Method, device and equipment for calculating crack width of three-dimensional crack

Abstract

The invention relates to the field of reservoir crack expansion, in particular to a crack width calculation method, device and equipment for a three-dimensional crack. The crack width calculation method of the three-dimensional crack comprises the following steps: dividing the three-dimensional crack into a plurality of rectangular crack units; according to the plurality of rectangular crack units, constructing a discrete superposition model of the fluid pressure in the three-dimensional crack and the crack width of the plurality of rectangular crack units; according to the discrete superposition model, determining a fluid-solid coupling equation based on the width of the three-dimensional crack; and calculating the crack width of the three-dimensional crack according to the Jacobian matrix of the partial derivative of the fluid-structure interaction equation. According to the embodiment of the invention, the three-dimensional crack is divided into a plurality of rectangular crack units to determine the Jacobian matrix of the partial derivative of the fluid-structure interaction equation, and each rectangular crack unit can independently consider the fluid pressure and the crack width, so that the geometric morphology of the three-dimensional crack can be more accurately described by using the Jacobian matrix; and the calculation speed and the calculation precision of the three-dimensional crack width are improved.

Description

Technical Field

[0001] The embodiments of this specification relate to the field of reservoir fracture expansion, and specifically to a method, device and equipment for calculating the fracture width of a three-dimensional fracture. Background Art

[0002] With the development of unconventional oil and gas reservoirs such as tight oil and gas, shale oil and gas, hydraulic fracturing has become the main transformation method, providing a powerful technical means for the economic development of unconventional oil and gas. After fracturing transformation, each fracturing cluster usually develops only one main fracture, providing an efficient flow channel for oil and gas production. Although hydraulic fracturing technology has been successfully promoted in recent decades, there are still large differences in the geometric parameters of fractures in different clusters. In order to further improve fracturing design and completion parameters, it is crucial to have a deep understanding of the geometry and properties of fractures in the hydraulic fracturing process. In recent years, distributed fiber optic sensing technology has been successfully applied in hydraulic fracturing monitoring, providing a powerful tool for downhole fracture monitoring.

[0003] The existing reservoir fracture calculation method first establishes a segmented multi-cluster fracturing reservoir model for oil and gas reservoirs based on the reservoir physical properties and hydraulic fracturing parameters provided at the oil and gas field site, and spatially discretizes the reservoir model. Then, a fluid-solid coupling mathematical model and numerical solution format of the wellbore-reservoir-fracture are established, and based on the actual production dynamic data of the fracturing wells at the oil and gas field site, a fluid-solid coupling numerical simulation of the fracturing well production process is performed, and the strain signal along the distributed optical fiber is calculated. Finally, the strain signal is compared with the actual monitoring signal, and the geometric morphology and property parameters of each cluster of hydraulic fractures are adjusted to match the strain signal with the monitoring signal, and the geometric morphology of each cluster of hydraulic fractures is interpreted.

[0004] However, the existing reservoir fracture calculation method technology uses the displacement discontinuity method combined with the numerical differential method to calculate the width of three-dimensional fractures, which has a slow calculation speed and unsatisfactory calculation accuracy. Therefore, how to overcome the problems of slow calculation speed and unsatisfactory calculation accuracy in the existing reservoir fracture calculation method and propose a three-dimensional fracture width calculation method with high calculation efficiency and calculation accuracy to meet the actual needs of unconventional oil and gas development is a key issue that needs to be solved urgently. Summary of the invention

[0005] The purpose of the embodiments of this specification is to provide a method, device and equipment for calculating the fracture width of three-dimensional fractures, so as to overcome the problems of slow calculation speed and unsatisfactory calculation accuracy in existing reservoir fracture calculation methods, and to propose a method for calculating the fracture width of three-dimensional fractures with high calculation efficiency and calculation accuracy to meet the actual needs of unconventional oil and gas development.

[0006] On the one hand, the embodiments of this specification propose a method for calculating the crack width of a three-dimensional crack. The method for calculating the crack width of the three-dimensional crack includes: dividing the three-dimensional crack into multiple rectangular crack units; constructing a discrete superposition model of the fluid pressure in the three-dimensional crack and the crack widths of the multiple rectangular crack units according to the multiple rectangular crack units; determining a fluid-structure interaction equation based on the crack width of the three-dimensional crack according to the discrete superposition model; and calculating the crack width of the three-dimensional crack according to the Jacobian matrix of the partial derivatives of the fluid-structure interaction equation.

[0007] On the other hand, there is a device for calculating the crack width of a three-dimensional crack. The device includes: a dividing module for dividing the three-dimensional crack into multiple rectangular crack units; a constructing module for constructing a discrete superposition model of the fluid pressure in the three-dimensional crack and the crack widths of the multiple rectangular crack units according to the multiple rectangular crack units; a determining module for determining a fluid-structure interaction equation based on the crack width of the three-dimensional crack according to the discrete superposition model; and a calculating module for calculating the crack width of the three-dimensional crack according to the Jacobian matrix of the partial derivatives of the fluid-structure interaction equation.

[0008] On yet another aspect, a computer device is provided, including a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor executes the above method for calculating the crack width of a three-dimensional crack.

[0009] As can be seen from the technical solutions provided by the embodiments of this specification above, the method for calculating the crack width of a three-dimensional crack provided by the embodiments of this specification can divide the three-dimensional crack into multiple rectangular crack units; construct a discrete superposition model of the fluid pressure in the three-dimensional crack and the crack widths of the multiple rectangular crack units according to the multiple rectangular crack units; determine a fluid-structure interaction equation based on the crack width of the three-dimensional crack according to the discrete superposition model; and calculate the crack width of the three-dimensional crack according to the Jacobian matrix of the partial derivatives of the fluid-structure interaction equation. Compared with the existing methods, by dividing the three-dimensional crack into multiple rectangular crack units to determine the Jacobian matrix of the partial derivatives of the fluid-structure interaction equation, each rectangular crack unit can independently consider its fluid pressure and crack width, and then the Jacobian matrix can more accurately describe the geometric shape of the three-dimensional crack, improving the calculation speed and calculation accuracy of the crack width of the three-dimensional crack. Description of the Drawings

[0010] In order to more clearly illustrate the technical solutions in the embodiments of this specification or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art.

[0011] Figure 1 It is a flowchart of a method for calculating the crack width of a three-dimensional crack provided by the embodiments of this specification;

[0012] Figure 2It is a schematic diagram of the fracture width of a three-dimensional fracture A obtained based on the Jacobian matrix of the partial derivatives of the three-dimensional fracture fluid-solid coupling equation provided by the embodiments of this specification;

[0013] Figure 3 It is a schematic diagram of the fracture width of a three-dimensional fracture B obtained based on the Jacobian matrix of the partial derivatives of the three-dimensional fracture fluid-solid coupling equation provided by the embodiments of this specification;

[0014] Figure 4 It is a schematic diagram of the fracture width of a three-dimensional fracture C obtained based on the Jacobian matrix of the partial derivatives of the three-dimensional fracture fluid-solid coupling equation provided by the embodiments of this specification;

[0015] Figure 5 It is a schematic diagram of the fracture width of a three-dimensional fracture D obtained based on the Jacobian matrix of the partial derivatives of the three-dimensional fracture fluid-solid coupling equation provided by the embodiments of this specification;

[0016] Figure 6 It is a schematic diagram of stress and fracture height in the forward fracture propagation result of a three-dimensional fracture E obtained based on the Jacobian matrix of the partial derivatives of the three-dimensional fracture fluid-solid coupling equation provided by the embodiments of this specification;

[0017] Figure 7 It is a schematic diagram of the fracture width in the forward fracture propagation result of a three-dimensional fracture E obtained based on the Jacobian matrix of the partial derivatives of the three-dimensional fracture fluid-solid coupling equation provided by the embodiments of this specification;

[0018] Figure 8 It is a schematic diagram of forward multi-fracture competition obtained based on the Jacobian matrix of the partial derivatives of the three-dimensional fracture fluid-solid coupling equation provided by the embodiments of this specification;

[0019] Figure 9 It is a schematic diagram of the structural composition of a fracture width calculation device for a three-dimensional fracture provided by the embodiments of this specification;

[0020] Figure 10 It is a schematic diagram of the structural composition of a computer device provided by the embodiments of this specification. Detailed implementation manners

[0021] Next, the technical solutions in the embodiments of this specification will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of this specification. Obviously, the described embodiments are only a part of the embodiments of this specification, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in this specification without creative efforts shall fall within the protection scope of this specification.

[0022] Figure 1The flowchart of a method for calculating the crack width of a three-dimensional crack provided by an embodiment of this specification. Specifically, in implementation, the method includes the following steps:

[0023] S101: Divide the three-dimensional crack into multiple rectangular crack units.

[0024] In some embodiments, the three-dimensional crack can be divided into multiple rectangular crack units.

[0025] By simplifying the complex three-dimensional crack into a set of regular rectangular crack units, the rectangular crack units are relatively simple in geometric shape and more direct and efficient in numerical implementation. Therefore, it can greatly simplify the construction and calculation process of the subsequent three-dimensional crack numerical model.

[0026] During the oil and gas exploitation process, three-dimensional cracks can be formed through technologies such as hydraulic fracturing to transform the reservoir and improve the exploitation efficiency and production of the reservoir. A three-dimensional crack refers to a crack morphology in which the length, width, and height of the crack in the reservoir all change. The three-dimensional crack has a complex morphology and distribution characteristics in space. Its crack systems are interconnected to form a three-dimensional polygon network, with small crack intervals and uniform distribution. The existence of three-dimensional cracks increases the fluid flow channels in the reservoir, improves the permeability of the reservoir, and is beneficial to the exploitation of resources such as oil and gas. The geometric morphology and distribution characteristics of three-dimensional cracks have an important impact on the fluid flow in the reservoir. The connectivity and directionality of the cracks determine the fluid flow path and velocity.

[0027] Refer to Figure 2 As shown, the three-dimensional crack can be divided into a series of small rectangular crack units. The physical properties (such as displacement, stress, etc.) inside each unit rectangular crack are considered to be uniform. Each rectangular crack unit has its own geometric dimensions (length, width, and height) and material properties (such as elastic modulus, Poisson's ratio, etc.). The connection between rectangular crack units is achieved through nodes, and displacements and deformations can occur at the nodes. Inside each rectangular crack unit, the displacement and stress can be represented by appropriate interpolation functions. By solving these interpolation functions, the displacement discontinuity and stress distribution on the surface of the three-dimensional crack can be obtained. Specifically, the three-dimensional crack can be described as a set of rectangular crack units. The global coordinates are (X, Y, Z). Each rectangular crack unit has its own local coordinate system (x1, x2, x3), and each rectangular crack unit has a positive side (x3 = 0+) and a negative side (x3 = 0-). Each rectangular crack unit D has the following three displacement discontinuity points as shown in the formula:

[0028] D1(x1, x2, 0) = u1(x1, x2, 0 - ) - u1(x1, x2, 0 + )

[0029] D2(x1,x2,0) = u2(x1,x2,0 - ) - u2(x1,x2,0 + );

[0030] D3(x1,x2,0) = u3(x1,x2,0 - ) - u3(x1,x2,0 + )

[0031] The three - dimensional fracture is divided into a series of small rectangular fracture elements. The rectangular fracture elements are relatively simple in geometric shape, so they are more direct and efficient in numerical implementation. Existing finite - element analysis software usually includes a solution module for rectangular fracture elements, so these software can be conveniently used to simulate and analyze the geometric shape problems of three - dimensional fractures. In addition, using a set of rectangular fracture elements can significantly improve the calculation efficiency because the mesh division of rectangular fracture elements is relatively simple and the connection relationship between elements is more direct, thus reducing the calculation complexity and time cost.

[0032] S102: Construct a discrete superposition model of the fluid pressure in the three - dimensional fracture and the fracture widths of multiple rectangular fracture elements according to the multiple rectangular fracture elements.

[0033] In some embodiments, according to the stress components of the multiple rectangular fracture elements, determine the minimum principal stress vector of the three - dimensional fracture; according to the kernel function of the three - dimensional fracture, determine the kernel coefficients of the multiple rectangular fracture elements; according to the minimum principal stress vector of the three - dimensional fracture and the kernel coefficients of the multiple rectangular fracture elements, use the formula to construct the discrete superposition model of the fluid pressure in the three - dimensional fracture and the fracture widths of the multiple rectangular fracture elements; where x is a point in the three - dimensional fracture; t is the injection time of the fluid in the three - dimensional fracture; p(x,t) is the fluid pressure vector in the three - dimensional fracture, with the unit of MPa; σ h (x) is the minimum principal stress vector of the three - dimensional fracture, with the unit of MPa; N is the total number of rectangular fracture elements; ξ i is the i - th rectangular fracture element; C(x,ξ i ) is the kernel coefficient of the i - th rectangular fracture element, with the unit of MPa / m; w(ξ i ) is the fracture width of the i - th rectangular fracture element, with the unit of m.

[0034] Through the formula A discrete superposition model of fluid pressure in a three-dimensional fracture and fracture widths of multiple rectangular fracture elements is constructed. Each rectangular fracture element in the discrete superposition model can independently consider its fluid pressure and fracture width, thus improving the accuracy of the model. By dividing the three-dimensional fracture into multiple rectangular fracture elements, the shape and distribution of the three-dimensional fracture can be described more precisely, and different shapes and sizes of three-dimensional fractures can be adapted by adjusting the division method and quantity of the rectangular fracture elements.

[0035] Based on the displacement discontinuity equations of multiple rectangular fracture elements, the stress components of multiple rectangular fracture elements can be determined using the geometric and physical equations of the three-dimensional fracture. After determining the stress components of multiple rectangular fracture elements, the minimum principal stress vector of the three-dimensional fracture can be obtained. After determining the stress components of multiple rectangular fracture elements, the kernel function of the three-dimensional fracture can also be obtained, and then the kernel coefficients of multiple rectangular fracture elements can be determined. Based on the minimum principal stress vector of the three-dimensional fracture and the kernel coefficients of multiple rectangular fracture elements, the following formula can be used to construct a discrete superposition model of fluid pressure in the three-dimensional fracture and fracture widths of multiple rectangular fracture elements:

[0036]

[0037] In the formula, x is a point in the three-dimensional fracture; t is the injection time of the fluid in the three-dimensional fracture; p(x, t) is the fluid pressure vector in the three-dimensional fracture, with the unit of MPa; σ h (x) is the minimum principal stress vector of the three-dimensional fracture, with the unit of MPa; N is the total number of rectangular fracture elements; ξ i is the i-th rectangular fracture element; C(x, ξ i ) is the kernel coefficient of the i-th rectangular fracture element, with the unit of MPa / m; w(ξ i) is the crack width of the i-th rectangular crack element, with the unit of m. The constructed discrete superposition model divides the three-dimensional crack into multiple rectangular crack elements, which can more precisely describe the shape and distribution of the three-dimensional crack. Each rectangular crack element can independently consider its fluid pressure and crack width, thereby improving the accuracy of the model. The constructed discrete superposition model can accurately simulate the pressure distribution of the fluid in the crack, helping to understand the fluid flow and crack propagation mechanism. And by considering the change of fluid pressure, the stability and propagation trend of the three-dimensional crack can be further analyzed. The constructed discrete superposition model can also adapt to three-dimensional cracks of different shapes and sizes, only by adjusting the division method and quantity of the rectangular crack elements, which makes the constructed discrete superposition model have higher flexibility in dealing with complex three-dimensional crack problems. With the in-depth research and data accumulation, the constructed discrete superposition model can be conveniently extended by adding more rectangular crack elements or considering more influencing factors. In addition, since the constructed discrete superposition model adopts the discretization method and divides the crack into multiple rectangular crack elements, the calculation efficiency can be improved by technologies such as parallel computing.

[0038] In some embodiments, construct the displacement discontinuity equations of the multiple rectangular crack elements; construct the geometric equations and physical equations of the three-dimensional crack; and determine the stress components of the multiple rectangular crack elements according to the displacement discontinuity equations of the multiple rectangular crack elements, using the geometric equations and physical equations of the three-dimensional crack.

[0039] Determine the stress components of the multiple rectangular crack elements through the displacement discontinuity equations, geometric equations and physical equations of the multiple rectangular crack elements. On the one hand, the displacement discontinuity equations can accurately describe the displacement discontinuity on the surface of the three-dimensional crack. Through this equation, the displacement field at and near the tip of the three-dimensional crack can be accurately calculated, and then the propagation trend and stability of the three-dimensional crack can be analyzed. On the other hand, the geometric equations establish the relationship between the displacement and strain of the rectangular crack element, enabling the strain field to be deduced from the known displacement field. In addition, the physical equations establish the relationship between the strain and stress of the rectangular crack element, enabling the stress field to be calculated from the known strain field.

[0040] The deformation of the three-dimensional crack belongs to elastic deformation. Therefore, the following geometric equations, physical equations and equilibrium equations of the three-dimensional crack can be established:

[0041] ε ij =0.5(u i,j +u j,i );

[0042]

[0043] σ ji,j +b i =0;

[0044] where: ε ij is the strain tensor, dimensionless; σ ij is the stress tensor, MPa; b i is the body force, MPa / m. For the problem of hydraulic fracturing crack propagation, the body force (gravity) acting on the three-dimensional crack has no effect on the three-dimensional crack deformation, so b i = 0. The geometric and physical equations of the three-dimensional crack can be substituted into the equilibrium equation to obtain the following second-order circular partial differential equation describing the three-dimensional crack deformation:

[0045] Gu i,kk +(2Gν / (1 - 2ν)+G)u k,ki = 0;

[0046] The specific boundary conditions of the three-dimensional crack (such as displacement boundary, stress boundary, etc.) can be combined to form a complete description of the three-dimensional crack deformation, and an integral equation equivalent to the following differential equation can be established:

[0047]

[0048] where Ω is the full-field calculation domain where the three-dimensional crack is located. The integration by parts and the Cauchy stress formula can be used, and combined with the loads of equal magnitude and opposite directions on both sides of the three-dimensional crack, and the displacement direction at the same time. Therefore, for the splitting problem, the integral equation equivalent to the above differential equation can be transformed into:

[0049]

[0050] where is the displacement of the upper and lower surfaces of the three-dimensional crack, m.

[0051] The displacement discontinuity of the three-dimensional crack can be defined as:

[0052]

[0053] Substituting the displacement discontinuity of the three-dimensional crack into the following formula is obtained:

[0054]

[0055] Taking the derivative of the above formula and substituting the derivative result into the Kelvin fundamental solution of the three-dimensional crack, the following formula is obtained to determine the force at any point in the three-dimensional crack space:

[0056]

[0057] The kernel function of the above formula is:

[0058]

[0059] Similarly, substituting the Kelvin fundamental solution of the three-dimensional crack into yields:

[0060]

[0061] The Kelvin fundamental solution of the three-dimensional crack can be expressed as:

[0062]

[0063] After constructing the geometric equations, physical equations, and equilibrium equations of the three-dimensional crack, the displacement discontinuity equations of multiple rectangular crack elements can be constructed based on the following Somigliana formula:

[0064]

[0065] For the rectangular crack element Γ e :

[0066]

[0067] In the formula, is the distance between the spatial point x = (x1, x2, x3) and the source point (matrix center) ξ = (ξ1, ξ2, 0), in m.

[0068] For the rectangular crack element Γ e in the local coordinate system, n1 = 0, n2 = 0, n3 = 1. Therefore, the derivation equation of the displacement discontinuity equation of the above rectangular crack element Γ e can be obtained:

[0069]

[0070] Assume that the distribution of the displacement discontinuity within the rectangular crack element Γ e is constant. Combining the coordinates of the local coordinate system of Γ e , it is determined that the main quantity to be solved is the integral function Ф as:

[0071]

[0072] The partial derivative of this integral function Ф can be calculated, and the derivation equation of the displacement discontinuity equation of the rectangular crack element Γ e is expressed as:

[0073]

[0074] According to the geometric equations and physical equations of the three-dimensional crack, the stress components of the rectangular crack element Γ e can be obtained:

[0075]

[0076] Based on the above formula, the stress components of all rectangular fracture elements within the three-dimensional fracture can be calculated.

[0077] In some embodiments, based on the stress components of a plurality of rectangular fracture elements, the kernel function of the three-dimensional fracture is determined.

[0078] Determining the kernel function of the three-dimensional fracture through the stress components of a plurality of rectangular fracture elements can, on the one hand, avoid the errors caused by global averaging, improve the local accuracy of the calculation, and thus more accurately capture the stress field and displacement field at the tip of the three-dimensional fracture and determine the kernel function. On the other hand, the stress state of the three-dimensional fracture is complex and variable, involving stress components in multiple directions. By comprehensively considering these stress components, the stress condition of the three-dimensional fracture can be more comprehensively reflected, and thus the kernel function can be determined more accurately.

[0079] According to the theory of fracture mechanics, the stress field at the tip of the three-dimensional fracture can be expressed as a function of the stress intensity factor. Using the stress components of all rectangular fracture elements included in the three-dimensional fracture and the geometric parameters of all rectangular fracture elements, the stress intensity factor of each rectangular fracture element is calculated. Considering the interaction between fracture elements and the continuity of the stress field, the stress intensity factors of all rectangular fracture elements can be superimposed or weighted averaged or iteratively optimized to obtain the kernel function of the entire three-dimensional fracture. The method of superposition or weighted averaging or iterative optimization depends on the geometric shape of the three-dimensional fracture and will not be elaborated here. For three-dimensional fractures with complex geometric shapes and stress states, through the analysis of a plurality of rectangular fracture elements, different situations can be more flexibly adapted.

[0080] S103: Determine the fluid-solid coupling equation based on the fracture width of the three-dimensional fracture according to the discrete superposition model.

[0081] In some embodiments, according to the law of conservation of mass, the formula is used to establish a solid mechanics model of the fluid pressure within the three-dimensional fracture and the fracture width of the three-dimensional fracture; where p is the fluid pressure within the three-dimensional fracture; w is the fracture width of the three-dimensional fracture, with the unit of m; t is the time corresponding to the fluid pressure within the three-dimensional fracture, with the unit of s; and μ is the dynamic viscosity of the fluid within the three-dimensional fracture.

[0082] A solid mechanics model of fluid pressure in a three-dimensional crack and the crack width of the three-dimensional crack is established through the law of conservation of mass. On the one hand, the law of conservation of mass is one of the basic laws of nature, providing a solid theoretical basis for establishing the solid mechanics model of fluid pressure in a three-dimensional crack and the crack width of the three-dimensional crack. On the other hand, through the law of conservation of mass, it can be ensured that the change of fluid pressure in the three-dimensional crack is correlated with the change of crack width and conforms to physical laws. This helps to more accurately simulate the flow state of fluid in the three-dimensional crack, thereby predicting the propagation behavior of the three-dimensional crack.

[0083] According to the law of conservation of mass, the following formula can be used to establish the solid mechanics model of fluid pressure in the three-dimensional crack and the crack width of the three-dimensional crack:

[0084]

[0085] In the formula, p is the fluid pressure in the three-dimensional crack; w is the crack width of the three-dimensional crack, with the unit of m; t is the time corresponding to the fluid pressure in the three-dimensional crack, with the unit of s; μ is the dynamic viscosity of the fluid in the three-dimensional crack. A small control volume can be taken in the three-dimensional crack. According to the law of conservation of mass, the mass of fluid flowing into the control volume should be equal to the mass of fluid flowing out of the control volume plus the increase in the mass of fluid in the control volume. Based on the law of conservation of mass, the established solid mechanics model can correlate the change of fluid pressure in the three-dimensional crack with the change of crack width, which helps to more accurately simulate the flow state of fluid in the three-dimensional crack. In addition, based on the law of conservation of mass, the established solid mechanics model can accurately describe the change of crack width, which is of great significance for analyzing the propagation speed and direction of cracks.

[0086] In some embodiments, a solid mechanics model of fluid pressure in a three-dimensional crack and the crack width of the three-dimensional crack can be constructed; the equation corresponding to the discrete superposition model is substituted into the equation corresponding to the solid mechanics model to determine the fluid-solid coupling equation based on the crack width of the three-dimensional crack.

[0087] By combining the discrete superposition model with the solid mechanics model, the interaction between fluid flow and solid deformation in the three-dimensional crack can be described more precisely. The discrete superposition model can be used to describe the spatial distribution of fluid pressure in the three-dimensional crack, while the solid mechanics model can be used to describe the stress and strain state of the solid around the three-dimensional crack. Combining the two can comprehensively consider the influence of fluid pressure and solid deformation on the crack width of the three-dimensional crack, and the accuracy of subsequent calculation of the crack width of the three-dimensional crack. In addition, by substituting the equation corresponding to the discrete superposition model into the equation corresponding to the solid mechanics model, it is not necessary to solve the two models separately, which can avoid repeated calculations and resource waste and improve the calculation efficiency.

[0088] According to the law of conservation of mass, the following formula can be used to establish a solid mechanics model for the fluid pressure in the three-dimensional fracture and the fracture width of the three-dimensional fracture:

[0089]

[0090] In the formula, p is the fluid pressure in the three-dimensional fracture; w is the fracture width of the three-dimensional fracture, with the unit of m; t is the time corresponding to the fluid pressure in the three-dimensional fracture, with the unit of s; μ is the dynamic viscosity of the fluid in the three-dimensional fracture.

[0091] After constructing the solid mechanics model for the fluid pressure in the three-dimensional fracture and the fracture width of the three-dimensional fracture, the equation corresponding to the discrete superposition model can be simplified into the following matrix form:

[0092] p = Cw + σ h ;

[0093] The matrix equation corresponding to the discrete superposition model can be substituted into the equation corresponding to the solid mechanics model to obtain the following formula:

[0094]

[0095] After arrangement, the following fluid-solid coupling equation based on the fracture width of the three-dimensional fracture is obtained:

[0096]

[0097] In the formula, P is the fluid pressure in the three-dimensional fracture; w is the fracture width of the three-dimensional fracture, with the unit of m; μ is the dynamic viscosity of the fluid in the three-dimensional fracture.

[0098] S104: Calculate the fracture width of the three-dimensional fracture according to the Jacobian matrix of the partial derivative of the fluid-solid coupling equation.

[0099] In some embodiments, based on the analytical solution, the partial derivative of the fluid-solid coupling equation with respect to the fracture width of the three-dimensional fracture can be obtained; use the formula to construct the Jacobian matrix of the partial derivative of the fluid-solid coupling equation; calculate the fracture width of the three-dimensional fracture according to the Jacobian matrix of the partial derivative of the fluid-solid coupling equation.

[0100] The crack width of a three-dimensional crack is calculated through the Jacobian matrix of the partial derivatives of the fluid-structure interaction equation, which greatly improves the calculation efficiency and accuracy of the crack width of the three-dimensional crack. First, the analytical solution is the exact solution of a mathematical equation or physical problem. By using the analytical solution to solve the fluid-structure interaction equation of the three-dimensional crack, a more accurate Jacobian matrix can be obtained, which can then accurately reflect the interaction relationship between fluid pressure and solid deformation, helping to more accurately describe the geometric shape of the three-dimensional crack and improve the calculation accuracy. Second, compared with the numerical solution, the analytical solution usually has a simpler form, which can improve the calculation efficiency and reduce the error accumulation in the calculation process of the crack width of the three-dimensional crack, thus more accurately determining the geometric shape of the three-dimensional crack. Therefore, using the analytical solution to solve the Jacobian matrix can reduce the calculation complexity of the three-dimensional crack width. Third, the stability analysis of the Jacobian matrix can reveal whether the interaction between fluid pressure and solid deformation is in a stable state. By using the analytical solution to solve the Jacobian matrix and performing stability analysis, the reliability of the model can be further evaluated. Fourth, by using the analytical solution to solve the Jacobian matrix, gradient information can be obtained, which helps to guide the optimization design and parameter adjustment of the crack geometric shape in the future.

[0101] Based on the analytical solution, the partial derivative of the fluid-structure interaction equation with respect to the crack width of the three-dimensional crack can be obtained; the Jacobian matrix of the partial derivatives of the fluid-structure interaction equation is constructed using the following formula:

[0102]

[0103] After obtaining the Jacobian matrix of the partial derivatives of the fluid-structure interaction equation, the crack width of the three-dimensional crack can be calculated according to the Jacobian matrix of the partial derivatives of the fluid-structure interaction equation.

[0104] In some embodiments, the fluid-structure interaction equation can be converted into where p is the matrix of the fluid pressure inside the three-dimensional crack; w is the matrix of the crack width of the three-dimensional crack; according to the Newton iteration method, the fluid-structure interaction equation is expanded as:

[0105]

[0106] According to the expanded form of the fluid-structure interaction equation, the matrix C and the matrix D are respectively defined using the following formula:

[0107]

[0108] The discrete superposition model of the fluid pressure inside the constructed three-dimensional crack and the crack widths of multiple rectangular crack units can be expressed as: p = Aw + σ h ; where the matrix A is defined as: According to matrix C, matrix D, and matrix A, represent the fluid-structure interaction equation as: f′(w n ) = C + D·A; Obtain the Jacobian matrix of the fluid-structure interaction equation f′(w n ) = C + D·A in matrix form.

[0109] Transform the fluid-structure interaction equation into matrix form through the Newton iteration method and then obtain the Jacobian matrix. On the one hand, the Newton iteration method has the property of quadratic convergence near the simple root of the fluid-structure interaction equation, which means that with each iteration, the accuracy of the finally obtained Jacobian matrix will approximately double (or the error will be reduced to the square of half of the original). On the other hand, the Newton iteration method has a fast convergence speed, so it can greatly improve the speed of subsequent three-dimensional fracture width calculation.

[0110] The fluid-structure interaction equation of the three-dimensional fracture can be expressed in the following form:

[0111]

[0112] After organizing it, we can get:

[0113]

[0114] Represent the fluid-structure interaction equation of the three-dimensional fracture by the Newton iteration method:

[0115]

[0116] Furthermore, the fluid-structure interaction equation can be converted into the following partial derivative form:

[0117]

[0118] In the formula, p is the matrix of the fluid pressure in the three-dimensional fracture; w is the matrix of the fracture width of the three-dimensional fracture;

[0119] According to the Newton iteration method, expand the partial derivative of the fluid-structure interaction equation as:

[0120]

[0121] Among them, let:

[0122]

[0123] Represent the discrete superposition model of the fluid pressure in the constructed three-dimensional fracture and the fracture widths of multiple rectangular fracture units in the following matrix form:

[0124] p = Aw + σ h ;

[0125] In the formula, matrix A is defined as:

[0126] According to matrix C, matrix D, and matrix A, the partial derivatives of the fluid-structure interaction equation are expressed in the following matrix form:

[0127] f′(w n ) = C + D·A;

[0128] Use the analytical solution to obtain the Jacobian matrix of the partial derivatives f′(w n ) = C + D·A of the fluid-structure interaction equation in matrix form:

[0129]

[0130] According to the Jacobian matrix of the partial derivatives of the fluid-structure interaction equation, the fracture width of the three-dimensional fracture can be calculated.

[0131] Refer to Figure 2 , Figure 3 , Figure 4 and Figure 5 for the fracture widths of the A, B, C, and D three-dimensional fractures obtained based on the Jacobian matrix of the partial derivatives of the fluid-structure interaction equation.

[0132] Refer to Figure 6 for the schematic diagram of the stress and fracture height in the forward fracture propagation result of the E three-dimensional fracture obtained based on the Jacobian matrix of the partial derivatives of the fluid-structure interaction equation.

[0133] Refer to Figure 7 for the schematic diagram of the fracture width of the E three-dimensional fracture obtained based on the Jacobian matrix of the partial derivatives of the fluid-structure interaction equation.

[0134] Refer to Figure 8 for the schematic diagram of the forward multi-fracture competition obtained based on the Jacobian matrix of the partial derivatives of the fluid-structure interaction equation.

[0135] Based on the above method for calculating the fracture width of the three-dimensional fracture, this specification also presents an embodiment of a device for calculating the fracture width of the three-dimensional fracture. As Figure 9 shown, the device 900 for calculating the fracture width of the three-dimensional fracture may specifically include the following modules:

[0136] A division module 901, which can be used to divide the three-dimensional fracture into multiple rectangular fracture units;

[0137] A construction module 902, which can be used to construct a discrete superposition model of the fluid pressure in the three-dimensional fracture and the fracture widths of the multiple rectangular fracture units according to the multiple rectangular fracture units;

[0138] A determination module 903, which can be used to determine a fluid-solid coupling equation based on the crack width of a three-dimensional crack according to the discrete superposition model;

[0139] A calculation module 904, which can be used to calculate the crack width of the three-dimensional crack according to the Jacobian matrix of the partial derivatives of the fluid-solid coupling equation;

[0140] In some embodiments, the above-mentioned construction module 902 can specifically be used for:

[0141] Determine the minimum principal stress vector of the three-dimensional crack according to the stress components of the multiple rectangular crack elements;

[0142] Determine the kernel coefficients of the multiple rectangular crack elements according to the kernel function of the three-dimensional crack;

[0143] According to the minimum principal stress vector of the three-dimensional crack and the kernel coefficients of the multiple rectangular crack elements, use the following formula to construct a discrete superposition model of the fluid pressure in the three-dimensional crack and the crack widths of the multiple rectangular crack elements:

[0144]

[0145] In the formula, x is a point in the three-dimensional crack; t is the injection time of the fluid in the three-dimensional crack; p(x, t) is the fluid pressure vector in the three-dimensional crack, with the unit of MPa; σ h (x) is the minimum principal stress vector of the three-dimensional crack, with the unit of MPa; N is the total number of rectangular crack elements; ξ i is the i-th rectangular crack element; C(x, ξ i ) is the kernel coefficient of the i-th rectangular crack element, with the unit of MPa / m; w(ξ i ) is the crack width of the i-th rectangular crack element, with the unit of m.

[0146] In some embodiments, the above-mentioned construction module 902 can specifically also be used for:

[0147] Construct the displacement discontinuity equation of the multiple rectangular crack elements;

[0148] Construct the geometric equation and physical equation of the three-dimensional crack;

[0149] According to the displacement discontinuity equation of the multiple rectangular crack elements, use the geometric equation and physical equation of the three-dimensional crack to determine the stress components of the multiple rectangular crack elements.

[0150] In some embodiments, the above-mentioned construction module 902 can specifically also be used for:

[0151] Determine the kernel function of the three-dimensional crack according to the stress components of the multiple rectangular crack elements.

[0152] In some embodiments, the above-mentioned determination module 903 may specifically be configured to:

[0153] According to the law of conservation of mass, establish a solid mechanics model of the fluid pressure in the three-dimensional fracture and the fracture width of the three-dimensional fracture using the following formula:

[0154]

[0155] In the formula, p is the fluid pressure in the three-dimensional fracture; w is the fracture width of the three-dimensional fracture, with the unit of m; t is the time corresponding to the fluid pressure in the three-dimensional fracture, with the unit of s; μ is the dynamic viscosity of the fluid in the three-dimensional fracture.

[0156] In some embodiments, the above-mentioned determination module 903 may also specifically be configured to:

[0157] Construct a solid mechanics model of the fluid pressure in the three-dimensional fracture and the fracture width of the three-dimensional fracture;

[0158] Substitute the equation corresponding to the discrete superposition model into the equation corresponding to the solid mechanics model to determine the fluid-solid coupling equation based on the fracture width of the three-dimensional fracture through the following formula:

[0159]

[0160] In the formula, P is the fluid pressure in the three-dimensional fracture; w is the fracture width of the three-dimensional fracture, with the unit of m; μ is the dynamic viscosity of the fluid in the three-dimensional fracture.

[0161] In some embodiments, the above-mentioned calculation module 904 may specifically be configured to:

[0162] Based on the analytical solution, obtain the partial derivative of the fluid-solid coupling equation with respect to the fracture width of the three-dimensional fracture;

[0163] Use the following formula to construct the Jacobian matrix of the partial derivative of the fluid-solid coupling equation:

[0164]

[0165] Calculate the fracture width of the three-dimensional fracture according to the Jacobian matrix of the partial derivative of the fluid-solid coupling equation.

[0166] In some embodiments, the above-mentioned calculation module 904 may also specifically be configured to:

[0167] Convert the fluid-solid coupling equation into the following partial derivative form:

[0168]

[0169] Wherein, p is the matrix of the fluid pressure in the three-dimensional crack; w is the crack width matrix of the three-dimensional crack;

[0170] According to the Newton iteration method, the partial derivatives of the fluid-solid coupling equation are expanded as:

[0171]

[0172] According to the expanded form of the partial derivatives of the fluid-solid coupling equation, matrices C and D are respectively defined using the following formulas:

[0173]

[0174] The discrete superposition model of the fluid pressure in the constructed three-dimensional crack and the crack widths of multiple rectangular crack units is expressed in the following matrix form:

[0175] p = Aw + σ h ;

[0176] Wherein, matrix A is defined as:

[0177] According to matrices C, D and matrix A, the partial derivatives of the fluid-solid coupling equation are expressed in the following matrix form:

[0178] f′(w n ) = C + D·A;

[0179] Obtain the Jacobian matrix of the partial derivative f′(w n ) = C + D·A in matrix form.

[0180] It should be noted that the units, devices or modules etc. illustrated in the above embodiments can be specifically implemented by computer chips or entities, or by products with certain functions. For the convenience of description, when describing the above devices, they are divided into various modules according to functions and described separately. Of course, when implementing this specification, the functions of each module can be realized in the same or multiple software and / or hardware, or the modules realizing the same function can be realized by the combination of multiple sub-modules or sub-units, etc. The device embodiments described above are only illustrative. For example, the division of the units is only a logical function division, and there may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point, the couplings or direct couplings or communication connections shown or discussed with each other can be through some interfaces, and the indirect couplings or communication connections of the devices or units can be in electrical, mechanical or other forms.

[0181] As can be seen from the above, based on the three-dimensional crack width calculation device provided in the embodiments of this specification, a three-dimensional crack can be divided into multiple rectangular crack units; according to the multiple rectangular crack units, a discrete superposition model of the fluid pressure in the three-dimensional crack and the crack widths of the multiple rectangular crack units can be constructed; according to the discrete superposition model, a fluid-solid coupling equation based on the crack width of the three-dimensional crack can be determined; according to the Jacobian matrix of the partial derivatives of the fluid-solid coupling equation, the crack width of the three-dimensional crack can be calculated. Compared with the existing methods, by dividing the three-dimensional crack into multiple rectangular crack units to determine the Jacobian matrix of the partial derivatives of the fluid-solid coupling equation, each rectangular crack unit can independently consider its fluid pressure and crack width, and then the Jacobian matrix can be used to more accurately describe the geometric shape of the three-dimensional crack, improving the calculation speed and calculation accuracy of the crack width of the three-dimensional crack.

[0182] The embodiments of this specification also provide a computer device for a three-dimensional crack width calculation method, including a processor and a memory for storing instructions executable by the processor. When the processor is specifically implemented, it can execute the following steps according to the instructions: divide a three-dimensional crack into multiple rectangular crack units; according to the multiple rectangular crack units, construct a discrete superposition model of the fluid pressure in the three-dimensional crack and the crack widths of the multiple rectangular crack units; according to the discrete superposition model, determine a fluid-solid coupling equation based on the crack width of the three-dimensional crack; according to the Jacobian matrix of the partial derivatives of the fluid-solid coupling equation, calculate the crack width of the three-dimensional crack.

[0183] In order to be able to complete the above instructions more accurately, refer to Figure 10 As shown, the embodiments of this specification also provide another specific computer device, wherein the computer device includes a network communication port 1001, a processor 1002, and a memory 1003. The above structures are connected by internal cables so that each structure can perform specific data interactions.

[0184] The processor 1002 can specifically be used to divide a three-dimensional crack into multiple rectangular crack units; according to the multiple rectangular crack units, construct a discrete superposition model of the fluid pressure in the three-dimensional crack and the crack widths of the multiple rectangular crack units; according to the discrete superposition model, determine a fluid-solid coupling equation based on the crack width of the three-dimensional crack; according to the Jacobian matrix of the partial derivatives of the fluid-solid coupling equation, calculate the crack width of the three-dimensional crack.

[0185] The memory 1003 can specifically be used to store the corresponding instruction programs.

[0186] In this embodiment, the network communication port 1001 can be bound to different communication protocols, so as to send or receive different data, which is a virtual port. For example, the network communication port can be a port responsible for web data communication, or a port responsible for FTP data communication, or a port responsible for mail data communication. In addition, the network communication port can also be a physical communication interface or communication chip. For example, it can be a wireless mobile network communication chip, such as GSM, CDMA, etc.; it can also be a Wifi chip; it can also be a Bluetooth chip.

[0187] In this embodiment, the processor 1002 can be implemented in any suitable manner. For example, the processor can take the form of, for example, a microprocessor or a processor and a computer-readable medium storing computer-readable program code (such as software or firmware) executable by the (micro)processor, logic gates, switches, an Application Specific Integrated Circuit (ASIC), a programmable logic controller, and an embedded microcontroller, etc. This specification does not make any limitations.

[0188] In this embodiment, the memory 1003 includes volatile memory and non-volatile memory. The memory 1003 can include multiple levels. In a digital system, anything that can store binary data can be a memory; in an integrated circuit, a circuit without a physical form but with a storage function is also called a memory, such as RAM, FIFO, etc.; in a system, a storage device with a physical form is also called a memory, such as a memory stick, a TF card, etc.

[0189] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program code.

[0190] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate for implementing in the processFigure 1 one process or multiple processes and / or blocks Figure 1 means for the functions specified in one block or multiple blocks.

[0191] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including an instruction means that implements the functions in the process Figure 1 one process or multiple processes and / or blocks Figure 1 specified in one block or multiple blocks.

[0192] These computer program instructions may also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in the process Figure 1 one process or multiple processes and / or blocks Figure 1 specified in one block or multiple blocks.

[0193] The specific embodiments described above further elaborate on the objectives, technical solutions, and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for calculating the crack width of a three-dimensional crack, characterized in that, Including: Dividing a three-dimensional crack into multiple rectangular crack units; Constructing a discrete superposition model of the fluid pressure in the three-dimensional crack and the crack widths of the multiple rectangular crack units according to the multiple rectangular crack units; Determining a fluid-solid coupling equation based on the crack width of the three-dimensional crack according to the discrete superposition model; Calculating the crack width of the three-dimensional crack according to the Jacobian matrix of the partial derivatives of the fluid-solid coupling equation; 2. The method according to claim 1, wherein The constructing of the discrete superposition model of the fluid pressure in the three-dimensional crack and the crack widths of the multiple rectangular crack units includes: Determining the minimum principal stress vector of the three-dimensional crack according to the stress components of the multiple rectangular crack units; Determining the kernel coefficients of the multiple rectangular crack units according to the kernel function of the three-dimensional crack; Constructing the discrete superposition model of the fluid pressure in the three-dimensional crack and the crack widths of the multiple rectangular crack units by using the following formula according to the minimum principal stress vector of the three-dimensional crack and the kernel coefficients of the multiple rectangular crack units: Wherein, x is a point in the three-dimensional crack; t is the injection time of the fluid in the three-dimensional crack; p(x, t) is the fluid pressure vector in the three-dimensional crack, with the unit of MPa; σ h (x) is the minimum principal stress vector of the three-dimensional crack, with the unit of MPa; N is the total number of rectangular crack elements; ξ i is the i-th rectangular crack element; C(x, ξ i ) is the kernel coefficient of the i-th rectangular crack element, with the unit of MPa / m; w(ξ i ) is the crack width of the i-th rectangular crack element, with the unit of m.

3. The method according to claim 2, wherein The method further includes: Constructing the displacement discontinuity equation of the multiple rectangular crack units; Constructing the geometric equation and physical equation of the three-dimensional crack; Determining the stress components of the multiple rectangular crack units according to the displacement discontinuity equation of the multiple rectangular crack units by using the geometric equation and physical equation of the three-dimensional crack; 4. The method according to claim 2, characterized in that The method further includes: Determining the kernel function of the three-dimensional crack according to the stress components of the multiple rectangular crack units; 5. The method according to claim 1, characterized in that The method further includes: Establishing a solid mechanics model of the fluid pressure in the three-dimensional crack and the crack width of the three-dimensional crack by using the following formula according to the law of conservation of mass: In the formula, p is the fluid pressure in the three-dimensional crack; w is the crack width of the three-dimensional crack, with the unit of m; t is the time corresponding to the fluid pressure in the three-dimensional crack, with the unit of s; μ is the dynamic viscosity of the fluid in the three-dimensional crack.

6. The method according to claim 1, wherein The determining of the fluid-solid coupling equation based on the crack width of the three-dimensional crack according to the discrete superposition model includes: Constructing a solid mechanics model of the fluid pressure in the three-dimensional crack and the crack width of the three-dimensional crack; Substituting the equation corresponding to the discrete superposition model into the equation corresponding to the solid mechanics model to determine the fluid-solid coupling equation based on the crack width of the three-dimensional crack by using the following formula: In the formula, P is the fluid pressure in the three-dimensional crack; w is the crack width of the three-dimensional crack, with the unit of m; μ is the dynamic viscosity of the fluid in the three-dimensional crack.

7. The method according to claim 1, characterized in that The calculating of the crack width of the three-dimensional crack according to the Jacobian matrix of the partial derivatives of the fluid-solid coupling equation includes: Obtaining the partial derivative of the fluid-solid coupling equation with respect to the crack width of the three-dimensional crack based on the analytical solution; Constructing the Jacobian matrix of the partial derivatives of the fluid-solid coupling equation by using the following formula: Calculating the crack width of the three-dimensional crack according to the Jacobian matrix of the partial derivatives of the fluid-solid coupling equation; 8. The method according to claim 7, wherein The obtaining of the partial derivative of the fluid-solid coupling equation with respect to the crack width of the three-dimensional crack based on the analytical solution includes: Converting the fluid-solid coupling equation into the following partial derivative form: In the formula, p is the matrix of the fluid pressure in the three-dimensional crack; w is the crack width matrix of the three-dimensional crack; According to Newton's iterative method, the partial derivatives of the fluid-structure interaction equation are expanded as follows: According to the expansion form of the partial derivatives of the fluid-structure interaction equation, matrices C and D are defined respectively using the following formulas: The discrete superposition model of the fluid pressure in the three-dimensional crack and the crack widths of multiple rectangular crack elements constructed is expressed in the following matrix form: p = Aw + σ h ; In the formula, matrix A is defined as: According to matrices C, D, and A, the partial derivatives of the fluid-structure interaction equation are expressed in the following matrix form: f′(w n ) = C + D·A; Obtain the Jacobian matrix of the partial derivative \(f'(w n ) = C + D\cdot A\) of the fluid-structure interaction equation in matrix form.

9. A device for calculating the crack width of a three-dimensional crack, characterized in that, The device includes: a partitioning module configured to partition a three-dimensional crack into multiple rectangular crack elements; a construction module configured to construct a discrete superposition model of the fluid pressure in the three-dimensional crack and the crack widths of multiple rectangular crack elements according to the multiple rectangular crack elements; a determination module configured to determine a fluid-structure interaction equation based on the crack width of the three-dimensional crack according to the discrete superposition model; a calculation module configured to calculate the crack width of the three-dimensional crack according to the Jacobian matrix of the partial derivatives of the fluid-structure interaction equation.

10. A computer device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the computer program, the method described in any one of claims 1-8 is implemented.

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