Method for calculating deformation and extension trajectory of main fracture and branch fracture of hydraulic fracturing

Abstract

The application discloses a kind of calculation method of hydraulic fracturing main fracture wall surface bifurcation crack formation and expansion, including establishing horizontal well model;The initial main crack in model is discretized processing;According to actual fracturing construction scheme, the first fracturing is carried out to horizontal well in horizontal well model, the relative discontinuous displacement amount of discrete crack unit on main crack is calculated, wall surface one side normal displacement and tangential displacement, then the normal displacement and tangential displacement of the other side, main crack tip rupture condition are calculated;Again, it is judged whether the crack wall surface of discrete crack unit has bifurcation point;When there is no bifurcation point, continue to carry out fracturing and calculate the initial crack initiation angle of bifurcation crack;When there is bifurcation crack, continue to fracture until main crack reaches predetermined length;The discontinuous displacement amount obtained by the last fracturing is the deformation amount of hydraulic fracturing main crack and bifurcation crack;According to the expansion length and angle of main crack tip and bifurcation crack tip, the trajectory of hydraulic fracturing main crack and bifurcation crack is obtained.

Description

Technical Field

[0001] This invention belongs to the field of hydraulic fracturing technology for oil and gas field development, specifically relating to a calculation method for the formation and propagation of bifurcated fractures on the wall of the main hydraulic fracturing fracture. Background Technology

[0002] Hydraulic fracturing is a crucial method for improving oil and gas recovery in unconventional reservoirs. The main idea is to inject high-pressure fluid into the formation after perforation in the wellbore, causing the reservoir rock to fracture under the pressure of the fluid and forming macroscopic fracture surfaces. This provides a flow channel for reservoir oil and gas to enter the wellbore. Since fractures in fracturing operations are often tens or even hundreds of meters long, research on the initiation and propagation trajectories of long-distance fractures in hydraulic fracturing primarily relies on numerical simulations.

[0003] The initiation and propagation mechanisms of hydraulic fracturing fractures are complex, involving multiple disciplines such as elastoplastic mechanics, fracture mechanics, seepage mechanics, heat transfer, and dynamics. The timing of fracture initiation and the trajectory of propagation are simultaneously influenced by both the fracturing operation plan and complex geological conditions. The fracturing operation plan includes factors such as fracturing fluid type, proppant strength, fracturing perforation azimuth, well spacing, segment spacing, cluster spacing, and fracturing flow rate. Formation conditions include the reservoir rock mineral composition and mechanical properties, rock mass structure (faults, joints, microfractures), and the magnitude and direction of in-situ stress.

[0004] To simplify calculations, current mathematical models for hydraulic fracturing fracture propagation assume that the reservoir rock is linearly elastic, fracture initiation and propagation occur at the fracture tip, are primarily influenced by the fracture tip stress intensity factor, and fracture bifurcation mainly arises from intersections with other natural fractures or occurs at the fracture tip. In reality, hydraulic fractures often do not propagate linearly due to local stress fields. The above assumptions do not account for the stress concentration that occurs at fracture surface bends when hydraulic fractures propagate non-linearly, leading to new fracture points and fracture bifurcation. Therefore, the simulations based on these assumptions cannot accurately reflect the actual fracture propagation process. Thus, a mathematical simulation method is urgently needed to quantitatively and accurately predict the formation of bifurcated fractures on the fracture surface and the mutual interference between bifurcated fractures and the main fracture during propagation. Summary of the Invention

[0005] To address the problems existing in the prior art, the present invention aims to provide a calculation method for the formation and propagation of bifurcation cracks on the wall of the main fracture in hydraulic fracturing. The present invention can quantitatively and accurately predict the formation of bifurcation cracks on the fracture surface, as well as the mutual interference between bifurcation cracks and the main fracture during the propagation process.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] The calculation method for the deformation and propagation trajectory of the main fracture and bifurcation fractures in hydraulic fracturing includes the following steps:

[0008] Step 1: Establish a horizontal well model, which includes the horizontal well and the initial main fracture of the perforated section;

[0009] Step 2: Discretize the initial main fracture in the horizontal well model by dividing it into discrete fracture elements;

[0010] Step 3: According to the actual fracturing construction plan, perform the first fracturing on the horizontal well in the horizontal well model. Calculate the relative discontinuity displacement, unilateral normal displacement, and tangential displacement of the discrete fracture elements on the main fracture using the pre-established rock stress and deformation calculation model of the main fracture wall. Based on the relative discontinuity displacement, unilateral normal displacement, and tangential displacement of the discrete fracture elements, calculate the normal and tangential displacements on the other side of the discrete fracture elements on the main fracture. The relative discontinuity displacement includes the relative normal and tangential discontinuity displacements of the discrete fracture elements. Calculate the fracture condition at the tip of the main fracture using the relative discontinuity displacement: determine whether the tip of the main fracture element has cracked. If the tip of the main fracture element cracks, calculate the extension length and extension angle of the discrete fracture element tip. Use the normal and tangential displacements of the discrete fracture elements to determine whether the fracture wall of the discrete fracture element is fractured. A bifurcation point is present, indicating the formation of a bifurcation crack. The initial initiation angle of the bifurcation crack is calculated. If no bifurcation point is present, fracturing continues until a bifurcation point appears on the crack wall of the discrete fracture element, and the initial initiation angle of the bifurcation crack is calculated. Once a bifurcation crack appears, fracturing continues until the main fracture reaches a predetermined length. During each fracturing operation, the relative discontinuous displacement of the discrete fracture elements of the main fracture and the bifurcation crack is calculated using a pre-established hydraulic fracturing main fracture and bifurcation crack deformation calculation model. This relative discontinuous displacement is used to calculate the fracture condition at the tips of the main fracture and the bifurcation crack until the main fracture reaches a predetermined length, at which point fracturing stops. The discontinuous displacement of the discrete fracture element obtained from the last fracturing operation is used as the deformation of the hydraulic fracturing main fracture and the bifurcation crack. The trajectories of the hydraulic fracturing main fracture and the bifurcation crack are obtained based on the extension length and extension angle of the tips of the main fracture and the bifurcation crack calculated after each fracturing operation.

[0011] Preferably, the calculation model for the stress-deformation of the rock on the main crack wall is as follows:

[0012]

[0013] In the formula, i,j represents the index of the discrete crack element, i,j=1,2,…,N_HF, and N_HF represents the total number of discrete crack elements on the main crack. Gij This is a correction factor; All are stress boundary influence coefficients, which are related to the coordinates of the discretized discrete crack elements. They represent the force exerted by the j-th discrete crack element on the i-th discrete crack element, and the unit is Pa. These are the tangential and normal relative discontinuities of the j-th discrete crack element on the main crack, respectively. These are the tangential stress and normal stress experienced by the i-th discrete crack element, respectively, in Pa.

[0014] Preferably, the matrix form of the calculation model for the stress-deformation of the rock on the main crack wall is as follows:

[0015]

[0016] In the formula,

[0017]

[0018]

[0019]

[0020] In the formula, D s j D represents the tangential relative discontinuity displacement of the j-th discrete crack element on the main crack, 1≤j≤N; n j σ represents the relative discontinuous normal displacement of the j-th discrete crack element on the main crack, 1≤j≤N; h σ represents the minimum horizontal principal stress; H p represents the maximum horizontal principal stress. fj This indicates that there is pressure within the j-th discrete crack element; θ j This represents the angle between the local coordinate system and the global coordinate system of the j-th discrete crack element.

[0021]

[0022] In the formula, + and - represent the two walls of the main crack, respectively. and These represent the normal and tangential displacements on one side of the wall of the j-th discrete crack element, respectively; and These represent the tangential and normal displacements on the other side of the wall of the j-th discrete crack element, respectively.

[0023] Preferably, the following formula is used to determine whether cracking has occurred at the tip of the main crack unit:

[0024]

[0025] When the above formula is true, it indicates that cracking has occurred at the tip of the main crack unit; otherwise, it indicates that cracking has not occurred at the tip of the main crack unit.

[0026] In the formula, K IC Rock fracture toughness, in MPa·m 1 / 2 θ0 is the turning angle at the crack tip when it breaks, in degrees.

[0027]

[0028] In the formula, K I K II These represent the stress intensity factors of rocks under type I and type II fracture, respectively, with units of Pa·m. 1 / 2 ;D n D s The normal and tangential relative discontinuous displacements of discrete fracture elements on the main fracture; E is the Young's modulus of the rock; v is the Poisson's ratio of the rock; a is the half-fracture length.

[0029] The propagation length ΔL at the tip of the i-th discrete crack element i Calculated using the following formula:

[0030]

[0031] In the formula: This represents the combined stress intensity at the crack tip when the discrete crack element first becomes the crack tip, expressed in Pa·m. 1 / 2 ;ΔL max This represents the maximum historical length of the crack tip, in meters; max{} is the maximum value function.

[0032] The propagation angle θ(K) at the tip of the i-th discrete crack element I ,K II Calculated using the following formula:

[0033]

[0034] Preferably, the process of determining whether there are bifurcation points on the crack wall of a discrete crack element using the normal and tangential displacements of the discrete crack element includes:

[0035] Calculate the tangential strain of the bending crack element surface, and then calculate the tangential stress of the crack element surface using the tangential strain. Using the tangential stress, determine whether tensile failure has occurred at the stress concentration point by the maximum tensile stress criterion. If tensile failure is determined to have occurred at the stress concentration point, it indicates that there is a bifurcation point on the crack wall of the discrete crack element; otherwise, there is no bifurcation point.

[0036] Preferred method: The tangential strain of the bending crack element surface is calculated based on the displacement gradient, where the tangential displacement gradient of the crack surface is equal to the tangential strain. The formula for calculating the tangential strain of the bending crack element surface is as follows:

[0037]

[0038]

[0039] Δs i =a i+1 cos(β i+1 -β i )+2a i +a i-1 cos(β i -β i-1 )

[0040] In the formula, a i This represents the half-slit length of the i-th crack element, in meters. This represents the tangential displacement of the (i+1)th element of the crack, in meters (m). β represents the tangential displacement of the (i-1)th element of the crack, in meters; i Δs represents the angle between the local coordinate system and the global coordinate system of the i-th crack element, in degrees. i The distance between the center points of the (i+1)th crack element and the (i-1)th crack element is expressed in meters; the ± symbol represents the upper and lower crack surfaces of the crack.

[0041] Preferably, the deformation calculation model for the main hydraulic fracturing fracture and the bifurcation fracture is as follows:

[0042]

[0043] In the formula, N_HF and N_branch are the number of discrete elements of the main crack and the bifurcation crack, respectively; These are the stress boundary influence coefficients, which are matrices of (N_branch+N_HF)×(N_branch+N_HF); G ij Correction factor to adjust for the effect of crack height on induced stress; Let N_branch be the relative displacement of the crack element in the sn coordinate system, which is a one-dimensional matrix of (N_branch+N_HF)×1.

[0044] σ s and σ n The following conditions must be met:

[0045]

[0046] In the formula, This represents the tangential stress experienced by the i-th discrete crack element; This represents the normal stress experienced by the i-th discrete crack element; This represents the tangential stress experienced by the i-th discrete crack element of the main crack; This represents the normal stress experienced by the discrete crack element on the i-th main crack; This represents the tangential stress experienced by the discrete crack element on the i-th bifurcated crack; This represents the normal stress experienced by the discrete crack element on the i-th bifurcation crack.

[0047] This invention also provides a system for calculating the deformation and propagation trajectory of the main fracture and bifurcation fractures in hydraulic fracturing, including:

[0048] Modeling module: Establishes a horizontal well model, which includes the horizontal well and the initial main fracture of the perforated section;

[0049] Discrete module; The initial main fracture in the horizontal well model is discretized and divided into discrete fracture elements;

[0050] The simulation module is used to perform the first fracturing of a horizontal well in a horizontal well model according to the actual fracturing construction plan. It calculates the relative discontinuity displacement, unilateral normal displacement, and tangential displacement of discrete fracture elements on the main fracture using a pre-established rock stress-deformation calculation model of the main fracture wall. Based on these displacements, it calculates the normal and tangential displacements on the other side of the discrete fracture elements on the main fracture. The relative discontinuity displacements include both the normal and tangential relative discontinuity displacements of the discrete fracture elements. It also calculates the fracture condition at the tip of the main fracture using these relative discontinuity displacements: determining whether cracking has occurred at the tip of the main fracture element; if cracking occurs, calculating the extension length and angle of the discrete fracture element tip; and using the normal and tangential displacements of the discrete fracture elements to determine the fracture wall condition of the discrete fracture elements. If a bifurcation point exists, it indicates the formation of a bifurcation crack, and the initial initiation angle of the bifurcation crack is calculated. If no bifurcation point exists, fracturing continues until a bifurcation point appears on the crack wall of the discrete fracture element, and the initial initiation angle of the bifurcation crack is calculated. Once a bifurcation crack appears, fracturing continues until the main fracture reaches the predetermined length. During each fracturing operation, the relative discontinuous displacement of the discrete fracture elements of the main fracture and the bifurcation crack is calculated using a pre-established hydraulic fracturing main fracture and bifurcation crack deformation calculation model. The fracture condition at the tip of the main fracture and the bifurcation crack is calculated using this relative discontinuous displacement until the main fracture reaches the predetermined length, at which point fracturing stops. The discontinuous displacement of the discrete fracture element obtained from the last fracturing operation is used as the deformation of the hydraulic fracturing main fracture and the bifurcation crack. The trajectories of the hydraulic fracturing main fracture and the bifurcation crack are obtained based on the extension length and extension angle of the tip of the main fracture and the tip of the bifurcation crack calculated after each fracturing operation.

[0051] The present invention also provides an electronic device, comprising:

[0052] One or more processors;

[0053] A storage device on which one or more programs are stored;

[0054] When the one or more programs are executed by the one or more processors, the one or more processors implement the method for calculating the deformation and propagation trajectory of the main hydraulic fracturing fracture and bifurcation fracture as described above in this invention.

[0055] The present invention also provides a storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements the method for calculating the deformation and propagation trajectory of the main hydraulic fracturing fracture and bifurcation fracture as described above.

[0056] The present invention has the following beneficial effects:

[0057] This invention provides a method for calculating the deformation and propagation trajectory of the main fracture and bifurcation fractures in hydraulic fracturing. By introducing a displacement gradient into the fracture propagation calculation model, the displacement of discontinuous surfaces is transformed into tangential tensile stress. Based on the tensile strength of the rock, a mathematical calculation model for the fracturing and bifurcation of weak points on the fracture surface during dynamic fracture propagation is obtained. This invention solves the problem of handling the bifurcation of turning hydraulic fractures in previous simulations of hydraulic fracture propagation in continuous medium models. It can be used to simulate the propagation trajectory of bifurcation fractures interacting with the main fracture under different geological and construction environments, which is beneficial for guiding field construction. Attached Figure Description

[0058] The above and other objects, features, and advantages of embodiments of the present disclosure will become readily apparent from the following detailed description taken in conjunction with the accompanying drawings. Several embodiments of the present disclosure are illustrated in the drawings by way of example and not limitation, in which:

[0059] Figure 1 This is a flowchart of a method for calculating the deformation and propagation trajectory of the main and bifurcation fractures in hydraulic fracturing, as provided in an embodiment of the present invention.

[0060] Figure 2 The initial crack element in this embodiment of the invention is subjected to force.

[0061] Figure 3 This refers to the discrete crack displacement discontinuity element and coordinate system in the embodiments of the present invention;

[0062] Figure 4 This is a schematic diagram of the tangential discontinuous displacement nodes on the upper and lower surfaces of the crack element in an embodiment of the present invention;

[0063] Figure 5 This is a schematic diagram of the displacement gradient when the main crack changes direction in an embodiment of the present invention;

[0064] Figure 6 This is a diagram showing the bifurcation crack morphology and stress distribution in an embodiment of the present invention, wherein, Figure 6 (a) is a diagram showing the direction and propagation of the hydraulic fracture. Figure 6 (b) is a schematic diagram showing the bifurcation point on the crack surface. Figure 6 (c) is a schematic diagram showing the completion of hydraulic fractures and branch fracture propagation. Figure 6 (d) represents the shear stress distribution σ xy Schematic diagram;

[0065] Figure 7 This is a diagram showing the location of the main crack bifurcation point and the crack morphology under different intracrack pressures in an embodiment of the present invention;

[0066] Figure 8 These are diagrams showing the location of the main crack bifurcation point and the crack morphology under different minimum horizontal principal stresses in embodiments of the present invention.

[0067] Figure 9 The diagram shows the location of the main crack bifurcation point and the crack morphology for different rock tensile strengths in this embodiment of the invention. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0069] Figure 1 The flowchart illustrates a method for calculating the deformation and propagation trajectory of the main and bifurcation fractures in hydraulic fracturing, as provided in an embodiment of the present invention. The invention specifically includes the following steps:

[0070] Step 1: Establish a horizontal well model, which includes the horizontal well and the initial main fracture of the perforated section;

[0071] The initial main fracture length and location, and the angle between the initial main fracture and the geostress (e.g., [missing information]) are determined based on the actual fracturing construction plan. Figure 2 (As shown). This constitutes a post-perforation crack distribution model.

[0072] Step 2: Discretize the initial main fracture in the horizontal well model by dividing it into discrete fracture elements.

[0073] Specifically, the initial main fracture is discretized to obtain N_HF discrete fracture elements. The discrete fracture elements and coordinate system are as follows: Figure 3 As shown, the coordinates of the center point and the starting point of each discrete crack element are determined. Figure 3 In the middle, x i y i x j y j n represents the coordinates of the midpoints of discrete crack elements i and j in the xy coordinate system. i s i n j s j Represents the local coordinate systems of discrete crack elements i and j; β represents the relative discontinuous displacement of the crack surface of discrete crack element j in the sn coordinate system; i β j The angle between the local coordinate system and the global coordinate system xy of discrete crack elements i and j; For discrete crack element i in local coordinate system s j -n j The coordinates of the midpoint of the lower unit i.

[0074] Step 3: According to the actual fracturing construction plan, perform the first fracturing on the horizontal well in the pre-established horizontal well model. Calculate the relative discontinuity displacement, unilateral normal displacement, and tangential displacement of the discrete fracture elements on the main fracture using the pre-established rock stress and deformation calculation model of the main fracture wall. Based on the relative discontinuity displacement, unilateral normal displacement, and tangential displacement of the discrete fracture elements, calculate the normal and tangential displacements on the other side of the discrete fracture elements on the main fracture. The relative discontinuity displacement includes the relative normal and tangential discontinuity displacements of the discrete fracture elements. Calculate the fracture condition at the tip of the main fracture using the relative discontinuity displacement: determine whether cracking has occurred at the tip of the main fracture element. If cracking occurs at the tip of the main fracture element, calculate the extension length and extension angle of the discrete fracture element tip. Use the normal and tangential displacements of the discrete fracture elements to determine the fracture wall surface of the discrete fracture elements. If a bifurcation point exists, it indicates the formation of a bifurcation crack, and the initial initiation angle of the bifurcation crack is calculated. If no bifurcation point exists, fracturing continues until a bifurcation point appears on the crack wall of the discrete fracture element, and the initial initiation angle of the bifurcation crack is calculated. Once a bifurcation crack appears, fracturing continues until the main fracture reaches the predetermined length. During each fracturing operation, the relative discontinuous displacement of the discrete fracture elements of the main fracture and the bifurcation crack is calculated using a pre-established hydraulic fracturing main fracture and bifurcation crack deformation calculation model. The fracture condition at the tip of the main fracture and the bifurcation crack is calculated using this relative discontinuous displacement until the main fracture reaches the predetermined length, at which point fracturing stops. The discontinuous displacement of the discrete fracture element obtained from the last fracturing operation is used as the deformation of the hydraulic fracturing main fracture and the bifurcation crack. The trajectories of the hydraulic fracturing main fracture and the bifurcation crack are obtained based on the extension length and extension angle of the tip of the main fracture and the tip of the bifurcation crack calculated after each fracturing operation.

[0075] Specifically, step 3 includes the following parts:

[0076] (1) Establish a calculation model for the stress and deformation of the rock on the main crack wall, and calculate the normal displacement, tangential displacement, normal relative discontinuous displacement and tangential relative discontinuous displacement of the discrete crack element through the calculation model.

[0077] The calculation model for the stress-deformation of the rock on the main crack wall is as follows:

[0078]

[0079] In the formula, i,j represents the index of the discrete crack element, i,j=1,2,…,N_HF, and N_HF represents the total number of discrete crack elements on the main crack. G ij This is a correction factor; All are stress boundary influence coefficients, which are related to the coordinates of the discretized discrete crack elements. They represent the force exerted by the j-th discrete crack element on the i-th discrete crack element, and the unit is Pa. These are the tangential and normal relative discontinuities of the j-th discrete crack element on the main crack, respectively. These are the tangential stress and normal stress experienced by the i-th discrete crack element, respectively, in Pa.

[0080] Furthermore, the calculation equation for the stress-deformation of the rock at the main crack wall is expressed in matrix form:

[0081]

[0082] In the formula,

[0083]

[0084]

[0085]

[0086] In the formula, D s j D represents the tangential relative discontinuity displacement of the j-th discrete crack element on the main crack, 1≤j≤N; n j σ represents the relative discontinuous normal displacement of the j-th discrete crack element on the main crack, 1≤j≤N; h σ represents the minimum horizontal principal stress; H p represents the maximum horizontal principal stress. fj This indicates that there is pressure within the j-th discrete crack element; θ j This represents the angle between the local coordinate system and the global coordinate system of the j-th discrete crack element.

[0087] Solving the above system of equations yields the tangential relative discontinuity displacement D of any discrete crack element on the main crack. s j Normal relative discontinuity displacement D n j , Discrete crack element wall unilateral normal displacement and tangential displacement Figure 4 This diagram illustrates the tangential displacement of the upper and lower surfaces of a crack element. It also shows the tangential and normal displacements on the other side of the wall of a discrete crack element. The solution can be obtained using the following formula:

[0088]

[0089] In the formula, + and - represent the two walls of the main crack, respectively. and These represent the normal and tangential displacements on one side of the wall of the j-th discrete crack element, respectively; and These represent the tangential and normal displacements on the other side of the wall of the j-th discrete crack element, respectively.

[0090] (2) Calculate the fracture condition at the tip of the main crack:

[0091] The stress intensity factor at the tip of the main crack is solved from the relative discontinuous displacement of the discrete crack elements:

[0092]

[0093] The initiation condition at the tip of the main crack is:

[0094]

[0095] In the formula, K IC For rock fracture toughness, MPa·m 1 / 2 θ0 is the turning angle at the crack tip when it breaks, in units of 1.

[0096] The propagation angle at the tip of the main crack when it breaks is:

[0097]

[0098] In the formula, K I K II These represent the stress intensity factors of rocks under type I and type II fracture, respectively, with units of Pa·m. 1 / 2 .

[0099] The length of the main crack tip extension is:

[0100]

[0101] In the formula: This represents the combined stress intensity at the crack tip when the discrete crack element first becomes the crack tip, expressed in Pa·m. 1 / 2 ;ΔL max This represents the maximum historical length of the crack tip, expressed in meters (m).

[0102] (3) Calculate the bifurcation points on both sides of the main crack:

[0103] First, calculate the tangential strain of the bending crack element surface. Then, calculate the tangential stress of the crack element surface using the tangential strain. Finally, use the maximum tensile stress criterion to determine whether tensile failure has occurred at the stress concentration point.

[0104] ① Calculation of tangential strain on bending crack element surface based on displacement gradient

[0105] Hydraulic fractures in reservoirs do not propagate linearly; they can bend and deflect under localized geostress. The tangential displacement gradient of the fracture surface during this bending is as follows: Figure 5 As shown, with n + Taking the front side of the crack surface as an example, the inclination angles of the (i+1), i, and (i-1)th elements are different. When calculating the inclination angle of the i-th discrete element in n... + When representing the strain on the crack surface, the discontinuous displacements of the three elements need to be placed in s. i -n i In the coordinate system, the specific formula for calculating discontinuous displacement is as follows:

[0106]

[0107]

[0108] The tangential displacement gradient at the crack surface can then be expressed as follows:

[0109]

[0110]

[0111] Δs i =a i+1 cos(β i+1 -β i )+2a i +a i-1 cos(β i -β i-1 )

[0112] In the formula, a i This represents the half-slit length of the i-th crack element, in meters. This represents the tangential displacement of the (i+1)th element of the crack, in meters (m). β represents the tangential displacement of the (i-1)th element of the crack, in meters; i Δs represents the angle between the local coordinate system and the global coordinate system of the i-th crack element, in degrees. i The distance between the center points of the (i+1)th crack element and the (i-1)th crack element is expressed in meters; the "±" symbol represents the upper and lower crack surfaces.

[0113] Here, the tangential displacement gradient of the crack surface is equal to the tangential strain.

[0114] ② Calculate the tangential stress on the bending crack element surface

[0115] Based on Hooke's law for linear elastic bodies, the tangential stress is solved by the tangential strain of the crack element surface. The solution formula is as follows:

[0116]

[0117] In the formula, σ represents the tangential stress on the upper and lower surfaces of the crack, measured in Pa. n The normal stress received by the fracture element is expressed in Pa; E represents the Young's modulus of the rock, also expressed in Pa; and v represents the Poisson's ratio of the rock.

[0118] ③ Determining the location of bifurcation points on the wall surface of bifurcation cracks

[0119] When the tensile stress at the crack surface exceeds the tensile strength of the rock, the crack surface fails under tensile stress and develops bifurcated cracks. The critical criterion for tensile failure at the crack surface can be expressed as:

[0120] T (Max) >T0

[0121] In the formula, T0 is the tensile strength of the crack surface, and the unit is Pa.

[0122] T (Max) The maximum tensile stress on the crack, expressed in Pa, can be represented as follows:

[0123]

[0124] In the formula, σ n σ represents the normal stress component acting on the crack surface, in Pa. sn The shear stress component on the crack surface is expressed in Pa. The stress components on both sides of the crack surface are expressed in Pa.

[0125] ④ Calculate the initial initiation angle of the bifurcation crack.

[0126] When the stress at the weak point of the crack meets the initiation condition for a bifurcated crack, it is necessary to determine the initial initiation angle of the bifurcated crack on the main crack surface. The calculation formula is as follows:

[0127]

[0128] In the formula: θ1 represents the initiation angle of the bifurcation crack, in degrees; σ sn This indicates the magnitude of the shear stress component acting on the crack surface, expressed in Pa.

[0129] Note: When a bifurcated crack occurs on the wall of the main crack, the method for determining the subsequent propagation of the tip of the bifurcated crack is the same as that for the main crack.

[0130] (4) Establish a calculation model for the deformation of the main fracture and the bifurcation fracture in hydraulic fracturing, and calculate the relative discontinuous displacement of the discrete fracture elements of the main fracture and the discrete fracture elements of the bifurcation fracture.

[0131] The calculation model for the deformation of the main fracture and bifurcation fracture in hydraulic fracturing is as follows:

[0132]

[0133] In the formula, N_HF and N_branch are the number of discrete elements of the main crack and the bifurcation crack, respectively; These are the stress boundary influence coefficients, which are matrices of (N_branch+N_HF)×(N_branch+N_HF); G ij This is a correction factor to adjust the effect of crack height on induced stress. σ represents the relative displacement of the crack element in the sn coordinate system, and is a one-dimensional matrix of (N_branch + N_HF) × 1; s and σ n Conditions met:

[0134]

[0135] In the formula, This represents the tangential stress experienced by the i-th discrete crack element; This represents the normal stress experienced by the i-th discrete crack element; This represents the tangential stress experienced by the i-th discrete crack element of the main crack; This represents the normal stress experienced by the discrete crack element on the i-th main crack; This represents the tangential stress experienced by the discrete crack element on the i-th bifurcation crack; This represents the normal stress experienced by the discrete crack element on the i-th bifurcation crack.

[0136] Solving the above matrix equations yields the relative discontinuity displacement D of the main crack discrete crack element and the bifurcation crack discrete crack element. s D n .

[0137] (5) Determine the deformation and propagation trajectory of the main fracture and bifurcation fractures when hydraulic fracturing is completed.

[0138] The fracturing conditions at the tips of the main fracture and the bifurcation fracture are calculated by the relative discontinuous displacement of the discrete fracture elements of the main fracture and the discrete fracture elements of the bifurcation fracture until the main fracture reaches the predetermined length, at which point fracturing is stopped. The discontinuous displacement of the discrete fracture elements obtained from the last fracturing is used as the deformation of the main fracture and the bifurcation fracture in hydraulic fracturing. The trajectories of the main fracture and the bifurcation fracture are obtained based on the extension length and extension angle of the tips of the main fracture and the bifurcation fracture calculated after each fracturing.

[0139] Example

[0140] Taking the tight reservoirs of the Ordos Basin in my country as an example, the initial simulation parameters were determined by collecting field data and conducting laboratory experiments: the Young's modulus of the rock was 30 GPa, the Poisson's ratio was 0.25, and the fracture toughness was 2.5 MPa·m. 1 / 2 The maximum horizontal principal stress of the formation is 40 MPa, the minimum horizontal principal stress is 35 MPa, the perforation angle is 89.9°, and the pressure inside the fracture is 45 MPa.

[0141] ① Formation process of bifurcated cracks on the wall of the main crack

[0142] Figure 6 The figure illustrates the formation process and stress distribution of bifurcated cracks on the crack wall during the dynamic propagation of the main crack under the aforementioned initial conditions. The stress distribution in the figure represents the change in the induced stress field generated by the main crack, expressed in Pa. Figure 6 (a) During the propagation of the main crack, it tends to deflect towards the direction of the maximum principal stress, and no bifurcation point is generated on the crack surface at this time; Figure 6 (b) It shows that after the main crack tip extends for 6.5m, tensile failure occurs on the concave surface at the crack turning point, and branch cracks are generated. Figure 6 (c) When the branch cracks extend outward, they do not strictly extend along the direction of the maximum horizontal principal stress. This is because the induced stress generated by the hydraulic main cracks changes the direction of the local ground stress.

[0143] ② Location of the main crack bifurcation point and crack morphology under different intracranial pressures

[0144] Figure 7 This study investigates the bifurcation points and morphology of the main hydraulic fracture under varying intra-fracture pressures. During the implementation, initial parameters were kept constant, and intra-fracture pressures were varied to 43 MPa, 46 MPa, and 49 MPa to simulate bifurcation during the hydraulic fracture's turning and propagation process. As the intra-fracture pressure decreases, the main hydraulic fracture becomes increasingly prone to turning. The bifurcation points also become closer to the initial fracture tip and further away from the current fracture tip. When the intra-fracture pressure reaches a certain level, the branching fractures can alter the turning trend of the main hydraulic fracture.

[0145] ③ Location of main crack bifurcation point and crack morphology under different minimum horizontal principal stresses

[0146] Figure 8 The graph shows the location of the main fracture bifurcation point and the fracture morphology under different minimum horizontal principal stresses. Keeping the initial parameters constant, the minimum horizontal principal stresses were varied to 33 MPa, 35 MPa, and 37 MPa. As shown in the figure, with the increase of the minimum horizontal principal stress, the horizontal principal stress difference gradually decreases, the hydraulic main fracture direction becomes gentler, and the bifurcation point gets closer and closer to the tip of the hydraulic main fracture. Meanwhile, σ... hAt a pressure of 37 MPa, although damage points appeared on the hydraulic fracture surface, no branch fractures were formed. This is because the relatively large minimum horizontal principal stress at this time inhibited the further propagation of branch fractures.

[0147] ④ Location of the main crack bifurcation point and crack morphology for different rock tensile strengths

[0148] Figure 9 The figures show the bifurcation points and fracture morphology of the main fracture for different rock tensile strengths. Keeping other parameters constant, the tensile strengths of the reservoir rock were varied to 1.5 MPa, 2.5 MPa, and 3.5 MPa. As shown in the figures, with increasing rock tensile strength, the tensile failure point on the fracture surface gradually moves backward. In this case, when the perforation angle and the principal stress angle are approximately 90°, and the tensile strength is relatively low, the propagation of the branch fractures significantly affects the trajectory of the hydraulic main fracture. This is because the lower the tensile strength, the closer the fracture initiation point is to the fracture tip. Premature bifurcation leads to better propagation conditions for the branch fractures, and the induced stress they generate changes the direction of the local stress field, causing the hydraulic main fracture to not propagate along the predetermined trajectory.

[0149] In summary, the embodiments of this invention fully consider the impact of stress concentration on the main fracture wall during hydraulic fracturing on bifurcation. This can be used to predict the formation of bifurcation fractures at weak points on the main fracture wall during hydraulic fracturing, and to assess the interaction between the main fracture and bifurcation fracture trajectories during their propagation. This is beneficial for guiding the design and adjustment of hydraulic fracturing construction schemes in oil and gas fields, providing a theoretical basis and technical support for achieving large-scale economical reservoir exploitation.

[0150] Based on the above scheme, the present invention provides a calculation system for the deformation and propagation trajectory of the main fracture and bifurcation fractures in hydraulic fracturing, characterized in that it includes:

[0151] Modeling module: Establishes a horizontal well model, which includes the horizontal well and the initial main fracture of the perforated section;

[0152] Discrete module; The initial main fracture in the model of the horizontal well and the perforated section is discretized and divided into discrete fracture units;

[0153] The simulation module is used to perform the first fracturing of a horizontal well in a horizontal well model according to the actual fracturing construction plan. It calculates the relative discontinuity displacement, unilateral normal displacement, and tangential displacement of discrete fracture elements on the main fracture using a pre-established rock stress-deformation calculation model of the main fracture wall. Based on these displacements, it calculates the normal and tangential displacements on the other side of the discrete fracture elements on the main fracture. The relative discontinuity displacements include both the normal and tangential relative discontinuity displacements of the discrete fracture elements. It also calculates the fracture condition at the tip of the main fracture using these relative discontinuity displacements: determining whether cracking has occurred at the tip of the main fracture element; if cracking occurs, calculating the extension length and angle of the discrete fracture element tip; and using the normal and tangential displacements of the discrete fracture elements to determine the fracture wall condition of the discrete fracture elements. If a bifurcation point exists, it indicates the formation of a bifurcation crack, and the initial initiation angle of the bifurcation crack is calculated. If no bifurcation point exists, fracturing continues until a bifurcation point appears on the crack wall of the discrete fracture element, and the initial initiation angle of the bifurcation crack is calculated. Once a bifurcation crack appears, fracturing continues until the main fracture reaches the predetermined length. During each fracturing operation, the relative discontinuous displacement of the discrete fracture elements of the main fracture and the bifurcation crack is calculated using a pre-established hydraulic fracturing main fracture and bifurcation crack deformation calculation model. The fracture condition at the tip of the main fracture and the bifurcation crack is calculated using this relative discontinuous displacement until the main fracture reaches the predetermined length, at which point fracturing stops. The discontinuous displacement of the discrete fracture element obtained from the last fracturing operation is used as the deformation of the hydraulic fracturing main fracture and the bifurcation crack. The trajectories of the hydraulic fracturing main fracture and the bifurcation crack are obtained based on the extension length and extension angle of the tip of the main fracture and the tip of the bifurcation crack calculated after each fracturing operation.

[0154] The embodiments of the present invention also provide corresponding devices and computer-readable storage media for implementing the solutions provided in the embodiments of the present invention.

[0155] The device includes a memory and a processor. The memory stores instructions or code, and the processor executes the instructions or code to enable the device to perform the multi-horizontal well asynchronous fracturing fracture deformation and propagation trajectory prediction method according to any embodiment of this application.

[0156] In practical applications, the computer-readable storage medium can be any combination of one or more computer-readable media. The computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium.

[0157] The various embodiments of this disclosure have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A method for calculating the deformation and propagation trajectory of the main fracture and bifurcation fractures in hydraulic fracturing, characterized in that, The process includes the following: Step 1: Establish a horizontal well model, which includes the horizontal well and the initial main fracture of the perforated section; Step 2: Discretize the initial main fracture in the horizontal well model by dividing it into discrete fracture elements; Step 3: According to the actual fracturing construction plan, perform the first fracturing on the horizontal well in the horizontal well model. Calculate the relative discontinuity displacement, unilateral normal displacement, and tangential displacement of the discrete fracture elements on the main fracture using the pre-established rock stress and deformation calculation model of the main fracture wall. Based on the relative discontinuity displacement, unilateral normal displacement, and tangential displacement of the discrete fracture elements, calculate the normal and tangential displacements on the other side of the discrete fracture elements on the main fracture. The relative discontinuity displacement includes the relative normal and tangential discontinuity displacements of the discrete fracture elements. Calculate the fracture condition at the tip of the main fracture using the relative discontinuity displacement: determine whether the tip of the main fracture element has cracked. If the tip of the main fracture element cracks, calculate the extension length and extension angle of the discrete fracture element tip. Use the normal and tangential displacements of the discrete fracture elements to determine whether the fracture wall of the discrete fracture element is fractured. A bifurcation point is present, indicating the formation of a bifurcation crack. The initial initiation angle of the bifurcation crack is calculated. If no bifurcation point is present, fracturing continues until a bifurcation point appears on the crack wall of the discrete fracture element, and the initial initiation angle of the bifurcation crack is calculated. Once a bifurcation crack appears, fracturing continues until the main fracture reaches a predetermined length. During each fracturing operation, the relative discontinuous displacement of the discrete fracture elements of the main fracture and the bifurcation crack is calculated using a pre-established hydraulic fracturing main fracture and bifurcation crack deformation calculation model. This relative discontinuous displacement is used to calculate the fracture condition at the tip of the main fracture and the bifurcation crack until the main fracture reaches a predetermined length, at which point fracturing stops. The discontinuous displacement of the discrete fracture element obtained from the last fracturing operation is used as the deformation of the hydraulic fracturing main fracture and the bifurcation crack. The trajectories of the hydraulic fracturing main fracture and the bifurcation crack are obtained based on the extension length and extension angle of the tip of the main fracture and the bifurcation crack calculated after each fracturing operation. The process of determining whether there are bifurcation points on the crack wall of a discrete crack element using the normal and tangential displacements of the discrete crack element includes: Calculate the tangential strain of the bending crack element surface, then calculate the tangential stress of the crack element surface using the tangential strain. Using the tangential stress, determine whether tensile failure has occurred at the stress concentration point using the maximum tensile stress criterion. If tensile failure is determined to have occurred at the stress concentration point, it indicates that there is a bifurcation point on the crack wall of the discrete crack element; otherwise, there is no bifurcation point. The tangential strain of the bending crack element surface is calculated based on the displacement gradient. The tangential displacement gradient of the crack surface is equal to the tangential strain. The formula for calculating the tangential strain of the bending crack element surface is as follows: In the formula, Indicates the first The half-slot length of a crack element, in meters; Indicates the crack number The tangential displacement of each element, in meters; Indicates the crack number The tangential displacement of each element, in meters; Indicates the first The angle between the local coordinate system and the global coordinate system of a crack element, in degrees; Indicates the first The first crack unit and the first The straight-line distance between the center points of each crack element, in meters; The symbol represents the upper and lower crack surfaces of the crack.

2. The method for calculating the deformation and propagation trajectory of the main and branching fractures in hydraulic fracturing according to claim 1, characterized in that, The calculation model for the stress-deformation of the rock on the main fracture wall is as follows: In the formula, Indicates the sequence number of the discrete crack element. , This represents the total number of discrete crack elements on the main crack. ; This is a correction factor; The stress boundary influence coefficient is related to the coordinates of the discretized crack element, representing the first... j The discrete crack element for the first i The force generated by each discrete crack element is expressed in Pa. , The first one on the main crack Tangential and normal relative discontinuous displacements of a discrete crack element; , The first i The tangential and normal stresses experienced by a discrete crack element, expressed in Pa.

3. The method for calculating the deformation and propagation trajectory of the main fracture and bifurcation fractures in hydraulic fracturing according to claim 2, characterized in that, The matrix form of the calculation model for the stress-deformation of the rock on the main fracture wall is as follows: In the formula, In the formula, This represents the tangential relative discontinuity displacement of the j-th discrete crack element on the main crack. ; This represents the relative discontinuity displacement in the normal direction of the j-th discrete crack element on the main crack. ; Indicates the minimum horizontal principal stress; Indicates the maximum horizontal principal stress; This indicates that there is pressure inside the j-th discrete crack element; This represents the angle between the local coordinate system and the global coordinate system of the j-th discrete crack element; In the formula, + and - represent the two walls of the main crack, respectively. and These represent the normal and tangential displacements on one side of the wall of the j-th discrete crack element, respectively; and These represent the tangential and normal displacements on the other side of the wall of the j-th discrete crack element, respectively.

4. The method for calculating the deformation and propagation trajectory of the main fracture and bifurcation fractures in hydraulic fracturing according to claim 1, characterized in that, The following formula can be used to determine whether cracking has occurred at the tip of the main crack element: When the above formula is true, it indicates that the tip of the main crack unit has cracked; otherwise, it indicates that the tip of the main crack unit has not cracked. In the formula, Rock fracture toughness, in MPa·m 1 / 2 ; The turning angle at the crack tip when it breaks is expressed in degrees. In the formula, K I , K II These represent the stress intensity factors of rocks under type I and type II fracture, respectively, in Pa·m. 1 / 2 ; , The normal relative discontinuity displacement and the tangential relative discontinuity displacement of discrete crack elements on the main crack; Young's modulus of rock; Poisson's ratio of the rock; It is half the seam length; No. i The extension length of the tip of each discrete crack element Calculated using the following formula: In the formula: This represents the combined stress intensity at the tip of a discrete crack element when it first becomes the crack tip, expressed in Pa•m. 1 / 2 ; This represents the maximum historical length of the crack tip, expressed in meters (m). It is a function for maximizing the value; No. i The propagation angle of the tip of each discrete crack element Calculated using the following formula: 。 5. The method for calculating the deformation and propagation trajectory of the main fracture and bifurcation fractures in hydraulic fracturing according to claim 1, characterized in that: The deformation calculation model for the main fracture and bifurcation fracture in hydraulic fracturing is as follows: In the formula, The number of discrete elements representing the main crack; The number of discrete elements for bifurcation cracks; , , , These are the stress boundary influence coefficients, which are ( )×( A matrix of ) This is a correction factor; , Let be the relative displacement of the crack element in the sn coordinate system, which is ( A one-dimensional matrix of 1 x 1; and The following conditions must be met: In the formula, Indicates the first i The tangential stress experienced by a discrete crack element; Indicates the first i The normal stress experienced by a discrete crack element; Indicates the first i The tangential stress experienced by each discrete crack element of the main crack; Indicates the first i The normal stress on discrete crack elements on a main crack; Indicates the first i The tangential stress experienced by discrete crack elements on a bifurcated crack; Indicates the first i The normal stress experienced by discrete crack elements on a bifurcated crack.

6. A calculation system for the deformation and propagation trajectory of the main fracture and bifurcation fractures in hydraulic fracturing, characterized in that, The method for calculating the deformation and propagation trajectory of the main fracture and bifurcation fractures in hydraulic fracturing as described in any one of claims 1-5 includes: Modeling module: Establishes a horizontal well model, which includes the horizontal well and the initial main fracture of the perforated section; Discrete module; The initial main fracture in the horizontal well model is discretized and divided into discrete fracture elements; The simulation module is used to perform the first fracturing of a horizontal well in a horizontal well model according to the actual fracturing construction plan. It calculates the relative discontinuity displacement, unilateral normal displacement, and tangential displacement of discrete fracture elements on the main fracture using a pre-established rock stress-deformation calculation model of the main fracture wall. Based on these displacements, it calculates the normal and tangential displacements on the other side of the discrete fracture elements on the main fracture. The relative discontinuity displacements include both the normal and tangential relative discontinuity displacements of the discrete fracture elements. It also calculates the fracture condition at the tip of the main fracture using these relative discontinuity displacements: determining whether cracking has occurred at the tip of the main fracture element; if cracking occurs, calculating the extension length and angle of the discrete fracture element tip; and using the normal and tangential displacements of the discrete fracture elements to determine the fracture wall condition of the discrete fracture elements. If a bifurcation point exists, it indicates the formation of a bifurcation crack, and the initial initiation angle of the bifurcation crack is calculated. If no bifurcation point exists, fracturing continues until a bifurcation point appears on the crack wall of the discrete fracture element, and the initial initiation angle of the bifurcation crack is calculated. Once a bifurcation crack appears, fracturing continues until the main fracture reaches the predetermined length. During each fracturing operation, the relative discontinuous displacement of the discrete fracture elements of the main fracture and the bifurcation crack is calculated using a pre-established hydraulic fracturing main fracture and bifurcation crack deformation calculation model. The fracture condition at the tip of the main fracture and the bifurcation crack is calculated using this relative discontinuous displacement until the main fracture reaches the predetermined length, at which point fracturing stops. The discontinuous displacement of the discrete fracture element obtained from the last fracturing operation is used as the deformation of the hydraulic fracturing main fracture and the bifurcation crack. The trajectories of the hydraulic fracturing main fracture and the bifurcation crack are obtained based on the extension length and extension angle of the tip of the main fracture and the tip of the bifurcation crack calculated after each fracturing operation.

7. An electronic device, characterized in that, include: One or more processors; A storage device on which one or more programs are stored; When the one or more programs are executed by the one or more processors, the one or more processors implement the method for calculating the deformation and propagation trajectory of the main and bifurcation fractures in hydraulic fracturing as described in any one of claims 1 to 5.

8. A storage medium, characterized in that, It stores a computer program, wherein when the computer program is executed by a processor, it implements the method for calculating the deformation and propagation trajectory of the main hydraulic fracturing fracture and bifurcation fracture as described in any one of claims 1 to 5.

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