Drilling fluid safety density range analysis and prediction method based on crustal stress change

Abstract

The invention discloses a drilling fluid safety density range analysis and prediction method based on crustal stress changes. The method comprises the steps that a three-dimensional axisymmetric multi-stratum oil and gas reservoir model is established; on the basis of a Navier static equilibrium equation of the porous medium, a general solution expression of volume strain and displacement is solved by combining with a displacement-strain relation, and unknown parameters in the general solution expression are solved by combining displacement continuity boundary conditions and stress continuity boundary conditions of the interlayer contact surface; further obtaining the displacement and stress analytical solution of each rock stratum caused by oil and gas reservoir exploitation; therefore, the well wall stress distribution of the drilled well in the exploited oil and gas reservoir and the surrounding rock stratum is obtained, and the relationship between the stress and the drilling fluid hydraulic pressure is obtained; and calculating a tensile failure threshold value and a shear failure threshold value of the hydraulic pressure of the drilling fluid by combining a rock tensile failure criterion and a Moire-Coulomb shear failure criterion, and performing conversion to obtain an upper limit and a lower limit of a safe density range of the drilling fluid. According to the invention, analytic quantitative characterization of the safe density range of the drilling fluid can be realized.

Description

Technical Field

[0001] The invention relates to the field of oil and gas reservoir drilling rock mechanics, and in particular to a method for analyzing and predicting a safe density range of drilling fluid based on changes in geostress of multiple rock layers during oil and gas reservoir exploitation. Background Art

[0002] During the drilling project, rocks on the trajectory of the drilling wellbore are continuously drilled out, and the stress of the rocks around the wellbore will be redistributed. The drilling fluid will exert corresponding pressure on the well wall, replacing the original stress and maintaining the stability of the well wall. In order to maintain the stability of the well wall during the drilling process, the density of the drilling fluid must be within an appropriate range.

[0003] In order to consider the fluid-solid coupling effect between drilling fluid and wellbore rock when wellbore is damaged, it is necessary to introduce the poroelastic theory.

[0004] Among them, Mehrabian and Abousleiman [1] Taking into account the transverse isotropy of the rock formation and the in-situ stress, the analytical solutions of the wellbore stress, strain and pore fluid pressure under arbitrary wellbore inclination and different wellbore permeability are obtained. ([1].

[0005] Mehrabian A,Abousleiman YN.Generalized poroelastic wellbore problem[J].International Journal for Numerical and Analytical Methods inGeomechanics,2013,37(16):2727-2754.)

[0006] Jinyan Team [2] By applying the poroelastic theory, the influence of factors such as anisotropy of the wellbore rock mass, multiple weak interlayers, and uneven in-situ stress on the safe density range of the drilling fluid when drilling in any direction is revealed. ([2]. Liu M, Jin Y, Lu Y, et al. A wellbore stability model for a deviated well in a transverselyisotropic formation considering poroelastic effects [J]. Rock Mechanics and Rock Engineering, 2016, 49: 3671-3686.)

[0007] Ma Tianshou et al. [3]The fluid-solid coupling analytical solution of the wellbore stress and pore pressure distribution at any drilling angle was solved, revealing the influence of factors such as wellbore rock elastic parameters, strength and permeability anisotropy on the wellbore stress and pore pressure distribution. ([3]. Qiu Y, Ma T, Peng N, et al. Wellbore stability analysis of inclined wells intransversely isotropic formations accounting for hydraulic-mechanical coupling[J]. Geoenergy Science and Engineering, 2023, 224: 211615.)

[0008] However, it should be pointed out that in all the studies on wellbore stability mentioned above, the in-situ geostress of the rock formation where the wellbore is located is given and unchanged. However, the relevant research that further reveals the law of wellbore stability changes caused by mining-induced rock deformation and stress changes is still very limited.

[0009] Li and Gray [4] The solution of reservoir stress change caused by production calculated by one-dimensional strain model is applied to analyze the change of drilling fluid safety density window when drilling in oil and gas reservoirs, and the influence of wellbore inclination and in-situ stress on the drilling fluid safety density range (window) is explored. ([4]. Li X, Gray KE. Wellbore stability of deviated wells in depleted reservoir [C]. Paper presented at the SPE Annual Technical Conference and Exhibition, 2015.)

[0010] Godley Team [5] Based on the Geertsma model, the influence of formation deformation caused by oil and gas reservoir development on the tensile and shear failure of completed casing was explored, and it was pointed out that buckling instability and collapse are the main failure mechanisms of casing under oil and gas reservoir compaction. ([5]. Yin Fei, Gao Deli, Zhao Jingfang, et al. Research on prediction of oil and gas reservoir compaction and evaluation of directional wellbore integrity [J]. Chinese Journal of Rock Mechanics and Engineering, 2015, 34(S2): 4171-4177.)

[0011] To date, a lot of research has been done on the issue of wellbore stability. However, the research on the analytical model of wellbore stability when drilling in produced oil and gas reservoirs and surrounding rock formations is still very limited. In particular, the influence mechanism of factors such as rock stratification, anisotropy and viscoelasticity on the instability and damage of wellbore when drilling in the corresponding rock formations is still unclear. There is a lack of quantitative characterization of the safe density range of drilling fluid and the safe drilling direction when drilling in produced oil and gas reservoirs and surrounding rock formations.

[0012] At present, the impact mechanism of mining-induced rock deformation and stress changes on the safe density range of drilling fluid and safe drilling direction in the rock formation is still unclear. The wellbore stability problem in drilling in the exploited oil and gas reservoirs and surrounding rock formations is a key scientific issue that needs to be urgently solved in the current stage of oil and gas development. Summary of the invention

[0013] The purpose of this application is to provide an analytical prediction method for the safe density range of drilling fluid based on ground stress changes, which can achieve analytical and quantitative characterization of the safe density range of drilling fluid.

[0014] The technical solution provided by the present invention is:

[0015] In a first aspect, the present application provides a method for analytically predicting a safe density range of drilling fluid based on changes in ground stress, comprising:

[0016] Step 1: Establish a three-dimensional axisymmetric multi-layer oil and gas reservoir model, in which the middle layer is the oil and gas reservoir layer, and the upper and lower layers are semi-infinite cap layers and underlying layers;

[0017] Step 2: Based on the Navier static equilibrium equation of porous media, the displacement-strain relationship is combined to obtain the control equation describing the strain-pore pressure relationship of the three-dimensional axisymmetric multi-layer oil and gas reservoir model;

[0018] Step 3: The control equation is converted to Hankel space by applying the Hankel integral transformation method to obtain the general solution expression of volume strain and displacement;

[0019] Step 4: Combine the displacement continuity boundary condition and stress continuity boundary condition of the interlayer contact surface, and jointly establish the general solution expression to obtain the unknown parameters in the general solution expression; combine the Hankel inverse transformation method to obtain the analytical solution of the displacement and stress of each rock layer caused by oil and gas reservoir exploitation;

[0020] Step 5, by applying multiple coordinate transformations and the improved Kirsch solution method, solve the stress distribution of the borehole wall in the produced oil and gas reservoir and the surrounding rock formations, and obtain the relationship between stress and drilling fluid hydraulic pressure;

[0021] Step 6: Based on the obtained stress tensor σ at any point on the wellbore wall (w) With drilling fluid hydraulic p wThe tensile failure threshold and shear failure threshold of drilling fluid hydraulic pressure are calculated based on the relationship between rock tensile failure criterion and Mohr-Coulomb shear failure criterion. The corresponding drilling fluid density is converted based on the tensile failure threshold and shear failure threshold of drilling fluid hydraulic pressure as the upper and lower limits of the safe density range of drilling fluid.

[0022] In a possible implementation, in step 4, the expressions for the analytical solutions of the displacement and stress of the oil and gas reservoir are:

[0023]

[0024] In step 4, the expressions for the analytical solutions of displacement and stress of the cap layer and the underlying layer are:

[0025]

[0026]

[0027] In the formula, and Refers to the radial displacement component and vertical displacement component of the oil and gas reservoir rock formation. are the radial stress, tangential stress, vertical stress and shear stress of the ith rock layer, respectively. p represents the pore fluid pressure, which can be in Pa or psi. represents the pore fluid pressure of the reservoir rock formation after conversion to Hankel space. The subscripts i=1, 2, and 3 of the above parameters correspond to the reservoir rock formation, cap rock formation, and underlying rock formation, respectively. J0 and J1 refer to the 0th and 1st order expressions of the first Bessel equation. The cosh and sinh appearing in the formula are hyperbolic functions, and μ is the stiffness ratio. ξ is the intermediate variable generated by Hankel transformation. h is the thickness of the reservoir. The uniaxial compression coefficient of the rock representing the oil and gas reservoir;

[0028] r is the coordinate of the first of the three coordinate axes (r, θ, z) in the three-dimensional cylindrical coordinate system;

[0029] is the parameter of the reservoir rock and is a function of the Poisson's ratio of the reservoir rock. is a parameter of the cap rock, which is a function of the Poisson's ratio of the cap rock; υ represents the Poisson's ratio of the rock, and its subscripts i = 1, 2 correspond to the reservoir rock and the cap rock, respectively;

[0030] Among them, c1-c6 and M1-M8 are intermediate variables;

[0031] The calculation process of each parameter in the formula is as follows, where:

[0032] μ=G2 / G1=G3 / G1, where G1 is the shear modulus of the oil and gas reservoir rock, G2 is the shear modulus of the cap rock or underlying rock, and G3 is the shear modulus of the cap rock or underlying rock;

[0033] M1=4a1h(1-μ)c1ξ;

[0034] M2=2a1(1-e hξ )(1-μ)c1z1ξ+e hξ c1c4-(1-μ)c5;

[0035] M3=e hξ c1c4-(1-μ)c5-2a1(1-e hξ )(1-μ)c1z1ξ;

[0036]

[0037] M5=[μ(3+μ)-2+a2(4μ 2 -2)]cosh(z1ξ)-2z1(1-μ)c1ξsinh(z1ξ);

[0038]

[0039] M7=[μ(3+μ)-2+a1(4μ 2 -2)]cosh(z1ξ)-2z1(1-μ)c1ξsinh(z1ξ);

[0040] M8=(1+2a1)μ(1+2a2μ)sinh(z1ξ)-4a1z1(1-μ)c1ξcosh(z1ξ);

[0041] c1=1+a2+a2μ;

[0042] c2=a1+μ+a1μ;

[0043] c3=(1-μ)[a1(1+a2)-(1+a1)a2μ];

[0044] c4=1-2(1+a1)μ-a1h(1-μ)ξ;

[0045] c5=(1+a1)(1+2a2μ)+a1hc1ξ;

[0046] c6=1+a1[2+h(1-μ)ξ].

[0047] In a possible implementation, step 5 includes:

[0048] Step 5.1: Convert the stress tensor of the oil and gas reservoir and the surrounding rock formations in the cylindrical coordinate system to the rectangular coordinate system to obtain the stress solution S of the oil and gas reservoir and the surrounding rock formations in the rectangular coordinate system. (p) ;

[0049] Step 5.2: S (p) and in-situ stress S (0) The superposition stress is the new formation stress S = S of the exploited oil and gas reservoir and the surrounding rock formations. (p) +S (0) ;

[0050] Step 5.3: Convert the new formation stress S to any drilling inclination i (w) and any drilling direction a (w) The stress tensor S in the rectangular coordinate system corresponding to the wellbore (w) ;

[0051] Step 5.4: Based on the stress tensor S (w) , using the improved Kirsch solution method, solve the stress (state) tensor σ at any point on the wellbore wall (w) The expression of (w) The expression for determining σ (w) With drilling fluid hydraulic p w relationship.

[0052] In a possible implementation, in step 6,

[0053] The tensile failure criterion for rock is:

[0054] σ max +p r ≥σ t

[0055] Among them, σ max is the maximum principal stress at any point on the borehole wall, σ (w) The maximum eigenvalue of t is the tensile strength of the rock; p r =p0+Δp is the pore pressure of the rock surrounding the wellbore, p0 is the initial pore pressure of the underground rock, and Δp is the change in pore fluid pressure in the rock formation under oil and gas reservoir production;

[0056] Meeting the rock tensile failure criterion will cause tensile failure of the wellbore wall.

[0057] In a possible implementation, determining the upper limit of the drilling fluid safety density window in step 6 includes:

[0058] By searching for the tangent angle θ' around the wellbore, the stress tensor σ at each point on the borehole wall is determined. (w) , and calculate σ(w) The maximum eigenvalue of

[0059] Based on the stress tensor σ (w) With drilling fluid hydraulic p w The relationship between σ (w) The maximum eigenvalue of max Indicated as containing p w Substituting the expression of the rock tensile failure criterion into the above rock tensile failure criterion, the drilling fluid hydraulic pressure p that will not cause tensile failure of the wellbore wall is determined w The maximum value of the drilling fluid hydraulic tension failure threshold p wt ;

[0060] The tensile failure threshold p of the drilling fluid hydraulic pressure wt The ratio p to the wellbore depth d wt / d is converted to obtain the equivalent drilling fluid density, which is used as the upper limit of the drilling fluid safety density window.

[0061] In a possible implementation, in step 6, the Mohr-Coulomb shear failure criterion is:

[0062]

[0063] Meeting the Mohr-Coulomb shear failure criterion will cause tensile failure of the wellbore wall.

[0064] In a possible implementation, in step 6,

[0065] By searching for the tangent angle θ' around the wellbore, the stress tensor σ at each point on the borehole wall is determined. (w) , and calculate σ (w) The minimum and maximum eigenvalues ​​of (w) With drilling fluid hydraulic p w The relationship between σ (w) The minimum and maximum eigenvalues ​​of min and σ max Indicated as containing p w Substituting the expression of Mohr-Coulomb shear failure criterion into the drilling fluid hydraulic pressure p that will not cause shear failure of the wellbore wall w The minimum value of drilling fluid hydraulic shear failure threshold p wt ;

[0066] The shear failure threshold p of the drilling fluid hydraulic pressure ws The ratio of depth p ws / d is converted to obtain the equivalent drilling fluid density, which is used as the lower limit of the safe density range of the drilling fluid.

[0067] In a second aspect, the present application provides an electronic device, including: a memory and a processor;

[0068] The memory is used to store computer programs;

[0069] The processor is used to call the computer program to execute the method as described above.

[0070] In a third aspect, the present application provides a computer-readable storage medium, in which a computer program is stored. When the computer program is executed on an electronic device, the electronic device implements the method as described above.

[0071] In a fourth aspect, the present application provides a computer program product, including a computer program, and when the computer program is executed on an electronic device, the electronic device implements the method as described above.

[0072] The specific implementation methods of the second to fifth aspects of the present application can refer to the implementation methods of the first aspect, which will not be repeated here.

[0073] Beneficial effects:

[0074] (1) A three-dimensional axisymmetric oil and gas reservoir deformation / stress model was established to analytically solve the deformation and stress changes of underground heterogeneous multi-layers caused by oil and gas reservoir exploitation, revealing the influence of exploitation-induced deformation and stress changes of oil and gas reservoirs and surrounding rock formations.

[0075] (2) Apply the reservoir deformation / stress model and its analytical solution to the calculation of drilling fluid safety density and the analysis of drilling wellbore stability, revealing the influence of key factors such as rock stratification, mechanical parameter differences of each rock layer, reservoir exploitation degree and reservoir size on the safe density range of drilling fluid and safe drilling direction in the exploited reservoir and surrounding rock formations. The method proposed in this application can be used for safe drilling in the exploited reservoir and surrounding rock formations, providing a theoretical basis and technical guidance for drilling projects in the exploited reservoir and surrounding rock formations. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 A schematic diagram of the wellbore stability problem in drilling in an already produced oil and gas reservoir and surrounding rock formations in an embodiment of the present application;

[0077] Figure 2 Schematic diagram of the axisymmetric numerical model and its discretization into finite element domain in the embodiment of the present application; wherein a is a schematic diagram of the size of the finite element numerical model, b is a schematic diagram of the discretization of the numerical domain, and c is an enlarged view of the adaptive grid of the oil and gas reservoir and the surrounding rock formation;

[0078] Figure 3Schematic diagram of an isotropic heterogeneous multi-layer oil and gas reservoir model, displacement and stress continuity boundary conditions and analytical solutions in the embodiment of the present application, wherein a is a transversely isotropic heterogeneous multi-layer oil and gas reservoir model, b is a displacement and stress continuity boundary condition, and c is a schematic diagram of an analytical solution of rock formation stress changes caused by mining in a cylindrical coordinate system;

[0079] Figure 4 The radial stress, tangential stress, vertical stress and shear stress change distribution caused by depletion at different stiffness ratios μ in the impermeable layer at z2 / h=0.1 in the embodiment of the present application; wherein a is the radial stress change distribution, b is the tangential stress change distribution, c is the vertical stress change distribution, and d is the shear stress change distribution;

[0080] Figure 5 This is a flow chart of the calculation of the borehole wall stress of the produced oil and gas reservoir and the surrounding rock formations based on the analytical solution of the oil and gas reservoir deformation / stress model in the embodiment of the present application;

[0081] Figure 6 A hemispherical diagram showing the tensile failure limit of a wellbore in an embodiment of the present application, with different stiffness ratios at (r / R,θ)=(0.8,30°) and 5 feet below the top surface of the oil and gas reservoir layer as the wellbore inclination angle i and azimuth angle a change;

[0082] Figure 7 This is a hemispherical diagram showing the shear failure limit of the wellbore in an embodiment of the present application. As the wellbore inclination angle i and the azimuth angle a change, there are different stiffness ratios at (r / R,θ) = (0.8, 30°) and 5 feet above the top surface of the oil and gas reservoir. DETAILED DESCRIPTION

[0083] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present application.

[0084] It should be noted that the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusions, so that a process, method, article or device including a series of elements includes not only those elements clearly listed, but also other elements not clearly listed, or may also include elements inherent to such process, method, product or device. In the absence of further restrictions, an element defined by the sentence "includes a ..." does not exclude the presence of other identical elements in the process, method, article or device including the element.

[0085] In the present application, the terms "upper", "lower", "left", "right", "front", "back", "top", "bottom", "inner", "outer", "middle", "vertical", "horizontal", "lateral", "longitudinal" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the drawings. These terms are mainly used to better describe the present application and its embodiments, and are not used to limit the indicated devices, elements or components to have a specific orientation, or to be constructed and operated in a specific orientation.

[0086] In addition, some of the above terms may be used to express other meanings in addition to indicating orientation or positional relationship. For example, the term "on" may also be used to express a certain dependency or connection relationship in some cases. For those of ordinary skill in the art, the specific meanings of these terms in this application can be understood according to specific circumstances.

[0087] The following will describe with reference to specific embodiments according to the present application.

[0088] In the first aspect, the present application provides a method for analyzing and predicting the safe density range of drilling fluid based on changes in ground stress:

[0089] Step 1: Figure 3 As shown in the left part, a three-dimensional axisymmetric multi-layer oil and gas reservoir model is established, in which the middle layer is the oil and gas reservoir layer, and the upper and lower layers are semi-infinite cap layers and underlying layers;

[0090] In the above multi-layer oil and gas reservoir model, the reservoir layer and the surrounding rock layers are regarded as porous elastic media, and each rock layer has different material parameters such as elastic modulus, Poisson's ratio, tensile and compressive strength. The exploitation reduces the pore fluid pressure inside the oil and gas reservoir by Δp(r). The remaining model dimensions are shown in Figure 3 Left part.

[0091] Step 2: Based on the Navier static equilibrium equation of porous media,

[0092] The Navier static equilibrium equation for porous media is:

[0093]

[0094] Where G represents the shear modulus of rock, and the unit can be Pa or psi; v represents the Poisson's ratio of rock, and α is the Biot coefficient;

[0095] u i,jj represents the displacement u of the rock i Calculate the second-order partial derivatives in each coordinate axis direction and sum them up, that is, The final result is a scalar; i = 1, 2, 3; in the three-dimensional rectangular coordinate system u i Include ux (i=1),u y (i=2) and u z (i=3); in cylindrical coordinate system, including u r (i=1),u θ (i=2) and u z (i=3), these two coordinate systems are used in the embodiments of the present application, so they are expressed in the form of tensors to unify the expression results of the two coordinate systems.

[0096] ε kk,i represents the volume strain of rock ε kk =ε rr +ε θθ +ε zz The derivative of the i-th coordinate axis in the coordinate system is the derivative of the x-direction, y-direction or z-direction in the rectangular coordinate system, and the derivative of the r-direction, theta-direction or z-direction in the cylindrical coordinate system;

[0097] p ,i It represents the derivative of pore water pressure p with respect to the i-th coordinate axis in the coordinate system.

[0098] In the three-dimensional rectangular coordinate system and the cylindrical coordinate system, equation (1) is expressed in tensor form. Equation (1) actually represents three equations, namely, the three equations in the case of i = 1, 2, 3. In the three-dimensional rectangular coordinate system, i = 1, 2, 3 corresponds to x, y, z respectively; in the cylindrical coordinate system, i = 1, 2, 3 corresponds to r, θ, z respectively.

[0099] Find the divergence of equation (1) and apply the operator properties, Simultaneous displacement-strain relationship u i,i =ε kk , the governing equation describing the strain-pore pressure relationship of the three-dimensional axisymmetric multi-layer oil and gas reservoir model, the Beltrami-Michell equation, can be obtained:

[0100]

[0101] In the above displacement-strain relationship u i,i =ε kk in, u i,i is the displacement u of the rock i Calculate the second-order partial derivatives in each coordinate axis direction and sum them up, that is, The displacement of the rock u i The first-order partial derivative in a certain coordinate axis direction is the strain in that direction, and the sum of the strains in all directions is the volume strain ε kk , so there is

[0102] In the above middle, is the gradient operator, which is a vector, When this operator acts on a scalar (i.e. a number) That is, we get a vector. When two vectors are operated on, we get a scalar, such as because It is just an operator, and it needs to act on a variable in the end, so we use express. Similarly, where × represents the cross product of vectors.

[0103] Operator Acts on For example,

[0104] In the formula, is the Geertsma uniaxial compression coefficient, where K represents the bulk modulus of the rock and the unit can be Pa or psi.

[0105] Step 3: By applying the Hankel integral transformation method, the control equation (2) is transformed into the Hankel space for solution. After the control equation is transformed into the Hankel space, combined with the porous elastic mechanics equation, the general solution expression of volume strain and displacement can be obtained (taking the oil and gas reservoir as an example):

[0106]

[0107] In the formula, Refers to the volume strain of the oil and gas reservoir rock formation in the Hankel transform domain, Refers to the first-order Hankel transform of the radial displacement component of the oil and gas reservoir rock formation, It refers to the 0th-order Hankel transform of the vertical displacement component of the oil and gas reservoir strata in the Hankel transform domain. The intermediate variable υ1 is the Poisson's ratio of the rock in the oil and gas reservoir. In the above variables, the subscripts r and z represent the components in the r and z directions in the cylindrical coordinate system of the oil and gas reservoir scale, and the subscript 1 represents the rock layer of the oil and gas reservoir. The symbol ^ on the variable represents the variable in the Hankel space, the superscript (0) represents the 0th order Hankel transform of the corresponding variable, and the superscript (1) represents the 1st order Hankel transform of the corresponding variable; the mth order Hankel transform of the variable f is The corresponding inverse transformation can be expressed as A 1,1 , A 1,2 , A 1,3 and A 1,4 They are all single rock layer parameters, where the first subscript refers to the rock layer, and the second subscript refers to the unknown quantity of the corresponding rock layer.

[0108] It indicates the uniaxial compression coefficient of the rock in the oil and gas reservoir, and the unit can be 1 / Pa or 1 / psi; represents the 0th-order Hankel transformation of the pore water pressure variable p, ξ is the intermediate variable generated by the Hankel transformation, and z1 is the third coordinate axis z of the three-dimensional rectangular coordinate system in the oil and gas reservoir;

[0109] From the above equations, it can be seen that a single rock layer has four unknown parameters (A 1,1 , A 1,2 , A 1,3 , A 1,4 ), while multiple rock layers have n×4 unknown parameters.

[0110] Step 4: Combine the displacement continuity boundary conditions (n×2 boundary conditions, n is the number of rock layers) and the stress continuity boundary conditions (n×2 boundary conditions) of the interlayer contact surface as follows: Figure 3 As shown in the middle part, by combining the general solution and the above n×4 boundary conditions, the corresponding unknown parameter A can be obtained i,j , and combined with the Hankel inverse transform method, the analytical solution of the displacement and stress of each rock layer caused by oil and gas reservoir exploitation is obtained.

[0111] exist Figure 3 The left part is a heterogeneous multi-layer oil and gas reservoir model, where E1, α1, v1, v u1 They represent the elastic modulus, Biot coefficient, Poisson's ratio, and impermeable Poisson's ratio of the oil and gas reservoir respectively;

[0112] E2,α2,v2,υ u2 They represent the elastic modulus, Biot coefficient, Poisson's ratio, and impermeable Poisson's ratio of the cap layer respectively;

[0113] E3,α3,v3,υ u3 They represent the elastic modulus, Biot coefficient, Poisson's ratio, and impermeable Poisson's ratio of the underlying layer respectively;

[0114] Among them, z1, z2, and z3 are the vertical distances between the coordinates of the point on the third coordinate axis z of the three-dimensional rectangular coordinate system and the symmetry plane of the oil and gas reservoir z1=0, the bottom of the cap layer z2=0, and the top of the underlying layer z3=0, respectively;

[0115] In the present embodiment, it is assumed that the material parameter values ​​of the cover layer and the underlying layer are the same. Figure 3 The middle part is shown.

[0116] Then the displacement continuity boundary condition is:

[0117] That is, at the upper contact surface (i.e. the top of the oil and gas reservoir Bottom of the cap layer z2 = 0) Radial displacement of the cap layer and radial displacement of the reservoir equal.

[0118] That is, at the upper contact surface (i.e. the top of the oil and gas reservoir Bottom of the cap layer z2 = 0) Vertical displacement of the cap layer and vertical displacement of oil and gas reservoirs equal.

[0119] The stress continuity boundary condition is:

[0120] That is, at the upper contact surface (i.e. the top of the oil and gas reservoir Bottom of the cap layer z2 = 0) Vertical stress of the cap layer and vertical stress of oil and gas reservoirs equal.

[0121] That is, at the upper contact surface (i.e. the top of the oil and gas reservoir Bottom of the cap layer z2 = 0) Shear stress of the cap layer and shear stress of oil and gas reservoirs equal.

[0122] Figure 3 The right part shows the stress changes of rock formation caused by mining in the cylindrical coordinate system. The analytical solution is:

[0123] represents the stress change of oil and gas reservoir caused by oil and gas reservoir exploitation, is the rock parameter and the reference point position (r,z);

[0124] It indicates the stress change of cap rock caused by oil and gas reservoir exploitation;

[0125] It indicates the change of underlying layer stress caused by oil and gas reservoir exploitation.

[0126] Among the above variables, the superscript (p) indicates the stress caused by oil and gas reservoir exploitation, the subscript ij refers to the stress tensor, and the subscripts 1, 2, and 3 refer to the oil and gas reservoir rock layer, the cap rock layer, and the underlying rock layer, respectively. Indicates the thickness of oil and gas reservoir / radius of oil and gas reservoir; υ i and ui They represent the Poisson’s ratio and impermeability Poisson’s ratio of the i-th rock layer, respectively, where i=1, 2, and 3 correspond to oil and gas reservoir rock layers, cap rock layers, and underlying rock layers, respectively.

[0127] Analytical expressions of displacement (deformation) and stress of oil and gas reservoirs:

[0128]

[0129] Analytical expressions for displacement and stress of cover and underlying layers:

[0130]

[0131]

[0132] In the formula and Refers to the radial displacement component and vertical displacement component of the oil and gas reservoir rock formation. are the radial stress, tangential stress, vertical stress and shear stress of the ith rock layer, represents the pore fluid pressure of the reservoir rock formation after conversion to Hankel space, h is the reservoir thickness, the unit can be m or ft; the subscripts i=1,2,3 of the above parameters correspond to the reservoir rock formation, cap rock formation and underlying rock formation respectively; J0 and J1 refer to the 0th and 1st order expressions of the first Bessel equation, cosh and sinh appearing in the formula are hyperbolic functions, and μ is the stiffness ratio;

[0133] r is the first coordinate axis (radial coordinate) of the three coordinate axes (r, θ, z) in the three-dimensional cylindrical coordinate system, and the unit can be m or ft;

[0134] It is a parameter of the oil and gas reservoir rock and a function of the Poisson's ratio of the oil and gas reservoir rock. It has no specific meaning. a2= is a parameter of the cap rock or underlying rock, and is a function of the Poisson's ratio of the cap rock or underlying rock;

[0135] Among them, c1-c6 and M1-M8 are intermediate variables;

[0136] The calculation process of each parameter in the formula is as follows, where:

[0137] μ=G2 / G1=G3 / G1, where G1 is the shear modulus of the oil and gas reservoir rock, G2 is the shear modulus of the cap rock or underlying rock, and G3 is the shear modulus of the cap rock or underlying rock;

[0138] M1=4a1h(1-μ)c1ξ; (18)

[0139] M2=2a1(1-e hξ )(1-μ)c1z1ξ+e hξ c1c4-(1-μ)c5; (19)

[0140] M3=e hξc1c4-(1-μ)c5-2a1(1-e hξ )(1-μ)c1z1ξ; (20)

[0141]

[0142] M5=[μ(3+μ)-2+a2(4μ 2 -2)]cosh(z1ξ)-2z1(1-μ)c1ξsinh(z1ξ); (22)

[0143]

[0144] M7=[μ(3+μ)-2+a1(4μ 2 -2)]cosh(z1ξ)-2z1(1-μ)c1ξsinh(z1ξ); (24)

[0145] M8=(1+2a1)μ(1+2a2μ)sinh(z1ξ)-4a1z1(1-μ)c1ξcosh(z1ξ); (25)

[0146] c1=1+a2+a2μ; (26)

[0147] c2=a1+μ+a1μ; (27)

[0148] c3=(1-μ)[a1(1+a2)-(1+a1)a2μ]; (28)

[0149] c4=1-2(1+a1)μ-a1h(1-μ)ξ; (29)

[0150] c5=(1+a1)(1+2a2μ)+a1hc1ξ; (30)

[0151] c6=1+a1[2+h(1-μ)ξ]. (31)

[0152] Step 5, by applying multiple coordinate transformations and the improved Kirsch solution method, solve the stress distribution of the borehole wall in the produced oil and gas reservoir and the surrounding rock formations, and obtain the relationship between stress and drilling fluid hydraulic pressure;

[0153] The specific calculation process is as follows:

[0154] Step 5.1: The stress tensor of the oil and gas reservoir and the surrounding rock formations in the cylindrical coordinate system Converted to the rectangular coordinate system, the stress solution S of the oil and gas reservoir and the surrounding rock formations in the rectangular coordinate system due to exploitation is obtained. (p) ;in, is the stress tensor change caused by exploitation in the oil and gas reservoir scale cylindrical coordinate system, S(p) The stress tensor change caused by exploitation in the rectangular coordinate system of the oil and gas reservoir scale can be in Pa or psi. The coordinate transformation formula used is: In the formula, the transformation matrix θ is the azimuth of the drilling position, θ = 0° represents the positive direction of the x-axis, where It can be expressed in matrix form as Shear stress and is 0;

[0155] Step 5.2: S (p) and in-situ stress S (0) The superposition stress is the new formation stress S = S of the exploited oil and gas reservoir and the surrounding rock formations. (p) +S (0) ;

[0156] in is the in-situ geostress tensor S (0) The three components of are the maximum horizontal principal stress, Horizontal minimum principal stress, Vertical stress, superscript (0) refers to the original position. S (0) is the in-situ stress tensor in the rectangular coordinate system at the reservoir scale.

[0157] Step 5.3: Convert the new formation stress S to any drilling (wellbore) inclination i (w) and any drilling (wellbore) direction a (w) The stress tensor in the rectangular coordinate system corresponding to the wellbore S (w) The superscript (w) indicates the stress value corresponding to the wellbore (well), that is, the change in the stress tensor caused by mining in the wellbore scale rectangular coordinate system, where each element is a component in different directions. Figure 5 Schematic diagram in the lower right corner; the coordinate transformation formula applied is: S (w) =TST -1 , where the transformation matrix

[0158] Wherein, the unit of drilling (wellbore) inclination angle i can be degree;

[0159] Step 5.4: Based on the stress tensor S (w) , using the improved Kirsch solution method, solve the stress (state) tensor σ at any point on the wellbore wall (w) , establish σ (w) With drilling fluid hydraulic p w The specific flow chart is as follows: Figure 5 shown.

[0160] Among them, σ (w) It is the stress tensor change caused by mining in the wellbore scale cylindrical coordinate system.

[0161] Figure 5 The flowchart of the calculation of borehole stress in the produced oil and gas reservoir and surrounding rock formations based on the analytical solution of the oil and gas reservoir deformation / stress model is shown.

[0162] The stress (state) tensor at any point on the wellbore wall is obtained σ r'r' etc. are the components of the stress tensor. Specifically, Figure 5 The schematic diagram in the lower left corner, the specific calculation method is as follows (Equation 21-26) The analytical solution is:

[0163] σ r'r' =-p w ; (32)

[0164]

[0165] σ r'θ' =0; (35)

[0166]

[0167] σ r'z' = 0. (37)

[0168] Among them, p w It is the drilling fluid hydraulic pressure, that is, the wellbore fluid pressure.

[0169] Step 6: Based on the obtained stress tensor σ at any point on the wellbore wall (w) With drilling fluid hydraulic p w The tensile failure threshold and shear failure threshold of drilling fluid hydraulic pressure are calculated based on the relationship between rock tensile failure criterion and Mohr-Coulomb shear failure criterion. The corresponding drilling fluid density is converted based on the tensile failure threshold and shear failure threshold of drilling fluid hydraulic pressure as the upper and lower limits of the safe density range of drilling fluid.

[0170] Tensile failure occurs when the maximum tensile effective principal stress of the wellbore exceeds the tensile strength of the rock. The corresponding tensile failure gradient is usually selected as the upper limit of the safe density range of the drilling fluid. Since the wellbore fluid cannot cause any shear stress, the principal stress always occurs on the plane tangent to the wellbore. Therefore, the rock tensile failure criterion can be expressed as:

[0171] σ max +p r ≥σ t . (38)

[0173] Among them, σ max is the maximum principal stress at any point on the borehole wall, σ (w) The maximum eigenvalue of t is the tensile strength of the rock, which is assumed to be zero here. r =p0+Δp is the pore pressure of the rock surrounding the wellbore, p0 is the initial pore pressure of the underground rock, and Δp is the change in pore fluid pressure in the rock formation under oil and gas reservoir production, and the unit can be Pa or psi.

[0174] If formula (38) is met, tensile failure of the wellbore wall will occur.

[0175] By searching for the tangent angle θ' around the wellbore (see Figure 5 ), determine the stress (state) tensor σ at each point on the wellbore wall (w) , and calculate σ (w) The maximum eigenvalue of . Based on the stress tensor σ (w) With drilling fluid hydraulic p w The relationship between σ (w) The maximum eigenvalue of max Indicated as containing p w Substituting the expression into the above formula (38), the drilling fluid hydraulic pressure p that will not cause tensile failure of the wellbore can be determined w The maximum value of the drilling fluid hydraulic tension failure threshold p wt .

[0176] In field practice, the tensile failure gradient of the wellbore can usually be expressed as the tensile failure threshold p of the drilling fluid hydraulic pressure. wt The ratio p to the wellbore depth d wt / d (usually in psi / ft), or it can be expressed by the equivalent drilling fluid density (in lbm / gal). wt / d, the equivalent wellbore fluid density, i.e., drilling fluid density, can be converted to serve as the upper limit of the drilling fluid safety density window.

[0177] The unit of wellbore depth d can be m or ft.

[0178] When the drilling fluid hydraulic pressure is too low, wellbore collapse may occur due to shear failure of the wellbore wall caused by high pressure stress generated by the surrounding rocks. This application uses the Mohr-Coulomb shear failure criterion to estimate the shear failure threshold of the wellbore wall. The failure criterion can be expressed as:

[0179]

[0180] Among them, σ min and σ maxis the minimum and maximum principal stress at any point on the borehole wall, σ (w) The minimum and maximum eigenvalues ​​of the wellbore; φ is the friction angle of the wellbore rock, σ c is the cohesive strength of the rock.

[0181] If formula (39) is met, tensile failure of the wellbore wall will occur.

[0182] By searching for the tangent angle θ' around the wellbore (see Figure 5 ), determine the stress (state) tensor σ at each point on the wellbore wall (w) , and calculate σ (w) The minimum and maximum eigenvalues ​​of the stress tensor σ (w) With drilling fluid hydraulic p w The relationship between σ (w) The minimum and maximum eigenvalues ​​of min and σ max Indicated as containing p w Substituting the expression into the above formula (39), the drilling fluid hydraulic pressure p that will not cause shear failure of the wellbore can be determined w The minimum value of drilling fluid hydraulic shear failure threshold p wt .

[0183] In field practice, the shear failure of the wellbore corresponding to the density gradient of the drilling fluid can usually be expressed as the shear failure threshold p of the drilling fluid hydraulic pressure. ws The ratio of depth p ws / d (usually in psi / ft), or it can be expressed by the equivalent drilling fluid density (in lbm / gal). ws / d, the equivalent drilling fluid density can be converted as the lower limit of the safe density range of the drilling fluid.

[0184] Based on the above steps, by calculating the different drilling inclination angles i (w) and drilling direction a (w) The safe density range of drilling fluid under certain conditions can be used to determine the corresponding safe drilling direction.

[0185] The embodiment of the present application also provides an electronic device, including: a memory and a processor;

[0186] The memory is used to store computer programs;

[0187] The processor is used to call the computer program to execute the method as described above.

[0188] An embodiment of the present application further provides a computer-readable storage medium, in which a computer program is stored. When the computer program is executed on an electronic device, the electronic device implements the method as described above.

[0189] An embodiment of the present application further provides a computer program product, including a computer program. When the computer program is executed on an electronic device, the electronic device implements the method as described above.

[0190] The embodiments of the present application also provide a system, an electronic device, a computer-readable storage medium, and a computer program product. The specific implementation methods can refer to the specific embodiments of the above methods and will not be repeated here.

[0191] Obviously, those skilled in the art should understand that the above-mentioned units or steps of the present application can be implemented by a general-purpose computing device, they can be concentrated on a single computing device, or distributed on a network composed of multiple computing devices, and optionally, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. In this way, the present application is not limited to any specific combination of hardware and software.

[0192] The following is a verification of the effect of the technical solution provided in the embodiments of the present application:

[0193] (1) Verification of the three-dimensional axisymmetric oil and gas reservoir deformation / stress analytical model:

[0194] The analytical solution derived above is verified here with a numerical solution of the same problem. To do this, use Multiphysics (2018) simulates the same problem. The axisymmetric numerical model and its discretization into finite element domains are as follows Figure 2 As shown. The bearing layer is an undrained layer, while the permeable layer has a negative uniform pore pressure variation, that is, the pore fluid pressure decreases in a cylinder with a radius of 500 feet and a thickness of 50 feet. The input parameters of each layer and the size of the numerical solution domain are shown in Table 1. In order to eliminate the far-field boundary effect, the size of the overall numerical solution domain is set to 60 times and 600 times the radial and vertical dimensions of the disturbed pore fluid pressure volume, respectively. The numerical solution domain is discretized using irregular triangular finite elements with adaptive meshes and quadratic shape functions. A local view of the infinite subsurface and permeable layer is shown in Figure 2 As shown in the schematic diagrams in the upper right and lower right corners.

[0195] The analytical solution is compared with the numerical solution using the parameter values ​​in the table below:

[0196] Table 1 Material parameters of each rock formation

[0197]

[0198] In Table 1, TVD is the abbreviation of true vertical depth. Since the true depth is constantly changing during the downward drilling process, the in-situ stress It will also change with depth, so it is generally used in the form of gradient, that is, To describe the in-situ stress in the model. In the process, the in-situ stress at the drilling depth can be obtained by simply multiplying the gradient by the true depth. In the table, E represents the Young's modulus of the rock.

[0199] In agreement with the numerical model, a uniform pore pressure drop p1 = ΔpH(rR) is used in the analytical solution. In Hankel transform space, the same pressure drop distribution can be expressed as Therefore, the displacement and stress solutions of the produced oil and gas reservoir and the surrounding rock formations can be obtained through equations (6) to (17). Figure 2 Points P1, P2, and P3 are selected in the schematic diagram at the lower right corner to compare the analytical solution with the numerical solution. The results are listed in Table 2 for the comparison of radial and tangential stress components; the results for vertical and shear stress components are listed in Table 3. Positive values ​​indicate stretching or counterclockwise rotational trends. The differences in all four stress components predicted by the two solutions are less than 1% at the three points, and the results are consistent for all three stiffness ratios μ = 0.5, 1, and 2.

[0200] Table 2. Comparison of radial stress and tangential stress between analytical solution and numerical solution

[0201]

[0202]

[0203] Table 3. Comparison of vertical stress and shear stress between analytical solution and numerical solution

[0204]

[0205] (2) Analytical prediction process of safe density range of drilling fluid in infill wells

[0206] ①Continue to apply the material parameters in Table 1 and bring them into the analytical solution of deformation stress of each rock layer. The results are as follows:

[0207] Figure 4 Shown in When the dimensionless stress at the radial distance of the symmetry axis of the impermeable layer changes Variation. The variation of pore fluid causes the change of normalized radial and tangential stresses in the impermeable layer under the conditions of μ = 0.5 and 1. Due to the Poisson effect, a larger stiffness ratio will generate tensile radial and tangential stress changes in the impermeable layer. When r increases, the induced radial and tangential stress changes gradually decrease. The vertical stress change is in a tensile state when r < R and turns into a compressive change when crossing the side interface of the disturbed pore pressure volume. In any region, a larger stiffness ratio will lead to greater vertical stress changes. The shear stress is relatively small, unless the observation point is close to the boundary of the disturbed pore pressure, where a high-gradient change with a finite peak is observed.

[0208] ② Apply the stress analytical solution of the exploited oil and gas reservoir and the surrounding rock layers obtained in the above step 5 to solve the stress state of the surrounding rock of the infill well.

[0209] Finally, the safety density range of the drilling fluid (w) and the drilling direction a (w) under different drilling inclinations i can be calculated to determine the corresponding safe drilling direction.

[0210] Figure 6 Shows the hemispherical diagram of the tensile failure gradient at (r / R, θ) = (0.8, 30°), 5 feet below the top surface of the middle layer. When the wellbore inclination aligns with the minimum horizontal stress before depletion, the maximum value of the tensile failure gradient appears at a wellbore inclination of approximately 45°. The predicted values of the tensile failure gradient vary significantly with the stiffness difference: when μ = 5, it is 0.32 lbm / gal smaller than the homogeneous case; when μ = 1 / 5, it is 1.25 lbm / gal larger than the homogeneous case.

[0211] Figure 7 Shows the hemispherical diagram of the shear failure gradient at (r / R, θ) = (0.8, 30°) with stiffness ratios of μ = 5, 1, and 0.2. Different from the distribution of the tensile failure gradient, the minimum value of the shear failure gradient appears in a vertical or slightly deviated wellbore, whether inside or outside the reservoir. The predicted minimum values of the shear failure gradient are also sensitive to the stiffness difference parameter: when μ = 5, it is 0.75 lbm / gal smaller than the predicted value for the homogeneous layer; when μ = 1 / 5, it is 0.39 lbm / gal larger than the predicted value for the homogeneous layer.

[0212] Based on the technical solution provided in the embodiments of the present application, the influence of factors such as differences in rock mechanical parameters, interlayer viscoelastic rheological differences, and rock anisotropy differences on the changes in the safety density range of the drilling fluid and the safe drilling direction caused by oil and gas reservoir exploitation can be revealed.

[0213] The above description of the embodiments of the present application is only a partial embodiment of the present application, which is used to enable professionals in the field to implement or use the content of the present application, and is not used to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A method for analyzing and predicting the safe density range of drilling fluid based on changes in ground stress, characterized in that: include: Step 1: Establish a three-dimensional axisymmetric multi-layer oil and gas reservoir model, in which the middle layer is the oil and gas reservoir layer, and the upper and lower layers are semi-infinite cap layers and underlying layers; Step 2: Based on the Navier static equilibrium equation of porous media, the displacement-strain relationship is combined to obtain the control equation describing the strain-pore pressure relationship of the three-dimensional axisymmetric multi-layer oil and gas reservoir model; Step 3: The control equation is converted to Hankel space by applying the Hankel integral transformation method to obtain the general solution expression of volume strain and displacement; Step 4: Combine the displacement continuity boundary condition and stress continuity boundary condition of the interlayer contact surface, and jointly establish the general solution expression to obtain the unknown parameters in the general solution expression; combine the Hankel inverse transformation method to obtain the analytical solution of the displacement and stress of each rock layer caused by oil and gas reservoir exploitation; Step 5, by applying multiple coordinate transformations and the improved Kirsch solution method, solve the stress distribution of the borehole wall in the produced oil and gas reservoir and the surrounding rock formations, and obtain the relationship between stress and drilling fluid hydraulic pressure; Step 6: Based on the obtained stress tensor σ at any point on the wellbore wall (w) With drilling fluid hydraulic p w The tensile failure threshold and shear failure threshold of drilling fluid hydraulic pressure are calculated based on the relationship between rock tensile failure criterion and Mohr-Coulomb shear failure criterion. The corresponding drilling fluid density is converted based on the tensile failure threshold and shear failure threshold of drilling fluid hydraulic pressure as the upper and lower limits of the safe density range of drilling fluid.

2. The method according to claim 1, characterized in that In step 4, the expressions of the analytical solutions of the displacement and stress of the oil and gas reservoir are as follows: In step 4, the expressions for the analytical solutions of displacement and stress of the cap layer and the underlying layer are: In the formula, and Refers to the radial displacement component and vertical displacement component of the oil and gas reservoir rock formation. are the radial stress, tangential stress, vertical stress and shear stress of the ith rock layer, respectively; p represents the pore fluid pressure, represents the pore fluid pressure of the reservoir rock formation after conversion to Hankel space. The subscripts i=1, 2, and 3 of the above parameters correspond to the reservoir rock formation, cap rock formation, and underlying rock formation, respectively. J0 and J1 refer to the 0th and 1st order expressions of the first Bessel equation. The cosh and sinh appearing in the formula are hyperbolic functions, and μ is the stiffness ratio. ξ is the intermediate variable generated by Hankel transformation. h is the thickness of the reservoir. The uniaxial compression coefficient of the rock representing the oil and gas reservoir; r is the coordinate of the first of the three coordinate axes (r, θ, z) in the three-dimensional cylindrical coordinate system; is the parameter of the reservoir rock and is a function of the Poisson's ratio of the reservoir rock. is a parameter of the cap rock, which is a function of the Poisson's ratio of the cap rock; υ represents the Poisson's ratio of the rock, and its subscripts i = 1, 2 correspond to the reservoir rock and the cap rock, respectively; Among them, c1, c2, c3, c4, c5, c6, M1, M2, M3, M4, M5, M6, M7, and M8 are all intermediate variables; The calculation process of each parameter in the formula is as follows, where: μ=G2 / G1=G3 / G1, where G1 is the shear modulus of the oil and gas reservoir rock, G2 is the shear modulus of the cap rock or underlying rock, and G3 is the shear modulus of the cap rock or underlying rock; M1=4a1h(1-μ)c1ξ; M2=2a1(1-e hξ )(1-μ)c1z1ξ+e hξ c1c4-(1-μ)c5; M3=e hξ c1c4-(1-μ)c5-2a1(1-ehξ)(1-μ)c1z1ξ; M5=[μ(3+μ)-2+a2(4μ 2 -2)]cosh(z1ξ)-2z1(1-μ)c1ξsinh(z1ξ); M7=[μ(3+μ)-2+a1(4μ 2 -2])cosh(z1ξ)-2z1(1-μ)c1ξsinh(z1ξ); M8=(1+2a1)μ(1+2a2μ)sinh(z1ξ)-4a1z1(1-μ)c1ξcosh(z1ξ); c1=1+a2+a2μ; c2=a1+μ+a1μ; c3=(1-μ)[a1(1+a2)-(1+a1)a2μ]; c4=1-2(1+a1)μ-a1h(1-μ)ξ; c5=(1+a1)(1+2a2μ)+a1hc1ξ; c6=1+a1[2+h(1-μ)ξ].

3. The method according to claim 2, characterized in that The step 5 comprises: Step 5.1: Convert the stress tensor of the oil and gas reservoir and the surrounding rock formations in the cylindrical coordinate system to the rectangular coordinate system to obtain the stress solution S of the oil and gas reservoir and the surrounding rock formations in the rectangular coordinate system. (p) ; Step 5.2: S (p) and in-situ stress S (0) The superposition stress is the new formation stress S = S of the exploited oil and gas reservoir and the surrounding rock formations. (p) +S (0) ; Step 5.3: Convert the new formation stress S to any drilling inclination i (w) and any drilling direction a (w) The stress tensor S in the rectangular coordinate system corresponding to the wellbore (w) ; Step 5.4: Based on the stress tensor S (w) , using the improved Kirsch solution method, the stress tensor σ at any point on the wellbore wall is solved (w) The expression of (w) The expression for determining σ (w) With drilling fluid hydraulic p w relationship.

4. The method according to claim 3, characterized in that In step 6, The tensile failure criterion for rock is: s max +p r ≥s t Among them, σ max is the maximum principal stress at any point on the borehole wall, σ (w) The maximum eigenvalue of t is the tensile strength of the rock; p r =p0+Δp is the pore pressure of the rock surrounding the wellbore, p0 is the initial pore pressure of the underground rock, and Δp is the change in pore fluid pressure in the rock formation under oil and gas reservoir production; Meeting the rock tensile failure criterion will cause tensile failure of the wellbore wall.

5. The method according to claim 3, characterized in that: Determining the upper limit of the drilling fluid safety density window in step 6 includes: By searching for the tangent angle θ' around the wellbore, the stress tensor σ at each point on the borehole wall is determined. (w) , and calculate σ (w) The maximum eigenvalue of Based on the stress tensor σ (w) With drilling fluid hydraulic p w The relationship between σ (w) The maximum eigenvalue of max Indicated as containing p w Substituting the expression of the rock tensile failure criterion into the above rock tensile failure criterion, the drilling fluid hydraulic pressure p that will not cause tensile failure of the wellbore wall is determined w The maximum value of the drilling fluid hydraulic tension failure threshold p wt ; The tensile failure threshold p of the drilling fluid hydraulic pressure wt The ratio p to the wellbore depth d wt / d is converted to obtain the equivalent drilling fluid density, which is used as the upper limit of the drilling fluid safety density window.

6. The method according to claim 3, characterized in that In step 6, the Mohr-Coulomb shear failure criterion is: Meeting the Mohr-Coulomb shear failure criterion will cause tensile failure of the wellbore wall.

7. The method according to claim 6, characterized in that In step 6, By searching for the tangent angle θ' around the wellbore, the stress tensor σ at each point on the borehole wall is determined. (w) , and calculate σ (w) The minimum and maximum eigenvalues ​​of ; Based on the stress tensor σ (w) With drilling fluid hydraulic p w The relationship between σ (w) The minimum and maximum eigenvalues ​​of min and σ max Indicated as containing p w Substituting the expression of Mohr-Coulomb shear failure criterion into the drilling fluid hydraulic pressure p that will not cause shear failure of the wellbore wall w The minimum value of drilling fluid hydraulic shear failure threshold p wt ; The shear failure threshold p of the drilling fluid hydraulic pressure ws The ratio of depth p ws / d is converted to obtain the equivalent drilling fluid density, which is used as the lower limit of the safe density range of the drilling fluid.

8. An electronic device, characterized in that: include: Memory and processor; The memory is used to store computer programs; The processor is configured to call the computer program to execute the method according to any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed on an electronic device, the electronic device implements the method according to any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed on an electronic device, the electronic device implements the method according to any one of claims 1 to 7.

Images