Deep coal bed gas reservoir multi-area coupling productivity evaluation method and system, processing equipment and storage medium
By establishing the four-zone physical model and seepage mathematical model of deep coalbed methane reservoirs, the problem that the existing technology cannot accurately and quickly predict the deep coalbed methane production capacity is solved, and efficient and accurate capacity prediction is achieved, which is suitable for deep coalbed methane reservoirs and other tight gas reservoirs.
Patent Information
- Application Number
- CN202411968713.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-30
- Publication Date
- 2025-03-18
- Estimated Expiration
- 2044-12-30
AI Technical Summary
The existing medium-shallow-stratum coalbed methane reservoir capacity evaluation method is not suitable for complex fracture networks formed after large-scale fracturing of deep coalbed methane reservoirs, and the calculation speed is complex and the calculation speed is slow. There is a lack of methods to accurately and quickly predict deep coalbed methane production capacity.
The multi-zone coupling capacity evaluation method of deep coalbed methane reservoirs is adopted. By establishing a physical model of four zones (crack zone, heavy transformation zone, weak transformation zone and matrix zone), the range and equivalent seepage parameters of each zone are calculated, a mathematical model of seepage is established and gas production is solved, and the multi-zone coupling capacity prediction is achieved.
It improves the accuracy and calculation speed of deep coalbed methane reservoir production capacity prediction, is suitable for deep coalbed methane reservoirs and other tight gas reservoirs, and promotes the efficient development of deep coalbed methane.
Smart Images

Figure CN119641331A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of coalbed methane development, and in particular to a method, system, processing equipment and storage medium for evaluating multi-zone coupling capacity of deep coalbed methane reservoirs. Background Art
[0002] China is rich in deep coalbed methane resources, and coalbed methane development has gradually extended from shallow to deep layers. Exploration and development practices have shown that deep coalbed methane has undergone great changes from the concept of fracturing to the fluid seepage mode after fracturing.
[0003] However, the existing methods for evaluating the productivity of medium- and shallow-layer coalbed methane reservoirs simply equate fractures of different scales after fracturing to one main fracture, which is not suitable for the complex fracture network formed by large-scale fracturing in deep coalbed methane reservoirs. In addition, the existing methods mostly use numerical methods for solving, and the model establishment process is complicated, the calculation amount is large, and the calculation speed is slow. Therefore, there is currently a lack of a method that can accurately and quickly predict the productivity of deep coalbed methane. Summary of the invention
[0004] In view of the above problems, the purpose of the present invention is to provide a multi-zone coupled capacity evaluation method, system, processing equipment and storage medium for deep coalbed methane reservoirs, which can accurately and quickly predict the deep coalbed methane capacity.
[0005] To achieve the above objectives, the present invention adopts the following technical solutions: In the first aspect, a method for evaluating the multi-zone coupling capacity of a deep coalbed methane reservoir is provided, comprising:
[0006] According to the fracture network characteristics and fluid seepage characteristics of deep coal reservoirs after fracturing, a four-zone physical model of deep coal reservoirs is established, including fracture zone, heavily reformed zone, weakly reformed zone and matrix zone.
[0007] Based on the four-zone physical model of deep coal reservoirs and the fracture network parameters after fracturing, the range and equivalent seepage parameters of the four zones of deep coal reservoirs are calculated;
[0008] Based on the range and equivalent seepage parameters of the four areas of deep coal reservoirs, the mathematical model of seepage in the four areas of deep coal reservoirs was established, and the gas production in the four areas of deep coal reservoirs was obtained by solving the model.
[0009] According to the gas production of four areas in the deep coal reservoir, the gas production of a single fracturing stage in the deep coal reservoir is obtained as the multi-zone coupling capacity.
[0010] Furthermore, the fracture network characteristics refer to the fracture morphology and fracture parameters of deep coal reservoirs after fracturing. The fracture morphology is a four-level complex fracture network of "high conductivity main fracture + branch fracture + shear self-supporting fracture + cleat", and the fracture parameters include the length, opening, height and conductivity of each level of fracture;
[0011] The fracture zone is the high-conductivity main fracture area formed by fracturing near the wellbore, which is dominated by free gas and the gas flow follows Darcy's law;
[0012] The heavily reformed area is the branch fracture filled with proppant and the reformed area around it, where free gas and desorbed gas coexist. The free gas follows Darcy's law, and the desorbed gas flows according to the law of "desorption-diffusion-seepage".
[0013] The weakly stimulated area is the shear self-propping fractures and the surrounding stimulated areas far from the wellbore where proppant is difficult to enter, and there are free gas and desorbed gas;
[0014] The matrix zone is the area not affected by the original reservoir fracturing, where free gas and desorbed gas coexist.
[0015] Furthermore, the range of the fracture zone is the length, width and height of the high conductivity main fracture, and the equivalent seepage parameters of the fracture zone are the equivalent permeability and equivalent porosity of the high conductivity main fracture;
[0016] The range of the matrix zone is determined according to the well control area, the equivalent permeability of the matrix zone is the permeability of the original reservoir, and the equivalent porosity of the matrix zone is the porosity of the original reservoir.
[0017] Furthermore, there are several branch fractures and small flow areas in the surrounding cleats in the remodeling zone, which are equivalent to two-dimensional elliptical radial flow as a whole. The range of the remodeling zone is a two-dimensional ellipse with the two end points of the high conductivity main fracture as the focus;
[0018] The calculation process of equivalent seepage parameters in the remodeled area is as follows:
[0019] Calculate the equivalent permeability of multiple branch fractures in the remodeled area;
[0020] Based on the equivalent permeability of multiple branch fractures in the heavily remodeled area, the equivalent permeability of branch fractures in the heavily remodeled area and the surrounding remodeled area is calculated;
[0021] Calculate the equivalent porosity of multiple branch fractures in the heavily reformed area;
[0022] Based on the equivalent porosity of multiple branch fractures in the heavily reformed zone, the equivalent porosity of the heavily reformed zone is calculated.
[0023] Furthermore, the weakly reformed area is equivalent to an ellipse with the major axis endpoint of the heavily reformed area ellipse as the focus;
[0024] The calculation process of equivalent seepage parameters in the weakly transformed area is as follows:
[0025] Calculate the equivalent permeability of multiple shear joints in the weak transformation area;
[0026] Based on the equivalent permeability of multiple shear joints in the weakly transformed area, the equivalent permeability of the shear joints in the weakly transformed area and the surrounding transformed areas is calculated;
[0027] Calculate the equivalent porosity of multiple shear fractures in the weak transformation zone;
[0028] Based on the equivalent porosity of multiple shear fractures in the weakly reformed zone, the equivalent porosity of the weakly reformed zone is calculated.
[0029] Furthermore, the mathematical model of seepage in the fracture zone is:
[0030]
[0031] In the formula, p F is the pressure in the fracture zone; k F is the equivalent permeability of the fracture zone; φ F is the porosity of the fracture zone; x F h is the half length of the main fracture with high conductivity; F is the height of the main fracture with high conductivity; Z is the gas compression factor; μ g is the gas viscosity; C r , C g are the compressibility coefficients of pores and gas, respectively; S g is gas saturation; t is time; p e is the original reservoir pressure; p wf is the bottom hole flowing pressure; Q gsc is the gas production in the fracture zone; T is the reservoir temperature; p sc is the pressure under standard conditions; Z sc is the deviation factor under standard conditions; T sc is the temperature under standard conditions;
[0032] The mathematical model of seepage in the remodeling area includes the free gas equation and the desorbed gas equation. The free gas equation is:
[0033]
[0034] Where r is the position with seepage radius r in the gas reservoir; p fn is the pressure in the remodeling zone; ρ gsc is the density of the gas under standard conditions; r fn The elliptical flow range of the remodeling area is equivalent to the radius of the circular supply; φ fn is the equivalent porosity of the heavily reformed area; h fn is the average height of multiple branch fractures; k fn is the equivalent permeability of the branch fractures in the heavily remodeled area and the surrounding remodeled area; q dfn It is the desorption gas in the heavy reforming area; fn is the equivalent seepage radius of the two-dimensional ellipse equivalent to the remodeling area;
[0035] The desorption gas equation in the mathematical model of seepage in the remodeling zone is:
[0036]
[0037] In the formula, p cd is the critical desorption pressure; V L is the Langmuir volume; p L is the Langmuir pressure;
[0038] The mathematical model of seepage in the weakly reformed zone includes the free gas equation and the desorbed gas equation. The free gas equation is:
[0039]
[0040] In the formula, k mf is the equivalent permeability of the shear fracture in the weak transformation area and the surrounding transformation area; p mf is the pressure in the weak transformation zone; r mf The elliptical flow range of the weak transformation zone is equivalent to the radius of the circular supply; q dmf It is the desorption gas in the weak reformation zone; ξ mf is the equivalent seepage radius of the weak transformation zone; φ mf is the equivalent porosity of the weakly reformed zone; h mf is the average height of multiple shear joints;
[0041] The desorption gas equation in the seepage mathematical model of the weak reformed area is:
[0042]
[0043] The mathematical model of seepage in the matrix zone includes the free gas equation and the desorption gas equation. The free gas equation is:
[0044]
[0045] In the formula, p m is the matrix pressure; q dm is the desorbed gas in the matrix area; ξ m is the equivalent seepage radius of the matrix area; k m is the equivalent permeability of the matrix area; φ m is the equivalent porosity of the matrix region;
[0046] The desorption gas equation in the matrix zone seepage mathematical model is:
[0047]
[0048] Furthermore, the multi-zone coupling capacity is:
[0049]
[0050] Among them, ψ F is the pseudo pressure in the fracture zone; ψ wf is the pseudo pressure corresponding to the bottom hole flowing pressure; R F is the seepage resistance in the fracture area; R fn is the seepage resistance term in the heavily transformed area; Q dfb is the desorption diffusion term in the heavy reforming zone; R mf is the seepage resistance term in the weakly transformed area; Q dmf is the desorption diffusion term in the weak reformed zone; R m is the seepage resistance term in the matrix area; Q dm is the desorption diffusion term in the matrix region.
[0051] In the second aspect, a multi-zone coupled production capacity evaluation system for deep coalbed methane reservoirs is provided, comprising:
[0052] The four-zone physical model building module is used to build a four-zone physical model of deep coal reservoirs based on the fracture network characteristics and fluid seepage characteristics of deep coal reservoirs after fracturing, including the fracture zone, heavily reformed zone, weakly reformed zone and matrix zone;
[0053] A parameter calculation module, which is used to calculate the range and equivalent seepage parameters of four areas of the deep coal reservoir based on the four-area physical model of the deep coal reservoir and the fracture network parameters of the deep coal reservoir after fracturing;
[0054] A seepage mathematical model building module is used to build a seepage mathematical model of the four areas of the deep coal reservoir based on the ranges and equivalent seepage parameters of the four areas of the deep coal reservoir, and solve to obtain the gas production of the four areas of the deep coal reservoir;
[0055] The gas production solving module is used to obtain the gas production of a single fracturing section in the deep coal reservoir as the multi-zone coupled production capacity according to the gas production of four areas in the deep coal reservoir.
[0056] In a third aspect, a processing device is provided, comprising computer program instructions, wherein the computer program instructions, when executed by the processing device, are used to implement the steps corresponding to the above-mentioned method for evaluating the multi-zone coupling capacity of deep coalbed methane reservoirs.
[0057] In a fourth aspect, a computer-readable storage medium is provided, on which computer program instructions are stored, wherein the computer program instructions, when executed by a processor, are used to implement the steps corresponding to the above-mentioned deep coalbed methane reservoir multi-zone coupled capacity evaluation method.
[0058] The present invention adopts the above technical solution, which has the following advantages:
[0059] 1. The present invention takes into account the four-level complex fracture network of "high conductivity main fracture + branch fracture + shear self-supporting fracture + cleat" formed after large-scale volume fracturing in deep coalbed methane reservoirs, and divides the four areas into fracture area, heavy reformation area, weak reformation area and matrix area. Compared with the existing production capacity model that simply equates fractures of different scales to one main fracture and cleat, it is more in line with the fracture characteristics after fracturing in the mine, and improves the accuracy of production capacity prediction of deep coalbed methane reservoirs.
[0060] 2. The present invention adopts the equivalent seepage resistance method to perform multi-zone coupling analytical solution. Compared with the numerical solution, the method is simple, the calculation speed is fast, and the mine application is more convenient.
[0061] 3. The present invention can be applied to other fields such as deep coalbed methane reservoirs and tight gas reservoirs developed by directional wells, horizontal wells, vertical wells and other well types, by simply substituting corresponding parameters.
[0062] In summary, the present invention can be widely used in the field of coalbed methane development. BRIEF DESCRIPTION OF THE DRAWINGS
[0063] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Throughout the accompanying drawings, the same reference numerals are used to represent the same components. In the accompanying drawings:
[0064] Figure 1 This is a schematic diagram of a complex fracture network formed after deep coal reservoir fracturing provided by an embodiment of the present invention;
[0065] Figure 2 is a schematic diagram of a four-zone physical model of a deep coal reservoir provided by an embodiment of the present invention;
[0066] Figure 3 It is a schematic diagram of calculating the equivalent range of the deep coal reservoir re-construction zone provided by an embodiment of the present invention;
[0067] Figure 4 It is a schematic diagram showing the calculation of the equivalent range of the weakly reformed zone of a deep coal reservoir provided by an embodiment of the present invention;
[0068] Figure 5 It is a schematic diagram comparing the calculated daily output and the actual daily output provided by an embodiment of the present invention. DETAILED DESCRIPTION
[0069] The exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.
[0070] It should be understood that the terms used herein are only for the purpose of describing specific example embodiments and are not intended to be limiting. Unless the context clearly indicates otherwise, the singular forms "one", "an" and "said" as used herein may also be meant to include plural forms. The terms "include", "comprise", "contain", and "have" are inclusive, and therefore specify the existence of stated features, steps, operations, elements and / or parts, but do not exclude the existence or addition of one or more other features, steps, operations, elements, parts, and / or combinations thereof. The method steps, processes, and operations described herein are not interpreted as necessarily requiring them to be performed in the specific order described or illustrated, unless the execution order is clearly indicated. It should also be understood that additional or alternative steps may be used.
[0071] Although the terms first, second, third, etc. can be used in the text to describe multiple elements, components, regions, layers and / or sections, these elements, components, regions, layers and / or sections should not be limited by these terms. These terms can only be used to distinguish an element, component, region, layer or section from another region, layer or section. Unless the context clearly indicates, terms such as "first", "second" and other numerical terms do not imply order or sequence when used in the text. Therefore, the first element, component, region, layer or section discussed below can be referred to as the second element, component, region, layer or section without departing from the teaching of the example embodiments.
[0072] The existing production capacity evaluation methods for shallow and medium-layer coalbed methane reservoirs simply equate different scale fractures after fracturing to one main fracture, which is not suitable for the complex fracture network formed by large-scale fracturing in deep coalbed methane reservoirs. In addition, the existing methods mostly use numerical methods for solving, which has a complex model establishment process, large amount of calculations, and slow calculation speed. The embodiment of the present invention provides a multi-zone coupled capacity evaluation method for deep coalbed methane reservoirs, including: according to the fracture network characteristics and fluid seepage characteristics of the deep coal reservoir after fracturing, a four-zone physical model of the deep coal reservoir is established, including four regions of the fracture zone, the heavy reformation zone, the weak reformation zone and the matrix zone; based on the four-zone physical model of the deep coal reservoir, according to the fracture network parameters of the deep coal reservoir after fracturing, the range and equivalent seepage parameters of the four regions of the deep coal reservoir are calculated; based on the range and equivalent seepage parameters of the four regions of the deep coal reservoir, a seepage mathematical model of the four regions of the deep coal reservoir is established, and the gas production of the four regions of the deep coal reservoir is obtained by solving; according to the gas production of the four regions of the deep coal reservoir, the gas production of a single fracturing section of the deep coal reservoir is obtained as the multi-zone coupled capacity. The present invention can further improve the accuracy and solution speed of the capacity prediction of the deep coalbed methane reservoir, and promote the efficient development process of the deep coalbed methane.
[0073] Example 1
[0074] This embodiment provides a method for evaluating the multi-zone coupled productivity of a deep coalbed methane reservoir, comprising the following steps:
[0075] 1) According to the fracture network characteristics and fluid seepage characteristics of deep coal reservoirs after fracturing, a four-zone physical model of deep coal reservoirs is established, including the fracture zone, heavily reformed zone, weakly reformed zone and matrix zone.
[0076] Specifically, the fracture network characteristics refer to the fracture morphology and fracture parameters after fracturing of deep coal reservoirs. The fracture morphology forms a four-level complex fracture network of "high conductivity main fracture + branch fracture + shear self-supporting fracture + cleat", and the fracture parameters include the length, opening, height and conductivity of each level of fracture.
[0077] Specifically, the fluid seepage characteristics refer to the occurrence characteristics and flow patterns of gases in the four areas of fracture, heavily reformed, weakly reformed and matrix. In the fracture area, there is only free gas but no adsorbed gas, which is Darcy seepage. In the heavily reformed, weakly reformed and matrix areas, there are both adsorbed and free gas, and the free gas is Darcy seepage, while the flow pattern of adsorbed gas is desorption-diffusion-seepage.
[0078] Specifically, under large-scale volume fracturing technology, a four-level complex fracture network of "high conductivity main fracture + branch fracture + shear self-supporting fracture + cleat" is formed, such as Figure 1After fracturing of deep coal reservoirs, the length, opening, height, conductivity and other parameters of each fracture are different, and the degree of transformation around fractures of different levels is also different. Based on the zoning concept, the deep coal reservoir after fracturing is divided into four areas: fracture area, heavy transformation area, weak transformation area and matrix area, as shown in Figure 2 As shown, the definition is as follows:
[0079] 1.1) Fracture zone: The high-conductivity main fracture area formed by fracturing near the wellbore is dominated by free gas, and the gas flow follows Darcy's law.
[0080] 1.2) Heavy reformation area: branch fractures filled with proppant and the reformed areas around them (dual medium of matrix and cleat), where free gas and desorbed gas coexist. There are a large number of branch fractures in this area. With the large-scale production of free gas, the reservoir pressure will quickly drop to the critical desorption pressure, and the adsorbed gas will begin to desorb and diffuse into the cleats and branch fractures to make up for the decrease of free gas. The free gas follows Darcy's law, and the desorbed gas flows according to the law of "desorption-diffusion-seepage".
[0081] 1.3) Weakly reformed zone: The shear self-supporting fractures and the surrounding reformed areas in the far wellbore area where proppants are difficult to enter. The degree of reservoir reformation in this area is lower than that in the heavily reformed area. The reservoir pressure drop rate in this area is lower than that in the heavily reformed area. There is free gas and slowly desorbed adsorbed gas.
[0082] 1.4) Matrix zone: The area not affected by the original reservoir fracturing, where free gas and desorbed gas coexist. The coal reservoir cleats and matrix conductivity in this area are very low, and the gas production is very low before the adsorbed gas is desorbed, which is similar to the depressurization and desorption development method of medium and shallow coal seams.
[0083] 2) Based on the four-zone physical model of the deep coal reservoir and according to the fracture network parameters of the deep coal reservoir after fracturing, the range and equivalent seepage parameters of the four zones of the deep coal reservoir are calculated, wherein the fracture network parameters of the deep coal reservoir after fracturing include the length, aperture, height and conductivity of each level of fracture.
[0084] Specifically, the range of the fracture zone is the volume of the fracture zone, and the range of the heavily reformed zone, weakly reformed zone and matrix zone is the equivalent seepage radius of the heavily reformed zone, weakly reformed zone and matrix zone; the equivalent seepage parameters of the four zones include equivalent permeability and equivalent porosity. The range and equivalent seepage parameters of the four zones in the deep coal reservoir are calculated as follows:
[0085] 2.1) Crack area
[0086] Specifically, the range of the fracture zone is the length, width and height of the high conductivity main fracture. The volume of the fracture zone is:
[0087] V F =2(x F -r w )ωF h F (1)
[0088] Where V F is the volume of the fracture zone, in m 3 ;x F ,ω F 、h F are the half-length, opening and height of the main high-conductivity fracture, in m; r w is the wellbore radius, in m.
[0089] Specifically, the equivalent permeability of the fracture zone is the initial permeability k of the high conductivity main fracture F , because all the fracture areas are main fractures with high conductivity, the equivalent porosity of the fracture area is φ F is the equivalent porosity of the high conductivity main fracture.
[0090] 2.2) Reconstruction area:
[0091] 2.2.1) The calculation process of the scope of the reconstruction area is as follows:
[0092] like Figure 3 As shown in the figure, there are several branch fractures and small flow areas in the surrounding cleats in the remodeled area, which are equivalent to a two-dimensional elliptical radial flow, that is, a two-dimensional ellipse with the two ends of the high-conductivity main fracture as the focus. The equivalent seepage radius ξ of the two-dimensional ellipse equivalent to the remodeled area is fn for:
[0093]
[0094] In the formula, a fn and b fn are the major and minor axes of the remodeling zone ellipse, respectively, in meters. The length and azimuth of multiple branch fractures in the remodeling zone are approximately calculated, and the calculation diagram is shown in the figure. Figure 3 As shown, where x fi is the length of the branch joint; Δx fi is the starting coordinate of the branch seam; θ fi is the branch seam angle.
[0095] 2.2.2) The calculation process of equivalent seepage parameters in the remodeled area is as follows:
[0096] 2.2.2.1) Calculate the equivalent permeability k of multiple branch fractures in the remodeled area f :
[0097]
[0098] In the formula, w fi is the width of each branch seam; unit is m; D fis the branch crack fractal dimension, dimensionless; D t is the branch crack fractal index, dimensionless; XX f is the distance from the center of each branch fracture to the starting point of this secondary fracture.
[0099] 2.2.2.2) Based on the equivalent permeability k of multiple branch fractures in the remodeled area f , calculate the equivalent permeability k of the branch fractures in the heavily transformed area and the surrounding transformed area fn :
[0100]
[0101] In the formula, and are the average length, width and height of branch fractures, in meters; H is the effective thickness of the reservoir, in meters; k m-fn is the permeability of the reformed area around the branch fracture, in units of 10 -3 μm 2 .
[0102] 2.2.2.3) Calculate the equivalent porosity φ of multiple branch fractures in the remodeling area f :
[0103]
[0104] In the formula, ρ f is the branch crack density, that is, the number of branch cracks per unit area.
[0105] 2.2.2.4) Based on the equivalent porosity of multiple branch fractures in the remodeling area f , calculate the equivalent porosity φ of the remodeled area fn for:
[0106]
[0107] 2.3) Weakly remodeled area:
[0108] 2.3.1) The calculation process of the weak transformation area is as follows:
[0109] The weakly modified area is similar to the heavily modified area. The weakly modified area is equivalent to an ellipse with the major axis endpoint of the heavily modified area ellipse as the focus, such as Figure 4 Specifically, the equivalent seepage radius ξ of the weakly transformed zone mf for:
[0110]
[0111] In the formula, a mf and b mfare the major and minor axes of the weak transformation zone ellipse, respectively, in meters. Based on the approximate calculation of the lengths and azimuths of multiple shear fractures, the calculation diagram is shown in Figure 4 As shown, where x fsi is the shear seam length; θ fsi is the shear seam angle.
[0112] 2.3.2) The calculation process of equivalent seepage parameters in the weakly transformed area is as follows:
[0113] 2.3.2.1) Calculate the equivalent permeability k of multiple shear fractures in the weak transformation area fs :
[0114]
[0115] In the formula, w fsi is the width of each shear seam, in m; D fs is the shear seam fractal dimension, dimensionless; D ts is the shear seam fractal index, dimensionless; △x fsi is the horizontal coordinate of the starting point of the shear seam; △y fsi is the ordinate of the starting point of the shear seam; XX fs It is the distance from the center of each shear seam to the starting point of the shear seam.
[0116] 2.3.2.2) Based on the equivalent permeability k of multiple shear fractures in the weak transformation area fs , calculate the equivalent permeability k of the shear joints in the weak transformation area and the surrounding transformation area mf :
[0117]
[0118] In the formula, and are the average length, width and height of the shear joint, in m; k m-mf is the permeability of the transformation area around the shear joint, in units of 10 -3 μm 2 .
[0119] 2.3.2.3) Calculate the equivalent porosity φ of multiple shear fractures in the weak transformation zone fs :
[0120]
[0121] In the formula, ρ fs is the branch crack density, that is, the number of shear cracks per unit area.
[0122] 2.3.2.4) Based on the equivalent porosity of multiple shear fractures in the weak transformation zone fs , calculate the equivalent porosity φ of the weakly reformed zonemf :
[0123]
[0124] 2.4) Matrix area:
[0125] 2.4.1) The range calculation process of the matrix area is as follows:
[0126] According to the well control area A weil Determine the range of the matrix region. Specifically, the equivalent seepage radius ξ of the matrix region m for:
[0127]
[0128] In the formula, r e The elliptical flow range of the matrix area is equivalent to the radius of the circular supply; a e is the major semi-axis of the matrix region ellipse.
[0129] 2.4.2) The calculation process of equivalent seepage parameters in the matrix area is as follows:
[0130] The equivalent permeability of the matrix zone is the permeability of the original reservoir k m , the equivalent porosity of the matrix zone is the porosity of the original reservoir φ m .
[0131] 3) Based on the range and equivalent seepage parameters of the four areas of deep coal reservoirs, a mathematical seepage model of the four areas of deep coal reservoirs is established, and the gas production of the four areas of deep coal reservoirs is solved.
[0132] 3.1) Based on the range of deep coal reservoir fracture zone and equivalent seepage parameters, a mathematical model of seepage in deep coal reservoir fracture zone is established, and the gas production in deep coal reservoir fracture zone is solved:
[0133] 3.1.1) Based on the range of deep coal reservoir fracture zone and equivalent seepage parameters, a mathematical model of seepage in deep coal reservoir fracture zone is established:
[0134]
[0135] In the formula, p F is the pressure in the fracture zone; k F is the equivalent permeability of the fracture zone; φ F is the porosity of the fracture zone; x F h is the half length of the main fracture with high conductivity; F is the height of the main fracture with high conductivity; Z is the gas compression factor; μ g is the gas viscosity, in mPa·s; C r , C g are the compressibility coefficients of pores and gas, respectively, in MPa-1 ; S g is gas saturation, dimensionless; t is time; p e is the original reservoir pressure, in MPa; p wf is the bottom hole flow pressure, in MPa; Q Fgsc is the gas production in the fracture zone; T is the reservoir temperature, in K; p sc is the pressure under standard conditions, in MPa; Z sc is the deviation factor under standard conditions, dimensionless; T sc It is the temperature under standard conditions, in K.
[0136] Specifically, pseudo-pressure and pseudo-time are introduced to deal with the nonlinear formulas (14) and (15) caused by the change of gas physical properties with pressure. The pressure of each region and the gas viscosity, compressibility factor and other parameters at each pressure are substituted into formulas (14) and (15) to convert the pressure and time of each region into pseudo-pressure and pseudo-time. The formula form of the four regions is common:
[0137]
[0138] Where ψ(p) is the pseudo pressure; P is the pressure; μ(p) is the gas viscosity; Z(p) is the gas compressibility factor; t a is the pseudo time; subscript ini, They represent the original formation pressure and the gas parameters under the average pressure in each area at each moment respectively.
[0139] 3.1.2) Based on the mathematical model of seepage in the fracture zone and the nonlinear formula of pseudo-pressure and pseudo-time, the pressure is considered constant at each small time step, and the gas production Q in the fracture zone is obtained. Fgsc :
[0140]
[0141] In the formula, ψ F is the pseudo pressure in the fracture zone; ψ wf is the pseudo pressure corresponding to the bottom hole flowing pressure; R F is the seepage resistance in the fracture zone.
[0142] 3.2) Based on the scope of the deep coal reservoir re-construction zone and the equivalent seepage parameters, a mathematical seepage model of the deep coal reservoir re-construction zone is established, and the gas production of the deep coal reservoir re-construction zone is obtained by solving the mathematical seepage model. The mathematical seepage model of the re-construction zone includes the free gas equation and the desorbed gas equation:
[0143] 3.2.1) Based on the scope of the deep coal reservoir re-construction zone and the equivalent seepage parameters, the free gas equation in the seepage mathematical model of the re-construction zone is established:
[0144]
[0145] Where r is the position with seepage radius r in the gas reservoir; p fn is the pressure in the remodeling zone; ρ gsc is the density of the gas under standard conditions, in kg / m 3 ; r fn The elliptical flow range of the remodeling area is equivalent to the radius of the circular supply; h fn is the average height of multiple branch fractures, that is, k fn is the equivalent permeability of the branch fractures in the heavily remodeled area and the surrounding remodeled area; q dfn It is the desorption gas in the heavy reforming area; Q fngsc is the gas production in the heavy transformation area.
[0146] 3.2.2) Based on the scope of the deep coal reservoir re-construction zone and the equivalent seepage parameters, the desorption gas equation in the seepage mathematical model of the re-construction zone is established:
[0147]
[0148] In the formula, p cd is the critical desorption pressure, in MPa; V L is the Langmuir volume, in m 3 / m 3 ;p L is the Langmuir pressure, in MPa.
[0149] 3.2.3) Based on the free gas equation and desorption gas equation in the mathematical model of the reformed area and the nonlinear formula of pseudo-pressure and pseudo-time, the pressure is considered constant at each small time step, and the gas production Q of the reformed area is obtained. fngsc for:
[0150]
[0151] In the formula, ψ fn is the simulated pressure in the remodeling area; R fn is the seepage resistance term in the heavily transformed area; Q dfn is the desorption / diffusion term in the heavy reforming zone.
[0152] 3.3) Based on the scope of the weakly reformed zone of deep coal reservoirs and the equivalent seepage parameters, a mathematical model of the seepage in the weakly reformed zone of deep coal reservoirs is established, and the gas production in the weakly reformed zone of deep coal reservoirs is obtained by solving the mathematical model. The mathematical model of the seepage in the weakly reformed zone includes the free gas equation and the desorbed gas equation:
[0153] 3.3.1) Based on the scope of the weakly reformed zone of deep coal reservoirs and the equivalent seepage parameters, the free gas equation in the seepage mathematical model of the weakly reformed zone is established:
[0154]
[0155] In the formula, k mf is the equivalent permeability of the shear fracture in the weak transformation area and the surrounding transformation area; p mf is the pressure in the weak transformation zone; r mf The elliptical flow range of the weak transformation zone is equivalent to the radius of the circular supply; q dmf is the desorbed gas in the weak reformation zone; h mf is the average height of multiple shear joints; Q mfgsc is the gas production in the weakly reformed area.
[0156] 3.3.2) Based on the scope of the weakly reformed zone of deep coal reservoirs and the equivalent seepage parameters, the desorption gas equation in the seepage mathematical model of the weakly reformed zone is established:
[0157]
[0158] 3.3.3) Based on the free gas equation and desorption gas equation in the mathematical model of the weak reformed zone and the nonlinear formula of pseudo-pressure and pseudo-time, the gas production Q of the weak reformed zone is obtained. mfgsc for:
[0159]
[0160] In the formula, ψ mf is the simulated pressure in the weak transformation zone; R mf is the seepage resistance term in the weakly transformed area; Q dmf is the desorption-diffusion term in the weakly reformed zone.
[0161] 3.4) Based on the range of the matrix area of the deep coal reservoir and the equivalent seepage parameters, a mathematical model of the seepage in the matrix area of the deep coal reservoir is established, and the gas production in the matrix area of the deep coal reservoir is obtained by solving the mathematical model. The mathematical model of the seepage in the matrix area includes the free gas equation and the desorbed gas equation:
[0162] 3.4.1) Based on the range of the matrix area of deep coal reservoirs and equivalent seepage parameters, the free gas equation in the seepage mathematical model of the matrix area is established:
[0163]
[0164] In the formula, p m is the matrix pressure; q dm is the desorbed gas in the matrix area; Q mgsc is the gas production in the matrix area.
[0165] 3.4.2) Based on the range of the matrix area of deep coal reservoirs and the equivalent seepage parameters, the desorption gas equation in the seepage mathematical model of the matrix area is established:
[0166]
[0167] 3.4.3) Based on the free gas equation and desorption gas equation in the matrix zone seepage mathematical model and the nonlinear formula of pseudo-pressure and pseudo-time, the gas production Q of the matrix zone is obtained. mgsc for:
[0168]
[0169] In the formula, R m is the seepage resistance term in the matrix area; Q dm is the desorption diffusion term in the matrix region.
[0170] 4) According to the gas production of the four areas of the deep coal reservoir, the gas production of a single fracturing section in the deep coal reservoir, i.e., the multi-zone coupled capacity, is obtained, and then the gas production of the multi-section fracturing horizontal well in the deep coal reservoir is obtained, specifically:
[0171] 4.1) According to the equivalent seepage resistance method, the four regions are connected in series and the pressure at the interface is equal. The gas production equations of the four regions in the deep coal reservoir are combined to obtain:
[0172]
[0173] 4.2) Based on the above-mentioned combined gas production equation (26), the gas production of a single fracturing stage in a deep coal reservoir is obtained as the multi-zone coupled production capacity:
[0174]
[0175] 4.3) Without considering the interference between fractures, the gas production Q of a single fracturing stage in a deep coal reservoir is gsc and the number of fracturing stages NF, the gas production NQ of multi-stage fracturing horizontal wells in deep coal reservoirs is obtained gsc for:
[0176]
[0177] Among them, NF is the number of fracturing stages.
[0178] Taking a deep coalbed methane well in China as an example, the daily production of the horizontal well is calculated using the fracturing reservoir parameters, gas PVT parameters, multi-stage fracturing horizontal well parameters and four regional parameters equivalent to the complex fracture network distribution after fracturing shown in Table 1 below to illustrate the effectiveness of the method of the present invention. It should be noted that this embodiment uses a horizontal well as an example, but the method of the present invention can be applied to each well type of horizontal well, vertical well, and directional well:
[0179] Table 1: Gas PVT parameters, horizontal well and fracture reservoir parameters
[0180]
[0181]
[0182] Using the data in Table 1 above, the time step is set to 1 day, the total time is 360 days, and the daily production of the horizontal well is calculated. The comparison results of the daily production of the horizontal well calculated by the present invention and the actual daily production are as follows: Figure 5 As shown. Figure 5 It can be seen that the calculated results are highly consistent with the actual data, which verifies the accuracy of the method of the present invention.
[0183] Example 2
[0184] This embodiment provides a multi-zone coupled productivity evaluation system for deep coalbed methane reservoirs, including:
[0185] The four-zone physical model building module is used to build a four-zone physical model of deep coal reservoirs based on the fracture network characteristics and fluid seepage characteristics of deep coal reservoirs after fracturing, including the fracture zone, heavily reformed zone, weakly reformed zone and matrix zone;
[0186] A parameter calculation module, for calculating the range and equivalent seepage parameters of four areas of the deep coal reservoir based on the four-area physical model of the deep coal reservoir and the fracture network parameters of the deep coal reservoir after fracturing;
[0187] A seepage mathematical model building module is used to build a seepage mathematical model of the four areas of the deep coal reservoir based on the ranges and equivalent seepage parameters of the four areas of the deep coal reservoir, and solve to obtain the gas production of the four areas of the deep coal reservoir;
[0188] The gas production solving module is used to obtain the gas production of a single fracturing section in the deep coal reservoir as the multi-zone coupled production capacity according to the gas production of four areas in the deep coal reservoir.
[0189] The system provided in this embodiment is used to execute the above-mentioned method embodiments. Please refer to the above-mentioned embodiments for specific processes and detailed contents, which will not be repeated here.
[0190] Example 3
[0191] This embodiment provides a processing device corresponding to the deep coalbed methane reservoir multi-zone coupling production capacity evaluation method provided in Example 1. The processing device can be suitable for client processing devices, such as mobile phones, laptops, tablet computers, desktop computers, etc., to execute the method of Example 1.
[0192] The processing device includes a processor, a memory, a communication interface and a bus, and the processor, the memory and the communication interface are connected through the bus to complete mutual communication. The memory stores a computer program that can be run on the processing device, and the processing device executes the deep coalbed methane reservoir multi-zone coupling capacity evaluation method provided in this embodiment 1 when running the computer program.
[0193] In some implementations, the memory may be a high-speed random access memory (RAM), and may also include a non-volatile memory, such as at least one disk memory.
[0194] In some other implementations, the processor may be a central processing unit (CPU), a digital signal processor (DSP), or other general-purpose processors of various types, which are not limited herein.
[0195] In addition, the logic instructions in the above-mentioned memory can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.
[0196] Those skilled in the art will understand that the structure of the above-mentioned computing device is only a partial structure related to the solution of the present invention, and does not constitute a limitation on the computing device to which the solution of the present invention is applied. The specific computing device may include more or fewer components, or combine certain components, or have a different arrangement of components.
[0197] Example 4
[0198] This embodiment provides a computer program product corresponding to the multi-zone coupled capacity evaluation method for deep coalbed methane reservoirs provided in Example 1. The computer program product may include a computer-readable storage medium on which computer-readable program instructions for executing the multi-zone coupled capacity evaluation method for deep coalbed methane reservoirs described in Example 1 are loaded.
[0199] Computer readable storage media can be tangible devices that hold and store instructions used by instruction execution devices. Computer readable storage media can be, for example, but not limited to, electronic storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any combination thereof.
[0200] The above embodiment provides a computer-readable storage medium, whose implementation principle and technical effect are similar to those of the above method embodiment, and will not be repeated here.
[0201] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.
[0202] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.
[0203] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.
[0204] The above embodiments are only used to illustrate the present invention, wherein the structure, connection mode and manufacturing process of each component may be changed. Any equivalent transformations and improvements based on the technical solution of the present invention should not be excluded from the protection scope of the present invention.
Claims
1. A method for evaluating the multi-zone coupling capacity of deep coalbed methane reservoirs, characterized in that: include: According to the fracture network characteristics and fluid seepage characteristics of deep coal reservoirs after fracturing, a four-zone physical model of deep coal reservoirs is established, including fracture zone, heavily reformed zone, weakly reformed zone and matrix zone. Based on the four-zone physical model of deep coal reservoirs and the fracture network parameters after fracturing, the range and equivalent seepage parameters of the four zones of deep coal reservoirs are calculated; Based on the range and equivalent seepage parameters of the four areas of deep coal reservoirs, the mathematical model of seepage in the four areas of deep coal reservoirs was established, and the gas production in the four areas of deep coal reservoirs was obtained by solving the model. According to the gas production of four areas in the deep coal reservoir, the gas production of a single fracturing stage in the deep coal reservoir is obtained as the multi-zone coupling capacity.
2. A method for evaluating the multi-zone coupling capacity of a deep coalbed methane reservoir according to claim 1, characterized in that: The fracture network characteristics refer to the fracture morphology and fracture parameters after fracturing of deep coal reservoirs. The fracture morphology is a four-level complex fracture network of "high conductivity main fracture + branch fracture + shear self-supporting fracture + cleat". The fracture parameters include the length, opening, height and conductivity of each level of fracture; The fracture zone is the high-conductivity main fracture area formed by fracturing near the wellbore, which is dominated by free gas and the gas flow follows Darcy's law; The heavily reformed area is the branch fracture filled with proppant and the reformed area around it, where free gas and desorbed gas coexist. The free gas follows Darcy's law, and the desorbed gas flows according to the "desorption-diffusion-seepage" law. The weakly stimulated area is the shear self-propping fractures and the surrounding stimulated areas far from the wellbore where proppant is difficult to enter, and there are free gas and desorbed gas; The matrix zone is the area not affected by the original reservoir fracturing, where free gas and desorbed gas coexist.
3. A method for evaluating the multi-zone coupling capacity of a deep coalbed methane reservoir as claimed in claim 2, characterized in that: The range of the fracture zone is the length, width and height of the high conductivity main fracture, and the equivalent seepage parameters of the fracture zone are the equivalent permeability and equivalent porosity of the high conductivity main fracture; The range of the matrix zone is determined according to the well control area, the equivalent permeability of the matrix zone is the permeability of the original reservoir, and the equivalent porosity of the matrix zone is the porosity of the original reservoir.
4. A method for evaluating the multi-zone coupling productivity of a deep coalbed methane reservoir as claimed in claim 2, characterized in that: There are several branch fractures and small flow areas in the surrounding cleats in the remodeling zone, which are equivalent to two-dimensional elliptical radial flow. The range of the remodeling zone is a two-dimensional ellipse with the two end points of the high-conductivity main fracture as the focus; The calculation process of equivalent seepage parameters in the remodeled area is as follows: Calculate the equivalent permeability of multiple branch fractures in the remodeled area; Based on the equivalent permeability of multiple branch fractures in the heavily remodeled area, the equivalent permeability of branch fractures in the heavily remodeled area and the surrounding remodeled area is calculated; Calculate the equivalent porosity of multiple branch fractures in the heavily reformed area; Based on the equivalent porosity of multiple branch fractures in the heavily reformed zone, the equivalent porosity of the heavily reformed zone is calculated.
5. A method for evaluating the multi-zone coupling productivity of deep coalbed methane reservoirs according to claim 4, characterized in that: The weakly reformed area is equivalent to an ellipse with the major axis endpoint of the heavily reformed area ellipse as the focus; The calculation process of equivalent seepage parameters in the weakly transformed area is as follows: Calculate the equivalent permeability of multiple shear joints in the weak transformation area; Based on the equivalent permeability of multiple shear joints in the weakly transformed area, the equivalent permeability of the shear joints in the weakly transformed area and the surrounding transformed areas is calculated; Calculate the equivalent porosity of multiple shear fractures in the weak transformation zone; Based on the equivalent porosity of multiple shear fractures in the weakly reformed zone, the equivalent porosity of the weakly reformed zone is calculated.
6. A method for evaluating the multi-zone coupling capacity of a deep coalbed methane reservoir according to claim 2, characterized in that: The mathematical model of seepage in the fracture zone is: In the formula, p F is the pressure in the fracture zone; k F is the equivalent permeability of the fracture zone; φ F is the porosity of the fracture zone; x F h is the half length of the main fracture with high conductivity; F is the height of the main fracture with high conductivity; Z is the gas compression factor; μ g is the gas viscosity; C r , C g are the compressibility coefficients of pores and gas, respectively; S g is gas saturation; t is time; p e is the original reservoir pressure; p wf is the bottom hole flowing pressure; Q gsc is the gas production in the fracture zone; T is the reservoir temperature; p sc is the pressure under standard conditions; Z sc is the deviation factor under standard conditions; T sc is the temperature under standard conditions; The mathematical model of seepage in the remodeling area includes the free gas equation and the desorbed gas equation. The free gas equation is: Where r is the position with seepage radius r in the gas reservoir; p fn is the pressure in the remodeling zone; ρ gsc is the density of the gas under standard conditions; r fn The elliptical flow range of the remodeling area is equivalent to the radius of the circular supply; φ fn is the equivalent porosity of the remodeled area; h fn is the average height of multiple branch fractures; k fn is the equivalent permeability of the branch fractures in the heavily remodeled area and the surrounding remodeled area; q dfn It is the desorption gas in the heavy reforming area; fn is the equivalent seepage radius of the two-dimensional ellipse equivalent to the remodeling area; The desorption gas equation in the mathematical model of seepage in the remodeling zone is: In the formula, p cd is the critical desorption pressure; V L is the Langmuir volume; p L is the Langmuir pressure; The mathematical model of seepage in the weakly reformed zone includes the free gas equation and the desorbed gas equation. The free gas equation is: In the formula, k mf is the equivalent permeability of the shear fracture in the weak transformation area and the surrounding transformation area; p mf is the pressure in the weak transformation zone; r mf The elliptical flow range of the weak transformation zone is equivalent to the radius of the circular supply; q dmf It is the desorption gas in the weak reformation zone; ξ mf is the equivalent seepage radius of the weak transformation zone; φ mf is the equivalent porosity of the weakly reformed zone; h mf is the average height of multiple shear joints; The desorption gas equation in the seepage mathematical model of the weak reformed area is: The mathematical model of seepage in the matrix zone includes the free gas equation and the desorption gas equation. The free gas equation is: In the formula, p m is the matrix pressure; q dm is the desorbed gas in the matrix area; ξ m is the equivalent seepage radius of the matrix area; k m is the equivalent permeability of the matrix area; φ m is the equivalent porosity of the matrix region; The desorption gas equation in the matrix zone seepage mathematical model is:
7. A method for evaluating the multi-zone coupling productivity of a deep coalbed methane reservoir according to claim 6, characterized in that: The multi-zone coupling capacity is: Among them, ψ F is the pseudo pressure in the fracture zone; ψ wf is the pseudo pressure corresponding to the bottom hole flowing pressure; R F is the seepage resistance in the fracture area; R fn is the seepage resistance term in the heavily transformed area; Q dfn is the desorption diffusion term in the heavy reforming zone; R mf is the seepage resistance term in the weakly transformed area; Q dmf is the desorption diffusion term in the weak reformed zone; R m is the seepage resistance term in the matrix area; Q dm is the desorption diffusion term in the matrix region.
8. A multi-zone coupled productivity evaluation system for deep coalbed methane reservoirs, characterized in that: include: The four-zone physical model building module is used to build a four-zone physical model of deep coal reservoirs based on the fracture network characteristics and fluid seepage characteristics of deep coal reservoirs after fracturing, including the fracture zone, heavily reformed zone, weakly reformed zone and matrix zone; A parameter calculation module, which is used to calculate the range and equivalent seepage parameters of four areas of the deep coal reservoir based on the four-area physical model of the deep coal reservoir and the fracture network parameters of the deep coal reservoir after fracturing; A seepage mathematical model building module is used to build a seepage mathematical model of the four areas of the deep coal reservoir based on the ranges and equivalent seepage parameters of the four areas of the deep coal reservoir, and to solve and obtain the gas production of the four areas of the deep coal reservoir; The gas production calculation module is used to obtain the gas production of a single fracturing section in the deep coal reservoir according to the gas production of four areas in the deep coal reservoir, and then obtain the gas production of multi-section fracturing horizontal wells in the deep coal reservoir.
9. A processing device, characterized in that: It includes computer program instructions, wherein the computer program instructions, when executed by a processing device, are used to implement the steps corresponding to the multi-zone coupled capacity evaluation method for deep coalbed methane reservoirs described in any one of claims 1-7.
10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer program instructions, wherein the computer program instructions, when executed by a processor, are used to implement steps corresponding to the multi-zone coupled capacity evaluation method for deep coalbed methane reservoirs described in any one of claims 1-7.
Citation Information
Patent Citations
Fractured tight gas reservoir gas well productivity evaluation method and three-dimensional seepage experiment device
CN115680643A
Shale gas / coal-bed gas well productivity evaluation method and system and electronic equipment
CN115860266A
Pressure dynamic analysis method for three-dimensional fracturing fracture network of deep coal-bed gas well
CN118940657A
Method for defining regions in reservoir simulation
US20090254324A1