Nonlinear inversion method for hydraulic fracture geometry parameters

Abstract

The application discloses a hydraulic fracture geometric parameter nonlinear inversion method, which comprises the following steps: a strain analytical model is established according to preset mechanical parameters; a fracture parameter nonlinear inversion model is established according to the established strain analytical model and axial strain observation data obtained by a low-frequency DAS system under a neighboring well monitoring scene; a global optimal inversion is solved by using a nonlinear least square iteration algorithm according to preset constraint conditions and the fracture parameter nonlinear inversion model, and a fracture height, a fracture height asymmetric offset and a net pressure are obtained by inversion; and a maximum fracture width is calculated according to the obtained fracture height and net pressure.

Description

Technical Field

[0001] This invention relates to the field of oil and gas field development technology, and in particular to an inversion method for nonlinear geometric parameters of hydraulic fractures. Background Technology

[0002] With the deepening development of unconventional oil and gas resources, distributed fiber optic strain monitoring (DAS) technology based on adjacent wells has become a key means for real-time diagnosis of fracture propagation morphology during hydraulic fracturing. This technology, through optical fibers deployed in monitoring wells, can continuously acquire strain field data induced by fracturing with high spatial resolution, offering significant advantages such as accurate monitoring and positioning, and comprehensive information dimensions. In particular, low-frequency DAS (LF-DAS) monitoring captures strain signals with a clear physical correspondence to the opening and closing processes of fractures, providing an effective approach for fine-grained cross-well fracture diagnosis in the current fracturing context.

[0003] However, despite the abundance of DAS (Digital Angiography and Surgery) data, existing interpretation and inversion methods based on this technology still have significant limitations. On the one hand, most methods fail to achieve direct and synchronous quantitative inversion of the two core parameters defining fracture geometry, fracture width w and fracture height h. They typically can only estimate one of the parameters indirectly or stepwise, or rely on strong simplification assumptions. This severely restricts the accuracy and efficiency of fracture diagnosis and makes it difficult to meet the needs of real-time optimization of fracturing processes in the field.

[0004] On the other hand, under actual reservoir conditions, influenced by factors such as interlayer stress differences, lithological interfaces, and natural fractures, hydraulic fractures often exhibit asymmetry during vertical propagation. This means the geometric center of the fracture shifts along the fracture height, denoted as y. This parameter is a key indicator for evaluating whether a fracture has broken through a barrier and effectively connected to the target reservoir, directly impacting the accurate assessment of the fracturing volume (SRV). However, most existing fracture diagnosis models and methods do not incorporate the asymmetric fracture height shift y into their inverse parameter systems, resulting in a blind spot in the evaluation of vertical fracture propagation behavior and potentially leading to erroneous judgments about fracturing effectiveness.

[0005] Therefore, current mainstream DAS-based crack diagnosis methods not only struggle to directly, synchronously, and efficiently invert crack geometric parameters, but also tend to make incorrect judgments about the fracturing effect.

[0006] The above content is only used to help understand the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention

[0007] The main objective of this invention is to provide an inversion method for the nonlinear geometric parameters of hydraulic fractures, which aims to solve or partially solve the above-mentioned problems.

[0008] To achieve the above objectives, the present invention provides an inversion method for the nonlinear geometric parameters of hydraulic fractures, characterized by comprising:

[0009] Based on the preset mechanical parameters, a strain analytical model is established;

[0010] Based on the established strain analytical model and the axial strain observation data obtained by the low-frequency DAS system in the adjacent well monitoring scenario, a nonlinear inversion model of fracture parameters is established.

[0011] A nonlinear least squares iterative algorithm is used to solve the global optimal inversion based on the preset constraints and the nonlinear inversion model of crack parameters, and the inversion results in crack height, crack height asymmetric offset and net pressure.

[0012] The maximum seam width is calculated based on the obtained seam height and net pressure.

[0013] Preferably, in the inversion method for the nonlinear geometric parameters of the hydraulic fracture, the step of establishing a strain analytical model based on preset mechanical parameters includes:

[0014] Based on the preset Young's modulus and Poisson's ratio, the following analytical strain model is established:

[0015] ;

[0016] ;

[0017] in, The normal strain is perpendicular to the crack surface.

[0018] The normal stress is perpendicular to the crack surface.

[0019] The normal stress is parallel to the crack surface.

[0020] The normal stress is perpendicular to the plane of the two-dimensional model.

[0021] E is Young's modulus;

[0022] This is the analytical solution of the strain corresponding to a certain measuring point, i.e., the theoretically calculated value;

[0023] ν is Poisson's ratio.

[0024] Preferably, in the inversion method for the nonlinear geometric parameters of the hydraulic fracture, the following strain analytical model is established based on the preset Young's modulus and Poisson's ratio, including:

[0025] Establish the first relationship between the distance between the fiber optic measuring point and the critical point of the crack, and the second relationship between the azimuth angle between the fiber optic measuring point and the critical point of the crack.

[0026] Based on the first relation, determine the distance between the fiber measuring point and the lower tip of the crack, and the distance between the fiber measuring point and the upper tip of the crack, respectively.

[0027] Based on the second relation, determine the azimuth angle of the fiber measuring point at the lower tip of the crack and the azimuth angle of the fiber measuring point at the upper tip of the crack, respectively.

[0028] Based on the determined distances between the fiber optic measuring point and the lower tip of the crack, the distance between the fiber optic measuring point and the upper tip of the crack, the azimuth angle of the fiber optic measuring point at the lower tip of the crack, and the azimuth angle of the fiber optic measuring point at the upper tip of the crack, the first intermediate stress function and the second intermediate stress function are determined. The first intermediate stress function characterizes the overall stress distribution around the crack and in the far field, while the second intermediate stress function characterizes the stress singularity behavior near the upper and lower tips of the crack and reflects the key local geometric features of the crack.

[0029] Based on the first intermediate stress function and the second intermediate stress function, the in-plane normal stress components are calculated. The in-plane normal stress components include normal stress perpendicular to the crack surface, normal stress parallel to the crack surface, and normal stress perpendicular to the plane of the two-dimensional model.

[0030] Based on the normal stress perpendicular to the crack surface, the normal stress parallel to the crack surface, and the normal stress perpendicular to the plane of the two-dimensional model, determine the normal strain perpendicular to the plane of the two-dimensional model, the normal strain parallel to the crack surface, and the normal strain perpendicular to the crack surface.

[0031] Preferably, in the inversion method for the nonlinear geometric parameters of the hydraulic fracture, the first relationship is:

[0032] ;

[0033] The second relation is:

[0034] ;

[0035] The distance between the fiber optic measuring point and the lower tip of the crack is:

[0036] ;

[0037] The distance between the fiber optic measuring point and the tip of the crack is:

[0038] ;

[0039] The azimuth angle of the fiber optic measuring point at the lower tip of the crack is:

[0040] ;

[0041] The azimuth angle of the fiber optic measuring point at the tip of the crack is:

[0042] ;

[0043] The first intermediate stress function is:

[0044] ;

[0045] The second intermediate stress function is:

[0046] ;

[0047] The formula for calculating the normal stress perpendicular to the crack surface is:

[0048] ;

[0049] The formula for calculating the normal stress parallel to the crack surface is:

[0050] ;

[0051] The formula for calculating the normal stress perpendicular to the plane of the two-dimensional model is:

[0052] ;

[0053] The formula for calculating the normal strain perpendicular to the plane of the two-dimensional model is:

[0054] ;

[0055] The formula for calculating the normal strain parallel to the crack surface is:

[0056] ;

[0057] The formula for calculating the normal strain perpendicular to the crack surface is:

[0058] ;

[0059] L is the distance between the optical fiber measuring point and the center of the crack;

[0060] z represents the coordinate of the fiber optic measuring point in the crack width direction within a coordinate system with the crack center as the origin;

[0061] y is the coordinate of the fiber optic measuring point in the direction of the crack height in the coordinate system with the crack center as the origin, that is, the asymmetric offset of the crack height.

[0062] L1 is the distance between the optical fiber measuring point and the lower tip of the crack;

[0063] h is the crack height;

[0064] L2 is the distance between the optical fiber measuring point and the tip of the crack;

[0065] θ is the azimuth angle of the fiber optic measuring point relative to the center of the crack;

[0066] θ1 is the azimuth angle of the fiber optic measuring point relative to the lower tip of the crack;

[0067] θ2 is the azimuth angle of the fiber optic measuring point relative to the tip of the crack;

[0068] p is the net pressure inside the crack;

[0069] This is the first intermediate stress function;

[0070] This is the second intermediate stress function;

[0071] The normal stress is perpendicular to the crack surface.

[0072] The normal stress is parallel to the crack surface.

[0073] The normal stress is perpendicular to the plane of the two-dimensional model.

[0074] Poisson's ratio;

[0075] The normal strain is perpendicular to the plane of the two-dimensional model.

[0076] E is Young's modulus;

[0077] The normal strain is parallel to the crack surface.

[0078] The normal strain is perpendicular to the crack surface.

[0079] Preferably, in the nonlinear inversion method for the geometric parameters of hydraulic fractures, the nonlinear inversion model for fracture parameters, established based on the established strain analytical model and the axial strain observation data obtained by the low-frequency DAS system in the adjacent well monitoring scenario, is as follows:

[0080] ;

[0081] Where n is the number of fiber optic measurement points;

[0082] This is the i-th fiber optic strain monitoring data;

[0083] This is the analytical solution of the strain corresponding to the i-th measuring point, i.e., the theoretically calculated value;

[0084] || is an operator.

[0085] Preferably, in the nonlinear inversion method for the geometric parameters of the hydraulic fracture, the step of using a nonlinear least squares iterative algorithm to solve for the global optimal inversion based on preset constraints and the nonlinear inversion model of the fracture parameters, and obtaining the fracture height, the asymmetric offset of the fracture height, and the net pressure, has the following constraints:

[0086] ;

[0087] w represents the crack width;

[0088] w max The maximum crack width;

[0089] p is the net pressure inside the crack;

[0090] p max This represents the maximum net pressure within the crack.

[0091] y represents the asymmetric offset of the seam height;

[0092] h is the seam height;

[0093] h max This is the maximum seam height.

[0094] Preferably, in the inversion method for the nonlinear geometric parameters of the hydraulic fracture, the calculation formula in the step of calculating the maximum fracture width based on the obtained fracture height and net pressure includes:

[0095] The distribution function of the opening displacement w(y) on the crack surface is:

[0096] ;

[0097] The maximum seam width is obtained at the center where y=0:

[0098] .

[0099] The present invention has at least the following beneficial effects:

[0100] This invention establishes a strain analytical model based on preset mechanical parameters; based on the established strain analytical model and axial strain observation data acquired by a low-frequency DAS system in a neighboring well monitoring scenario, a nonlinear inversion model of fracture parameters is established; using a nonlinear least squares iterative algorithm, based on preset constraints and the nonlinear inversion model of fracture parameters, the global optimal inversion is solved to obtain the fracture height, fracture height asymmetric offset, and net pressure; based on the obtained fracture height and net pressure, the maximum fracture width is calculated. Thus, by simultaneously considering the fracture geometric parameters (fracture height), location parameters (fracture height asymmetric offset y), and mechanical parameters (pressure p), and determining the quantitative relationship with the formation strain field, w can be simultaneously determined through a single coupled solution. max The method, along with h, fundamentally overcomes the inherent defects of traditional step-by-step or indirect inversion methods, such as low efficiency and the gradual propagation and amplification of errors; it significantly improves the accuracy and computational efficiency of the integrated interpretation of crack size and spatial distribution.

[0101] Furthermore, by introducing the asymmetric offset y of the fracture height as a key variable into the hydraulic fracture parameter inversion system, the vertical offset of the fracture geometric center is directly quantified, enabling precise characterization of the asymmetric propagation behavior of fractures influenced by stress barriers or lithological interfaces. The inversion results are of irreplaceable importance for objectively evaluating whether fractures effectively connect to the target producing layer and accurately calculating the effective stimulation volume, filling the evaluation blind spot of existing diagnostic methods in this dimension.

[0102] Furthermore, compared to the distributed inversion of various parameters, the present invention simultaneously inverts the crack height and maximum crack width, thereby improving the accuracy and efficiency of crack diagnosis. Attached Figure Description

[0103] Figure 1 A schematic diagram of the inversion method for nonlinear geometric parameters of hydraulic fractures provided by the present invention;

[0104] Figure 2 A graph showing the relationship between joint height h and construction time t;

[0105] Figure 3 For the asymmetric offset of seam height A graph showing the relationship between the curve and the construction time t;

[0106] Figure 4 This is a graph showing the relationship between net pressure p and construction time t.

[0107] Figure 5 Maximum seam width A graph showing the relationship between construction time t and the time t.

[0108] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0109] In this embodiment of the invention, the term "and / or" describes the relationship between associated objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The character " / " generally indicates that the preceding and following associated objects have an "or" relationship.

[0110] It should be noted that the terms "first," "second," etc., in the specification, claims, and drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0111] In this embodiment of the invention, the term "multiple" refers to two or more, and other quantifiers are similar.

[0112] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details are presented in the embodiments of the present invention to facilitate a better understanding of the invention. However, the technical solutions claimed in the present invention can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the following embodiments is for ease of description and should not constitute any limitation on the specific implementation of the present invention. The various embodiments can be combined with and referenced by each other without contradiction.

[0113] Traditional DAS-based crack inversion methods often employ a step-by-step or indirect strategy, first inverting the crack height and then estimating the crack width, or vice versa. The fundamental reason for this is the lack of a physical model that can simultaneously describe the closed-loop relationship between crack height, crack width, asymmetric offset, and the strain field. Furthermore, because the crack asymmetric offset y has a weak influence on far-field strain and contradicts traditional symmetric assumptions, this parameter has long been neglected. This invention, by constructing a unified inversion framework based on the Sneddon analytical strain model, achieves for the first time the inversion of crack height h and crack width w. max The simultaneous quantitative inversion of asymmetric offset y and net pressure p overcomes the ill-conditioned problem of multi-parameter coupled inversion, fills the gap in current fracture diagnosis in the evaluation of asymmetric propagation, and marks the upgrade of fracture interpretation from focusing on a single static parameter to a systematic and real-time diagnosis of fracture morphology, spatial location, mechanical state and its evolution process, laying a solid foundation for real-time data analysis and decision-making for intelligent fracturing and efficient oil and gas reservoir development.

[0114] Furthermore, traditional hydraulic fracture models (such as PKN and KGD models) artificially decoupled fracture geometric parameters at their inception to simplify the solution. For example, the PKN model assumes a constant fracture height and focuses on calculating fracture length and width; while the KGD model is suitable for fractures with heights much greater than their lengths. These "classical models" became the theoretical foundation for inversion methods over the following decades, leading to a "step-by-step, model-by-model" mindset in the industry. When new data types like DAS emerged, researchers naturally followed the old framework, attempting to fit a parameter using strain data (e.g., inverting fracture height using strain amplitude) and then substituting the result into another model to estimate fracture width. For example, they first used strain amplitude to invert fracture height using one model, and then substituted the result into another fracture width formula based on different assumptions for calculation. This strategy leads to the fatal flaw of "error propagation and amplification": any error in the first step will be used as incorrect input in the second step, severely distorting the final result. A deeper challenge lies in the fact that low-frequency DAS measures axial strain, which is a one-dimensional projection signal that is a comprehensive response to multiple geometric and mechanical parameters of the fracture. Traditional methods attempt to separate multiple parameters from a composite signal, essentially solving a single equation for multiple unknowns, which is inherently ill-posed. To avoid unsolvable problems, engineers are forced to introduce strong assumptions (such as symmetry, elliptical cross-sections, and constant pressure), effectively reducing multi-parameter problems to single-parameter or two-parameter problems. Furthermore, the objective function in traditional algorithms exhibits multiple local extrema and flat regions in the parameter space, making it highly susceptible to convergence to physically invalid solutions, resulting in extremely poor computational efficiency and stability.

[0115] This invention fundamentally abandons the traditional "step-by-step solution" approach and constructs a unified inversion framework based on the analytical solution of Sneddon's elasticity mechanics. This framework, through rigorous mathematical formulas, naturally integrates the seam height h, net pressure p (which directly controls the seam width), and strain field. The equations are placed within the same closed system. Based on the Levenberg-Marquardt (LM) algorithm, a nonlinear least-squares solution strategy integrating multi-initial-value global search and physical constraints is employed. By optimizing in parallel from multiple physically meaningful initial points and applying effective constraints, the system systematically penetrates local extrema barriers, robustly finding the global optimum, thus outputting h and p simultaneously. The maximum slit width w is then accurately calculated using analytical formulas. max .

[0116] This represents a qualitative leap from "indirect estimation" to "direct inversion." It not only completely eliminates the error propagation chain in step-by-step inversion, improving the overall inversion accuracy by an order of magnitude, but more importantly, it establishes the crack geometry (h, w) maxThe inherent consistency and linkage between the net pressure (p) and mechanical properties (p) are illustrated. For example, when real-time inversion shows that "the net pressure p continues to rise, but the maximum gap width w obtained from synchronous inversion..." max When growth stagnates or even declines, this contradictory signal can be directly diagnosed as clear evidence of severe near-wellbore distortion or proppant bridging, thereby immediately triggering engineering intervention, such as adjusting fluid viscosity or suspending proppant injection. This provides an unprecedented dynamic decision-making basis for diagnosing near-wellbore complexity and optimizing pumping procedures, transforming inversion from a "post-hoc interpretation" tool into a key link for "in-process control".

[0117] Furthermore, when interpreting high-resolution DAS data, subtle asymmetries in the strain profile caused by the asymmetric offset y of the fracture height (potentially only a few microstrains) are easily misinterpreted as instrument noise, poor fiber coupling, or rock anisotropy, rather than genuine physical signals. Its inversion faces severe challenges: first, the signal strength of y is much lower than that of h and p, resulting in a low signal-to-noise ratio; second, y and h exhibit strong parameter interchangeability—a "short and off-center" fracture and a "tall and medium" fracture may produce similar far-field strain modes, leading to highly unstable and non-unique inversion results without strong constraints. To address these issues, this invention, in the Sneddon model, theoretically captures the unique influence of y on the strain field distribution morphology by precisely characterizing the asymmetric distances (L1≠ L2) and angles (θ1≠θ2) between the measuring point and the upper and lower tips of the fracture.

[0118] In the inversion practice, by setting physical constraints and using a multi-initial-value strategy to explore the possibility of y taking a positive value (upward bias) or a negative value (downward bias), the ill-conditioned nature of the inversion is effectively overcome, and a stable and quantitative estimate of y is achieved.

[0119] Introducing the inversion of y, while considering y, h, and p, is of great significance, including: First, it is a direct criterion for evaluating whether the vertical propagation of fractures is controlled and whether it effectively communicates with the target producing layer, providing precise guidance for optimizing the spacing between sections and the location of perforations; Second, it is a core indicator for early warning of fracturing risks (such as perforation of the caprock / bottom layer, or communication with aquifers), achieving "precise navigation" of the vertical propagation of fractures. For example, if the inversion shows that y continuously shifts significantly towards the caprock (e.g., upwards), this is a red alert, indicating that the fracture is about to or has already breached the interlayer. This may lead to: (1) fracturing fluid and proppant entering non-target layers (such as aquifers or gas caps), resulting in resource waste and potential pollution; (2) uncontrolled fracture height, unable to form effective support within the producing layer; (3) inducing crosstalk between adjacent layers, affecting subsequent well placement. Real-time monitoring of y is equivalent to installing a "vertical navigation system" for fracturing operations. Third, based on the true geometry including y, the prediction of effective stimulated volume (SRV) and final production capacity will move from rough estimation to precise calculation, greatly improving the scientific rigor of fracturing design and effect evaluation: Assuming a design fracture height of 50m and a producing layer thickness of 30m. If the inverted y=0, the fracture is entirely within the producing layer, and the SRV estimate is based on a height of 50m. If the inverted y=-15m, the fracture top has penetrated 15m beyond the upper boundary of the producing layer, and the bottom is 35m within the producing layer. The effective, production-contributing stimulated volume changes dramatically, and the predicted production capacity may differ by more than 30%.

[0120] This invention provides an inversion method for nonlinear geometric parameters of hydraulic fractures. Figure 1 The flowchart illustrates the inversion method for the nonlinear geometric parameters of hydraulic fractures.

[0121] In step S100, a strain analytical model is established based on preset mechanical parameters.

[0122] Step S100 includes:

[0123] Based on the preset Young's modulus and Poisson's ratio, the following analytical strain model is established:

[0124] (1)

[0125] (2)

[0126] in, The normal strain is perpendicular to the crack surface.

[0127] The normal stress is perpendicular to the crack surface.

[0128] The normal stress is parallel to the crack surface.

[0129] The normal stress is perpendicular to the plane of the two-dimensional model.

[0130] E is Young's modulus;

[0131] This is the analytical solution of the strain corresponding to a certain measuring point, i.e., the theoretically calculated value;

[0132] ν is Poisson's ratio.

[0133] It should be noted that since DAS measures strain along the fiber axis, the Sneddon strain analytical model is (2).

[0134] More specifically, step S100 includes steps S110 to S160.

[0135] In step S110, a first relationship is established regarding the distance between the fiber optic measuring point and the critical point of the crack, and a second relationship is established regarding the azimuth angle between the fiber optic measuring point and the critical point of the crack. The coordinates of the fiber optic measuring point are defined as (z, y), and the model uses the crack center as the origin. The distance between the measuring point and the critical point of the crack is calculated as follows:

[0136] The first relation is:

[0137] ;(3)

[0138] L is the distance between the optical fiber measuring point and the center of the crack;

[0139] z represents the coordinate of the fiber optic measuring point in the crack width direction within a coordinate system with the crack center as the origin;

[0140] y represents the coordinate of the fiber optic measuring point in the direction of the crack height in a coordinate system with the crack center as the origin, i.e., the asymmetric offset of the crack height.

[0141] The azimuth angle of the measuring point relative to the critical point of the crack is calculated using the second formula:

[0142] ;(4)

[0143] The azimuth angle of the fiber optic measuring point relative to the center of the crack.

[0144] In step S120, the distance between the fiber measuring point and the lower tip of the crack and the distance between the fiber measuring point and the upper tip of the crack are determined according to the first relation.

[0145] The distance between the fiber optic measuring point and the lower tip of the crack is:

[0146] ;(5)

[0147] L1 is the distance between the optical fiber measuring point and the lower tip of the crack;

[0148] h is the crack height;

[0149] The distance between the fiber optic measuring point and the tip of the crack is:

[0150] ;(6)

[0151] L2 is the distance between the optical fiber measuring point and the tip of the crack.

[0152] In step S130, the azimuth angle of the fiber measuring point at the lower tip of the crack and the azimuth angle of the fiber measuring point at the upper tip of the crack are determined according to the second relation.

[0153] The azimuth angle of the fiber optic measuring point at the lower tip of the crack is:

[0154] ;(7)

[0155] The azimuth angle of the fiber optic measuring point relative to the lower tip of the crack.

[0156] The azimuth angle of the fiber optic measuring point at the tip of the crack is:

[0157] ;(7)

[0158] The azimuth angle of the fiber optic measuring point relative to the tip of the crack.

[0159] In step S140, based on the determined distances between the fiber optic measuring point and the lower tip of the crack, the distance between the fiber optic measuring point and the upper tip of the crack, the azimuth angle of the fiber optic measuring point at the lower tip of the crack, and the azimuth angle of the fiber optic measuring point at the upper tip of the crack, a first intermediate stress function and a second intermediate stress function are determined. The first intermediate stress function characterizes the overall stress distribution around the crack and in the far field, while the second intermediate stress function characterizes the stress singularity behavior near the upper and lower tips of the crack and reflects the key local geometric features of the crack.

[0160] It should be noted that, It dominates the overall stress distribution around the crack and in the far field. The physical meaning of its expression is the stress field caused by the uniform net pressure p in the crack in the elastic medium, which decays with distance. This field is exactly equal to -p on the crack surface and tends to zero in the far field. It dominates the stress singularity behavior near the upper and lower tips of the crack and is key to reflecting the local geometric characteristics of the crack.

[0161] The first intermediate stress function is:

[0162] (8)

[0163] The second intermediate stress function is:

[0164] ;(9)

[0165] In step S150, the in-plane normal stress components are calculated based on the first intermediate stress function and the second intermediate stress function. The in-plane normal stress components include normal stress perpendicular to the crack surface, normal stress parallel to the crack surface, and normal stress perpendicular to the plane of the two-dimensional model.

[0166] The formula for calculating the normal stress perpendicular to the crack surface is:

[0167] ;(10)

[0168] The formula for calculating the normal stress parallel to the crack surface is:

[0169] ;(11)

[0170] The formula for calculating the normal stress perpendicular to the plane of the two-dimensional model is:

[0171] ;(12)

[0172] In step S160, based on the normal stress perpendicular to the crack surface, the normal stress parallel to the crack surface, and the normal stress perpendicular to the plane of the two-dimensional model, the normal strain perpendicular to the plane of the two-dimensional model, the normal strain parallel to the crack surface, and the normal strain perpendicular to the crack surface are determined.

[0173] The formula for calculating the normal strain perpendicular to the plane of the two-dimensional model is:

[0174] (13)

[0175] The formula for calculating the normal strain parallel to the crack surface is:

[0176] (14)

[0177] The formula for calculating the normal strain perpendicular to the crack surface is:

[0178] (15)

[0179] p is the net pressure inside the crack;

[0180] This is the first intermediate stress function;

[0181] This is the second intermediate stress function;

[0182] The normal stress is perpendicular to the crack surface.

[0183] The normal stress is parallel to the crack surface.

[0184] The normal stress is perpendicular to the plane of the two-dimensional model.

[0185] Poisson's ratio;

[0186] The normal strain is perpendicular to the plane of the two-dimensional model.

[0187] E is Young's modulus;

[0188] The normal strain is parallel to the crack surface.

[0189] The normal strain is perpendicular to the crack surface.

[0190] It should be noted that in actual hydraulic fracturing projects, when the length of a fracture along a certain direction (usually the direction of the minimum horizontal principal stress) is much greater than its height (i.e., a long fracture), the middle section of the fracture can be approximated as a plane strain state. In this case, the displacement perpendicular to the model plane (x-direction) is constrained, and the strain... =0.

[0191] Depend on =0 can be used to derive formula (12). The introduction of this assumption not only simplifies the three-dimensional elasticity problem into a two-dimensional problem that can be solved analytically, but more importantly, it ensures the mathematical closure of the inversion model, laying a theoretical foundation for inverting three-dimensional crack parameters from two-dimensional strain observation data.

[0192] In step S200, a nonlinear inversion model of fracture parameters is established based on the established strain analytical model and the axial strain observation data obtained by the low-frequency DAS system in the adjacent well monitoring scenario.

[0193] Specifically, in the process of establishing a nonlinear inversion model for fracture parameters based on the established strain analytical model and the axial strain observation data obtained by the low-frequency DAS system in the adjacent well monitoring scenario, the nonlinear inversion model for fracture parameters is as follows:

[0194] (16)

[0195] Where n is the number of fiber optic measurement points;

[0196] This is the i-th fiber optic strain monitoring data;

[0197] The analytical solution of strain corresponding to the i-th measuring point, i.e., the theoretically calculated value.

[0198] || is an operator.

[0199] After the inversion model is established, nonlinear least squares solution is achieved through constraints (for example, the Levenberg-Marquardt method can be used). By introducing effective constraints and multiple initial value methods, global optimal inversion is achieved, and the inversion seam height h, seam height asymmetric offset y, and net pressure p are obtained.

[0200] The constraints can be:

[0201] (17)

[0202] w represents the crack width;

[0203] w max The maximum crack width;

[0204] p is the net pressure inside the crack;

[0205] p max This represents the maximum net pressure within the crack.

[0206] y represents the asymmetric offset of the seam height;

[0207] h is the seam height;

[0208] h max This is the maximum seam height.

[0209] In step S300, a nonlinear least squares iterative algorithm is used to solve the global optimal inversion based on the preset constraints and the nonlinear inversion model of crack parameters, and the inversion results in crack height, crack height asymmetric offset, and net pressure.

[0210] More specifically, the Levenberg-Marquardt (LM) algorithm is used as the core solver, and a parallel computing architecture is used to simultaneously initiate nonlinear least squares optimization from all starting points in the set, with each thread subject to uniform physical constraints. Feasible solutions generated by all parallel optimization threads are collected and double-checked: (1) physical constraint satisfaction check; (2) objective function residual norm calculation. Finally, the feasible solution with the smallest residual is selected as the globally optimal inversion result, thereby synchronously and robustly obtaining the optimal estimates of seam height h, seam height asymmetric offset y, and net pressure p.

[0211] In step S400, the maximum seam width is calculated based on the obtained seam height and net pressure.

[0212] More specifically, in the step of calculating the maximum seam width based on the obtained seam height and net pressure, the calculation formula includes:

[0213] The distribution function of the opening displacement w(y) on the crack surface is:

[0214] (18)

[0215] The maximum seam width is obtained at the center where y=0:

[0216] ;(19)

[0217] Example:

[0218] Artificially synthesized fiber optic strain observation data, in this case: interlayer stress profile is 65-60-65 MPa, rock elastic modulus is 30.0 GPa, Poisson's ratio is 0.2, and fracture toughness is 0.5 MPa·m. 0.5 The displacement for single-cluster fracturing is 4.0 m³ / s. 3 The fracturing fluid viscosity was 10 mPa·s, the orifice diameter was 5 mm, the orifice abrasion coefficient was 0.8, and the number of perforations per cluster was 16. The total operation time was 60 min, including 40 min of pumping time and 20 min of pump shutdown time. The monitoring well spacing was 150 m, and the fiber optic gauge length Lg was 1 m. The inversion results are as follows: Figure 2 , Figure 3 , Figure 4 and Figure 5 .

[0219] Solution: Based on fiber optic strain monitoring data, the Levenberg-Marquardt algorithm is used to retrieve the crack height h, crack height asymmetric offset y, and net pressure p at the hit location, as follows: Figure 2 , Figure 3 , Figure 4 As shown.

[0220] Based on the inverted seam height h and net pressure p, the maximum seam width is calculated using formula (19). ,like Figure 5 As shown.

[0221] The crack height h, crack height asymmetric offset y, net pressure p, and maximum crack width were calculated. Subsequently, it can be used to evaluate the dynamics of fracturing operations and quantitatively diagnose fracture geometry. Specific application schemes are as follows:

[0222] 1. Evaluation of crack geometry and morphological stability

[0223] Seam height h ( Figure 2Throughout the 30-60 minute observation period, the fracture height curve exhibited a "high-level stability with slight attenuation" pattern, with its value fluctuating narrowly between 52 and 53 meters. This highly stable and slowly attenuating trend is direct evidence that the vertical expansion of the fracture has been largely completed and entered a geometrically stable stage. It quantitatively indicates that the final vertical scale of the fracture has been effectively controlled, with neither unexpected continuous upward or downward extension nor dramatic height retraction. Therefore, this parameter is not only a core basis for assessing the vertical coverage of the fracturing stimulation volume (SRV), but its stable temporal characteristics also indicate the certainty of the fracture geometry in the later stages of construction, providing a key stability criterion for accurately assessing fracturing effectiveness, optimizing segment spacing, and predicting production capacity.

[0224] asymmetric offset of seam height y ( Figure 3 Throughout the process, this parameter remained constant at 0 meters. This result has crucial geological and engineering significance, as it definitively demonstrates that the fracture extends strictly symmetrically and uniformly in the vertical direction, with no vertical shift in its geometric center. This proves that under the current construction parameters and geological conditions, the fracture was effectively controlled within the producing layer, preventing unintended upward or downward extension, avoiding the risk of communication with the caprock, strata, or adjacent aquifers, and achieving precise "navigation" of the fracture's vertical location.

[0225] 2. Construction dynamics and crack conductivity analysis

[0226] Net pressure p ( Figure 4 The "rapid rise followed by a slow decline" trend shown by the curve is a key indicator for diagnosing the matching relationship between construction dynamics and formation response. The rising phase reflects the energy accumulation process of fracture propagation overcoming formation stress, while the gradual decline after the peak (approximately 1.2 MPa) directly indicates that the construction flow rate and formation filtration characteristics are basically matched—that is, the injected fluid can effectively compensate for filtration and maintain fracture extension, without a sudden pressure drop due to excessive filtration. Simultaneously, the curve is relatively smooth in both the rising and declining phases, without significant abnormal fluctuations or secondary rises. This indirectly indicates low near-wellbore friction, relatively simple fracture initiation and propagation, and no significant near-wellbore complexity or competition among multiple fractures. Therefore, the dynamic evolution of net pressure comprehensively reflects the fluid energy state within the fracture, formation filtration characteristics, and near-wellbore flow efficiency, providing direct quantitative basis for real-time assessment of the rationality of construction parameters, diagnosis of near-wellbore complexity, and optimization of pumping procedures.

[0227] Maximum seam width ( Figure 5 Its changing trend exhibits a highly coordinated dynamic coupling with the net pressure p, and also shows a clear "increase followed by decrease" pattern during the observation period. Specifically, it manifests as follows: It rose in tandem with net pressure to approximately 3.8 × 10⁻⁶.-3 The peak value of the crack is in meters, after which both almost simultaneously enter a gradual decay phase. This close coordination is not accidental; its physical essence lies in the fact that net pressure is the direct mechanical cause driving crack opening, while crack width is the intuitive geometric response of this mechanical action. Therefore, The peak value and dynamics directly quantify the effective conduction space and time-varying characteristics of the fracture under maximum opening conditions, and are key geometric parameters for evaluating the dynamic conduction capacity of the fracture. More importantly, The evolution of the crack has clear construction guidance value. Its peak size determines the potential space for proppant delivery and retention, while the decay rate and morphology after the peak directly reflect the crack closure dynamics and pressure propping efficiency. Combined with net pressure analysis, the coordinated upward phase of both indicates that the crack is effectively opened, while... The steady decay during the net pressure decline phase indicates that the fracture is undergoing a controlled, gradual closure process under the dominance of filtration. This information has irreplaceable direct guiding significance for determining the proppant delivery window, optimizing the proppant addition procedure, and predicting the final propped fracture width and conductivity.

[0228] Combining the above information, it can be seen that the operation resulted in the expected symmetrical fractures, whose dynamics conformed to the laws of mechanics, and the fracture propagation scale was well matched with the operation energy. This comprehensive, quantitative, dynamic, and mutually verifying set of parameters goes beyond the description of a single parameter, realizing a systematic and integrated diagnosis of the fracturing operation effect from "geometric morphology" to "dynamic process." It provides an unprecedentedly solid data foundation and scientific decision-making basis for real-time optimization of fracturing operations, accurate evaluation of post-fracturing effects, production capacity prediction, and subsequent well network deployment.

[0229] Obviously, the embodiments described above are merely some, not all, embodiments of the present invention. Based on the embodiments of the present invention, those skilled in the art can make other variations or modifications without creative effort, and all such variations or modifications should fall within the scope of protection of the present invention.

Claims

1. A method for inverting the nonlinear geometric parameters of hydraulic fractures, characterized in that, include: Based on the preset mechanical parameters, a strain analytical model is established; Based on the established strain analytical model and the axial strain observation data obtained by the low-frequency DAS system in the adjacent well monitoring scenario, a nonlinear inversion model of fracture parameters is established. A nonlinear least squares iterative algorithm is used to solve the global optimal inversion based on the preset constraints and the nonlinear inversion model of crack parameters, and the inversion results in crack height, crack height asymmetric offset and net pressure. The maximum seam width is calculated based on the obtained seam height and net pressure. The nonlinear inversion model for crack parameters is as follows: ； Where n is the number of fiber optic measurement points; This is the i-th fiber optic strain monitoring data; This is the analytical solution of the strain corresponding to the i-th measuring point, i.e., the theoretically calculated value; || is an operator; The step of establishing a strain analytical model based on preset mechanical parameters includes: Based on the preset Young's modulus and Poisson's ratio, the following analytical strain model is established: ；（1） ；（2） in, The normal strain is perpendicular to the crack surface. The normal stress is perpendicular to the crack surface. The normal stress is parallel to the crack surface. The normal stress is perpendicular to the plane of the two-dimensional model. E is Young's modulus; This is the analytical solution of the strain at a certain measuring point, i.e., the theoretically calculated value; v represents Poisson's ratio.

2. The inversion method for nonlinear geometric parameters of hydraulic fractures as described in claim 1, characterized in that, Based on the preset Young's modulus and Poisson's ratio, the following strain analytical model is established, including: Establish the first relationship between the distance between the fiber optic measuring point and the critical point of the crack, and the second relationship between the azimuth angle between the fiber optic measuring point and the critical point of the crack. Based on the first relation, determine the distance between the fiber measuring point and the lower tip of the crack, and the distance between the fiber measuring point and the upper tip of the crack, respectively. Based on the second relation, determine the azimuth angle of the fiber measuring point at the lower tip of the crack and the azimuth angle of the fiber measuring point at the upper tip of the crack, respectively. Based on the determined distances between the fiber optic measuring point and the lower tip of the crack, the distance between the fiber optic measuring point and the upper tip of the crack, the azimuth angle of the fiber optic measuring point at the lower tip of the crack, and the azimuth angle of the fiber optic measuring point at the upper tip of the crack, the first intermediate stress function and the second intermediate stress function are determined. The first intermediate stress function characterizes the overall stress distribution around the crack and in the far field, while the second intermediate stress function characterizes the stress singularity behavior near the upper and lower tips of the crack and reflects the key local geometric features of the crack. Based on the first intermediate stress function and the second intermediate stress function, the in-plane normal stress components are calculated. The in-plane normal stress components include normal stress perpendicular to the crack surface, normal stress parallel to the crack surface, and normal stress perpendicular to the plane of the two-dimensional model. Based on the normal stress perpendicular to the crack surface, the normal stress parallel to the crack surface, and the normal stress perpendicular to the plane of the two-dimensional model, determine the normal strain perpendicular to the plane of the two-dimensional model, the normal strain parallel to the crack surface, and the normal strain perpendicular to the crack surface.

3. The inversion method for nonlinear geometric parameters of hydraulic fractures as described in claim 2, characterized in that, The first relation is: ； The second relation is: ； The distance between the fiber optic measuring point and the lower tip of the crack is: ； The distance between the fiber optic measuring point and the tip of the crack is: ； The azimuth angle of the fiber optic measuring point at the lower tip of the crack is: ； The azimuth angle of the fiber optic measuring point at the tip of the crack is: ； The first intermediate stress function is: ； The second intermediate stress function is: ； The formula for calculating the normal stress perpendicular to the crack surface is: ； The formula for calculating the normal stress parallel to the crack surface is: ； The formula for calculating the normal stress perpendicular to the plane of the two-dimensional model is: ； The formula for calculating the normal strain perpendicular to the plane of the two-dimensional model is: ； The formula for calculating the normal strain parallel to the crack surface is: ； The formula for calculating the normal strain perpendicular to the crack surface is: ； L is the distance between the optical fiber measuring point and the center of the crack; z represents the coordinate of the fiber optic measuring point in the crack width direction within a coordinate system with the crack center as the origin; y is the coordinate of the fiber optic measuring point in the direction of the crack height in the coordinate system with the crack center as the origin, that is, the asymmetric offset of the crack height. L1 is the distance between the optical fiber measuring point and the lower tip of the crack; h is the crack height; L2 is the distance between the optical fiber measuring point and the tip of the crack; The azimuth angle of the fiber optic measuring point relative to the center of the crack; The azimuth angle of the fiber optic measuring point relative to the lower tip of the crack; The azimuth angle of the fiber optic measuring point relative to the tip of the crack; p is the net pressure inside the crack; This is the first intermediate stress function; This is the second intermediate stress function; The normal stress is perpendicular to the crack surface. The normal stress is parallel to the crack surface. The normal stress is perpendicular to the plane of the two-dimensional model. Poisson's ratio; The normal strain is perpendicular to the plane of the two-dimensional model. E is Young's modulus; The normal strain is parallel to the crack surface. The normal strain is perpendicular to the crack surface.

4. The inversion method for nonlinear geometric parameters of hydraulic fractures as described in claim 1, characterized in that, The step of employing a nonlinear least squares iterative algorithm to solve for the globally optimal inversion based on preset constraints and a nonlinear inversion model of crack parameters, and obtaining the crack height, crack height asymmetric offset, and net pressure, has the following constraints: ； w represents the crack width; w max The maximum crack width; p is the net pressure inside the crack; p max This represents the maximum net pressure within the crack. y represents the asymmetric offset of the seam height; h is the seam height; h max This is the maximum seam height.

5. The inversion method for nonlinear geometric parameters of hydraulic fractures as described in claim 4, characterized in that, In the step of calculating the maximum seam width based on the obtained seam height and net pressure, the calculation formula includes: The distribution function of the opening displacement w(y) on the crack surface is: ； The maximum seam width is obtained at the center where y=0: 。

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