Выпуск: 6 , Том: 17 , Год издания: 2025

We propose numerical methods for determining the full porosity, effective conductivity, and absolute permeability of a geological medium's samples whose internal structure is represented as layer-by-layer tomographic images. The principle of multiscale decomposition of the computational domain is applied to construct a discrete hierarchical mesh model of the sample. It allows us to describe the structure of a heterogeneous medium in sufficient detail. We present the step-by-step averaging procedure for a rock sample's electrical and transport properties by determining the effective characteristics of individual macroelements of the mesh decomposition, and their further averaging based on the proposed algorithms. To determine the effective specific electrical conductivity, the problem of the electrical field potential's distribution in the sample volume is solved numerically, using a multiscale modification of the scalar finite element method. The absolute permeability tensor is computed by numerically simulating the fluid dynamics based on computational schemes using nonconforming finite element methods. In the first stage, in each subarea from the decomposition, the problem of recovering the effective specific conductivity coefficient and the absolute permeability coefficient tensor is solved. In the second stage, a union of subareas with effective physical characteristics is considered as the computational domain, and the procedure of numerical homogenization is implemented, applying one of the proposed algorithms. We present the results of computational experiments using inconsistent decomposition and formulate the limitations of this approach. The developed algorithms have a natural parallel computational structure and can be adapted for the numerical determination of other physical characteristics of heterogeneous media.