An analytical prediction method for drilling fluid safe density range based on ground stress changes

Abstract

This application discloses a method for analytically predicting the safe density range of drilling fluid based on changes in ground stress. The method includes: establishing a three-dimensional, axisymmetric, multi-layer oil and gas reservoir model; solving the Navier static equilibrium equation for porous media, simultaneously establishing the displacement-strain relationship, and obtaining a general solution for volumetric strain and displacement. Combining the displacement continuity boundary conditions and stress continuity boundary conditions at the interlayer contact surface, the unknown parameters in the general solution are obtained; then, an analytical solution for the displacement and stress of each rock layer caused by oil and gas reservoir exploitation is obtained; thereby, the wellbore stress distribution during drilling in the exploited oil and gas reservoir and surrounding rock layers is obtained, and the relationship between stress and drilling fluid hydraulic pressure is obtained; combining the rock tensile failure criterion and the Mohr-Coulomb shear failure criterion, the tensile failure threshold and shear failure threshold of the drilling fluid hydraulic pressure are calculated, and the upper and lower limits of the drilling fluid safe density range are converted. This application can achieve an analytical and quantitative characterization of the safe density range of drilling fluid.

Description

Technical Field

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

[0002] During drilling, rocks along the borehole trajectory are continuously drilled out, and the stress of the rocks around the borehole will be redistributed. The drilling fluid will exert corresponding pressure on the well wall, replacing the in-situ stress and maintaining the stability of the well wall. To maintain the stability of the well wall during drilling, the drilling fluid density must be within an appropriate range.

[0003] In order to consider the fluid-solid coupling between drilling fluid and wellbore rock mass when the wellbore is damaged, it is necessary to introduce the poroelasticity 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 are obtained for arbitrary wellbore inclination and different wellbore permeability conditions. ([1]. Mehrabian A, Abousleiman YN. Generalized poroelastic wellbore problem[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(16): 2727-2754.)

[0005] Jin Yan Team [2] By applying the poroelastic theory, the authors reveal how factors such as wellbore anisotropy, multiple weak interlayers, and uneven in-situ stresses affect the safe density range of drilling fluid when drilling in any direction. ([2]. Liu M, Jin Y, Lu Y, et al. A wellbore stability model for a deviated well in a transversely isotropic formation considering poroelastic effects[J]. RockMechanics and Rock Engineering, 2016, 49: 3671-3686.)

[0006] Ma Tianshou et al. [3]The fluid-solid coupling analytical solution of the wellbore stress and pore pressure distribution at any drilling angle was obtained, revealing the influence of factors such as the elastic parameters, strength and permeability anisotropy of the wellbore rock mass on the wellbore stress and pore pressure distribution. ([3]. Qiu Y, Ma T, Peng N, et al. Wellbore stability analysis of inclined wells in transversely isotropic formations accounting for hydraulic-mechanical coupling[J]. Geoenergy Science and Engineering, 2023, 224:211615.)

[0007] However, it should be noted that in all of the aforementioned studies on wellbore stability, the in-situ in-situ stress of the rock formation within which the wellbore is located was assumed to be fixed. Further research exploring the mechanisms by which mining-induced rock deformation and stress changes lead to changes in wellbore stability remains limited.

[0008] Li and Gray [4] The solution to the stress change in oil and gas reservoirs caused by production, calculated using a one-dimensional strain model, was applied to analyze the changes in the safe density window of drilling fluid during drilling in oil and gas reservoirs. The effects of wellbore inclination and in-situ stress on the safe density range (window) of drilling fluid were 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.)

[0009] 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 well 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 oil and gas reservoir compaction prediction and directional wellbore integrity evaluation [J]. Chinese Journal of Rock Mechanics and Engineering, 2015, 34(S2): 4171-4177.)

[0010] To date, a large amount of research has been conducted on the issue of wellbore stability. However, the research on analytical models 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 wellbore instability and failure when drilling in corresponding rock formations is still unclear. There is a lack of quantitative characterization of the safe density range of drilling fluid and safe drilling direction when drilling in produced oil and gas reservoirs and surrounding rock formations.

[0011] At present, the mechanism by which mining-induced rock deformation and stress changes affect the safe density range and safe drilling direction of drilling fluids in these rock formations remains unclear. The wellbore stability issue when drilling in already mined oil and gas reservoirs and surrounding rock formations is a key scientific issue that needs to be urgently addressed in oil and gas development at this stage. Summary of the Invention

[0012] 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.

[0013] The technical solution provided by the present invention is:

[0014] 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:

[0015] Step 1: Establish a three-dimensional axisymmetric multi-layer oil and gas reservoir model, where the middle layer is the oil and gas reservoir layer, and the upper and lower layers are semi-infinite cap rock and underlying layer;

[0016] Step 2: Based on the Navier static equilibrium equation of porous media, the displacement-strain relationship is simultaneously established to obtain the governing equation describing the strain-pore pressure relationship of the three-dimensional axisymmetric multi-layer oil and gas reservoir model;

[0017] Step 3: The governing equations are converted to Hankel space by applying the Hankel integral transformation method to obtain the general solution expressions of volume strain and displacement;

[0018] Step 4: Combine the displacement continuity boundary condition and the 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; and use the Hankel inverse transform method to obtain the analytical solution of the displacement and stress of each rock layer caused by oil and gas reservoir production;

[0019] Step 5: By applying multiple coordinate transformations and the improved Kirsch solution method, the stress distribution of the borehole wall in the produced oil and gas reservoir and the surrounding rock formation is solved to obtain the relationship between stress and drilling fluid hydraulic pressure;

[0020] Step 6: Based on the obtained stress tensor at any point on the wellbore wall and drilling fluid hydraulics The tensile failure threshold and shear failure threshold of drilling fluid hydraulic pressure are calculated based on the relationship between the rock tensile failure criterion and the 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, which serves as the upper and lower limits of the safe density range of drilling fluid.

[0021] 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:

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] .

[0028] In step 4, the expressions for the analytical solutions of displacement and stress of the cap layer and the underlying layer are:

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] .

[0035] Where, and Refers to the radial displacement component and vertical displacement component of the oil and gas reservoir rock formation, Respectively The radial stress, tangential stress, vertical stress and shear stress of each rock layer, Indicates the pore fluid pressure, the unit can be or , represents the pore fluid pressure of the oil and gas reservoir after conversion to Hankel space. The subscripts of the above parameters are They correspond to oil and gas reservoir strata, cap rock strata and underlying rock strata respectively; Refers to the 0th and 1st order expressions of the first Bessel equation, where and is a hyperbolic function, is the stiffness ratio; is the intermediate variable produced by Hankel transformation; is the reservoir thickness; The uniaxial compression coefficient of the rock in the oil and gas reservoir is expressed;

[0036] are the three coordinate axes in the three-dimensional cylindrical coordinate system ( , ,z) in the first coordinate axis coordinate;

[0037] is a parameter of the reservoir rock and 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; represents the Poisson's ratio of the rock, and its subscript They correspond to the reservoir rock formation and the cap rock formation respectively;

[0038] in, ;

[0039] The calculation process of each parameter in the formula is as follows, where:

[0040] ,in is the shear modulus of the oil and gas reservoir rock, is the shear modulus of the cap rock, is the shear modulus of the underlying rock;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] ;

[0046] ;

[0047] ;

[0048] ;

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] .

[0055] In a possible implementation, step 5 includes:

[0056] 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 of the oil and gas reservoir and the surrounding rock formations in the rectangular coordinate system. ;

[0057] Step 5.2, In situ stress Superposition, the superimposed stress is the new formation stress of the mined oil and gas reservoir and the surrounding rock formations ;

[0058] Step 5.3: Add the new formation stress Convert to any drilling inclination and any drilling direction The stress tensor in the rectangular coordinate system corresponding to the wellbore ;

[0059] Step 5.4: Based on stress tensor , using the improved Kirsch solution method, solve the stress (state) tensor at any point on the wellbore wall The expression based on The expression is determined and drilling fluid hydraulics relationship.

[0060] In a possible implementation, in step 6, the rock tensile failure criterion is:

[0061] ;

[0062] in, is the maximum principal stress at any point on the wellbore wall, which is The maximum eigenvalue of is the tensile strength of the rock; is the pore pressure of the rock surrounding the wellbore, is the initial pore pressure of the underground rock, Changes in pore fluid pressure in rock formations during oil and gas reservoir development;

[0063] Meeting the rock tensile failure criterion will cause tensile failure of the wellbore wall.

[0064] In one possible implementation, determining the upper limit of the drilling fluid safety density window in step 6 includes:

[0065] By tangentially angled around the wellbore Search to determine the stress tensor at each point on the wellbore wall , and calculate The maximum eigenvalue of

[0066] Based on the stress tensor and drilling fluid hydraulics relationship, will The maximum eigenvalue of Indicated as containing Substitute the expression of the rock tensile failure criterion mentioned above to determine the drilling fluid hydraulic pressure that will not cause tensile failure of the wellbore wall. The maximum value of the drilling fluid hydraulic tensile failure threshold ;

[0067] Tensile failure threshold using drilling fluid hydraulics and wellbore depth Ratio The equivalent drilling fluid density is converted and used as the upper limit of the drilling fluid safety density window.

[0068] In one possible implementation, in step 6, the Mohr-Coulomb shear failure criterion is:

[0069] ;

[0070] If the Mohr-Coulomb shear failure criterion is met, tensile failure of the wellbore will occur.

[0071] In a possible implementation, in step 6, by tangentially angled around the wellbore Search to determine the stress tensor at each point on the wellbore wall , and calculate The minimum and maximum eigenvalues ​​of and drilling fluid hydraulics relationship, will The minimum and maximum eigenvalues ​​of and Indicated as containing The expression of is substituted into the Mohr-Coulomb shear failure criterion to determine the drilling fluid hydraulic pressure that will not cause shear failure of the wellbore wall. The minimum value of the drilling fluid hydraulic shear failure threshold ;

[0072] Shear failure threshold using drilling fluid hydraulic pressure Ratio to depth The equivalent drilling fluid density is converted as the lower limit of the drilling fluid safety density range.

[0073] In a second aspect, the present application provides an electronic device, comprising: a memory and a processor;

[0074] The memory is used to store computer programs;

[0075] The processor is configured to call the computer program to execute the method described above.

[0076] 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 described above.

[0077] In a fourth aspect, the present application provides a computer program product, including a computer program, which, when executed on an electronic device, enables the electronic device to implement the method described above.

[0078] The specific implementation methods of the second to fifth aspects of this application can refer to the implementation method of the first aspect above, and will not be repeated here.

[0079] Beneficial effects:

[0080] (1) A three-dimensional axisymmetric deformation / stress model of oil and gas reservoirs was established to analytically solve the deformation and stress changes of underground heterogeneous multi-layers caused by oil and gas reservoir exploitation, and to reveal the influence of deformation and stress changes of oil and gas reservoirs and surrounding rock formations caused by exploitation.

[0081] (2) Applying the reservoir deformation / stress model and its analytical solution to the calculation of safe drilling fluid density and the analysis of drilling wellbore stability reveals the influence of key factors such as rock stratification, differences in mechanical parameters of each rock layer, reservoir production level, and reservoir size on the safe drilling fluid density range and safe drilling direction for drilling in produced reservoirs and surrounding rock formations. The method proposed in this application can be used for safe drilling in produced reservoirs and surrounding rock formations, providing a theoretical basis and technical guidance for drilling projects in produced reservoirs and surrounding rock formations. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 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;

[0083] Figure 2Schematic 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 dimensions 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 formations;

[0084] Figure 3 Schematic diagram of the isotropic heterogeneous multi-layer oil and gas reservoir model, displacement and stress continuity boundary conditions, and analytical solutions in the embodiments of the present application, wherein a is the transversely isotropic heterogeneous multi-layer oil and gas reservoir model, b is the displacement and stress continuity boundary conditions, and c is a schematic diagram of the analytical solution of rock formation stress changes caused by mining in a cylindrical coordinate system;

[0085] Figure 4 In the embodiment of this application =0.1, different stiffness ratios in the impermeable layer The distribution of radial stress, tangential stress, vertical stress and shear stress caused by depletion; a is the distribution of radial stress, b is the distribution of tangential stress, c is the distribution of vertical stress, and d is the distribution of shear stress;

[0086] Figure 5 This is a flow chart for calculating the stress of the wellbore wall of an already 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 an embodiment of the present application;

[0087] Figure 6 This is a hemispherical diagram showing the tensile failure limit of the wellbore in the embodiment of the present application; wherein a, b, and c are respectively and azimuth changes in and 5 feet below the top surface of the reservoir layer, with different stiffness ratios =5, =1 and =1 / 5 condition of the tensile failure limit of the wellbore hemispherical diagram;

[0088] Figure 7 This is a hemispherical diagram showing the shear failure limit of the wellbore in the embodiment of the present application; wherein a, b, and c are respectively and azimuth changes in and 5 feet above the top surface of the reservoir layer, with different stiffness ratios =5, =1 and =1 / 5. DETAILED DESCRIPTION

[0089] In order to enable those skilled in the art to better understand the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of this application.

[0090] It should be noted that the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or apparatus comprising a series of elements includes not only those elements explicitly listed, but also other elements not explicitly listed, or may also include elements inherent to such process, method, product, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or apparatus comprising the element.

[0091] In this application, terms such as "upper," "lower," "left," "right," "front," "back," "top," "bottom," "inner," "outer," "center," "vertical," "horizontal," "transverse," and "longitudinal" indicate positions or locations based on the positions or locations shown in the accompanying drawings. These terms are primarily intended to better describe this application and its embodiments and are not intended to limit the devices, elements, or components indicated to having a specific orientation, or to being constructed or operated in a specific orientation.

[0092] Furthermore, some of the above terms may be used to express other meanings besides indicating a position or location. For example, the term "on" may also be used to indicate a dependency or connection in certain circumstances. Those skilled in the art will understand the specific meanings of these terms in this application based on the specific circumstances.

[0093] Hereinafter, reference will be made to describing specific embodiments according to the present application.

[0094] In the first aspect, the present application provides a method for analytically predicting the safe density range of drilling fluid based on changes in ground stress:

[0095] 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 rock and underlying layer;

[0096] 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; mining reduces the pore fluid pressure inside the oil and gas reservoir. , other model sizes see Figure 3 Left part.

[0097] Step 2: Based on the Navier static equilibrium equation of porous media,

[0098] The Navier static equilibrium equation for porous media is:

[0099] (1)

[0100] Where, Represents the shear modulus of rock, and the unit can be or ; represents the Poisson's ratio of the rock, is the Biot coefficient;

[0101] Represents the displacement of the rock Calculate the second-order partial derivatives in the direction of each coordinate axis and sum them up, that is, The final result is a scalar; ; In the three-dimensional rectangular coordinate system include ( ), ( )and ( ); in cylindrical coordinates, ( ), ( )and ( ), 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.

[0102] Represents the volume strain of rock For the coordinate system The derivative of the coordinate axis direction is the derivative of the x direction, y direction or z direction in the rectangular coordinate system, and the derivative of the cylindrical coordinate system is the derivative of direction, Direction or Directional differentiation;

[0103] Indicates pore water pressure For the coordinate system Derivatives about the coordinate axes.

[0104] In the three-dimensional rectangular coordinate system and cylindrical coordinate system, equation (1) is expressed in tensor form. Equation (1) actually represents three equations, namely, The three equations in the case of Corresponding respectively , , ; In cylindrical coordinate system Corresponding respectively , , .

[0105] Find the divergence of equation (1) and apply the operator properties, , the simultaneous displacement-strain relationship , 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:

[0106] (2)

[0107] In the above displacement-strain relationship middle, The displacement of the rock Calculate the second-order partial derivatives in the direction of each coordinate axis and sum them up, that is, , and the displacement of the rock 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 , so there is .

[0108] 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, a vector is obtained. When two vectors are operated, a scalar is obtained, such as = ,because It is just an operator that ultimately needs to act on a variable, so use express. Represents the cross product of vectors.

[0109] Operator Acts on For example, .

[0110] Where, is the Geertsma one-way compressibility coefficient, where Represents the bulk modulus of rock, and the unit can be or .

[0111] Step 3: Transform the governing equation (2) into Hankel space by applying the Hankel integral transformation method for solution. After transforming the governing equation into Hankel space, combined with the poroelasticity equation, the general solution expression of volume strain and displacement can be obtained (taking the oil and gas reservoir as an example):

[0112] ;(3)

[0113] ;(4)

[0114] (5)

[0115] Where, Refers to the volume strain of oil and gas reservoir rock 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 rock formation in the Hankel transform domain. The intermediate variable , is the Poisson's ratio of the rock in the oil and gas reservoir; in the above variables, the subscript and Represents the cylindrical coordinate system of the oil and gas reservoir scale Direction and The symbol ^ on the variable indicates the variable in Hankel space, and the superscript denotes the 0th-order Hankel transform of the corresponding variable, and the superscript represents the first-order Hankel transform of the corresponding variable; variable of The Hankel transform is , the corresponding inverse transformation can be expressed as . 、 、 and All are 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.

[0116] It represents the uniaxial compression coefficient of the rock in the oil and gas reservoir layer. The unit can be or ; Represents the pore water pressure variable The 0th-order Hankel transform of is the intermediate variable generated by Hankel transformation, It is the manifestation of the third coordinate axis z-axis of the three-dimensional rectangular coordinate system in oil and gas reservoirs;

[0117] From the above equations, it can be seen that a single rock layer has four unknown parameters ( , , , ), while multi-layered rocks have layers 4 unknown parameters.

[0118] Step 4: Combine the displacement continuity boundary conditions of the interlayer contact surface ( 2 boundary conditions, is the number of rock layers) and the stress continuity boundary condition ( 2 boundary conditions) such as Figure 3 As shown in the middle part, the general solution and the above 4 boundary conditions, the corresponding unknown parameters can be obtained , 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.

[0119] exist Figure 3 The left part is a heterogeneous multi-layer oil and gas reservoir model, in which: They represent the elastic modulus, Biot coefficient, Poisson's ratio and impermeable Poisson's ratio of the oil and gas reservoir respectively;

[0120] They represent the elastic modulus, Biot coefficient, Poisson's ratio, and impermeable Poisson's ratio of the cap layer respectively;

[0121] They represent the elastic modulus, Biot coefficient, Poisson's ratio and impermeable Poisson's ratio of the underlying layer respectively;

[0122] in, 、 、 They are the coordinates of the third coordinate axis z of the three-dimensional rectangular coordinate system and the symmetry plane of the oil and gas reservoir. , bottom of the cap layer and the top of the volt layer The vertical distance;

[0123] In the embodiment of the present application, it is assumed that the material parameter values ​​of the cover layer and the underlying layer are the same. Figure 3 Shown in the middle part.

[0124] Then the displacement continuity boundary condition is:

[0125] , that is, at the upper contact surface (i.e., the top of the oil and gas reservoir , bottom of the cap layer ) Radial displacement of the cap layer and radial displacement of the oil and gas reservoir equal.

[0126] , that is, at the upper contact surface (i.e., the top of the oil and gas reservoir , bottom of the cap layer ) Vertical displacement of the cover layer and vertical displacement of oil and gas reservoirs equal.

[0127] The stress continuity boundary condition is:

[0128] , that is, at the upper contact surface (i.e., the top of the oil and gas reservoir , bottom of the cap layer ) Vertical stress of the cap layer and vertical stress of oil and gas reservoirs equal.

[0129] , that is, at the upper contact surface (i.e., the top of the oil and gas reservoir , bottom of the cap layer ) Shear stress of the caprock and shear stress of oil and gas reservoirs equal.

[0130] Figure 3 The right part shows the stress changes of rock formation caused by mining in the cylindrical coordinate system. The analytical solution is:

[0131] , represents the stress change of the reservoir layer caused by oil and gas reservoir exploitation, is the rock parameter ( ) and reference point position ( ) function;

[0132] , represents the stress change of cap rock caused by oil and gas reservoir exploitation;

[0133] , which represents the stress change of the underlying layer caused by oil and gas reservoir exploitation.

[0134] Among the above variables, the superscript Indicates that the oil and gas reservoir exploitation causes 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. = ; Represents reservoir thickness / reservoir radius; and Respectively represent Poisson's ratio and impermeability Poisson's ratio of the rock layer, where They correspond to oil and gas reservoir strata, cap rock strata and underlying rock strata respectively.

[0135] Analytical expressions for displacement (deformation) and stress of oil and gas reservoirs:

[0136] ;(6)

[0137] ;(7)

[0138] ;(8)

[0139] ;(9)

[0140] ;(10)

[0141] (11)

[0142] Analytical expressions for displacement and stress of cover layer and underlying layer:

[0143] ;(12)

[0144] ;(13)

[0145] ;(14)

[0146] ;(15)

[0147] ; (16)

[0148] (17)

[0149] In the formula and Refers to the radial displacement component and vertical displacement component of the oil and gas reservoir rock formation, Respectively The radial stress, tangential stress, vertical stress and shear stress of each rock layer, represents the pore fluid pressure of the oil and gas reservoir after conversion to Hankel space, is the thickness of the reservoir, and the unit can be or ; Subscript of the above parameters They correspond to oil and gas reservoir strata, cap rock strata and underlying rock strata respectively; Refers to the 0th and 1st order expressions of the first Bessel equation, where and is a hyperbolic function, is the stiffness ratio;

[0150] are the three coordinate axes in the three-dimensional cylindrical coordinate system ( , , z) in the first coordinate axis coordinate (radial coordinate), the unit can be or ;

[0151] 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. is a parameter of the cap or underlying rock, and is a function of the Poisson's ratio of the cap or underlying rock;

[0152] in, All are intermediate variables;

[0153] The calculation process of each parameter in the formula is as follows, where:

[0154] ,in is the shear modulus of the oil and gas reservoir rock, is the shear modulus of the cap rock, is the shear modulus of the underlying rock;

[0155] ; (18)

[0156] ;(19)

[0157] ; (20)

[0158] ;(twenty one)

[0159] ;(twenty two)

[0160] ;(twenty three)

[0161] ;(twenty four)

[0162] ; (25)

[0163] ; (26)

[0164] ; (27)

[0165] ; (28)

[0166] ;(29)

[0167] ; (30)

[0168] (31)

[0169] Step 5: By applying multiple coordinate transformations and the improved Kirsch solution method, the stress distribution of the borehole wall in the produced oil and gas reservoir and the surrounding rock formation is solved to obtain the relationship between stress and drilling fluid hydraulic pressure;

[0170] The specific calculation process is as follows:

[0171] Step 5.1: The stress tensor of the oil and gas reservoir and the surrounding rock formations in the cylindrical coordinate system is calculated as follows: Converted to the rectangular coordinate system, the stress solution of the oil and gas reservoir and the surrounding rock formations under the rectangular coordinate system is obtained. ;in, The stress tensor changes caused by exploitation in the oil and gas reservoir scale cylindrical coordinate system are: is the stress tensor change caused by exploitation in the rectangular coordinate system of the oil and gas reservoir scale, and the unit can be or ; The applied coordinate transformation formula is: , where the transformation matrix , is the azimuth of the drilling position, represent Axis positive direction, where It can be expressed in matrix form as , shear stress and is 0;

[0172] Step 5.2, In situ stress Superposition, the superimposed stress is the new formation stress of the mined oil and gas reservoir and the surrounding rock formations ;

[0173] in , , , is the in-situ stress tensor The three components of are the maximum horizontal principal stress, Horizontal minimum principal stress, Vertical stress, superscript (0) refers to in situ. is the in-situ stress tensor in the rectangular coordinate system at the reservoir scale.

[0174] Step 5.3: Add the new formation stress Convert to any drilling (wellbore) inclination and any drilling (wellbore) direction The stress tensor in the rectangular coordinate system corresponding to the wellbore , superscript That is, it represents the stress value corresponding to the wellbore (well), that is, the stress tensor change caused by mining in the wellbore scale rectangular coordinate system, where each element is a component in different directions, which can be seen in detail. Figure 5 Schematic diagram in the lower right corner; the applied coordinate transformation formula is: , where the transformation matrix ;

[0175] Among them, the drilling (wellbore) inclination The unit can be degrees;

[0176] Step 5.4: Based on stress tensor , using the improved Kirsch solution method, solve the stress (state) tensor at any point on the wellbore wall ,Establish and drilling fluid hydraulics The specific flow chart is as follows: Figure 5 shown.

[0177] in, It is the stress tensor change caused by mining in the wellbore scale cylindrical coordinate system.

[0178] Figure 5 The flowchart of the calculation of wellbore 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.

[0179] The stress (state) tensor at any point on the wellbore wall is obtained

[0180] , etc. are the components of the stress tensor, which can be seen in detail. Figure 5 The schematic diagram in the lower left corner, the specific calculation method is shown below (Equations 21-26) The analytical solution is:

[0181] ; (32)

[0182] ; (33)

[0183] ;(34)

[0184] ; (35)

[0185] ; (36)

[0186] (37)

[0187] in, It is the drilling fluid hydraulic pressure, that is, the wellbore fluid pressure.

[0188] Step 6: Based on the obtained stress tensor at any point on the wellbore wall and drilling fluid hydraulics The tensile failure threshold and shear failure threshold of drilling fluid hydraulic pressure are calculated based on the relationship between the rock tensile failure criterion and the 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, which serves as the upper and lower limits of the safe density range of drilling fluid.

[0189] Tensile failure occurs when the maximum effective tensile principal stress in the wellbore exceeds the rock's tensile strength. The corresponding tensile failure gradient is usually chosen as the upper limit of the safe drilling fluid density range. Since the wellbore fluid cannot induce any shear stress, the principal stress always occurs in the plane tangential to the wellbore. Therefore, the rock tensile failure criterion can be expressed as:

[0190] (38)

[0191] in, is the maximum principal stress at any point on the wellbore wall, which is The maximum eigenvalue of is the tensile strength of the rock, which is assumed to be zero here. is the pore pressure of the rock surrounding the wellbore, is the initial pore pressure of the underground rock, is the change in pore fluid pressure of the rock formation under oil and gas reservoir production, and the unit can be or .

[0192] If the formula (38) is met, tensile failure of the wellbore wall will occur.

[0193] By tangentially angled around the wellbore Search (see Figure 5 ), determine the stress (state) tensor of each point on the wellbore wall , and calculate The maximum eigenvalue of . Based on the stress tensor and drilling fluid hydraulics The relationship can be The maximum eigenvalue of Indicated as containing Substituting the expression into the above formula (38), the drilling fluid hydraulic pressure that will not cause tensile damage to the wellbore wall can be determined. The maximum value of the drilling fluid hydraulic tensile failure threshold .

[0194] In field practice, the wellbore tensile failure gradient can usually be expressed as the tensile failure threshold of the drilling fluid hydraulic pressure. and wellbore depth Ratio (Units are usually ) can also be represented by equivalent drilling fluid density (unit can be ) to characterize it. Therefore, we can get After that, the equivalent wellbore fluid density, i.e., drilling fluid density, can be converted and used as the upper limit of the drilling fluid safety density window.

[0195] The wellbore depth The unit can be or .

[0196] When the drilling fluid hydraulic pressure is too low, the wellbore may collapse due to shear failure of the wellbore wall caused by the high pressure stress generated by the surrounding rock. 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:

[0197] (39)

[0198] in, and are the minimum and maximum principal stresses at any point on the wellbore wall, The minimum and maximum eigenvalues ​​of ; is the friction angle of the wellbore rock, is the cohesive strength of the rock.

[0199] If the formula (39) is met, tensile failure of the wellbore will occur.

[0200] By tangentially angled around the wellbore Search (see Figure 5 ), determine the stress (state) tensor of each point on the wellbore wall , and calculate The minimum and maximum eigenvalues ​​of the stress tensor. and drilling fluid hydraulics The relationship can be The minimum and maximum eigenvalues ​​of and Indicated as containing Substituting the expression into the above formula (39), the drilling fluid hydraulic pressure that will not cause shear failure of the wellbore can be determined The minimum value of the drilling fluid hydraulic shear failure threshold .

[0201] In field practice, the shear failure threshold corresponding to the drilling fluid density gradient can usually be expressed as the shear failure threshold of the drilling fluid hydraulic pressure. Ratio to depth (Units are usually ) can also be represented by equivalent drilling fluid density (unit can be ) to characterize it. Therefore, we can get After that, the equivalent drilling fluid density can be converted as the lower limit of the drilling fluid safety density range.

[0202] Based on the above steps, by calculating the different drilling inclinations and drilling direction The safe density range of drilling fluid under the given conditions can be used to determine the corresponding safe drilling direction.

[0203] An embodiment of the present application further provides an electronic device, comprising: a memory and a processor;

[0204] The memory is used to store computer programs;

[0205] The processor is configured to call the computer program to execute the method described above.

[0206] An embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program. When the computer program is executed on an electronic device, the electronic device implements the method described above.

[0207] An embodiment of the present application further provides a computer program product, including a computer program. When the computer program is run on an electronic device, the electronic device implements the method described above.

[0208] 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.

[0209] Obviously, those skilled in the art should understand that the above-mentioned units or steps of the present application can be implemented using a general-purpose computing device. They can be concentrated on a single computing device or distributed across a network composed of multiple computing devices. Alternatively, they can be implemented using program codes executable by the 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 can be made into a single integrated circuit module for implementation. Thus, the present application is not limited to any specific combination of hardware and software.

[0210] The following is a verification of the effects of the technical solutions provided in the examples of this application:

[0211] (1) Verification of the three-dimensional axisymmetric oil and gas reservoir deformation / stress analytical model:

[0212] The analytical solution derived above is verified here with the numerical solution of the same problem. To this end, COMSOL® Multiphysics (2018) is used to simulate the same problem. The axisymmetric numerical model and its discretization into finite element domains are shown in 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 layer and the permeable layer is shown in Figure 2 As shown in the diagrams in the upper right and lower right corners.

[0213] Apply the parameter values ​​in the table below to compare the analytical solution with the numerical solution:

[0214]

[0215] In Table 1, It is the abbreviation of true vertical depth. Since the true depth is constantly changing during the downward drilling process, the in-situ stress ( , , ) 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. , , ) process, only the gradient The actual depth can be used to obtain the in-situ stress at the drilling depth. represents the Young's modulus of rock.

[0216] In agreement with the numerical model, a uniform pore pressure reduction is adopted 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 were selected in the diagram in the lower right corner to compare the analytical and numerical solutions. The results are listed in Table 2 for the radial and tangential stress components; Table 3 lists the results for the vertical and shear stress components. Positive values ​​indicate a tensile or counterclockwise rotational trend. The differences between the two solutions for all four stress components at the three points are less than 1%, and for all three stiffness ratios, the difference is less than 1%. The following results are consistent.

[0217]

[0218]

[0219] (2) Analytical prediction process of safe density range of drilling fluid for infill wells

[0220] ① Continue 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:

[0221] Figure 4 Shown in = 0.1, the dimensionless stress change at the radial distance of the symmetry axis of the impermeable layer The changes in pore fluid = 0.5 and 1, which results in compressive normalized radial and tangential stress changes in the impermeable layer. Due to the Poisson effect, a larger stiffness ratio will produce tensile radial and tangential stress changes in the impermeable layer. As the induced radial and tangential stress changes gradually decrease, the vertical stress changes gradually decrease. The vertical stress is in tension when the stress is observed, but changes to compression when crossing the lateral boundary of the disturbed pore pressure volume. Within any region, a larger stiffness ratio results in a larger vertical stress change. Shear stress is relatively small unless the observation point is close to the disturbed pore pressure boundary, where a high gradient with a limited peak is observed.

[0222] ② According to step 5 above, the analytical stress solution of the produced oil and gas reservoir and the surrounding rock formation is applied to solve the stress state of the surrounding rock of the infill well.

[0223] Finally, we can calculate the different drilling inclinations and drilling direction The safe density range of drilling fluid under certain conditions is used to determine the corresponding safe drilling direction.

[0224] Figure 6 Shown in A hemispherical plot of the tensile failure gradient at 5 feet below the top surface of the intermediate layer. The maximum tensile failure gradient occurs at a wellbore inclination of approximately 45°, when the wellbore inclination aligns with the minimum horizontal stress before depletion. The predicted tensile failure gradient value varies significantly with stiffness differences: when =5, it is 0.32 lbm / gal less than the homogeneous case; when =1 / 5, it is 1.25 lbm / gal greater than the homogeneous case.

[0225] Figure 7 Shown in The stiffness ratio is = 5, 1, and 0.2. Unlike the tensile failure gradient distribution, the minimum shear failure gradient occurs in vertical or slightly deviated wellbores, whether inside or outside the reservoir. The predicted minimum shear failure gradient value is also sensitive to the stiffness difference parameter: when = 5, it is 0.75 lbm / gal less than the predicted value for the homogeneous layer; when =1 / 5, it is 0.39 lbm / gal greater than the predicted value for the homogeneous layer.

[0226] The technical solution provided in the embodiments of the present application can reveal the influence of factors such as differences in rock mechanical parameters, interlayer viscoelastic rheological differences, and rock anisotropy differences on the changes in the safe density range of drilling fluid and safe drilling direction caused by oil and gas reservoir exploitation.

[0227] 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 this field to implement or use the contents of the present application, and is not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A method for analytically 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, where the middle layer is the oil and gas reservoir layer, and the upper and lower layers are semi-infinite cap rock and underlying layer; Step 2: Based on the Navier static equilibrium equation of porous media, the displacement-strain relationship is simultaneously established to obtain the governing equation describing the strain-pore pressure relationship of the three-dimensional axisymmetric multi-layer oil and gas reservoir model; Step 3: The governing equations are converted to Hankel space by applying the Hankel integral transformation method to obtain the general solution expressions of volume strain and displacement; Step 4: Combine the displacement continuity boundary condition and the 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; and use the Hankel inverse transform method to obtain the analytical solution of the displacement and stress of each rock layer caused by oil and gas reservoir production; Step 5: By applying multiple coordinate transformations and the improved Kirsch solution method, the stress distribution of the borehole wall in the produced oil and gas reservoir and the surrounding rock formation is solved to obtain the relationship between stress and drilling fluid hydraulic pressure; Step 6: Based on the obtained stress tensor at any point on the wellbore wall and drilling fluid hydraulics The tensile failure threshold and shear failure threshold of drilling fluid hydraulic pressure are calculated based on the relationship between the rock tensile failure criterion and the 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, which serves 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 for the analytical solutions of the displacement and stress of the oil and gas reservoir are: ； ； ； ； ； ； In step 4, the expressions for the analytical solutions of displacement and stress of the cap layer and the underlying layer are: ； ； ； ； ； ； Where, and Refers to the radial displacement component and vertical displacement component of the oil and gas reservoir rock formation, Respectively The radial stress, tangential stress, vertical stress and shear stress of each rock layer, represents the pore fluid pressure, represents the pore fluid pressure of the oil and gas reservoir after conversion to Hankel space. The subscripts of the above parameters are They correspond to oil and gas reservoir strata, cap rock strata and underlying rock strata respectively; Refers to the 0th and 1st order expressions of the first Bessel equation, where and is a hyperbolic function, is the stiffness ratio; is the intermediate variable produced by Hankel transformation; is the reservoir thickness; The uniaxial compression coefficient of the rock in the oil and gas reservoir is expressed; are the three coordinate axes in the three-dimensional cylindrical coordinate system ( , ,z) in the first coordinate axis coordinate; is a parameter of the reservoir rock and 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; represents the Poisson's ratio of the rock, and its subscript They correspond to the reservoir rock formation and the cap rock formation respectively; in, 、 、 、 、 、 、 、 、 、 、 、 、 、 All are intermediate variables; The calculation process of each parameter in the formula is as follows, where: ,in is the shear modulus of the oil and gas reservoir rock, is the shear modulus of the cap rock, is the shear modulus of the underlying rock; ； ； ； ； ； ； ； ； ； ； ； ； ； 。 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 of the oil and gas reservoir and the surrounding rock formations in the rectangular coordinate system. ; Step 5.2, In situ stress Superposition, the superimposed stress is the new formation stress of the mined oil and gas reservoir and the surrounding rock formations ; Step 5.3: Add the new formation stress Convert to any drilling inclination and any drilling direction The stress tensor in the rectangular coordinate system corresponding to the wellbore ; Step 5.4: Based on stress tensor , using the improved Kirsch solution method, solve the stress tensor at any point on the wellbore wall The expression based on The expression is determined and drilling fluid hydraulics relationship.

4. The method according to claim 3, characterized in that In step 6, The tensile failure criterion for rock is: ； in, is the maximum principal stress at any point on the wellbore wall, which is The maximum eigenvalue of is the tensile strength of the rock; is the pore pressure of the rock surrounding the wellbore, is the initial pore pressure of the underground rock, Changes in pore fluid pressure in rock formations during oil and gas reservoir development; Meeting the rock tensile failure criterion will cause tensile failure of the wellbore wall.

5. The method according to claim 4, characterized in that Determining the upper limit of the drilling fluid safety density window in step 6 includes: By tangentially angled around the wellbore Search to determine the stress tensor at each point on the wellbore wall , and calculate The maximum eigenvalue of Based on the stress tensor and drilling fluid hydraulics relationship, will The maximum eigenvalue of Indicated as containing Substitute the expression of rock tensile failure criterion into the drilling fluid hydraulic pressure that will not cause tensile failure of the wellbore wall. The maximum value of the drilling fluid hydraulic tensile failure threshold ; Tensile failure threshold using drilling fluid hydraulics and wellbore depth Ratio The equivalent drilling fluid density is converted and 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: ； in, and are the minimum and maximum principal stresses at any point on the wellbore wall, respectively. The minimum and maximum eigenvalues ​​of ; is the friction angle of the wellbore rock, is the cohesive strength of the rock; If the Mohr-Coulomb shear failure criterion is met, tensile failure of the wellbore will occur.

7. The method according to claim 6, characterized in that In step 6, By tangentially angled around the wellbore Search to determine the stress tensor at each point on the wellbore wall , and calculate The minimum and maximum eigenvalues ​​of ; Based on the stress tensor and drilling fluid hydraulics relationship, will The minimum and maximum eigenvalues ​​of and Indicated as containing The expression of is substituted into the Mohr-Coulomb shear failure criterion to determine the drilling fluid hydraulic pressure that will not cause shear failure of the wellbore wall. The minimum value of the drilling fluid hydraulic shear failure threshold ; Shear failure threshold using drilling fluid hydraulic pressure Ratio to depth The equivalent drilling fluid density is converted as the lower limit of the drilling fluid safety density range.

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 is enabled to implement the method according to any one of claims 1 to 7.

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