True three-dimensional numerical simulation method for analyzing fault activity tendency based on extended finite element

Abstract

The invention discloses an extended finite element-based true three-dimensional numerical simulation method for analyzing fault activity tendency, which comprises the following steps of: representing linear elasticity of a three-dimensional space geologic body by adopting a true three-dimensional model, controlling displacement by passive quantity balance, and adopting a within-plane model; the stress displacement condition of the true three-dimensional fault is represented by constructing a three-dimensional curved surface discontinuous equation; a fluid-solid coupling model is obtained through analysis; representing the change of the permeability in the rock stratum along with the strain; and characterizing the change of fault water flow capacity caused by stress. According to the method, curved surface faults with various dip angles can be analyzed, fault activity is performed according to stick-slip, changes of hydraulic parameters such as permeability in the fault serving as a fracture zone during fault activity are fully considered, the parameters are arranged according to points, the influence of heterogeneity can be considered, and two fluid injection modes (according to flow and water injection pressure) are provided; and the earthquake magnitude can be predicted.

Description

TECHNICAL FIELD

[0001] The present application relates to true three-dimensional numerical simulation technology, in particular to a true three-dimensional numerical simulation method for analyzing fault activity tendency based on extended finite element. BACKGROUND

[0002] In many industrial fields such as carbon dioxide geological storage, oil and gas field development, shale gas exploitation, geothermal exploitation (high temperature dry rock mass), and brine injection into rock formation, we need to inject / extract fluid into the rock formation. The injection or extraction of fluid will cause changes in the stress field inside the rock formation. Since the strength of rock is much greater than the strength of the existing fault interface, the activity instability of the existing fault will occur prior to rock rupture. Therefore, the changes in the stress field inside the rock formation may cause the activity instability of the existing fault and induce the occurrence of earthquakes. In recent years, with the attention to carbon emissions, carbon dioxide geological storage has attracted more and more attention from scientists around the world as an effective means to reduce carbon emissions in the atmosphere ([K.S. Lackner. A guide to CO2 sequestration [J]. Science, 2003, 300 (5626): 1677-1678.], [S. Pacala, R. Socolow. Stability wedges: Solving the climate problem for the next 50 years with current technologies [J]. Science, 2004, 305: 968-972.]). In the process of carbon dioxide geological storage, the activity instability of the existing closed fault will form a carbon dioxide conducting fracture, which determines whether carbon dioxide can be successfully stored.

[0003] Therefore, it is an urgent key scientific and technological problem concerning the development of national economy and society to develop a three-dimensional numerical solution method for predicting the activity tendency of faults when fluid is injected / extracted into the rock formation, and to further determine whether it will cause the activity instability of the fault and induce earthquakes.

[0004] CN119312628A discloses a numerical simulation method for analyzing the influence of vibration load on the stability of a front water-containing fault based on extended finite elements, which is used for analyzing whether vibration load will cause the front water-containing fault to be active and unstable to induce water inrush accidents, and can be used in industrial fields such as coal mining and tunneling, can analyze curved faults of various inclinations, and the fault activity is done according to stick-slip, fully considers the changes of hydraulic parameters such as permeability in the fault as a fracture zone during fault activity, and the parameters are arranged according to points, and the influence of heterogeneity can be considered. The patent focuses on developing a two-and-a-half-dimensional numerical simulation program to solve related problems, but in reality, it is a three-dimensional problem, so we need to develop a three-dimensional numerical simulation program to solve this problem. SUMMARY

[0005] In view of the problems in the prior art, the present application provides a true three-dimensional numerical simulation method for analyzing the activity tendency of a fault based on extended finite elements, which is used for predicting whether a fault will be active and unstable to induce an earthquake when fluid is injected / extracted into a rock formation, and can be used in industrial fields such as oil and gas field development, carbon dioxide geological storage, injection of brine into a rock formation, and geothermal exploitation, can analyze curved faults of various inclinations, and the fault activity is done according to stick-slip, fully considers the changes of hydraulic parameters such as permeability in the fault as a fracture zone during fault activity, and the parameters are arranged according to points, and the influence of heterogeneity can be considered, and two injection fluid modes (according to flow rate and according to injection pressure) are provided, and the earthquake magnitude can be predicted.

[0006] The object of the present application is achieved by the following technical solutions.

[0007] A true three-dimensional numerical simulation method for analyzing the activity tendency of a fault based on extended finite elements, comprising the following steps:

[0008] 1) A true three-dimensional model is used to represent the linear elasticity of a three-dimensional geological body, wherein the displacement is controlled by passive momentum balance, and a within-plane model is used;

[0009] 2) The stress and displacement of a true three-dimensional fault are represented by constructing a three-dimensional curved surface discontinuous equation;

[0010] 3) A fluid-structure interaction model is obtained by analysis;

[0011] 5) The change of permeability in the rock formation with strain is represented;

[0012] 5) The change of fault water carrying capacity caused by stress is represented.

[0013] The true three-dimensional model in step 1) is:

[0014]

[0015] σ3≡ σ3(u3) = λtr(ε3(u3))I + 2με3(u3),

[0016]

[0017] where p is the density, σ is the stress, ε is the strain, λ and μ are Lame’s parameters, and I is the identity tensor.

[0018] The fluid-structure interaction model in step 3) is:

[0019]

[0020] where u is the displacement, v is the flow velocity, γ is the fault, f v is a general forcing term.

[0021] The model for characterizing the change in permeability with strain in the rock formation in step 4) is:

[0022]

[0023] where φ is the porosity at a given pressure, φ0 is the initial porosity, ε v is the bulk strain, k is the permeability at a given pressure, k0 is the initial permeability, and n is the power-law exponent.

[0024] The model for characterizing the change in fault transmissivity due to stress in step 5) is:

[0025]

[0026] where T is the fault transmissivity, b h is the fault hydrologic radius, p is the fluid density, μ is the viscosity, g is the gravitational acceleration, K is the hydraulic conductivity, b h0 is the initial hydrologic radius, b hres is the residual radius at high effective stress, σ nref is the effective normal stress that causes a 90% reduction in the initial radius, b hs is the radius growth due to shear displacement.

[0027] Compared with the prior art, the application has the advantages that the application can be used for predicting whether a fault will move and induce an earthquake when fluid is injected into a rock formation, can be used in the industrial fields of oil and gas field development, carbon dioxide geological storage, injection of brine into a rock formation, geothermal exploitation, etc., can analyze curved surface faults of various inclinations in a three-dimensional situation, the fault movement is made according to stick-slip, the change of the hydraulic parameters such as permeability in the fault as a fracture zone when the fault moves is fully considered, two injection fluid modes (according to flow rate and according to injection pressure) are provided, compared with the prior art, the application can calculate specific problems in a true three-dimensional situation, including how to represent the linear elastic problem of a three-dimensional geological body, how to represent the stress displacement condition of a true three-dimensional fault, how to represent the fluid-structure coupling problem, and how to represent the change of the hydraulic parameters such as porosity and permeability with the change of the stress displacement. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 The figure is a schematic diagram of fluid pressure of the application.

[0029] Figure 2 The figure is a schematic diagram of solid displacement of the application.

[0030] Figure 3 The figure is a schematic diagram of solid displacement of the application.

[0031] Figure 4 The figure is a schematic diagram of curved surface fault of the application.

[0032] Figure 5 The figure is a schematic diagram of fluid-structure coupling of the application.

[0033] Figure 6 The figure is a schematic diagram of injection of fluid into a rock formation containing a curved surface fault of the application.

[0034] Figure 7 The figure is a schematic diagram of simplification of fluid flow in a fracture zone into fluid flow in an interface of the application.

[0035] Figure 8 The figure is a schematic diagram of injection and extraction of fluid into a rock formation containing a curved surface fault of the application.

[0036] Figure 9 The figure is a schematic diagram of a rock formation containing a vertical fault when displacement is added on both sides to induce an earthquake of the application.

[0037] Figure 10 The figure is a schematic diagram of fault activity (judging whether a fault will move and induce an earthquake) of the application. DETAILED DESCRIPTION

[0038] The application will be described in detail below in combination with the drawings of the specification and specific examples.

[0039] As Figures 1-10A true 3D numerical solution method is proposed to analyze the tendency of fault activity when injecting / extracting fluid into the rock formation, and to predict whether it will cause fault activity instability and induce an earthquake, by using the extended finite element method to handle fluid flow and the discontinuity of porous solids in true 3D cases. A corresponding true 3D numerical simulation program is developed.

[0040] (1) A true 3D model is used to represent the linear elastic problem of a 3D geological body, in which displacement is controlled by momentum balance, rather than the Mode I / II (in-plane) model used in two and a half dimensions. The true 3D model is:

[0041]

[0042] σ3≡σ3(u3)=λtr(ε3(u3))I+2με3(u3),

[0043]

[0044] where ρ is the density, σ is the stress, ε is the strain, λ and μ are Lame's parameters, and I is the unit tensor.

[0045] (2) In contrast to the two and a half dimensional program, where the fault is a curve, the stress and displacement of a 3D fault are represented by constructing a 3D curved surface discontinuity equation according to Anderson's fault theory.

[0046] (3) Through analysis, the fluid-structure coupling model is obtained as:

[0047]

[0048] where u is the displacement, v is the flow rate, γ is the fault, and f v is a general forcing term, such as gravity.

[0049] (4) For the change of permeability in the rock formation with strain, the model proposed by Chin et al. [Chin, L. Y., Raghavan, R., Thomas, L. K., 2000. Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. SPE J. 5(1), 32-45, Paper 58968.] is used:

[0050]

[0051]

[0052] where φ is the porosity at a given pressure, φ0 is the initial porosity, ε v is the bulk strain, k is the permeability at a given pressure, k0 is the initial permeability, and n is the power law exponent.

[0053] (5) For the change in fault transmissivity caused by stress, we use

[0054]

[0055] where T is the hydraulic conductivity of the fault, b h is the hydraulic radius of the fault, p is the fluid density, μ is the viscosity, g is the gravitational acceleration, K is the hydraulic conductance, b h0 is the initial hydraulic radius, b hres is the residual radius at high effective stress, s nref is the effective normal stress that causes the initial radius to decrease by 90%, b hs is the radius growth due to shear displacement.

Claims

1. A true three-dimensional numerical simulation method for analyzing fault activity tendency based on extended finite element method, characterized by the following steps: include: 1) A true 3D model is used to characterize the linear elasticity of a 3D spatial geological body, where displacement is controlled by passive quantity balance, and a within-plane model is adopted; 2) The stress and displacement of true three-dimensional faults are characterized by constructing three-dimensional surface discontinuity equations; 3) A fluid-structure interaction model was derived through analysis; 4) Characterize the change in permeability in rock strata with strain; 5) The changes in the water-carrying capacity of the fault caused by stress are characterized.

2. The true three-dimensional numerical simulation method for analyzing fault activity tendency based on extended finite element method according to claim 1, characterized in that... The true 3D model in step 1) is: σ3≡σ3(u3)=λtr(ε3(u3))I+2με3(u3), Where ρ is density, σ is stress, ε is strain, λ and μ are Lamé's parameters, and I is the unit tensor.

3. The true three-dimensional numerical simulation method for analyzing fault activity tendency based on extended finite element method according to claim 1, characterized in that... The fluid-structure interaction model in step 3) is as follows: Where u is displacement, v is flow velocity, γ is fault, and f v It is a general mandatory item.

4. The true three-dimensional numerical simulation method for analyzing fault activity tendency based on extended finite element method according to claim 1, characterized in that... The model for characterizing the change in permeability in rock strata with strain in step 4) is as follows: Where φ is the porosity at a given pressure, φ0 is the initial porosity, and ε v Here, k is the volumetric strain, k is the permeability under a given pressure, k0 is the initial permeability, and n is the power law exponent.

5. The true three-dimensional numerical simulation method for analyzing fault activity tendency based on extended finite element method according to claim 1, characterized in that... The characterization model for the change in the fault's water-carrying capacity caused by stress in step 5) is as follows: Where T is the water conductivity of the fault, b h Where ρ is the fault hydraulic radius, ρ is the fluid density, μ is the viscosity, g is the gravitational acceleration, K is the hydraulic conductivity, and b is the fluid density. h0 It is the initial hydraulic radius, b hres It is the residual radius under high effective stress, σ nref It is the effective normal stress that causes the initial radius to decrease by 90%, b hs The radius increase is due to shear displacement.

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