CN114662420B - Method and equipment for simulating temporary plugging steering fracturing in seam - Google Patents

Abstract

The application provides a temporary plugging steering fracturing simulation method and equipment in a seam. The method comprises the following steps: constructing a discrete crack model based on a discrete element method; based on a weak coupling method, combining a fluid flow equation and a rock mass deformation equation, performing discrete and iterative processing on the fluid flow equation to obtain a slit fluid pressure, and inputting the slit fluid pressure into the rock mass deformation equation to obtain a slit width; obtaining stress born by the virtual spring based on the width of the crack, judging whether the virtual spring is broken or not according to the stress born by the virtual spring and the maximum stress of the virtual spring, and if so, expanding the crack; and obtaining an advantageous expansion path of the fluid based on crack expansion, and arranging a temporary plugging unit on the advantageous expansion path to simulate temporary plugging steering fracturing in the crack. The method can quantitatively study the influences of different reservoir parameters, natural fracture distribution, mechanical parameters, temporary plugging parameters and the like on the fracture expansion behavior, and provides a basis for in-fracture temporary plugging diverting fracturing simulation and design optimization.

Description

Temporary plugging and diversion fracturing simulation method and equipment in fractures

Technical Field

The present application relates to hydraulic fracturing fracture technology, and in particular to a method and device for simulating temporary plugging and diverting fracturing in fractures.

Background Art

Horizontal well multi-cluster fracturing technology can create complex hydraulic fracture networks and increase reservoir drainage capacity, and is widely used in the development of tight oil and gas reservoirs. However, due to the uneven distribution of hydraulic fractures, the fracture network usually cannot form sufficient coverage and complexity.

In recent years, temporary plugging and diversion fracturing technology, which can promote the uniform fracturing and expansion of multiple fractures, has received widespread attention and has been widely used. The principle is to add temporary plugging agents to the fracturing fluid to plug the perforations or the dominant growth channels of the fractures, forcing the fluid to divert, thereby causing more perforations to fracture or fracture deflection. In natural fracture reservoirs, temporary plugging and fracturing technology can overcome the high closure stress in natural fractures, promote the generation of multi-branch fractures, and increase the complexity of the fracture network.

Existing technologies have developed a variety of numerical simulation methods to study the hydraulic fracturing fracture propagation behavior in unconventional oil and gas reservoirs, but they do not take into account the deflection issues such as how the fractures deflect after temporary plugging during the complex temporary plugging fracturing process.

Summary of the invention

The present application provides a method and device for simulating temporary plugging and diverting fracturing in a fracture, which are used to solve diverting problems such as how the fracture deflects after temporary plugging during a complex temporary plugging and fracturing process.

In a first aspect, the present application provides a method for simulating temporary plugging and diverting fracturing in a fracture, comprising:

A discrete fracture model is constructed based on a discrete element method, wherein the discrete fracture model includes a plurality of block units simulating discrete rock matrices, and the block units are connected by virtual springs;

Based on the weak coupling method, the fluid flow equation and the rock deformation equation are combined, the fluid flow equation is discretized and iteratively processed to obtain the fluid pressure in the fracture, and the fluid pressure in the fracture is input into the rock deformation equation to obtain the fracture width;

The stress of the virtual spring is obtained based on the crack width, and whether the virtual spring is broken is determined according to the stress of the virtual spring and the maximum stress of the virtual spring, and if so, the crack expands;

The dominant expansion path of the fluid is obtained based on the fracture expansion, and a temporary plugging unit is set on the dominant expansion path to realize the simulation of temporary plugging and diverting fracturing in the fracture.

In one possible design, the fluid flow equation is constructed based on the flow equation between parallel plates of an incompressible fluid:

Where w is the crack width that changes dynamically with time, p is the fluid pressure in the crack that changes dynamically with time, q is the injection rate, μ is the fluid viscosity, and _ql is the fluid loss rate.

In a possible design, the rock mass deformation equation is constructed based on the linear elastic dynamic equilibrium equation: σ _ij,j +b _i -ρu _i,tt -αu _i,t = 0,

Where σ _ij,j is the derivative of the Cauchy stress tensor, _bi is the force per unit volume, ρ is the rock density, ui _,t is the velocity of the crack displacement u in time t, ui _,tt is the acceleration of the crack displacement u in time t, and α is the damping coefficient.

In a possible design, the fluid pressure in the fracture is input into the rock mass deformation equation to obtain the fracture width, including:

The derivative σ _ij,j of the Cauchy stress tensor is solved based on the fluid pressure in the crack. The contact force exerted by the fluid pressure in the crack on the block unit surface satisfies the following relationship:

p＝σ _ij n _j ，

Where σ _ij is the Cauchy stress tensor, n _j is the direction cosine of the external normal on the block element surface;

After the derivative σ _ij,j of the Cauchy stress tensor is input into the rock mass deformation equation, the cracking displacement u is obtained;

The crack displacement u is equivalent to the crack width.

In a possible design, the virtual spring is subjected to stresses including tangential stress _Fs and normal stress _Fn , and the stress of the virtual spring is obtained based on the crack width, including:

Where _ks and _kn are the tangential stiffness and normal stiffness of the virtual spring, _us and _un are the tangential displacement and normal displacement of the block element at the crack, and the superscript n represents the time step.

In one possible design, the maximum stress of the virtual spring includes the maximum normal stress and maximum tangential stress

Where A is the contact area, _T0 is the tensile strength, _S0 is the matrix shear strength, is the internal friction angle.

In a possible design, judging whether the virtual spring is broken according to the stress applied to the virtual spring and the maximum stress of the virtual spring includes:

when and When , the virtual spring does not break and no crack expands. At this time, the stress formula is:

Where k _n and k _s are the normal and tangential spring stiffnesses, _Δus and _Δus are the normal and tangential relative displacements between adjacent nodes, and the superscript n represents the time step.

when When , the virtual spring breaks under tension, and the block units separate from each other. At this time, the stress formula is:

when When , the virtual spring shears and breaks, and the block units slide against each other. At this time, the stress formula is:

In the formula, is the residual shear resistance after the spring breaks.

In a possible design, the method of setting a temporary plugging unit on the dominant expansion path is: based on the principle that temporary plugging reduces the flow capacity of the fluid in the fracture, the reduction coefficient α _p is used to characterize the effect of temporary plugging on the fracture permeability, and the permeability of the temporary plugging unit is:

k _PE = α _p k, where α _p is the reduction coefficient and k is the matrix block permeability.

In a possible design, the discrete fracture model also includes joint units for simulating fluid flow between block units. According to the parallel plate model, before the block unit is damaged, the initial joint unit has the same permeability as the block unit, and the initial joint unit crack width can be equivalently obtained by the permeability of the matrix block unit:

In one possible design, the minimum crack width to avoid the overlap of two block elements is constructed as the residual crack width w _res , which is:

Where _w0 is the initial joint unit width, and _Fn0 is the normal stress at _w0 /2.

In a second aspect, the present application provides a temporary plugging and diverting fracturing device for fracture permeability based on the principle of reducing the flow capacity of fluid in the fracture by temporary plugging, including: a processor, and a memory connected to the processor in communication;

The memory stores computer-executable instructions;

The processor executes the computer-executable instructions stored in the memory to implement a method for simulating temporary plugging and diverting fracturing in fractures.

The simulation method, device and storage medium for temporary plugging and diverting fracturing in fractures provided by the present application construct a discrete fracture model based on the discrete element method, wherein the discrete fracture model includes a plurality of block units simulating discrete rock matrices, and the block units are connected by virtual springs; based on the weak coupling method, the fluid flow equation and the rock deformation equation are combined, and the fluid flow equation is discretized and iteratively processed to obtain the fluid pressure in the fracture, and the fluid pressure in the fracture is input into the rock deformation equation to obtain the fracture width; based on the fracture width, the stress on the virtual spring is obtained, and according to the stress on the virtual spring and the maximum stress of the virtual spring, it is determined whether the virtual spring is broken, and if so, the fracture expands. The discrete fracture model constructed by the present application and the corresponding fluid flow equation and rock deformation equation can effectively analyze the fluid pressure in the fracture and the fracture width of the rock mass, and realize the mathematical simulation effect of the complex fracture expansion and diverting behavior during temporary plugging and fracturing.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

FIG1 is a flow chart of a method for simulating temporary plugging and diverting fracturing in a fracture according to the present invention;

FIG2 is a schematic diagram of a discrete fracture model constructed in this application;

FIG3 is a schematic diagram of the force analysis of a virtual spring in the discrete crack model of the present application;

FIG4 is a schematic diagram of the multi-fracture expansion morphology in a specific embodiment of the present application; wherein FIG4a is a conventional hydraulic fracture morphology, and FIG4b-d are hydraulic fracture morphologies after the first, second and third plugging of temporary plugging diversion fracturing, respectively;

FIG5 is a schematic diagram of an injection pressure curve in a specific embodiment of the present application;

FIG6 is a schematic diagram of the structure of the temporary plugging and diverting fracturing equipment in the fracture of the present application.

The above drawings have shown clear embodiments of the present application, which will be described in more detail later. These drawings and text descriptions are not intended to limit the scope of the present application in any way, but to illustrate the concept of the present application to those skilled in the art by referring to specific embodiments.

DETAILED DESCRIPTION

Exemplary embodiments will be described in detail herein, examples of which are shown in the accompanying drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the present application. Instead, they are merely examples of devices and methods consistent with some aspects of the present application as detailed in the appended claims.

First, the terms involved in this application are explained:

Discrete element method: refers to a particle discrete body material analysis method, a numerical simulation method used to solve discontinuous medium problems. By considering the jointed rock mass as consisting of discrete rock blocks and joint surfaces between the rock blocks, the rock blocks are allowed to translate, rotate and deform, while the joint surfaces can be compressed, separated or slide.

Preset simulation software: refers to a modeling tool that performs three-dimensional modeling of underground reservoir fractures based on ground stress distribution, rock mechanical parameters of the matrix, natural fracture distribution and mechanical property parameters, pumping parameters, temporary plugging position and number, etc. The preset simulation software in this application includes the formula corresponding to the intra-fracture temporary plugging and diversion fracturing simulation method, and obtains the construction pressure curve and multi-fracture extension morphology diagram through simulation;

Galerkin finite element method: refers to a numerical analysis method that uses the weak form corresponding to the differential equation. Its principle is to select finite polynomial functions (also known as basis functions or shape functions), superimpose them, and then require the weighted integral of the result in the solution domain and on the boundary (the weight function is the test function itself) to satisfy the original equation. In this way, a set of linear algebraic equations that are easy to solve can be obtained, and the natural boundary conditions can be automatically satisfied.

Picard iteration method: refers to a major approximate calculation method for solutions to ordinary differential equations.

In the present application, when simulating the redirection of the temporary plugging and redirecting fracturing process in the fracture, the most important step is to determine whether the fracture has expanded, and the fracture expansion is the result of the interaction between the fluid and the rock mass. This requires the construction of motion equations for simulating the fluid and the rock mass respectively. After combining the fluid flow equation and the rock deformation equation, it is only necessary to obtain the injection rate, fluid viscosity, fluid filtration rate, force per unit volume, rock density, damping coefficient and other data, and then bring them into the equation to solve them jointly to obtain the fracture width. Then, based on the fracture width, it is determined whether the virtual spring is broken, and then the fracture redirection distribution is simulated according to the fracture condition of the virtual spring.

The method provided in this application is intended to solve the above technical problems of the prior art.

The technical solution of the present application and how the technical solution of the present application solves the above-mentioned technical problems are described in detail below with specific embodiments. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments. The embodiments of the present application will be described below in conjunction with the accompanying drawings.

FIG1 is a flow chart of the method for simulating temporary plugging and diverting fracturing in the fracture of the present invention. As shown in FIG1 , the method comprises the following steps:

S101. Construct a discrete crack model based on discrete element method.

Figure 2 is a schematic diagram of a discrete fracture model constructed in this application. As shown in Figure 2, the model includes a plurality of block units 1 simulating discrete rock matrices, joint units 2 simulating fluid flow between block units, hydraulic fracture units 3 simulating rock fractures, and temporary plugging units 4 simulating temporary plugging sections. The block units are triangular prism structures, and the block units are connected by virtual springs 5. When the virtual springs 5 break, separation or sliding dislocation occurs between the block units 1, thereby generating fractures. The injected fluid will preferentially pass through the fractures. For block units 1 with more fractures, the fluid will form a dominant expansion path of the fluid according to the width of the fracture. After artificially setting the temporary plugging unit 4 on the dominant expansion path of the fluid, the fluid pressure in the fracture is affected, so that the fluid avoids the dominant expansion path and reselects the flow path, thereby increasing the complexity of the fracture network.

S102, based on the weak coupling method, the fluid flow equation and the rock deformation equation are combined, the fluid flow equation is discretized and iteratively processed to obtain the fluid pressure in the fracture, and the fluid pressure in the fracture is input into the rock deformation equation to obtain the fracture width.

Preferably, the fluid flow equation is constructed using the flow equation between parallel plates of an incompressible fluid, wherein the fluid viscosity, injection rate and fluid loss velocity of the incompressible fluid are measurable physical parameters, and the fluid flow equation that associates the fracture width with the fluid pressure in the fracture can be established using the above physical parameters. Since the above fracture width and fluid pressure in the fracture equation are dynamic physical quantities based on position function and time, the corresponding fluid pressure in the fracture under certain fluid viscosity, injection rate and fluid loss velocity conditions can be obtained through discretization and iteration.

Preferably, the obtained fluid pressure in the fracture is converted into a contact force on the surface of the block unit 1, and the contact force is the main force in the rock deformation equation. The rock deformation equation is constructed by the linear elastic dynamic equilibrium equation. When the contact force is known, by obtaining physical parameters such as the force per unit volume of the block unit 1, the rock density and the damping coefficient, the dynamic physical quantity of the crack displacement between the block units 1 changing with time can be established. When the time is determined, the corresponding crack displacement is obtained, and the crack displacement between the block units 1 can be equivalent to the crack width, thereby obtaining the key physical quantity for judging the state of the virtual spring 5.

S103, obtaining the stress of the virtual spring based on the crack width, and judging whether the virtual spring is broken according to the stress of the virtual spring and the maximum stress of the virtual spring, and if so, the crack expands.

According to the schematic diagram of force analysis of virtual spring 5 in discrete crack model in Fig. 2, the stress force of virtual spring 5 is divided into stress along the normal direction of block unit 1 and stress along the tangential direction of block unit 1, and the crack width is also decomposed into normal displacement and tangential displacement. Therefore, based on the basic formula of spring force, only the constant spring stiffness and the independent variable crack width need to be obtained to obtain the stress of dependent variable virtual spring 5. The maximum stress of virtual spring 5 in the normal direction is related to the contact area and tensile strength of block unit 1, while the maximum stress in the tangential direction is related to the contact area, matrix shear strength and internal friction angle of block unit 1. When the positions of two adjacent block units 1 are fixed, the maximum stress that the corresponding virtual spring 5 can withstand is also fixed.

FIG3 is a schematic diagram of the force analysis of the virtual spring in the discrete crack model of the present application. According to FIG3 , the schematic diagram of the force analysis of the virtual spring 5 in the discrete crack model can be seen:

When the normal stress on the virtual spring 5 is less than the maximum normal stress, and the tangential stress is less than the maximum tangential stress, the virtual spring 5 does not break, no new cracks are generated, and the tangential and normal stresses do not change;

When the normal stress is greater than the maximum normal stress, the block elements 1 separate from each other, and the virtual spring 5 breaks under tension. After the two block elements 1 break, they are not subjected to stress on each other.

When the tangential stress is greater than the maximum tangential stress, the block units 1 slide against each other, and the virtual spring 5 shears and breaks. Since there is still contact between the two blocks, there is still stress between them, and the normal stress remains unchanged, and the tangential stress becomes residual shear resistance.

S104, based on the expansion of the cracks, the dominant expansion path of the fluid is obtained, and a temporary plugging unit is set on the dominant expansion path to simulate the temporary plugging and fracturing in the cracks. After the cracks expand, the fluid will flow into all the crack expansion positions, and according to the crack width, the cracks with larger crack widths are connected in series to form the dominant expansion path of the fluid. The rock pressure on the dominant expansion path is the smallest, and the fluid will flow preferentially on the dominant expansion path, thereby reducing the impact pressure of the fluid on the rock mass, resulting in no more increase in rock cracks. At this time, after the temporary plugging unit is set on the dominant expansion path, the permeability at the temporary plugging unit is greatly reduced, causing the fluid to turn to fracturing. The formula of the above steps is recalculated to determine whether the cracks expand, thereby simulating the fracturing diversion process after temporary plugging in the rock mass cracks, and providing a design optimization basis for how to increase the complexity of the cracks in the future.

This embodiment constructs a discrete fracture model based on the discrete element method; based on the weak coupling method, the fluid flow equation and the rock deformation equation are combined, and the fluid flow equation is discretized and iteratively processed to obtain the fluid pressure in the fracture, and the fluid pressure in the fracture is input into the rock deformation equation to obtain the fracture width; based on the fracture width, the stress of the virtual spring is obtained, and according to the stress of the virtual spring and the maximum stress of the virtual spring, it is judged whether the virtual spring is broken, and if so, the method of fracture expansion is used to achieve the mathematical simulation effect of complex diversion after temporary plugging in the fracture. Since the state change of the virtual spring 5 leads to the change of the stress formula, which in turn causes the fluid to move toward different fractures, the simulation of the complex fracture expansion behavior during temporary plugging and fracturing is achieved by mathematical methods. This method can quantitatively study the influence of different reservoir parameters, natural fracture distribution and mechanical parameters, temporary plugging parameters, etc. on the fracture expansion behavior, and can optimize the fracturing construction parameters according to the complexity of the fracture network and the coverage area. The method is theoretically reliable and has strong versatility, which makes up for the shortcomings of the existing technology and can provide a strong basis for the simulation of temporary plugging and diversion fracturing in the fracture.

A possible embodiment is further described below to illustrate how to implement a method for temporary plugging and diverting fracturing in a fracture.

A method for simulating temporary plugging and diverting fracturing in a fracture, comprising:

Firstly, a discrete fracture model is constructed, wherein the discrete fracture model includes a plurality of block units simulating discrete rock matrices, and the block units are connected by virtual springs;

Then, a fluid flow equation and a rock deformation equation are constructed, the fluid flow equation is discretized and iteratively processed to obtain the fluid pressure in the fracture, and the fluid pressure in the fracture is input into the rock deformation equation to obtain the fracture width;

Finally, the stress on the virtual spring is obtained based on the crack width, and whether the virtual spring is broken is determined according to the stress on the virtual spring and the maximum stress of the virtual spring. If so, the crack expands.

In one possible design, the fluid flow equation and rock deformation equation are constructed separately based on the discrete fracture model, and then the fracture width is solved jointly. The specific steps are as follows:

S201, constructing the fluid flow equation based on the parallel plate flow equation of the incompressible fluid:

Wherein, w is the fracture width that changes dynamically with time, m; p is the fluid pressure in the fracture that changes dynamically with time, Pa; q is the injection rate, m ³ /s; μ is the fluid viscosity, Pa·s; q _l is the fluid loss velocity, m/s.

After the injection rate q, fluid viscosity μ and fluid loss velocity q _l are introduced, the fluid flow equation is discretized by the Galerkin finite element method, and then the Picard iterative method is used to solve the fluid pressure p in the fracture.

When the iterative method does not meet the convergence requirements, the accelerated algorithm is used to solve the problem:

p _m+1 =(1-β)p _m +βp _m+1 ,

w _m+1 =(1-β)w _m +βw _m+1 ,

Where the subscript m represents the iteration step, and β ranges from 0 to 0.5.

S202, constructing the rock mass deformation equation based on the linear elastic dynamic equilibrium equation:

_σij,j +bi _- ρui _,tt - _αui,t =0,

Wherein, σ _ij,j is the derivative of the Cauchy stress tensor, N/m ³ ; _bi is the force per unit volume, N/m ³ ; ρ is the rock density, kg/m ³ ; ui _,t is the velocity of the crack displacement u in time t, m/s ; ui _,tt is the acceleration of the crack displacement u in time t, m/s ² ; α is the damping coefficient, (kg·s)/m ³ .

The contact force exerted by the fluid pressure in the crack on the block unit surface satisfies the following relationship:

p＝σ _ij n _j ，

Where σ _ij is the Cauchy stress tensor, Pa; n _j is the direction cosine of the external normal on the block element surface;

S203. Combine the fluid flow equation and the rock deformation equation to obtain the crack displacement, which is the crack width:

The obtained fluid pressure in the fracture is brought in to solve the derivative of the Cauchy stress tensor σ _ij,j , and then the derivative of the Cauchy stress tensor σ _ij,j is input into the rock mass deformation equation to obtain the crack displacement u;

Since there is a corresponding relationship between the crack displacement between block units and the crack width, the crack displacement u can be equivalent to the crack width.

In a possible design, in order to avoid the overlap of two block elements, the minimum crack width is constructed as the residual crack width w _res , the formula is:

Where _w0 is the initial joint unit width, m; _Fn0 is the normal stress at _w0 /2, Pa;

According to the parallel plate model, before the block unit is damaged, the initial joint unit has the same permeability as the block unit, so the initial joint unit width can be equivalent to the permeability of the matrix block unit:

Where k is the permeability of the matrix block; after the initial joint unit width is determined, its corresponding _Fn0 can be obtained, thereby determining the value of the residual crack width _wres .

Permeability indicates the ability of fluid to pass through pores. After temporary plugging, it is difficult for fluid to pass through the temporary plugging unit, so the permeability of the temporary plugging unit can be reduced to a very low level to achieve temporary plugging simulation. The width of the crack after temporary plugging satisfies the formula of the initial joint unit width:

Based on the principle that temporary plugging reduces the flow capacity of fluid in fractures, the reduction coefficient _αp is used to characterize the effect of temporary plugging on fracture permeability. The initial joint unit width can be obtained by substituting it into the temporary plugging unit, where the permeability of the temporary plugging unit is:

k _PE = α _p k, where α _p is the reduction coefficient.

Then, the stress of the virtual spring is obtained according to the obtained crack displacement.

The virtual spring is subjected to stresses including tangential stress _Fs and normal stress _Fn , and the stress of the virtual spring is obtained based on the crack width, including:

Where _ks and _kn are the tangential stiffness and normal stiffness of the virtual spring, respectively, in N/m; u _s and u _s are the tangential displacement and normal displacement of the block element at the crack, respectively, in m; and the superscript n represents the time step.

The maximum stress of the virtual spring includes the maximum normal stress and maximum tangential stress

Where A is the contact area, m ³ ; T ₀ is the tensile strength, Pa; S ₀ is the matrix shear strength, Pa; is the internal friction angle, °.

In a possible design, judging whether the virtual spring is broken according to the stress applied to the virtual spring and the maximum stress of the virtual spring includes:

when and When , the virtual spring does not break and no crack expands. At this time, the stress formula is:

Where k _n and k _s are the normal and tangential spring stiffness, N/m; Δu _n and Δu _s are the normal and tangential relative displacements between adjacent nodes, m; the superscript n represents the time step;

when When , the virtual spring breaks and the block elements separate from each other. At this time, the stress formula is:

when When , the virtual spring shears and breaks, and the block units slide against each other. At this time, the stress formula is:

In the formula, is the residual shear resistance after the spring breaks, N.

Enter the basic model parameters of the demonstration example in the preset simulation software, as shown in Table 1 below:

Table 1. Demonstration example model parameters

Figure 4 is a schematic diagram of the expansion morphology of hydraulic fractures in natural fracture reservoirs based on the above demonstration example. As shown in Figure 4a, when there is no temporary plugging, the hydraulic fracture directly passes through the natural fracture, and the fracture morphology formed is relatively simple, and the coverage area of the fracture network is relatively low. This is because the horizontal stress difference is large, and conventional fracturing is difficult to open natural fractures to form a complex fracture network. Therefore, it is necessary to plug the potential advantageous expansion paths of the fractures to increase the complexity of the fracture network. As shown in Figures 4b-d, after the plugging position and number of plugging measures are optimized, the plugging measures are carried out, and then the fractures are deflected multiple times, and multiple natural fractures are opened, and finally a relatively complex fracture network is formed in the target area of the reservoir transformation.

Figure 5 is a schematic diagram of the injection pressure curve. It can be seen from the figure that the injection pressure increases significantly after the internal plugging of the fracture. When the injection pressure reaches a certain value, the natural fracture can be opened, increasing the complexity of the fracture network. In this embodiment, it is shown that a reasonable optimization design of temporary plugging and fracturing in the fracture can promote the expansion of hydraulic fractures, increase the complexity and coverage of the fracture network, and improve the post-fracturing effect.

This embodiment specifically constructs a discrete fracture model, a fluid flow equation and a rock deformation equation, obtains the fluid pressure in the fracture after discretizing and iteratively processing the fluid flow equation, and inputs the fluid pressure in the fracture into the rock deformation equation to obtain the fracture width; obtains the stress of the virtual spring based on the fracture width, and determines whether the virtual spring is broken according to the stress of the virtual spring and the maximum stress of the virtual spring, thereby completing a mathematical model for temporary plugging and fracturing of fluid in the fracture, facilitating the subsequent optimization design of the temporary plugging position and the temporary plugging quantity through the mathematical model, and providing technical support for actual underground mining scenarios.

Figure 6 is a schematic diagram of the structure of the in-fracture temporary plugging and diverting fracturing device of the present application. As shown in Figure 6, the present embodiment provides an in-fracture temporary plugging and diverting fracturing device, including a memory 602 and a processor 601, the memory 602 is used to store programs, and the memory 602 can be connected to the processor 601 via a bus 603. The memory 602 can be a non-volatile memory, such as a hard disk drive and a flash memory, and the memory 602 stores software programs and device drivers. The software program can perform various functions of the above-mentioned method provided in the embodiment of the present invention; the device driver can be a network and interface driver. The processor 601 is used to execute the software program, and when the software program is executed, the method for in-fracture temporary plugging and diverting fracturing in the embodiment of the present invention can be implemented:

Specifically, the fluid flow equation is constructed based on the flow equation between parallel plates of an incompressible fluid:

Where w is the crack width that changes dynamically with time, p is the fluid pressure in the crack that changes dynamically with time, q is the injection rate, μ is the fluid viscosity, and _ql is the fluid loss rate.

Specifically, the rock mass deformation equation is constructed based on the linear elastic dynamic equilibrium equation:

_σij,j +bi _- ρui _,tt - _αui,t =0,

Where σ _ij,j is the derivative of the Cauchy stress tensor, _ni is the force per unit volume, ρ is the rock density, ui _,t is the velocity of the crack displacement u in time t, ui _,tt is the acceleration of the crack displacement u in time t, and α is the damping coefficient.

Specifically, the fluid pressure in the fracture is input into the rock mass deformation equation to obtain the fracture width, including:

The derivative σ _ij,j of the Cauchy stress tensor is solved based on the fluid pressure in the crack. The contact force exerted by the fluid pressure in the crack on the block unit surface satisfies the following relationship:

p＝σ _ij n _j ，

Where σ _ij is the Cauchy stress tensor, n _j is the direction cosine of the external normal on the block element surface;

After the derivative σ _ij,j of the Cauchy stress tensor is input into the rock mass deformation equation, the cracking displacement u is obtained;

The crack displacement u is equivalent to the crack width.

Specifically, the virtual spring is subjected to stresses including tangential stress _Fs and normal stress _Fn , and the stress of the virtual spring is obtained based on the crack width, including:

Where _ks and _kn are the tangential stiffness and normal stiffness of the virtual spring, _us and _un are the tangential displacement and normal displacement of the block element at the crack, and the superscript n represents the time step.

Specifically, the maximum stress of the virtual spring includes the maximum normal stress and maximum tangential stress

Where A is the contact area, _T0 is the tensile strength, _S0 is the matrix shear strength, is the internal friction angle.

Specifically, judging whether the virtual spring is broken according to the stress applied to the virtual spring and the maximum stress of the virtual spring includes:

when and When , the virtual spring does not break and no crack expands. At this time, the stress formula is:

Where k _n and k _s are the normal and tangential spring stiffnesses, Δu _n and Δu _s are the normal and tangential relative displacements between adjacent nodes, and the superscript n represents the time step.

when When , the virtual spring breaks under tension, and the block units separate from each other. At this time, the stress formula is:

when When , the virtual spring shears and breaks, and the block units slide against each other. At this time, the stress formula is:

In the formula, is the residual shear resistance after the spring breaks.

Specifically, based on the principle that temporary plugging reduces the flow capacity of fluid in fractures, the reduction coefficient _αp is used to characterize the effect of temporary plugging on fracture permeability. The permeability of the temporary plugging unit is:

k _PE = α _p k, where α _p is a reduction coefficient. Specifically, the discrete fracture model also includes joint units for simulating fluid flow between block units, and the minimum fracture width to avoid overlap of two block units is constructed as the residual fracture width w _res , formula:

Where w ₀ is the initial joint unit width, F _n0 is the normal stress at w ₀ /2;

According to the parallel plate model, before the block unit is damaged, the initial joint unit has the same permeability as the block unit, so the initial joint unit width can be equivalent to the permeability of the matrix block unit:

Where k is the matrix bulk permeability.

The in-fracture temporary plugging and diverting fracturing equipment provided in this embodiment can be used to execute the in-fracture temporary plugging and diverting fracturing simulation method described above. Its implementation principle and technical effects are similar and will not be described in detail in this embodiment.

The embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the method provided in the first embodiment of the present invention is implemented.

The computer-readable storage medium provided in this embodiment can be used to execute the above-mentioned intra-fracture temporary plugging and diverting fracturing simulation method, and its implementation principle and technical effects are similar, which will not be described in detail in this embodiment.

The professionals should further realize that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in the above description according to the function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

The steps of the method or algorithm described in conjunction with the embodiments disclosed herein may be implemented using hardware, a software module executed by a processor, or a combination of the two. The software module may be placed in a random access memory (RAM), a memory, a read-only memory (ROM), an electrically programmable ROM, an electrically erasable programmable ROM, a register, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.

Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the invention disclosed herein. The present application is intended to cover any modification, use or adaptation of the present application, which follows the general principles of the present application and includes common knowledge or customary techniques in the art that are not disclosed in the present application. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present application are indicated by the following claims.

It should be understood that the present application is not limited to the precise structures that have been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present application is limited only by the appended claims.

Claims (9)

1. A method for simulating temporary plugging and diverting fracturing in a fracture, characterized by comprising: A discrete fracture model is constructed based on a discrete element method, wherein the discrete fracture model includes a plurality of block units simulating discrete rock matrices and a temporary plugging unit for simulating a temporary plugging agent, the block units are connected by virtual springs, and the temporary plugging unit is connected to the block unit with a clearance fit; Based on the weak coupling method, the fluid flow equation and the rock deformation equation are combined, the fluid flow equation is discretized and iteratively processed to obtain the fluid pressure in the fracture, and the fluid pressure in the fracture is input into the rock deformation equation to obtain the fracture width; The stress of the virtual spring is obtained based on the crack width, and whether the virtual spring is broken is determined according to the stress of the virtual spring and the maximum stress of the virtual spring, and if so, the crack expands; Based on the fracture expansion, the dominant expansion path of the fluid is obtained, and a temporary plugging unit is set on the dominant expansion path to realize the simulation of temporary plugging and diverting fracturing in the fracture; The fluid flow equation is constructed based on the flow equation between parallel plates of incompressible fluid: Where w is the crack width that changes dynamically with time, p is the fluid pressure in the crack that changes dynamically with time, q is the injection rate, μ is the fluid viscosity, and q _l is the fluid loss rate; Based on the weak coupling method, the fluid flow equation and the rock deformation equation are combined, and the fluid pressure in the fracture is obtained after discretization and iterative processing of the fluid flow equation, including: Discretize the fluid flow equations by using the Galerkin finite element method; The Picard iteration method is used to solve the fluid pressure p in the crack; When the Picard iterative method does not meet the convergence requirements, an accelerated algorithm is used to solve the problem: P _m+1 =(1-β)p _m +βp _m+1 , w _m+1 =(1-β)w _m +βw _m+1 , Where the subscript m represents the iteration step, and β ranges from 0 to 0.5. 2. The method according to claim 1 is characterized in that the rock mass deformation equation is constructed based on a linear elastic dynamic equilibrium equation: σ _{ij, j} +b _i -pu _{i, tt} -αu _{i, t} = 0, Where σ _ij,j is the derivative of the Cauchy stress tensor, _bi is the force per unit volume, p is the rock density, ui _,t is the velocity of the crack displacement u in time t, ui _,tt is the acceleration of the crack displacement u in time t, and α is the damping coefficient. 3. The method according to claim 2, characterized in that the fluid pressure in the fracture is input into the rock mass deformation equation to obtain the fracture width, comprising: The derivative σ _ij,j of the Cauchy stress tensor is solved based on the fluid pressure in the crack. The contact force exerted by the fluid pressure in the crack on the block unit surface satisfies the following relationship: p＝σ _ij n _j ， Where σ _ij is the Cauchy stress tensor, n _j is the direction cosine of the external normal on the block element surface; After the derivative σ _ij,j of the Cauchy stress tensor is input into the rock mass deformation equation, the cracking displacement u is obtained; The crack displacement u is equivalent to the crack width. 4. The method according to claim 1, characterized in that the virtual spring is subjected to stress including tangential stress _Fs and normal stress _Fn , and obtaining the stress of the virtual spring based on the crack width comprises: Where k _s and k _n are the tangential stiffness and normal stiffness of the virtual spring, u _s and _un are the tangential displacement and normal displacement of the block element at the crack, and the superscript n represents the time step; The maximum stress of the virtual spring includes the maximum normal stress and maximum tangential stress Where A is the contact area, _T0 is the tensile strength, _S0 is the matrix shear strength, is the internal friction angle. 5. The method according to claim 4, characterized in that judging whether the virtual spring is broken according to the stress applied to the virtual spring and the maximum stress of the virtual spring comprises: when and When , the virtual spring does not break and no crack expands. At this time, the stress formula is: Where k _n and k _s are the normal and tangential spring stiffnesses, Δu _n and Δu _s are the normal and tangential relative displacements between adjacent nodes, and the superscript n represents the time step. when When , the virtual spring breaks under tension, and the block units separate from each other. At this time, the stress formula is: when When , the virtual spring shears and breaks, and the block units slide against each other. At this time, the stress formula is: In the formula, is the residual shear resistance after the spring breaks. 6. The method according to claim 1 is characterized in that the method of setting a temporary plugging unit on the dominant expansion path is: based on the principle that temporary plugging reduces the flow capacity of the fluid in the fracture, the reduction coefficient α _p is used to characterize the influence of temporary plugging on the fracture permeability, and the permeability of the temporary plugging unit is: k _PE = α _p k, where α _p is the reduction coefficient and k is the matrix block permeability. 7. The method according to claim 6, characterized in that the discrete fracture model also includes joint units for simulating fluid flow between block units. According to the parallel plate model, before the block unit is destroyed, the initial joint unit has the same permeability as the block unit, and the initial joint unit crack width can be equivalently obtained by the permeability of the matrix block unit: 8. The method according to claim 7, characterized in that the minimum crack width to avoid the overlap of two block units is constructed as the residual crack width w _res , and the formula is: Where _w0 is the initial joint unit width, and _Fn0 is the normal stress at _w0 /2. 9. A temporary plugging and diverting fracturing device in a fracture, characterized by comprising: a processor, and a memory connected to the processor in communication; The memory stores computer-executable instructions; The processor executes the computer-executable instructions stored in the memory to implement the method according to any one of claims 1 to 8.