Simulation method for reservoir hydraulic crack propagation and matrix seepage coupling

Abstract

The invention provides a reservoir hydraulic crack propagation and matrix seepage coupling simulation method, which comprises the following steps: solving a seepage equation in the implementation process of crack propagation and seepage coupling calculation; solving the pressure equation to obtain a pressure field, correcting the seepage velocity according to the pressure field, and obtaining a seepage velocity field Uf; solving the kinetic equation of skeleton deformation to obtain the movement speed Us of the skeleton structure; solving a solid-phase volume fraction equation according to the movement speed of the skeleton structure; the sum of the volume fraction of the solid and the porosity of the matrix is 1, and calculating a porosity distribution field according to the relation; correcting the spatial distribution of the permeability according to the spatial distribution of the porosity; repeating the steps until the preset physical time is ended; and counting parameter information to obtain information of crack propagation characteristics. An integrated kinetic model for crack propagation and matrix seepage coupling calculation in the pressure driving process is constructed, and the simulation calculation speed is increased.

Description

Technical Field

[0001] The present invention relates to the field of hydraulic cracks and macroscopic seepage in porous media, and particularly to a simulation method for coupling the propagation of reservoir hydraulic cracks and matrix seepage. Background Art

[0002] The pressure drive technology combines hydraulic fracturing equipment with water injection development. By increasing the injection pressure, a large amount of water is rapidly injected into the formation, achieving the effects of increasing the reservoir pressure, improving the seepage capacity, and enhancing the oil well productivity in a relatively short time. In recent years, the Shengli Oilfield has carried out pilot tests in the field using this technology and achieved good application results. Compared with traditional water flooding, both the injection rate and injection pressure of the fluid are significantly increased during the application of this technology. The high-speed injection of the fluid causes significant changes in the pore pressure and effective stress around the injection well, resulting in deformation of the reservoir skeleton and even crack generation, and the cracks continuously expand outward with the high-speed seepage of the fluid. The deformation of the matrix and the generation and expansion of cracks have a significant impact on the seepage capacity of the reservoir. The current on-site measurement means and test methods have limited effects on deepening the understanding of the seepage law during the pressure drive process. The traditional reservoir numerical simulation model is based on the mass conservation equations of oil, gas, and water phases, simulating various physical properties of the reservoir and the flow law of fluids in it, lacking an accurate description of the changes in reservoir physical properties and fluid migration when the effective stress changes sharply, and thus needs to be improved.

[0003] There are the following challenges in constructing the numerical simulation method for the pressure drive process: (1) During the pressure drive process, the displacement speed is too large, and the formation medium undergoes severe deformation and cracking, so the conventional numerical methods based on the small deformation assumption (such as the linear deformation in the black oil system) are no longer applicable; (2) The crack propagation and porous zone seepage are coupled together. During the pressure drive process, the formation belongs to dual media, and during the displacement process, the dual media region is constantly changing, and the conventional numerical simulation methods cannot describe it; (3) There is a lack of an effective method that can simultaneously simulate the crack propagation and the change laws of porosity and permeability in the porous region. Therefore, starting from an in-depth study of the interaction between fluids and porous media, the present invention constructs an integrated coupling mathematical model and simulation method for matrix deformation, cracking, and seepage, providing a means for studying the crack propagation law, matrix seepage law, and pore-seepage change law during the pressure drive process, and laying a foundation for the adjustment and optimization of the reservoir pressure drive development plan. Summary of the Invention

[0004] In view of the above problems, the present invention is proposed to provide a simulation method for coupling the propagation of reservoir hydraulic cracks and matrix seepage that overcomes or at least partially solves the above problems.

[0005] According to one aspect of the present invention, there is provided a simulation method for coupling the propagation of reservoir hydraulic cracks and matrix seepage, the simulation method comprising:

[0006] In the implementation process of the coupled calculation of crack propagation and seepage, the seepage equation is solved to obtain the predicted distribution of the seepage velocity field in the pore space;

[0007] The pressure equation is solved to obtain the pressure field, and the seepage velocity is corrected according to the pressure field, and the seepage velocity field U is obtained f ;

[0008] The dynamic equation of the skeleton deformation is solved to obtain the motion velocity Us of the skeleton structure;

[0009] According to the motion velocity of the skeleton structure, the solid volume fraction equation is solved to obtain the spatial distribution of the solid volume fraction at the new time;

[0010] The sum of the volume fraction of the solid and the porosity of the matrix is 1, and the porosity distribution field is calculated according to the relationship;

[0011] The spatial distribution of the permeability is corrected according to the spatial distribution of the porosity, providing data for the solution of the next seepage process and solid deformation process;

[0012] Repeat the above steps until the preset physical time ends;

[0013] Statistical parameter information is obtained to obtain information on crack propagation characteristics.

[0014] Optionally, the statistical parameter information specifically includes: statistics of velocity, pressure, and solid volume fraction.

[0015] Optionally, the implementation process of the coupled calculation of crack propagation and seepage further includes:

[0016] Describing the free fluid flow in the crack and the seepage in the matrix, and distinguishing the crack area and the matrix area by the pore volume fraction;

[0017] When the pore volume fraction in a certain grid is between 0 and 1, the grid is in the matrix area, and when the pore volume fraction is 1, the grid is in the crack area.

[0018] Optionally, the description of the fluid flow in the crack and the fluid seepage in the matrix within the same framework describes the motion of the fluid under the framework of the Darcy-Brinkman-Stokes equation, taking into account the influence of the skeleton deformation,

[0019]

[0020] Optionally, to describe the deformation of the skeleton structure, a dynamic model of the skeleton is constructed, and the plastic stress of the skeleton, the influence of the pore pressure, and the force of the fluid on the skeleton are considered in the dynamic model

[0021]

[0022] Optionally, in the process of crack formation and propagation, a tracking equation for the volume fraction of the skeleton is constructed.

[0023]

[0024] The sum of the pore volume fraction and the skeleton volume fraction is 1.

[0025] Optionally, after obtaining the skeleton volume fraction by solving Equation (3), the pore volume fraction can be obtained through the relationship.

[0026] Optionally, the fluid flow and the deformation of the skeleton are treated using the quasi-static assumption, that is, the first and second terms on the left side of Equation (1) and Equation (2) are ignored.

[0027] Equation (1) and Equation (2) become

[0028]

[0029]

[0030] Equation (4) includes the fluid velocity equation and the pressure equation.

[0031] Writing Equation (4) in semi-discrete form gives

[0032]

[0033] where A p is the coefficient on the diagonal of the matrix of the discrete algebraic equation, A N is the value on the off-diagonal of the matrix of the discrete algebraic equation, and S is the source after explicit discretization except for the pressure term.

[0034] Optionally, the fluid porosity tracking evolution equation is written in the following form

[0035]

[0036] Substituting Equation (6) into Equation (7) gives

[0037]

[0038] Equation (8) is the pressure equation, and solving it gives the pressure p f . Substituting the pressure p f into Equation (6) gives the fluid velocity U f ;

[0039] Obtaining the pressure p f and U fAfter that, solve Equation (5) to obtain the solid deformation velocity Us, and further solve Equation (3) to obtain the solid phase volume fraction.

[0040] Optionally, the solving of the seepage equation and the skeleton deformation equation specifically includes:

[0041] Using a steady-state algorithm to solve the seepage equation and the skeleton deformation equation within a time step, which enlarges the time step of the solution.

[0042] A simulation method for coupling reservoir hydraulic crack propagation and matrix seepage provided by the present invention, the simulation method includes: during the implementation of the coupled calculation of crack propagation and seepage, solving the seepage equation to obtain the predicted distribution of the seepage velocity field in the pore space; solving the pressure equation to obtain the pressure field, and correcting the seepage velocity according to the pressure field to obtain the seepage velocity field U f ; solving the kinetic equation of skeleton deformation to obtain the movement velocity Us of the skeleton structure; according to the movement velocity of the skeleton structure, solving the solid phase volume fraction equation to obtain the spatial distribution of the solid volume fraction at the new moment; the sum of the volume fraction of the solid and the porosity of the matrix is 1, and the porosity distribution field is calculated according to the relationship; the spatial distribution of the permeability is corrected according to the spatial distribution of the porosity to provide data for the solution of the next seepage process and solid deformation process; repeat the above steps until the preset physical time ends; count the parameter information to obtain the information of the crack propagation characteristics. An integrated kinetic model for the coupled calculation of crack propagation and matrix seepage during the pressure drive process is constructed. By adopting a quasi-static assumption for the seepage process of the fluid and the deformation and cracking process of the skeleton, the calculation speed of the simulation is improved.

[0043] The above description is only an overview of the technical solution of the present invention. In order to be able to understand the technical means of the present invention more clearly, it can be implemented according to the content of the specification. And in order to make the above and other purposes, features and advantages of the present invention more obvious and understandable, the specific embodiments of the present invention are specifically given below. Brief Description of the Drawings

[0044] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to these drawings without creative efforts.

[0045] Figure 1 It is a flowchart of a simulation method for coupling reservoir hydraulic crack propagation and matrix seepage provided by an embodiment of the present invention;

[0046] Figure 2 It is a crack distribution diagram at different times (a) 3s (b) 6s (c) 9s (d) 12s;

[0047] Figure 3 Velocity distribution diagrams at different times (a) 3s (b) 6s (c) 9s (d) 12s;

[0048] Figure 4 Pressure distribution diagrams at different times (a) 3s (b) 6s (c) 9s (d) 12s. Detailed implementation manners

[0049] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present disclosure can be more thoroughly understood and the scope of the present disclosure can be fully conveyed to those skilled in the art.

[0050] The terms "including" and "having" and any variations thereof in the description, claims and drawings of the present invention are intended to cover non-exclusive inclusion. For example, a series of steps or units are included.

[0051] The technical solutions of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

[0052] As Figure 1 shown, the specific steps of the numerical simulation are as follows:

[0053] In the implementation process of the coupled calculation of crack propagation and seepage, first solve the seepage equation to obtain the predicted distribution of the seepage velocity field in the pore space;

[0054] Solve the pressure equation to obtain the pressure field, and correct the seepage velocity according to the pressure field to obtain the accurate seepage velocity field U f ;

[0055] Solve the dynamic equation of the skeleton deformation to obtain the movement velocity U of the skeleton structure s ;

[0056] According to the movement velocity of the skeleton, solve the solid volume fraction equation to obtain the spatial distribution of the solid volume fraction at the new moment;

[0057] The sum of the volume fraction of the solid and the porosity of the matrix is 1. Calculate the porosity distribution field according to this relationship;

[0058] Correct the spatial distribution of the permeability according to the spatial distribution of the porosity to provide data for the next solution of the seepage process and the solid deformation process.

[0059] Repeat the above steps until the preset physical time ends.

[0060] Statistical analysis is carried out on parameters such as velocity, pressure, and solid-phase volume fraction to obtain information on crack propagation characteristics.

[0061] A numerical simulation method for coupling hydraulic crack propagation and matrix seepage is implemented as follows:

[0062] (1) To describe the free fluid flow in cracks and seepage in the matrix, the present invention uses the pore volume fraction to distinguish between the crack region and the matrix region. When the pore volume fraction in a certain grid is between 0 and 1, the grid is in the matrix region; when the pore volume fraction is 1, the grid is in the crack region.

[0063] (2) To describe the fluid flow in cracks and fluid seepage in the matrix within the same framework, the present invention describes the motion of the fluid under the framework of the Darcy - Brinkman - Stokes equation, while considering the influence of the skeleton deformation.

[0064]

[0065] (3) To describe the deformation of the skeleton, the present invention constructs a dynamic model of the skeleton, considering the plastic stress of the skeleton, the influence of pore pressure, and the force exerted by the fluid on the skeleton in the dynamic model.

[0066]

[0067]

[0068] (4) To describe the formation and propagation process of cracks, the present invention constructs a tracking equation for the skeleton volume fraction.

[0069] Since the sum of the pore volume fraction and the skeleton volume fraction is 1. After solving Equation (3) to obtain the skeleton volume fraction, the pore volume fraction can be obtained through this relationship.

[0070] (5) In the actual process, both the fluid flow and the skeleton deformation are transient processes, resulting in a large computational amount. To reduce the computational amount, the present invention adopts a quasi - static assumption, that is, ignoring the first and second terms on the left side of Equation (1) and Equation (2). At this time, the above two equations become

[0071]

[0072]

[0073] Equation (4) includes the fluid velocity equation and the pressure equation. Writing Equation (4) in semi - discrete form gives

[0074]

[0075] Among them, A p is the coefficient on the diagonal of the discrete algebraic equation matrix, and A N is the value on the off-diagonal of the discrete algebraic equation matrix. S is the source after discretization of other terms except the pressure term.

[0076] The fluid porosity tracking evolution equation can be written in the following form

[0077]

[0078] Substituting Equation (6) into Equation (7) gives

[0079]

[0080] Equation (8) is the pressure equation, and after solving, the pressure p f is obtained. Substituting the pressure p f into Equation (6) can obtain the fluid velocity U f . After obtaining the pressure p f and U f , solving Equation (5) can obtain the solid deformation velocity Us, and further solving Equation (3) can obtain the solid phase volume fraction.

[0081] Using the steady-state algorithm to solve the seepage equation (Equation (1)) and the skeleton deformation equation (Equation (2)) within a time step can increase the time step of the solution and improve the calculation speed.

[0082] Figure 2 The crack distribution diagrams at different times are given. In the figures, the gray area is the matrix area, the black area is the crack area, and the center white is the well. The spatial size of the model is that the pore structure size is 50 m and the number of grids is 363233. On the premise of given initial porosity and permeability, water is injected into the pore medium through the well. Under the hydraulic action, the matrix structure will break, and the initially formed cracks are relatively small (such as Figure 2 b). With the continuous injection of liquid volume, the cracks around the well continue to expand. At 9 s and 12 s, the crack distributions are as shown in Figure 2 (c) and (d).

[0083] Figure 3 The velocity contour diagrams at different times are given. The darker the color in the figure, the higher the velocity. It can be seen from the figure that the velocity around the well is relatively high at the initial moment, while the velocity is lower far from the wellhead. Although cracks have occurred around the well at 6 s (as shown in Figure 2 (b)), due to the small cracks, the crack network has no obvious influence on the seepage velocity field. As water is continuously injected into the matrix and the crack network expands outward, finally the cracks have an obvious influence on the velocity (such as Figure 3(c) at 9 s and Figure 3 (d) the velocity field at 12 s).

[0084] Figure 4 The pressure field distributions at different times are given. At the initial time, the pressure is mainly concentrated around the well. As the injection volume continuously increases, the pressure at the wellhead diffuses outward continuously. At 3 s, although cracks have formed, the crack network has no obvious influence on the pressure field distribution. As the cracks expand, the pressure will expand outward along the cracks and affect the spatial distribution of the pressure (such as Figure 4 (c) at 9 s and Figure 4 (d) the pressure field distribution at 12 s).

[0085] The numerical model of the present invention reproduces the crack propagation process and the spatio-temporal distribution changes of pressure-velocity during the pressure-driven process, can deepen the understanding of the interaction between crack propagation and matrix seepage during the pressure-driven process, and provides an important tool for the study of the seepage law during the pressure-driven process.

[0086] Beneficial effects: By deeply exploring the mechanical characteristics of the interaction between fluid and matrix during the pressure-driven process, an integrated dynamic model for coupled calculation of crack propagation and matrix seepage during the pressure-driven process is constructed. By adopting the quasi-static assumption for the seepage process of the fluid and the deformation and cracking process of the skeleton, the calculation speed of the simulation is improved.

[0087] The above specific implementation manners further elaborate in detail the purpose, technical solution and beneficial effects of the present invention. It should be understood that the above are only specific implementation manners of the present invention and are not used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A simulation method for coupling reservoir hydraulic crack propagation and matrix seepage, characterized in that, the simulation method includes: During the implementation of the coupled calculation of crack propagation and seepage, solve the seepage equation to obtain the predicted distribution of the seepage velocity field in the pore space; Solve the pressure equation to obtain the pressure field, correct the seepage velocity according to the pressure field, and obtain the seepage velocity field U f ; Solve the dynamic equation of the skeleton deformation to obtain the motion velocity Us of the skeleton structure; According to the motion velocity of the skeleton structure, solve the solid volume fraction equation to obtain the spatial distribution of the solid volume fraction at the new moment; The sum of the volume fraction of the solid and the porosity of the matrix is 1, and the porosity distribution field is calculated according to the relationship; Correct the spatial distribution of the permeability according to the spatial distribution of the porosity, and provide data for the solution of the next seepage process and solid deformation process; Repeat the above steps until the preset physical time ends; Statistical parameter information is obtained to obtain information on crack propagation characteristics.

2. A simulation method for coupling reservoir hydraulic crack propagation and matrix seepage according to claim 1, characterized in that, the statistical parameter information specifically includes: statistically analyzing the velocity, pressure, and solid volume fraction.

3. A simulation method for coupling reservoir hydraulic crack propagation and matrix seepage according to claim 1, characterized in that, the implementation process of the coupled calculation of crack propagation and seepage further includes: Describe the free fluid flow in the crack and the seepage in the matrix, and use the pore volume fraction to distinguish between the crack area and the matrix area; When the pore volume fraction in a certain grid is between 0 and 1, the grid is in the matrix area, and when the pore volume fraction is 1, the grid is in the crack area.

4. A simulation method for coupling reservoir hydraulic crack propagation and matrix seepage according to claim 1, characterized in that, the description of the fluid flow in the crack and the fluid seepage in the matrix within the same framework describes the motion of the fluid under the framework of the Darcy - Brinkman - Stokes equation, and at the same time considers the influence of the skeleton deformation, 5. A simulation method for coupling reservoir hydraulic crack propagation and matrix seepage according to claim 4, characterized in that, Describe the deformation of the skeleton structure, construct a dynamic model of the skeleton, and consider the plastic stress of the skeleton, the influence of pore pressure, and the force of the fluid on the skeleton in the dynamic model 6. A simulation method for coupling reservoir hydraulic crack propagation and matrix seepage according to claim 1, characterized in that, For the formation and propagation process of the crack, a skeleton volume fraction tracking equation is constructed The sum of the pore volume fraction and the skeleton volume fraction is 1.

7. A simulation method for coupling reservoir hydraulic crack propagation and matrix seepage according to claim 6, characterized in that, After solving equation (3) to obtain the skeleton volume fraction, the pore volume fraction can be obtained through the relationship.

8. A simulation method for coupling reservoir hydraulic crack propagation and matrix seepage according to claim 5, characterized in that, The fluid flow and the skeleton deformation are processed by the quasi - static assumption, that is, the first term and the second term on the left side of equations (1) and (2) are ignored; Equations (1) and (2) become Equation (4) includes the fluid velocity equation and the pressure equation; The equation (4) is written in semi-discrete form as where A p is the coefficient on the diagonal of the discrete algebraic equation matrix, and A N is the value on the off-diagonal of the discrete algebraic equation matrix. S is the source after explicit discretization except for the pressure term.

9. A simulation method for coupling reservoir hydraulic crack propagation and matrix seepage according to claim 8, characterized in that the fluid porosity tracking evolution equation is written in the following form Substituting equation (6) into equation (7) gives Equation (8) is the pressure equation, and after solving, the pressure p is obtained. f Substituting the pressure p f into Equation (6) gives the fluid velocity U f ; Obtain the pressure p f and U f After that, solve Equation (5) to obtain the solid deformation velocity Us, and further solve Equation (3) to obtain the solid volume fraction.

10. A simulation method for coupling reservoir hydraulic crack propagation and matrix seepage according to claim 5, characterized in that the specific steps of solving the seepage equation and the skeleton deformation equation include: Using a steady-state algorithm to solve the seepage equation and the skeleton deformation equation within a time step, which enlarges the time step of the solution.

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