Maximum horizontal ground stress prediction method based on caving geometry of well wall in any shape

Abstract

The invention discloses a maximum horizontal ground stress prediction method based on well wall caving geometry in any shape, and relates to the technical field of well drilling and completion, and the method comprises the steps: constructing a well wall caving geometric model based on well wall logging data; according to the well wall caving geometric model and the rock mechanics experiment data, a well wall strength mechanical model considering the scale effect is established, and the well wall caving rock cohesion strength is obtained; establishing a semi-analytical well periphery coupling temperature-seepage-stress calculation mechanical model by utilizing a well wall caving geometric model to obtain a total stress field; the total stress field comprises an elastic stress field, a pore elastic stress field and a thermal elastic stress field; establishing a well wall caving stable stress intensity criterion; according to the well wall caving geometric model, the well wall caving rock cohesion strength and the total stress field, the well wall caving stable stress strength criterion is used, an inversion model is established, the magnitude and direction of the maximum horizontal ground stress are predicted, and the maximum horizontal ground stress prediction efficiency and accuracy are remarkably improved.

Description

Technical Field

[0001] The present application relates to the technical field of drilling and completion, and in particular to a method for predicting the maximum horizontal in-situ stress based on the geometry of borehole wall breakouts of arbitrary shapes. Background Art

[0002] The continuous growth of global energy consumption has made the needs for exploration, development, and storage of conventional and new energy sources increasingly prominent. Geological energy storage and drilling and completion technologies play an important role in exploring energy sustainable development with high energy efficiency and low carbon emissions. In-situ stress information is extremely important for analyzing geological structures and the stability and integrity of borehole walls. For oil and gas basins with relatively flat surface topographies, the in-situ stress can be characterized by one vertical principal stress and two horizontal principal stresses. The vertical and minimum horizontal principal stresses can be obtained relatively intuitively by mature methods, but the maximum horizontal in-situ stress cannot be directly measured and can only be predicted indirectly.

[0003] Drilling changes the local stress state around the borehole in the rock formation and causes stress concentration in the borehole, which will in turn cause spalling failure of the borehole wall rocks, making the cross-section of the borehole extend. The geometry of borehole wall breakouts is closely related to the stress state around the borehole and in the rock formation. Therefore, a large amount of research work has been devoted to predicting in-situ stress through the geometry of borehole wall breakouts. The widely used analytical method is to establish the relationship between the stress around the borehole and the far-field horizontal in-situ stress by using the classical Cauchy elastic stress solution, analyze the stress state and failure mode of the rocks around the borehole according to the Mohr-Coulomb strength criterion, and predict the horizontal in-situ stress by considering the stress and rock strength balance at the edges and tips of the geometry of borehole wall breakouts. The limitations of this method are as follows: The breakout of the borehole wall causes the initial circular borehole cross-section to extend along the direction of the minimum horizontal in-situ stress, forming a non-circular cross-section. Therefore, the classical Cauchy solution based on the circular cross-section borehole cannot accurately predict the stress distribution around the borehole; at the same time, this method is only applicable to the initial breakout stage with a relatively wide and flat breakout geometry, while the actually observed breakout geometry often shows complex geometries such as V-shaped, irregular, and asymmetric shapes. In addition, this method ignores the influence of the breakout depth and only uses the breakout width to predict the maximum horizontal in-situ stress, and the prediction result is significantly low. Numerical methods such as finite element and boundary element and semi-analytical methods have also been used to simulate the process of borehole wall spalling failure and deeply understand the mechanical mechanism of breakout stability. Compared with numerical methods, the advantage of the semi-analytical method based on conformal transformation and plane elastic complex variable function theory lies in high computational efficiency. Various methods for simulating and analyzing the geometry of borehole wall breakouts usually assume that there is an ideal impermeable mud cake on the borehole wall and the pore fluid pressure in the reservoir rocks around the borehole is uniformly distributed, ignoring the influence of poroelastic effects on the borehole wall spalling failure. In addition, as drilling and completion continuously advance to deeper and ultra-deeper depths, the temperature effect gradually increases, and the influence of thermal stress on the borehole wall spalling failure needs to be considered. Therefore, there is an urgent need for a computational method that can quickly and accurately simulate the evolution of the stress distribution around the borehole with the geometry of borehole wall breakouts of arbitrary shapes. Summary of the Invention

[0004] The purpose of this application is to provide a method for predicting the maximum horizontal in-situ stress based on the geometry of borehole wall breakouts with arbitrary shapes, which can significantly improve the prediction efficiency and accuracy of the maximum horizontal in-situ stress.

[0005] To achieve the above object, this application provides the following solutions:

[0006] This application provides a method for predicting the maximum horizontal in-situ stress based on the geometry of borehole wall breakouts with arbitrary shapes, including:

[0007] Construct a borehole wall breakout geometry model based on borehole logging data;

[0008] According to the borehole wall breakout geometry model and rock mechanics experiment data, establish a borehole wall strength mechanical model considering scale effect to obtain the cohesive strength of the rock in the borehole wall breakout;

[0009] Using the borehole wall breakout geometry model, establish a semi-analytical mechanical model for calculating the coupling of temperature, seepage and stress around the borehole to obtain the total stress field; the total stress field includes an elastic stress field, a poroelastic stress field and a thermoelastic stress field;

[0010] Establish a stable stress strength criterion for borehole wall breakouts;

[0011] According to the borehole wall breakout geometry model, the cohesive strength of the rock in the borehole wall breakout and the total stress field, use the stable stress strength criterion for borehole wall breakouts to establish an inversion model to predict the magnitude and direction of the maximum horizontal in-situ stress.

[0012] According to the specific embodiments provided by this application, the following technical effects are disclosed:

[0013] This application provides a method for predicting the maximum horizontal in-situ stress based on the geometry of borehole wall breakouts with arbitrary shapes. Through the borehole wall breakout geometry model, establish a semi-analytical mechanical model for calculating the coupling of temperature, seepage and stress around the borehole to obtain the total stress field. According to the borehole wall breakout geometry model, the cohesive strength of the rock in the borehole wall breakout and the total stress field, use the stable stress strength criterion for borehole wall breakouts to establish an inversion model to predict the magnitude and direction of the maximum horizontal in-situ stress. Give full play to the advantages of high calculation efficiency and simulation accuracy of the semi-analytical model, consider the influence of the geometry of borehole wall breakouts with arbitrary shapes on the stress distribution around the borehole, construct steady-state coupled poroelastic solutions and thermoelastic solutions, simulate the non-uniform pore fluid pressure distribution and poroelastic effect, non-uniform temperature perturbation and thermoelastic effect (elastic stress field, poroelastic stress field and thermoelastic stress field), establish a scale-effect breakout strength mechanical model based on the stable mechanical mechanism of borehole wall breakouts, and perform inversion according to the borehole wall breakout geometry model to predict the magnitude and direction of the maximum horizontal in-situ stress. Compared with the related technical methods, this application can significantly improve the prediction efficiency and accuracy of the maximum horizontal in-situ stress, and has a wider application range. Description of the Drawings

[0014] To more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the accompanying drawings required for use in the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0015] Figure 1 It is an application environment diagram of a method for predicting the maximum horizontal in-situ stress based on the geometry of borehole wall breakage of any shape in an embodiment of the present application.

[0016] Figure 2 It is a schematic flowchart of a method for predicting the maximum horizontal in-situ stress based on the geometry of borehole wall breakage of any shape provided in an embodiment of the present application.

[0017] Figure 3 It is a schematic diagram of the conformal mapping relationship between an infinite plane containing a borehole of any shape and a unit circle in an embodiment of the present application.

[0018] Figure 4 It is a schematic diagram of the corresponding relationship between the orthogonal coordinate system of the unit circle in the mathematical domain, an asymmetric borehole wall breakage geometry, and the conformal transformation coordinate system in the physical domain provided in an embodiment of the present application.

[0019] Figure 5 It is a schematic diagram of the conformal mapping relationship between non-uniform pore fluid pressure and temperature boundary conditions in the physical domain and the unit annulus domain provided in an embodiment of the present application.

[0020] Figure 6 It is a schematic diagram of the stable mechanical mechanism of borehole wall breakage and the maximum horizontal in-situ stress prediction model provided in an embodiment of the present application. Detailed implementation manners

[0021] The following will clearly and completely describe the technical solutions in the embodiments of the present application in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, rather than all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present application.

[0022] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0023] The method for predicting the maximum horizontal in-situ stress based on the geometry of borehole wall breakage of any shape provided in the embodiments of the present application can be applied to, for example Figure 1In the application environment shown. Among them, the terminal 102 communicates with the server 104 through the network. The data storage system can store the data that the server 104 needs to process. The data storage system can be set separately, integrated on the server 104, placed on the cloud or other servers. The terminal 102 can send the borehole wall logging data to the server 104. After receiving the borehole wall logging data, for the borehole wall logging data, the server 104 constructs a borehole wall collapse geometric model based on the borehole wall logging data, establishes a borehole wall strength mechanical model considering the scale effect according to the borehole wall collapse geometric model and the rock mechanics experiment data, obtains the cohesive strength of the rock in the borehole wall collapse, uses the borehole wall collapse geometric model to establish a semi-analytical calculation mechanical model of temperature-seepage-stress coupling around the borehole, obtains the total stress field, establishes a borehole wall collapse stable stress intensity criterion, and according to the borehole wall collapse geometric model, the cohesive strength of the rock in the borehole wall collapse and the total stress field, applies the borehole wall collapse stable stress intensity criterion to establish an inversion model to predict the magnitude and direction of the maximum horizontal in-situ stress. The server 104 can feedback the magnitude and direction of the maximum horizontal in-situ stress obtained for the borehole wall logging data to the terminal 102. In addition, in some embodiments, the method for predicting the maximum horizontal in-situ stress based on the borehole wall collapse geometry of any shape can also be implemented separately by the server 104 or the terminal 102. For example, the terminal 102 can directly predict the maximum horizontal in-situ stress for the borehole wall logging data, or the server 104 can obtain the borehole wall logging data from the data storage system and predict the maximum horizontal in-situ stress for the borehole wall logging data.

[0024] Among them, the terminal 102 can be, but is not limited to, various desktop computers, laptop computers, smart phones, tablet computers, Internet of Things devices and portable wearable devices. The Internet of Things devices can be smart speakers, smart TVs, smart air conditioners, smart in-vehicle devices, etc. The portable wearable devices can be smart watches, smart bracelets, head-mounted devices, etc. The server 104 can be implemented by an independent server or a server cluster composed of multiple servers, and can also be a cloud server.

[0025] In an exemplary embodiment, as Figure 2 shown, a method for predicting the maximum horizontal in-situ stress based on the borehole wall collapse geometry of any shape is provided. This method is executed by a computer device, and specifically can be executed separately by a computer device such as a terminal or a server, or jointly executed by a terminal and a server. In the embodiments of the present application, taking this method applied to Figure 1 the server 104 in it as an example for illustration, it includes the following steps 201 to step 205.

[0026] Step 201, construct a borehole wall collapse geometric model based on the borehole wall logging data.

[0027] Step 202: According to the borehole wall breakout geometric model and the rock mechanics experimental data, establish a borehole wall strength mechanical model considering the scale effect to obtain the cohesive strength of the rocks in the borehole wall breakout.

[0028] Step 203: Using the borehole wall breakout geometric model, establish a semi-analytical calculation mechanical model for coupled temperature-seepage-stress around the wellbore to obtain the total stress field; the total stress field includes an elastic stress field, a poroelastic stress field, and a thermoelastic stress field.

[0029] Step 204: Establish a stability stress strength criterion for borehole wall breakout.

[0030] Step 205: According to the borehole wall breakout geometric model, the cohesive strength of the rocks in the borehole wall breakout, and the total stress field, apply the stability stress strength criterion for borehole wall breakout to establish an inversion model to predict the magnitude and direction of the maximum horizontal in-situ stress.

[0031] Implementing the above Steps 201 to 205, giving full play to the advantages of high calculation efficiency and simulation accuracy of the semi-analytical model, considering the influence of the borehole wall breakout geometry of any shape on the stress distribution around the wellbore, constructing steady-state coupled poroelastic solutions and thermoelastic solutions, simulating the non-uniform pore fluid pressure distribution and poroelastic effects, non-uniform temperature perturbations and thermoelastic effects (elastic stress field, poroelastic stress field, and thermoelastic stress field), establishing a scale effect breakout strength mechanical model based on the stability mechanical mechanism of borehole wall breakout, and performing inversion according to the borehole wall breakout geometry to predict the magnitude and direction of the maximum horizontal in-situ stress. Compared with related technical methods, the present application can significantly improve the prediction efficiency and accuracy of the maximum horizontal in-situ stress and has a wider application range.

[0032] To solve the problems existing in predicting the maximum horizontal in-situ stress using the borehole wall breakout geometry by traditional models and analysis methods, the present application establishes a calculation method for quickly and accurately simulating the evolution of the stress distribution around the wellbore with the borehole wall breakout geometry of any shape, considering the influence of the non-uniform pore fluid pressure and poroelastic effects around the wellbore, the non-uniform formation temperature change around the wellbore, and the thermoelastic stress on the breakout failure process and stability mechanism, quickly and accurately predicting the maximum horizontal in-situ stress, and providing theoretical guidance and technical support for analyzing the stability and integrity of geological structures and borehole walls and hydraulic fracturing transformation.

[0033] In another exemplary embodiment of the present application, a method for predicting the maximum horizontal in-situ stress based on the borehole wall breakout geometry of any shape is provided, including the following Steps S1 to S5.

[0034] S1: Through borehole logging data, construct a borehole wall breakout geometric model to obtain the curve of the geometric shape parameters of the borehole wall breakout.

[0035] S2. Using the borehole wall breakout geometric model obtained in step S1 and combining with the rock mechanics experimental data, establish a borehole wall strength mechanical model considering the scale effect to obtain the cohesive strength of the rocks in the borehole wall breakout.

[0036] S3. Using the borehole wall breakout geometric model obtained in step S1, establish a semi-analytical calculation mechanical model of coupled temperature-seepage-stress around the borehole to obtain the temperature around the borehole, pore fluid pressure, and total stress field.

[0037] S4. Establish a stress intensity criterion based on the stability mechanical mechanism of borehole wall breakout with arbitrary shape (i.e., the stability stress intensity criterion of borehole wall breakout).

[0038] S5. According to the borehole wall breakout geometric model obtained in step S1, using the cohesive strength of the rocks in the borehole wall breakout obtained in step S2, and the circumferential stress around the borehole (i.e., the total stress field) obtained in step S3, apply the stability stress intensity criterion of borehole wall breakout established in step S4 to establish an inversion model to predict the magnitude and direction of the maximum horizontal in-situ stress.

[0039] In another exemplary embodiment of the present application, the borehole wall logging data includes borehole televiewer observation images and borehole radius logging data. By stacking the borehole televiewer observation images and combining with the borehole radius logging data, identify the borehole wall breakout shape and digitize it to obtain the borehole wall breakout geometric shape represented by a series of discrete points, and the borehole wall breakout geometric shape represented by a series of discrete points is the borehole wall breakout geometric model.

[0040] {(x i ,y i ), i = 1, 2, …, N} (1);

[0041] In the formula: x i is the abscissa of the i-th discrete point on the borehole wall, y i is the ordinate of the i-th discrete point on the borehole wall, and N is the total number of discrete points.

[0042] The determination process of the geometric curvature radius of the borehole wall breakout specifically includes: the borehole wall breakout geometric model is represented by a series of discrete points; using the cubic spline interpolation method, perform curve fitting on the discrete points to obtain the borehole wall breakout geometric curve; calculate the geometric curvature radius of the borehole wall breakout according to the borehole wall breakout geometric curve.

[0043] Perform curve fitting on the discrete points in the obtained borehole wall breakout geometric model using cubic spline interpolation to obtain the analytical expression y(x) of the borehole wall breakout geometric curve:

[0044]

[0045] In the formula: S i (x) is in the interval [x i , x i+1A cubic polynomial on it, where \(i = 1, 2, \ldots, N\). Further calculate the radius of curvature of the borehole wall sloughing geometric curve, denoted as the borehole wall sloughing geometric radius of curvature \(r\). c , and its calculation formula is shown as follows:

[0046]

[0047] In the formula: \(r\) c (x, y) is the radius of curvature at the point (x, y) on the borehole wall sloughing geometric curve, and \(y'\) and \(y''\) respectively represent the first and second derivatives of the borehole wall sloughing geometric curve \(y(x)\) with respect to \(x\).

[0048] In another exemplary embodiment of the present application, the above step 202 is replaced by the following steps 301 to 303.

[0049] Step 301: Obtain the borehole wall strength related to the specimen scale by using the thick-walled cylinder rock mechanics experiment; the borehole wall strength related to the specimen scale is the rock mechanics experiment data.

[0050] Step 302: Establish a borehole wall strength mechanical model considering the scale effect according to the borehole wall sloughing geometric radius of curvature and the borehole wall strength related to the specimen scale, and calculate the borehole wall strength considering the scale effect according to the borehole wall strength mechanical model considering the scale effect.

[0051] Obtain the borehole wall strength related to the specimen scale by using the thick-walled cylinder rock mechanics experiment, and calculate the borehole wall strength considering the scale effect according to the borehole wall sloughing geometric radius of curvature. The calculation formula is:

[0052]

[0053] In the formula: \(\sigma\) θB (x, y) and \(\sigma\) Ref are respectively the local borehole wall strength (the borehole wall strength considering the scale effect) and the reference borehole wall strength; \(r\) c (x, y) is the radius of curvature at the point (x, y) on the borehole wall sloughing geometric curve; \(D\) Ref = 8.47 mm, which is the inner diameter of the reference thick-walled cylinder.

[0054] Step 303: Calculate the cohesive strength of the borehole wall sloughing rock according to the borehole wall strength considering the scale effect by using the Mohr-Coulomb strength criterion.

[0055] Assume that the internal friction angle of the rock remains unchanged. According to the Mohr-Coulomb strength criterion, obtain the cohesive strength of the borehole wall sloughing rock. The calculation formula is:

[0056]

[0057] Where: \(S_0(x, y)\) is the cohesive strength of the rock at the wellbore caving point \((x, y)\), that is, the cohesive strength of the caved wellbore rock; \(\varphi\) is the internal friction angle of the rock.

[0058] The above step 203 may include the following steps 401 to 408.

[0059] Step 401: Using the conformal transformation method, map the wellbore caving geometric model to the unit circle in the mathematical domain plane.

[0060] Using the conformal transformation method, map the wellbore caving geometry in the physical domain to the unit circle in the mathematical domain. The conformal transformation calculation formula is:

[0061]

[0062] Where: \(z\) is the complex number representation of a point in the physical plane, \(x\) and \(y\) are the abscissa and ordinate of the point in the physical plane respectively, \(\zeta\) is the complex number representation of a point in the unit circle domain of the mathematical plane, \(\xi\) and \(\eta\) are the abscissa and ordinate of the point in the unit circle domain respectively. The corresponding unit circle domain polar coordinates are composed of the radial coordinate \(\rho\) and the angular coordinate \(\theta\), \(\omega(\zeta)\) is the transformation function from the unit circle domain to the physical domain, and the transformation coefficient \(c\) k-1 (k = 0, 1, …, n) are complex constants.

[0063] Step 40101: To obtain the transformation coefficient, as Figure 3 shown, take \(m\) first reference points \(\zeta\) k (k = 1, 2, …, m) on the wellbore in the physical plane and the second reference points \(z\) k (k = 1, 2, …, m) on the unit circle circumference in the mathematical plane, where the first reference points \(\zeta\) k are evenly distributed in order, and the second reference points \(z\) k are arbitrarily distributed in order. It is required that the number of points is greater than the number of transformation coefficients, that is, \(m>n + 1\). Without loss of generality, let the fixed reference point \(z_1\) be mapped to \(\zeta_1\). Substitute the \(k\)th first reference point \(\zeta\) k and the \(k\)th second reference point \(z\) k into the conformal transformation calculation formula to obtain the algebraic equations shown in the following formula (8), denoted as an overdetermined linear equation system. Figure 3 Shows the conformal mapping relationship from the unit circle domain to the physical domain. Figure 3 In (a), it is the coordinate system of the unit domain in the mathematical plane and the distribution of the reference points \(\zeta\) k (k = 1, 2, …, m). Figure 3 In (b), it is the coordinate system of the infinite plane with an arbitrarily shaped wellbore in the physical plane domain and the distribution of the corresponding reference points \(z\) k (k = 1, 2, …, m).

[0064] AX = Y (8);

[0065] In the formula:

[0066]

[0067] In the formula: i = 1, 2, …, m - 1; j = 1, 2, …, n; A is the coefficient matrix of the linear equations, a ij , b ij are the corresponding matrix elements; is the angular coordinate of the (i + 1)-th point; Y is the update vector; A i and B i (i = 0, 1, …, n - 1) are respectively the real part and the imaginary part of the transformation coefficient c i .

[0068] Step 40102: Solve the overdetermined linear equations obtained in Step 40101 by using the least squares method to obtain the transformation coefficient vector X:

[0069] X = (A T A) -1 A T Y (13);

[0070] In the formula: the superscripts T and -1 respectively represent matrix transpose and inverse.

[0071] Step 40103: Substitute the first reference point ζ k (k = 1, 2, …, m) defined in Step 40101 and the transformation coefficient vector X obtained in Step 40102 into the conformal transformation calculation formula to obtain the new coordinates of the second reference point z k (k = 2, 3, …, m), and update the coordinates of the second reference point z k by using the following formula (14) to ensure that all the second reference points z k are on the wellbore wall. The coordinate update calculation formula is:

[0072] θ k = tan -1 (y k / x k ) (14);

[0073] r k cosθ k = S(r k sinθ k ) (15);

[0074]

[0075] In the formula: The updated coordinates of the k-th second reference point; S( ) is the analytical expression of the above-mentioned borehole wall sloughing geometric curve, i.e., formula (2); θ k is the angular coordinate of point z k ; r k is the radial coordinate of point z k ; is the abscissa of the updated point ; is the ordinate of the updated point ;

[0076] Step 40104: Calculate the coordinate change amount and replace the coordinates z before the update of the second reference point in step 40101 with the updated coordinates , calculate the update vector Y, and calculate the new transformation coefficient vector X using step 40102. k

[0077] Step 40105: Repeat steps 40102 to 40104 until the following accuracy condition is met:

[0078]

[0079] where: δ is the given error tolerance. When the above accuracy condition is reached, the transformation coefficients A k-1 , B k-1 (k = 1, 2,..., n) are obtained, and A -1 and B -1 are calculated using the following formula;

[0080]

[0081] Furthermore, all transformation coefficients c k-1 = A k-1 + iB k-1 (k = 0, 1, 2,..., n) are obtained. As shown in Figure 4 , it is a set of corresponding conformal transformation coordinate systems on a non-symmetric and irregular borehole wall sloughing geometry and physical domain obtained after conformal transformation of an orthogonal coordinate system ( Figure 4 (a) in) on the unit circle and the unit circular domain to the corresponding ( Figure 4 (b) in).

[0082] Step 402: Using the conformal transformation method and the theory of plane elastic complex variable functions, calculate the stress field of the borehole wall sloughing geometric model under the combined action of the minimum horizontal in-situ stress, the maximum horizontal in-situ stress, the fluid pressure on the borehole wall surface, and the temperature in the far-field boundary, and obtain the stress components of the mathematical plane unit circular domain.

[0083] Using the conformal transformation method and the theory of plane elastic complex variable functions, calculate the minimum horizontal in-situ stress S h and the maximum horizontal in-situ stress S H on the wellbore wall obtained in step 201, the fluid pressure p w on the wellbore surface, and the temperature T w under their combined action. The calculation formulas for the elastic stress components in the mathematical unit circle domain of the plane are as follows:

[0084]

[0085] In the formula: (·)′ represents taking the derivative, represents taking the complex conjugate, represents taking the real part, σ ρρ , are the radial normal stress, circumferential normal stress, and shear stress respectively, is 's first derivative with respect to ζ, ω′(ζ) is (ζ)'s first derivative with respect to ζ, ψ′(ζ) is ψ(ζ)'s first derivative with respect to ζ, β is the angle between the minimum horizontal in-situ stress S h and the x-axis, and ψ0(ζ) are analytic functions on the unit circle domain and can be obtained by solving the wellbore surface boundary conditions according to the standard method of plane elastic complex variable functions. The calculation formula for the wellbore surface boundary conditions is:

[0086]

[0087] In the formula: represents a point on the unit circle; F0(σ) is the stress boundary condition on the unit circle.

[0088] Step 403: Using the conformal transformation method, transform the stress components in the mathematical unit circle domain of the plane to the physical plane domain and calculate the elastic stress field in the physical plane domain.

[0089] Using the conformal transformation method, transform the stress components in the mathematical unit circle domain of the plane obtained in step S31 to the physical plane domain and calculate the elastic stress field in the physical plane domain. The calculation formula is:

[0090]

[0091] In the formula: σ xx , σ yy , σ xy are the normal stress in the x-axis direction, the normal stress in the y-axis direction, and the shear stress in the physical domain respectively.

[0092] Step 404: Using the conformal transformation method and the plane poroelastic complex variable function theory, calculate the steady-state pore fluid pressure within the mathematical plane unit circle domain under the combined action of the pore fluid pressure at the far-field boundary and the pore fluid pressure at the wellbore surface boundary of the wellbore caving geometric model.

[0093] The conformal mapping relationships of the non-uniform pore fluid pressure and temperature boundary conditions between the physical domain and the unit circular ring domain are as Figure 5 shown. Figure 5 (a) and (b) in ∞ are the conformal mapping relationships of the non-uniform pore fluid, temperature and the unit circular ring in the physical plane and the mathematical plane respectively. Using the conformal transformation method and the plane poroelastic complex variable function theory, calculate the steady-state pore fluid pressure within the mathematical plane unit circle domain under the combined action of the far-field boundary pore fluid pressure p ∞ and the wellbore surface boundary pore fluid pressure p w . The calculation formula for the steady-state pore fluid pressure within the mathematical plane unit circle domain is:

[0094]

[0095] In the formula: p f is the pore fluid pressure, p ∞ is the far-field pore fluid pressure boundary, that is, the pore fluid pressure at the far-field boundary of the wellbore.

[0096] Step 405: According to the steady-state pore fluid pressure within the mathematical plane unit circle domain, calculate the poroelastic stress field within the mathematical plane unit circle domain; using the conformal transformation method, transform the poroelastic stress field within the mathematical plane unit circle domain to the physical plane domain (Formula (26)) and calculate the poroelastic stress field on the physical plane domain.

[0097] According to the steady-state pore fluid pressure within the mathematical plane unit circle domain obtained in the above Step 404, calculate the poroelastic stress distribution within the mathematical plane unit circle domain. The calculation formula is:

[0098]

[0099]

[0100] In the formula: λ is the plane poroelastic stress coefficient, α is the Biot-Willis poroelastic coefficient, v is the Poisson's ratio (drained condition), the complex functions Φ(ζ) and Ψ(ζ) are the analytic potential functions on the mathematical plane circular ring domain (ρ ∞ ≤ρ≤1), and the corresponding constant coefficients a j and b l are obtained by solving the stress-free boundary condition equation. The calculation formula for the boundary condition (stress-free boundary condition equation) is:

[0101]

[0102] In the formula: represents the point on the boundary, p f (ρ * = ρ ∞ ) = p ∞ , p f (ρ * = 1) = p w are the pore fluid pressure boundary conditions of the far - field boundary and the well - bore boundary respectively. The above algebraic equations are composed of 4n + 2 independent equations. By solving them simultaneously, 4n + 2 independent coefficients a j and b l (l = -n,...,-1,0,1,…,n) can be uniquely determined. Furthermore, the pore - elastic stress distribution within the mathematical plane unit - circular - ring domain is obtained. Substituting it into the calculation formula of the elastic stress field in the physical - plane domain in step 403, the pore - elastic stress field in the physical - plane domain is obtained.

[0103] Step 406: Using the conformal - transformation method and the theory of plane thermo - elastic complex - variable functions, calculate the steady - state temperature distribution in the mathematical - plane unit - circle domain of the well - bore caving geometric model under the combined action of the far - field boundary formation temperature and the well - bore surface boundary fluid temperature.

[0104] Using the conformal - transformation method and the theory of plane thermo - elastic complex - variable functions, calculate the steady - state temperature distribution in the mathematical - plane unit - circle domain of the well - bore obtained in step 201 under the combined action of the far - field boundary formation temperature T ∞ and the well - bore surface boundary fluid temperature T w . The calculation formula for the steady - state temperature increment in the mathematical - plane unit - circle domain is:

[0105]

[0106] In the formula: is the temperature field, is the increment relative to the far - field temperature.

[0107] Step 407: Calculate the thermo - elastic stress field in the mathematical - plane unit - circle domain according to the steady - state temperature distribution in the mathematical - plane unit - circle domain; use the conformal - transformation method to transform the thermo - elastic stress field in the mathematical - plane unit - circle domain to the physical - plane domain (formula (26)) and calculate the thermo - elastic stress field in the physical - plane domain.

[0108] According to the steady - state temperature increment in the mathematical - plane unit - circle domain obtained in step 406, calculate the thermo - elastic stress distribution in the mathematical - plane unit - circle domain. The calculation formula is:

[0109]

[0110] where: α T is the coefficient of thermal expansion, E is Young's modulus, the complex functions Φ(ζ) and Ψ(ζ) are analytic potential functions in the mathematical plane annulus domain (ρ ∞ ≤ρ≤1), and the corresponding constant coefficients g j and h l are obtained by solving the stress-free boundary condition equation, and the stress-free boundary condition equation is;

[0111]

[0112] where: t(ρ * =ρ ∞ ) = 0, t(ρ * =1) = T w -T ∞ are the far-field boundary temperature increment boundary condition and the wellbore boundary temperature increment boundary condition respectively. The above algebraic equations are composed of 4n + 2 independent equations. By solving them simultaneously, 4n + 2 independent coefficients g j and h l (l = -n,...,-1,0,1,…,n) can be uniquely determined. Furthermore, the thermoelastic stress distribution in the mathematical plane unit annulus domain is obtained. Substituting it into the calculation formula of the elastic stress field in the physical plane domain in step 403, the thermoelastic stress field in the physical plane domain is obtained.

[0113] Step 408: Superimpose the elastic stress field, the poroelastic stress field, and the thermoelastic stress field to obtain the total stress field. Superimpose the elastic stress field obtained in step 403, the poroelastic stress field obtained in step 405, and the thermoelastic stress field obtained in step 407 to obtain the total stress field.

[0114] The above step 204 specifically includes: using the three-dimensional modified Lade strength criterion to establish the wellbore collapse stability stress strength criterion according to the cohesive strength of the wellbore collapse rock.

[0115] Using the three-dimensional modified Lade strength criterion and combining the cohesive strength of the wellbore collapse rock considering the scale effect obtained in step 202, establish the wellbore collapse stability stress strength criterion. The calculation formula of the wellbore collapse stability stress strength criterion is as follows:

[0116]

[0117] I1 = (σ′1 + s a )+(σ′2 + s a )+(σ′3 + s a ) (39);

[0118] I3 = (σ′1 + s a )(σ′2 + s a)(σ′3 + s a ) (40);

[0119] σ′1 = σ1 - αp f σ′2 = σ2 - αp f σ′3 = σ3 - αp f (41);

[0120]

[0121] Where: F ml is the dimensionless failure index, F ml <0 indicates no failure. σ1, σ2, and σ3 are the maximum principal stress, intermediate principal stress, and minimum principal stress respectively. σ′1, σ′2, and σ′3 are the maximum effective principal stress, intermediate effective principal stress, and minimum effective principal stress respectively. The material parameters s a (x, y) and η are determined by the rock internal friction angle φ and the cohesive strength S0(x, y) of the rock caving in the wellbore.

[0122] Based on the wellbore caving geometry obtained in step 201, the mechanical strength of the wellbore scale effect obtained in step S2, and the circumferential stress of the wellbore obtained in step 203, using the wellbore caving stability stress strength criterion established in step 204, an inversion model is established to predict the magnitude and direction of the maximum horizontal in-situ stress.

[0123] The above step 205 may include the following steps 501 to step 502.

[0124] Step 501: Calculate all local minimum curvature radii in the wellbore caving geometry model according to the curvature radius of the wellbore caving geometry.

[0125] According to the analytical formula of the curvature radius of the wellbore caving geometry obtained in step 201 (i.e., formula (3)), calculate all local minimum curvature radii {r c (x i , y i ), i = 1, 2,..., M}, where M is the total number of local minimum curvature radii of the wellbore caving geometry.

[0126] Step 502: According to all local minimum curvature radii, the cohesive strength of the wellbore caving rock, and the total stress field, using the wellbore caving stability stress strength criterion, establish an inversion model to predict the magnitude and direction of the maximum horizontal in-situ stress.

[0127] According to the local minimum curvature radii of the wellbore caving geometry and their positions obtained in step 501, calculate the wellbore strength and total stress at the corresponding positions by the methods of steps 202 and 203 respectively, and using the wellbore caving stability stress strength criterion established in step 204, establish a weighted least squares inversion model to predict the maximum horizontal in-situ stress SH and direction β. The inversion model is a weighted least squares inversion model, and the weighted least squares inversion model is shown as follows:

[0128]

[0129] In the formula: w i > 0 is the weighting coefficient of the stable stress intensity at the i-th local minimum curvature radius of the borehole wall caving geometry. The L-BFGS algorithm is used to solve the above nonlinear optimization problem to obtain the maximum horizontal in-situ stress S H and direction β. The stable mechanical mechanism of borehole wall caving and the prediction model of the maximum horizontal in-situ stress are as Figure 6 shown.

[0130] The present application also provides an application scenario, which applies the above-mentioned method for predicting the maximum horizontal in-situ stress based on the borehole wall caving geometry of any shape. Specifically: The method for predicting the maximum horizontal in-situ stress based on the borehole wall caving geometry of any shape provided in this embodiment can be applied in the scenario of predicting the maximum horizontal in-situ stress. The scenario of predicting the maximum horizontal in-situ stress includes a data acquisition link, a prediction link for the maximum horizontal in-situ stress, and a prediction result output link; the borehole wall logging data enters the prediction link for the maximum horizontal in-situ stress from the data acquisition link, and the prediction results of the magnitude and direction of the corresponding maximum horizontal in-situ stress are obtained and enter the downstream prediction result output link. The method for predicting the maximum horizontal in-situ stress based on the borehole wall caving geometry of any shape provided in this embodiment belongs to the prediction link for the maximum horizontal in-situ stress. Specifically, in the process of the prediction link for the maximum horizontal in-situ stress for the borehole wall logging data, a borehole wall caving geometry model can be constructed based on the borehole wall logging data, a borehole wall strength mechanical model considering the scale effect can be established according to the borehole wall caving geometry model and the rock mechanics experimental data, the cohesive strength of the caved rock of the borehole wall can be obtained, a semi-analytical calculation mechanical model of temperature-seepage-stress coupling around the wellbore can be established by using the borehole wall caving geometry model, the total stress field can be obtained, a stable stress intensity criterion for borehole wall caving can be established, and an inversion model can be established by using the stable stress intensity criterion for borehole wall caving according to the borehole wall caving geometry model, the cohesive strength of the caved rock of the borehole wall, and the total stress field to predict the magnitude and direction of the maximum horizontal in-situ stress.

[0131] The present application can quickly and accurately simulate the stress distribution around the wellbore during the evolution process of the borehole wall caving geometry of any shape, consider the non-uniform pore fluid pressure distribution and the coupled poroelastic effect, the non-uniform formation temperature change and the coupled thermoelastic effect, establish a scale-effect caving strength mechanical model based on the caving stable mechanism, and perform inversion according to the caving geometry of any shape to predict the maximum horizontal in-situ stress, improving the efficiency and accuracy of predicting the maximum horizontal in-situ stress.

[0132] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0133] Specific examples are used in this text to elaborate on the principles and implementation manners of the present application. The description of the above embodiments is only used to help understand the method and its core idea of the present application; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation manners and application scopes. To sum up, the content of this specification should not be construed as a limitation to the present application.

Claims

1. A method for predicting the maximum horizontal in-situ stress based on the geometry of borehole wall breakage of any shape, characterized in that The method for predicting the maximum horizontal in-situ stress based on the borehole wall sloughing geometry of any shape includes: Constructing a borehole wall sloughing geometry model based on borehole logging data; Establishing a borehole wall strength mechanical model considering the scale effect according to the borehole wall sloughing geometry model and rock mechanics experimental data, and obtaining the cohesive strength of the rock for borehole wall sloughing; Using the borehole wall sloughing geometry model to establish a semi-analytical mechanical model for calculating the coupling temperature-seepage-stress around the borehole, and obtaining the total stress field; the total stress field includes an elastic stress field, a poroelastic stress field, and a thermoelastic stress field; Establishing a stability stress intensity criterion for borehole wall sloughing; According to the borehole wall sloughing geometry model, the cohesive strength of the rock for borehole wall sloughing, and the total stress field, using the stability stress intensity criterion for borehole wall sloughing to establish an inversion model to predict the magnitude and direction of the maximum horizontal in-situ stress.

2. The maximum horizontal in-situ stress prediction method based on the geometry of borehole wall breakage of any shape according to claim 1, wherein Establishing a borehole wall strength mechanical model considering the scale effect according to the borehole wall sloughing geometry model and rock mechanics experimental data, and obtaining the cohesive strength of the rock for borehole wall sloughing, specifically including: Obtaining the borehole wall strength related to the specimen scale through thick-walled cylinder rock mechanics experiments; the borehole wall strength related to the specimen scale is rock mechanics experimental data; According to the curvature radius of the borehole wall sloughing geometry and the borehole wall strength related to the specimen scale, establishing a borehole wall strength mechanical model considering the scale effect, and calculating the borehole wall strength considering the scale effect according to the borehole wall strength mechanical model considering the scale effect; Using the Mohr-Coulomb strength criterion to calculate the cohesive strength of the rock for borehole wall sloughing according to the borehole wall strength considering the scale effect.

3. The maximum horizontal in-situ stress prediction method based on the wellbore breakout geometry of any shape according to claim 2, characterized in that, The determination process of the curvature radius of the borehole wall sloughing geometry specifically includes: The borehole wall sloughing geometry model is represented by a series of discrete points; Using the cubic spline interpolation method to perform curve fitting on the discrete points to obtain the borehole wall sloughing geometry curve; Calculating the curvature radius of the borehole wall sloughing geometry according to the borehole wall sloughing geometry curve.

4. The maximum horizontal in-situ stress prediction method based on the geometry of borehole wall breakage of arbitrary shape according to claim 1, wherein, Using the borehole wall sloughing geometry model to establish a semi-analytical mechanical model for calculating the coupling temperature-seepage-stress around the borehole, and obtaining the total stress field, specifically including: Adopting the conformal transformation method to map the borehole wall sloughing geometry model to the unit circle in the mathematical domain plane; Using the conformal transformation method and the plane elastic complex variable function theory to calculate the stress field of the borehole wall sloughing geometry model under the combined action of the minimum horizontal in-situ stress, the maximum horizontal in-situ stress, the fluid pressure on the borehole wall surface, and the temperature at the far-field boundary, and obtaining the stress components in the unit circle domain of the mathematical plane; Using the conformal transformation method to transform the stress components in the unit circle domain of the mathematical plane to the physical plane domain, and calculating the elastic stress field on the physical plane domain; Using the conformal transformation method and the plane poroelastic complex variable function theory to calculate the steady-state pore fluid pressure in the unit circle domain of the mathematical plane of the borehole wall sloughing geometry model under the combined action of the pore fluid pressure at the far-field boundary and the pore fluid pressure at the borehole wall surface boundary; Calculating the poroelastic stress field in the unit circle domain of the mathematical plane according to the steady-state pore fluid pressure in the unit circle domain of the mathematical plane; using the conformal transformation method to transform the poroelastic stress field in the unit circle domain of the mathematical plane to the physical plane domain, and calculating the poroelastic stress field on the physical plane domain; Using the conformal transformation method and the theory of plane thermoelastic complex variable functions, calculate the steady-state temperature distribution in the mathematical plane unit circle domain of the borehole wall sloughing geometric model under the combined action of the far-field boundary formation temperature and the wellbore wall boundary fluid temperature; According to the steady-state temperature distribution in the mathematical plane unit circle domain, calculate the thermoelastic stress field in the mathematical plane unit circle domain; using the conformal transformation method, transform the thermoelastic stress field in the mathematical plane unit circle domain to the physical plane domain, and calculate the thermoelastic stress field on the physical plane domain; Superimpose the elastic stress field, the poroelastic stress field, and the thermoelastic stress field to obtain the total stress field.

5. The maximum horizontal in-situ stress prediction method based on the wellbore breakout geometry of any shape according to claim 1, characterized in that Establish a borehole wall sloughing stability stress intensity criterion, specifically including: Using the three-dimensional modified Lade strength criterion, establish a borehole wall sloughing stability stress intensity criterion according to the cohesive strength of the rocks in the borehole wall sloughing.

6. The maximum horizontal in-situ stress prediction method based on the geometry of borehole wall breakage of any shape according to claim 3, wherein According to the borehole wall sloughing geometric model, the cohesive strength of the rocks in the borehole wall sloughing, and the total stress field, apply the borehole wall sloughing stability stress intensity criterion to establish an inversion model to predict the magnitude and direction of the maximum horizontal in-situ stress, specifically including: According to the geometric curvature radius of the borehole wall sloughing, calculate all the local minimum curvature radii in the borehole wall sloughing geometric model; According to all the local minimum curvature radii, the cohesive strength of the rocks in the borehole wall sloughing, and the total stress field, apply the borehole wall sloughing stability stress intensity criterion to establish an inversion model to predict the magnitude and direction of the maximum horizontal in-situ stress.

7. The maximum horizontal in-situ stress prediction method based on the geometry of borehole wall breakage of any shape according to claim 1, characterized in that, The inversion model is a weighted least squares inversion model.

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