is established; according to the seepage models of the matrix system and the fracture system, a gas-water two-phase seepage model for shale gas reservoirs is established; the gas-water two-phase seepage model of shale gas wells is solved using the Galerkin meshless method and the corresponding numerical integration method is given; the support domain of the meshless method is determined according to the adjacent average method, and a set of node arrangement and encryption methods considering the complex seepage characteristics of fractured horizontal wells and the generation of meshless nodes and background grids are designed, thereby constructing a meshless node system; according to the characteristics of the constructed meshless node system, the COO organization matrix is compressed and stored in the CSR format, and finally brought into the PARDISO solver for solution to ensure the accuracy of the numerical well test analysis method. Divide different flow characteristic segments to form a numerical well test analysis method for fractured horizontal wells in shale gas reservoirs. Fit the measured data of shale gas wells based on this method to obtain the typical curve of well test analysis for fractured horizontal wells in shale gas reservoirs, forming a set of numerical well test analysis methods for typical fractured horizontal wells in shale gas reservoirs suitable for actual oil fields. Compared with the calculation methods in the prior art, the accuracy of the numerical well test analysis for fractured horizontal wells in shale gas reservoirs using the above method is higher.

[0100] Among them, in step S1, the complex flow mechanism includes special mechanisms such as desorption mechanism, pseudo-steady diffusion, unsteady diffusion, and seepage mechanism.

[0101] Among them, in step S1, the establishment process of the gas-phase seepage model for the matrix system of shale reservoirs is as follows:

[0102] S11: Establish a shale gas isothermal adsorption model to obtain:

[0103]

[0104] In the formula: V is the adsorbed gas volume, with the unit of cm 3 / g; V L is the Langmuir volume, with the unit of cm 3 / g; P L is the Langmuir pressure, with the unit of MPa;

[0105] S12: Establish a gas-phase seepage model for the matrix system of shale reservoirs, and the established formula is:

[0106]

[0107] The gas cross - flow rate from the matrix to the fracture system is expressed as:

[0108]

[0109] The shape factor is expressed as:

[0110]

[0111] The compressibility of the matrix rock is expressed as:

[0112]

[0113] The compressibility of the formation gas is:

[0114]

[0115] In the formula: L x , L y , L z are the lengths of the matrix rock block in the x, y, and z directions, with the unit of m; α is the dimensional factor, dimensionless; K m is the effective permeability of the matrix, with the unit of μm 2 ; μ mg is the viscosity of the matrix gas, with the unit of mPa·s; B g is the gas volume factor, with the unit of m 3 / m 3 ; P m is the pore pressure of the matrix, with the unit of MPa; φ m is the porosity of the matrix; P fg is the gas - phase pressure in the fracture system, with the unit of MPa.

[0116] Among them, in step S2, the establishment process of the gas - phase and water - phase seepage models of the shale reservoir fracture system is as follows:

[0117] S21: Considering the influence of stress sensitivity, establish an exponential - type stress - sensitivity - corrected fracture - system permeability:

[0118]

[0119] Among them:

[0120]

[0121] In the formula: K0 is the initial permeability of the fracture system, with the unit of μm 2 ; is the compressibility of the rock, with the unit of MPa -1; σ is the effective stress of the rock, with the unit of MPa; A is the cross-sectional area through which the fluid flows, with the unit of m 2 ; N is the number of fractures; l is the fracture length, with the unit of m; ξ is the effective width of the fracture, with the unit of m;

[0122] S22: Establish a gas-phase and water-phase seepage model for the fracture system of shale reservoirs considering complex flow mechanisms, and obtain:

[0123] Gas phase:

[0124]

[0125] Water phase:

[0126]

[0127] In the formula: α is the dimensional factor, dimensionless; λ fg 、λ fw are the mobilities of the gas phase and water phase in the fracture system; B g 、B w are the volume coefficients of gas and water in the fracture system, with the unit of m 3 / m 3 ; P fg is the pressure of the gas phase in the fracture system, with the unit of MPa; q smfg is the cross-flow rate of gas from the matrix to the fracture system; q sg 、q sw are the wellbore production rates of gas and water in the fracture system, with the unit of kg / s; φ f is the porosity of the fracture system; S fw is the water saturation in the fracture system.

[0128] Among them, in step S3, the establishment process of the gas-water two-phase seepage model of the shale gas well is as follows:

[0129] S31: In a period of time after the well is switched on and off, since the surface production affected by wellbore storage is not equal to the bottom-hole production, a numerical well test production model for fractured horizontal wells is derived, including a pressure-drop production model for fractured horizontal wells and a pressure build-up production model for fractured horizontal wells, and obtain:

[0130] Pressure-drop production model for fractured horizontal wells:

[0131]

[0132] Pressure build-up production model for fractured horizontal wells:

[0133]

[0134] Among them:

[0135]

[0136] Where: is the formation gas flow rate of the ith node in the mth fracture; C is the wellbore storage coefficient; f m,i is the production fraction of the i-th node in the m-th fracture; P fm,i is the formation pressure; N is the number of fractures;

[0137] S32: The gas phase continuity equation established in the matrix system and the gas and water continuity equations established in the fracture system are combined to obtain the basic seepage equation of shale gas considering the complex flow mechanism:

[0138]

[0139] Where: α is the dimension factor, dimensionless; φ m is the matrix porosity; C m is the matrix rock compression coefficient, C g Formation gas compressibility factor; P L is the Langmuir pressure constant, in MPa; V L is the Langmuir volume constant, in cm 3 / g;P m is the matrix pore pressure, in MPa; q smfg is the gas flow from the matrix to the fracture system; P fg is the gas phase pressure of the fracture system, in MPa; B g , B w is the volume coefficient of gas and water in the fracture system, in m 3 / m 3 ;q sg ,q sw is the wellbore production of gas and water in the fracture system, in kg / s; φ f is the porosity of the fracture system; S fw is the saturation of water phase in the fracture system;

[0140] S33: Before numerically simulating and solving the basic seepage equation of shale gas, the initial conditions and boundary conditions need to be defined. The solution conditions of the model include the boundary conditions and initial conditions of the fracture and matrix system. The initial conditions need to give the pressure and saturation parameter distribution at the initial time. Assuming that the initial pressure of the fracture and matrix system is the same, the initial pressure condition is:

[0141]

[0142] S34: Since the research object is a closed unit, the outer boundary of the mathematical model is closed, and the inner boundary is a constant bottom hole pressure production, so the inner boundary condition of the model is:

[0143] P fg (x, y, t) = P wf (t)

[0144] The outer boundary conditions are as follows:

[0145]

[0146] Among them, in step S4, before solving using the numerical solution method of alternating implicit pressure and explicit saturation, the corresponding equations are discretized first:

[0147] EFGM numerical model of the gas-phase flow equation in the matrix system:

[0148]

[0149] EFGM numerical model of the gas-phase flow equation in the fracture system:

[0150]

[0151] EFGM numerical model of the water-phase flow equation in the fracture system:

[0152]

[0153] Since the above EFGM numerical model has an integral function, an integration method for solving this numerical model needs to be given to obtain:

[0154]

[0155] In the formula: n c is the number of background cells; G is the integrand; Ω k is the domain of the k-th background cell.

[0156] Among them, in step S5, when constructing the meshless node system, considering the complex seepage characteristics near the fractured horizontal well, the size of the support domain of the meshless method is determined by the adjacent averaging method, and the calculation formula is:

[0157]

[0158] In the formula: A ns is the sum of the areas of all triangular cells in the neighborhood; is the number of field nodes; d c is the average spacing of field nodes;

[0159] The node encryption method based on the isoparametric transformation of the integral grid is used to encrypt the fractures of the fractured horizontal well, and a transition zone with a density between the encrypted area and the non-encrypted area is added between the encrypted area and the non-encrypted area. The encryption formula is:

[0160]

[0161] where: x i , y i are the global coordinates of the i-th corner point of the triangular element; L i,k is the i-th local coordinate of the k-th newly added node;

[0162] Based on the above research on the generation and encryption methods of meshless method nodes and background grids, a program for node layout and background grid generation is compiled in Matlab language and displayed to complete the construction of the meshless node system.

[0163] Among them, in step S6, the specific steps to solve the problem of complex calculation of the node system constructed by the Galerkin meshless method are as follows:

[0164] Construct a stiffness matrix of a large-scale, symmetric and sparse linear equation system for numerical well testing of fractured horizontal wells in shale gas reservoirs. When assembling the global weak form meshless method matrix in COO format, only the upper triangular matrix needs to be considered. Therefore, the COO compression storage strategy is adopted to assemble the stiffness matrix;

[0165] After that, the equation system is stored. The equation system stored in CSR format requires 30% less memory than the COO format during the solution process. Therefore, the CSR format is adopted to store the linear equation system of the system to be solved;

[0166] Based on the node system matrix in CSR storage form, the converted numerical well testing global weak form meshless method CSR format system equation system is brought into the PARDISO solver for solution.

[0167] In this embodiment, according to the fracturing parameters, reservoir parameters, node parameters, core data, etc. of a typical shale gas well, the following basic simulation parameters are set as shown in the table below:

[0168]

[0169]

[0170] First, it is necessary to verify the correctness of the numerical well testing curve calculated by the global weak form meshless method, that is, to calculate the numerical well testing curve of the fractured horizontal well in the shale gas reservoir through the reservoir parameters and fracturing parameter values, divide the corresponding flow stages, and compare and verify the numerical solution calculated by the meshless method simulator with the Zerzar analytical solution in combination with the simplified model and basic simulation parameters.

[0171] Based on the numerical solution of the meshless method simulator obtained after verification, the measured pressure data of shale gas wells are analyzed and fitted. Combining with the EFGM discrete mathematical model of fractured horizontal wells derived by the Galerkin meshless method and the well test analysis theory of fractured horizontal wells in shale gas reservoirs, the well test analysis typical curve of fractured horizontal wells in shale gas reservoirs is obtained by simulation calculation using the meshless method simulator. Through comprehensive analysis of the curve: the skin factor is 0.878, and there is slight pollution at the bottom hole; in the shale reservoir, the permeability of the fracture system is 0.00175 mD, and the permeability of the matrix system is 2.75×10 -6 mD, indicating that the shale reservoir is a low-permeability reservoir; the number of fracturing stages is 32, and the fracture half-length of each fracturing stage is 37.7 meters, which can effectively communicate the fracture system in the near-wellbore area; the Langmuir volume is 0.013 m 3 / kg, and the Langmuir pressure is 7 MPa, reflecting the influence of matrix adsorption and desorption in the shale gas reservoir; the extrapolated formation pressure is 56.72 MPa, reflecting the current formation energy.

[0172] The above-disclosed is only a preferred embodiment of the present invention. Of course, the scope of rights of the present invention cannot be limited thereby. Those of ordinary skill in the art can understand all or part of the processes of implementing the above embodiments, and the equivalent changes made according to the claims of the present invention still fall within the scope covered by the invention.

Claims

1. A numerical well test analysis method for fractured horizontal wells based on the complex flow mechanism of shale gas, characterized in that: The steps include: S1: Establish a gas phase seepage model for shale reservoir matrix system considering complex flow mechanisms; S2: Establish a gas and water seepage model for shale reservoir fracture systems taking into account complex flow mechanisms; S3: Based on the seepage models of the matrix system and fracture system, a gas-water two-phase seepage model of shale gas reservoirs is established; S4: Use the Galerkin meshless method to solve the gas-water two-phase seepage model of shale gas wells and give the corresponding numerical integration method; S5: Determine the support domain of the meshless method according to the neighbor averaging method, thereby constructing a meshless node system; When constructing the gridless node system, the complex seepage characteristics near the fractured horizontal well are considered, and the size of the support domain of the gridless method is determined by the neighboring average method. The calculation formula is: Where: A ns is the sum of the areas of all triangular elements in the neighborhood; is the number of field nodes; d c is the average spacing of field nodes; The node encryption method based on integral grid isoparametric transformation is used to encrypt the fractures of the horizontal wells, and the density of the transition zone between the encrypted zone and the non-encrypted zone is increased. The encryption formula is: Where: x i ,y i is the global coordinate of the i-th corner point of the triangle unit; L i,k is the i-th local coordinate of the k-th newly added node; Based on the generation and encryption methods of meshless nodes and background grids studied above, the node arrangement and background grid generation program is compiled and displayed through Matlab language to complete the construction of the meshless node system. S6: According to the characteristics of the constructed gridless node system, the COO organization matrix is ​​compressed and stored in CSR format, and finally brought into the PARDISO solver for solving to ensure the accuracy of the numerical well test analysis method; S7: Numerical well test analysis method for forming fractured horizontal wells in shale gas reservoirs by dividing different flow characteristic sections; S8: Based on the numerical well test analysis method of fractured horizontal wells in shale gas reservoirs, the measured data of shale gas wells are fitted to obtain the typical curve of well test analysis of fractured horizontal wells in shale gas reservoirs.

2. The method for numerical well testing analysis of fractured horizontal wells based on complex flow mechanism of shale gas according to claim 1, characterized in that: In step S1, the complex flow mechanism includes desorption mechanism, quasi-steady-state diffusion, unsteady-state diffusion and percolation mechanism.

3. The method for numerical well testing analysis of fractured horizontal wells based on the complex flow mechanism of shale gas according to claim 2, characterized in that: In step S1, the process of establishing the gas phase seepage model of the shale reservoir matrix system is as follows: S11: Establish a shale gas isothermal adsorption model, and obtain: Where: V is the adsorbed gas volume, unit is cm 3 / g; V L is the Langmuir volume in cm 3 / g;P L is the Langmuir pressure, in MPa; S12: Establish a gas phase seepage model for the shale reservoir matrix system, and establish the formula as follows: The gas flow from the matrix to the fracture system is expressed as: The shape factor is expressed as: The matrix rock compressibility coefficient is expressed as: The formation gas compressibility factor is: Where: L x ,L y ,L z is the length of the matrix rock in the x, y, and z directions, in meters; α is the dimension factor, dimensionless; K m is the effective permeability of the matrix, in μm 2 ; μ mg is the matrix gas viscosity, in mPa·s; B g is the gas volume coefficient, in m 3 / m 3 ; P m is the matrix pore pressure, in MPa; φ m is the matrix porosity; P fg is the gas phase pressure of the fracture system, in MPa.

4. The method for numerical well testing analysis of fractured horizontal wells based on complex flow mechanism of shale gas according to claim 3, characterized in that: In step S2, the process of establishing the gas phase and water phase seepage model of the shale reservoir fracture system is as follows: S21: Considering the influence of stress sensitivity, an exponential stress sensitivity correction fracture system permeability is established: in: Where: K0 is the initial permeability of the fracture system, in μm 2 ; is the rock compression coefficient, in MPa -1 ; σ is the effective stress of rock, in MPa; A is the cross-sectional area through which the fluid flows, in m 2 ; N is the number of cracks; l is the length of the crack, in m; ξ is the effective width of the crack, in m; S22: Establish a gas and water seepage model for a shale reservoir fracture system that takes into account complex flow mechanisms, and obtain: Gas phase: Aqueous phase: Where: α is the dimension factor, dimensionless; λ fg , fw B is the mobility of gas and water phases in the fracture system; g , B w is the volume coefficient of gas and water in the fracture system, in m 3 / m 3 ;P fg is the pressure of the gas phase in the fracture system, in MPa; q smfg is the gas flow from the matrix to the fracture system; q sg ,q sw is the wellbore production of gas and water in the fracture system, in kg / s; φ f is the porosity of the fracture system; S fw is the saturation of water phase in the fracture system.

5. The method for numerical well testing analysis of fractured horizontal wells based on complex flow mechanism of shale gas according to claim 4, characterized in that: In step S3, the process of establishing the gas-water two-phase seepage model of the shale gas well is as follows: S31: In a period of time after the well is switched on and off, since the surface production affected by the wellbore reservoir is not equal to the bottom hole production, the numerical well test production model of the fractured horizontal well is derived, including the pressure drop production model of the fractured horizontal well and the pressure recovery production model of the fractured horizontal well, and the result is: Fracturing horizontal well pressure drop production model: Fracturing horizontal well pressure recovery production model: in: Where: is the formation gas flow rate of the ith node in the mth fracture; C is the wellbore storage coefficient; f m,i is the production fraction of the i-th node in the m-th fracture; P fm,i is the formation pressure; N is the number of fractures; S32: The gas phase continuity equation established in the matrix system and the gas and water continuity equations established in the fracture system are combined to obtain the basic seepage equation of shale gas considering the complex flow mechanism: Where: α is the dimension factor, dimensionless; φ m is the matrix porosity; C m is the matrix rock compression coefficient, C g Formation gas compressibility factor; P L is the Langmuir pressure constant, in MPa; V L is the Langmuir volume constant, in cm 3 / g;P m is the matrix pore pressure, in MPa; q smfg is the gas flow from the matrix to the fracture system; P fg is the gas phase pressure of the fracture system, in MPa; B g , B w is the volume coefficient of gas and water in the fracture system, in m 3 / m 3 ;q sg ,q sw is the wellbore production of gas and water in the fracture system, in kg / s; φ f is the porosity of the fracture system; S fw is the saturation of water phase in the fracture system; S33: Before numerically simulating and solving the basic seepage equation of shale gas, the initial conditions and boundary conditions need to be defined. The solution conditions of the model include the boundary conditions and initial conditions of the fracture and matrix system. The initial conditions need to give the pressure and saturation parameter distribution at the initial time. Assuming that the initial pressure of the fracture and matrix system is the same, the initial pressure condition is: S34: Since the research object is a closed unit, the outer boundary of the mathematical model is closed, and the inner boundary is a constant bottom hole pressure production, so the inner boundary condition of the model is: P fg (x,y,t)=P wf (t) The outer boundary conditions are:

6. The method for numerical well testing analysis of fractured horizontal wells based on complex shale gas flow mechanism according to claim 5, characterized in that: In step S4, the corresponding equation is discretized before solving by using the numerical solution method of alternating implicit pressure and explicit saturation: EFGM numerical model of gas phase flow equation of matrix system: EFGM numerical model of gas phase flow equation in fracture system: EFGM numerical model of water phase flow equation in fracture system: Since the above EFGM numerical model has an integral function, it is necessary to give an integral method to solve the numerical model: Where: n c is the number of background units; G is the integrand; Ω k is the domain of the kth background unit.

7. The method for numerical well testing analysis of fractured horizontal wells based on complex flow mechanism of shale gas according to claim 6, characterized in that: In step S6, the specific steps to solve the problem of complex calculation of the node system constructed by the Galerkin meshless method are: The stiffness matrix of the large-scale, symmetrical and sparse numerical well test linear equations for fractured horizontal wells in shale gas reservoirs is constructed, and the stiffness matrix is ​​assembled using the COO compression storage strategy. Use CSR format to store and solve the system of linear equations; Based on the node system matrix in CSR storage format, the converted numerical well testing global weak meshless method CSR format system equations are brought into the PARDISO solver for solution.

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