Hydraulic fracturing integrated monitoring and joint inversion method coupling rock deformation and injection and drainage pressure
By constructing a three-dimensional planar multi-resolution parametric model of fractures and a fluid pressure distribution model, and combining multi-source monitoring data, a global optimization method was used to perform hydraulic fracturing inversion, which solved the problem of unreliable fracture inversion results and achieved higher accuracy and reliability.
Patent Information
- Application Number
- CN202511807142.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-03
- Publication Date
- 2026-02-06
AI Technical Summary
In the process of hydraulic fracturing, the accuracy and reliability of the fracture inversion results are low. In particular, due to the mutual influence of fracture direction and shape parameters, the inversion results are unreliable, and the commonly used optimization methods can only obtain local optimal solutions.
A multi-resolution parametric model of a three-dimensional planar crack with arbitrary orientation and shape is constructed. Combined with a fluid pressure distribution model, a semi-analytical forward model of the crack is established. A joint inversion mathematical model is established using multi-source monitoring data and weighted least squares method. A global optimization method is used for inversion.
It improves the accuracy and reliability of hydraulic fracturing parameter inversion results, enables rapid and accurate simulation of cracks of arbitrary direction and shape in a three-dimensional plane, and improves the simulation accuracy of crack-induced deformation and stress.
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Figure CN121473784A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of drilling and completion technology and oil and gas reservoir stimulation and production enhancement technology, and particularly relates to a hydraulic fracturing integrated monitoring and joint inversion method coupling rock deformation and injection and discharge pressure. BACKGROUND
[0002] Hydraulic fracturing technology is one of the key technologies for realizing large-scale and efficient development of unconventional energy. The physical and mechanical properties of unconventional reservoirs such as shale and the in-situ stress usually exhibit strong heterogeneity and anisotropy, natural fracture development and geological structure discontinuity, so that the artificial fracture propagation behavior in the hydraulic fracturing reconstruction process of unconventional reservoirs is significantly different from that of conventional reservoirs, which often leads to complex fracture geometry, and the real fracture geometry is usually much more complex than the expected design or simulation.
[0003] Hydraulic fracturing parameters are characterized by fracture direction and fracture size, and fracture fluid pressure, which jointly affect the rock deformation and fluid response induced by fracturing. The inversion of hydraulic fracturing parameters from the monitoring data of fracturing-induced deformation is a strong nonlinear and coupled inverse problem, and the inversion results of the fracture direction parameters and the inversion results of the fracture shape and size parameters influence each other, while the related inversion method usually first obtains the fracture direction parameters by inversion using a simple fracture model, and then fixes the fracture direction parameters to obtain the fracture shape and size parameters by secondary inversion using a complex fracture model, which leads to poor reliability and interpretability of the inversion results. The fracture inversion problem usually presents a multi-modal characteristic in mathematics, and the commonly used derivative-based optimization method can only obtain a local optimal solution, not a global optimal solution, and the obtained local optimal solution depends on the initial parameter estimation, which further leads to low accuracy and reliability of the hydraulic fracturing parameters in the inversion results. SUMMARY
[0004] The purpose of the present application is to provide a hydraulic fracturing integrated monitoring and joint inversion method coupling rock deformation and injection and discharge pressure, which can improve the accuracy and reliability of the inversion results of hydraulic fracturing parameters.
[0005] To achieve the above-mentioned purpose, the present application provides the following solutions. The present application provides a hydraulic fracturing integrated monitoring and joint inversion method coupling rock deformation and injection and discharge pressure, comprising: constructing a three-dimensional planar fracture multi-resolution parameterized fracture geometry model and a fluid pressure distribution model of an arbitrary direction and shape; constructing a semi-analytical fracture forward calculation mechanics model based on the three-dimensional planar fracture multi-resolution parameterized fracture geometry model and the fluid pressure distribution model of an arbitrary direction and shape; obtaining multi-source monitoring data of fracturing-induced rock deformation and injection and discharge pressure; Based on multi-source monitoring data and semi-analytical fracture forward calculation mechanics model, a multi-source data joint fracture inversion mathematical model is established by using weighted least squares method. Based on the multi-source data joint fracture inversion mathematical model, a global optimization method is used to perform inversion on hydraulic fracturing to obtain the hydraulic fracturing parameters.
[0006] Preferably, constructing the three-dimensional planar fracture multi-resolution parameterized fracture geometry model of arbitrary direction and shape specifically comprises: The orientation of the fracture plane is determined by the strike angle, dip angle and reference point of the fracture; Based on the orientation of the fracture plane, a local rectangular coordinate system of the fracture is determined, and by using the key nodes in the fracture plane, a cubic spline interpolation is used for processing to obtain the parametric spline curve of the front boundary geometry curve of the planar fracture; wherein the coordinates of the key nodes are represented by the local rectangular coordinate system of the fracture; Based on the orientation of the fracture plane, the key nodes and the parametric spline curve, the three-dimensional planar fracture multi-resolution parameterized fracture geometry model of arbitrary direction and shape is obtained.
[0007] Preferably, constructing the fluid pressure distribution model specifically comprises: A bidirectional conformal transformation numerical method is used to map the fracture plane domain surrounded by the parametric spline curve to the mathematical plane unit circle domain to obtain the fluid pressure distribution model; The expression of the fluid pressure distribution model is: ; Wherein, is the fluid pressure acting on the point on the surface of the fracture, is the complex representation of the coordinates of the point on the unit circle domain, is the polar coordinate of the polar coordinate system of the unit circle domain, represents the transformation function from the unit circle domain to the surface of the fracture.
[0008] Preferably, constructing the semi-analytical fracture forward calculation mechanics model based on the three-dimensional planar fracture multi-resolution parameterized fracture geometry model of arbitrary direction and shape and the fluid pressure distribution model specifically comprises: Based on the three-dimensional planar fracture multi-resolution parameterized fracture geometry model of arbitrary direction and shape and the fluid pressure distribution model, a displacement discontinuity method is used to obtain a hypersingular integral equation representing the relationship between the fluid pressure in the fracture and the fracture opening width; The fracture opening width under the given fluid pressure condition is solved by using the hypersingular integral equation; According to the fracture opening width, the semi-analytical fracture forward calculation mechanics model is obtained by using the displacement discontinuity method.
[0009] Preferably, the expression of the hypersingular integral equation is: ; in, For point The net fluid pressure at the location, and These are shear modulus and Poisson's ratio, respectively. For the point The cosine of the normal direction of the crack surface along the first Components in each direction, For the point The cosine of the normal direction of the crack surface along the first Components in each direction, For the integral kernel function, and They are respectively at point The cosine of the normal direction of the crack surface along the first The direction and along the first Components in each direction, For the point The width of the crack opening, The surface of the crack.
[0010] Preferably, the expression for the semi-analytical crack forward model computational mechanics is: ; ; ; ; ; in, For point First Displacement in each direction, and These are shear modulus and Poisson's ratio, respectively. , , and Both are integral kernel functions. and Points Along the first The direction and along the first Each direction corresponds to the crack opening width. The dislocation vector, and They are respectively at point The cosine of the normal direction of the crack surface along the first The direction and along the first Components in each direction, For the surface of the crack, For point The direction of the normal is the first Along the plane in the direction of the first direction Strain in one direction, For point First Rotational deformation in all directions, For point The direction of the normal is the first Along the plane in the direction of the first direction Stress components in each direction, For the point Fiber strain at the location The length of the fiber optic strain gauge. and They are respectively at point The cosine of the fiber axis direction along the first The direction and along the first Components in each direction.
[0011] Preferably, the multi-source monitoring data includes monitoring data of rotational deformation, monitoring data of fiber optic strain, and monitoring data of fluid pressure.
[0012] Preferably, the hydraulic fracturing parameters include fracture direction, fracture size, and fracture fluid pressure.
[0013] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides an integrated monitoring and joint inversion method for hydraulic fracturing that couples rock deformation with injection and drainage pressure. By using a multi-resolution parameterized fracture geometry model and a fluid pressure distribution model of three-dimensional plane fractures of arbitrary orientation and shape, it can quickly and accurately simulate deformation and stress induced by multiple fractures in a three-dimensional plane with arbitrary orientation and shape. Furthermore, considering the coupling effect between fluid pressure distribution within the fracture and fracture geometry, a semi-analytical forward model of fracture computational mechanics is established. Based on this, and taking into account the complementary characteristics of the multi-source responses induced by fracturing, a multi-source data joint fracturing inversion mathematical model is established by combining multi-source monitoring data. A global optimization method is used to solve the inversion problem of hydraulic fracturing, obtaining hydraulic fracturing parameters and improving the accuracy and reliability of the hydraulic fracturing parameter inversion results. Attached Figure Description
[0014] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0015] Figure 1 This is a flowchart illustrating an integrated monitoring and joint inversion method for hydraulic fracturing that couples rock deformation with injection and discharge pressure, provided as an embodiment of this application.
[0016] Figure 2(a) is a schematic diagram of the overall reference coordinate system, the local rectangular coordinate system of the crack, and their relationship with the crack plane.
[0017] Figure 2(b) shows a schematic diagram of the distribution of key nodes on the crack surface and the crack leading edge curve.
[0018] Figure 3 This is a schematic diagram of a bidirectional conformal mapping relationship provided in an embodiment of this application.
[0019] Figure 4 This is a schematic diagram of the spatial distribution of the crack plane, surface inclinometer, downhole inclinometer, and fiber optic strain measurement points provided in an embodiment of this application.
[0020] Figure 5(a) is a schematic diagram showing the comparison between the inversion results of the crack opening width distribution and the crack-induced surface rotation vector and the composite results.
[0021] Figure 5(b) is a schematic diagram comparing the results of the downhole rotation vector inversion and the synthesis results.
[0022] Figure 5(c) is a schematic diagram comparing the fiber strain inversion results and the synthesis results. Detailed Implementation
[0023] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0024] To make the objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0025] The hydraulic fracturing integrated monitoring and joint inversion method that couples rock deformation and injection / discharge pressure provided in this application embodiment, such as Figure 1 As shown, a method for integrated monitoring and joint inversion of hydraulic fracturing coupled with rock deformation and injection / discharge pressure is provided, including steps 101 to 105. Wherein: Step 101: Construct a three-dimensional planar crack multi-resolution parametric crack geometry model and a fluid pressure distribution model with arbitrary orientation and shape.
[0026] Step 102: Construct a semi-analytical forward modeling computational mechanics model of the crack based on a multi-resolution parametric crack geometry model and a fluid pressure distribution model of a three-dimensional planar crack with arbitrary orientation and shape.
[0027] Step 103: Obtain multi-source monitoring data on rock deformation induced by hydraulic fracturing and injection / discharge pressure.
[0028] Step 104: Based on multi-source monitoring data and a semi-analytical fracture forward modeling computational mechanics model, a weighted least squares method is used to establish a multi-source data joint fracturing inversion mathematical model.
[0029] Step 105: Based on the multi-source data joint fracturing inversion mathematical model, the hydraulic fracturing is inverted using a global optimization method to obtain the hydraulic fracturing parameters.
[0030] By implementing steps 101 to 105 above, this application can improve the accuracy and reliability of the hydraulic fracturing parameter inversion results.
[0031] In an exemplary embodiment, step 101, which involves constructing a multi-resolution parametric crack geometry model of a three-dimensional planar crack with arbitrary orientation and shape, specifically includes steps 11-13: Step 11: Determine the orientation of the fracture plane using the crack's strike angle, dip angle, and a reference point. The fracture plane is also called the crack plane.
[0032] Specifically, through the direction angle of the crack Inclination angle Reference points Define the orientation of the fracture plane in a semi-infinite space, and define a local rectangular coordinate system for the fracture based on the fracture plane. , Let O be the origin of the local coordinate system. and These are the coordinate axes along the dip angle and strike angle directions within the crack plane, respectively. The coordinate axes are along the normal direction of the crack plane. Figure 2(a) shows the global reference coordinate system. o-xyz Coordinate system), local rectangular coordinate system of the crack and its relationship with the crack plane.
[0033] Step 12: Determine the local rectangular coordinate system of the crack based on the orientation of the fracture plane, and use cubic spline interpolation to process the key nodes in the fracture plane to obtain the parametric spline curve of the geometric curve of the leading edge boundary of the planar crack; wherein, the coordinates of the key nodes are represented by the local rectangular coordinate system of the crack.
[0034] At the fracture plane Internal definition Key Nodes The key node is in the local coordinate system of the crack. The coordinates in the middle are: , In the formula, and Key nodes Polar and angular coordinates within the fracture plane.
[0035] As shown in Figure 2(b), the angular coordinates of the key nodes are uniformly distributed in this embodiment, therefore the shape and size of the crack are determined by the parameters. Sure.
[0036] At key nodes, cubic parametric spline interpolation is performed on the fracture plane to define a simple, closed, smooth curve representing the crack front, thus obtaining the analytical expression of the cubic parametric spline curve of the planar crack front boundary geometry: (2) In the formula: For the dimensionless cumulative chord length parameter, The division of the parametric axis satisfies parametric spline curve It is an interval A cubic polynomial satisfies the following continuity and periodicity end boundary conditions: In the formula, For parametric spline curves At key junctures The value, and They are respectively The first and second derivatives, equation (3) forms A set of independent algebraic equations, which can uniquely determine the [missing information] by solving the set of algebraic equations. coefficients 、 、 、 This leads to the parametric spline curve. The parsing expression.
[0037] Step 13: Based on the orientation of the fracture plane, key nodes, and parametric spline curves, obtain a three-dimensional planar crack multi-resolution parametric crack geometry model with arbitrary orientation and shape.
[0038] For the case of multiple cracks, repeat steps 11-13 above to obtain multiple three-dimensional planar crack multi-resolution parametric crack geometric models with arbitrary directions and shapes. Figure 2(b) shows the crack leading edge curve obtained by key nodes on the crack surface and cubic spline interpolation, which is the parametric spline curve.
[0039] Step 101, which involves constructing the fluid pressure distribution model, specifically includes steps 21-23: A two-way conformal numerical method is used to map the fracture plane domain enclosed by parametric spline curves to the mathematical plane unit circle domain, thus obtaining a fluid pressure distribution model. For example... Figure 3 As shown, this embodiment uses the Zipper algorithm to calculate the bidirectional conformal transformation mapping relationship.
[0040] The numerical calculation formula for bidirectional conformal transformation is as follows: (4) (5) (6) In the formula: For imaginary numbers, Let be the complex number representation of the coordinates of a point within the crack surface. Let be the complex number representation of the coordinates of a point on the unit circle. and Let x and y be the x and y coordinates of a point on the unit circle, respectively. The polar coordinates are those of the unit circle polar coordinate system. The angular coordinates are in the polar coordinate system of the unit circle domain. This represents the transformation function that maps from the crack surface to the unit circle domain. This represents the transformation function that maps from the unit circle domain to the crack surface.
[0041] Considering the quasi-steady-state hydraulic fracturing propagation behavior, based on the hydraulic fracturing mechanics theory, it is assumed that the fluid pressure within a unit circular region is only in polar coordinates. The function, with angular coordinates Regardless, based on the conformal transformation numerical calculation formula, the expression for the fluid pressure distribution function acting on the crack surface is: (7) in, For the point acting on the crack surface Fluid pressure at the location, A point on the unit circle.
[0042] In an exemplary embodiment, step 102 includes steps 31-33: Step 31: Based on the three-dimensional planar crack multi-resolution parameterized crack geometry model and fluid pressure distribution model with arbitrary orientation and shape, the displacement discontinuity method is used to obtain the hypersingular integral equation characterizing the relationship between fluid pressure in the crack and crack opening width.
[0043] Specifically, considering a semi-infinite isotropic elastic body, based on the displacement discontinuity method, a hypersingular integral equation characterizing the relationship between fluid pressure within a crack and crack opening width is obtained, and its expression is: (8) get: (9) In the formula: For point Net pressure of the fluid at the point of application For point Fluid pressure at the location, For point The compressive stress in the normal direction acting on the surface of the crack (including geostress and other crack-induced stresses). and These represent shear modulus and Poisson's ratio, respectively. For the point The cosine of the normal direction of the crack surface along the first Components in each direction, For the point The cosine of the normal direction of the crack surface along the first Components in each direction, For the point The cosine of the normal direction of the crack surface along the first Components in each direction, For the point The cosine of the normal direction of the crack surface along the first Components in each direction, For the point The width of the crack opening, The integral region is the crack surface.
[0044] In this embodiment, the upper and lower indicators 、 、 、n All are tensor indices. By convention, unless otherwise stated, the value range of tensor indices is [missing information]. Where 1, 2, and 3 represent the coordinates in the global reference coordinate system, respectively. Axial direction, Axial direction and Axial direction.
[0045] This hypersingular integral equation follows Einstein's summation convention, and the integral kernel function... The expression is: (10) (11) In the formula: For tensor indices and The Kronecker function, Indicates at point The direction of the normal is the first The surface acting along the direction of the first direction When a unit dislocation occurs in one direction at a point The direction of the normal generated at point is the first Along the surface in the direction of the first direction Stress in each direction, , and In the superscript ",", it means to take the differential about the corresponding coordinate axis, so we have formula (11).
[0046] Integral kernel function The expression is: (12) In the formula, Indicates at point The first one along the edge The magnitude of the directional effect is The force at point The first generated at the place Displacement in each direction, Indicates at point Along the first The magnitude of the effect in each direction is The force at point The first generated at the place Displacement in each direction; Indicates at point Along the first The magnitude of the effect in each direction is The force at point The first generated at the place Displacement in each direction; Indicates at point No. Coordinates in each direction, Indicates at point No. Coordinates in each direction, Indicates at point No. Coordinates in each direction, Indicates at point The magnitude of the effect is , direction perpendicular to When a planar force dipole is at a point The first generated at the place Displacement in each direction.
[0047] Step 32: Solve for the crack opening width under given fluid pressure conditions using the hypersingular integral equation.
[0048] Step 33: Based on the crack opening width, obtain the semi-analytical crack forward model computational mechanics using the displacement discontinuity method. The expression for the semi-analytical crack forward model computational mechanics is: (13) (14) , (15) (16) (17) in, For point The first Displacement in direction, and These are shear modulus and Poisson's ratio, respectively. , , and Both are integral kernel functions. and Points Along the first The direction and along the first Each direction corresponds to the crack opening width. The dislocation vector, i.e. , , and They are respectively at point The cosine of the normal direction of the crack surface along the first The direction, the first The direction and along the first Components in each direction, For the surface of the crack, For point The direction of the normal is the first Along the plane in the direction of the first direction Strain in one direction, For point The first Rotational deformation of direction For point The direction of the normal is the first Along the plane in the direction of the first direction Stress components in each direction, For the point Fiber strain at the location The length of the fiber optic strain gauge. and They are respectively at point The cosine of the fiber axis direction along the first The direction and along the first Components in each direction, upper and lower indicators , , , , All are tensor indices. By convention, unless otherwise stated, the value range of tensor indices is [missing information]. Where 1, 2, and 3 represent the coordinates in the global reference coordinate system, respectively. Axial direction, Axial direction and Axial direction.
[0049] Integral kernel function and The expressions are as follows: (18) (19) In the formula, Indicates at point The direction of the normal is the first The surface acting along the direction of the first direction The unit of displacement in direction at point The direction of the normal generated at point is the first Along the surface in the direction of the first direction Strain in one direction, Indicates at point The direction of the normal is the first The surface acting along the direction of the first direction When a unit dislocation occurs in one direction at a point The first generated at the place Rotational deformation in all directions.
[0050] In an exemplary embodiment, step 103 specifically includes: using integrated multiple monitoring technologies to perform fracturing monitoring and obtain multi-source monitoring data; wherein, the multiple monitoring technologies include inclinometer technology, fiber optic technology, and pressure diagnostic technology.
[0051] In practical applications, on-site monitoring is conducted to obtain multi-source monitoring data, including monitoring data of rotational deformation, fiber optic strain, and fluid pressure. The obtained multi-source monitoring data is then used for subsequent inversion. However, in this embodiment, simulated values of the multi-source monitoring data are used for inversion. The semi-analytical fracture forward model constructed above is used to perform forward modeling of hydraulic fracturing. Based on the forward modeling results, simulated values of the multi-source monitoring data are obtained by superimposing random noise.
[0052] The parameters involved in this embodiment are shown in Table 1. Figure 4 The spatial distribution of the fracture plane, surface inclinometer, downhole inclinometer, and fiber optic strain measurement points in this embodiment is shown. This embodiment considers observation of a single near-horizontal fracture and a vertical well. However, the method of this application is not limited by the fracture direction or the direction and location of the observation well. The fracture can be a vertical fracture or a fracture with arbitrary spatial orientation, and the fiber optic observation well can be an inclined well or a horizontal well.
[0053] Table 1
[0054] The forward modeling process of hydraulic fracturing specifically includes steps 41-42: Step 41: Discretize the crack surface defined in step 201 into M uniform rectangular elements, as shown in Figure 2(b). Each element... m The crack opening width and the net fluid pressure acting on the element are uniformly distributed. Using the collocation method, the hypersingular integral equation is transformed into an algebraic equation through numerical integration. The discrete algebraic equation is expressed as: (20) In the formula: For the point The net fluid pressure of the unit, and They represent the first The first point and the second Coordinates of each point, pressure coefficient matrix It consists of two parts: a regular part and a hypersingular part. The regular part is calculated using conventional numerical integration, while the hypersingular part is calculated using the following finite part integral analytical expression: (twenty one) In the formula: ， ， ， , and These are the elements along the coordinate axes. and Length in direction, The coordinates of the center of any element within the crack surface are represented by the equation (20). The algebraic equation system is obtained by solving the algebraic equation system to obtain the crack opening width.
[0055] Step 42: Based on the crack opening width obtained in Step 41, substitute it into the expression obtained in Step 33 to calculate the crack-induced rotational deformation and fiber strain. The expression is as follows: (twenty two) (twenty three) In the formula: At point Along the first Rotational deformation of direction At point Fiber strain at the location This is the matrix of rotational deformation influence coefficients. This represents the fiber strain influence coefficient.
[0056] Rotational Deformation Influence Coefficient Matrix and fiber strain influence coefficient They are calculated using the following formulas respectively: (twenty four) (25) In the formula: and Calculated according to equation (19), Calculate according to equation (18).
[0057] In an exemplary embodiment, step 104 specifically includes steps 51-52: Step 51, Define the crack model parameter vector Monitoring data vector Crack model parameter vector This includes all parameters in the 3D planar multi-resolution parametric fracture geometry model and fluid pressure distribution model of arbitrary orientation and shape constructed in step 201, namely hydraulic fracturing parameters, specifically fracture direction, fracture size, and fracture fluid pressure, and monitoring data vectors. This includes monitoring data for rotational deformation, fiber optic strain, and fluid pressure, with the following defined formulas: (26) (27) In the formula: the superscript "T" indicates transpose. and Representing the number of crack size parameters and The number of fluid pressure parameters, , and These represent monitoring data for rotational deformation, fiber optic strain, and fluid pressure, respectively. , and These represent the number of monitoring data points for rotational deformation, fiber optic strain, and fluid pressure, respectively.
[0058] In this embodiment, the monitoring array includes 30 surface inclinometers, 10 downhole inclinometers, 30 fiber optic strain measurement points, and 1 fluid pressure measurement point. Each inclinometer measures two components, therefore the corresponding number of monitoring data is: , , .
[0059] In this embodiment, random noise is superimposed on the crack forward modeling results in steps 41-42 to obtain the simulated values of multi-source monitoring data, which is the synthetic monitoring data, for joint inversion analysis.
[0060] Step 52: Discretize the semi-analytical fracture forward modeling computational mechanics model. Based on the discretized semi-analytical fracture forward modeling computational mechanics model, establish a multi-source data joint fracturing inversion mathematical model using the weighted least squares method. Its expression is: (28) (29) In the formula: To optimize the objective function, the model operator matrix The coefficient matrix defined in steps 41 and 42 、 and The covariance matrix of the monitoring data was calculated. Calculated based on measurement data, This represents the total number of parameters in the crack model. and They represent the first Crack model parameters The lower and upper bounds.
[0061] In an exemplary embodiment, step 105 specifically includes steps 61-65: Step 61, Initialization: Define the population size as... The Replacement crack model parameter vector The group of model parameters is as follows: (30) Population size The total number of model parameter vectors in the population remains constant during evolution. Given the model parameter vector search space, the initial generation... No. The first crack model parameter vector Each component is randomly generated within a given boundary, and the calculation formula is as follows: (31) In the formula: Generate a value for each crack model parameter. Random numbers that are uniformly distributed within a range.
[0062] Step 62, Mutation: By combining three different, randomly selected crack model parameter vectors , , and Generate a mutation vector , The calculation formula is as follows: (32) Where: scaling factor It is a positive real number used to control the evolutionary rate of the population; it is a vector index index. 、 and From the scope Randomly selected indexes that are distinct from each other and different from the mutation vector. ,Right now .
[0063] Step 63, Crossover: By crossing the mutated vectors With the target vector Cross-generating test vectors The calculation formula is: (33) Where: crossover probability Control the proportion of crack model parameter values copied from the mutation vector. It is an index indicator randomly selected from the mutation vector.
[0064] Step 64, Select: If the experimental vector The corresponding objective function value is better than its objective vector. The corresponding objective function value is updated by differential evolution by replacing the objective vector with the trial vector; otherwise, the objective vector remains unchanged in the population. The selection process is calculated using the following formula: (34) In the formula: To optimize the objective function.
[0065] Step 65: Repeat steps 62-64 until the set termination condition is met, and obtain the optimal crack model parameter vector. .
[0066] Table 2 compares the inversion results of single monitoring technology and integrated monitoring, as well as the joint inversion results under different synthetic data noise levels. In Table 2, 、 、 、 These represent the standard deviations of monitoring data from surface inclinometers, downhole inclinometers, fiber optic strain gauges, and fluid pressure gauges, respectively. The volume of the fracture is represented by the inversion result. The results show that compared with the single monitoring technology, the integrated monitoring and joint inversion prediction of fracture parameters are more accurate and reliable. Figure 5(a) is a schematic diagram comparing the inversion results and the composite results of the fracture opening width distribution and the fracture-induced surface rotation vector. The red arrow represents the composite surface rotation vector, and the blue arrow represents the inverted surface rotation vector. The moiré pattern represents the fracture opening width distribution. The irregular circular black solid line and black dashed line distribution represent the inverted fracture front and the composite fracture front. The color scale and value on the right side of Figure 5(a) represent the fracture opening width value corresponding to the color. Figure 5(b) is a schematic diagram comparing the downhole rotation vector inversion results and the composite results. Figure 5(c) is a schematic diagram comparing the fiber strain inversion results and the composite results.
[0067] Table 2
[0068] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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, they should be considered to be within the scope of this specification.
[0069] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.
Claims
1. A method for integrated monitoring and joint inversion of hydraulic fracturing coupled with rock deformation and injection / discharge pressure, characterized in that, include: Construct multi-resolution parametric crack geometry models and fluid pressure distribution models for three-dimensional planar cracks of arbitrary orientation and shape; A semi-analytical forward modeling computational mechanics model of cracks is constructed based on a multi-resolution parametric crack geometry model and a fluid pressure distribution model of three-dimensional planar cracks with arbitrary orientation and shape. Acquire multi-source monitoring data on fracturing-induced rock deformation and injection / discharge pressure; Based on multi-source monitoring data and a semi-analytical fracture forward modeling computational mechanical model, a weighted least squares method is used to establish a joint fracturing inversion mathematical model for multi-source data. Based on a multi-source data joint fracturing inversion mathematical model, a global optimization method is used to invert hydraulic fracturing and obtain hydraulic fracturing parameters.
2. The integrated monitoring and joint inversion method for hydraulic fracturing coupled with rock deformation and injection / discharge pressure as described in claim 1, characterized in that, Constructing a multi-resolution parametric crack geometry model for 3D planar cracks of arbitrary orientation and shape specifically includes: The orientation of the fracture plane is determined by the direction angle, dip angle, and reference point of the crack. The local rectangular coordinate system of the crack is determined based on the orientation of the fracture plane, and the parametric spline curve of the geometric curve of the leading edge boundary of the planar crack is obtained by using cubic spline interpolation with the key nodes in the fracture plane; wherein the coordinates of the key nodes are represented by the local rectangular coordinate system of the crack. Based on the orientation of the fracture plane, key nodes, and parametric spline curves, a multi-resolution parametric crack geometry model of a three-dimensional planar crack with arbitrary orientation and shape is obtained.
3. The integrated monitoring and joint inversion method for hydraulic fracturing coupled with rock deformation and injection / discharge pressure as described in claim 2, characterized in that, Constructing a fluid pressure distribution model specifically includes: A two-way conformal transformation numerical method is used to map the fracture plane domain enclosed by the parametric spline curve to the mathematical plane unit circle domain to obtain the fluid pressure distribution model. The expression for the fluid pressure distribution model is: ； in, For the point acting on the crack surface Fluid pressure at the location, Let be the complex number representation of the coordinates of a point on the unit circle. The polar coordinates are those of the unit circle polar coordinate system. This represents the transformation function that maps from the unit circle domain to the crack surface.
4. The hydraulic fracturing inversion method based on a multi-source data joint fracturing inversion mathematical model according to claim 1, characterized in that, The semi-analytical forward modeling computational mechanics model of cracks is constructed based on a multi-resolution parametric crack geometry model and a fluid pressure distribution model of three-dimensional planar cracks with arbitrary orientation and shape. Specifically, this includes: Based on a multi-resolution parametric crack geometry model and fluid pressure distribution model of a three-dimensional planar crack with arbitrary orientation and shape, the displacement discontinuity method is used to obtain a supersingular integral equation characterizing the relationship between fluid pressure and crack opening width within the crack. Solving for the crack opening width under given fluid pressure conditions using hypersingular integral equations; Based on the crack opening width, a semi-analytical forward model of the crack is obtained using the displacement discontinuity method.
5. The hydraulic fracturing inversion method based on a multi-source data joint fracturing inversion mathematical model according to claim 4, characterized in that, The expression for the hypersingular integral equation is: ； in, For point The net fluid pressure at the location, and These are shear modulus and Poisson's ratio, respectively. For the point The cosine of the normal direction of the crack surface along the first Components in each direction, For the point The cosine of the normal direction of the crack surface along the first Components in each direction, For the integral kernel function, and They are respectively at point The cosine of the normal direction of the crack surface along the first The direction and along the first Components in each direction, For the point The width of the crack opening, The surface of the crack.
6. The hydraulic fracturing inversion method based on a multi-source data joint fracturing inversion mathematical model according to claim 4, characterized in that, The expression for the semi-analytical crack forward model computational mechanics is as follows: ； ； ； ； ； in, For point First Displacement in each direction, and These are shear modulus and Poisson's ratio, respectively. , , and Both are integral kernel functions. and Points Along the first The direction and along the first Each direction corresponds to the crack opening width. The dislocation vector, and They are respectively at point The cosine of the normal direction of the crack surface along the first The direction and along the first Components in each direction, For the surface of the crack, For point The direction of the normal is the first Along the plane in the direction of the first direction Strain in one direction, For point First Rotational deformation in all directions, For point The direction of the normal is the first Along the plane in the direction of the first direction Stress components in each direction, For the point Fiber strain at the location, The length of the fiber optic strain gauge and They are respectively at point The cosine of the fiber axis direction along the first The direction and along the first Components in each direction.
7. The integrated monitoring and joint inversion method for hydraulic fracturing coupled with rock deformation and injection / discharge pressure as described in claim 1, characterized in that, The multi-source monitoring data includes monitoring data of rotational deformation, monitoring data of fiber optic strain, and monitoring data of fluid pressure.
8. The integrated monitoring and joint inversion method for hydraulic fracturing coupled with rock deformation and injection / discharge pressure as described in claim 1, characterized in that, Hydraulic fracturing parameters include fracture direction, fracture size, and fracture fluid pressure.