Method of visualization and numerical description of pore space of digital twin of core

Abstract

FIELD: image processing and information visualization.SUBSTANCE: invention relates to methods of visualizing and numerically describing the pore space of a three-dimensional digital twin of a core for use in industrial fields related to the development of mineral deposits. The invention consists in increasing the information content of the analysis of the pore structure of the digital twin of the core in terms of its transport properties, and reducing the loss of time and resources. The user is provided with a visual interface and numerical characteristics of the pore space of the digital twin of the core, which allows the selection of an appropriate method and parameters for fluid flow modelling, as well as the avoidance of modelling if the digital twin does not meet the requirements of the simulators.EFFECT: improved performance.7 cl, 3 dwg

Description

[0001] The present invention relates to methods of image processing and information visualization, and more specifically to methods of visualizing and numerically describing the pore space of a three-dimensional digital twin of a core for the purpose of selecting a hydrodynamic simulator and fluid flow modeling parameters for use in industrial fields related to the development of mineral deposits.

[0002] The development of technical tools such as high-resolution X-ray computed microtomography has led to the construction of highly accurate models—digital twins—of the pore space structure of rock cores in mineral deposit development. Specifically, in the oil and gas industry, pore space microstructure models are used, for example, to select and optimize hydrocarbon reservoir development methods and agents. In the mining industry, core models are used, for example, to optimize leaching systems. Three-dimensional digital twins of core microstructure created using microtomography and the hydrodynamic fluid flow modeling performed on them are called "digital rock" (or digital core).

[0003] To obtain adequate modeling results, it is necessary to evaluate the applicability of the created digital twins for compliance with the requirements of hydrodynamic simulators for the specific tasks for which they are intended to be used. For example, when modeling multiphase hydrodynamic problems using digital core models, it is necessary to ensure sufficient spatial resolution of the pore space conductive channels. Failure to conduct a preliminary, operational assessment of the structure, homogeneity, and connectivity of the core pore space can lead to significant losses of time and computational resources due to inappropriate modeling or using an inadequate digital twin (model) of the core.

[0004] To generally characterize the pores in a digital twin of a rock sample, parameters such as total porosity, open porosity, closed porosity, connectivity, tortuosity, and Minkowski functionals are used. Such general parameters do not provide an indication of the homogeneity of the pore space, nor do they allow one to determine the channel size through which fluids primarily transport between opposite faces of the sample model, nor the channel shape. Digital twins may have similar parameters, but their pore space structure may differ significantly for the selection of the hydrodynamic modeling method and parameters. An example would be a sample in which the connection between two highly permeable parts of the sample is achieved by several thin pore channels through a thin, low-permeability layer.The pore space parameters of such a sample will not differ significantly from the parameters of a sample without a low-permeability layer, but the results of hydrodynamic modeling, as a rule, differ significantly.

[0005] Three-dimensional (3D) visualization of a digital twin requires rotating the model and plotting numerous cross-sections to roughly estimate the shape and size of the pore channels. However, this is time-consuming, the pore channel sizes can only be determined approximately, and the pore space structure parameters are not described by numerical characteristics.

[0006] When constructing pore-network models, the pore space is divided into so-called pore bodies connected by throats. Both are represented using standard 3D geometric primitives such as cylinders, spheres, tetrahedrons, and the like. Thus, the actual pore space is replaced by an extremely simplified model. The size distribution of pore bodies and throats provides researchers with generalized information about the pore space, but does not allow them to determine which throats are key (i.e., their size may be a constraint) for fluid transport. The size of key throats can be indirectly determined using the capillary pressure curve constructed for a digital twin of the core. However, this method does not allow one to determine the number of such throats or their location in the 3D digital twin of the core.

[0007] The constructed pore-network model also contains information about the sample's pore space, but its visual analysis is difficult, as such a model is a 3D graph with tens of thousands or more nodes. Coloring the nodes and connections in the graph based on the size of pore bodies and throats somewhat facilitates visual analysis, but overall it remains ineffective, as it requires significant time to navigate the enormous 3D graph.

[0008] To improve the information content of the digital twin's pore structure analysis in terms of its transport properties, we propose a quantitative description of the key characteristics primarily responsible for hydrodynamic conductivity. This will allow us to draw conclusions about the applicability, advantages, and disadvantages of various hydrodynamic modeling methods for the core digital twin under consideration.

[0009] The technical result of the invention is to increase the information content of the analysis of the pore structure of the digital twin of the core in terms of its transport properties, to reduce the loss of time and resources by providing the user with a visual interface and numerical characteristics of the pore space of the digital twin of the core, which allow the selection of an appropriate method and parameters for modeling fluid flow, as well as not to perform modeling in the event that the digital twin does not meet the requirements of the simulators.

[0010] The stated technical result is achieved by using the proposed method for visualizing and describing the pore space of a digital core twin to obtain a three-dimensional image of the core sample using tomography. An initial digital twin of the core sample is then created, in which the pore space voxels are marked and two opposite faces are defined through which fluid flow is modeled. In the next step, the geodetic sinuosity value is calculated for each voxel of the initial digital twin of the core sample, and an initial three-dimensional image of geodetic sinuosity is created. Next, two-dimensional projections of the initial three-dimensional image of geodetic sinuosity are calculated onto two mutually orthogonal planes, orthogonal to the faces through which fluid flow is modeled. The resulting two-dimensional projections of the initial three-dimensional image of geodetic sinuosity are used to calculate the initial numerical characteristics of the pore space.The pore throats of the original digital twin of the core sample are narrowed at least once using a morphological erosion operation. Then, for each voxel of the digital twin of the core sample with narrowed pore throats, the geodetic sinuosity value is calculated and a 3D image of the geodetic sinuosity is created. Two-dimensional projections of the 3D image of the geodetic sinuosity onto two mutually orthogonal planes orthogonal to the faces through which the fluid flow is modeled are calculated, and the numerical properties of the pore space are calculated from the resulting 2D projections. All resulting 2D projections of the 3D image of the geodetic sinuosity and all calculated numerical properties of the pore space are then displayed. The applicability, type, and parameters of the hydrodynamic simulator for the core digital twin in question are then determined based on the type of projections and the values ​​of the numerical properties of the pore space.

[0011] In accordance with one embodiment of the invention, when outputting two-dimensional projections to the screen, the first color denotes those pixels where the projection beam intersected only voxels that are not pores, the second color denotes those pixels where the beam from among the pores intersected only non-through pores, the remaining pixels of the projections are visualized using a gradient color palette that does not include the first and second colors, where the color is selected depending on the minimum value of the geodesic tortuosity of the voxels intersected by the projection beam.

[0012] In accordance with one embodiment of the invention, the following numerical characteristics of the pore space are calculated from the obtained two-dimensional projections of the three-dimensional image of the geodetic sinuosity: average geodetic sinuosity, standard deviation of geodetic sinuosity, connectivity and coverage.

[0013] In accordance with one embodiment of the invention, narrowing the pore channels of a digital twin of a core sample using a morphological erosion operation, then creating an image of the digital twin of the core sample with narrowed pore channels, where each voxel of the digital twin of the core is equal to the geodesic tortuosity, calculating two-dimensional projections of a three-dimensional image of the geodesic tortuosity onto two mutually orthogonal planes orthogonal to the faces through which the fluid flow is modeled and calculating the numerical characteristics of the pore space based on the obtained two-dimensional projections is repeated until through pores exist in the digital twin of the core sample.

[0014] In accordance with another embodiment of the invention, all obtained two-dimensional projections of the three-dimensional image of geodetic tortuosity are displayed on the screen in the form of animation.

[0015] In accordance with another embodiment of the invention, all obtained numerical characteristics of the pore space are displayed on the screen in the form of graphs.

[0016] The invention is explained by drawings, where Fig. 1 shows a block diagram of a method for visualizing and describing the pore space of a digital twin; Fig. 2 shows an example of visualization by the proposed method for a digital twin of a core sample, where Fig. 2a shows a projection of the geodesic tortuosity image onto the XZ plane for the original digital twin of the core sample and the corresponding projections of the numerical characteristics of the pore space, Fig. 2b shows a projection of the geodesic tortuosity image onto the YZ plane for the original digital twin of the core sample and the corresponding projections of the numerical characteristics of the pore space, Fig. 2c shows a projection of the geodesic tortuosity image onto the XZ plane for a digital twin of a core sample with pores narrowed by two voxels and the corresponding projections of the numerical characteristics of the pore space, Fig.2g shows the projection of the geodetic sinuosity image onto the YZ plane for the digital twin of the core sample with pores narrowed by two voxels and the corresponding projections of the numerical characteristics of the pore space, Fig. 2d shows the projection of the geodetic sinuosity image onto the XZ plane for the digital twin of the core sample with pores narrowed by six voxels and the corresponding projections of the numerical characteristics of the pore space, Fig. 2e shows the projection of the geodetic sinuosity image onto the YZ plane for the digital twin of the core sample with pores narrowed by six voxels and the corresponding projections of the numerical characteristics of the pore space. Fig. 3 shows an example of visualization by the proposed method of a digital twin of the core with wide, weakly sinuous pore channels, where in Fig.3a shows the projection of the geodetic sinuosity image onto the XZ plane for the original digital twin of the core and the corresponding projections of the numerical characteristics of the pore space, Fig. 3b shows the projection of the geodetic sinuosity image onto the YZ plane for the original digital twin of the core and the corresponding projections of the numerical characteristics of the pore space, Fig. 3c shows the projection of the geodetic sinuosity image onto the XZ plane for the digital twin of the core with pores narrowed by two voxels and the corresponding projections of the numerical characteristics of the pore space, Fig. 3d shows the projection of the geodetic sinuosity image onto the YZ plane for the digital twin of the core with pores narrowed by two voxels and the corresponding projections of the numerical characteristics of the pore space, Fig.3d shows the projection of the geodetic tortuosity image onto the XZ plane for a digital twin of the core with pores narrowed by six voxels and the corresponding projections of the numerical characteristics of the pore space; Fig. 3e shows the projection of the geodetic tortuosity image onto the YZ plane for a digital twin of the core with pores narrowed by six voxels and the corresponding projections of the numerical characteristics of the pore space.

[0017] Figure 1 shows a flowchart of the method for visualizing and describing the pore space of a digital twin of a core sample. In the first step (block 1 in Figure 1), a 3D image of the core sample is obtained using tomography. Depending on the size of the pore channels being analyzed, X-ray computed microtomography (microCT) or a focused ion beam electron microscope (FIB-SEM) can be used.

[0018] Next (block 2 in Fig. 1), an initial three-dimensional digital twin of the core sample is created from the image, in which the pore space voxels are marked. For this purpose, segmentation using thresholding, or the indicator kriging segmentation method [Oh W., Lindquist B. Image thresholding by indicator kriging / / IEEE Transactions on Pattern Analysis and Machine Intelligence. - 1999. - Vol. 21. - No. 7. - P. 590-602], or segmentation using deep neural networks [Varfolomeev I., Yakimchuk I., Safonov I. An application of deep neural networks for segmentation of microtomographic images of rock samples / / Computers. - 2019. - Vol. 8. - No. 4. - P. 72] can be used. After segmentation, the digital twin of the core sample can be represented as a binary three-dimensional (volumetric) image:

[0019]

[0020] where , , and the given image dimensions , , .

[0021]

[0022] Also, for the original digital twin, two opposite faces are specified through which the fluid flow is modeled, which is equivalent to specifying an axis , or along which the flow occurs. Note that for the method under consideration, it does not matter which of the two opposite faces is considered the inflow face (IN) and which is the outflow face (OUT) of the fluid.

[0023] The next step (block 3 in Fig. 1) creates an initial 3D image of geodesic tortuosity: for each voxel of the initial digital twin of the core sample, geodesic tortuosity is calculated, i.e., the ratio of the sum of the lengths of the shortest paths through the pore space from a given voxel to given edges and the distance between these edges. Geodesic tortuosity is a quantitative characteristic used to assess how much the path of a fluid passing through the digital twin of the sample deviates from a straight line [Ghanbarian, B., Hunt, A.G., Ewing, R.P., Sahimi, M. (2013). Tortuosity in porous media: a critical review. Soil science society of America journal, 77(5), 1461–1477]:

[0024]

[0025] at , Where - the length of the path passed through the material from the starting point to the end point; - the distance between the edges of fluid inflow and outflow.

[0026] For digital 3D image as for the voxel in which it is calculated , is the length of the shortest path , passing through it , from any voxel belonging to the pore and located on the plane of the inflow face (dots when directed ), to any point of the pore on the plane of the outflow edge (dots when directed ), Where - the set of all possible paths passing only through pore voxels and starting at points from and ending at points from As . the image size is taken along the selected axis ( when directed ). In order for geodetic tortuosity for the selected direction was defined for all voxels , we point out [Barman, Sandra, et al. New characterization measures of pore shape and connectivity applied to coatings used for controlled drug release. Journal of Pharmaceutical Sciences 110.7 (2021): 2753-2764]:

[0027]

[0028] where - the smallest geodesic distance between voxels and any of the voxels of the subset ; work - the number of voxels in V; ; condition true for voxels of blind pores; condition true for non-pore voxels.

[0029] At the fourth stage (block 4 in Fig. 1), two-dimensional (2D) parallel projections of the original 3D image of geodetic tortuosity are calculated in a special way onto two mutually orthogonal planes, orthogonal to the faces through which the fluid flow is modeled. The projection planes belong to the selected direction In case these are projections onto planes And During projection, rays pass through voxels perpendicular to the projection plane. The projection pixel value is equal to the minimum geodesic tortuosity of the voxels intersected by the projection ray:

[0030]

[0031] where , at .

[0032] Note that if the projection ray passes only through the voxels of non-through pores, then the pixel value in the projection is ; if the projection ray passes only through non-pore voxels, then the pixel value is ; the geodesic tortuosity of any voxel related to through pores is, by definition, obviously less than the number of voxels in the 3D image .

[0033] At the next stage (block 5 in Fig. 1), the initial numerical characteristics of the pore space are calculated from two-dimensional projections: the average value of geodetic tortuosity , standard deviation geodetic tortuosity, connectivity and coverage.

[0034] Connectivity [Barman, Sandra, et al. New characterization measures of pore shape and connectivity applied to coatings used for controlled drug release. Journal of Pharmaceutical Sciences 110.7 (2021): 2753–2764] and coverage based on the obtained projections are calculated as follows:

[0035]

[0036]

[0037] Connectivity indicates how effectively pores are connected along a given direction, providing a continuous path for fluid transport. The closer the connectivity is to one, the greater the proportion of pores that participate in the formation of continuous, interconnected paths along a given direction, ensuring transport throughout the entire volume of the digital twin. A connectivity value of zero indicates a complete absence of connected pores, meaning either the digital twin is non-porous or there is no continuous path.

[0038] Coverage shows the proportion of the projection area where the projection ray intersects pore voxels. The closer the coverage is to one, the greater the proportion of rays passing through the digital twin along the selected direction intersects at least one pore—regardless of whether it is a through pore or not.

[0039] In order to investigate the width of the channels and throats that ensure fluid transport in the selected direction, the described process of calculating projections and numerical parameters must be performed several times for a digital twin with narrowed pore channels obtained from the original digital twin. by means of a binary morphological erosion operation with an increasing size of the structural element (aperture) [Soille, P., Morphological Image Analysis: Principles and Applications, 2 ndEdition, Secaucus, NJ, Springer-Verlag, 2003, pp. 65-68]. Therefore, in the sixth step (block 6 in Fig. 1), the pore channels of the original digital twin of the core sample are narrowed using a morphological erosion operation. Condition 7 in Fig. 1 checks whether the condition for terminating the iterations, i.e., repetitions of steps three through six, has been reached. It is recommended to repeat steps three through six at least twice, but a different number of iterations can be selected. In another embodiment of the invention, the iterations (repetition of steps three through six) continue as long as through pores exist in the digital twin of the core sample.

[0040] At the eighth stage (block 8 in Fig. 1), all obtained 2D projections of the 3D image of geodetic tortuosity and numerical characteristics of the pore space are displayed on the screen. When displaying two-dimensional projections And The first specified color, such as white, is used to represent pixels where the ray intersects only non-pore voxels, while the second specified color, such as blue, is used to represent pixels where the ray intersects only non-through pores. The remaining projection pixels are rendered using a gradient color palette that does not include the first and second colors. The color is chosen based on the minimum geodesic tortuosity of the voxels intersected by the projection ray. For example, a color palette ranging from yellow to green could be used.

[0041] Projections obtained at various iterations can be displayed as separate images or animation frames. Numerical characteristics can be displayed as separate fields next to the projections from which they were calculated, either in tables or as graphs.

[0042] Further (block 9 in Fig. 1), based on the projection type and calculated numerical characteristics of both the original digital twin of the core sample and the digital twin with narrowed channels, conclusions are drawn regarding the channel size that provides the primary connectivity and fluid transport in the selected direction, the degree of tortuousness of these channels, and how completely and uniformly they are distributed within the digital twin. Based on the pore space characteristics, it is possible to classify digital twins by type, select an appropriate hydrodynamic simulator and fluid flow simulation parameters, and also to avoid simulation if the given digital twin of the core is not applicable to existing simulators.

[0043] Let's consider the application of this method to two examples. In the first example, a 3D image of a core sample with a resolution of 0.4 voxels per µm is obtained using X-ray microtomography. Next, using indicator kriging segmentation, an initial digital twin of the core sample is created in the shape of a cuboid, in which pore voxels are equal to one and rock voxels are equal to zero. Two opposite faces are selected in the XY plane, perpendicular to the direction of fluid flow along the OZ axis. For each voxel of the initial digital twin of the core sample, the geodetic sinuosity value is calculated, and an initial 3D image of geodetic sinuosity is created. For the resulting initial 3D digital image of geodetic sinuosity, 2D projections are calculated onto the XZ and YZ planes. Next, for each projection, the following initial numerical characteristics of the pore space are calculated: average geodetic tortuosity, standard deviation of geodetic tortuosity, connectivity and coverage.The digital twin then shrinks the pore space by two voxels using a morphological erosion operation.

[0044] For a digital twin with pores reduced by two voxels, the geodetic sinuosity image is constructed, two projections and numerical characteristics are calculated, and the process is repeated. Next, in the digital twin, the pore space is reduced by six voxels, and the geodetic sinuosity image is constructed, two projections and numerical characteristics are calculated, and the process is repeated. Three pairs of two-dimensional projections of the three-dimensional geodetic sinuosity image and the corresponding numerical characteristics of the pore space are displayed. Fig. 2 shows an example of the projection and numerical characteristics displayed, where the following elements can be highlighted:

[0045] Fig. 2a - projection 10 of the original image of geodetic tortuosity onto the XZ plane for the original digital twin of the core and the corresponding projections of the numerical characteristics 12 of the pore space;

[0046] Fig. 2b - projection 11 of the original image of geodetic tortuosity onto the YZ plane for the original digital twin of the core and the corresponding projections of the numerical characteristics 13 of the pore space;

[0047] Fig. 2c - projection 10 of the image of geodetic tortuosity onto the XZ plane for a digital twin of a core with pores narrowed by two voxels and the corresponding projections of the numerical characteristics 12 of the pore space;

[0048] Fig. 2g - projection 11 of the image of geodetic tortuosity onto the YZ plane for a digital twin of a core with pores narrowed by two voxels and the corresponding projections of the numerical characteristics 13 of the pore space;

[0049] Fig. 2d - projection 10 of the image of geodetic tortuosity onto the XZ plane for a digital twin of a core with pores narrowed by six voxels and the corresponding projections of the numerical characteristics 12 of the pore space;

[0050] Fig. 2e - projection 11 of the geodetic tortuosity image onto the YZ plane for a digital twin of a core with pores narrowed by six voxels and the corresponding projections of the numerical characteristics 13 of the pore space.

[0051] When outputting two-dimensional projections And Pixels where the ray intersected only non-pore voxels are shown on the screen in white, and pixels where the ray intersected only non-pore voxels are shown in blue. The remaining projection pixels are visualized using a gradient color palette from yellow to green.

[0052] Based on the projection type and numerical pore space characteristic values, the following conclusions can be drawn. The digital twin has narrow, tortuous pore channels that are distributed more or less uniformly. Critical pore throats, which provide flow connections between opposite faces of the digital twin, have cross-sections of less than three cells. Phase boundaries in a direct hydrodynamic description within the class of diffuse boundary methods (see Anderson DM, McFadden GB, Wheeler AA Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30, 139-165, 1998), which is the most widely used in the oil and gas industry, should be resolved over several cells (voxels), typically at least 5-7. Promptly determining the inapplicability of a given digital twin for modeling multiphase fluid flow using direct methods reduces time and resources.Moreover, the original digital twin is suitable for modeling single-phase hydrodynamic flow; in particular, an approximate estimate of absolute permeability can be obtained from the digital twin.

[0053] The information obtained from Fig. 2 not only allows us to draw conclusions about the practical applicability of this digital twin within the framework of classes of methods for specific tasks but also allows us to quantitatively understand the extent to which the digital twin's resolution must be increased to make it suitable for simulating multiphase fluid flow using direct methods. Given that the connectivity of the original digital twin is equal to unity and remains quite high when the pore size is reduced by two voxels, it is necessary to increase the computed tomography resolution by at least 2.5 times (i.e., to 1 voxel per μm) to obtain a digital twin suitable for simulating multiphase flow using direct methods.

[0054] In the second example, a 3D image of a core sample with a resolution of 0.4 voxels per µm is also obtained using X-ray microtomography. Next, through segmentation using deep neural networks, an initial digital twin of the core sample is created in the form of a cuboid, in which the pore voxels are equal to 1 and the rock voxels are equal to 0. Two opposite faces in the XY plane are selected, perpendicular to the direction of fluid flow along the OZ axis. The steps of the method for creating 3D images of geodetic tortuosity, calculating projections and numerical characteristics of the pore space, narrowing the pore space, and displaying them are similar to the first example. Fig. 3 shows an example of displaying projections and numerical characteristics, where the designations are identical to the elements in Fig. 2.

[0055] Based on the projections and numerical characteristics of the pore space, it can be concluded that this digital twin has a more or less uniform distribution of wide pore channels (throat diameter greater than 6 voxels) with minor tortuosity. Such digital twins are applicable for modeling both single-phase and multiphase hydrodynamic flows using virtually the entire range of known mathematical and numerical methods. Moreover, when using direct modeling methods, the achieved accuracy is sufficient for most practical problems.

Claims

1. A method for visualizing and numerically describing the pore space of a digital twin of a core, according to which: - a three-dimensional image of the core sample is obtained using tomography; - from the obtained image, an initial three-dimensional digital twin of the core sample is created, in which the voxels of the pore space are marked and two opposite faces are specified through which the fluid flow is modeled; - for each voxel of the original digital twin of the core, the value of geodetic sinuosity is calculated and an initial three-dimensional image of geodetic sinuosity is created; - calculate two-dimensional projections of the original three-dimensional image of geodetic tortuosity onto two mutually orthogonal planes, orthogonal to the faces through which the fluid flow is modeled; - based on the obtained two-dimensional projections of the initial three-dimensional image of geodetic sinuosity, the initial numerical characteristics of the pore space are calculated; - at least once the pore channels of the original digital twin of the core are narrowed using the morphological erosion operation, after which for each voxel of the digital twin of the core with narrowed channels the value of geodetic tortuosity is calculated and a three-dimensional image of geodetic tortuosity is created, two-dimensional projections of the created three-dimensional image of geodetic tortuosity are calculated onto two mutually orthogonal planes orthogonal to the faces through which the fluid flow is modeled and numerical characteristics of the pore space are calculated from the two-dimensional projections and display on the screen all the obtained images of two-dimensional projections of the three-dimensional image of geodetic tortuosity and the numerical characteristics of the pore space.

2. A method for visualizing and numerically describing the pore space of a digital twin of a core sample according to paragraph 1, in accordance with which, based on the type of two-dimensional projections obtained and the obtained values ​​of the numerical characteristics of the pore space, the applicability, type, and parameters of the hydrodynamic simulator for the original digital twin of the core sample are determined.

3. A method for visualizing and numerically describing the pore space of a digital twin of a core according to paragraph 1, according to which, when displaying two-dimensional projections on a screen, the first color denotes those pixels where the projection beam intersected only voxels that are not related to pores, the second color denotes those pixels where the beam from among the pores intersected only non-through pores, the remaining pixels of the projections are visualized using a gradient color palette that does not include the first and second colors, where the color is selected depending on the minimum value of the geodesic tortuosity of the voxels intersected by the projection beam.

4. A method for visualizing and numerically describing the pore space of a digital twin of a core according to paragraph 1, according to which, based on the obtained two-dimensional projections of a three-dimensional image of geodetic sinuosity, the following numerical characteristics of the pore space are calculated: average geodetic sinuosity, standard deviation of geodetic sinuosity, connectivity and coverage.

5. A method for visualizing and numerically describing the pore space of a digital twin of a core sample according to paragraph 1, according to which the narrowing of the pore channels of the digital twin of a core sample using a morphological erosion operation, the subsequent creation of an image of the digital twin of the core sample with narrowed pore channels, where each voxel of the digital twin of the core is equal to the geodesic sinuosity, the calculation of two-dimensional projections of a three-dimensional image of the geodesic sinuosity onto two mutually orthogonal planes orthogonal to the faces through which the fluid flow is modeled and the calculation of the numerical characteristics of the pore space based on the obtained two-dimensional projections are repeated until through pores exist in the digital twin of the core sample.

6. A method for visualizing and numerically describing the pore space of a digital twin of a core according to paragraph 1, in accordance with which all obtained two-dimensional projections of a three-dimensional image of geodetic sinuosity are displayed on the screen in the form of animation.

7. A method for visualizing and numerically describing the pore space of a digital twin of a core according to paragraph 1, in accordance with which all obtained numerical characteristics of the pore space are displayed on the screen in the form of graphs.

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