Method, device and equipment for determining electrical tortuosity of reservoir core and storage medium

Abstract

The invention relates to a method, a device and equipment for determining the electrical tortuosity of a reservoir core and a storage medium, and belongs to the technical field of resistivity or conductivity measurement. Based on the microstructure image and fractal theory modeling, pore structure parameters are generated; constructing a digital core model based on the pore structure parameters, and generating pore distribution of the digital core model through a three-dimensional reconstruction technology; finite element electrical conduction simulation is executed based on the pore distribution of the digital core model to calculate electric field distribution and generate electrical parameters, and the electrical parameters are used for determining the electrical tortuosity; the finite element electrical conduction simulation refers to discretizing a continuous electric field into a finite element grid, and solving an electrostatic field equation to simulate current distribution; according to the method, high-precision digital characterization of the heterogeneity of the pore structure of the reservoir core is realized, and the electric tortuosity reflecting the conductivity of the pore structure is accurately calculated.

Description

Technical Field

[0001] This application relates to the technical field of resistivity or conductivity measurement, and in particular to a method, apparatus, equipment and storage medium for determining the electrical tortuosity of reservoir cores. Background Technology

[0002] In the field of reservoir exploration and development technology, electrical tortuosity is a key parameter reflecting the current conduction characteristics in the porous media of rocks. Its accurate calculation plays an important supporting role in core tasks such as reservoir evaluation and fluid identification. As exploration and development advances into complex reservoir areas, the actual reservoir environment places higher demands on the accuracy and applicability of electrical tortuosity calculation.

[0003] In existing technologies, the calculation of electrical tortuosity mainly relies on empirical formulas or semi-empirical models. Specifically, the KC equation and Hagen-Poiseuille equation obtained by fitting core experimental data can be used to construct a quantifiable calculation model by simplifying the geometric shape of the rock pore structure, thereby realizing the solution of electrical tortuosity.

[0004] However, existing methods generally assume that the pore structure of rocks is an idealized, regular geometric shape such as cylindrical capillaries or parallel conductive networks. But the pore structure of actual reservoir rocks is highly complex and heterogeneous. This idealized assumption deviates significantly from the actual reservoir conditions, which directly leads to the limited applicability of empirical formulas in complex pore structures and insufficient calculation accuracy. Summary of the Invention

[0005] This application provides a method, apparatus, equipment, and storage medium for determining the electrical tortuosity of reservoir cores, in order to solve the problem of low accuracy of electrical tortuosity determined by the prior art.

[0006] In a first aspect, embodiments of this application provide a method for determining the electrical tortuosity of reservoir cores, including:

[0007] Obtain microstructure images of reservoir cores; the microstructure images are used to identify the microstructure of the pores and skeleton inside the reservoir cores;

[0008] Pore ​​structure parameters are generated based on the microstructure image and fractal theory modeling; the fractal theory modeling is based only on the fractal geometry principle to mathematically model the heterogeneity and complexity of the pore structure, and the pore structure parameters are used to represent the heterogeneity of the pore structure of the reservoir core.

[0009] A digital core model is constructed based on the pore structure parameters, and the digital core model is used to digitally represent the pore structure parameters.

[0010] The pore distribution of the digital core model was generated using three-dimensional reconstruction technology;

[0011] Based on the pore distribution of the digital core model, a finite element electric conduction simulation is performed to calculate the electric field distribution and generate electrical parameters, which are used to determine the electric tortuosity. The finite element electric conduction simulation refers to discretizing the continuous electric field into a finite element mesh and solving the electrostatic field equation to simulate the current distribution.

[0012] Secondly, embodiments of this application provide an apparatus for determining the electrical tortuosity of reservoir cores, comprising:

[0013] The acquisition module is used to acquire microstructure images of reservoir cores; the microstructure images are used to identify the microstructure of the pores and skeleton inside the reservoir cores.

[0014] The generation module is used to generate pore structure parameters based on the microstructure image and fractal theory modeling; the fractal theory modeling is based only on the fractal geometry principle to mathematically model the heterogeneity and complexity of the pore structure, and the pore structure parameters are used to represent the heterogeneity of the pore structure of the reservoir core.

[0015] A construction module is used to construct a digital core model based on the pore structure parameters, wherein the digital core model is used to digitally represent the pore structure parameters;

[0016] The generation module is also used to generate the pore distribution of the digital core model through three-dimensional reconstruction technology;

[0017] The execution module is used to perform a finite element electric conduction simulation based on the pore distribution of the digital core model to calculate the electric field distribution and generate electrical parameters, which are used to determine the electric tortuosity; the finite element electric conduction simulation refers to discretizing the continuous electric field into a finite element mesh and solving the electrostatic field equation to simulate the current distribution.

[0018] Thirdly, embodiments of this application provide a device for determining the electrical tortuosity of reservoir cores, including: a sensor, a receiver, a transmitter, a memory, and a processor;

[0019] Receiver, used to receive instructions and data;

[0020] A transmitter is used to send commands and data;

[0021] The memory stores computer-executed instructions;

[0022] The processor executes computer execution instructions stored in the memory, causing the processor to perform the first aspect and / or various possible implementations of the first aspect as described above.

[0023] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the first aspect and / or various possible implementations of the first aspect.

[0024] Fifthly, embodiments of this application provide a computer program product, including a computer program that, when executed by a processor, implements the first aspect and / or various possible implementations of the first aspect.

[0025] The method for determining the electrical tortuosity of reservoir cores provided in this application achieves high-precision digital characterization of the heterogeneity of reservoir core pore structure by integrating microstructure image acquisition, fractal theory modeling, and finite element electrical conduction simulation. First, microstructure images accurately identify the pore and framework distribution within the reservoir core, laying the foundation for subsequent analysis. Next, mathematical modeling based on fractal theory effectively captures the complexity and heterogeneity of the pore structure, generating specific pore structure parameters. These parameters are used to construct a digital core model, enabling the digital reproduction of the core's pore structure and clearly demonstrating the pore distribution through 3D reconstruction technology. Finally, finite element electrical conduction simulation is used to calculate the electrical tortuosity, reflecting the core's conductivity. This method not only considers the true complexity of the core's internal structure but also accurately assesses its electrical properties by simulating current distribution. Attached Figure Description

[0026] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0027] Figure 1 Flowchart of the method for determining the electrical tortuosity of reservoir cores provided in this application Figure 1 ;

[0028] Figure 2 Flowchart of the method for determining the electrical tortuosity of reservoir cores provided in this application Figure 2 ;

[0029] Figure 3 A flowchart for reconstructing a three-dimensional digital core from the reservoir core CT scan images provided in this application;

[0030] Figure 4 Three-dimensional digital rock visualization of saturated conductive and non-conductive phases of reservoir cores provided in this application;

[0031] Figure 5 Digital rock potential distribution map after performing finite element electrical conduction simulation on the reservoir core provided in this application;

[0032] Figure 6 A schematic diagram of the structure of the device for determining the electrical tortuosity of reservoir cores provided in this application;

[0033] Figure 7 A schematic diagram of the structure of the device for determining the electrical tortuosity of reservoir cores provided in this application.

[0034] The accompanying drawings have illustrated specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to specific embodiments. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions 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, not all embodiments. Based on the embodiments of this application, other embodiments obtained by those skilled in the art without creative effort are all within the scope of protection of this application.

[0036] In the field of reservoir exploration and development, electrical tortuosity is a key parameter characterizing the tortuosity of current paths in rock porous media, directly affecting the accuracy of resistivity logging interpretation. Its accurate acquisition plays a crucial supporting role in core geological and engineering tasks such as reservoir property evaluation and fluid-bearing property identification. As oil and gas exploration continues to expand into complex reservoirs such as tight, shale, and carbonate rocks, traditional methods face severe challenges in dealing with highly heterogeneous and multi-scale pore structures, necessitating more accurate and adaptable methods for calculating electrical tortuosity.

[0037] Currently, the mainstream methods for calculating electrical tortuosity mainly rely on empirical or semi-empirical models, such as the Kozeny-Carman (KC) equation and the Hagen-Poiseuille (HP) equation derived from core experimental data. These methods simplify complex pore networks into regular geometric shapes (such as cylindrical capillary bundles or parallel conductive channels), establishing a quantitative relationship between porosity, permeability, and electrical tortuosity, thereby achieving indirect estimation of electrical tortuosity.

[0038] However, such idealized assumptions severely neglect the true complexity of natural rock pore structures, including irregular pore throat shapes, significant differences in connectivity, multi-scale distribution, and heterogeneous mineral composition. Therefore, when dealing with complex reservoirs such as fracture-pore dual media, highly heterogeneous carbonate rocks, or nanoscale shale pores, existing empirical formulas often fail to accurately reflect the actual current conduction path, leading to significant deviations in electrical tortuosity calculations and limiting their application in high-precision reservoir evaluation. To address these issues,

[0039] The method for determining the electrical tortuosity of reservoir cores provided in this application accurately characterizes the heterogeneity of the pore structure and its electrical conductivity through a multi-scale, multi-physics field fusion approach. First, microscopic images of the reservoir core are acquired to clearly identify the spatial distribution of internal pores and the framework. Then, based on fractal geometry principles, the complexity and heterogeneity of the pore structure are mathematically modeled to generate pore structure parameters that quantify its heterogeneous characteristics. Subsequently, a digital core model is constructed using these parameters, and its true pore spatial distribution is reconstructed using 3D reconstruction technology. Based on this, the finite element method is used to simulate the electrical conduction of the digital core model—discrete the continuous electric field into a finite element mesh, solve the electrostatic field control equations to obtain the current and electric field distribution, thereby extracting electrical parameters reflecting the tortuosity of the current path and calculating the electrical tortuosity accordingly. The entire process organically integrates microscopic imaging, fractal theory, and numerical simulation, achieving cross-scale digital characterization from the core's microstructure to its macroscopic electrical response.

[0040] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0041] Figure 1 Flowchart of the method for determining the electrical tortuosity of reservoir cores provided in this application Figure 1 In this embodiment, the execution entity is the control system. For example... Figure 1 As shown, the method includes:

[0042] S101: Obtain microstructure images of reservoir cores; microstructure images are used to identify the microstructure of pores and skeleton inside reservoir cores.

[0043] Among them, microstructure images refer to image data obtained by taking pictures or scanning that can clearly show the morphology, distribution and combination relationship of pores (spaces inside the rock that are not filled by minerals) and skeleton (the main structure composed of mineral grains in the rock) inside the reservoir core.

[0044] Specifically, firstly, representative reservoir core samples are selected and preprocessed, including cutting and polishing to create a smooth observation surface. If necessary, vacuum coating (such as gold sputtering) is performed to enhance image contrast. Then, appropriate imaging techniques are selected according to requirements, such as scanning electron microscopy, focused ion beam scanning electron microscopy, and X-ray computed tomography. Finally, images of the core observation area are acquired using imaging equipment to obtain microstructural images at different magnifications and resolutions.

[0045] S102: Pore structure parameters are generated based on microstructure images and fractal theory modeling; fractal theory modeling only uses fractal geometry principles to mathematically model the heterogeneity and complexity of pore structure, and pore structure parameters are used to represent the heterogeneity of pore structure in reservoir cores.

[0046] Fractal theory modeling refers to the modeling process that, based on the principles of fractal geometry, regards the pore structure of reservoir cores as a fractal system with self-similarity (parts and the whole are similar in morphology and structure), and uses mathematical methods to quantify the heterogeneity (the degree of non-uniformity in pore size, shape, and distribution) and complexity of the pore structure.

[0047] Pore ​​structure parameters are the core indicators output by this modeling process, used to quantitatively characterize the non-uniformity of reservoir core pore structure. Common parameters include fractal dimension, pore radius distribution range, and pore connectivity coefficient.

[0048] Specifically, the microstructure image is preprocessed, including grayscale conversion, noise reduction, and image segmentation (distinguishing between pore and skeleton regions); geometric features of the segmented pore regions are extracted, such as pore boundary contours, pore area, and pore equivalent radius; based on fractal geometry principles, a fractal mathematical model of the pore structure is constructed, and the model parameters are solved by calculating the fractal relationships of pore feature parameters (such as the power-law relationship between the number of pores and the pore radius); finally, based on the model output results, pore structure parameters that can characterize pore non-uniformity are determined.

[0049] S103: Construct a digital core model based on pore structure parameters. The digital core model is used to digitally represent the pore structure parameters.

[0050] Among them, the digital core model transforms the pore structure parameters (such as fractal dimension, pore radius distribution, and skeleton composition) of reservoir cores into digital three-dimensional or two-dimensional virtual models, transforming abstract pore structure parameters into intuitive and quantifiable digital carriers, thereby achieving accurate replication and digital characterization of the pore-skeleton spatial structure of real reservoir cores.

[0051] Specifically, the following steps are taken: First, the dimensions (two-dimensional or three-dimensional) and accuracy requirements of the digital core model are defined, and the spatial resolution of the model is determined. Based on the generated pore structure parameters, the basic framework of the model is constructed, including the spatial distribution of the skeleton region and the initial distribution of the pore region. The pore structure parameters are then integrated into the model through parameter mapping, such as adjusting the complexity of the pores according to the fractal dimension and determining the pore size of different regions according to the pore radius distribution. Finally, the model is verified and optimized to ensure that the error between the pore structure parameters of the model and the parameters of the real core sample is within the allowable range.

[0052] S104: Pore distribution of digital core model generated by three-dimensional reconstruction technology.

[0053] Among them, three-dimensional reconstruction technology refers to the reconstruction of the true distribution of pores in three-dimensional space based on the basic data of digital core models (such as two-dimensional cross-sectional information and pore structure parameters) through computer algorithms.

[0054] Pore ​​distribution refers to the spatial location, shape, size, and connectivity of pores in a three-dimensional digital core model, presented in digital form.

[0055] Specifically, two-dimensional cross-sectional data of the digital core model are extracted, including two-dimensional cross-sectional images at different depths and orientations and the corresponding pore-skeleton distribution information. Three-dimensional reconstruction algorithms (such as volume data interpolation algorithms, Markov random field algorithms, phase field simulation algorithms, etc.) are used to perform three-dimensional stitching and interpolation on the pore distribution information of multiple sets of two-dimensional cross-sections to restore the continuous distribution state of pores in three-dimensional space. Post-processing is performed on the reconstructed pore distribution, including removing pseudo-pores (non-existent pores) generated during the reconstruction process and correcting pore connectivity. Finally, complete three-dimensional pore distribution data is output, which can be presented as an intuitive three-dimensional pore distribution image through visualization software.

[0056] S105: Based on the pore distribution of the digital core model, perform finite element electric conduction simulation to calculate the electric field distribution and generate electrical parameters, which are used to determine the electric tortuosity; finite element electric conduction simulation refers to discretizing the continuous electric field into a finite element mesh and solving the electrostatic field equation to simulate the current distribution.

[0057] Finite element electric conduction simulation refers to a numerical simulation method that discretizes the continuous electric field region corresponding to the pore distribution of a digital core model into several non-overlapping finite element mesh elements, and simulates the conduction process of current in a porous medium (usually filled with conductive liquid) by solving the basic equations of electrostatic field (such as the Laplace equation and the Poisson equation), thereby obtaining the electric field distribution.

[0058] Electrical parameters are indicators that characterize the electric field conduction properties of the simulation output, including resistivity, conductivity, and variance of electric field intensity distribution. These parameters are the basis for determining electric tortuosity (the degree of bending of the current conduction path in the pore).

[0059] Specifically, firstly, the pore distribution region of the digital core model is meshed, discretizing the pore region into a large number of tetrahedral or hexahedral finite element meshes, while defining the physical properties of the mesh elements (such as the conductivity of the conductive liquid filling the pores); next, boundary conditions for the electrical conduction simulation are set, including applying a constant voltage or constant current at both ends of the model, and defining the skeleton region as an insulating boundary (non-conductive); a finite element mathematical model of electrical conduction is established, transforming the electrostatic field equations into finite element discrete equations; the discrete equations are solved using numerical calculation methods (such as Gaussian elimination and iterative methods) to obtain the electric field distribution data such as electric field intensity and electric potential for each finite element mesh element; finally, electrical parameters are calculated based on the electric field distribution data, such as calculating the overall conductivity using the voltage and current at both ends of the model, and calculating the electric field strength variance using the electric field strength distribution.

[0060] The method for determining the electrical tortuosity of reservoir cores provided in this application involves acquiring microstructure images of the reservoir cores. These microstructure images are used to identify the microstructure of pores and the framework within the reservoir core. Pore structure parameters are generated based on the microstructure images and fractal theory modeling. The fractal theory modeling mathematically models the heterogeneity and complexity of the pore structure based solely on fractal geometry principles. The pore structure parameters represent the heterogeneity of the pore structure in the reservoir core. A digital core model is constructed based on the pore structure parameters, which is used to digitally represent the pore structure parameters. The method generates the pore distribution of a digital core model using 3D reconstruction technology; performs finite element electrical conduction simulation based on the pore distribution of the digital core model to calculate the electric field distribution and generate electrical parameters, which are used to determine the electrical tortuosity; finite element electrical conduction simulation refers to discretizing the continuous electric field into a finite element mesh and solving the electrostatic field equation to simulate the current distribution; by combining microstructure images, fractal theory modeling and finite element electrical conduction simulation, this method achieves high-precision digital characterization of the heterogeneity of reservoir core pore structure and accurately calculates the electrical tortuosity reflecting its conductivity.

[0061] Figure 2 Flowchart of the method for determining the electrical tortuosity of reservoir cores provided in this application Figure 2 , Figure 3 A flowchart for reconstructing a three-dimensional digital core from the CT scan images of the reservoir core provided in this application; such as Figure 2 and Figure 3 As shown, in this embodiment... Figure 1 Based on the examples, a detailed description is provided of the method for determining the electrical tortuosity of reservoir cores. This method includes:

[0062] S201: Perform layered scanning of reservoir cores to obtain CT images of different layers.

[0063] Layered scanning refers to the process of using X-ray computed tomography (CT) technology to scan along the axial or radial direction of the core at set intervals to obtain tomographic images (CT images) of different depths and orientations of the core.

[0064] CT images at different layers are grayscale images that reflect the spatial distribution of pores (low density, low grayscale) and skeleton (high density, high grayscale) within the corresponding layer.

[0065] Specifically, first, the surface of the core is cleaned of oil and impurities, and it is then processed into a plunger shape with a uniform diameter (to ensure scanning stability). Loose cores require additional cementation to solidify them. Next, the core is fixed on the CT stage, and the scanning voltage, current, resolution, and step interval are set. The step interval is calculated using the following formula: (in, For step interval, The effective length of the core. To ensure the planned number of layers is obtained, images of adjacent layers are not missed and the entire core is covered; finally, layer-by-layer scanning and data saving: start the equipment to scan layer by layer along the set direction, acquire CT grayscale images of each layer and save them in layer order.

[0066] S202: A representative volume element REV is extracted using the center cutting method, and threshold segmentation is performed using filtering and the Otsu algorithm OTSU to obtain a microstructure image containing only pores and skeleton.

[0067] Among them, the representative volume element (REV) is the smallest volume unit that can represent the overall pore structure characteristics of the core, and its physical properties are consistent with and stable with the overall average parameters of the core.

[0068] The center-cutting method is a method of symmetrically cutting a set-size area based on the center of the CT image to extract the REV; filtering is a preprocessing operation to eliminate image noise.

[0069] The Otsu algorithm is an adaptive threshold segmentation algorithm that determines the optimal threshold by maximizing the inter-class variance, and separates grayscale images into two classes: pores and skeletons.

[0070] The microstructure image is a binary image, using only two numerical values ​​to distinguish between pores and the skeleton.

[0071] Specifically, firstly, taking the geometric center of each CT image layer as the origin, the edge length is cut... A square area of ​​pixels (corresponding to actual size) The scan resolution is used to obtain the REV images of each layer; then, a Gaussian filter is applied with a kernel size of 3×3 and the Gaussian function is: (in, It is the standard deviation. (Using values ​​from 0.8 to 1.2), scan noise is eliminated; next, the image grayscale histogram is calculated using the formula: (in, For inter-class variance, The percentage of pixels with pores. For the pixel percentage of the skeleton, The average gray value for pores. Let g be the average gray value of the skeleton class and T be the gray value threshold to be determined. Maximize g to determine the optimal threshold T. Then, set the pores with gray values ​​< T to 0 and the skeletons with gray values ​​≥ T to 1 to obtain a microstructure image containing only pores and skeletons.

[0072] S203: By statistically analyzing the number of minimum boxes covering pores in grids of different sizes in microstructure images, the fractal dimension of the pore structure is calculated, and the pore structure parameters are obtained. The fractal dimension is a parameter that characterizes the complexity and heterogeneity of the pore structure. The higher the value of the fractal dimension, the more complex the pore distribution.

[0073] Among them, fractal dimension is the core parameter characterizing the complexity and heterogeneity of pore structure, and its value can be 3 (three-dimensional image).

[0074] Different sized grids refer to dividing a microstructure image into square "boxes" with different side lengths.

[0075] The minimum number of boxes required to cover the pores refers to the minimum number of boxes needed to completely enclose all the pore areas.

[0076] Specifically, firstly, select A grid (box) with different side lengths, side length Take values ​​according to a geometric or arithmetic sequence (e.g.) Pixels Pixels (pixels); then, for each size The mesh overlay is used to cover the microstructure image, and the number of minimum boxes covering all pore regions (pixel value = 0) is counted. Finally, according to the principles of fractal geometry, it satisfies Taking the logarithm yields the linear formula. (in, For fractal dimension, (as a constant); x-axis The fractal dimension is the absolute value of the slope of the line fitted to the ordinate. ,Should These are the pore structure parameters.

[0077] S204: Construct a digital core model based on pore structure parameters. The digital core model is used to digitally represent the pore structure parameters.

[0078] Specifically, firstly, the dimensionality (three-dimensional) and accuracy requirements of the digital core model are defined, and the spatial resolution of the model is determined. Simultaneously, the obtained pore structure parameters (core being the fractal dimension) and the acquired basic distribution information of pores and the pore skeleton are incorporated. Next, based on parameters such as the effective length of the core and the REV size, a three-dimensional empty model framework matching the size of the micro-regions in the actual core is constructed. Then, combining the distribution patterns of the skeleton and pores in the binary image, the approximate ranges of the skeleton region (e.g., quartz skeleton) and pore region within the model are preliminarily defined. Next, pore structure parameters such as the fractal dimension are integrated into the model, and the morphology of the pore region is adjusted through a parameter-driven algorithm—the higher the fractal dimension, the more irregular the pore contour and the number of branches are increased through the algorithm. Simultaneously, the pore size in different regions is determined by combining pore radius distribution parameters. Finally, the porosity calculation formula is used. ,in, This represents the total number of pixels in the aperture area. The porosity of the constructed model is calculated (total number of skeleton pixels). The porosity of the model is compared with that of the real core and the set pore structure parameters. If the error exceeds 5%, the parameter mapping relationship is readjusted until the model parameters match the real parameters.

[0079] S205: Pore distribution of digital core model generated through three-dimensional reconstruction technology.

[0080] Among them, three-dimensional reconstruction technology refers to the technology of using a series of continuous two-dimensional microstructure images to restore the three-dimensional spatial distribution of pores and skeleton inside the rock core through computer algorithms.

[0081] Digital core models are virtual models created by converting two-dimensional images into three-dimensional models, which can accurately replicate the microstructure of real cores.

[0082] Its pore distribution refers to the digital representation of the position, shape, size and connectivity of pores in three-dimensional space in the model, which is the basic carrier for subsequent generation of multiphase fluid and electrical conduction simulation.

[0083] Specifically, first, it is confirmed that the obtained binary images of each layer are free of noise and that pores and skeletons are clearly distinguishable, and then they are sorted according to layer order; next, a volume data interpolation algorithm is used to interpolate the continuous two-dimensional binary images along... The registration formula is as follows: (Core axis stacking) (in, For the first Layer image Axis coordinates The scanning step interval is used to ensure accurate alignment of images from adjacent layers without misalignment. Next, a three-dimensional connectivity analysis algorithm is used to extract pore regions (pixel value = 0) from the stacked model, generating three-dimensional spatial distribution data of pores, including the three-dimensional coordinates, equivalent radius, and connectivity channel size of the pores. Finally, the digital core model containing the pore distribution is saved in volumetric data format, and its three-dimensional morphology can be displayed through visualization software.

[0084] S206: A four-parameter random growth algorithm is used to generate non-conductive phase fluid in the pore distribution of a digital core model. The four-parameter random growth algorithm is used to control the distribution of non-conductive phase fluid in the pores through random parameters.

[0085] Among them, the Quasi-Static Growth Simulation (QSGS) algorithm is an algorithm used to generate multiphase fluid distribution in the pore space of digital cores. By setting key random parameters such as model size, porosity, and initial growth probability (core distribution probability), it controls the growth trajectory and distribution pattern of non-conductive phase fluid (such as oil phase) in the pores.

[0086] Non-conductive fluids are fluids that do not possess electrical conductivity; their distribution within pores directly affects the current conduction path. (e.g.) Figure 4 (As shown)

[0087] Specifically, the initial grid size of the digital core model is first set to determine the model dimensions. Each pixel in the grid represents a potential initial growth point for non-conductive fluid phases or the rock skeleton. The model is constructed by replacing pixel values. Next, the target porosity is defined and used as the core criterion for terminating the algorithm's loop, based on the formula... (in, This represents the total number of pixels in the pores. The porosity is calculated based on the total number of skeleton pixels, and the algorithm stops when the porosity of the generated model reaches a set value. Then, the initial growth probability (core distribution probability, or cdd) is configured. This parameter controls the distribution of the initial growth points of the non-conductive phase fluid. A larger cdd value results in a scattered distribution and weak connectivity of the non-conductive phase fluid, while a smaller value results in a concentrated distribution and strong connectivity. Finally, the directional growth probability is set. For the two-dimensional digital core model, eight growth directions are set with expansion probabilities. If the probabilities of each direction are consistent, the non-conductive phase fluid is isotropically distributed. If the probability of a certain direction is higher, the fluid will concentrate and extend in that direction to control its growth trajectory. Since this implementation only focuses on the single-phase growth of the non-conductive phase fluid, the setting of the growth probability of interaction is not involved. After the algorithm starts, it first searches for the initial growth points of multiple non-conductive phase fluids in a loop, and then performs a growth cycle according to the set parameter rules to continuously expand the distribution range of the non-conductive phase fluid. The percentage of pore pixels is detected in real time until the preset porosity is reached. Finally, a digital core model with a non-conductive phase fluid (such as oil phase) distribution pattern that meets the requirements is output.

[0088] Optionally, a four-parameter random growth algorithm can be used to generate a non-conductive phase fluid in the pore distribution of the digital core model. Specific implementation methods include:

[0089] During the growth of the non-conductive phase, pore points in contact with the skeleton in the pore distribution of the digital core model are excluded as initial growth points. Furthermore, the selection strategy for the growth points of the non-conductive phase is adjusted based on wettability experimental data. The wettability experimental data refers to the difference in wettability between the non-conductive and conductive phases obtained through experiments such as contact angle measurement.

[0090] Among them, the wettability experimental data are quantitative data characterizing the difference in wettability between the non-conductive phase (oil phase) and the conductive phase (water phase) on the core skeleton surface, obtained through contact angle measurement experiments. The core indicator is the contact angle. ( It is a non-wetting phase. (The wetting phase).

[0091] The initial growth point selection strategy is a rule based on wettability differences to determine the initial growth location of the non-conductive phase. Its purpose is to make the distribution of the non-conductive phase more closely match the actual reservoir fluid occurrence state.

[0092] Specifically, firstly, the core parameters of the four-parameter random growth algorithm are determined, and simultaneously, wettability experimental data (contact angle measurement results) and pore-skeleton distribution data from the digital core model are imported. An image recognition algorithm is then used to mark all pore points in the model that are in contact with the skeleton. Next, if the wettability experimental data shows that the non-conductive phase is a non-wetting phase (contact angle...),... If the pores are in contact with the skeleton, all marked pore points are strictly excluded, and initial growth points are randomly selected only in the region inside the pores away from the skeleton; if it is a wetting phase ( If the initial growth point is selected, the pore point in contact with the skeleton is selected first. Then, based on the selected initial growth point, the growth proceeds along the 26 connectivity directions (three-dimensional space) according to the set growth probability. The growth step size is executed according to the parameters, and the growth only extends within the pore channels that meet the connectivity threshold, ensuring that the growth process complies with the pore space constraints. Finally, the growth range of the non-conductive phase is counted in real time to determine whether there is any case of erroneous growth into the skeleton region or illegal use of prohibited initial growth points. If so, the current growth branch is terminated and a new growth point is selected to ensure that the growth process is consistent with the strategy.

[0093] S207: Adjust the distribution ratio of the non-conductive phase according to the set conductive phase saturation; the conductive phase saturation is the volume ratio of the conductive fluid in the pores.

[0094] Among them, the saturation of the conductive phase This refers to the volume percentage of conductive fluid (such as brine) in the total pore volume of a rock core. It is a core parameter characterizing the distribution ratio of conductive and non-conductive fluid phases within the pores. The calculation formula is: (in, For the volume of the conductive fluid, (This refers to the total pore volume).

[0095] Adjusting the distribution ratio of the non-conductive phase, by increasing or decreasing the volume of the non-conductive fluid, allows the volume ratio of the conductive fluid to precisely match the set parameters. .

[0096] Specifically, the volume of the current non-conductive phase fluid is calculated using pixel statistics. Total pore volume The current conductive phase saturation is obtained by multiplying the total number of pore pixels in the digital core model by the volume of a single pixel. ;contrast With set value ,like If there are too many non-conductive phases, the volume of the non-conductive phases will be reduced proportionally, and some edge-grown non-conductive phase pixels will be deleted; if If the non-conductive phase is insufficient, continue growing the non-conductive phase according to the QSGS algorithm parameters until... (Tolerable error range); Finally, after adjustment and verification, perform statistics again. and Calculate the adjusted After confirming that it meets the set requirements, the distribution ratio of the non-conductive phase is finally determined.

[0097] S208: Calculates the electric field distribution and generates electrical parameters.

[0098] Specifically, such as Figure 5As shown, firstly, finite element meshing is performed only on the conductive fluid region (conductive phase in pores) of the digital core model, using a hexahedral mesh, with each pixel volume equivalent to a hexahedral mesh; then, a constant current is applied to the inlet face of the model. The outlet end face is grounded ( The skeleton and fluid interface are set as an insulating boundary (current density normal vector). Next, based on Maxwell's equations, the electrostatic field conduction equation is: (in, The conductivity of a conductive fluid. (where the potential is denoted as electric potential). The equations are discretized into a system of algebraic equations using the finite element method, and solved iteratively to obtain the potential of each mesh element. and electric field strength Next, the potential difference between the inlet and outlet of the model is calculated. By Ohm's Law Calculate resistance Then, using the resistivity formula (in, For the cross-sectional area of ​​the model, Macroscopic resistivity is generated (for the length of the current conduction direction). ,Should These are the core electrical parameters.

[0099] The method for determining the electrical tortuosity of reservoir cores provided in this application first involves layered scanning of the reservoir core to obtain CT images of different layers. Representative volume elements (REVs) are then extracted using a center-cutting method. Thresholding processing is performed using filtering and the Otsu algorithm (OTSU) to obtain a microstructure image containing only pores and the framework. Based on this image, the fractal dimension is calculated by statistically analyzing the number of minimum boxes covering pores in grids of different sizes, thereby obtaining pore structure parameters characterizing the complexity and heterogeneity of the pore structure. Next, a digital core model is constructed based on these parameters, and a 3D reconstruction technique is used to generate the pore distribution of the model. Then, a four-parameter random growth algorithm is used to generate a non-conductive fluid phase within the pore distribution. The distribution ratio of the non-conductive phase is adjusted according to a set conductive phase saturation level to simulate the actual fluid environment. Finally, finite element electrical conduction simulation technology is used to calculate the electric field distribution and generate electrical parameters reflecting the core's conductivity, achieving high-precision digital characterization of the reservoir core's pore structure and conductivity, and accurate calculation of the electrical tortuosity.

[0100] In one possible implementation, the electric tortuosity is calculated as follows:

[0101] The theoretical formula for electrical tortuosity is derived based on fractal theory, capillary model, and parallel conduction model. The capillary model is a model that describes the resistance characteristics of the conductive phase in a single capillary. The parallel conduction model is used to sum the resistances of all capillaries in parallel to calculate the total resistance.

[0102] Substitute the electrical parameters into the formula to calculate the electrical tortuosity.

[0103] Among them, electrical tortuosity is a dimensionless parameter that describes the degree of tortuosity of the actual flow path of current in a porous medium relative to a straight path, reflecting the influence of pore structure on conductivity.

[0104] The theoretical formula for electrical tortuosity is based on three core models: the capillary model is used to characterize the resistance characteristics of a single pore channel contributed only by formation water (conductive phase); fractal theory is used to quantitatively characterize the statistical self-similarity of the complex and disordered pore throat structure inside the rock; and the parallel conductivity model treats all capillaries as interconnected conductive channels and calculates the equivalent resistance of the entire core by superimposing the total conductivity.

[0105] Specifically, firstly, by using the capillary model in conjunction with the law of resistance, the relationship between the resistance of a single capillary and its diameter, length, and formation water resistivity is established.

[0106] For a single capillary tube, since the resistivity of oil is much greater than that of formation water, the current is almost entirely transmitted through the formation water. Therefore, the resistivity of a single capillary tube can be expressed as: ,in, The diameter of the pipe is represented as The capillary resistance value, This represents the resistance value caused by electrical conduction of formation water within the capillary. According to the law of resistance, its calculation method is as follows: ,in, This represents the size of the effective conductive cross-section caused by the conductive phase. It should be noted that only formation water is conductive inside the capillary. Therefore, the size of the effective conductive cross-sectional area can be obtained by the following formula: Therefore, the resistivity of a single capillary channel can be obtained as follows: Secondly, we introduce fractal theory, specifically the box method for calculating the fractal dimension: ,in, Let fractal dimension be the number of the object under study. Let's say it's the side length of the box. The total number of boxes in the research object. Since the pore structure and distribution inside a rock core are chaotic and disordered, introducing fractal theory allows for the regularization of these disordered pore structure variations. In rock physics, the core idea of ​​fractal theory is that the diameter of pores and throats inside a rock is greater than or equal to... The total number satisfies: ,in, This represents a diameter greater than or equal to the throat diameter. The total number of orifices and throats, This represents the maximum pore throat diameter. In real porous media samples, the number of pore throats is large, therefore it can be considered as a continuous and differentiable function, expressed as: Therefore, by introducing fractal theory, the internal structure of the chaotic porous medium can be characterized in an ordered manner.

[0107] The pore throat size distribution is represented as a continuous function, allowing for an integral description of the number of capillaries within any diameter range. Finally, based on the principle of parallel conduction and combined with parallel conduction theory, the total resistance of all capillaries is summed to obtain the total resistance of the digital core model. Size: Combining fractal theory, we obtain the following equation: Considering and The difference is too large, therefore the influence of the ratio of the minimum throat diameter to the maximum throat diameter on the results can be ignored. ,in, The cross-sectional area represents the digital core model. Since the pore portion of the core model is entirely equivalent to capillaries of different diameters, the total porosity of the core is equal to the ratio of the sum of the volumes of all capillaries to the apparent total volume of the core, as shown in the following formula: Similar to the simplification steps above, ignoring the influence of the ratio of the minimum to the maximum pore throat diameter on the results, the simplified formula for calculating the equivalent cross-sectional area of ​​the core is as follows: Simplified to: .

[0108] Optionally, the verification of the digital core model corresponding to the electrical tortuosity of the reservoir core provided in this application includes the following specific implementation methods:

[0109] First, three plunger core samples from a specific block were selected and sequentially washed for oil and salt to remove impurities and fluids. The treated cores were then cemented and fixed to prevent morphological deformation during scanning. Subsequently, grayscale scan images of different layers of the cores were acquired using X-ray CT scanning equipment. For these CT grayscale images, representative volumetric elements of the plunger core slices were first processed using image processing algorithms to ensure the analysis area exhibits typical pore structure. Filtering was then performed to eliminate scanning noise. Next, the Otsu method was used for threshold segmentation to accurately distinguish between the core skeleton and pore phases and perform binarization. Finally, the binarized images were stacked layer by layer according to the CT scan layer order to reconstruct a three-dimensional digital rock model.

[0110] Based on the reconstructed 3D digital rock model, a four-parameter random growth algorithm was used to uniformly generate non-conductive fluid within the pore space, constructing a digital core model containing both conductive and non-conductive fluids. Finite element method (FEM) electrical conduction simulations were then used to solve for the distribution characteristics of electric potential, current density, and electric field intensity within the model, providing electrical field distribution data for calculating the electric tortuosity. Subsequently, the electric field distribution was calculated by combining the model's pore distribution characteristics with the simulation results, further deriving the calculated electric tortuosity value. To verify the model's applicability and accuracy over a wide range of conductive phase saturation, the electric tortuosity of each core sample was calculated at conductive phase saturation levels of 1, 0.85, 0.7, 0.5, and 0.35. Simultaneously, the true values ​​of the electric tortuosity at different saturation levels were obtained based on fractal theory, capillary models, and parallel conduction models. The comparison results show that the calculated and actual values ​​of the electrical tortuosity of the three samples at each saturation level are all controlled within 10%, with very small differences. This indicates that the digital core model can effectively characterize the electrical tortuosity characteristics of digital cores at different conductive phase saturations.

[0111] Figure 6 A schematic diagram of the device for determining the electrical tortuosity of reservoir cores provided in this application is shown below. Figure 6 As shown, the reservoir core electrical tortuosity determination device 300 provided in this embodiment includes:

[0112] The acquisition module 301 is used to acquire microstructure images of reservoir cores; the microstructure images are used to identify the microstructure of pores and skeleton inside the reservoir cores.

[0113] The generation module 302 is used to generate pore structure parameters based on microstructure images and fractal theory modeling. The fractal theory modeling only uses fractal geometry principles to mathematically model the heterogeneity and complexity of the pore structure. The pore structure parameters are used to represent the heterogeneity of the pore structure of the reservoir core.

[0114] Module 303 is used to construct a digital core model based on pore structure parameters. The digital core model is used to digitally represent the pore structure parameters.

[0115] The generation module 302 is also used to generate the pore distribution of a digital core model through three-dimensional reconstruction technology;

[0116] The execution module 304 is used to perform finite element electric conduction simulation based on the pore distribution of the digital core model to calculate the electric field distribution and generate electrical parameters, which are used to determine the electric tortuosity. Finite element electric conduction simulation refers to discretizing the continuous electric field into a finite element mesh and solving the electrostatic field equation to simulate the current distribution.

[0117] In one possible implementation, the electric tortuosity determining device further includes: a calculation module 305;

[0118] The calculation module 305 is used to calculate the fractal dimension of the pore structure by statistically analyzing the number of minimum boxes covering pores in grids of different sizes in the microstructure image, and obtain the pore structure parameters. The fractal dimension is a parameter that characterizes the complexity and heterogeneity of the pore structure. The higher the value of the fractal dimension, the more complex the pore distribution.

[0119] In one possible implementation, the electric tortuosity determining device further includes: an adjustment module 306;

[0120] The generation module 302 is also used to generate non-conductive phase fluid in the pore distribution of the digital core model using a four-parameter random growth algorithm. The four-parameter random growth algorithm is used to control the distribution of non-conductive phase fluid in the pores through random parameters.

[0121] The adjustment module 306 is used to adjust the distribution ratio of the non-conductive phase according to the set conductive phase saturation; the conductive phase saturation is the volume ratio of the conductive fluid in the pores.

[0122] In one possible implementation, the electric tortuosity determining device further includes: a selection module 307;

[0123] Selection module 307 is used to exclude pore points in contact with the skeleton in the pore distribution of the digital core model as initial growth points during the growth of the non-conductive phase, and to adjust the selection strategy of the growth points of the non-conductive phase based on wettability experimental data; the wettability experimental data is the difference data between the non-conductive phase and the conductive phase obtained through experiments such as contact angle measurement.

[0124] In one possible implementation, the electric tortuosity determining device further includes: a determining module 308;

[0125] Module 308 is used to obtain the theoretical formula for electrical tortuosity based on fractal theory, capillary model and parallel conduction model; the capillary model is a model that describes the resistance characteristics of the conductive phase in a single capillary, and the parallel conduction model is used to sum the resistances of all capillaries in parallel to calculate the total resistance.

[0126] The calculation module 305 is used to calculate the electric tortuosity by substituting electrical parameters into the formula.

[0127] In one possible implementation, the electric tortuosity determining device further includes: a processing module 309;

[0128] The acquisition module 301 is used to perform layered scanning of reservoir cores to acquire CT images of different layers;

[0129] The processing module 309 is used to extract representative volume elements (REV) using the center cutting method, and to perform threshold segmentation through filtering and the Otsu algorithm (OTSU) to obtain a microstructure image containing only pores and skeleton.

[0130] Figure 7 A schematic diagram of the device for determining the electrical tortuosity of reservoir cores provided in this application. Figure 7 As shown, this application provides an electrical tortuosity determination device for reservoir cores. The electrical tortuosity determination device 400 for reservoir cores includes: a receiver 401, a transmitter 402, a processor 403, and a memory 404.

[0131] Receiver 401 is used to receive instructions and data;

[0132] Transmitter 402 is used to send commands and data;

[0133] Memory 404 is used to store instructions executed by the computer;

[0134] Processor 403 is configured to execute computer execution instructions stored in memory 404 to implement the various steps of the electric tortuosity determination method in the above embodiments. For details, please refer to the relevant descriptions in the foregoing embodiments of the electric tortuosity determination method.

[0135] Alternatively, the memory 404 can be either standalone or integrated with the processor 403.

[0136] When the memory 404 is set up independently, the electronic device also includes a bus for connecting the memory 404 and the processor 403.

[0137] This application also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the method for determining the electrical tortuosity of a reservoir core as described above by the reservoir core electrical tortuosity determination device.

[0138] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the method provided in any of the foregoing embodiments.

[0139] It will be understood by those skilled in the art that all or some of the steps, systems, or apparatuses disclosed above, and their functional modules / units, can be implemented as software, firmware, hardware, or suitable combinations thereof. In hardware implementations, the division between functional modules / units mentioned above does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed collaboratively by several physical components. Some or all of the physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit (ASIC). Such software may be distributed on a computer-readable medium, which may include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and can be accessed by a computer. Furthermore, it is well known to those skilled in the art that communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0140] The technical solutions of this application have been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it is readily understood by those skilled in the art that the scope of protection of this application is obviously not limited to these specific embodiments. The above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. These modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for determining the electrical tortuosity of reservoir cores, characterized in that, The method includes: Obtain microstructure images of reservoir cores; the microstructure images are used to identify the microstructure of the pores and skeleton inside the reservoir cores; Pore ​​structure parameters are generated based on the microstructure image and fractal theory modeling; the fractal theory modeling is based only on the fractal geometry principle to mathematically model the heterogeneity and complexity of the pore structure, and the pore structure parameters are used to represent the heterogeneity of the pore structure of the reservoir core. A digital core model is constructed based on the pore structure parameters, and the digital core model is used to digitally represent the pore structure parameters. The pore distribution of the digital core model was generated using three-dimensional reconstruction technology; Based on the pore distribution of the digital core model, a finite element electric conduction simulation is performed to calculate the electric field distribution and generate electrical parameters, which are used to determine the electric tortuosity. The finite element electric conduction simulation refers to discretizing the continuous electric field into a finite element mesh and solving the electrostatic field equation to simulate the current distribution.

2. The method according to claim 1, characterized in that, The generation of pore structure parameters based on the microstructure image and fractal theory modeling includes: By statistically analyzing the number of minimum boxes covering pores in grids of different sizes in the microstructure image, the fractal dimension of the pore structure is calculated, and the pore structure parameters are obtained. The fractal dimension is a parameter characterizing the complexity and heterogeneity of the pore structure. The higher the value of the fractal dimension, the more complex the pore distribution.

3. The method according to claim 2, characterized in that, During the finite element electrical conduction simulation based on the pore distribution of the digital core model, the following process is executed: A four-parameter stochastic growth algorithm is used to generate a non-conductive phase fluid in the pore distribution of the digital core model. The four-parameter stochastic growth algorithm is used to control the distribution of the non-conductive phase fluid in the pores through random parameters. The distribution ratio of the non-conductive phase is adjusted according to the set conductive phase saturation; the conductive phase saturation is the volume ratio of the conductive fluid in the pores.

4. The method according to claim 3, characterized in that, The generation of non-conductive phase fluid in the pore distribution of the digital core model using a four-parameter random growth algorithm includes: During the growth of the non-conductive phase, pore points in contact with the skeleton in the pore distribution of the digital core model are excluded as initial growth points. Furthermore, the selection strategy for the growth points of the non-conductive phase is adjusted based on wettability experimental data. The wettability experimental data refers to the difference in wettability between the non-conductive and conductive phases obtained through experiments such as contact angle measurement.

5. The method according to any one of claims 1-4, characterized in that, The method further includes: The theoretical formula for electrical tortuosity is derived based on fractal theory, capillary model, and parallel conduction model. The capillary model describes the resistance characteristics of the conductive phase in a single capillary, and the parallel conduction model is used to sum the resistances of all capillaries in parallel to calculate the total resistance. Substitute the electrical parameters into the formula to calculate the electrical tortuosity.

6. The method according to any one of claims 1-4, characterized in that, The acquisition of microstructural images of reservoir cores includes: The reservoir core was subjected to layered scanning to obtain CT images of different layers; A representative volume element REV was extracted using the center cutting method, and threshold segmentation was performed using filtering and the Otsu algorithm to obtain the microstructure image containing only pores and skeleton.

7. A device for determining the electrical tortuosity of reservoir cores, characterized in that, include: The acquisition module is used to acquire images of the microstructure of reservoir cores; The microstructure images are used to identify the microstructure of the pores and skeleton inside the reservoir core; The generation module is used to generate pore structure parameters based on the microstructure image and fractal theory modeling. The fractal theory modeling is based solely on the fractal geometry principle to mathematically model the heterogeneity and complexity of the pore structure. The pore structure parameters are used to represent the heterogeneity of the pore structure of the reservoir core. A construction module is used to construct a digital core model based on the pore structure parameters, wherein the digital core model is used to digitally represent the pore structure parameters; The generation module is also used to generate the pore distribution of the digital core model through three-dimensional reconstruction technology; An execution module is used to perform a finite element electrical conduction simulation based on the pore distribution of the digital core model to calculate the electric field distribution and generate electrical parameters, which are used to determine the electric tortuosity. The finite element electric conduction simulation refers to discretizing a continuous electric field into a finite element mesh and solving the electrostatic field equations to simulate the current distribution.

8. A device for determining the electrical tortuosity of reservoir cores, characterized in that, include: Memory, processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory, causing the processor to perform the method as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method as described in any one of claims 1-6.

10. A computer program product, characterized in that, Includes a computer program that, when executed by a processor, implements the method described in any one of claims 1-6.

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