A method for calculating temporary plugging and turning cracking pressure and cracking time of shale gas horizontal well

Abstract

The present application provides a kind of shale gas horizontal well temporary plugging diversion initiation pressure and initiation time calculation method.The calculation method includes: obtaining engineering and geological parameters;According to the engineering and geological parameters, the initial net pressure in the crack before temporary plugging is calculated;Using the modified two-dimensional displacement discontinuity method to establish the induced stress field calculation model around the cluster fracture, the hydraulic fracture width and the induced stress field around the cluster fracture are solved;According to the cluster fracture induced stress, combined with the original stress field, the cluster fracture tensile initiation pressure calculation model is established, the natural fracture tensile initiation pressure and the initiation time of temporary plugging diversion when shale gas horizontal well temporary plugging diversion fracturing can be solved.The present application considers the influence of filtration loss of fracturing fluid on initiation pressure, the calculation result is more accurate, can quickly calculate the horizontal well temporary plugging diversion initiation pressure and initiation time, can provide theoretical basis for shale gas horizontal well temporary plugging diversion fracturing optimization design.

Description

Technical Field

[0001] This invention relates to the field of unconventional oil and gas production enhancement technology, specifically to a method for calculating the initiation pressure of temporary plugging and fracturing in shale gas horizontal wells and a method for calculating the initiation time of temporary plugging and fracturing in shale gas horizontal wells. Background Technology

[0002] Shale gas is a vast unconventional natural gas resource, primarily found in shale reservoirs. Due to the typically low porosity and permeability of shale reservoirs, oil and gas migration is highly unfavorable, leading to significant challenges in shale gas extraction. Therefore, without effective production enhancement measures, natural shale gas production is extremely low, making it virtually uncommercially viable. Compared to marine shale in the United States, Chinese shale reservoirs are characterized by complex geological structures, strong heterogeneity, and significant stress differences, making fracture network creation extremely difficult. Due to the inherent brittleness of shale, the formation typically contains numerous unactivated natural fractures, requiring temporary plugging and diversion to activate these fractures and create a fracture network. Temporary plugging and diversion fracturing involves using low-viscosity slickwater pumped into horizontal wells to inject a temporary plugging agent, combined with high-flow-rate, low-sand-ratio temporary plugging and diversion fracturing technology. This effectively activates natural fractures, forming a high-conductivity fracture network system.

[0003] During temporary plugging and diversion fracturing operations in shale gas horizontal wells, natural fractures are initiated by fluid pressure within the fractures and hydraulically induced stress, resulting in a fracture network. Therefore, calculating the fracture initiation pressure and determining the initiation time of temporary plugging and diversion fracturing are crucial for determining whether a fracture network will form and whether temporary plugging and diversion fracturing can improve production. Thus, calculating the initiation time of temporary plugging and diversion fracturing in shale gas horizontal wells not only provides a theoretical reference for fracture network formation but also offers important guidance for field operations.

[0004] However, currently, there is a lack of theoretical research on the calculation of initiation pressure and initiation time for temporary plugging and diversion in shale gas horizontal wells. For example, patent document CN107609258A, published on January 19, 2018, entitled "A Method for Calculating Initiation Pressure of Diversion Fractures in Repeated Shale Fracturing," describes a method for calculating the initiation pressure of diversion fractures in repeated shale gas fracturing. Although this method uses the two-dimensional displacement discontinuity method to discretize the repeated shale gas fracturing fractures and obtain the induced stress of the diversion fractures to calculate the initiation pressure, it does not consider the influence of fracture height on the induced stress. Patent document CN106869892A, also published on January 19, 2018, entitled "A Method for Judging Temporary Pluging Initiation in Repeatedly Fracturing Wells," describes a method for judging temporary plugging initiation in repeated fracturing wells. This method uses an analytical solution method to calculate the induced stress at each point of the hydraulic fracture, but the calculation accuracy is low. Because shale is brittle and typically contains numerous natural fractures, these fractures can be activated during fracturing. The inflow of fracturing fluid into these activated fractures results in significant fluid loss. Therefore, the impact of fracturing fluid loss cannot be ignored. Neither of the methods described above considers the effect of fracturing fluid loss on the initiation pressure, and neither method can determine whether a directional fracture has initiated or the initiation time of such fractures. Summary of the Invention

[0005] The purpose of this invention is to address at least one of the aforementioned deficiencies in the prior art. For example, this invention provides a method for calculating the fracturing pressure in shale gas horizontal wells by temporary plugging and diversion, overcoming the defect that conventional fracturing pressure calculation methods do not consider the impact of fracturing fluid loss on the fracturing pressure.

[0006] To achieve the above objectives, the present invention provides a method for calculating the initiation pressure of temporary plugging and diversion in shale gas horizontal wells. The method for calculating the initiation pressure includes the following steps: S1, obtaining engineering and geological parameters, including maximum horizontal principal stress, minimum horizontal principal stress, Young's modulus, Poisson's ratio, tensile strength of natural fractures, approach angle of natural fractures, filtration coefficient, hydraulic fracture length, hydraulic fracture height, fracturing fluid viscosity, and pump injection rate.

[0007] S2. Calculate the initial net pressure inside the joint before temporary plugging based on engineering and geological parameters;

[0008] S3. Using the modified two-dimensional displacement discontinuity method, establish a calculation model of the induced stress field around the clustered fractures, and solve for the hydraulic fracture width and the induced stress field around the clustered fractures. The calculation model of the induced stress field around the clustered fractures includes the stress balance equations of the fracture elements, which are shown below:

[0009]

[0010]

[0011] Among them, (σ n ) i Let be the normal stress of element i in the local coordinate system, in Pa; Let m be the tangential strain of element j in the local coordinate system; Let m be the normal strain of element j in the local coordinate system; (A nt ) ij Let be the normal stress component caused by the tangential displacement of element j on element i, where i and j take values ​​from 1 to N; (A nn ) ij Let d be the normal stress component caused by the discontinuity of normal displacement of element j on element i, where i and j take values ​​from 1 to N; ij Let m be the distance between crack element i and crack element j; h be the distance between them. f G represents the height of the hydraulic fracture, in meters (m). ij is the crack height correction factor, which is dimensionless; i and j are any two discrete crack elements.

[0012] S4. Based on the induced stress of clustered fractures and combined with the original geostress field, establish a calculation model for the tensile initiation pressure of clustered fractures, and calculate the tensile initiation pressure of natural fractures through a numerical calculation process.

[0013] In an exemplary embodiment of the method for calculating the initiation pressure of temporary plugging and redirection in shale gas horizontal wells according to the present invention, in step S3, the induced stress field calculation model around the clustered fractures may further include induced stress field solution equations, which are shown below:

[0014]

[0015]

[0016]

[0017] Where, Δσ xx Let σ be the formation-induced stress component in the x-direction, Pa; Δσ yy Let σ be the formation-induced stress component in the y-direction, Pa; Δσ xy Let n be the formation-induced stress component in the xy direction, Pa; j The cosine of the angle between the global z-axis and the local z-axis of the j-element is dimensionless; j ζ is the cosine of the angle between the global x-axis and the local ξ-axis of element j, and is dimensionless; x and y represent the global coordinates, and ζ and ξ represent the local coordinates corresponding to the x and y coordinates, respectively; F kLet G be the partial derivative equation of the Papkovitch function, k∈{3~6}; G is the shear modulus, Pa.

[0018] In an exemplary embodiment of the method for calculating the initiation pressure of temporary plugging and redirection in shale gas horizontal wells according to the present invention, the calculation model for the tensile initiation pressure of clustered fractures in step S4 may include the calculation equation for the net pressure of fluid within the fracture and the calculation equation for the initiation pressure.

[0019] Specifically, the equation for calculating the net pressure of the fluid within the slit is as follows:

[0020]

[0021] Where p is the net pressure of the fluid inside the fracture, in Pa; y is the coordinate value along the fracture length, in meters; μ is the fluid viscosity, in mPa·s; w f Let m be the crack aperture and q be the crack opening. L t represents the fracturing fluid loss rate, in m / s; t represents time, in s.

[0022] The equation for calculating the initiation pressure is shown below:

[0023]

[0024] in, Tensile initiation pressure of natural fracture, MPa; σ n The normal stress at the natural crack surface is expressed in MPa. The normal stress of the natural fracture element at the intersection of the natural fracture and the hydraulic fracture is given in MPa and S. t The tensile strength of the natural crack is expressed in MPa.

[0025] In an exemplary embodiment of the method for calculating the initiation pressure of temporary plugging and redirection in shale gas horizontal wells according to the present invention, step S4 may include the following steps: S41, determining the fracturing fluid loss rate, and combining it with the hydraulic fracture width determined in step S3, coupling and solving the calculation equation for the net fluid pressure inside the fracture to obtain the net fluid pressure inside the fracture; S42, determining whether the net fluid pressure inside the fracture has converged, if yes, calculating the pumped fluid volume, if no, returning the net fluid pressure inside the fracture obtained in sub-step 41 to step S3 for iterative calculation until the net fluid pressure inside the fracture converges; S43, determining whether the flow rate at the fracture opening has converged, if no, changing the net fluid pressure inside the fracture and returning to step S3 for iterative calculation until the flow rate at the fracture opening converges; S44, determining the normal stress on the natural fracture surface, combining it with the induced stress of the natural fracture element obtained in step S3, substituting it into the initiation pressure calculation equation to obtain the tensile initiation pressure of the natural fracture.

[0026] In an exemplary embodiment of the method for calculating the initial fracture initiation pressure of a shale gas horizontal well under temporary plugging and redirection according to the present invention, the calculation equation for the initial net pressure within the fracture can be as follows:

[0027]

[0028] Where p0 is the initial net pressure of the fluid inside the crevice, in Pa; h f L0 is the hydraulic fracture height (m); μ is the fracturing fluid viscosity (mPa·s); L0 is the initial hydraulic fracture length (m); ν is Poisson's ratio (dimensionless); E is Young's modulus (Pa); q is the pumping flow rate (m³). 3 / s.

[0029] In an exemplary embodiment of the method for calculating the initiation pressure of temporary plugging and redirection in shale gas horizontal wells according to the present invention, the implicit backward difference method can be used to couple and solve the calculation equation of net fluid pressure within the fracture. The one-dimensional three-point difference format of the calculation equation of net fluid pressure within the fracture is shown below:

[0030]

[0031]

[0032]

[0033]

[0034]

[0035] In an exemplary embodiment of the method for calculating the initiation pressure of temporary plugging and redirection in shale gas horizontal wells according to the present invention, the normal stress on the natural fracture element at the intersection of the hydraulic fracture and the natural fracture can be:

[0036]

[0037] Where, σ H The maximum horizontal principal stress in place is σ, MPa; h θ represents the minimum horizontal principal stress in situ, in MPa; θ is the angle between the hydraulic fracture and the natural fracture, in degrees.

[0038] In an exemplary embodiment of the method for calculating the initiation pressure of temporary plugging and redirection in shale gas horizontal wells according to the present invention, in sub-step S43, the net pressure of the fluid inside the fracture can be changed by increasing Δp, where Δp is the pressure increment.

[0039] Another aspect of the present invention provides a method for calculating the initiation time of temporary plugging and reversing in shale gas horizontal wells. The method includes the following steps: determining the tensile initiation pressure of natural fractures using the method described above for calculating the initiation pressure of temporary plugging and reversing in shale gas horizontal wells; determining whether natural fractures have initiated; if not, changing the pumping time and recalculating the tensile initiation pressure of natural fractures; if so, determining the current pumping time as the initiation time of natural fractures; the expression for determining the initiation time of natural fractures is: Where p is the fluid pressure at the intersection of the hydraulic fracture and the natural fracture, in MPa; The tensile initiation pressure of a natural fracture is MPa.

[0040] In an exemplary embodiment of the method for calculating the initiation time of temporary plugging and fracturing in a shale gas horizontal well according to the present invention, the pumping time can be changed by increasing Δt, where Δt is the pumping time increment.

[0041] Compared with the prior art, the beneficial effects of the present invention may include at least one of the following:

[0042] (1) The present invention uses a modified two-dimensional displacement discontinuity method to calculate the induced stress field generated by clustered cracks. This modified two-dimensional displacement discontinuity method, by correcting the crack height, can not only consider the influence of the limited crack height on the induced stress, but also has a faster calculation speed.

[0043] (2) In the process of calculating the initiation pressure and initiation time, this invention takes into account the influence of the filtration loss of fracturing fluid on the net pressure of the fluid in the fracture during the fracturing process, and establishes a tensile initiation pressure calculation model for natural fractures. This model can calculate the tensile initiation pressure of any intersecting natural fractures in the clustered fractures. According to the initiation judgment expression of natural fractures, it can be determined whether the natural fracture has started to crack, and it can also calculate the initiation time of natural fractures after temporary plugging.

[0044] (3) The present invention is accurate in calculation and can provide guidance for the optimization design of temporary plugging, diversion and fracturing of shale gas horizontal wells and on-site construction. Attached Figure Description

[0045] The above and other objects and / or features of the present invention will become clearer from the following description taken in conjunction with the accompanying drawings, in which:

[0046] Figure 1 The diagram shows a temporary plugging and redirection fracture initiation model, which is an exemplary embodiment of the method for calculating the initiation pressure of temporary plugging and redirection fractures in a shale gas horizontal well according to the present invention.

[0047] Figure 2 The diagram shows a flowchart of a numerical model solution for the fracturing pressure in an exemplary embodiment of a method for calculating the fracturing initiation time of a shale gas horizontal well under temporary plugging and diversion according to the present invention.

[0048] Figure 3 A schematic diagram of the XY section of a hydraulic fracture discrete element is shown as an exemplary embodiment of a method for calculating the initiation pressure of temporary plugging and deflection in a shale gas horizontal well according to the present invention.

[0049] Figure 4 The diagram shows the initiation pressure at various points along the fracture length direction in an exemplary embodiment of the method for calculating the initiation time of temporary plugging and redirection in a shale gas horizontal well according to the present invention.

[0050] Figure 5 A diagram showing the natural fracture initiation time is provided as an exemplary embodiment of the method for calculating the fracture initiation time of a shale gas horizontal well under temporary plugging and diversion according to the present invention. Detailed Implementation

[0051] The following text will describe in detail the calculation method of the shale gas horizontal well temporary plugging and fracturing initiation pressure and fracturing time according to the present invention, with reference to specific embodiments.

[0052] The inventors discovered through research that most existing numerical calculation methods for initiation pressure and / or initiation time have the following defects: ① The two-dimensional displacement discontinuity method is used to determine the induced stress, but the influence of the finite height of the fracture on the induced stress is not considered. Therefore, there is a certain error between the calculated induced stress field and the actual induced stress field. This error will inevitably affect the subsequent calculation of initiation pressure and initiation time; ② When establishing a calculation model for the tensile initiation pressure of natural fractures, conventional calculation methods do not consider the influence of the filtration of fracturing fluid during the fracturing process on the net pressure of the fluid in the fracture. However, in the actual fracturing process, the filtration of fracturing fluid often has a significant impact on the pressure distribution in the fracture.

[0053] To address the aforementioned issues, this application presents a method for calculating fracturing initiation pressure and time that considers fracturing fluid loss. This method uses a modified two-dimensional displacement discontinuity method (DDM) to calculate the induced stress field generated by clustered fractures. This modified DDM, by correcting for fracture height, not only considers the influence of finite fracture height on induced stress but also boasts a faster computation speed. Furthermore, considering the impact of fracturing fluid loss during fracturing on the net fluid pressure within the fracture, a tensile initiation pressure calculation model for natural fractures is established. This model can calculate the tensile initiation pressure of any intersecting natural fractures within a clustered fracture system. Based on the natural fracture initiation judgment expression, it can determine whether a natural fracture has initiated and calculate the initiation time of natural fractures after temporary plugging. The calculation method of this invention yields accurate results, providing theoretical basis and practical guidance for the optimized design and field construction of temporary plugging and redirection fracturing in shale gas horizontal wells. It also provides a theoretical reference for the formation of fracture networks in temporary plugging and redirection fracturing in shale gas horizontal wells.

[0054] To achieve the above objectives, the present invention provides a method for calculating the fracturing initiation pressure of temporary plugging and diversion in shale gas horizontal wells.

[0055] In an exemplary embodiment of the method for calculating the initiation pressure of temporary plugging and reversing fracturing in a shale gas horizontal well according to the present invention, the method includes the following steps:

[0056] Step S1: Obtain engineering and geological parameters, including maximum horizontal principal stress, minimum horizontal principal stress, Young's modulus, Poisson's ratio, tensile strength of natural fractures, approach angle of natural fractures, filtration coefficient, hydraulic fracture length, hydraulic fracture height, fracturing fluid viscosity, and pumping flow rate.

[0057] Step S2: Calculate the initial net pressure inside the joint before temporary plugging based on engineering and geological parameters.

[0058] Specifically, the equation for calculating the initial net pressure within the joint is as follows:

[0059]

[0060] In equation (1), p0 is the initial net pressure of the fluid inside the gap, in Pa; h f L0 is the hydraulic fracture height (m); μ is the fracturing fluid viscosity (mPa·s); L0 is the initial hydraulic fracture length (m); ν is Poisson's ratio (dimensionless); E is Young's modulus (Pa); q is the pumping flow rate (m³). 3 / s.

[0061] Step S3: Use the modified two-dimensional displacement discontinuity method (DDM) to establish a calculation model of the induced stress field around the clustered fractures, and solve for the hydraulic fracture width and the induced stress field around the clustered fractures.

[0062] Specifically, the calculation model of the induced stress field around the clustered cracks includes the stress balance equation of the crack element and the solution equation of the induced stress field.

[0063] Specifically, the stress balance equations are as follows:

[0064]

[0065] In the stress balance equation, (G) ij The seam height correction factor is expressed as follows:

[0066]

[0067] In equation (3), (σ n ) i Let be the normal stress of element i in the local coordinate system, in Pa; Let m be the tangential strain of element j in the local coordinate system; Let m be the normal strain of element j in the local coordinate system; (A nt ) ij Let be the normal stress component caused by the tangential displacement of element j on element i, where i and j take values ​​from 1 to N; (A nn ) ij Let d be the normal stress component caused by the discontinuity of normal displacement of element j on element i, where i and j take values ​​from 1 to N; ij Let m be the distance between crack element i and crack element j; h be the distance between them. f G represents the height of the hydraulic fracture, in meters (m). ij is the crack height correction factor, which is dimensionless; i and j are any two discrete crack elements.

[0068] Furthermore, the equations for solving the induced stress field are as follows:

[0069]

[0070]

[0071]

[0072] In equations (4) to (6), Δσ xx Let σ be the formation-induced stress component in the x-direction, Pa; Δσ yy Let σ be the formation-induced stress component in the y-direction, Pa; Δσ xy Let n be the formation-induced stress component in the xy direction, Pa; j The cosine of the angle between the global z-axis and the local z-axis of the j-element is dimensionless; j ζ is the cosine of the angle between the global x-axis and the local ξ-axis of element j, and is dimensionless; x and y represent the global coordinates, and ζ and ξ represent the local coordinates corresponding to the x and y coordinates, respectively; F k Let G be the partial derivative equation of the Papkovitch function, k∈{3~6}; G is the shear modulus, Pa.

[0073] Step S4: Based on the induced stress of clustered fractures and combined with the original geostress field, establish a calculation model for the tensile initiation pressure of clustered fractures, and calculate the tensile initiation pressure of natural fractures through a numerical calculation process.

[0074] The calculation model for the tensile initiation pressure of clustered fractures includes the calculation equations for the net pressure of fluid within the fracture and the calculation equation for the initiation pressure; the calculation equations for the net pressure of fluid within the fracture include the equations for the pressure drop within the hydraulic fracture and the equations for the continuity of fluid within the fracture.

[0075] Specifically, in temporary plugging and redirection fracturing, the fracturing fluid is generally considered to be an incompressible Newtonian fluid; therefore, the pressure drop equation within the hydraulic fracture can be expressed as:

[0076]

[0077] In equation (7), p is the fluid pressure inside the crack, Pa; y is the coordinate of the crack length direction (y-axis direction), m; μ is the liquid viscosity, mPa·s; w f Let m be the crack aperture.

[0078] Furthermore, during fracturing, fracturing fluid loss is usually present. Therefore, the volume of fracturing fluid injected into the fracture within a certain time is equal to the sum of the dynamic volume of the fracture and the volume of fracturing fluid lost. Thus, the fluid continuity equation within the fracture is:

[0079]

[0080] The filtration velocity equation is as follows:

[0081]

[0082] In equation (9), C L The filtration loss coefficient is , m / s 0.5 τ is the initial filtration time, in seconds.

[0083] When calculating the pressure inside the crack, the pressure drop equation (7) and the continuity equation (8) are first combined to obtain the net pressure calculation equation for the fluid inside the crack, as shown below:

[0084]

[0085] The calculation model for the initiation pressure is established, and its formula is shown below:

[0086]

[0087] In equation (11), The initiation pressure of a natural fracture, MPa; σ n The normal stress at the natural crack surface is expressed in MPa. The normal stress of the natural fracture element at the intersection of the natural fracture and the hydraulic fracture is given in MPa and S. t The tensile strength of the natural crack is expressed in MPa.

[0088] Figure 1 This is a physical model diagram of the forces acting at the intersection of a natural fissure and a hydraulic fissure. It should be noted that... Figure 1 In this diagram, A represents a hydraulic fracture, B represents a natural fracture, and C represents a temporary plug. When pumping is performed after temporary plugging, the net pressure of the fluid within the fracture will increase. When a hydraulic fracture is temporarily plugged, the natural fracture intersecting the hydraulic fracture experiences the following forces during pumping: Figure 1 As shown.

[0089] In this embodiment, the implicit backward difference method can be used to couple and solve the equation for calculating the net pressure of the fluid within the slit. That is, equation (10) can be simplified to the standard one-dimensional three-point difference scheme shown below by using the finite difference method and the implicit backward difference:

[0090]

[0091]

[0092]

[0093]

[0094]

[0095] Of course, the present invention is not limited to this, and other finite element methods can also be used to solve the equation for calculating the net pressure of fluid in the crevice.

[0096] In this embodiment, step S4, the numerical calculation process for the tensile initiation pressure of natural fractures may include the following sub-steps:

[0097] Sub-step S41: Determine the fracturing fluid loss rate, combined with the hydraulic fracture width determined in step S3 (i.e., the normal strain of element j in the local coordinate system in formula (2)). The net pressure of the fluid inside the joint is obtained by coupling the equations for calculating the net pressure of the fluid inside the joint.

[0098] Sub-step S42: Determine whether the net pressure of the fluid inside the crevice has converged. If yes, calculate the volume of the pumped liquid. If no, return the net pressure of the fluid inside the crevice obtained in sub-step 41 to step S3 for iterative calculation until the net pressure of the fluid inside the crevice converges.

[0099] Sub-step S43: Determine whether the flow rate at the seam converges by setting a minimum error value. When the difference between the pumped flow rate and the fluid volume and filtration loss in the seam is less than the error value, the flow rate has converged. If not, change the net pressure of the fluid in the seam and return to step S3 for iterative calculation until the flow rate at the seam converges.

[0100] For example, the net pressure of the fluid inside the gap can be changed by adding an increment Δp within the gap. Here, Δp is the pressure increment. It should be noted that, to accelerate convergence, Δp changes with each cycle.

[0101] Sub-step S44: Determine the normal stress on the natural crack surface, combine it with the induced stress of the natural crack element obtained in step S3, and substitute it into the crack initiation pressure calculation equation (i.e. formula (11)) to obtain the tensile crack initiation pressure of the natural crack.

[0102] For example, at the intersection of a hydraulic fracture and a natural fracture, the normal stress on the natural fracture element can be:

[0103]

[0104] Where, σ H The maximum horizontal principal stress in place is σ, MPa; h θ represents the minimum horizontal principal stress in situ, in MPa; θ is the angle between the hydraulic fracture and the natural fracture, in degrees.

[0105] Of course, the present invention is not limited to this, and other numerical calculation processes can also be used to solve for the crack initiation pressure in the crack.

[0106] Another aspect of the present invention provides a method for calculating the fracturing initiation time of temporary plugging and diversion in shale gas horizontal wells.

[0107] In an exemplary embodiment of the calculation method for the fracturing initiation time of a shale gas horizontal well based on temporary plugging and diversion, the method includes the following steps:

[0108] Step S1: Obtain engineering and geological parameters, including maximum horizontal principal stress, minimum horizontal principal stress, Young's modulus, Poisson's ratio, tensile strength of natural fractures, approach angle of natural fractures, filtration coefficient, hydraulic fracture length, hydraulic fracture height, fracturing fluid viscosity, and pumping flow rate.

[0109] Step S2: Calculate the initial net pressure inside the joint before temporary plugging based on engineering and geological parameters.

[0110] Specifically, the equation for calculating the initial net pressure within the joint is as follows:

[0111]

[0112] In the formula, p0 is the initial net pressure of the fluid inside the gap, in Pa; h f L0 is the hydraulic fracture height (m); μ is the fracturing fluid viscosity (mPa·s); L0 is the initial hydraulic fracture length (m); ν is Poisson's ratio (dimensionless); E is Young's modulus (Pa); q is the pumping flow rate (m³). 3 / s.

[0113] Step S3: Use the modified two-dimensional displacement discontinuity method (DDM) to establish a calculation model of the induced stress field around the clustered fractures, and solve for the hydraulic fracture width and the induced stress field around the clustered fractures.

[0114] Specifically, the calculation model of the induced stress field around the clustered cracks includes the stress balance equation of the crack element and the solution equation of the induced stress field.

[0115] Specifically, the stress balance equations are as follows:

[0116]

[0117] In the stress balance equation, (G) ij The seam height correction factor is expressed as follows:

[0118]

[0119] In the formula, (σ n ) i Let be the normal stress of element i in the local coordinate system, in Pa; Let m be the tangential strain of element j in the local coordinate system; Let m be the normal strain of element j in the local coordinate system; (A nt ) ij Let be the normal stress component caused by the tangential displacement of element j on element i, where i and j take values ​​from 1 to N; (A nn ) ij Let d be the normal stress component caused by the discontinuity of normal displacement of element j on element i, where i and j take values ​​from 1 to N; ij Let m be the distance between crack element i and crack element j; h be the distance between them. f G represents the height of the hydraulic fracture, in meters (m). ij is the crack height correction factor, which is dimensionless; i and j are any two discrete crack elements.

[0120] The equations for solving the induced stress field are shown below:

[0121]

[0122]

[0123]

[0124] In the formula, Δσ xx Let σ be the formation induced stress component in the x-direction, Pa; Δσ yy Let σ be the formation-induced stress component in the y-direction, Pa; Δσ xyLet n be the formation induced stress component in the xy direction, Pa; j The cosine of the angle between the global z-axis and the j-element local ζ-axis, dimensionless; j The cosine of the angle between the global x-axis and the local ξ-axis of element j is dimensionless; ζ and ξ represent the coordinates corresponding to the x and y coordinates, respectively. The two coordinate systems are transformed using the displacement discontinuity method. F k Let G be the partial derivative equation of the Papkovitch function, k∈{3~6}; G is the shear modulus, Pa.

[0125] Step S4: Based on the induced stress of clustered fractures and combined with the original geostress field, establish a calculation model for the tensile initiation pressure of clustered fractures, and calculate the tensile initiation pressure of natural fractures through a numerical calculation process.

[0126] The calculation model for tensile initiation pressure of clustered fractures includes the calculation equations for net fluid pressure within the fracture and the calculation equations for initiation pressure.

[0127] Specifically, the equation for calculating the net pressure of the fluid inside the crevice is as follows:

[0128]

[0129] The filtration velocity equation is as follows:

[0130] The implicit backward difference method can be used to couple and solve the equation for calculating the net pressure of the fluid within the fracture. The simplified standard one-dimensional three-point difference scheme is as follows:

[0131]

[0132]

[0133]

[0134]

[0135]

[0136] The calculation formula for the initiation pressure of natural fractures is shown below:

[0137]

[0138] In the formula, The initiation pressure of a natural fracture, MPa; σ n The normal stress at the natural crack surface is expressed in MPa. The normal stress of the natural fracture element at the intersection of the natural fracture and the hydraulic fracture is given in MPa and S. t The tensile strength of the natural crack is expressed in MPa.

[0139] In this embodiment, the numerical calculation process for the tensile initiation pressure of natural fractures may include the following sub-steps:

[0140] Sub-step S41: Determine the fracturing fluid loss rate, and in conjunction with the hydraulic fracture width determined in step S3, perform a coupled solution to the calculation equation for the net pressure of the fluid inside the fracture to obtain the net pressure of the fluid inside the fracture.

[0141] Sub-step S42: Determine whether the net pressure of the fluid inside the crevice has converged. If yes, calculate the volume of the pumped liquid. If no, return the net pressure of the fluid inside the crevice obtained in sub-step 41 to step S3 for iterative calculation until the net pressure of the fluid inside the crevice converges.

[0142] Sub-step S43: Determine whether the flow rate at the seam converges. If not, change the net pressure of the fluid inside the seam and return to step S3 for iterative calculation until the flow rate at the seam converges.

[0143] For example, the net pressure of the fluid inside the gap can be changed by increasing or decreasing Δp, where Δp is the pressure increment.

[0144] Sub-step S44: Determine the normal stress on the natural crack surface, combine it with the induced stress of the natural crack element obtained in step S3, and substitute it into the crack initiation pressure calculation equation (i.e. formula (11)) to obtain the tensile crack initiation pressure of the natural crack.

[0145] For example, at the intersection of a hydraulic fracture and a natural fracture, the normal stress on the natural fracture element can be:

[0146]

[0147] Where, σ H The maximum horizontal principal stress in place is σ, MPa; h θ represents the minimum horizontal principal stress in situ, in MPa; θ is the angle between the hydraulic fracture and the natural fracture, in degrees.

[0148] Step S5: Based on the tensile initiation pressure of the natural fracture obtained in step S4, determine whether the natural fracture has started to crack. If not, change the pumping time and recalculate the tensile initiation pressure of the natural fracture. If so, determine the current pumping time as the initiation time of the natural fracture.

[0149] For example, the initiation judgment expression for natural cracks can be used to determine whether a natural crack has started. The initiation judgment expression for natural cracks can be:

[0150] Where p is the fluid pressure at the intersection of the hydraulic fracture and the natural fracture, in MPa; The tensile initiation pressure of a natural fracture is MPa.

[0151] For example, the pumping time can be changed by increasing Δt, where Δt is the increment of the pumping time. It should be noted that the value of Δt depends on the specific calculation example. The smaller the value of Δt, the longer the calculation time and the more accurate the crack initiation time. The larger the value of Δt, the shorter the calculation time. The range of Δt is not explained here.

[0152] Based on the above calculation flow and process, the flowchart for solving the numerical model of crack initiation pressure is shown below. Figure 2 As shown.

[0153] To better understand the present invention, the following description, in conjunction with the accompanying drawings and examples, further clarifies the content of the present invention, but the content of the present invention is not limited to the following embodiments.

[0154] The geological engineering parameters of a certain shale gas horizontal well are shown in Table 1. Based on the data in Table 1, a method for calculating the initiation time of temporary plugging and deflection in a shale gas horizontal well is used to calculate the example. The specific calculation steps are as follows.

[0155] Step 1: Obtain engineering and geological parameters and input them into the program. Engineering and geological parameters include maximum horizontal principal stress, minimum horizontal principal stress, Young's modulus, Poisson's ratio, tensile strength of natural fractures, natural fracture approach angle, filtration coefficient, hydraulic fracture length, hydraulic fracture height, fracturing fluid viscosity, and pumping rate.

[0156] Table 1 Example parameters for crack initiation time calculation

[0157] parameter numerical values unit <![CDATA[Maximum horizontal principal stress σ H > 110.34 MPa <![CDATA[Minimum horizontal principal stress σ h > 93.67 MPa Young's modulus E 32.58 GPa Poisson's ratio v 0.272 Dimensionless <![CDATA[Tensile strength S of natural fractures t > 0.5 MPa Natural crack approach angle 60 ° <![CDATA[Filter loss coefficient C L > <![CDATA[2.1×10 -4 ]]> <![CDATA[m / s 0.5 <!-- 11 -->]]> <![CDATA[Fracture length L f > 200 m <![CDATA[Fracture height h f > 60 m fracturing fluid viscosity μ 10 mPa·s Pump displacement 12 <![CDATA[m 3 / min]]>

[0158] Step 2: Calculate the initial net pressure within the fracture before temporary plugging based on engineering and geological parameters, and use the modified two-dimensional displacement discontinuity method to solve the induced stress field around the clustered fractures.

[0159] Specifically, the calculation steps for the initial net pressure within the joint and the induced stress field include:

[0160] ① Based on the relevant parameters input in step one, the program automatically divides the mesh area and automatically discretizes the hydraulic fractures into several fracture elements. For example... Figure 3 The image shown is a cross-sectional view of a discrete element in a hydraulic fracture. It should be noted that... Figure 3 The shaded area in the diagram represents the crack element mesh automatically generated by the program. N+1 represents the (N+1)th cell, Ds represents the tangential relative displacement, and Dn represents the normal relative displacement. The initial net pressure of the fluid inside the crack is calculated using equation (1).

[0161] ②The width of the hydraulic crack can be obtained by combining the calculated net pressure of the fluid inside the crack with equations (2) to (3);

[0162] ③The induced stress field around the crack can be calculated based on equations (4) to (6).

[0163] Step 3: Calculate the hydraulic crack width (that is, the width in formula (2)). The fluid pressure calculation model inside the fracture is coupled and solved, and the fracture initiation pressure is calculated.

[0164] like Figure 2 As shown, the specific calculation process for the initiation pressure is as follows:

[0165] ① Calculate the fracturing fluid loss rate according to equation (9), and combine it with the fracture width in step two into equations (12) to (16) for coupled solution. Then, combine the calculated fracturing fluid loss rate with the hydraulic fracture width into the fracturing pressure calculation model for coupled solution to obtain the fluid pressure inside the fracture. Then, determine whether the fluid pressure inside the fracture converges. If the pressure does not converge, update the pressure distribution inside the fracture and iterate until the pressure inside the fracture converges.

[0166] ② Calculate the volume of the pumped liquid and determine whether the flow rate at the joint converges. If it does not converge, change the pressure distribution and the new net pressure of the fluid in the joint, and repeat the above calculation steps until the flow rate at the joint converges.

[0167] In the aforementioned fracture initiation pressure calculation model, the normal stress on the natural fracture element in the stress initiation model at the intersection of hydraulic fracture and natural fracture is:

[0168]

[0169] In the formula: σ H The maximum horizontal principal stress in place is σ, MPa; h θ represents the minimum horizontal principal stress in situ, in MPa; θ is the angle between the hydraulic fracture and the natural fracture, in degrees.

[0170] ③ Calculate the normal stress on the surface of the natural crack according to equation (17), and combine it with the induced stress of the natural crack element obtained in step 2, and substitute it into equation (16) to calculate the crack initiation pressure of the natural crack.

[0171] Step 4: Calculate the crack initiation time.

[0172] Specifically, the method for calculating crack initiation time can include the following sub-steps:

[0173] ① According to the crack initiation judgment expression (19), determine whether the natural cracks at each point have started to crack. If the natural cracks have not started to crack, increase the pumping time and use the calculated crack pressure as the initial fluid pressure in step three, and repeat steps two to three.

[0174] ②If a natural crack initiates, output the initiation time and terminate the program.

[0175] Based on the above calculation process and results, a fracture initiation pressure diagram at any location on the hydraulic fracture is plotted (e.g., Figure 4 As shown in the figure), and the graph showing the changes in initiation pressure and fluid pressure within the natural fracture (as shown in the figure). Figure 5 (As shown). From Figure 4 and Figure 5 It can be seen that due to stress concentration, the initiation pressure near the fracture tip drops sharply. After temporary plugging, fracturing fluid is pumped in, and the fluid pressure increases sharply in a short time. When the fluid pressure exceeds the natural fracture initiation pressure, the fracture begins to initiate. In this example, the time from temporary plugging to fracture initiation is about 6.3 minutes.

[0176] Although the present invention has been described above in conjunction with exemplary embodiments and accompanying drawings, those skilled in the art should understand that various modifications can be made to the above embodiments without departing from the spirit and scope of the claims.

Claims

1. A method for calculating the initiation pressure of temporary plugging and fracturing in a shale gas horizontal well, characterized in that, The method for calculating the initiation pressure includes the following steps: S1. Obtain engineering and geological parameters, including maximum horizontal principal stress, minimum horizontal principal stress, Young's modulus, Poisson's ratio, tensile strength of natural fractures, approach angle of natural fractures, filtration coefficient, hydraulic fracture length, hydraulic fracture height, fracturing fluid viscosity, and pump injection rate. S2. Calculate the initial net pressure inside the joint before temporary plugging based on engineering and geological parameters; S3. Using the modified two-dimensional displacement discontinuity method, establish a calculation model of the induced stress field around the clustered fractures, and solve for the hydraulic fracture width and the induced stress field around the clustered fractures. The calculation model of the induced stress field around the clustered fractures includes the stress balance equations of the fracture elements, which are shown below: Among them, (σ n ) i Let be the normal stress of element i in the local coordinate system, in Pa; Let m be the tangential strain of element j in the local coordinate system; Let m be the normal strain of element j in the local coordinate system; (A nt ) ij Let be the normal stress component caused by the tangential displacement of element j on element i, where i and j take values ​​from 1 to N; (A nn ) ij Let d be the normal stress component caused by the discontinuity of normal displacement of element j on element i, where i and j take values ​​from 1 to N; ij Let m be the distance between crack element i and crack element j; h be the distance between them. f G represents the height of the hydraulic fracture, in meters (m). ij is the crack height correction factor, which is dimensionless; i and j are any two discrete crack elements. S4. Based on the induced stress of clustered fractures and combined with the original geostress field, establish a calculation model for the tensile initiation pressure of clustered fractures, and calculate the tensile initiation pressure of natural fractures through a numerical calculation process.

2. The method for calculating the initiation pressure of temporary plugging and fracturing in shale gas horizontal wells according to claim 1, characterized in that, In step S3, the induced stress field calculation model around the clustered cracks also includes the induced stress field solution equation, which is shown below: Where, Δσ xx Let σ be the formation-induced stress component in the x-direction, Pa; Δσ yy Let σ be the formation-induced stress component in the y-direction, Pa; Δσ xy Let n be the formation-induced stress component in the xy direction, Pa; j The cosine of the angle between the global z-axis and the local z-axis of the j-element is dimensionless; j ζ is the cosine of the angle between the global x-axis and the local ξ-axis of element j, and is dimensionless; x and y represent the global coordinates, and ζ and ξ represent the local coordinates corresponding to the x and y coordinates, respectively; F k Let G be the partial derivative equation of the Papkovitch function, k∈{3~6}; G is the shear modulus, Pa.

3. The method for calculating the initiation pressure of temporary plugging and fracturing in shale gas horizontal wells according to claim 2, characterized in that, The tensile initiation pressure calculation model for clustered fractures in step S4 includes the calculation equation for the net fluid pressure within the fracture and the calculation equation for the initiation pressure. The calculation equation for the net fluid pressure within the fracture is as follows: Where p is the net pressure of the fluid inside the fracture, in Pa; y is the coordinate value along the fracture length, in meters; μ is the fluid viscosity, in mPa·s; w f Let m be the crack aperture and q be the crack opening. L The fracturing fluid loss rate is m / s; t is time, s. The equation for calculating the initiation pressure is as follows: in, Tensile initiation pressure of natural fracture, MPa; σ n The normal stress at the natural crack surface is expressed in MPa. The normal stress of the natural fracture element at the intersection of the natural fracture and the hydraulic fracture is given in MPa and S. t The tensile strength of the natural crack is expressed in MPa.

4. The method for calculating the initiation pressure of temporary plugging and fracturing in a shale gas horizontal well according to claim 3, characterized in that, Step S4 includes the following sub-steps: S41. Determine the fracturing fluid loss rate, and in conjunction with the hydraulic fracture width determined in step S3, perform a coupled solution to the calculation equation for the net pressure of the fluid inside the fracture to obtain the net pressure of the fluid inside the fracture. S42. Determine whether the net pressure of the fluid inside the crevice has converged. If yes, calculate the volume of the pumped liquid. If no, return the net pressure of the fluid inside the crevice obtained in sub-step 41 to step S3 for iterative calculation until the net pressure of the fluid inside the crevice converges. S43. Determine whether the flow rate at the seam converges by setting a minimum error value for the flow rate at the seam. When the difference between the pumped flow rate and the fluid volume and filtration loss in the seam is less than the error value, the flow rate has converged. If not, change the net pressure of the fluid in the seam and return to step S3 for iterative calculation until the flow rate at the seam converges. S44. Determine the normal stress on the natural fracture surface, and combine it with the induced stress of the natural fracture element obtained in step S3. Substitute it into the fracture initiation pressure calculation equation to obtain the tensile fracture initiation pressure of the natural fracture.

5. The method for calculating the initiation pressure of temporary plugging and fracturing in a shale gas horizontal well according to claim 4, characterized in that, The equation for calculating the initial net pressure within the joint is as follows: Where p0 is the initial net pressure of the fluid inside the crevice, in Pa; h f L0 is the hydraulic fracture height (m); μ is the fracturing fluid viscosity (mPa·s); L0 is the initial hydraulic fracture length (m); ν is Poisson's ratio (dimensionless); E is Young's modulus (Pa); q is the pumping flow rate (m³). 3 / s.

6. The method for calculating the initiation pressure of temporary plugging and fracturing in a shale gas horizontal well according to claim 4, characterized in that, In sub-step S41, the implicit backward difference method is used to couple and solve the equation for calculating the net pressure of the fluid inside the fracture. The one-dimensional three-point difference scheme of the equation for calculating the net pressure of the fluid inside the fracture is shown below:

7. The method for calculating the initiation pressure of temporary plugging and fracturing in a shale gas horizontal well according to claim 4, characterized in that, At the intersection of hydraulic fractures and natural fractures, the normal stress on the natural fracture element is: Where, σ H The maximum horizontal principal stress in place is σ, MPa; h θ represents the minimum horizontal principal stress in situ, in MPa; θ is the angle between the hydraulic fracture and the natural fracture, in degrees.

8. The method for calculating the initiation pressure of temporary plugging and fracturing in a shale gas horizontal well according to claim 4, characterized in that, In sub-step S43, the net pressure of the fluid inside the gap is changed by increasing Δp, where Δp is the pressure increment.

9. A method for calculating the initiation time of temporary plugging and fracturing in a shale gas horizontal well, characterized in that, The method for calculating the crack initiation time includes the following steps: The tensile fracture initiation pressure of natural fractures is determined using the calculation method for the temporary plugging and deflection fracture initiation pressure of shale gas horizontal wells as described in any one of claims 1 to 8. Determine whether a natural fracture has initiated. If not, change the pumping time and recalculate the tensile initiation pressure of the natural fracture. If so, determine the current pumping time as the initiation time of the natural fracture. The expression for judging the initiation of natural cracks is: Where p is the fluid pressure at the intersection of the hydraulic fracture and the natural fracture, in MPa; The tensile initiation pressure of a natural fracture, in MPa.

10. The method for calculating the initiation time of temporary plugging and fracturing in a shale gas horizontal well according to claim 9, characterized in that, The injection time is changed by increasing Δt, where Δt is the injection time increment.

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