A multi-mineral rock numerical modeling method based on gradient perturbation and hybrid sorting

Abstract

The application relates to a multi-mineral rock numerical modeling method based on gradient disturbance and mixed sorting, which comprises the following steps: (1) arranging an initial seed point set in a two-dimensional rectangular domain through a hexagonal close packing mode; (2) applying a random displacement vector on a regular grid point to apply a random micro disturbance, and adopting a boundary layer gradient control method to eliminate the boundary effect; (3) distributing the crystal grains to different mineral phases based on a random seed sequence rearrangement method, and constructing a multi-mineral crystal model; (4) introducing the generated random seed position into Neper software, and constructing a non-uniform multi-mineral rock numerical model with specific mineral size, roundness and distribution characteristics. Compared with the prior art, the technical scheme of the application can quickly and accurately establish a non-uniform multi-mineral rock numerical core model with specific mineral size, roundness and distribution model.

Description

Technical Field

[0002] This application relates to the field of oil and gas engineering technology, and in particular to a numerical modeling method for multi-mineral rocks based on gradient perturbation and hybrid sorting. Background Technology

[0003] Rock is an inherently heterogeneous natural material, composed of minerals with varying chemical compositions, grain sizes, morphologies, and spatial distributions. This inherent heterogeneity creates a complex internal structure, including bonding methods and arrangement sequences. These inherent heterogeneities control the mechanical behavior of rocks, including their strength, stiffness, deformability, and failure characteristics. Under external loads, the inherent mineral morphology and random distribution lead to a non-uniform stress field, thereby controlling the accumulation and evolution of damage within the rock and influencing the initiation and propagation of cracks.

[0004] To investigate the influence mechanisms of these microscopic mineral parameters on rock mechanical behavior, two main approaches have been developed: experimental testing and numerical simulation. Due to inherent limitations in experimental testing regarding scale effects, material simplification, and control of multivariate coupling effects, numerical simulation has become a key research tool for exploring the impact of multi-mineral behavior on rock mechanical responses. Grain-based models can characterize mineral grains and their mechanical interactions, thus enabling more realistic numerical simulations of fracture processes in heterogeneous rocks. The Voronoi tessellation-based mineral crystal model (GBM) is widely used in the numerical simulation of multi-mineral rocks. This modeling technique helps assess the influence of morphological changes and mineral grain properties on crack initiation and propagation, and numerous studies have demonstrated the rationality of this method.

[0005] However, traditional mineral crystal generation methods based on the Poisson-Voronoi method produce mineral models that are too random in morphology. Furthermore, it is difficult to control and quickly establish numerical core models with appropriate sphericity, size, and heterogeneous distribution. Geometric distortions easily occur at the boundaries of the simulation region, leading to a decrease in the quality of the numerical grid. In addition, traditional methods struggle to quantitatively control the transition of minerals from "homogeneous mixing" to "layered sedimentation" using a single parameter. Summary of the Invention

[0006] This application provides a numerical modeling method for multi-mineral rocks based on gradient perturbation and hybrid sorting. This method can quickly and accurately establish numerical core models with specific mineral sizes, sphericity, and distribution patterns, avoiding the shortcomings of the traditional Poisson-Voronoi mineral crystal generation method.

[0007] The method provided in this application is as follows: a numerical modeling method for multi-mineral rocks based on gradient perturbation and hybrid sorting, comprising the following steps: (1) Using a hexagonal close-packing method in a two-dimensional rectangular domain Initial seed point set is arranged inside. ; (2) At regular grid points Apply a random displacement vector By applying random micro-perturbations, boundary layer gradient control is used to eliminate boundary effects; (3) Based on the random seed order rearrangement method, the grains are assigned to different mineral phases to construct a multi-mineral crystal model; (4) Import the generated random seed positions into Neper software to construct a non-uniform multi-mineral rock numerical model with specific mineral size, roundness and distribution characteristics.

[0008] Furthermore, in step (1), for the outermost seed point in the initial seed point set, the basic grid spacing Δ in each direction is... x and Δ y Defined as: in, W The width of the two-dimensional rectangular simulation region Ω is... H The height of the two-dimensional rectangular simulation region Ω is given. For the number of grid rows, This represents the number of grid columns.

[0009] Furthermore, in step (2), the random displacement vector Follows a uniform distribution: in, The global shape noise level; The size matrix is ​​a local feature matrix; For interval A random vector within.

[0010] Furthermore, in step (2), the boundary layer gradient control method is used to eliminate boundary effects, including: Define the topological distance from the seed point to the nearest vertical boundary as: Introducing position-dependent damping coefficients , The corrected perturbation equation is: in, This represents the minimum value of the perturbation coefficient at the boundary layer; This represents the maximum value of the perturbation coefficient at the boundary layer; The number of controlled boundary layers.

[0011] Furthermore, in step (2), for the outermost seed point, i.e. Forced application of lateral locking constraints To ensure that the model edges are straight, boundary conditions are applied.

[0012] Furthermore, in step (3), the sorting score for each seed point is defined. : in: The normalized vertical coordinate represents the ordered terms and drives the layered distribution; , which are uniformly distributed random numbers, represent unordered terms, and drive random mixing; , is the non-uniformity coefficient.

[0013] Furthermore, in step (4), the size of the mineral particles is determined by their equivalent area. S Characterization, mineral equivalent area S With equivalent particle size D The expression is as follows: .

[0014] Furthermore, in step (4), the roundness of the mineral particles is determined by the ratio of the circumference of the circle equivalent to the area of ​​the mineral polygon to the actual circumference of the polygon: In the formula: C This is the roundness value; P circle It is the circumference of a circle equivalent to the area of ​​a mineral polygon; P It is the actual perimeter of the mineral polygon; A Let be the area of ​​the polygon.

[0015] Due to the adoption of the above technical solution, the beneficial effects achieved by the present invention compared with the prior art are as follows: The method provided by the present invention can quickly and accurately establish numerical core models with specific mineral size, sphericity and distribution models, avoiding the shortcomings of traditional mineral crystal generation methods based on Poisson-Voronoi. Attached Figure Description

[0016] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0017] Figure 1 A flowchart illustrating the method of this invention; Figure 2 These are the modeling results for different noise values ​​in the embodiments of the present invention; Figure 3 This is a diagram showing the relationship between random noise η and roundness in an embodiment of the present invention. Figure 4 These are the numerical core model results for different particle sizes in the embodiments of the present invention; Figure 5 The mineral distribution results of the numerical model under different non-uniformity coefficients in the embodiments of the present invention are shown. Detailed Implementation

[0018] To better explain and facilitate understanding of the present invention, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings and specific implementation methods.

[0019] like Figure 1 As shown, the numerical modeling method for non-uniform multi-mineral rocks based on gradient micro-perturbation and hybrid sorting provided by the present invention includes the following steps: (1) Using a hexagonal close-packing method in a two-dimensional rectangular domain Initial seed point set is arranged inside. ; (2) At regular grid points Apply a random displacement vector By applying random micro-perturbations, boundary layer gradient control is used to eliminate boundary effects; (3) Based on the random seed order rearrangement method, the grains are assigned to different mineral phases to construct a multi-mineral crystal model; (4) Import the generated random seed positions into Neper software to construct a non-uniform multi-mineral rock numerical model with specific mineral size, roundness and distribution characteristics.

[0020] In step (1), it is necessary to construct the basic crystal lattice and set the mineral grain size. In this invention, the basic crystal lattice is first constructed and the mineral grain size is set in a two-dimensional rectangular domain by means of hexagonal close packing. Initial seed point set is arranged inside. .

[0021] Wherein, the width of the two-dimensional rectangular simulation region Ω is... W The height is H ,Right now: Set the target mineral particle count as According to the principle of geometric conservation, the number of rows and columns of the grid ( The calculation is as follows: in, H The height of the simulation area is in mm; W The simulated area width is in mm; To simulate the aspect ratio of the region, is the geometric factor of the hexagonal close packing.

[0022] To ensure that the outermost seed point is strictly attached to the left and right physical boundaries ( x =0 and x = W To eliminate minute gaps and acute angle distortion at the boundaries, the basic mesh spacing Δ in each direction is adjusted. x and Δ y Defined as: For any node within the grid ( i , j ), where row indices ∈ {0,1,..., n y -1}, column index j ∈{0,1,..., n x -1}. Combining basic grid coordinates, odd / even row misalignment compensation, and boundary locking constraints, any initial rule seed point within the rectangular domain. of X coordinates and Y The expression for coordinates is: in: m i Parity indicator function; Φ ( j ) is the internal column indicator function, and its expression is: In step (2), random micro-perturbations are applied and boundary gradient constraints are set. In order to simulate the irregular morphology of real rock grains, regular grid points are used. Apply a random displacement vector The coordinates of the perturbed seed point P ij Defined as: random displacement vector Follows a uniform distribution: in, For global shape noise level, For local feature size matrix, For interval A random vector within.

[0023] To eliminate boundary effects and avoid generating tiny particles at the boundaries that affect mesh quality, a boundary layer gradient control method is introduced. The topological distance (layer number) from the seed point to the nearest vertical boundary is defined as... Introducing position-dependent damping coefficients : The corrected perturbation equation is: The number of controlled boundary layers is 2 in this invention; The minimum value of the perturbation coefficient at the boundary layer is 0.2 in this invention to maintain the regular arrangement of the boundary grains; The maximum value of the perturbation coefficient is 1 in this invention; for the outermost seed point ( Forced application of lateral locking constraints This ensures that the model edges are straight, making it easier to apply boundary conditions.

[0024] In step (3), after the geometric model is generated, the grains need to be assigned to different mineral phases (such as quartz, feldspar, etc.) to construct a multi-mineral crystal model. This invention is based on a seed point ID rearrangement method to achieve control over the mineral distribution.

[0025] To quantitatively control the non-uniformity of mineral distribution, i.e., the continuous transition from "layered structure" to "random mixed structure", a ranking score is defined for each seed point. : in: , is the normalized vertical coordinate, representing the ordered terms, driving the layered distribution; , which are uniformly distributed random numbers, represent unordered terms, and drive random mixing; , is the non-uniformity coefficient.

[0026] By adjusting Values ​​can enable parameterized control of the microstructure of rocks; when (Layered structure): Primarily determined by location, the grain ID increases with height. If grouped by ID, layered rocks with distinct interfaces will be generated. (Homogeneous structure): Primarily determined by random numbers, the grain IDs are spatially completely randomly distributed, resulting in a homogeneous mixture of mineral phases.

[0027] In step (4), numerical modeling and mineral morphology control are required. After generating random seed points, this invention uses Neper software to construct a mineral crystal model with multiple mineral distributions. Neper is a toolkit for polycrystalline generation and mesh generation. It can be used to generate polycrystalline structures with various morphological characteristics, from very simple morphologies (simple mosaics, grain growth microstructures, etc.) to complex, multiphase, or multiscale microstructures involving grain subdivision. By importing the generated random seed positions into Neper software, a numerical model with specific mineral size, roundness, and distribution characteristics can be constructed.

[0028] The mineral morphology control process is as follows: Mineral particle size control: The size of mineral particles is determined by their equivalent area. S Characterization, then mapping to equivalent particle size D This allows the generation of mineral particle models with different particle sizes, and the equivalent area of ​​the minerals. S With equivalent particle size D The expression is as follows: Mineral particle roundness control: by setting random noise By generating random seed points with different noise levels, the roundness of mineral particles can be controlled.

[0029] In this invention, the roundness of mineral particles is defined as the ratio of the circumference of the equivalent surface area to the perimeter of the polygon.

[0030] In the formula: C This represents the roundness value of the polygon; P circle It is the circumference of a circle equivalent to the area of ​​the mineral polygon, in meters; P It is the actual perimeter of the mineral polygon, in meters (m). A m is the area of ​​the polygon. 2 .

[0031] Mineral particle distribution control: The arrangement order of the generated random seeds corresponds to the distribution location of the minerals. This is achieved by adjusting the non-uniformity coefficient. The value changes the order of the random seeds, thereby controlling the distribution of minerals.

[0032] Example 1: Using the method provided in this invention, a numerical core model is established for a rectangular area with a height of 50 mm and a width of 25 mm as an example to represent the proportional size of the downhole core. In Example 1, numerical models with different roundness, size and mineral distribution are established respectively.

[0033] Figure 2 The figure shows numerical core models with different roundnesses, with random noise set. The value generates a random seed point. The values ​​were 0, 0.1, 0.2, 0.3, 0.4, and 0.5. The average roundness of the mineral particles in the established numerical model was calculated, and then random noise was introduced. A chart showing the correspondence between roundness and... Figure 3 As shown, when a mineral grain model with a certain degree of roundness is needed, the corresponding random noise can be obtained by querying the chart. The value is then obtained, allowing for the creation of numerical models of minerals with varying roundness. Compared to the traditional standard Poisson-Voronoi method, this invention eliminates the need to generate initial seed points and then optimize the seed point distribution based on the required mineral morphology parameters, thus discarding the optimization process and significantly improving modeling speed. Simultaneously, it achieves specific control over the roundness of mineral grains, preventing the generated grains from having non-physically short sides and extremely small acute angles, which could affect subsequent numerical model calculations.

[0034] Figure 4 The figure shows numerical core models of different sizes, with the equivalent area of ​​mineral grains set. S This is converted into the number of mineral particles, which corresponds to the number of random seeds generated. N Modeling is performed, and then numerical models of the average size of different mineral grains can be established. For example... Figure 4 As shown, an equivalent area of ​​2.5 μm was established. 2 3 μm 2 3.5 μm 2 4 μm 2 4.5 μm 2 5 μm 2 Numerical core model under certain conditions.

[0035] Traditional mineral crystal generation methods based on the Poisson-Voronoi model typically produce mineral crystal models with a fixed Poisson random distribution, making it impossible to control the mineral distribution. In this invention, the non-uniformity coefficient is adjusted... It can construct numerical core models with different mineral distributions. Figure 5 The figure shows a numerical core model with different mineral distributions, and the non-uniformity coefficient is adjusted. It can construct numerical core models with different mineral distributions. Figure 5 Four types of minerals were considered: quartz, feldspar, carbonate rocks, and clay minerals. A non-uniformity coefficient was set. Numerical core models were established with values ​​of 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. It can be seen that as the non-uniformity coefficient increases... With the increase of [amount], the minerals exhibit a layered, orderly arrangement, which can be used for subsequent numerical simulations.

[0036] Therefore, the numerical modeling method for non-uniform multi-mineral rocks based on gradient micro-perturbation and hybrid sorting provided by this invention generates seed points with specific conditions within the model region, and then uses the multi-crystal generation software Neper to construct a numerical core model with specific roundness, size, and mineral distribution. This method employs two core algorithms: a lattice seed generation algorithm based on gradient micro-perturbation and an ID seed rearrangement algorithm based on hybrid weights. The former controls grain morphology and boundary quality by setting random perturbation coefficients to generate random seeds with different sphericities, and then establishes a multi-mineral rock model. The latter controls the non-uniformity of mineral distribution by introducing a random distribution uniformity coefficient, which controls the arrangement order of the generated random seed points to control different mineral distribution patterns. Within the model region, the mineral grain size is controlled by controlling the number of seed points. This method can quickly and accurately establish numerical core models with specific mineral sizes, sphericities, and distribution patterns, avoiding the shortcomings of traditional Poisson-Voronoi-based mineral crystal generation methods.

Claims

1. A numerical modeling method for multi-mineral rocks based on gradient perturbation and hybrid sorting, characterized in that, Includes the following steps: (1) Using a hexagonal close-packing method in a two-dimensional rectangular domain Initial seed point set is arranged inside. ; (2) At regular grid points Apply a random displacement vector By applying random micro-perturbations, boundary layer gradient control is used to eliminate boundary effects; (3) Based on the random seed order rearrangement method, the grains are assigned to different mineral phases to construct a multi-mineral crystal model; (4) Import the generated random seed positions into Neper software to construct a non-uniform multi-mineral rock numerical model with specific mineral size, roundness and distribution characteristics.

2. The numerical modeling method for non-uniform multi-mineral rocks based on gradient micro-perturbation and hybrid sorting according to claim 1, characterized in that, In step (1), for the outermost seed point in the initial seed point set, the basic grid spacing Δ in each direction is... x and Δ y Defined as: in, W The width of the two-dimensional rectangular simulation region Ω is... H The height of the two-dimensional rectangular simulation region Ω is given. For the number of grid rows, This represents the number of grid columns.

3. The numerical modeling method for non-uniform multi-mineral rocks based on gradient micro-perturbation and hybrid sorting according to claim 1, characterized in that, In step (2), the random displacement vector Follows a uniform distribution: in, The global shape noise level; The size matrix is ​​a local feature matrix; For interval A random vector within.

4. The numerical modeling method for non-uniform multi-mineral rocks based on gradient micro-perturbation and hybrid sorting according to claim 1, characterized in that, In step (2), the boundary layer gradient control method is used to eliminate boundary effects, including: Define the topological distance from the seed point to the nearest vertical boundary as: Introducing position-dependent damping coefficients , The corrected perturbation equation is: in, This represents the minimum value of the perturbation coefficient at the boundary layer; This represents the maximum value of the perturbation coefficient at the boundary layer; The number of controlled boundary layers.

5. The numerical modeling method for non-uniform multi-mineral rocks based on gradient micro-perturbation and hybrid sorting according to claim 1, characterized in that, In step (2), for the outermost seed point, i.e. Forced application of lateral locking constraints To ensure that the model edges are straight, boundary conditions are applied.

6. The numerical modeling method for non-uniform multi-mineral rocks based on gradient micro-perturbation and hybrid sorting according to claim 1, characterized in that, In step (3), the sorting score for each seed point is defined. : in: The normalized vertical coordinate represents the ordered terms and drives the layered distribution; , which are uniformly distributed random numbers, represent unordered terms, and drive random mixing; , is the non-uniformity coefficient.

7. The numerical modeling method for non-uniform multi-mineral rocks based on gradient micro-perturbation and hybrid sorting according to claim 1, characterized in that, In step (4), the size of the mineral particles is determined by their equivalent area. S Characterization, mineral equivalent area S With equivalent particle size D The expression is as follows: 。 8. The numerical modeling method for non-uniform multi-mineral rocks based on gradient micro-perturbation and hybrid sorting according to claim 1, characterized in that, In step (4), the roundness of the mineral particles is determined by the ratio of the circumference of the circle equivalent to the area of ​​the mineral polygon to the actual circumference of the polygon: In the formula: C This is the roundness value; P circle It is the circumference of a circle equivalent to the area of ​​a mineral polygon; P It is the actual perimeter of the mineral polygon; A Let be the area of ​​the polygon.

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