Abstract:
We propose numerical methods for determining the full porosity, effective conductivity,
and absolute permeability of geological medium 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 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 electric field potential distribution in the sample volume is solved numerically, using a multiscale modification of the scalar finite element method. To calculate
the tensor of absolute permeability coefficients, numerical simulation of the fluid dynamics process is implemented based on computational schemes of non-conforming 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.
Keywords:digital core, numerical modeling, effective specific conductivity, absolute permeability.
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