Coal bed gas staged fracturing horizontal well reinforced extraction numerical simulation method

Abstract

The invention relates to a coal bed gas staged fracturing horizontal well enhanced extraction numerical simulation method which comprises the following steps: constructing a fracture system gas-water two-phase seepage control equation based on a porous medium of COMSOL software, a Darcy law physical field of an underground water flow interface and a porous medium phase transfer physical field of a fluid flow interface; a diffusion mass source is introduced into the Darcy law physical field and the porous medium phase transfer physical field; constructing a matrix system coal bed gas diffusion control equation based on a general form partial differential equation physical field of a partial differential equation interface of COMSOL software; a solver based on COMSOL software is used for solving, and the gas phase saturation of the fracture system, the water phase pressure of the fracture system and the gas pressure of the matrix system are obtained. According to the method, related parameters and variables of the staged fracturing horizontal well extraction model are automatically set and modified, the capability of solving different special problems is higher, the accuracy of the model is greatly improved, and the simulation process and result better conform to the actual working condition.

Description

Technical Field

[0001] The present application relates to the field of numerical simulation, and specifically, to a numerical simulation method for enhanced extraction of coalbed methane in a multi-stage fractured horizontal well. Background Art

[0002] The multi-stage fractured horizontal well is an effective method for coalbed methane development. Among them, the numerical simulation technology for extraction is the main evaluation method for coalbed methane development, which has important theoretical value for guiding coalbed methane development. At the present stage, the development of coalbed methane numerical simulation technology is relatively slow, and the corresponding software function modules are relatively fixed, and accurate numerical simulation under specific parameters cannot be realized. Summary of the Invention

[0003] In order to overcome at least one deficiency in the prior art, the present application provides a numerical simulation method for enhanced extraction of coalbed methane in a multi-stage fractured horizontal well.

[0004] In a first aspect, there is provided a numerical simulation method for enhanced extraction of coalbed methane in a multi-stage fractured horizontal well, including:

[0005] Based on the COMSOL software, a simulation model for the extraction of a multi-stage fractured horizontal well is built, including: constructing a two-phase seepage control equation for gas and water in the fracture system based on the Darcy's law physical field of the porous medium and groundwater flow interface and the porous medium phase transfer physical field of the fluid flow interface in the COMSOL software, and introducing a diffusion mass source into the Darcy's law physical field and the porous medium phase transfer physical field; constructing a diffusion control equation for coalbed methane in the matrix system based on the general form partial differential equation physical field of the partial differential equation interface in the COMSOL software;

[0006] Based on the solver in the COMSOL software, the two-phase seepage control equation for gas and water in the fracture system and the diffusion control equation for coalbed methane in the matrix system are solved to obtain the gas saturation in the fracture system, the water pressure in the fracture system, and the gas pressure in the matrix system.

[0007] In one embodiment, the diffusion control equation for coalbed methane in the matrix system is:

[0008]

[0009] where p m is the gas pressure in the matrix system, t is the time, V M is the molar volume of coalbed methane under standard conditions, p g is the gas pressure in the fracture system, P L is the Langmuir pressure constant, τ is the adsorption time, V L is the Langmuir volume constant, R is the universal gas constant, T is the gas temperature, ρ c is the coal density, and φ m is the matrix porosity.

[0010] In one embodiment, the governing equations for two-phase gas-water flow in the fracture system are as follows:

[0011]

[0012] Wherein, is the Hamiltonian operator, ρ w is the density of the aqueous phase, k is the absolute permeability of the fracture system, k rw is the relative permeability of the aqueous phase, u w is the kinetic viscosity coefficient of coalbed methane, p w is the aqueous phase pressure in the fracture system, is the aqueous phase pressure gradient, φ is the porosity of the fracture system, S w is the aqueous phase saturation, ρ g is the gas density, k rg is the relative permeability of the gas phase, u n is the kinetic viscosity coefficient of coalbed methane, p g is the gas pressure in the fracture system, is the gas phase pressure gradient, p m is the gas pressure in the matrix system, S g is the gas phase saturation in the fracture system, t is time, M is the molar mass of the gas, R is the universal gas constant, T is the gas temperature, and τ is the adsorption time.

[0013] In one embodiment, a simulation model for the extraction of a multi-stage fractured horizontal well based on the COMSOL software further includes:

[0014] Adding a parameter node and an interpolation function node in the global definition, inputting the basic parameters of the calculation model in the parameter node, and inputting the bottom-hole flowing pressure interpolation function in the interpolation function node;

[0015] Adding a variable node in the global definition, and inputting the variable expressions of the relative permeability of the aqueous phase, the relative permeability of the gas phase, and the capillary pressure in the variable node. The variable expressions are as follows:

[0016]

[0017] Wherein, P c is the capillary pressure; P e is the inlet capillary pressure; S w is the aqueous phase saturation; k rw is the relative permeability of the aqueous phase; k rg is the relative permeability of the gas phase; is the standard aqueous phase saturation; S wr is the residual aqueous phase saturation; S gr is the residual gas phase saturation; η is the curvature; λ is the fracture size distribution parameter;

[0018] Add a variable node to the component definition, and enter the gas density variable expression under the variable node Diffusion mass source variable expression M is the molar mass of the gas, p g is the gas pressure in the fracture system, R is the universal gas constant, T is the gas temperature, p m is the gas pressure in the matrix system, and τ is the adsorption time.

[0019] In one embodiment, a simulation model for drainage of a segmented fracturing horizontal well is built based on the COMSOL software, and it further includes:

[0020] Build a physical geometry model under the geometric node of the component in the COMSOL software; add a rectangle node, adopt the symmetry principle, enter the 1 / 4 model length × width parameters, refer to the fracturing microseismic monitoring data, add a fracturing fracture rectangle node, and enter the half-length × width parameters of the fracturing fracture to complete the simplified construction of the model.

[0021] In one embodiment, a matrix system coalbed methane diffusion control equation is built based on the general form partial differential equation physical field of the partial differential equation interface of the COMSOL software, including:

[0022] Add the general form partial differential equation physical field of the partial differential equation interface under the component node of the COMSOL software, including: the equation dependent variable is the gas pressure p in the matrix system m ; input the corresponding terms of the matrix system coalbed methane diffusion control equation into the corresponding parts of the partial differential equation physical field, where the source phase f inputs the expression p g is the gas pressure in the fracture system, R is the universal gas constant, T is the gas temperature, V M is the molar volume of coalbed methane under standard conditions, p m is the gas pressure in the matrix system, τ is the adsorption time, V L is the Langmuir volume constant, P L is the Langmuir pressure constant, ρ c is the coal density, φ m is the matrix porosity; the conserved flux Γ is default, and the damping or mass coefficient d a is set to 1, and the mass coefficient e a is set to 0; set the initial pressure P0 of the physical field; set the right boundary and upper boundary of the physical field to zero flux boundary conditions, set the left boundary and lower boundary of the physical field to symmetric boundary conditions; set the inner boundary of the physical field to Dirichlet boundary conditions, and call the bottom hole flowing pressure interpolation function under the global definition.

[0023] In one embodiment, based on the Darcy's law physical field of the porous media and groundwater flow interface and the porous media phase transfer physical field of the fluid flow interface in COMSOL software, a two-phase gas-water seepage control equation for the fracture system is constructed, and a diffusion mass source is introduced into the Darcy's law physical field and the porous media phase transfer physical field, including:

[0024] Add the porous media phase transfer physical field of the fluid flow interface under the component node in COMSOL software, including: setting the water phase saturation as a constraint term and the equation dependent variable as the gas phase saturation S of the fracture system g ; Add a phase and porous media transfer property node, and input the water phase density, water phase dynamic viscosity, gas phase dynamic viscosity, gas phase density, gas phase relative permeability, water phase relative permeability, and capillary pressure. Among them, the gas phase density calls the corresponding variable expression under the component definition, and the gas phase relative permeability, water phase relative permeability, and capillary pressure call the corresponding variable expressions under the global definition; Add a mass source node and call the diffusion mass source variable expression under the component definition node; Set the initial gas phase saturation as 1 - S w0 , S w0 is the initial water phase saturation; Set the right and upper boundaries of the physical field as the no-flux boundary condition, the left and lower boundaries of the physical field as the symmetric boundary condition, and the inner boundary of the physical field as the outflow boundary condition;

[0025] Add the Darcy's law physical field of the porous media and groundwater flow interface under the component node in COMSOL software, including: the equation dependent variable is the water phase pressure p of the fracture system w ; Add a macroscopic fracture porous media node and input the macroscopic fracture porosity and permeability; Add a fractured fracture porous media node and input the fractured fracture porosity and permeability; Add a mass source node and call the diffusion mass source variable expression under the component definition node; Set the initial pressure P0 of the physical field; Set the right and upper boundaries of the physical field as the no-flow boundary condition, the left and lower boundaries of the physical field as the symmetric boundary condition; Set the inner boundary of the physical field as the pressure boundary condition and call the bottom hole flowing pressure interpolation function under the global definition.

[0026] In one embodiment, the method further includes:

[0027] Divide the grid of the segmented fracturing horizontal well drainage simulation model using the user-controlled grid method; Calibrate the grid form to hydrodynamics, encrypt the grid in the fractured fracture area, set the grid size to ultra-fine or extremely fine, and set the grid size of the remaining part to normal or refined to complete the uniform division of the grid.

[0028] In one embodiment, the method further includes: verifying the accuracy of the segmented fracturing horizontal well drainage simulation model; The verification process includes:

[0029] Taking the actual bottom-hole flowing pressure of the multi-stage fractured horizontal well as the inner boundary condition of the physical field of Darcy's law and the physical field of the general form partial differential equation, adjusting the permeability data of the macroscopic fractures and the fractured fracture area in the model, and obtaining the fitted dynamic function of the macroscopic fracture permeability and the dynamic function of the fractured fracture permeability;

[0030] Inputting the fitted dynamic function of the macroscopic fracture permeability and the dynamic function of the fractured fracture permeability into the corresponding permeability variables of the model, calculating the model again, obtaining the simulated drainage data of the multi-stage fractured horizontal well in the subsequent time period, and comparing with the actual drainage data again to obtain the verification result.

[0031] Compared with the prior art, the present application has the following beneficial effects:

[0032] 1. With the help of COMSOL software, a simulation model for the drainage of multi-stage fractured horizontal wells is constructed. The port integration and numerical solution of the gas-water two-phase seepage control equation in the fracture system and the coalbed methane diffusion control equation in the matrix system with COMSOL software are realized. The simulation model can set and modify the relevant parameters and variables of the whole process of reservoir fluid migration by itself, and various working conditions can be defined according to the actual situation, with stronger ability to solve different special problems, greatly improving the accuracy of the model, and the simulation process and results are more in line with the actual working conditions.

[0033] 2. The simulation model for the drainage of multi-stage fractured horizontal wells divides the grid in the way of user-controlled grid. The grid form is calibrated to hydrodynamics, and the grid in the fractured fracture area is encrypted. The user-controlled grid method ensures the uniformity and accuracy of the model calculation results, effectively avoids the sudden change of the calculated values, and improves the convergence of the model.

[0034] 3. The accuracy of numerical simulation is verified by multi-stage simulation. Taking the actual bottom-hole flowing pressure data of the multi-stage fractured horizontal well as the inner boundary condition of the model, the dynamic functions of the macroscopic fracture permeability and the fractured fracture permeability are fitted, and the model is further calculated to test the accuracy of the model. The multi-stage simulated drainage data and the actual drainage data have a high degree of fitting, verifying the accuracy of the calculation and improving the application range of the model. Description of the Drawings

[0035] The present application can be better understood by referring to the description given in the following text in combination with the drawings. The drawings, together with the following detailed description, are included in this specification and form a part of this specification. In the drawings:

[0036] Figure 1 The flowchart of the numerical simulation method for the enhanced drainage of multi-stage fractured horizontal wells in coalbed methane is shown;

[0037] Figure 2 The schematic diagram of the physical model of the coal reservoir is shown;

[0038] Figure 3 The figure shows the bottom-hole flowing pressure interpolation function diagram of the numerical model;

[0039] Figure 4 The figure shows the physical geometry model diagram of the numerical model;

[0040] Figure 5 The figure shows the computational domain grid division diagram of the numerical model;

[0041] Figure 6 The figure shows the change diagram of the result output gas content of the numerical model; among them, (a) is the change diagram for 90 days, (b) is the change diagram for 180 days, (c) is the change diagram for 225 days, (d) is the change diagram for 270 days, (e) is the change diagram for 360 days, and (f) is the change diagram for 452 days

[0042] Figure 7 The figure shows the schematic diagram of the macroscopic fracture permeability dynamic function;

[0043] Figure 8 The figure shows the simulated drainage data and the actual drainage data diagram. Specific implementation manners

[0044] In the following, exemplary embodiments of the present application will be described in conjunction with the accompanying drawings. For clarity and conciseness, not all features of the actual embodiments are described in the specification. However, it should be understood that many embodiment-specific decisions can be made during the development of any such actual embodiment to achieve the specific goals of the developer, and these decisions may vary with different embodiments.

[0045] Here, it should also be noted that, in order to avoid obscuring the present application with unnecessary details, only the device structures closely related to the solution of the present application are shown in the drawings, while other details less related to the present application are omitted.

[0046] It should be understood that the present application is not limited to the described embodiments due to the following description with reference to the drawings. In this document, where feasible, embodiments can be combined with each other, features can be replaced or borrowed between different embodiments, and one or more features can be omitted in one embodiment.

[0047] The embodiments of the present application provide a numerical simulation method for enhanced drainage of coalbed methane by staged fracturing horizontal wells, Figure 1 The figure shows the flow block diagram of the numerical simulation method for enhanced drainage of coalbed methane by staged fracturing horizontal wells. The method mainly includes:

[0048] Step S1: Establish a simulation model for the drainage of a multi-stage fractured horizontal well based on COMSOL software, including: constructing a two-phase gas-water seepage control equation for the fracture system based on the Darcy's law physical field of the porous medium and groundwater flow interface and the porous medium phase transfer physical field of the fluid flow interface in COMSOL software, and introducing a diffusion mass source into the Darcy's law physical field and the porous medium phase transfer physical field; constructing a coalbed methane diffusion control equation for the matrix system based on the general form partial differential equation physical field of the partial differential equation interface in COMSOL software.

[0049] In this embodiment, first, simplify and assume each element of the coal reservoir to form a generalization of the coal reservoir geological model. The coal reservoir geological model has the following characteristics: The coal reservoir has a dual-medium structure of fractures and pores; the coal reservoir has compressibility and shrinkage-expansion properties; the coal reservoir has fractured cracks; the fluids in the coal reservoir have compressibility, with strong gas compressibility, conforming to the gas state equation, and coal seam water is a slightly compressible fluid; the fluid migration process is an isothermal process, and the reservoir temperature remains constant, with a value of 302.15K; the coal reservoir structure is simple, horizontally distributed, without complex structures such as faults and folds; the hydraulic conditions are relatively simple, the hydraulic conditions at the reservoir boundary are of a closed type, and the drainage process belongs to depletion-type mining.

[0050] Then, simplify and assume the spatial medium form of the coal reservoir to establish a physical model of the coal reservoir. Figure 2 The schematic diagram of the physical model of the coal reservoir is shown. The spatial medium form of the coal reservoir consists of multiple cubes, and each cube is composed of multiple coal matrix blocks. The interior of the cube is cut by fractured cracks and macrofractures distributed orthogonally to each other. Among them, the fractured cracks are distributed along the direction perpendicular to the minimum principal stress, and the macrofractures are evenly distributed. The coal matrix block is the main storage place for adsorbed methane gas, and the macrofractures and fractured cracks are both the storage places for coal seam water and the main seepage and migration channels for the fluids in the coal reservoir (free methane and coal seam water).

[0051] Then, construct a mathematical model for the fluid migration of a multi-stage fractured horizontal well. The mathematical model for the fluid migration of a multi-stage fractured horizontal well mainly includes the coalbed methane diffusion control equation for the matrix system and the two-phase gas-water seepage control equation for the fracture system. Note: The fracture system refers to the macrofractures and fractured cracks, and the matrix system refers to the micropores in the matrix blocks.

[0052] The migration mode of methane gas from the matrix system to the fracture system adjacent to the matrix system follows Fick's first law. The amount of free methane gas replenished to the fracture system adjacent to the matrix system is proportional to the rate of change of the average gas content in the matrix system over time, and the above relationship is described by the coalbed methane diffusion control equation for the matrix system.

[0053] Specifically, the coalbed methane diffusion control equation for the matrix system is:

[0054]

[0055] Among them, p m is the gas pressure of the matrix system, in MPa, t is the time, and V M is the molar volume of coalbed methane under standard conditions, in m 3 / mol, p g is the gas pressure of the fracture system, in MPa, P L is the Langmuir pressure constant, in MPa, τ is the adsorption time, in d (days), and V L is the Langmuir volume constant, in m 3 / kg, R is the universal gas constant, in J / (mol·K), T is the gas temperature, in K, and ρ c is the coal density, in kg / m 3 , and φ m is the matrix porosity. Note: Italic symbols represent variables, and regular symbols represent constants.

[0056] The migration mode of water and free methane gas in the coal seam in the fracture system is mainly the Darcy seepage flow mode based on laminar flow. The amount of free methane gas replenished to the fracture system adjacent to the matrix system is treated as the supplementary source phase of the Darcy seepage in the fracture system, and the fluid migration in the fracture system is described by the gas-water two-phase seepage control equation of the fracture system.

[0057] Specifically, the gas-water two-phase seepage control equation of the fracture system is as follows:

[0058]

[0059] Among them, is the Hamiltonian operator, ρ w is the water phase density, in kg / m 3 , k is the absolute permeability of the fracture system, in um 2 , k rw is the relative permeability of the water phase, u w is the kinetic viscosity coefficient of coalbed methane, in Pa·s, p w is the water phase pressure of the fracture system, in MPa, is the water phase pressure gradient, in atm / cm, φ is the porosity of the fracture system, and S w is the water phase saturation, ρ g is the gas density, in kg / m 3 , k rg is the relative permeability of the gas phase, u g is the kinetic viscosity coefficient of coalbed methane, in Pa·s, p g is the gas pressure of the fracture system, in MPa, is the gas-phase pressure gradient, with the unit of atm / cm, p m is the gas pressure in the matrix system, with the unit of MPa, S g is the gas-phase saturation in the fracture system, t is the time, M is the molar mass of the gas, with the unit of g / mol, R is the universal gas constant, with the unit of J / (mol·K), T is the gas temperature, with the unit of K, and τ is the adsorption time, with the unit of d (days).

[0060] Step S2: Solve the gas-water two-phase seepage control equation for the fracture system and the coalbed methane diffusion control equation for the matrix system based on the solver of COMSOL software to obtain the gas-phase saturation in the fracture system, the water-phase pressure in the fracture system, and the gas pressure in the matrix system.

[0061] Here, during the solution, set the numerical calculation time St under the research node, set the output time step in_t, and select the fully coupled mode for the solver configuration.

[0062] Furthermore, step S1: Build a simulation model for the extraction of a segmented fractured horizontal well based on COMSOL software, which also includes:

[0063] Add a parameter node and an interpolation function node in the global definition. Input the basic parameters of the calculation model at the parameter node, as shown in Table 1, and input the bottom-hole flowing pressure interpolation function int5(t) at the interpolation function node. Figure 3 Shows the bottom-hole flowing pressure interpolation function diagram of the numerical model.

[0064] Add a variable node in the global definition. Input the variable expressions of the relative permeability of the water phase, the relative permeability of the gas phase, and the capillary pressure at the variable node. The variable expressions are:

[0065]

[0066] where, P c is the capillary pressure; P e is the inlet capillary pressure; S w is the water-phase saturation; k rw is the relative permeability of the water phase; k rg is the relative permeability of the gas phase; is the standard water-phase saturation; S wr is the residual water-phase saturation; S gr is the residual gas-phase saturation; η is the curvature; λ is the fracture size distribution parameter; coefficient parameters: λ = 2, η = 0.5, S wr = 0.05, S gr = 0.

[0067] Add a variable node in the component definition. Input the variable expression of the gas density the variable expression of the diffusion mass source M is the molar mass of the gas, p g is the gas pressure in the fracture system, R is the universal gas constant, T is the gas temperature, p m is the gas pressure in the matrix system, and τ is the adsorption time.

[0068] Table 1

[0069] Parameter Name Value Unit Model Size 400×1100 m×m <![CDATA[Macroscopic fracture permeability k h > 1.95 mD <![CDATA[Fracture permeability k f > 19.5 mD <![CDATA[Macroscopic fracture porosity φ h > 0.049 / <![CDATA[Fracture porosity φ f > 0.147 / <![CDATA[Matrix porosity φ m > 0.079 / <![CDATA[Langmuir volume constant V L > 0.0356 <![CDATA[m 3 / kg <!-- 6 -->]]> <![CDATA[1 / 2V L Langmuir pressure constant P at L > 2.84 MPa <![CDATA[Coal density ρ c > 1380 <![CDATA[kg / m 3 > Adsorption Time Constant τ 6.98 d <![CDATA[Inlet capillary pressure P e > 0.01 MPa <![CDATA[Temperature T0]]> 305.15 K Fracture Half-Length L 100 m <![CDATA[Initial pressure P0]]> 1.844 MPa <![CDATA[Initial aqueous phase saturation S w0 > 0.95 / Coal Seam Thickness h 4 m <![CDATA[The density ρ of water w > 1000 <![CDATA[kg / m 3 > <![CDATA[Water viscosity coefficient μ w > <![CDATA[1×10 -3 > Pa·s <![CDATA[Standard condition methane density ρ ga > 0.72 <![CDATA[kg / m 3 > <![CDATA[Gas viscosity coefficient μ g > <![CDATA[1.84×10 -5 > Pa·s Gas Molar Mass M 0.016 kg / mol <![CDATA[The molar volume V of coalbed methane under standard conditions M > 22.4 L / mol Universal Gas Constant R 8.314 J / (mol·K) Calculation Time St 452 d Output Time Step in_t 1 d

[0070] Furthermore, in step S1, based on the COMSOL software, a simulation model for the extraction of a multi-stage fractured horizontal well is built, which further includes:

[0071] Construct a physical geometry model under the geometric node of the components of the COMSOL software. Add a rectangle node, adopt the symmetry principle, input the length×width parameters of the 1 / 4 model, refer to the hydraulic fracturing microseismic monitoring data, add a hydraulic fracturing crack rectangle node, and input the half-length×width parameters of the hydraulic fracturing crack to complete the simplified construction of the model.

[0072] Considering the large amount of calculation, the geometric model is constructed using one-fourth. The constructed model has a length×width of 550m×200m, the spacing between hydraulic fracturing crack segments is 100m, and the half-length×width of the hydraulic fracturing crack is 100m×50m. In the subsequent physical field module, introduce symmetric boundary conditions to simplify the overall model, save the calculation cost, and shorten the calculation time.

[0073] In one embodiment, in step S1, based on the general form of the partial differential equation interface of the COMSOL software, a control equation for the diffusion of coalbed methane in the matrix system is constructed, including:

[0074] Add the general form of the partial differential equation physical field of the partial differential equation interface under the component node of the COMSOL software, including: the dependent variable of the equation is the gas pressure p m in the matrix system. Input the corresponding terms of the control equation for the diffusion of coalbed methane in the matrix system into the corresponding parts of the partial differential equation physical field. Among them, the source phase f inputs the expression p g is the gas pressure in the fracture system, R is the universal gas constant, T is the gas temperature, V M is the molar volume of coalbed methane under standard conditions, p m is the gas pressure in the matrix system, τ is the adsorption time, V L is the Langmuir volume constant, P L is the Langmuir pressure constant, ρ c is the coal density, φ m is the matrix porosity; the conserved flux Γ is default, and the damping or mass coefficient d a is set to 1, and the mass coefficient e aSet to 0. Set the initial pressure P0 of the physical field. The right and upper boundaries of the physical field are set as zero-flux boundary conditions, and the left and lower boundaries of the physical field are set as symmetric boundary conditions; the inner boundary of the physical field is set as a Dirichlet boundary condition, specifically referring to the bottom-hole flowing pressure interpolation function int5(t) under the global definition.

[0075] In one embodiment, in step S1, based on the Darcy's law physical field of the porous media and groundwater flow interface and the porous media phase transfer physical field of the fluid flow interface in COMSOL software, a two-phase gas-water seepage control equation for the fracture system is constructed, and a diffusion mass source is introduced into the Darcy's law physical field and the porous media phase transfer physical field, including:

[0076] Add the porous media phase transfer physical field of the fluid flow interface under the component node in COMSOL software, including: setting the water-phase saturation as a constraint term, and the equation dependent variable as the gas-phase saturation S of the fracture system g . Add a phase and porous media transfer property node, input parameters such as water-phase density, water-phase dynamic viscosity, and gas-phase dynamic viscosity, input variables such as gas-phase density, gas-phase relative permeability, water-phase relative permeability, and capillary pressure, where the gas-phase density variable refers to the corresponding variable expression defined by the above component, and variables such as gas-phase relative permeability, water-phase relative permeability, and capillary pressure refer to the corresponding variable expressions defined by the above global definition; add a mass source node, referring to the diffusion mass source variable expression under the component definition node. Set the initial gas-phase saturation as 1 - S w0 , S w0 is the initial water-phase saturation; the right and upper boundaries of the physical field are set as no-flux boundary conditions, the left and lower boundaries of the physical field are set as symmetric boundary conditions, and the inner boundary of the physical field is set as an outflow boundary condition.

[0077] Add the Darcy's law physical field of the porous media and groundwater flow interface under the component node in COMSOL software, including: the equation dependent variable is the water-phase pressure p of the fracture system w . Add a macroscopic fracture porous media node, input the macroscopic fracture porosity and permeability; add a fractured-fracture porous media node, input the fractured-fracture porosity and permeability; add a mass source node, and again refer to the diffusion mass source variable expression under the component definition node. Set the initial pressure P0 of the physical field. The right and upper boundaries of the physical field are set as no-flow boundary conditions, the left and lower boundaries of the physical field are set as symmetric boundary conditions; the inner boundary of the physical field is set as a pressure boundary condition, specifically referring to the bottom-hole flowing pressure interpolation function int5(t) under the global definition. Different regional flow performances are set under the Darcy's law physical field, realizing low-speed Darcy seepage in the macroscopic fracture region and high-speed Darcy seepage in the fractured-fracture region, and the simulation process is more in line with the actual working conditions.

[0078] In one embodiment, in step S1, the mesh of the segmented fracturing horizontal well drainage simulation model is divided by the user-controlled mesh method, including:

[0079] The mesh is divided by the user-controlled mesh method, and the mesh form is calibrated to hydrodynamics to ensure the overall uniformity of the mesh. The mesh in the fracturing fracture area is encrypted. The mesh size in the fracturing fracture area is set to ultra-fine or extremely fine, and the mesh size of the remaining part is set to normal or refined. The setting of the mesh size needs to consider factors such as the model space position, the model calculation speed, and the result uniformity. If the mesh is selected as coarsened, coarser, etc., the calculated result value is coarser. If the mesh is selected as ultra-fine, extremely fine, etc., the calculation time is longer. Calibrating the mesh form to hydrodynamics and encrypting the mesh in the fracturing fracture area ensure the uniformity and accuracy of the model calculation results, effectively avoid the sudden change of the calculated value, and improve the convergence of the model. Figure 5 The figure shows the mesh division diagram of the calculation area of the numerical model.

[0080] Furthermore, in step S2, it further includes:

[0081] The calculation data of three dependent variables, p m , p w , and S g , are stored under the result node. With the help of the post-processing module of COMSOL software, the gas content change diagram is output.

[0082] It can be seen from the gas content change diagram that the gas content data change gradient in the fracturing fracture area is relatively large, which is consistent with the concept of enhanced drainage by hydraulic fracturing. Figure 6 The figure shows the gas content change diagram of the result output of the numerical model. The legend unit is m 3 / t. Among them, (a) is the change diagram for 90 days, (b) is the change diagram for 180 days, (c) is the change diagram for 225 days, (d) is the change diagram for 270 days, (e) is the change diagram for 360 days, and (f) is the change diagram for 452 days.

[0083] In one embodiment, the method further includes: verifying the accuracy of the segmented fracturing horizontal well drainage simulation model; the verification process includes:

[0084] Taking the actual bottom-hole flowing pressure of the segmented fracturing horizontal well as the inner boundary condition of the Darcy's law physical field and the general form partial differential equation physical field, adjusting the permeability data of the macroscopic fracture and the fracturing fracture area of the model, so that the simulated drainage data and the actual drainage data of the segmented fracturing horizontal well are kept consistent, obtaining the fitted dynamic function of the macroscopic fracture permeability pw3(t), and the dynamic function of the fracturing fracture permeability pw(t)=10×pw3(t). The permeability during the drainage of the segmented fracturing horizontal well is dynamically changing. As the drainage progresses, the permeability increases proportionally. The fitted order of magnitude and change law of the permeability conform to the actual drainage conditions of the segmented fracturing horizontal well.Figure 7 Shows a schematic diagram of the dynamic function of macro-fracture permeability pw3(t).

[0085]

[0086] Input the fitted dynamic function of macro-fracture permeability and the dynamic function of hydraulic fracture permeability into the corresponding permeability variables of the model, calculate the model again, obtain the simulated drainage data of the multi-stage fractured horizontal well in the subsequent time period, and compare it with the actual drainage data again to obtain the verification result. After verification, the simulated drainage data of the multi-stage fractured horizontal well in this embodiment has a high degree of fitting with the actual drainage data. Figure 8 Shows the graph of simulated drainage data and actual drainage data.

[0087] Compared with the prior art, the present application has the following technical effects:

[0088] 1. With the help of COMSOL software, a simulation model for the drainage of multi-stage fractured horizontal wells is constructed. The port integration and numerical solution of the gas-water two-phase seepage control equation of the fracture system and the coalbed methane diffusion control equation of the matrix system with COMSOL software are realized. The simulation model can set and modify the relevant parameters and variables of the whole process of reservoir fluid migration by itself, and various working conditions can be defined according to the actual situation. It has stronger ability to solve different special problems, greatly improves the accuracy of the model, and the simulation process and results are more in line with the actual working conditions.

[0089] 2. The simulation model for the drainage of multi-stage fractured horizontal wells divides the grid by the user-controlled grid method. The grid form is calibrated to hydrodynamics, and the grid in the hydraulic fracture area is encrypted. The user-controlled grid method ensures the uniformity and accuracy of the model calculation results, effectively avoids the sudden change of calculation values, and improves the convergence of the model.

[0090] 3. Use multi-stage simulation to verify the accuracy of numerical simulation. Taking the actual bottom-hole flowing pressure data of the multi-stage fractured horizontal well as the inner boundary condition of the model, the dynamic functions of permeability in the macro-fracture and hydraulic fracture areas are fitted, and the model is further calculated to test the accuracy of the model. The multi-stage simulated drainage data has a high degree of fitting with the actual drainage data, verifying the accuracy of the calculation and improving the application range of the model.

[0091] As described above, the above are only various embodiments of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present application can easily think of changes or substitutions, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A numerical simulation method for enhanced extraction of coalbed methane in a staged fracturing horizontal well, characterized in that, Including: Build a simulation model for the extraction of a multi-stage fractured horizontal well based on COMSOL software, including: constructing the gas-water two-phase seepage control equation for the fracture system based on the Darcy's law physical field of the porous medium and groundwater flow interface and the porous medium phase transfer physical field of the fluid flow interface in COMSOL software, and introducing a diffusion mass source into the Darcy's law physical field and the porous medium phase transfer physical field; constructing the coalbed methane diffusion control equation for the matrix system based on the general form partial differential equation physical field of the partial differential equation interface in COMSOL software. Solve the gas-water two-phase seepage control equation for the fracture system and the coalbed methane diffusion control equation for the matrix system based on the solver in COMSOL software to obtain the gas phase saturation in the fracture system, the water phase pressure in the fracture system, and the gas pressure in the matrix system.

2. The method according to claim 1, characterized in that, The coalbed methane diffusion control equation for the matrix system is: where p m is the gas pressure of the matrix system, t is time, V M is the molar volume of coalbed methane under standard conditions, p g is the gas pressure of the fracture system, P L is the Langmuir pressure constant, τ is the adsorption time, V L is the Langmuir volume constant, R is the universal gas constant, T is the gas temperature, ρ c is the coal density, φ m is the matrix porosity.

3. The method according to claim 1, characterized in that The gas-water two-phase seepage control equation for the fracture system is: Among them, is the Hamiltonian operator, ρ w is the aqueous phase density, k is the absolute permeability of the fracture system, k rw is the relative permeability of the aqueous phase, u w is the kinetic viscosity coefficient of coalbed methane, p w is the aqueous phase pressure of the fracture system, is the aqueous phase pressure gradient, φ is the porosity of the fracture system, S w is the aqueous phase saturation, ρ g is the gas density, k rg is the relative permeability of the gas phase, u g is the kinetic viscosity coefficient of coalbed methane, p g is the gas pressure of the fracture system, is the gas phase pressure gradient, p m is the gas pressure of the matrix system, S g is the gas phase saturation of the fracture system, t is the time, M is the molar mass of the gas, R is the universal gas constant, T is the gas temperature, and τ is the adsorption time.

4. The method according to claim 1, characterized in that, Wherein, Building a simulation model for the extraction of a multi-stage fractured horizontal well based on COMSOL software further includes: Adding a parameter node and an interpolation function node in the global definition, inputting the basic parameters of the calculation model at the parameter node, and inputting the bottom-hole flowing pressure interpolation function at the interpolation function node. Adding a variable node in the global definition, and inputting the variable expressions of the relative permeability of the water phase, the relative permeability of the gas phase, and the capillary pressure at the variable node. The variable expressions are: where, P c is the capillary pressure; P e is the inlet capillary pressure; S w is the water phase saturation; k rw is the relative permeability of the water phase; k rg is the relative permeability of the gas phase; is the standard water phase saturation; S wr is the residual water phase saturation; S gr is the residual gas phase saturation; η is the curvature; λ is the fracture size distribution parameter; Add a variable node to the component definition and enter the gas density variable expression under the variable node Diffusion mass source variable expression M is the molar mass of the gas, p g is the gas pressure in the fracture system, R is the universal gas constant, T is the gas temperature, p m is the gas pressure in the matrix system, and τ is the adsorption time.

5. The method according to claim 1, characterized in that, Wherein, Building a simulation model for the extraction of a multi-stage fractured horizontal well based on COMSOL software further includes: Constructing a physical geometry model under the geometric node of the component in COMSOL software; adding a rectangular node, adopting the symmetry principle, inputting the 1 / 4 model length × width parameters, referring to the hydraulic fracturing microseismic monitoring data, adding a hydraulic fracturing fracture rectangular node, and inputting the half-length × width parameters of the hydraulic fracturing fracture to complete the simplified construction of the model.

6. The method according to claim 1, characterized in that, Wherein, Constructing the coalbed methane diffusion control equation for the matrix system based on the general form partial differential equation physical field of the partial differential equation interface in COMSOL software includes: Under the component node of the COMSOL software, add the general form of the partial differential equation interface for the partial differential equation physical field, including: the dependent variable of the equation is the gas pressure p of the matrix system m ; Input the corresponding terms of the matrix system coalbed methane diffusion control equation into the corresponding part of the partial differential equation physical field. Among them, the source phase f inputs the expression p g is the gas pressure of the fracture system, R is the universal gas constant, T is the gas temperature, V M is the molar volume of coalbed methane under standard conditions, p m is the gas pressure of the matrix system, τ is the adsorption time, V L is the Langmuir volume constant, P L is the Langmuir pressure constant, ρ c is the coal density, φ m is the matrix porosity; the conserved flux Γ is default, and the damping or mass coefficient d a is set to 1, and the mass coefficient e a is set to 0; set the initial pressure P0 of the physical field; set the right boundary and upper boundary of the physical field to the zero-flux boundary condition, and set the left boundary and lower boundary of the physical field to the symmetric boundary condition; set the inner boundary of the physical field to the Dirichlet boundary condition, and call the bottom-hole flowing pressure interpolation function under the global definition.

7. The method according to claim 1, wherein Wherein, Constructing the gas-water two-phase seepage control equation for the fracture system based on the Darcy's law physical field of the porous medium and groundwater flow interface and the porous medium phase transfer physical field of the fluid flow interface in COMSOL software, and introducing a diffusion mass source into the Darcy's law physical field and the porous medium phase transfer physical field, including: Add the porous media phase transfer physical field of the fluid flow interface under the component node of the COMSOL software, including: setting the water phase saturation as a constraint term and the equation dependent variable as the gas phase saturation S of the fracture system g ; Add the phase and porous media transfer property node, and input the water phase density, water phase dynamic viscosity, gas phase dynamic viscosity, gas phase density, gas phase relative permeability, water phase relative permeability, and capillary pressure. Among them, the gas phase density calls the corresponding variable expression under the component definition, and the gas phase relative permeability, water phase relative permeability, and capillary pressure call the corresponding variable expressions under the global definition; Add the mass source node and call the diffusion mass source variable expression under the component definition node; Set the initial gas phase saturation as 1 - S w0 , S w0 is the initial water phase saturation; Set the right and upper boundaries of the physical field as the no - flux boundary condition, the left and lower boundaries of the physical field as the symmetric boundary condition, and the inner boundary of the physical field as the outflow boundary condition; Add the Darcy's law physical field of porous media and groundwater flow interfaces under the component node of COMSOL software, including: the equation dependent variable is the aqueous phase pressure p of the fracture system w ; Add a macroscopic fracture porous media node and input the macroscopic fracture porosity and permeability; Add a fractured fracture porous media node and input the fractured fracture porosity and permeability; Add a mass source node and call the diffusion mass source variable expression under the component definition node; Set the initial pressure P0 of the physical field; Set the right and upper boundaries of the physical field as no-flow boundary conditions, and set the left and lower boundaries of the physical field as symmetric boundary conditions; Set the inner boundary of the physical field as a pressure boundary condition and call the bottom-hole flowing pressure interpolation function under the global definition.

8. The method according to claim 1, wherein The method further includes: Dividing the grid of the simulation model for the extraction of a multi-stage fractured horizontal well by the user-controlled grid method; calibrating the grid form to hydrodynamics, encrypting the grid in the hydraulic fracturing fracture area, setting the grid size to ultra-fine or extremely fine, and setting the grid size of the remaining part to normal or refined to complete the uniform division of the grid.

9. The method according to claim 1, characterized in that The method further includes: verifying the accuracy of the simulation model for the extraction of a multi-stage fractured horizontal well; the verification process includes: Taking the actual bottom-hole flowing pressure of the multi-stage fractured horizontal well as the inner boundary conditions of the Darcy's law physical field and the general form partial differential equation physical field, and adjusting the permeability data of the macroscopic fractures and the hydraulic fracturing fracture area in the model to obtain the fitted dynamic functions of the macroscopic fracture permeability and the hydraulic fracturing fracture permeability. Input the fitted dynamic function of the macroscopic fracture permeability and the dynamic function of the hydraulic fracture permeability into the corresponding permeability variables of the model, calculate the model again to obtain the simulated drainage data of the staged hydraulic fracturing horizontal well in the subsequent time period, and compare it with the actual drainage data again to obtain the verification result.

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