CN118029969A - Method for calculating yield of coalbed methane fracturing well based on embedded flow exchange - Google Patents
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Abstract
The invention discloses a method for calculating the yield of a coalbed methane fracturing well based on embedded flow exchange, which belongs to the technical field of geological resource exploration and development and comprises the following steps of establishing a coalbed methane seepage control equation, utilizing an embedded discrete fracture model to represent a multi-scale fracture system and solving pressure distribution based on a finite volume method; establishing heterogeneous distribution of coal bed permeability based on Gaussian distribution, and introducing multiple seepage mechanism functions to characterize coal bed permeability evolution rules; based on Fisher distribution function, a coal seam cutting torch/crack system is established, dynamic crack width evolution is considered, and a self-supporting crack permeability evolution model is established by combining cube law; after the multi-scale seepage solution of the coal bed methane fracturing well is completed, a basic equation of the productivity of the coal bed methane fracturing well is established, discrete summation is carried out on the equation on an orthogonal grid, and the overall pressure solution is substituted into the productivity equation to obtain the productivity of the coal bed methane fracturing well. The invention improves the productivity calculation efficiency and accuracy of the coal bed gas fracturing well.
Description
Technical Field
The invention belongs to the technical field of geological resource exploration and development, in particular relates to the technical field of yield calculation, and particularly relates to a method for calculating the yield of a coalbed methane fracturing well based on embedded flow exchange.
Background
The horizontal well closely-cutting volume fracturing technology has great success in the development of unconventional oil and gas resources, the firmness coefficient of deep coal and rock is higher, the pore structure is similar to shale, coal and rock cutting lines and cracks are developed, and fracturing is easy to form a complex fracture network with certain diversion capacity; the compression strength of the coal rock is far lower than that of the roof limestone and the floor mudstone, the crack height is controlled, and the horizontal well tight cutting volume fracturing technology is provided with a volume fracturing foundation, so that the horizontal well tight cutting volume fracturing technology can be well used for efficient development of deep coal bed gas reservoirs. The accurate evaluation of post-volumetric fracturing capacity is of great importance.
The gas is mainly adsorbed gas, the free gas content is low, and the productivity is difficult to release. Because the coal rock stratum is softer, the propping agent is seriously embedded under the condition of high closure stress in the production process, the seam width is reduced, and the diversion capacity is reduced. Conventional commercial software and analysis/semi-analysis algorithms cannot be coupled with a multi-scale fracture system after volume fracturing, the conventional numerical algorithm reduces the calculation efficiency due to grid encryption, the capacity calculation application of a volume fracturing well with high-density fracture network characteristics is limited, in recent years, an embedded discrete fracture model is widely applied to numerical simulation of shale, sandstone and other fracture unconventional hydrocarbon reservoirs due to the advantage of rapid processing of a complex fracture system, therefore, the numerical model of the hydrocarbon reservoir is established based on a limited volume method, and the influence of the multi-scale fracture system (cutting/bedding, natural fracture and hydraulic fracture) on flow is represented by using the embedded fracture model of flow exchange. Simultaneously coupling dynamic evolution of matrix, cutting torch and hydraulic fracture permeability, calculating single well yield by solving coal bed pressure distribution and combining a well model, wherein the method only considers free gas flowing into a well bore, ignores adsorption gas in the coal bed, and causes larger error in productivity calculation, therefore, the flow characteristics of the coal bed gas volume fracturing well are necessary to be fully considered, multiple extraction concepts are introduced, free gas in matrix adsorption gas and a fracture system is calculated respectively, and a new productivity calculation method suitable for the coal bed gas fracturing well is established.
Multiple extraction effects are different from a single gas supply mechanism and are influenced by physical properties, cutting profile and transformation degree of a reservoir. The embedded flow exchange is different from the traditional well model, the flow exchange of different discrete units at different moments is calculated respectively by utilizing the embedded principle, and the flow exchange among matrix desorption, matrix-cracks and crack-cracks can be accurately captured, so that the accurate calculation of productivity is realized. The existing capacity calculation method also has the following disadvantages: (1) By adopting an analytic/semi-analytic calculation method, the heterogeneity of a coal bed and the distribution of a multi-scale fracture system cannot be fully considered; (2) The calculation method of combining numerical simulation with a well model cannot reveal the productivity rule under the multi-production effect; (3) The global capacity is calculated by using a single pressure drop (bottom hole), and the flux of each flow exchanging unit at different moments cannot be accurately described. .
Disclosure of Invention
In order to solve the problems, the invention aims to provide a coalbed methane fracturing well yield calculation method based on embedded flow exchange.
The invention is realized by the following technical scheme:
a coalbed methane fracturing well yield calculation method based on embedded flow exchange comprises the following steps:
Step 1, establishing a seepage control equation by using a continuity equation, a motion equation and a state equation of single-phase seepage of simultaneous coal bed gas, utilizing an embedded discrete fracture model to represent a multi-scale fracture system, dispersing the seepage control equation of the coal bed gas based on a finite volume method, and finally solving pressure distribution by using a Gauss-Seidel method;
step 2, based on a Gaussian distribution function, establishing heterogeneous distribution of the permeability of the coal bed, and introducing a multiple seepage mechanism function to represent the evolution rule of the permeability of the coal bed; based on Fisher distribution function, a coal seam cutting torch/fracture system is established, dynamic fracture width evolution is considered, and a self-supporting fracture permeability evolution model is established by combining cube law, wherein hydraulic fracture conductivity meets index decrease;
and 3, after the multi-scale seepage solution of the coal bed methane fracturing well is completed by combining the steps 1 and 2, a basic equation of the capacity of the coal bed methane fracturing well is established by considering a multi-extraction mechanism including matrix adsorption gas, matrix free gas, cutting torch free gas and main fracture free gas, discrete summation is carried out on the equation on an orthogonal grid, and the global pressure solution is substituted into the capacity equation, so that the capacity calculation of the coal bed methane fracturing well is finally realized.
Compared with the prior art, the invention has the beneficial effects that:
The invention fully considers the characteristics of multi-scale and multi-extraction in the development process of coal bed methane fracturing, and couples the dynamic evolution of matrix, cutting torch and hydraulic fracture permeability under different pressure conditions. And (3) utilizing a limited volume method discrete coalbed methane seepage control equation, and characterizing seepage characteristics of the multi-scale fracture system through an embedded discrete fracture model. On the basis, the capacity calculation method under the condition of multiple extraction of free gas and adsorption gas of the matrix and the fracture system is comprehensively considered by utilizing flow exchange of the embedded discrete units at different moments, so that the capacity calculation efficiency and accuracy of the coal bed methane fracturing well are greatly improved.
Drawings
In order to more clearly illustrate the technical solution of the embodiments of the present invention, the drawings that are required to be used in the embodiments will be briefly described.
FIG. 1 is a graph of typical production of a fractured well based on embedded flow exchange;
FIG. 2 is a graph comparing contribution rates of different extraction mechanisms;
FIG. 3 is a graph showing the effect of different cutting blade numbers on productivity;
FIG. 4 is a graph showing the effect of various Lane pressures on throughput;
FIG. 5 is a graph showing the effect of various Langmuir volumes on throughput;
FIG. 6 is a graph showing the effect of different cluster spacing on throughput;
FIG. 7 is a graph showing the effect of half-length of different cracks on productivity.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, based on the embodiments of the invention, which are apparent to those of ordinary skill in the art without inventive faculty, are intended to be within the scope of the invention.
Example 1
Step 1, establishing a seepage control equation by using a continuity equation, a motion equation and a state equation of single-phase seepage of the simultaneous coal bed gas, utilizing an embedded discrete fracture model to represent a multi-scale fracture system, dispersing the seepage control equation of the coal bed gas based on a finite volume method, and finally solving pressure distribution by using a Gauss-Seidel method.
1.1. Matrix seepage control equation
The single-phase seepage continuity equation in a coalbed methane reservoir can be expressed as:
the seepage velocity in the coal reservoir meets the generalized Darcy law, and the relation between macroscopic mass transmission and pressure of the coal bed gas is described by using the Darcy equation, specifically:
the state equation in the coal bed gas flowing process is as follows:
Z3+(A-2B-3B2)Z-(1-B)Z2-(AB-B2-B3)＝0 (3)
α(T)＝[1+(0.37646+1.54226ω-0.26992ω2)(1-Tr 0.5)]2 (6)
φm＝φm0exp[cm(p-pref)]＝φm0[1+cm(p-pref)] (8)
Substituting equations 2, 7 and 8 into equation 1 yields the following for the coalbed methane seepage pressure diffusion equation:
Wherein ρ g represents the coalbed methane density, kg/m 3;ρgsc represents the coalbed methane density under standard conditions, kg/m 3;φm represents the matrix porosity, dimensionless; phi m0 represents the matrix porosity in the initial state, dimensionless; v g represents the coal bed methane seepage velocity; m/s; q s represents a desorption mass source term, kg/s; q s represents a desorption volume source term, m 3/s; p represents reservoir pressure, MPa; p ref represents reservoir reference pressure, MPa; t represents reservoir temperature, K; k m represents matrix permeability, mD; mu g represents the viscosity of the coalbed methane, mPa.s; z represents a coalbed methane compression factor, and is dimensionless; p r represents the critical pressure of the coalbed methane and MPa; t r represents the critical temperature of coal bed gas, K; r represents a gas constant of 8.314, J/mol.K; omega represents a state equation coefficient, 0.5, dimensionless; b g represents the gas volume coefficient of the coal bed, and has no dimension; c m represents the compression coefficient of the coal bed, 1/MPa; t represents time, s.
1.2 Embedded discrete crack model
For a pair of non-adjacent connection points, the expression for discrete fracture source sink strength is defined as:
Qf＝TNNCΔpNNC (10)
Crack-matrix conductivity is defined as follows:
fracture-fracture conductivity is defined as follows:
wherein:
Wherein, Q f represents the strength of the embedded discrete fracture source and sink, m 3/s;TNNC represents the conduction coefficient of a pair of adjacent connection points, and m 3/s·MPa;pNNC represents the pressure of a pair of adjacent connection points, and MPa; d NNC denotes the average distance of a pair of adjacent connection points, m; t m-f and T f-m represent the conductivity of the matrix to the crack, the crack to the matrix, respectively, m 3/s·MPa;Tf-f represents the conductivity of the crack to the crack, m 3/s·MPa;Tm represents the conductivity of the matrix, m 3/s·MPa;Tf represents the conductivity of the crack, m 3/s·MPa;Am-f =ΔxΔy represents the contact area of the crack to the matrix, m 2;Vc =ΔxΔyΔz represents the volume of the control body, m 3;Tf i represents the conductivity of the ith crack, m 3/s·mpa; n represents the normal vector of the crack, and is dimensionless; x represents the distance of the crack from the center of the matrix lattice, m.
1.3. Numerical discrete based on finite volume method
After considering the multi-scale fracture system after volume fracturing, equation (9) can be rewritten as:
And (3) performing numerical discrete on an established multiscale seepage pressure diffusion equation (15)) by adopting a finite volume method, wherein the integration of two ends of the equation (15) in a control volume can be obtained:
The fully implicit discrete format of equation (16) on an orthogonal grid is:
further coupling the fracture to matrix flow exchange, equation (16) may be further expressed as:
wherein:
Wherein Δx=l x/Nx,Δy＝Ly/Ny and Δz=l z/Nz denote grid dimensions in x, y and z directions, m, respectively; l x,Lx and L z represent the coalbed methane reservoir sizes in the x, y and z directions, m, respectively; n x,Nx and N z represent the number of grids in the x, y and z directions, respectively; superscripts n and n+1 represent the current and next time steps, respectively; subscript i, j represents a grid index and c represents a grid center; Δt, time step, day; omega m represents a matrix domain; omega HF represents hydraulic fracture domain; omega NF represents a natural fracture domain; p L represents the Langerhans pressure, MPa; v L represents the Lanceolat volume, m 3/kg.
1.4. Numerical model solution
Solving each grid in the domain satisfies the discrete format in equation 17, a nonlinear system of equations shaped as ap=b can be obtained as follows:
solving by using the Gauss-Seidel method, the pressure solution at any iteration step can be expressed as:
Each iteration step error satisfies:
Wherein a mm,Amf,Afm and a ff represent matrix-matrix, and fracture-fracture coefficient matrices, respectively; p m and P f represent matrix and fracture pressure vectors, respectively; b m and B f represent matrix and fracture constant vectors, respectively; δp represents the pressure solving error, MPa; n represents the total number of grids, one.
And 2, establishing heterogeneous distribution of the permeability of the coal bed based on a Gaussian distribution function, and introducing a multiple seepage mechanism function to represent the evolution rule of the permeability of the coal bed. Based on Fisher distribution function, a coal seam cutting torch/crack system is established, dynamic crack width evolution is considered, and a self-supporting crack permeability evolution model is established by combining cube law. Meanwhile, the hydraulic fracture conductivity meets the index decrease.
2.1. Heterogeneous permeability of coal seam
Reservoir permeability heterogeneity is characterized by a random gaussian distribution, specifically:
wherein:
The multi-mechanism of mass transfer of the coal bed gas is fully considered, and the evolution equation of the permeability of the coal bed gas matrix is as follows:
Wherein μ represents a standard deviation of the permeability heterogeneous distribution, mD; σ 2 represents permeability non-uniform distribution variance, mD 2;VDP represents non-uniform distribution coefficient, 0.05, dimensionless; rand represents a random number between 0 and 1; dimensionless; alpha and beta respectively represent slip coefficients, 0.5 and 1, and have no dimension; kn=k BT/(2πdm 2 p)/r represents the knudsen number, dimensionless; k B represents the Boltzmann constant, J/K; d m represents the methane molecule diameter, m; m represents the molecular mass of methane, kg/mol; r represents the pore diameter of the coal reservoir matrix and m; r max and r min represent the maximum and minimum pore sizes, m, respectively, of the pores of the coal reservoir matrix; d s represents the surface adsorption coefficient, m 2/s;Camax represents the maximum adsorption concentration, and mol/m 3;Df represents the fractal dimension of the pores of the coal reservoir matrix, dimensionless.
2.2. Cutting torch/natural fracture distribution and permeability thereof
The random discrete fracture network model (DFN) is adopted to quantitatively represent the pressed self-supporting fracture network, and the parameter distribution including coordinates, the fracture length, the fracture width and the dip angle meets the following Fisher random function:
In the coalbed methane exploitation process, the opening of the self-supporting crack can dynamically evolve along with the decrease of the formation pressure, and the evolution rule can be summarized into three mechanisms: matrix compression, crack compression and desorption expansion, specifically:
Using cube law, the permeability of a single cutting/natural fracture satisfies the following:
Meanwhile, the hydraulic fracture flow conductivity can be reduced along with exploitation after being pressed, and the following index decreasing relation is satisfied:
kHF＝216.7t-0.249 (31)
CHF＝wHFkHF＝43.21t-0.249 (32)
Wherein x NF、yNF,LNF and w NF represent coordinates of a cutting torch/a natural fracture, length and width, m, respectively; ζ represents a distribution index, 1, dimensionless; f (θ) represents a Fisher distribution density function; θ represents the cutting torch/natural fracture dip angle, °; k represents Fisher distribution coefficient, dimensionless; And/> Respectively representing crack width increment, m, caused by matrix compression, crack compression and desorption expansion; w NFini denotes the initial crack width, m; e represents Young's modulus of a coal reservoir matrix and GPa; v represents poisson ratio of coal reservoir matrix, dimensionless; c fini represents the initial compression coefficient of the crack, 1/MPa; p ini represents the initial pore pressure, MPa; s L represents Lane strain, dimensionless; k NF represents the cleat/natural fracture permeability, mD; k HF represents hydraulic fracture permeability, mD; w HF represents hydraulic fracture width, m; c HF represents the hydraulic fracture conductivity, D.cm.
And 3, after the multi-scale seepage solution of the coal bed methane fracturing well is completed, a multi-extraction mechanism including matrix adsorption gas, matrix free gas, cutting torch free gas and main fracture free gas is considered, a basic equation of the productivity of the coal bed methane fracturing well is established, the equation is subjected to discrete summation on an orthogonal grid, the global pressure solution is substituted into the productivity equation, and finally the productivity calculation of the coal bed methane fracturing well is realized.
Based on the material balance, the coalbed methane fracturing well gas consists of matrix adsorption gas, matrix free gas, cutting torch free gas and main fracture free gas, and the capacity calculation basic equation is defined as follows:
equation (33) cannot be directly calculated, so on the orthogonal grid in step 1, equation (33) can be rewritten as follows, based on the global/local embedded traffic exchange principle:
Substituting the numerically solved pressure distribution into equation (34) to obtain a coalbed methane fracturing well productivity calculation formula taking into consideration multi-scale seepage and multi-extraction mechanisms, wherein the calculation formula specifically comprises the following steps:
Wherein phi NF and phi HF respectively represent the porosity of the natural fracture and the hydraulic fracture, and have no dimension; q S,QFm,QFNF and Q FHF respectively represent the gas production rates of matrix adsorption gas, matrix free gas, cutting free gas and main fracture free gas, and m 3/s; q represents the total gas yield of the coal bed gas fracturing well and m 3/s.
The basic parameters are shown in Table 1:
Table 1 basic parameters
(2) Calculation result
As can be seen from fig. 1: under the influence of multi-scale and multi-production, the production capacity curve of the coal bed methane fracturing well based on embedded flow exchange can be divided into 5 typical stages, including an initial high-production stage, a desorption rising stage, a middle-stage stable production stage, a later-stage attenuation stage and a final-stage depletion stage, which shows that the initial gas production is mainly determined by a main fracture transformation range, and further the pressure diffusion is subjected to the forward promotion effect of a multi-scale fracture system, so that a large amount of adsorbed gas is converted into free gas, and the free gas and the adsorbed gas are produced simultaneously. When the free gas is extracted to a certain extent, the reservoir pressure is obviously reduced, the adsorbed gas becomes a main gas supply source, and the current situation gradually transits from the stable production stage to the middle and later stage to be attenuated and exhausted along with further exploitation. Therefore, the gas production rule of the coalbed methane fracturing well is fully revealed.
As can be seen from fig. 2: as the coalbed methane is further mined, the reservoir pressure is reduced, and the adsorbed gas in the matrix is largely desorbed, so that the contribution rate of the adsorbed gas to the productivity is increased, on the contrary, as the free gas in the main fracture and the cutting/natural fracture is mined, the contribution rate of the adsorbed gas and the free gas are equal in about 200 days of production after the initial high post-production, and the adsorbed gas is the main gas supply source after 1200 days of production.
As can be seen from fig. 3: by comparing the gas production curves of different cutting torch numbers, the result shows that the initial productivity is almost unchanged as the cutting torch number is increased from 100 to 300, and the gas production rate is higher as the pressure is further diffused to the cutting torch area after free gas in the main crack is mined out. Meanwhile, the more cutting lines, the more methane is present in the coal reservoir, so that the later the critical time for entering the mid-late decay is.
As can be seen from fig. 4: by comparing the gas production curves of different Lane pressures, the result shows that the lower the Lane pressure is, the faster the gas production increases after entering the desorption rising stage. Meanwhile, the lower Lane pressure means that the coalbed methane is easier to desorb, so that the gas production rate mainly based on the adsorption gas in the middle and later stages is higher, when the Lane pressure is 3.4MPa, the coalbed stops producing gas after 3000 days of production, which indicates that part of methane cannot be desorbed and is retained in a reservoir, and therefore, further reduction of the Lane pressure is an important means for prolonging the production period of the coalbed methane fracturing well.
As can be seen from fig. 5: the results show that the method is similar to the Lane pressure by comparing the gas production curves of different Lane volumes, the increasing of the Lane volume does not affect the initial gas production, under the condition of certain Lane pressure, the higher the Lane volume is, the larger the initial adsorption gas quantity of the coal bed is, the higher the gas production is after the coal bed enters the desorption rising stage, but the higher the later-stage decay rate is due to the balance of substances, but the higher the total critical depleted gas production is.
As can be seen from fig. 6: the result shows that as the gas is extracted, the free gas provided by the initial hydraulic fracture is dominant, the cluster distance is reduced, the coal reservoir is cut into pieces, the adsorbed gas is converted into the free gas, the productivity in the initial high-yield stage is obviously improved, as the adsorbed gas is converted into the free gas in advance for extraction, and after 1000 days of production, the stable gas yield and the cluster distance are positively correlated in the middle-stage desorption.
As can be seen from fig. 7: the result shows that the gas production curve with different main cracks being half-long is increased, the initial transformation is more sufficient, the control range is larger, the pressure release area of a single well is larger, more free gas is released, higher yield can be obtained in the initial stage, the cluster spacing is similar, the material balance principle enables the initial stage to be high in yield, but the desorption gas supply in the middle and later stages is dominant, and the subsequent productivity is reduced.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the technical scope of the present invention disclosed in the embodiments of the present invention should be covered by the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (5)
1. The method for calculating the yield of the coalbed methane fracturing well based on embedded flow exchange is characterized by comprising the following steps of:
Step 1, establishing a seepage control equation by using a continuity equation, a motion equation and a state equation of single-phase seepage of simultaneous coal bed gas, utilizing an embedded discrete fracture model to represent a multi-scale fracture system, dispersing the seepage control equation of the coal bed gas based on a finite volume method, and finally solving pressure distribution by using a Gauss-Seidel method;
step 2, based on a Gaussian distribution function, establishing heterogeneous distribution of the permeability of the coal bed, and introducing a multiple seepage mechanism function to represent the evolution rule of the permeability of the coal bed; based on Fisher distribution function, a coal seam cutting torch/fracture system is established, dynamic fracture width evolution is considered, and a self-supporting fracture permeability evolution model is established by combining cube law, wherein hydraulic fracture conductivity meets index decrease;
and 3, after the multi-scale seepage solution of the coal bed methane fracturing well is completed by combining the steps 1 and 2, a basic equation of the capacity of the coal bed methane fracturing well is established by considering a multi-extraction mechanism including matrix adsorption gas, matrix free gas, cutting torch free gas and main fracture free gas, discrete summation is carried out on the equation on an orthogonal grid, and the global pressure solution is substituted into the capacity equation, so that the capacity calculation of the coal bed methane fracturing well is finally realized.
2. The method for calculating the production rate of the coalbed methane fracturing well based on the embedded flow rate exchange according to claim 1, wherein in the step S1,
The matrix seepage control equation includes:
single phase seepage continuity equation in coalbed methane reservoirs:
coal bed methane movement equation:
coalbed methane state equation:
Z3+(A-2B-3B2)Z-(1-B)Z2-(AB-B2-B3)＝0 (3)
φm＝φm0[1+cm(p-pref)] (8)
The coalbed methane seepage pressure diffusion equation:
Wherein ρ g represents the coalbed methane density, kg/m 3;ρgsc represents the coalbed methane density under standard conditions, kg/m 3;φm represents the matrix porosity, dimensionless; phi m0 represents the matrix porosity in the initial state, dimensionless; v g represents the coal bed methane seepage velocity; m/s; q s represents a desorption mass source term, kg/s; q s represents a desorption volume source term, m 3/s; p represents reservoir pressure, MPa; p ref represents reservoir reference pressure, MPa; t represents reservoir temperature, K; k m represents matrix permeability, mD; mu g represents the viscosity of the coalbed methane, mPa.s; z represents a coalbed methane compression factor, and is dimensionless; p r represents the critical pressure of the coalbed methane and MPa; t r represents the critical temperature of coal bed gas, K; r represents a gas constant of 8.314, J/mol.K; omega represents a state equation coefficient, 0.5, dimensionless; b g represents the gas volume coefficient of the coal bed, and has no dimension; c m represents the compression coefficient of the coal bed, 1/MPa; t represents time, s;
The embedded discrete fracture model includes:
for a pair of non-adjacent connection points, the discrete fracture source sink intensities are calculated by:
Qf＝TNNCΔpNNC (10)
Calculation of fracture-matrix conductivity:
fracture-fracture conductivity calculation formula:
wherein:
Wherein, Q f represents the strength of the embedded discrete fracture source and sink, m 3/s;TNNC represents the conduction coefficient of a pair of adjacent connection points, and m 3/s·MPa;pNNC represents the pressure of a pair of adjacent connection points, and MPa; d NNC denotes the average distance of a pair of adjacent connection points, m; t m-f and T f-m represent the conductivity of the matrix to the crack, the crack to the matrix, respectively, m 3/s·MPa;Tf-f represents the conductivity of the crack to the crack, m 3/s·MPa;Tm represents the conductivity of the matrix, m 3/s·MPa;Tf represents the conductivity of the crack, m 3/s·MPa;Am-f =ΔxΔy represents the contact area of the crack to the matrix, m 2;Vc =ΔxΔyΔz represents the volume of the control body, m 3;Tf i represents the conductivity of the ith crack, m 3/s·mpa; n represents the normal vector of the crack, and is dimensionless; x represents the distance of the crack from the center of the matrix lattice, m.
3. The method for calculating the yield of the coalbed methane fracturing well based on the embedded flow exchange according to claim 2, wherein in the step S1, a coalbed methane seepage control equation is discretized based on a finite volume method, and finally the pressure distribution is solved by a Gauss-Seidel method, which comprises the following steps:
Adopting a finite volume method to carry out numerical discrete on a coalbed methane seepage pressure diffusion equation, and integrating two ends of the equation in a control volume to obtain:
the fully implicit discrete format of the above equation on an orthogonal grid is:
Further coupling the crack and the matrix flow exchange to obtain:
wherein:
Wherein Δx=l x/Nx,Δy＝Ly/Ny and Δz=l z/Nz denote grid dimensions in x, y and z directions, m, respectively; l x,Lx and L z represent the coalbed methane reservoir sizes in the x, y and z directions, m, respectively; n x,Nx and N z represent the number of grids in the x, y and z directions, respectively; superscripts n and n+1 represent the current and next time steps, respectively; subscript i, j represents a grid index and c represents a grid center; Δt, time step, day; omega m represents a matrix domain; omega HF represents hydraulic fracture domain; omega NF represents a natural fracture domain; p L represents the Langerhans pressure, MPa; v L represents the Lanceolat volume, m 3/kg;
in the solving process, each grid in the solving domain satisfies the discrete format in equation (17), and a nonlinear equation set of the form ap=b is obtained as follows:
Solving by using Gauss-Seidel method, the pressure solution under any iteration step is expressed as:
Each iteration step error satisfies:
Wherein a mm,Amf,Afm and a ff represent matrix-matrix, and fracture-fracture coefficient matrices, respectively; p m and P f represent matrix and fracture pressure vectors, respectively; b m and B f represent matrix and fracture constant vectors, respectively; δp represents the pressure solving error, MPa; n represents the total number of grids, one.
4. The method for calculating the production rate of the coalbed methane fracturing well based on the embedded flow rate exchange according to claim 3, wherein the step S2 comprises the following steps of,
Reservoir permeability heterogeneity is characterized by a random gaussian distribution, specifically:
wherein:
evolution equation of the permeability of the coalbed methane matrix:
Wherein μ represents a standard deviation of the permeability heterogeneous distribution, mD; σ 2 represents permeability non-uniform distribution variance, mD 2;VDP represents non-uniform distribution coefficient, 0.05, dimensionless; rand represents a random number between 0 and 1; dimensionless; alpha and beta respectively represent slip coefficients, 0.5 and 1, and have no dimension; kn=k BT/(2πdm 2 p)/r represents the knudsen number, dimensionless; k B represents the Boltzmann constant, J/K; d m represents the methane molecule diameter, m; m represents the molecular mass of methane, kg/mol; r represents the pore diameter of the coal reservoir matrix and m; r max and r min represent the maximum and minimum pore sizes, m, respectively, of the pores of the coal reservoir matrix; d s represents the surface adsorption coefficient, m 2/s;Camax represents the maximum adsorption concentration, and mol/m 3;Df represents the fractal dimension of pores of the coal reservoir matrix, and the dimensionless;
The random discrete fracture network model is adopted to quantitatively represent the pressed self-supporting fracture network, and the parameter distribution including coordinates, the fracture length, the fracture width and the dip angle meets the following Fisher random function:
the self-supporting fracture permeability evolution model comprises:
opening evolution equation of self-supporting fracture:
Using cube law, the permeability of a single cutting/natural fracture satisfies the following:
the hydraulic fracture conductivity satisfies the following exponential decreasing relationship:
kHF＝216.7t-0.249 (31)
CHF＝wHFkHF＝43.21t-0.249 (32)
Wherein x NF、yNF,LNF and w NF represent coordinates of a cutting torch/a natural fracture, length and width, m, respectively; ζ represents a distribution index, 1, dimensionless; f (θ) represents a Fisher distribution density function; θ represents the cutting torch/natural fracture dip angle, °; k represents Fisher distribution coefficient, dimensionless; And/> Respectively representing crack width increment, m, caused by matrix compression, crack compression and desorption expansion; w NFini denotes the initial crack width, m; e represents Young's modulus of a coal reservoir matrix and GPa; v represents poisson ratio of coal reservoir matrix, dimensionless; c fini represents the initial compression coefficient of the crack, 1/MPa; p ini represents the initial pore pressure, MPa; s L represents Lane strain, dimensionless; k NF represents the cleat/natural fracture permeability, mD; k HF represents hydraulic fracture permeability, mD; w HF represents hydraulic fracture width, m; c HF represents the hydraulic fracture conductivity, D.cm.
5. The method for calculating the production rate of the coalbed methane fracturing well based on the embedded flow rate exchange of claim 4, wherein the step S3 comprises:
the basic equation of the productivity of the coalbed methane fracturing well is as follows:
based on the global/local embedded flow exchange principle, on the orthogonal grid in the step 1, the basic equation of the productivity of the fracturing well of the coalbed methane is changed into written:
substituting the pressure distribution solved in the step S1 into a rewritten basic equation of the productivity of the coal-bed methane fracturing well to obtain a calculation formula of the productivity of the coal-bed methane fracturing well considering the multi-scale seepage and multi-extraction mechanism, wherein the calculation formula specifically comprises the following steps:
Wherein phi NF and phi HF respectively represent the porosity of the natural fracture and the hydraulic fracture, and have no dimension; q S,QFm,QFNF and Q FHF respectively represent the gas production rates of matrix adsorption gas, matrix free gas, cutting free gas and main fracture free gas, and m 3/s; q represents the total gas yield of the coal bed gas fracturing well and m 3/s.
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