Deep reservoir rock temperature dependent nonlinear strength criterion and three-dimensional characterization method

Abstract

The invention belongs to the field of deep rock engineering, and particularly provides a deep reservoir rock temperature dependent nonlinear strength criterion and three-dimensional characterization method based on rock mechanics and elastic-plastic mechanics concepts, and the method comprises the following steps: (1) carrying out a mechanics experiment under real-time high-temperature and high-stress conditions to obtain a rock stress-strain curve and related experiment data; (2) based on experimental data, drawing a Moire circle in a tau-sigma coordinate system, and constructing a two-dimensional nonlinear strength criterion on which the deep reservoir rock temperature depends; (3) deriving a principal stress expression of a rock temperature dependent two-dimensional strength criterion; (4) deducing a three-dimensional strength criterion expression based on rock temperature dependence represented by stress tensor invariants; (5) deducing a rock temperature dependent three-dimensional strength criterion expression represented by the average normal stress p, the generalized shear stress q and the lode angle theta; and (6) representing a three-dimensional failure surface of a deep reservoir rock strength criterion.

Description

Technical Field

[0001] The present invention belongs to the field of deep and ultra-deep resource exploitation and deep rock engineering. Specifically, it involves proposing a temperature-dependent nonlinear strength criterion and a three-dimensional characterization method for deep reservoir rocks based on the principles and concepts of rock mechanics and elastoplastic mechanics. The method can accurately reflect the nonlinear failure characteristics of deep and ultra-deep reservoir rocks under high temperature and high stress environments, and provide theoretical support and engineering guidance for deep and ultra-deep resource exploitation. Background Art

[0002] The exploration and development of deep resources is the focus of the energy strategy layout of various countries. However, the development of deep and ultra-deep oil and gas reservoirs faces the extreme environment of "high temperature and high stress". The mechanical properties of deep reservoir rocks are still unclear, and the existing mechanical theory cannot guide the actual engineering practice, resulting in problems such as wellbore instability, leakage and blockage during drilling, which seriously restricts the effective development of large-scale ultra-deep and large oil and gas reservoirs. Therefore, it is urgent to carry out mechanical experiments that match the actual engineering environment of 10,000 meters deep (temperature up to 200℃, stress up to 180MPa), and propose nonlinear strength criteria suitable for describing deep and ultra-deep reservoir rocks, so as to provide scientific theoretical support for the large-scale development of deep and ultra-deep oil and gas reservoirs. At the same time, the proposed three-dimensional characterization method of deep reservoir rock strength criteria plays an important role in the construction of three-dimensional yield surface criteria, providing an effective tool for the visualization analysis of rock failure mechanisms in actual engineering, and further enhancing the guiding value of rock strength criteria in actual engineering applications.

[0003] At present, there are few reports on the nonlinear strength criteria of deep reservoir rocks under the real-time high temperature and high stress coupling. Studies have shown that reservoir rocks exhibit strong brittle failure characteristics at low confining pressure, and their strength shows a linear growth trend with the increase of confining pressure. When the confining pressure increases to a certain threshold, the peak strength of the rock shows a nonlinear strengthening behavior, and the failure mode changes from brittle to ductile. In addition, the high temperature environment has a significant effect on the mechanical characteristics of reservoir rocks. On the one hand, the initiation and expansion of microcracks are induced by thermal expansion inside the reservoir rock; on the other hand, the thermal expansion effect causes stress concentration inside the rock, thereby weakening the peak strength of the rock. Under the conditions of high temperature and high stress coupling, the nonlinear evolution characteristics of the strength of reservoir rocks are further aggravated. Therefore, establishing an accurate description of the nonlinear strength criterion of deep reservoir rocks under high temperature and high stress coupling conditions is one of the key scientific issues that need to be solved in the current deep earth engineering and rock mechanics fields.

[0004] The construction of the three-dimensional failure surface of rocks usually relies on extending the two-dimensional failure criterion to the tensor expression in three-dimensional space, and then intuitively presenting the three-dimensional failure surface of rocks based on drawing tools. This process involves complex mathematical derivations, resulting in limited universality. Therefore, it is of great significance to propose an efficient, accurate, and three-dimensional characterization method applicable to many rock strength criteria for revealing the complex mechanical behavior of rocks.

[0005] For this reason, based on the concepts of rock mechanics and elastoplastic mechanics, considering the high-temperature and high-stress problems faced in actual engineering during the development of deep and ultra-deep reservoirs, a non-linear strength criterion for describing the temperature dependence of deep reservoir rocks is constructed, and a method for characterizing the three-dimensional failure surface of rocks based on the mean normal stress p, the generalized shear stress q, and the Lode angle θ is proposed.

[0006] The current research on relevant non-linear strength criteria and three-dimensional characterization methods of rocks at home and abroad is as follows:

[0007] 1. In the article "Research on the Evolution Model and Strength Criterion of Rock Energy Storage Limit", by introducing the Lode angle parameter, a rock energy storage limit evolution model under complex stress states is established, and a rock strength criterion is established. Its physical meaning is clear and the accuracy is relatively high, which can better reflect the energy evolution during the deformation and failure process of rocks. (See "Chinese Journal of Rock Mechanics and Engineering", 2025, 44(1): 140-151. Liu Ji, Guo Jianqiang, Wang Jiaojiao, etc.);

[0008] 2. In the patent "A True Triaxial Rock Strength Criterion and Parameter Determination Method", a true triaxial rock strength criterion and parameter determination method are disclosed, which has a high fitting degree for the experimental rock strength experimental data. (See "A True Triaxial Rock Strength Criterion and Parameter Determination Method", 202310628975.8. May 30, 2023.).

[0009] 3. In the article "Three-dimensional strength criterion for rocks: A review", a complex mathematical derivation method is used to characterize the three-dimensional failure surfaces of multiple rock strength criteria. (See "Energy Reviews", 2024, 3(4): 100102. Jiacun Liu, Xing Li, Junjie, Xiao, Yachen Xie, Kaiwen Zhang.). Summary of the Invention

[0010] To overcome the deficiencies of the prior art, the present invention proposes a non-linear strength criterion and three-dimensional characterization method for deep reservoir rocks depending on temperature by means of combining experiments and theories. To achieve the above object, the present invention adopts the following technical solutions:

[0011] Based on the concepts of rock mechanics and elastoplastic mechanics, the research steps of the temperature-dependent nonlinear strength criterion and three-dimensional characterization method for deep reservoir rocks are as follows:

[0012] (1) Conduct rock mechanics experiments under real-time high temperature and high stress conditions, simulate different deep reservoir environments, and obtain the stress-strain curves and relevant experimental data of deep reservoir rocks;

[0013] (2) Based on the experimental data, draw Mohr circles under different working conditions in the τ-σ coordinate system, establish a strength criterion suitable for describing deep reservoir rocks, and construct a two-dimensional nonlinear strength criterion for deep reservoir rocks that depends on temperature;

[0014] (3) Derive the principal stress expression of the two-dimensional nonlinear strength criterion for deep reservoir rocks that depends on temperature;

[0015] (4) Derive the expression of the three-dimensional nonlinear strength criterion for deep reservoir rocks that depends on temperature, which is represented by stress tensor invariants;

[0016] (5) Derive the expression of the three-dimensional nonlinear strength criterion for deep reservoir rocks that depends on temperature, which is represented by the mean normal stress p, the generalized shear stress q, and the Lode angle θ;

[0017] (6) Characterize the three-dimensional failure surface of the strength criterion for deep reservoir rocks.

[0018] Based on the above, the process is as follows:

[0019] 1. Conduct real-time high temperature and high stress rock mechanics experiments that match the actual working conditions of deep and ultra-deep reservoirs to obtain the stress-strain curve graphs of rock triaxial compression and relevant experimental data under different deep reservoir environments: the experimental temperatures are 25°C, 100°C, and 200°C respectively, and the stress conditions are 0 MPa, 10 MPa, 20 MPa, 30 MPa, 40 MPa, 50 MPa, 60 MPa, 120 MPa, and 180 MPa respectively; draw the rock stress-strain curve graphs according to the experimental data.

[0020] 2. Based on the rock mechanics experimental data, draw the Mohr circles of the rock under different working conditions in the τ-σ coordinate system. By comparing the linear M-C strength criterion, the power function type M-C strength criterion, the hyperbolic type M-C strength criterion, and the parabolic type M-C strength criterion, analyze the applicability of each criterion in describing the rock strength of deep reservoir rocks under high temperature and high stress conditions, and construct a two-dimensional nonlinear strength criterion for deep reservoir rocks that depends on temperature. The expression is as follows:

[0021]

[0022] Where: τ represents the shear stress on the rock shear plane, σ represents the normal stress on the rock shear plane, T represents the temperature, a, b, d, e represent experimentally fitted parameters, a = 1.22, b = 0.1869, d = 1.052, e = -0.08, c represents the rock cohesion, and c = 32.6T -0.177 .

[0023] 3. Derive the principal stress expression of the two-dimensional non-linear strength criterion of deep reservoir rocks dependent on temperature.

[0024] Based on the concepts of rock mechanics and elastoplastic mechanics, considering the influence of temperature on the failure characteristics of reservoir rocks, and combining the relationship between the normal stress and shear stress on the rock section, the principal stress expression of the two-dimensional non-linear strength criterion of deep reservoir rocks dependent on temperature is obtained as follows:

[0025]

[0026] Where: σ1 represents the first principal stress, σ3 represents the third principal stress, represents the temperature-dependent internal friction angle of the rock, a(T) and b(T) represent the temperature-dependent experimentally fitted parameters, and c(T) represents the temperature-dependent rock cohesion.

[0027] 4. Derive the expression of the three-dimensional non-linear strength criterion of deep reservoir rocks dependent on temperature represented by stress tensor invariants.

[0028] In the present invention, the stress state of a point P is decomposed into a normal stress component σ π and a shear stress component τ π on the π plane, and the principal stress axis σ i is projected onto the π plane. According to the coordinate transformation formula and the relationship between the three invariants of the stress tensor and the three invariants of the deviatoric stress tensor, the principal stress expression represented by the stress tensor invariants is obtained:

[0029]

[0030] Where: I1 represents the first invariant of the stress tensor, and θ represents the Lode angle.

[0031] Substituting Equation (3) into Equation (2), the expression of the three-dimensional non-linear strength criterion of deep reservoir rocks dependent on temperature represented by stress tensor invariants is obtained:

[0032]

[0033] 5. Derive the expression of the three-dimensional non-linear strength criterion of deep reservoir rocks dependent on temperature represented by the mean normal stress p, the generalized shear stress q, and the Lode angle θ.

[0034] Define the expressions for the average normal stress \(p\) and the generalized shear stress \(q\) as follows:

[0035]

[0036] Substitute Equation (5) into Equation (3) to obtain the principal stress formula expressed in terms of the average normal stress \(p\), the generalized shear stress \(q\), and the Lode angle \(\theta\) as follows:

[0037]

[0038] Substitute Equation (6) into Equation (2) to obtain the expression of the temperature-dependent three-dimensional nonlinear strength criterion for deep reservoir rocks expressed in terms of the average normal stress \(p\), the generalized shear stress \(q\), and the Lode angle \(\theta\) as follows:

[0039]

[0040] 6. Draw the three-dimensional failure surface of the strength criterion for deep reservoir rocks.

[0041] Along the hydrostatic pressure direction, increment with a step size \(s\), given a radius \(r\) perpendicular to the hydrostatic pressure axis, and use the expression of the temperature-dependent three-dimensional nonlinear strength criterion for deep reservoir rocks expressed in terms of the average normal stress \(p\), the generalized shear stress \(q\), and the Lode angle \(\theta\) for judgment. If \(f(\sigma_1,\sigma_2,\sigma_3)\lt0\), then increase the radius \(r\) until \(f(\sigma_1,\sigma_2,\sigma_3)=0\) is satisfied, and record the corresponding stress data points \((\sigma_1,\sigma_2,\sigma_3)\). Subsequently, under the current step size \(s\) and radius \(r\), increase the angle \(\theta\), traverse \([0,2\pi]\), and record the data distribution of the complete failure surface. Then increase the step size \(s\), repeat the above steps, and record the data sets \((\sigma_1,\sigma_2,\sigma_3)\) corresponding to different step sizes \(s\). Finally, combine the mechanical experimental data of reservoir rocks at different temperatures, substitute them into Equation (7), and repeat the above steps. Plot the recorded stress points as a surface in the principal stress space to obtain the three-dimensional failure surface of the strength criterion for deep reservoir rocks.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] 1. Based on the theoretical calculations and derivations of rock mechanics and elastoplastic mechanics, considering the extreme environments of high temperature and high stress faced by deep reservoir rocks, the present invention constructs a temperature-dependent nonlinear strength criterion for deep reservoir rocks, which can be widely applied to the research on the mechanical properties of high-temperature and high-stress rock masses in fields such as deep energy exploitation and deep earth engineering development, and has a wide range of application fields.

[0044] 2. The characterization method of the three-dimensional strength criterion of rock proposed by the present invention deduces the principal stress expression represented by the mean normal stress, the generalized shear stress and the Lode angle, which can quickly and efficiently construct the three-dimensional failure surface of different rock failure criteria in the principal stress space, avoiding the complex mathematical calculations in the traditional method, breaking through the problem of efficient visualization analysis of the failure surface, deepening the understanding of the failure characteristics of rocks under different environmental conditions, and can be widely applied to rock mechanics related fields such as tunnel engineering, deep mineral resource exploitation and geothermal energy development. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flow chart of a non-linear strength criterion and three-dimensional characterization method of deep reservoir rock temperature-dependent proposed by the present invention;

[0046] Figure 2 is a triaxial stress-strain curve of deep reservoir rock under real-time high temperature and high stress conditions;

[0047] Figure 3 is the Mohr stress circle and failure envelope of rock under real-time high temperature and high stress conditions;

[0048] Figure 4 is the temperature-dependent a, b, c values and fitting curves under real-time high temperature and high stress conditions;

[0049] Figure 5 is the Mohr circle of rock and the strength envelope of the power function type M-C criterion;

[0050] Figure 6 is the stress state of a point P in the principal stress space;

[0051] Figure 7 is the projection of the principal stress axis on the π plane;

[0052] Figure 8 is a schematic diagram of the three-dimensional characterization method of the rock non-linear strength criterion;

[0053] Figure 9 is the three-dimensional failure surface of the strength of deep reservoir rock. DETAILED DESCRIPTION OF THE INVENTION

[0054] 1. Conduct rock mechanics experiments under real-time high temperature and high stress conditions: The experimental temperatures are 25°C, 100°C, and 200°C respectively, and the stress conditions are 0 MPa, 10 MPa, 20 MPa, 30 MPa, 40 MPa, 50 MPa, 60 MPa, 120 MPa, and 180 MPa respectively. During the uniaxial test, first heat up to the specified temperature at a heating rate of 4°C·min -1 and keep it warm for 8 h, and then adopt the displacement loading method at an axial rate of 0.003 mm·s -1The loading rate until the specimen fails. In the triaxial test, first heat at a rate of 4 °C·min -1 to the specified temperature and hold for 8 h, then apply the confining pressure at a rate of 0.5 MPa·s -1 to the predetermined value, finally clear the displacement record, and apply the axial pressure at a rate of 0.003 mm·s -1 until the specimen fails. According to the experimental data, plot the rock stress-strain curve as shown in Figure 2 .

[0055] 2. Based on the experimental data, plot Mohr circles under different working conditions in the τ-σ coordinate system, establish a strength criterion applicable to describe the rocks in deep reservoirs, and construct a two-dimensional nonlinear strength criterion that depends on the temperature of the rocks in deep reservoirs. The specific steps are as follows:

[0056] Analyze the deficiencies of the linear M-C strength criterion in describing the failure of rocks under high temperature and high stress conditions. By comparing the linear M-C strength criterion, the power function type M-C strength criterion, the hyperbolic type M-C strength criterion, and the parabolic type M-C strength criterion, analyze the applicability of each criterion in describing the strength of the rocks in deep reservoirs under real-time high temperature and high stress conditions.

[0057] The formula of the linear M-C strength criterion is as follows:

[0058]

[0059] where: τ is the shear stress on the rock shear plane, σ is the normal stress on the rock shear plane, is the internal friction angle, and c is the cohesion.

[0060] The expression of the non-linear power function type M-C strength criterion is as follows:

[0061] τ = aσ b + c (2)

[0062] where: the values of a and b are experimental parameters.

[0063] The expression of the parabolic M-C strength criterion is:

[0064] σ = aτ 2 + b (3)

[0065] where: the values of a and b are determined by the uniaxial tensile and uniaxial compressive experiments, R t represents the tensile strength of the rock, R c represents the compressive strength of the rock, where b = -R t ,

[0066] The expression of the hyperbolic type M-C criterion in the rectangular coordinate system is:

[0067]

[0068] As Figure 3 shown, the power function type M-C strength envelope is well tangent to the Mohr circle, and it is considered that the power function type M-C criterion can better describe the failure characteristics of deep reservoir rocks under different real-time high temperature and high stress conditions. Comparing the expressions of the power function type M-C criterion under different high temperature and high stress conditions, the values of a and b are both related to temperature: a = 1.22T 0 . 1869 , b = 1.052T - 0.008 , and the correlation degrees are 0.9742 and 0.8972 respectively. The cohesion c = 32.6T -0.177 , and the correlation degree is 0.9785. The fitting curve is shown in Figure 4 .

[0069] That is, the two-dimensional nonlinear strength criterion expression of deep reservoir rock temperature dependence is as follows:

[0070] τ = aT b σ dTe + c (5)

[0071] τ = 1.22T 0.1869 σ 1.052T-0.08 + 32.6T -0.177 (6)

[0072] In the formula: τ represents the shear stress on the shear plane, σ represents the normal stress on the shear plane, T represents the temperature, a, b, d, e represent the test fitting parameters, c represents the rock cohesion, and c = 32.6T -0.177 .

[0073] 3. Derive the principal stress expression of the two-dimensional nonlinear strength criterion of deep reservoir rock temperature dependence.

[0074] The specific steps are as follows:

[0075] According to Figure 3 the M-C strength criterion in calculate the internal friction angle of reservoir rock to obtain the internal friction angle of reservoir rock

[0076]

[0077] which is related to temperature, and its expression is as follows:

[0078]

[0079] As Figure 5As shown in the figure, the expressions for the normal stress and shear stress on the rock section are as follows:

[0080]

[0081] Substitute Eqs. (8) and (9) into Eq. (5) to obtain the expression for the principal stress of the two-dimensional nonlinear strength criterion dependent on the rock temperature in the deep reservoir:

[0082]

[0083] 4. Derive the expression for the three-dimensional nonlinear strength criterion dependent on the rock temperature in the deep reservoir represented by stress tensor invariants. The specific steps are as follows:

[0084] As Figure 6 shown, based on the theory of elastoplastic mechanics, the normal stress component σ π and shear stress component τ π of the stress state (σ1, σ2, σ3) at a point P on the π-plane are respectively expressed as:

[0085]

[0086] In the formula: r represents the distance between point Q on the hydrostatic pressure line and the origin O, OP is the vector representation of point P in the principal stress space, OP = OQ + QP, OQ is the normal stress component σ π on the π-plane, QP is the shear stress component on the π-plane, I1 represents the first invariant of the stress tensor, and J2 represents the second invariant of the deviatoric stress tensor.

[0087] As Figure 7 shown, project the principal stress axis σ i onto the π-plane. According to the coordinate transformation formula, obtain the projection expression of the stress σ′ i in the xQy coordinate:

[0088]

[0089] In the formula: The angle between QP and the x-axis is θ, representing the Lode angle.

[0090] From Figure 7 it is known that:

[0091]

[0092] Substitute Eqs. (12) and (13) into Eq. (11) to obtain the expression for the principal stress:

[0093]

[0094] According to the theory of elastoplastic mechanics, the three invariants of the stress tensor and the second invariant J2 and the third invariant J3 of the deviatoric stress tensor satisfy the following relationships:

[0095]

[0096] Combining Equation (14) and Equation (15), the expressions for the principal stresses in terms of the invariants of the stress tensor are obtained as follows:

[0097]

[0098] Substituting Equation (16) into Equation (10), the expression for the three-dimensional nonlinear strength criterion of deep reservoir rocks dependent on temperature in terms of the invariants of the stress tensor is obtained:

[0099]

[0100] 5. Derive the expression for the three-dimensional nonlinear strength criterion of deep reservoir rocks dependent on temperature in terms of the mean normal stress p, the generalized shear stress q, and the Lode angle θ. The specific steps are as follows:

[0101] Define the expressions for the mean normal stress p and the generalized shear stress q as follows:

[0102]

[0103] Substituting Equation (18) into Equation (16), the expressions for the principal stresses in terms of the mean normal stress p, the generalized shear stress q, and the Lode angle θ are obtained as follows:

[0104]

[0105] Substituting Equation (19) into Equation (10), the expression for the three-dimensional nonlinear strength criterion of deep reservoir rocks dependent on temperature in terms of the mean normal stress p, the generalized shear stress q, and the Lode angle θ is obtained as follows:

[0106]

[0107] 6. Draw the three-dimensional failure surface of the strength criterion of deep reservoir rocks. The specific steps are as follows:

[0108] As Figure 8As shown, along the hydrostatic pressure direction, with a step size of s increasing and a given radius r perpendicular to the hydrostatic pressure axis, the expression of the temperature-dependent three-dimensional nonlinear strength criterion of deep reservoir rocks represented by the average normal stress p, the generalized shear stress q, and the Lode angle θ is used for judgment. If f(σ1, σ2, σ3) < 0, then increase the radius r until f(σ1, σ2, σ3) = 0 is satisfied, and record the corresponding stress data points (σ1, σ2, σ3). Subsequently, under the current step size s and radius r, increase the angle θ and traverse [0, 2π] to record the data distribution of the complete failure surface. Then increase the step size s, repeat the above steps, and record the data groups (σ1, σ2, σ3) corresponding to different step sizes s. Finally, combine the mechanical experiment data of reservoir rocks at different temperatures, substitute them into Equation (20), and repeat the above steps; plot the recorded stress points as a surface in the principal stress space to obtain the three-dimensional failure surface of the strength criterion of deep reservoir rocks.

[0109] Based on experimental data, the present invention plots the failure surface of the linear M-C strength criterion and the failure surface of the nonlinear strength criterion at 25°C as Figure 9 (a) shown; plot the nonlinear three-dimensional failure surfaces of the strength criteria of reservoir rocks under the conditions of 25°C, 100°C, and 200°C, as Figure 9 (b) shown. It can be seen from Figure 9 this that the temperature-dependent nonlinear strength criterion and the three-dimensional characterization method of deep reservoir rocks proposed by the present invention accurately describe the nonlinear failure characteristics of deep reservoir rocks and have the following characteristics:

[0110] (1) The temperature-dependent nonlinear strength criterion of deep reservoir rocks proposed by the present invention accurately describes the nonlinear mechanical response of deep reservoir rocks under high-temperature and high-stress conditions, making up for the deficiency of the applicability of existing strength criteria in ultra-deep environments.

[0111] (2) The characterization method of the three-dimensional failure surface of rocks proposed by the present invention deduces the principal stress expression represented by the average normal stress, the generalized shear stress, and the Lode angle, and can quickly and efficiently construct the three-dimensional failure surfaces of different rock failure criteria in the principal stress space, providing a simple method for the visualization of rock failure surfaces.

Claims

1. A nonlinear strength criterion and three-dimensional characterization method dependent on the temperature of deep reservoir rocks, characterized in that The specific steps are as follows: (1) Conduct rock mechanics experiments under real-time high temperature and high stress conditions, simulate different deep reservoir environments, and obtain the stress-strain curves and relevant experimental data of deep reservoir rocks; (2) Based on the experimental data, draw Mohr circles under different working conditions in the τ-σ coordinate system, establish a strength criterion applicable to describe deep reservoir rocks, and construct a two-dimensional nonlinear strength criterion of deep reservoir rocks dependent on temperature; (3) Derive the principal stress expression of the two-dimensional nonlinear strength criterion of deep reservoir rocks dependent on temperature; (4) Derive the expression of the three-dimensional nonlinear strength criterion of deep reservoir rocks dependent on temperature represented by stress tensor invariants; (5) Derive the expression of the three-dimensional nonlinear strength criterion of deep reservoir rocks dependent on temperature represented by the mean normal stress p, the generalized shear stress q, and the Lode angle θ; (6) Characterize the three-dimensional failure surface of the strength criterion of deep reservoir rocks.

2. The non-linear strength criterion and three-dimensional characterization method of deep reservoir rock temperature dependence according to claim 1, characterized in that Conduct rock mechanics experiments under real-time high temperature and high stress conditions, simulate different deep reservoir environments, and obtain the stress-strain curves and relevant experimental data of deep reservoir rocks. The method is as follows: Conduct real-time high temperature and high stress rock mechanics experiments matching the actual working condition environment. The experimental temperatures are 25°C, 100°C, and 200°C respectively, and the stress conditions are 0 MPa, 10 MPa, 20 MPa, 30 MPa, 40 MPa, 50 MPa, 60 MPa, 120 MPa, and 180 MPa respectively; According to the experimental data, draw the rock stress-strain curve graph.

3. The nonlinear strength criterion and three-dimensional characterization method for deep reservoir rocks dependent on temperature according to claim 1, characterized in that, Based on the experimental data, draw Mohr circles under different working conditions in the τ-σ coordinate system, establish a strength criterion applicable to describe deep reservoir rocks, and construct a two-dimensional nonlinear strength criterion of deep reservoir rocks dependent on temperature. The method is as follows: According to the rock mechanics experimental data, draw the Mohr circles of the rock under different working conditions in the τ-σ coordinate system. By comparing the linear M-C strength criterion, the power function type M-C strength criterion, the hyperbolic type M-C strength criterion, and the parabolic type M-C strength criterion, analyze the applicability of each criterion to describe the rock strength of deep reservoir rocks under high temperature and high stress conditions, and propose a two-dimensional nonlinear strength criterion of deep reservoir rocks dependent on temperature. The expression is as follows: Where: τ represents the shear stress on the rock shear plane, σ represents the normal stress on the rock shear plane, T represents the temperature, a, b, d, and e represent experimentally fitted parameters, a = 1.22, b = 0.1869, d = 1.052, e = -0.08, c represents the rock cohesion, and c = 32.6T -0.177 .

4. The non-linear strength criterion and three-dimensional characterization method of deep reservoir rocks dependent on temperature according to claim 1, characterized in that Derive the principal stress expression of the two-dimensional nonlinear strength criterion of deep reservoir rocks dependent on temperature. The method is as follows: Based on the concepts of rock mechanics and elastoplastic mechanics, considering the influence of temperature on the failure characteristics of reservoir rocks, and combining the relationship between the normal stress and shear stress on the rock section, the principal stress expression of the two-dimensional nonlinear strength criterion of deep reservoir rocks dependent on temperature is obtained: Where: σ1 represents the first principal stress, and σ3 represents the third principal stress. represents the temperature-dependent rock internal friction angle, a(T) and b(T) represent the temperature-dependent experimental fitting parameters, and c(T) represents the temperature-dependent rock cohesion.

5. The nonlinear strength criterion and three-dimensional characterization method dependent on the deep reservoir rock temperature according to claim 1, characterized in that, Derive the expression of the three-dimensional nonlinear strength criterion of deep reservoir rocks dependent on temperature represented by stress tensor invariants. The method is as follows: In the present invention, the stress state of a point P is decomposed into a normal stress component σ π and a shear stress component τ π on the π-plane, and the principal stress axes σ i are projected onto the π-plane. According to the coordinate transformation formula and the relationships between the three invariants of the stress tensor and the three invariants of the deviatoric stress tensor, the expressions for the principal stresses in terms of the invariants of the stress tensor are obtained: Where: I1 represents the first invariant of the stress tensor, and θ represents the Lode angle; Substitute Equation (3) into Equation (2) to obtain the expression of the three-dimensional nonlinear strength criterion of deep reservoir rocks dependent on temperature represented by stress tensor invariants:

6. The nonlinear strength criterion and three-dimensional characterization method for deep reservoir rocks dependent on temperature according to claim 1, characterized in that Derive the expression of the three-dimensional nonlinear strength criterion of deep reservoir rocks dependent on temperature represented by the mean normal stress p, the generalized shear stress q, and the Lode angle θ. The method is as follows: The expressions for defining the average normal stress \(p\) and the generalized shear stress \(q\) are as follows: Substitute Equation (5) into Equation (3), and the principal stress formula expressed in terms of the average normal stress \(p\), the generalized shear stress \(q\), and the Lode angle \(\theta\) is obtained as follows: Substitute Equation (6) into Equation (2), and the expression for the temperature-dependent three-dimensional nonlinear strength criterion of deep reservoir rocks expressed in terms of the average normal stress \(p\), the generalized shear stress \(q\), and the Lode angle \(\theta\) is obtained as follows:

7. The non-linear strength criterion and three-dimensional characterization method of deep reservoir rocks dependent on temperature according to claim 1, characterized in that, The method for characterizing the three-dimensional failure surface of the strength criterion of deep reservoir rocks is as follows: Along the hydrostatic pressure direction, increment with a step size \(s\), and given a radius \(r\) perpendicular to the hydrostatic pressure axis, judge using the expression for the temperature-dependent three-dimensional nonlinear strength criterion of deep reservoir rocks expressed in terms of the average normal stress \(p\), the generalized shear stress \(q\), and the Lode angle \(\theta\); if \(f(\sigma_1,\sigma_2,\sigma_3)<0\), then increase the radius \(r\) until \(f(\sigma_1,\sigma_2,\sigma_3) = 0\) is satisfied, and record the corresponding stress data points \((\sigma_1,\sigma_2,\sigma_3)\); subsequently, under the current step size \(s\) and radius \(r\), increase the angle \(\theta\), traverse \([0, 2\pi]\), and record the data distribution of the complete failure surface; then increase the step size \(s\), repeat the above steps, and record the data sets \((\sigma_1,\sigma_2,\sigma_3)\) corresponding to different step sizes \(s\); finally, combine the mechanical experimental data of reservoir rocks at different temperatures, substitute into Equation (7), and repeat the above steps; plot the recorded stress points as a surface in the principal stress space to obtain the three-dimensional failure surface of the strength criterion of deep reservoir rocks.

Images