CN114662420B - Method and equipment for simulating temporary plugging steering fracturing in seam - Google Patents
Method and equipment for simulating temporary plugging steering fracturing in seam Download PDFInfo
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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
Technical Field
The application relates to a hydraulic fracturing fracture technology, in particular to a temporary plugging steering fracturing simulation method and equipment in a fracture.
Background
The horizontal well staged multi-cluster fracturing technology can create a complex hydraulic fracture network, increase the oil drainage capacity of a reservoir, and is widely applied to the development of a tight oil and gas reservoir. But fracture networks often do not form adequate coverage area and complexity due to the uneven distribution of hydraulic fractures.
In recent years, a temporary plugging diverting fracturing technology capable of promoting uniform initiation and expansion of multiple cracks has been widely focused and applied on a large scale. The principle is that temporary plugging agent is added into fracturing fluid to plug perforation holes or to plug dominant growth channels of cracks, so that fluid is forced to split, and more perforation holes are cracked or cracks are deflected. In a natural fracture type reservoir, the temporary plugging fracturing technology can overcome high closure stress in a natural fracture, promote multi-branch fracture generation and increase the complexity of a fracture network.
In the prior art, various numerical simulation methods have been developed to study the hydraulic fracture propagation behavior in unconventional oil and gas reservoirs, but the steering problems of how to deflect the fracture after temporary plugging and the like in the complex temporary plugging fracturing process are not considered.
Disclosure of Invention
The application provides a method and equipment for simulating temporary plugging turning fracturing in a seam, which are used for solving the turning problems of how to deflect the seam after temporary plugging in a complex temporary plugging fracturing process.
In a first aspect, the application provides a temporary plugging diverting fracturing simulation method in a seam, comprising the following steps:
Constructing a discrete fracture model based on a discrete element method, wherein the discrete fracture model comprises a plurality of block units simulating a discrete rock matrix, and the block units are connected through virtual springs;
Based on a weak coupling method, a fluid flow equation and a rock mass deformation equation are combined, the fluid flow equation is subjected to discrete and iterative processing to obtain a slit fluid pressure, and the slit fluid pressure is input into the rock mass deformation equation to obtain a slit width;
Acquiring 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.
In one possible design, the fluid flow equation is constructed based on an inter-parallel plate flow equation for an incompressible fluid:
Where w is the width of the slit dynamically changing with time, p is the pressure of the fluid in the slit dynamically changing with time, q is the fluid injection rate, μ is the fluid viscosity, and q l is the fluid loss rate.
In one possible design, the rock mass deformation equation is constructed based on a linear elastic dynamic balance equation: σ ij,j+bi-ρui,tt-αui,t =0,
Where σ ij,j is the derivative of the cauchy stress tensor, b i is the force per unit volume, ρ is the rock density, u i,t is the velocity of the crack displacement u over time t, u i,tt is the acceleration of the crack displacement u over time t, and α is the damping coefficient.
In one possible design, inputting the in-seam fluid pressure into the rock mass deformation equation to obtain a seam width includes:
solving a derivative sigma ij,j of the cauchy-stress tensor based on the in-seam fluid pressure, wherein the contact force exerted by the in-seam fluid pressure on the block unit surface satisfies the following relationship:
p＝σijnj，
Wherein, sigma ij is the cauchy stress tensor, n j is the direction cosine of the external normal on the block unit surface;
inputting the derivative sigma ij,j of the cauchy stress tensor into the rock mass deformation equation to obtain a cracking displacement u;
The cleavage displacement u is equivalent to the cleavage width.
In one possible design, the virtual spring is stressed including tangential stress F s and normal stress F n, the stress of the virtual spring is obtained based on the slit width, comprising:
Where k s and k n are the tangential stiffness and the normal stiffness of the virtual spring, respectively, u s and u n are the tangential displacement and the normal displacement of the block unit at the time of cracking, respectively, and the superscript n indicates the time step.
In one possible design, the maximum stress of the virtual spring includes a maximum normal stressAnd maximum tangential stress
Wherein A is the contact area, T 0 is the tensile strength, S 0 is the matrix shear strength,Is the internal friction angle.
In one possible design, determining whether the virtual spring is broken according to the stress to which the virtual spring is subjected and the maximum stress of the virtual spring includes:
When (when) AndWhen the virtual spring is broken, no crack is expanded, and the stress formula is as follows:
Wherein k n and k s are normal and tangential spring rates respectively, deltau s and Deltau s are normal and tangential relative displacements between adjacent nodes respectively, and the superscript n represents a time step;
When (when) During the time, virtual spring takes place tensile fracture, and block unit separates each other, and the stress formula is this moment:
When (when) During the time, the virtual spring is sheared and broken, and the block units slide mutually, and the stress formula is:
In the method, in the process of the invention, Is the residual shear resistance after the spring breaks.
In one possible design, the method for setting the temporary blocking unit on the dominant expansion path includes: based on the principle of reducing the fluid flow capacity of the seam by temporary plugging, the influence of the temporary plugging on the permeability of the seam is represented by a reduction coefficient alpha p, and the permeability of the temporary plugging unit is as follows:
k PE＝αp k, wherein α p is a reduction coefficient, and k is a matrix bulk permeability.
In one possible design, the discrete fracture model further includes an interface unit for simulating fluid flow between the bulk units, and according to the parallel plate model, the initial interface unit and the bulk units have equal permeability before the bulk units are broken, and the initial interface unit seam width is equivalent to the permeability of the matrix bulk units:
In one possible design, the minimum seam width to avoid overlapping of two block units is constructed as the residual seam width w res, the formula:
Where w 0 is the initial joint cell seam width and F n0 is the normal stress at w 0/2.
Based on the second aspect of the principle of temporary plugging to reduce the flow capacity of fluid in a seam to the permeability of the seam, the application provides temporary plugging steering fracturing equipment in the seam, which comprises the following components: a processor, and a memory communicatively coupled to the processor;
The memory stores computer-executable instructions;
And the processor executes the computer execution instructions stored in the memory to realize the in-seam temporary plugging steering fracturing simulation method.
According to the in-seam temporary plugging steering fracturing simulation method, the in-seam temporary plugging steering fracturing simulation equipment and the storage medium, a discrete fracture model is constructed based on a discrete element method, wherein the discrete fracture model comprises a plurality of block units for simulating discrete rock matrixes, and the block units are connected through virtual springs; based on a weak coupling method, a fluid flow equation and a rock mass deformation equation are combined, the fluid flow equation is subjected to discrete and iterative processing to obtain a slit fluid pressure, and the slit fluid pressure is input into the rock mass deformation equation to obtain a slit width; and acquiring the 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. The discrete fracture model constructed by the application and the corresponding fluid flow equation and rock mass 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 steering behavior in the temporary plugging fracturing process.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the application and together with the description, serve to explain the principles of the application.
FIG. 1 is a flow chart of a temporary plugging diverting fracturing simulation method in a seam of the application;
FIG. 2 is a schematic view of a discrete fracture model constructed in accordance with the present application;
FIG. 3 is a schematic diagram of a virtual spring force analysis in a discrete fracture model according to the present application;
FIG. 4 is a schematic diagram of a multi-crack propagation configuration in accordance with an embodiment of the present application; wherein, fig. 4a is a conventional hydraulic fracture morphology, and fig. 4b-d are hydraulic fracture morphologies after 1 st, 2 nd and 3 rd plugging of temporary plugging diverting fracturing, respectively;
FIG. 5 is a schematic diagram of injection pressure curves in accordance with an embodiment of the present application;
FIG. 6 is a schematic diagram of a temporary plugging diverting fracturing device in a seam according to the present application.
Specific embodiments of the present application have been shown by way of the above drawings and will be described in more detail below. The drawings and the written description are not intended to limit the scope of the inventive concepts in any way, but rather to illustrate the inventive concepts to those skilled in the art by reference to the specific embodiments.
Detailed Description
Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, the same numbers in different drawings refer to the same or similar elements, unless otherwise indicated. The implementations described in the following exemplary examples do not represent all implementations consistent with the application. Rather, they are merely examples of apparatus and methods consistent with aspects of the application as detailed in the accompanying claims.
First, the terms involved in the present application will be explained:
the discrete element method comprises the following steps: the method is a numerical simulation method for solving the problem of discontinuous medium, and the method is characterized in that a jointed rock mass is regarded as being composed of discrete rock masses and joint surfaces among the rock masses, the rock masses are allowed to translate, rotate and deform, and the joint surfaces can be compressed, separated or slid;
Presetting simulation software: the modeling tool is used for carrying out three-dimensional modeling on underground reservoir cracks according to ground stress distribution, rock mechanical parameters of a matrix, natural crack distribution and mechanical property parameters, pumping parameters, temporary plugging positions, times and the like;
Galerkin finite element method: the principle of the numerical analysis method is that a set of linear algebraic equations which are easy to solve can be obtained by selecting finite polynomial functions (also called basis functions or shape functions) and superposing the finite polynomial functions, and then requiring weighted integration (the weight function is a test function) of the result in a solving domain and on a boundary to meet the original equation, and natural boundary conditions can be automatically met;
picard iteration method: refers to a principal approximation calculation method of ordinary differential equation solution.
When the steering of the temporary plugging steering fracturing process in the simulated joint is carried out, the most important step is to judge whether the crack is expanded or not, and the crack expansion is the interaction result of fluid and rock mass, so that the motion equation of the simulated fluid and the rock mass is required to be constructed respectively, after the fluid flow equation and the rock mass deformation equation are combined, only data such as the fluid injection rate, the fluid viscosity, the fluid loss rate, the force of unit volume, the rock density and the damping coefficient are required to be obtained, the data can be brought into the equation to be combined and solved to obtain the crack width, then whether the virtual spring is broken or not is judged based on the crack width, and further the crack steering distribution condition is simulated according to the breaking condition of the virtual spring.
The method provided by the application aims to solve the technical problems in the prior art.
The following describes the technical scheme of the present application and how the technical scheme of the present application solves the above technical problems in detail with specific embodiments. The following embodiments may be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments. Embodiments of the present application will be described below with reference to the accompanying drawings.
FIG. 1 is a flow chart of a temporary plugging diverting fracturing simulation method in a seam of the application. As shown in fig. 1, the method comprises the following steps:
S101, constructing a discrete crack model based on a discrete element method.
FIG. 2 is a schematic representation of a discrete fracture model constructed in accordance with the present application. As shown in fig. 2, the model includes a plurality of block units 1 simulating discrete rock matrix, joint units 2 simulating fluid flow among the block units, hydraulic fracture units 3 simulating rock fracture, and temporary plugging units 4 simulating temporary plugging sections, the block units are in a triangular prism structure, the block units are connected through virtual springs 5, when the virtual springs 5 are broken, separation or sliding dislocation occurs among the block units 1, so that cracks are generated, injected fluid can preferentially pass through the cracks, and for the block units 1 with more cracks, the fluid can form a dominant expansion path of the fluid according to the width of the cracks, after the temporary plugging units 4 are artificially arranged on the dominant expansion path of the fluid, the fluid pressure in the cracks is influenced, so that the fluid is enabled to reselect the flow path after avoiding the dominant expansion path, and the complexity of a crack network is increased.
S102, dispersing and iterating the fluid flow equation based on a weak coupling method to obtain the pressure of the fluid in the seam, and inputting the pressure of the fluid in the seam into the rock deformation equation to obtain the width of the seam.
Preferably, the fluid flow equation is constructed using an inter-parallel plate flow equation for an incompressible fluid, wherein the fluid viscosity, fluid injection rate, and fluid loss rate of the incompressible fluid are measurable physical parameters by which a fluid flow equation for the fracture width as a function of fluid pressure within the fracture can be established. Because the slit width and the slit fluid pressure equation are dynamic physical quantities based on a position function and time, the corresponding slit fluid pressure under certain fluid viscosity, fluid injection rate and fluid filtering stall conditions can be obtained through dispersion and iteration.
Preferably, the obtained in-seam fluid pressure is converted into a contact force on the surface of the block unit 1, the contact force is the main acting force in a rock mass deformation equation, the rock mass deformation equation is constructed through a linear elastic dynamic balance equation, under the condition that the contact force is known, dynamic physical quantities of the split displacement between the block units 1 changing along with time can be established by acquiring physical parameters such as force, rock density, damping coefficient and the like of the unit volume of the block unit 1, after the time is determined, the corresponding split displacement is obtained, and the split displacement between the block units 1 can be equivalent to the split width, so that the key physical quantities for judging the state of the virtual spring 5 are obtained.
S103, obtaining stress received by the virtual spring based on the crack width, and judging whether the virtual spring is broken or not according to the stress received by the virtual spring and the maximum stress of the virtual spring, if so, expanding the crack.
According to the stress analysis schematic diagram of the virtual spring 5 in the discrete crack model of fig. 2, the stress component force applied to the virtual spring 5 is divided into the stress along the normal direction of the block unit 1 and the stress along the tangential direction of the block unit 1, and the crack width is equally decomposed into normal displacement and tangential displacement, so that the stress applied to the dependent variable virtual spring 5 can be obtained only by acquiring the constant spring stiffness and the independent variable crack width based on the basic formula of the spring stress. The maximum stress of the virtual spring 5 in the normal direction is related to the contact area and tensile strength of the block units 1, while the maximum stress in the tangential direction is related to the contact area, matrix shear strength and internal friction angle of the block units 1, and when the positions of two adjacent block units 1 are fixed, the maximum stress that the corresponding virtual spring 5 can bear is also fixed.
FIG. 3 is a schematic diagram of a virtual spring force analysis in a discrete crack model according to the present application. From the schematic diagram of the stress analysis of the virtual spring 5 in the discrete crack model of fig. 3, it can be seen that:
When the normal stress received by the virtual spring 5 is smaller than the maximum normal stress and the tangential stress is smaller than the maximum tangential stress, the virtual spring 5 is not broken, no new cracks are generated at the moment, and the tangential stress and the normal stress are not changed;
when the normal stress is larger than the maximum normal stress, the block units 1 are separated from each other, at the moment, the virtual spring 5 is subjected to tensile fracture, and the two block units 1 are not stressed after being broken;
When the tangential stress is greater than the maximum tangential stress, the block units 1 slide each other, and at this time, the virtual spring 5 is sheared and broken, and because there is contact between the two blocks, there is stress between each other, the normal stress is unchanged, and the tangential stress becomes residual shearing resistance.
S104, 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. After the crack is expanded, fluid flows into all crack expansion positions, cracks with larger width are connected in series according to the width of the crack to form a dominant expansion path of the fluid, the pressure of the rock mass born by the fluid on the dominant expansion path is minimum, the fluid can preferentially flow on the dominant expansion path, so that the impact pressure of the fluid on the rock mass is reduced, the rock mass crack is not increased any more, at the moment, after the temporary plugging unit is arranged on the dominant expansion path, the permeability of the temporary plugging unit is greatly reduced, the fluid is diverted and fractured, whether the crack is expanded is calculated according to the formula of the steps, so that the temporary plugging post-fracturing diversion process in the rock mass crack is simulated, and a design optimization basis is provided for how to increase the complexity of the crack subsequently.
In the embodiment, a discrete crack model is constructed based on a discrete element method; based on a weak coupling method, a fluid flow equation and a rock mass deformation equation are combined, the fluid flow equation is subjected to discrete and iterative processing to obtain a slit fluid pressure, and the slit fluid pressure is input into the rock mass deformation equation to obtain a slit width; and acquiring the 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, realizing the mathematical simulation effect of complex steering after temporary plugging in the crack by using a crack expansion method. The state change of the virtual spring 5 causes the change of a stress formula and then fluid moves towards different cracks, so that the simulation of complex crack expansion behaviors in the temporary plugging and fracturing process is realized by using a mathematical method.
One possible embodiment is further described below to illustrate how an intra-fracture temporary plugging diverting fracturing method can be implemented.
An in-seam temporary plugging diverting fracturing simulation method comprises the following steps:
firstly, constructing a discrete fracture model, wherein the discrete fracture model comprises a plurality of block units simulating a discrete rock matrix, and the block units are connected through virtual springs;
then, constructing 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;
And finally, obtaining the stress born by the virtual spring based on the crack width, and 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, if so, expanding the crack.
In one possible design, a fluid flow equation and a rock mass deformation equation are constructed based on discrete fracture models, respectively, and then the fracture widths are solved concurrently. The method comprises the following specific steps:
S201, constructing a fluid flow equation based on an incompressible fluid parallel plate flow equation:
Wherein w is the width of the crack which dynamically changes along with time, and m; p is the fluid pressure in the slit, pa, which dynamically changes with time; q is the liquid injection rate, m 3/s; mu is the viscosity of the fluid, pa.s; q l is fluid loss velocity, m/s.
After the liquid injection rate q, the fluid viscosity mu and the fluid filtration stall degree q l are brought in, the fluid flow equation is discretized by a Galerkin finite element method, and then the fluid pressure p in the seam is solved by a Picard iteration method.
When the iteration method solves the problem that the convergence is not satisfied, adopting an acceleration algorithm to solve the problem:
pm+1＝(1-β)pm+βpm+1，
wm+1＝(1-β)wm+βwm+1，
wherein, the subscript m represents an iteration step, and the value of beta is 0 to 0.5.
S202, constructing a rock mass deformation equation based on a linear elastic dynamic balance equation:
σij,j+bi-ρui,tt-αui,t＝0，
Where 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 cleavage displacement u in time t, m/s; u i,tt is the acceleration of the cleavage displacement u over time t, m/s 2; alpha is the damping coefficient, (kg.s)/m 3.
The contact force exerted on the block unit face due to the fluid pressure in the slit satisfies the following relationship:
p＝σijnj，
Wherein, sigma ij is the Cauchy stress tensor, pa; n j is the direction cosine of the external normal on the block unit surface;
S203, combining a fluid flow equation and a rock mass deformation equation to obtain a crack displacement, namely the crack width:
Carrying in the obtained slit fluid pressure, solving the derivative sigma ij,j of the cauchy stress tensor, and inputting the derivative sigma ij,j of the cauchy stress tensor into the rock mass deformation equation to obtain a splitting displacement u;
Since there is a correspondence between the crack displacement and the crack width between the block units, the crack displacement u can be equivalent to the crack width.
In one possible design, to avoid overlapping of two block units, the minimum seam width is constructed as the residual seam width w res, the formula:
Wherein w 0 is the initial joint unit seam width, m; f n0 is the normal stress at w 0/2, pa;
According to the parallel plate model, before the block units are damaged, the initial joint units and the block units have equal permeability, and then the seam width of the initial joint units can be equivalently obtained by the permeability of the matrix block units:
Wherein k is the matrix block permeability; after the initial joint cell seam width is determined, its corresponding F n0 is available, thereby determining the value of the residual seam width w res.
Permeability refers to the ability of a fluid to pass through a pore. After temporary plugging, the fluid is difficult to pass through the temporary plugging unit, so that the permeability of the temporary plugging unit can be reduced to be very low, and the temporary plugging simulation is realized. The seam width after temporary plugging meets the seam width formula of an initial joint unit:
Based on the principle that the flow capacity of fluid in a joint is reduced by temporary plugging, the influence of the temporary plugging on the permeability of the joint is represented by a reduction coefficient alpha p, and the joint width of an initial joint unit can be obtained after the temporary plugging is brought in, wherein the permeability of the temporary plugging unit is as follows:
k PE＝αp k, where α p is a reduction coefficient.
Then, the stress of the dummy spring is obtained from the obtained split displacement.
Wherein the virtual spring is stressed including tangential stress F s and normal stress F n, obtain the stress of virtual spring based on crack width, include:
wherein k s and k n are respectively the tangential stiffness and the normal stiffness of the virtual spring, N/m; u s and u s are tangential displacement and normal displacement, m, respectively, of the block unit during cracking; the superscript n indicates a time step.
Wherein the maximum stress of the virtual spring comprises the maximum normal stressAnd maximum tangential stress
Wherein A is the contact area, m 3;T0 is the tensile strength and Pa; s 0 is matrix shear strength, pa; Is the internal friction angle, °.
In one possible design, determining whether the virtual spring is broken according to the stress to which the virtual spring is subjected and the maximum stress of the virtual spring includes:
When (when) AndWhen the virtual spring is broken, no crack is expanded, and the stress formula is as follows:
Wherein k n and k s are the normal and tangential spring rates, N/m, respectively; Δu n and Δu s are the normal and tangential relative displacements, m, between adjacent nodes, respectively; superscript n denotes the time step;
When (when) During the time, virtual spring takes place tensile fracture, and block unit separates each other, and the stress formula is this moment:
When (when) During the time, virtual spring takes place shearing fracture, and block unit slides each other, and the stress formula is this moment:
In the method, in the process of the invention, And N is the residual shearing resistance after the spring breaks.
Model basic parameters of the demonstration examples are input into preset simulation software, and are shown in the following table 1:
TABLE 1 demonstration of example model parameters
Fig. 4 is a schematic diagram of the hydraulic fracture propagation morphology in a natural fracture reservoir based on the demonstration example described above. As shown in fig. 4a, when the temporary plugging is not performed, the hydraulic fracture directly passes through the natural fracture, the formed fracture is simpler in shape, and the coverage area of the fracture network is lower. This is because the horizontal stress difference is large, and conventional fracturing is difficult to open natural fractures to form complex slotted networks. It is desirable to block the potentially advantageous propagation path of the fracture to increase the complexity of the mesh. As shown in fig. 4b-d, after the plugging location and number are preferred, plugging is performed, whereupon the fracture deflects multiple times and multiple natural fractures are opened, eventually forming a more complex network of fractures in the target area of reservoir formation.
FIG. 5 is a schematic diagram of injection pressure curves, in which the injection pressure increases significantly after the seam is plugged, and when the injection pressure reaches a certain value, the natural seam is opened, increasing the complexity of the seam net. In the embodiment, the reasonable in-seam temporary plugging steering fracturing optimization design can promote hydraulic fracture expansion, improve the complexity and coverage area of a seam net and improve the post-pressing effect.
In the embodiment, a discrete fracture model, a fluid flow equation and a rock mass deformation equation are specifically constructed, the fluid flow equation is subjected to discrete and iterative processing to obtain the pressure of fluid in a fracture, and the pressure of the fluid in the fracture is input into the rock mass deformation equation to obtain the width of the fracture; and obtaining the 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 completing a mathematical model of temporary plugging and turning fracturing of fluid in the crack, so that the temporary plugging position and the temporary plugging quantity can be optimally designed through the mathematical model conveniently, and technical support is provided for underground actual exploitation scenes.
FIG. 6 is a schematic diagram of a temporary plugging diverting fracturing device in a seam according to the present application. As shown in fig. 6, the present embodiment provides an in-slot temporary plugging and steering fracturing device, which includes a memory 602 and a processor 601, wherein the memory 602 is used for storing a program, and the memory 602 is connectable with the processor 601 through a bus 603. The memory 602 may be a non-volatile memory such as a hard disk drive and a flash memory, with software programs and device drivers stored in the memory 602. The software program can execute various functions of the method provided by the embodiment of the application; the device driver may be a network and interface driver. The processor 601 is configured to execute a software program, where the software program is capable of implementing the method for temporary plugging and diverting fracturing in a seam according to the embodiment of the present application:
Specifically, the fluid flow equation is constructed based on an inter-parallel plate flow equation for an incompressible fluid:
Where w is the width of the slit dynamically changing with time, p is the pressure of the fluid in the slit dynamically changing with time, q is the fluid injection rate, μ is the fluid viscosity, and q l is the fluid loss rate.
Specifically, the rock mass deformation equation is constructed based on a linear elastic dynamic balance equation:
σij,j+bi-ρui,tt-αui,t＝0，
Where σ ij,j is the derivative of the cauchy stress tensor, n i is the force per unit volume, ρ is the rock density, u i,t is the velocity of the crack displacement u in time t, u i,tt is the acceleration of the crack displacement u in time t, and α is the damping coefficient.
Specifically, inputting the fluid pressure in the seam to the rock mass deformation equation to obtain a seam width, including:
solving a derivative sigma ij,j of the cauchy-stress tensor based on the in-seam fluid pressure, wherein the contact force exerted by the in-seam fluid pressure on the block unit surface satisfies the following relationship:
p＝σijnj，
Wherein, sigma ij is the cauchy stress tensor, n j is the direction cosine of the external normal on the block unit surface;
inputting the derivative sigma ij,j of the cauchy stress tensor into the rock mass deformation equation to obtain a cracking displacement u;
The cleavage displacement u is equivalent to the cleavage width.
Specifically, the stress of the virtual spring includes tangential stress F s and normal stress F n, and the stress of the virtual spring is obtained based on the crack width, including:
Where k s and k n are the tangential stiffness and the normal stiffness of the virtual spring, respectively, u s and u n are the tangential displacement and the normal displacement of the block unit at the time of cracking, respectively, and the superscript n indicates the time step.
Specifically, the maximum stress of the virtual spring includes the maximum normal stressAnd maximum tangential stress
Wherein A is the contact area, T 0 is the tensile strength, S 0 is the matrix shear strength,Is the internal friction angle.
Specifically, according to the stress suffered by the virtual spring and the maximum stress of the virtual spring, judging whether the virtual spring is broken or not includes:
When (when) AndWhen the virtual spring is broken, no crack is expanded, and the stress formula is as follows:
Wherein k n and k s are normal and tangential spring rates respectively, deltau n and Deltau s are normal and tangential relative displacements between adjacent nodes respectively, and the superscript n represents a time step;
When (when) During the time, virtual spring takes place tensile fracture, and block unit separates each other, and the stress formula is this moment:
When (when) During the time, the virtual spring is sheared and broken, and the block units slide mutually, and the stress formula is:
In the method, in the process of the invention, Is the residual shear resistance after the spring breaks.
Specifically, based on the principle that the flow capacity of fluid in a seam is reduced by temporary plugging, the influence of temporary plugging on the permeability of the seam is represented by a reduction coefficient alpha p, and the permeability of a temporary plugging unit is as follows:
k PE＝αp k, where α p is a reduction coefficient. Specifically, the discrete fracture model further includes an joint unit for simulating fluid flow between the block units, and the minimum fracture width for avoiding overlapping of the two block units is constructed as a residual fracture width w res, and the formula is as follows:
Wherein w 0 is the initial joint unit seam width, and F n0 is the normal stress when w 0/2;
According to the parallel plate model, before the block units are damaged, the initial joint units and the block units have equal permeability, and then the seam width of the initial joint units can be equivalently obtained by the permeability of the matrix block units:
Where k is matrix bulk permeability.
The temporary plugging steering fracturing equipment in the seam provided by the embodiment can be used for executing the temporary plugging steering fracturing simulation method in the seam, and the implementation principle and the technical effect are similar, so that the description is omitted here.
The embodiment of the invention also provides a computer readable storage medium, and a computer program is stored on the computer readable storage medium, and when the computer program is executed by a processor, the method provided by the embodiment of the invention is realized.
The computer readable storage medium provided in this embodiment may be used to execute the temporary plugging steering fracturing simulation method in the seam, and its implementation principle and technical effect are similar, and this embodiment is not repeated here.
Those of skill would further appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative elements and steps are described above generally in terms of function in order to clearly illustrate the interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied in hardware, in a software module executed by a processor, or in a combination of the two. The software modules may be disposed in Random Access Memory (RAM), memory, read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
Other embodiments of the application will be apparent to those skilled in the art from consideration of the specification and practice of the application disclosed herein. This application is intended to cover any variations, uses, or adaptations of the application following, in general, the principles of the application and including such departures from the present disclosure as come within known or customary practice within the art to which the application pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the application being indicated by the following claims.
It is to be understood that the application is not limited to the precise arrangements and instrumentalities shown in the drawings, which have been described above, and that various modifications and changes may be effected without departing from the scope thereof. The scope of the application is limited only by the appended claims.
Claims (9)
1. The method for simulating temporary plugging steering fracturing in the seam is characterized by comprising the following steps of:
Constructing a discrete fracture model based on a discrete element method, wherein the discrete fracture model comprises a plurality of block units simulating discrete rock matrixes and temporary plugging units for simulating temporary plugging agents, the block units are connected through virtual springs, and the temporary plugging units are in clearance fit connection with the block units;
Based on a weak coupling method, a fluid flow equation and a rock mass deformation equation are combined, the fluid flow equation is subjected to discrete and iterative processing to obtain a slit fluid pressure, and the slit fluid pressure is input into the rock mass deformation equation to obtain a slit width;
Acquiring 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;
Obtaining an advantageous expansion path of 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;
constructing the fluid flow equation based on an inter-parallel plate flow equation of an incompressible fluid:
Wherein w is the width of the crack which dynamically changes along with time, p is the pressure of the fluid in the crack which dynamically changes along with time, q is the liquid injection rate, mu is the fluid viscosity, and q l is the fluid filtration rate;
Based on a weak coupling method, a fluid flow equation and a rock mass deformation equation are combined, and the fluid flow equation is subjected to discrete and iterative processing to obtain the pressure of the fluid in the seam, which comprises the following steps:
discrete fluid flow equations by the Galerkin finite element method;
solving the fluid pressure p in the seam by adopting a Picard iteration method;
When the Picard iteration method solves the problem that convergence is not met, adopting an acceleration algorithm to solve:
Pm+1＝(1-β)pm+βpm+1，
wm+1＝(1-β)wm+βwm+1，
wherein, the subscript m represents an iteration step, and the value of beta is 0 to 0.5.
2. The method of claim 1, wherein the rock mass deformation equation is constructed based on a linear elastic dynamic balance equation:
σij,j+bi-pui,tt-αui,t＝0，
Where σ ij,j is the derivative of the cauchy stress tensor, b i is the force per unit volume, p is the rock density, u i,t is the velocity of the cleavage displacement u in time t, u i,tt is the acceleration of the cleavage displacement u in time t, and α is the damping coefficient.
3. The method of claim 2, wherein inputting the in-seam fluid pressure into the rock mass deformation equation yields a fracture width, comprising:
solving a derivative sigma ij,j of the cauchy-stress tensor based on the in-seam fluid pressure, wherein the contact force exerted by the in-seam fluid pressure on the block unit surface satisfies the following relationship:
p＝σijnj，
Wherein, sigma ij is the cauchy stress tensor, n j is the direction cosine of the external normal on the block unit surface;
inputting the derivative sigma ij,j of the cauchy stress tensor into the rock mass deformation equation to obtain a cracking displacement u;
The cleavage displacement u is equivalent to the cleavage width.
4. The method of claim 1, wherein the virtual spring being stressed comprises tangential stress F s and normal stress F n, the stress of the virtual spring being obtained based on the slit width, comprising:
Wherein k s and k n are respectively tangential stiffness and normal stiffness of the virtual spring, u s and u n are respectively tangential displacement and normal displacement of the block unit during cracking, and the superscript n represents a time step;
the maximum stress of the virtual spring comprises the maximum normal stress And maximum tangential stress
Wherein A is the contact area, T 0 is the tensile strength, S 0 is the matrix shear strength,Is the internal friction angle.
5. The method of claim 4, wherein determining whether the virtual spring is broken based on the stress experienced by the virtual spring and the maximum stress of the virtual spring comprises:
When (when) AndWhen the virtual spring is broken, no crack is expanded, and the stress formula is as follows:
Wherein k n and k s are normal and tangential spring rates respectively, deltau n and Deltau s are normal and tangential relative displacements between adjacent nodes respectively, and the superscript n represents a time step;
When (when) During the time, virtual spring takes place tensile fracture, and block unit separates each other, and the stress formula is this moment:
When (when) During the time, the virtual spring is sheared and broken, and the block units slide mutually, and the stress formula is:
In the method, in the process of the invention, Is the residual shear resistance after the spring breaks.
6. The method of claim 1, wherein the method for setting a temporary blocking unit on the dominant expansion path comprises: based on the principle of reducing the fluid flow capacity of the seam by temporary plugging, the influence of the temporary plugging on the permeability of the seam is represented by a reduction coefficient alpha p, and the permeability of the temporary plugging unit is as follows:
k PE＝αp k, wherein α p is a reduction coefficient, and k is a matrix bulk permeability.
7. The method of claim 6, wherein the discrete fracture model further comprises an element of joints for simulating fluid flow between the bulk cells, wherein according to the parallel plate model, the initial element of joints and the bulk cells have equal permeability before failure of the bulk cells, and the initial element of joints seam width is equivalent to the permeability of the matrix bulk cells:
8. The method of claim 7, wherein constructing the minimum seam width that avoids overlapping of two block units is a residual seam width w res, formula:
Where w 0 is the initial joint cell seam width and F n0 is the normal stress at w 0/2.
9. An in-seam temporary plugging diverting fracturing device, comprising: a processor, and a memory communicatively coupled to the processor;
The memory stores computer-executable instructions;
the processor executes computer-executable instructions stored in the memory to implement the method of any one of claims 1 to 8.
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