Simulation method of hydraulic fracturing process and related device

Abstract

The present disclosure provides a simulation method of hydraulic fracturing process and related equipment. Specifically, the simulation method comprises: constructing a rock mass model by using smoothed particle hydrodynamics based on rock mass mechanical parameters and fracture distribution of a target rock mass; the rock mass model comprises fluid particles, and the fluid particles are endowed with a preset water pressure; calculating characteristic parameters of particles of the rock mass model based on a partial differential equation of a preset seepage field, a preset control equation and a preset time parameter; wherein the characteristic parameters comprise position and velocity; the preset control equation comprises a plurality of control equations; and the plurality of control equations correspond to different types and states of particles. Such a technical solution combines smoothed particle hydrodynamics and seepage field to simulate the hydraulic fracturing process, and the conversion from continuous domain to discontinuous domain is realized under the SPH framework, which can significantly improve the calculation efficiency.

Description

Technical Field

[0001] This disclosure relates to the field of civil engineering technology, and in particular to a simulation method and related equipment for hydraulic fracturing processes. Background Technology

[0002] Hydraulic fracturing is commonly used for the development of unconventional oil and gas resources such as shale gas, tight oil, and coalbed methane, and is also applied to enhance oil recovery in traditional oil and gas fields. However, in-situ and large-scale hydraulic fracturing still faces numerous challenges, such as high cost and poor repeatability. Therefore, numerical simulation methods are often used to explore the propagation mechanisms of hydraulic fracturing.

[0003] Traditional numerical simulation methods such as the finite element method, finite difference method, and extended finite element method require mesh refinement around the fractures. When natural fractures are densely distributed, mesh generation is difficult and computationally inefficient, making them unsuitable for reservoir-scale problems. Discrete element method (DEM) and discontinuous deformation analysis (DDA) do not require mesh generation when simulating hydraulic fractures, but microscopic parameters cannot directly characterize macroscopic parameters extracted from the reservoir, requiring extensive manual calibration and exhibiting relatively low computational efficiency, making them difficult to apply in practical engineering. Therefore, there is an urgent need to develop a novel hydraulic fracturing simulation method for field-scale applications, where parameters can be obtained directly from the field. Summary of the Invention

[0004] In view of this, the purpose of this disclosure is to propose a simulation method and related equipment for the hydraulic fracturing process.

[0005] To achieve the above objectives, this disclosure provides a simulation method for the hydraulic fracturing process, comprising:

[0006] Based on the rock mass mechanical parameters and fracture distribution of the target rock mass, a rock mass model is constructed using smooth particle fluid dynamics; the rock mass model includes fluid particles, which are subjected to a preset water pressure.

[0007] Based on the partial differential equations of the preset seepage field, the preset control equations, and the preset time parameters, the characteristic parameters of the particles in the rock mass model are calculated; wherein, the characteristic parameters include position and velocity; the preset control equations include multiple control equations; the multiple control equations correspond to different types and states of particles.

[0008] Based on the same inventive concept, this disclosure also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the simulation method as described in any of the foregoing embodiments.

[0009] Based on the same inventive concept, this disclosure also provides a non-transitory computer-readable storage medium that stores computer instructions for causing a computer to perform any of the simulation methods described above.

[0010] As described above, the simulation method and related equipment for hydraulic fracturing provided in this disclosure acquire and construct a rock mass model using Smoothed Particle Hydrodynamics (SPH) based on the rock mass's mechanical parameters and fracture distribution. The model calculates characteristic parameters of the particles in the rock mass model based on the partial differential equations of a pre-defined seepage field, pre-defined control equations, and pre-defined time parameters. These characteristic parameters include position and velocity. The pre-defined control equations include multiple control equations, each corresponding to different particle types and states. This technical solution combines SPH with seepage field simulation to model the hydraulic fracturing process. The transition from continuous to discontinuous domains is achieved within the SPH framework, significantly improving computational efficiency. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in this disclosure or related technologies, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This diagram illustrates the principle of rock mass change under hydraulic fracturing conditions according to an embodiment of the present disclosure.

[0013] Figure 2 This diagram illustrates a two-dimensional hydraulic fracturing rock mass model provided in an embodiment of the present disclosure.

[0014] Figure 3A This diagram illustrates the maximum principal stress distribution at different times according to an embodiment of the present disclosure.

[0015] Figure 3B This diagram illustrates a water pressure distribution at different times according to an embodiment of the present disclosure.

[0016] Figure 3C This diagram illustrates the change of crack damage over time according to an embodiment of the present disclosure.

[0017] Figure 3D A schematic diagram showing the numerical simulation results of a discontinuous particle according to an embodiment of this disclosure is provided.

[0018] Figure 3E A schematic diagram showing the test results of hydraulic fracturing according to an embodiment of this disclosure is provided;

[0019] Figure 4 This diagram illustrates the structure of an electronic device provided in an embodiment of the present disclosure. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this disclosure clearer, the following detailed description is provided in conjunction with specific embodiments and the accompanying drawings.

[0021] It should be noted that, unless otherwise defined, the technical or scientific terms used in the embodiments of this disclosure should have the ordinary meaning understood by one of ordinary skill in the art to which this disclosure pertains. The terms "first," "second," and similar terms used in the embodiments of this disclosure do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0022] As described in the background section, the relevant simulation methods suffer from problems such as difficulty in mesh generation, low computational efficiency, and a large amount of manual calibration work.

[0023] In view of this, embodiments of this disclosure provide a simulation method and related equipment for hydraulic fracturing processes. The simulation method includes: acquiring and constructing a rock mass model using smoothed particle hydrodynamics (SPH) based on the rock mass's mechanical parameters and fracture distribution; calculating characteristic parameters of particles in the rock mass model based on a preset seepage field partial differential equation, a preset control equation, and preset time parameters; wherein the characteristic parameters include position and velocity; the preset control equation includes multiple control equations; and the multiple control equations correspond to different particle types and states. This technical solution combines smoothed particle hydrodynamics and seepage field to simulate the hydraulic fracturing process, and the conversion from continuous to discontinuous domains is achieved within the SPH framework, significantly improving computational efficiency.

[0024] To make the technical solution of this disclosure clearer and easier to understand, the principle of the simulation method for the hydraulic fracturing process provided in the embodiments of this disclosure will be introduced below with reference to the accompanying drawings.

[0025] Figure 1 This diagram illustrates the principle of rock mass change under hydraulic fracturing conditions according to an embodiment of this disclosure. Figure 1 As shown, a simulation of the target rock mass and its cracks is performed. Exemplarily, based on a smooth particle hydrodynamics framework, the matrix in the rock mass is discretized into matrix particles, and the fluid at the crack location is discretized into fluid particles. Matrix particles in continuous region 101 interact with each other, and with fluid particles, through particle bonds. As shown in hydraulic fracturing region 102, under hydraulic fracturing, when tensile and shear failures between matrix particles exceed a certain limit, the matrix particles become damaged particles and their particle bonds break. At this point, the permeability coefficient of the matrix particles conforms to Darcy's theorem, for example, a constant; the permeability coefficient of the fluid particles is determined based on the cubic law. Next, the damaged particles transform into new fluid particles, forming new fractures, where the fracture path and the position of the new fluid particles remain consistent, as shown in transition region 103. Further, as the stress increases and the degree of damage increases to a certain extent, some matrix particles become discontinuous particles. There are no particle bonds between discontinuous particles and other matrix particles, but contact bonds exist, see contact generation region 104. Finally, matrix particles and discontinuous particles in contact region 105 engage in frictional contact.

[0026] Next, the simulation method for the hydraulic fracturing process provided in the embodiments of this disclosure will be described in detail.

[0027] First, based on the rock mass mechanics parameters and fracture distribution of the target rock mass, a rock mass model is constructed using smoothed particle fluid dynamics. It should be noted that natural fractures typically exist within the target rock mass. Obtaining the fracture distribution of the target rock mass facilitates the simulation of fractures in the rock mass model, such as... Figure 2 This diagram illustrates a two-dimensional hydraulic fracturing rock mass model provided in an embodiment of the present disclosure.

[0028] In some embodiments, the rock matrix is ​​discretized into matrix particles, and the fractures are discretized into fluid particles.

[0029] In some embodiments, rock mechanics parameters include initial particle velocity, initial stress, material parameters, position, stress boundary conditions, etc.

[0030] For example, multiple layers, such as three layers of virtual particles, are arranged outside the boundary. Stress is applied to the virtual boundary composed of these three layers of virtual particles. Taking a transverse stress of 24.95 MPa as an example, multiple layers of particles are first selected at the boundary, and the stress value reached on the boundary is calculated continuously. Before reaching the required stress of 24.95 MPa, the virtual particles continue to be loaded. When the stress exceeds 24.95 MPa, the virtual particles begin to apply a reverse tensile force to the boundary particles, bringing it closer to the required value. However, this reverse tensile force may cause the boundary stress to be far below the required 24.95 MPa, making it difficult to accurately equal to 24.95 MPa. Therefore, a floating limit range value is set, such as 0.01 MPa. When the boundary stress reaches 24.95 ± 0.01 MPa, the virtual particles do not apply any force. Through this strategy, the real geostress boundary conditions and stress loading process are simulated.

[0031] Next, we calculate the changes in density and internal forces stored in the rock.

[0032] For example, the mass conservation equation and momentum conservation equation of SPH yield the density change and internal forces:

[0033] (1)

[0034] in, Indicates density, Represents particle velocity. x Indicates particle displacement. Representing adjacent particles i With ground particles j Speed ​​difference, m Indicates quality, This represents the Cauchy stress tensor. This represents the additional force acting on the ground particle. This represents the artificial viscosity achieved in the calculation to suppress non-physical vibrations; external force. It is generally set as the stored gravity. In the formula... (Right now ) and (Right now ) are the smooth kernel function of the particle and its gradient, respectively. Equation (1) corresponds to the first governing equation.

[0035] In some embodiments, the kernel function is determined by searching for surrounding particles using a link-list search algorithm, as follows:

[0036] (2)

[0037] In the formula, R For the core radius, Let be the coefficient factor of the kernel function at a two-dimensional scale, taken as . .

[0038] Next, Darcy's law is used to solve for the permeability coefficient of the rock matrix (corresponding matrix particles), and the cubic law is used to simulate the water flow in the rock cracks (fluid particles) to simulate the seepage field.

[0039] In some embodiments, the seepage field is simulated using the following partial differential equations:

[0040] (3)

[0041] (4)

[0042] in, It's water head. For seepage velocity, The water content, or unit storage capacity, represents the amount of water released per unit volume of porous media due to its own compression and water expansion when the head decreases by one unit. Here, it can be set to 10. -6 . is the permeability coefficient.

[0043] Furthermore, regardless of whether the fractures are natural or hydraulically fractured, the permeability coefficient of the fluid particles within the fracture... The calculation formula conforms to the law of cubes as follows:

[0044] (5)

[0045] in, It is the acceleration due to gravity. is the viscosity coefficient of water flow, typically taken as 1e⁻³ (assuming a temperature of 20℃). For the maximum principal stress, For the minimum principal stress, The initial crack width can be set directly based on the on-site crack conditions. This is the stiffness coefficient of the crack, generally a constant taken to be consistent with the initial elastic modulus, for example, 15e9 Pa. u Poisson's ratio, The normal deformation coefficient; Pw This refers to the water pressure.

[0046] It should be noted that in equation (5) It can be updated iteratively, for example, by using the formula (15) for iterative updates.

[0047] Furthermore, according to formulas (3) and (4), the head can be obtained. Hi, Therefore, we can obtain the following formula: Pw :

[0048] (6);

[0049] in The acceleration due to gravity is set to 9.8 m / s². 2 , For density.

[0050] It should be noted that, ; ;in and From equation (1) Superscript takes different x, y It indicates that something has been received.

[0051] Based on this, the permeability coefficient at this point is calculated using the maximum principal stress, minimum principal stress, and water pressure. It should be understood that the new permeability coefficient is used in the calculation of formula (3) for the next time step, thereby achieving dynamic updating of the permeability coefficient.

[0052] Furthermore, since the permeability coefficient of the matrix particles conforms to Darcy's law, it can be directly set as a constant, without considering the influence of the degree of change in matrix porosity on matrix seepage.

[0053] Then, the hydraulic pressure generated by the seepage field is superimposed on the initial stress field of the storage. In some embodiments, the formula for superimposing the stress field with water pressure is as follows:

[0054] (7)

[0055] in, , , They are respectively In Take respectively x, y As a result, The normal deformation coefficient is... S It is the deviatoric stress tensor.

[0056] For example, the formula for solving S is:

[0057] (8)

[0058] Among them, shear modulus G=E / (2×(1+u)) , E For elastic modulus, u Let be Poisson's ratio. In equation (8), , The strain rate tensor is defined as:

[0059] (9)

[0060] To align the material information with strain, a continuity equation is derived by introducing the Jaumann rate of change:

[0061] (10)

[0062] and These are torsion rate tensors, which are defined as:

[0063] (11)

[0064] Where P is the isotropic pressure, calculated as follows:

[0065] (12)

[0066] in, , Represents the initial density of the particles. P H Let Γ represent the Hugoniot curve function, where Γ is the Grüneisen parameter.

[0067] Therefore, the momentum equation for SPH considering fracture seepage-stress can be:

[0068] (13)

[0069] It should be noted that, U This represents a complete matrix particle.

[0070] Next, the state of particle interaction pairs within the reservoir is determined. When particles meet the following conditions, they are considered to have suffered damage. The Mohr-Coulomb criterion with tensile truncation is used to determine whether tensile or shear failure occurs within the rock material:

[0071] (14)

[0072] in, , These are the tensile stress and shear stress on the failure surface, respectively. The tensile strength of the rock mass c For cohesive strength, ϕ It is the internal friction angle.

[0073] Under water pressure, when the stress field of the rock mass satisfies the Mohr-Coulomb failure criterion with tensile truncation, matrix particle damage can be considered the start of failure. The particle bonds between matrix particles break, generating crack channels (corresponding to hydraulic cracks). The equivalent crack width of the hydraulic crack is updated according to the stress as shown below:

[0074] (15)

[0075] The permeability coefficient is directly transformed from a constant to a cubic law (corresponding to the location of damaged particles filling fluid particles), and the new crack width can be directly used for permeability coefficient calculation: This updates the seepage field.

[0076] Furthermore, when the damage to the particles reaches a certain level, the particles transform into discontinuous particles, allowing them to establish contact relationships with each other.

[0077] In some embodiments, the degree of particle damage The ratio of all damaged particles within twice the nuclear radius to the total number of particles within twice the nuclear radius of that particle is as follows:

[0078] (16)

[0079] in, This represents the number of all damaged particles within twice the nuclear radius. This represents the number of all particles within twice the nuclear radius.

[0080] For matrix particles with a damage level of 0.5, which are discontinuous particles (DP particles), contact relationships between particles can be established to construct the contact state after particle destruction. When the damage level reaches 0.5, it is assumed that the particle forms frictional contact with the surrounding rock particles, and the frictional contact is calculated. The governing equation (corresponding to the third governing equation) is calculated as follows:

[0081] (17)

[0082] in and These represent the normal and tangential contact forces, respectively, and their solution method is as follows:

[0083] (18)

[0084] (19)

[0085] (20)

[0086] In the formula k n For normal stiffness, U n The normal overlap is... n It is the unit outward normal vector at the point of contact; R i , R dLet be the radius of the two particles, usually taken as Δ, and let Δ be the initial interparticle distance of the matrix particles. P / 2, and the radius of discontinuous particles. d id This represents the distance between the matrix particles and the discontinuous particles. E i and E d These are the Young's moduli of the matrix particles and the DP particles, respectively.

[0087] The formula for calculating the tangential contact force is:

[0088] (twenty one)

[0089] (twenty two)

[0090] (twenty three)

[0091] In the formula, k s For tangential stiffness, This is the ratio of tangential stiffness to normal stiffness. For shear increment, n It is the unit outward normal vector at the point of contact; This represents the velocity difference between the two matrix particles and the discontinuous particles. This is the tangential contact force from the previous step.

[0092] Finally, the governing equations for seepage-stress-damage-contact (corresponding to the fourth governing equation) are as follows:

[0093] (twenty four)

[0094] Based on a preset time step, the frog-leap algorithm is used for time integration to obtain the position, velocity, and density of each matrix particle, as shown in the following formula:

[0095] (25)

[0096] In the formula: t and t 0 represents the calculation time and the initial time, respectively; Δ t To calculate the time step; ρ The density of the particles; v The velocity of the particle; x These are the particle's position coordinates. This represents the rate of change of water head.

[0097] It should be noted that the appropriate governing equations are selected based on the type (fluid particles, matrix particles) and state (damaged particles, discontinuous particles) of the particles within the search domain. The determination of the particle state can be based on equations (14) and (16).

[0098] By repeatedly calculating the position, velocity, and density of particles until the preset calculation step, the entire process of crack propagation under hydraulic pressure can be obtained.

[0099] Optionally, the above simulation method can be used for hydraulic fracturing simulation of reservoir size and deep-buried reservoirs.

[0100] In summary, the simulation method based on hydraulic fracturing and SPH provided in this disclosure does not require a fixed mesh. The particle resolution can be adaptively adjusted according to the seepage requirements, making it easier to capture fracture propagation and seepage field changes during hydraulic fracturing. This solves the problems of difficult mesh generation, low computational efficiency, and limited applicability to reservoir-scale applications in existing technologies. This disclosure derives the seepage equations for fractures and matrix based on the SPH framework, as well as the seepage-stress-damage-contact control equations under seepage force. A single SPH framework can accurately capture the entire process of fracture seepage, crack initiation and propagation, contact formation, and frictional slip. Furthermore, the conversion from continuous to discontinuous domains is achieved within a single SPH framework, significantly improving computational efficiency and making it suitable for hydraulic fracturing problems in reservoirs of different scales.

[0101] Furthermore, the mechanical parameters, such as elastic modulus and Poisson's ratio, of the partial differential equations upon which the control equations of the embodiments of this disclosure are based can be directly obtained from the field to be simulated without repeated adjustments.

[0102] Next, this disclosure will provide a detailed description of the above-described simulation method for a hydraulic fracturing process in conjunction with specific embodiments.

[0103] Step S101: First, construct the matrix and pre-fabricated fracture particles, and apply continuously increasing water pressure to the pre-fabricated fractures up to 10 MPa. Here, the pre-fabricated fractures can be natural fractures in the rock mass.

[0104] Specifically, such as Figure 2 As shown, a two-dimensional model of hydraulic fracturing was established, for example, a square numerical model with a side length of 1 m. Fracturing fluid was injected from a pre-fabricated fracture, applied to the surface of the fracture. The pre-fabricated fracture was located at the center of the square model and was 0.2 m long. The injection pressure was gradually increased to 10 MPa to deform the sample, uniformly discretizing the rock sample into 40,000 solid particles with an initial particle spacing of 5 mm. Three layers of virtual particles, totaling 2,400 particles, were arranged on each side of the boundary.

[0105] It should be noted that solid particles include matrix particles (for rock masses) and fluid particles (corresponding to the liquid in the fractures).

[0106] Step S102: Assign the corresponding material parameters to the particles, as shown in Table 1. Set the pressure boundary by applying velocity through a layer of external virtual particles to obtain the pressure boundary within the internal computational domain. The pressure magnitude is determined according to the burial depth of the reservoir; in this case, it can be set to 0 MPa.

[0107] Stress is applied to a virtual boundary consisting of three layers of virtual particles. The thickness of the numerical model is one layer of real particles, therefore the model can be considered as a plane strain problem.

[0108] Furthermore, by introducing the Weibull distribution function, the non-uniformity coefficient of tensile strength was set to 20. The time step for this simulation was set to 1×10⁻⁶. -6 s.

[0109] Table 1 Mechanical and physical parameters of the rock mass

[0110]

[0111] Step S103: Calculate key parameters for model particles in a single time step: including pairing between smooth particles, for example, the complete particles of the matrix particles are searched for and paired with neighboring particles based on twice the smooth kernel radius, the smooth kernel function is calculated using formula (2), the density change is calculated using formula (1), and the Cauchy stress change is calculated using formula (1).

[0112] It should be noted that all particles within twice the radius of the smooth core are matrix particles, and the density change, Cauchy stress change, etc. are calculated using formula (1).

[0113] Further, the formulas for the change in water flow velocity due to head difference (3) and head change (4) are calculated, and the water pressure is superimposed on the Cauchy stress (7). At the same time, the formula for the fracture state of the particles (14) is calculated according to the failure criterion, thereby obtaining a new permeability coefficient in the crack and thus updating the new seepage field. Meanwhile, the formula for the damage degree of the particles (16) is calculated. If the damage degree is not less than 0.5, the particles become discontinuous particles, and the intact matrix particles and DP particles come into frictional contact, thus obtaining the final damage-tensile failure control equation formula (24) with hydraulic coupling. Among them, the calculation of the normal force and tangential force of the intact matrix particles and DP particles can be carried out using formulas (18)-(23), etc. Thus, the crack distribution, seepage field change, particle density change rate, acceleration, and velocity can be obtained within a single time step.

[0114] Step S104: Perform time integration on the key parameters within a single time step. The integration method adopts the frog leap algorithm, for example, formula (25) to obtain the characteristic parameter values ​​of each time step on the particle.

[0115] Step S105: Determine whether the calculation step has reached the set calculation step. If the maximum calculation step has not been reached, repeat steps S103 to S104. If the maximum calculation step has been reached, the reservoir fracturing calculation is terminated.

[0116] It should be noted that the type and state of the particles may change for different calculation steps. In step S103, the corresponding control equation is selected according to the type and state of the neighboring particles in the search domain, such as formula (1), formula (13), formula 17, and formula (24).

[0117] Through the above steps, the maximum principal stress distribution of the reservoir under water pressure was finally obtained (e.g. Figure 3A As shown), water pressure distribution (such as) Figure 3B (as shown) and the change of crack damage over time (e.g.) Figure 3C (As shown).

[0118] Figure 3D A schematic diagram showing the numerical simulation results of discontinuous particles in this embodiment is provided. Figure 3E This diagram illustrates the test results of hydraulic fracturing of the rock mass in this embodiment. (Comparison) Figure 3D and Figure 3E As can be seen, the water pressure path in both cases is horizontal, leading to fracturing and dominant seepage. Therefore, the simulation method provided in this embodiment demonstrates accuracy in simulating reservoir hydraulic fracturing.

[0119] Based on the same inventive concept, this disclosure also provides a method for simulating the hydraulic fracturing process, including:

[0120] Referring to steps S101~S102: Obtain and construct a rock mass model based on the rock mass mechanical parameters and fracture distribution of the target rock mass using smooth particle fluid dynamics; the rock mass model includes fluid particles, which are given a preset water pressure;

[0121] Referring to steps S103~S105: Based on the partial differential equations of the preset seepage field, the preset control equations, and the preset time parameters, the characteristic parameters of the particles in the rock mass model are calculated; wherein, the characteristic parameters include position and velocity; the preset control equations include multiple control equations; the multiple control equations correspond to different types and states of particles.

[0122] In some embodiments, referring to formulas (3) and (4), the rock mass model further includes matrix particles; the partial differential equation of the seepage field includes a seepage coefficient; wherein the seepage coefficient of the matrix particles is determined based on Darcy's law; and the seepage coefficient of the fluid particles is determined based on the cubic law (e.g., formula 5).

[0123] Optionally, the permeation coefficient of the matrix particles can be a constant.

[0124] In some embodiments, such as Figure 2 As shown, the rock mass model includes a matrix region and a fracture region; wherein the fluid particles are located in the fracture region; the fracture region is determined based on the fracture distribution.

[0125] In some embodiments, the control method includes Cauchy stress; the calculation of characteristic parameters of particles in the rock mass model based on the partial differential equation of the preset seepage field, the preset control equation, and the preset time parameter includes:

[0126] Referring to formulas (3), (4), and (6), the hydraulic pressure of the particles is determined based on the partial differential equation of the preset seepage field and the rock mass model; wherein the hydraulic pressure is superimposed on the Cauchy stress. Here, the specific superposition formula is shown in formula (7).

[0127] In some embodiments, the particle state includes discontinuous particles and damaged particles; wherein,

[0128] The discontinuous particles are determined based on particle damage degree and a preset threshold; wherein, the particle damage degree is determined based on the proportion of damaged particles to all particles within a preset distance; here, the damage degree can be calculated using formula (16); the preset threshold can be not less than 0.5;

[0129] The damage particles are determined based on the Mohr–Coulomb criterion with stretching truncation, for example, Equation (14).

[0130] In some embodiments, the rock mass model includes matrix particles and fluid particles; the simulation method further includes:

[0131] like Figure 1 As shown in 103, in response to determining that the matrix particle meets the criteria of the damaged particle, the matrix particle is converted into a new fluid particle.

[0132] In some embodiments, the plurality of governing equations includes a first governing equation, such as Equation (1), a second governing equation (Equation 13), a third governing equation (Equation 17), and a fourth governing equation (Equation 24); the calculation of the characteristic parameters of the particles in the rock mass model based on the partial differential equation of the preset seepage field, the preset governing equation, and the preset time parameter includes:

[0133] In response to determining that only intact matrix particles exist within the search domain, the density change rate, velocity, and acceleration of the matrix particles are calculated using the first governing equation;

[0134] In response to determining that only intact matrix particles and fluid particles exist within the search domain, the density change rate, velocity, and acceleration of the matrix particles are calculated using the second governing equation;

[0135] In response to determining that only intact matrix particles and discontinuous particles exist within the search domain, the density change rate, velocity, and acceleration of the matrix particles are calculated using the third governing equation.

[0136] In response to determining that only intact matrix particles, fluid particles, and discontinuous particles exist within the search domain, the density change rate, velocity, and acceleration of the matrix particles are calculated using the fourth governing equation.

[0137] Optionally, the search domain can be preset, for example, it can be twice the smooth kernel radius.

[0138] In some embodiments, the preset time parameter includes a time step, such as 1×10. -6 s and steps;

[0139] The partial differential equations, control equations, and time parameters based on the preset seepage field are used to calculate the characteristic parameters of the particles in the rock mass model, including:

[0140] Based on the partial differential equations and the pre-defined control equations of the pre-defined seepage field, the density change, velocity, and acceleration of the particles are determined.

[0141] Based on the time step, the density change, velocity, and acceleration are integrated to obtain the particle's density, position, and velocity, for example, using formula (25).

[0142] It should be noted that the method of this disclosure embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this disclosure embodiment, and the multiple devices will interact with each other to complete the method described.

[0143] It should be noted that the above description describes some embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0144] Based on the same inventive concept, corresponding to the methods of any of the above embodiments, this disclosure also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the simulation method described in any of the above embodiments.

[0145] Figure 4 This embodiment illustrates a more specific hardware structure of an electronic device. The device may include a processor 1010, a memory 1020, an input / output interface 1030, a communication interface 1040, and a bus 1050. The processor 1010, memory 1020, input / output interface 1030, and communication interface 1040 are interconnected internally via the bus 1050.

[0146] The processor 1010 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this specification.

[0147] The memory 1020 can be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage device, dynamic storage device, etc. The memory 1020 can store the operating system and other applications. When the technical solutions provided in the embodiments of this specification are implemented by software or firmware, the relevant program code is stored in the memory 1020 and is called and executed by the processor 1010.

[0148] The input / output interface 1030 is used to connect input / output modules to realize information input and output. Input / output modules can be configured as components within the device (not shown in the figure) or externally connected to the device to provide corresponding functions. Input devices may include keyboards, mice, touchscreens, microphones, various sensors, etc., while output devices may include displays, speakers, vibrators, indicator lights, etc.

[0149] The communication interface 1040 is used to connect a communication module (not shown in the figure) to enable communication between this device and other devices. The communication module can communicate via wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0150] Bus 1050 includes a pathway for transmitting information between various components of the device, such as processor 1010, memory 1020, input / output interface 1030, and communication interface 1040.

[0151] It should be noted that although the above-described device only shows the processor 1010, memory 1020, input / output interface 1030, communication interface 1040, and bus 1050, in specific implementations, the device may also include other components necessary for normal operation. Furthermore, those skilled in the art will understand that the above-described device may only include the components necessary for implementing the embodiments of this specification, and not necessarily all the components shown in the figures.

[0152] The electronic devices described above are used to implement the corresponding simulation methods in any of the foregoing embodiments and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0153] Based on the same inventive concept, corresponding to the methods of any of the above embodiments, this disclosure also provides a non-transitory computer-readable storage medium that stores computer instructions for causing the computer to perform the simulation method as described in any of the above embodiments.

[0154] The computer-readable medium of this embodiment includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. Information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transfer medium that can be used to store information accessible by a computing device.

[0155] The computer instructions stored in the storage medium of the above embodiments are used to cause the computer to execute the simulation method as described in any of the above embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0156] Based on the same inventive concept, corresponding to the simulation method described in any of the above embodiments, this disclosure also provides a computer program product, which includes computer program instructions. In some embodiments, the computer program instructions can be executed by one or more processors of a computer to cause the computer and / or the processors to perform the simulation method. Corresponding to the execution entity for each step in each embodiment of the simulation method, the processor executing the corresponding step may belong to the corresponding execution entity.

[0157] The computer program products of the above embodiments are used to cause the computer and / or the processor to perform the simulation method as described in any of the above embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0158] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of this disclosure (including the claims) is limited to these examples; within the framework of this disclosure, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of the embodiments of this disclosure as described above, which are not provided in detail for the sake of brevity.

[0159] Additionally, to simplify the description and discussion, and to avoid obscuring the embodiments of this disclosure, the provided drawings may or may not show well-known power / ground connections to integrated circuit (IC) chips and other components. Furthermore, the apparatus may be shown in block diagram form to avoid obscuring the embodiments of this disclosure, and this also takes into account the fact that the details of implementation of these block diagram apparatuses are highly dependent on the platform on which the embodiments of this disclosure will be implemented (i.e., these details should be fully understood by those skilled in the art). While specific details (e.g., circuits) have been set forth to describe exemplary embodiments of this disclosure, it will be apparent to those skilled in the art that the embodiments of this disclosure can be implemented without these specific details or with variations thereof. Therefore, these descriptions should be considered illustrative rather than restrictive.

[0160] Although this disclosure has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed.

[0161] This disclosure is intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A simulation method for the hydraulic fracturing process, characterized in that, include: Based on the rock mass mechanical parameters and fracture distribution of the target rock mass, a rock mass model is constructed using smooth particle fluid dynamics; the rock mass model includes matrix particles and fluid particles, and the fluid particles are subjected to a preset water pressure. Based on the partial differential equations of the preset seepage field, the preset governing equations, and the preset time parameters, the characteristic parameters of the particles in the rock mass model are calculated; among which, The preset time parameters include time steps and number of steps; the feature parameters include position and velocity; The partial differential equations, control equations, and time parameters based on the preset seepage field are used to calculate the characteristic parameters of the particles in the rock mass model, including: Based on the partial differential equations and control equations of the pre-defined seepage field, the crack distribution, seepage field changes, particle density changes, velocity and acceleration are obtained within a single time step. Based on the time step, the density change, velocity, and acceleration are integrated to obtain the particle's density, position, and velocity. The preset control equations include multiple control equations; these multiple control equations correspond to different types and states of particles; wherein... In response to determining that only intact matrix particles exist within the search domain, the density change rate, velocity, and acceleration of the matrix particles are calculated using the first governing equation; the first governing equation includes equation (1). Equation (1); In response to the determination that only intact matrix particles and fluid particles exist within the search domain, the density change rate, velocity, and acceleration of the matrix particles are calculated using the second governing equation; the second governing equation includes equation (13). Equation (13); In response to the determination that only intact matrix particles and discontinuous particles exist within the search domain, the density change rate, velocity, and acceleration of the matrix particles are calculated using the third governing equation; the third governing equation includes equation (17). Equation (17); In response to the determination that only intact matrix particles, fluid particles and discontinuous particles exist within the search domain, the density change rate, velocity and acceleration of the matrix particles are calculated using the fourth governing equation; the fourth governing equation includes equation (24). Equation (24); The discontinuous particles are determined based on particle damage degree and a preset threshold; wherein, the particle damage degree is determined based on the proportion of damaged particles to all particles within a preset distance; The damage particles were determined based on the Mohr–Coulomb criterion with tensile truncation. The simulation method further includes: In response to determining that the matrix particle meets the criteria of the damaged particle, the matrix particle is converted into a new fluid particle; in, Indicates density, Represents particle velocity. x Indicates particle displacement. Indicates adjacent particles i With ground particles j Speed ​​difference, m Indicates quality, This represents the Cauchy stress tensor. This represents the additional force acting on the ground particle. This represents the artificial viscosity achieved in the calculation to suppress non-physical vibrations; external force. For gravity; and These are the smooth kernel function of the particle and its gradient, respectively; t N represents time; N represents the number of intact matrix particles within the search domain. The normal deformation coefficient; Pw Water pressure; U Represents a complete matrix particle; and These represent the normal and tangential contact forces, respectively. h It's water head. For seepage velocity, Water content or unit storage capacity; Permeability coefficient; α and β Indicates that they can be taken in Cartesian coordinate systems respectively. x , y and z The summation convention, also known as Einstein's summation convention, is applied to duplicate indexes. This is the Dirac function.

2. The simulation method according to claim 1, characterized in that, The partial differential equation of the seepage field includes the seepage coefficient; wherein, the seepage coefficient of the matrix particles is determined based on Darcy's law; and the seepage coefficient of the fluid particles is determined based on the cubic law.

3. The simulation method according to claim 2, characterized in that, The rock mass model includes a matrix region and a fracture region; wherein the fluid particles are located in the fracture region; the fracture region is determined based on the fracture distribution.

4. The simulation method according to claim 1, characterized in that, The governing equations include Cauchy stress; The partial differential equations, control equations, and time parameters based on the preset seepage field are used to calculate the characteristic parameters of the particles in the rock mass model, including: The hydraulic pressure of the particles is determined based on the partial differential equation of the preset seepage field and the rock mass model; wherein the hydraulic pressure is superimposed on the Cauchy stress.

5. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable by the processor, characterized in that, The processor implements the simulation method according to any one of claims 1 to 4 when executing the computer program.

6. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions for causing the computer to perform the simulation method according to any one of claims 1 to 4.

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