Conductivity of geological environment with plane-parallel system of joints

The article discusses conductivity of two-dimensional and three-dimensional medium containing a plane-parallel system of conductive or insulating thin fractures. Using the known formulas for small increments of conductivity in a medium with a single crack, the differential equations are derived for the conductivity in a medium with cracks of a considerable concentration. The equations are exponential and contain no percolation thresholds. In the two-dimensional case, the cracks represented short segments, and in the three-dimensional case, the cracks were thin circular disks, which allowed modeling jointed rocks. Then, in COMSOL Multiphysics, agreement was checked between the numerical results and theoretical relationships of two-component medium conductivity and crack concentrations, and also with the EMA predictions in 2D case. In two dimensions, at random arrangement of centers of conductive cracks, the increment in conductivity with the increasing concentration of cracks is linear. The change in conductivity of a medium with insulating cracks is dual relative to the change in conductivity of a medium with insulating cracks. At a regular arrangement of cracks, conductivity is described well using the EMA and the method of addition of singular defects. In three dimensions, conductivity of a medium both with conductive and insulating cracks is described well using the method of adding singular defects. Advantages of the proposed technique over the EMA are the mathematical simplicity and applicability to a wider class of defects and cracks.

Sizin P. E. Conductivity of geological environment with plane-parallel system of joints. MIAB. Mining Inf. Anal. Bull. 2024;(8):79-91. [In Russ]. DOI: 10.25018/0236_1493_ 2024_8_0_79.

P.E. Sizin, Cand. Sci. (Phys. Mathem.), Assistant Professor, NUST MISIS, 119049, Moscow, Russia, e-mail: mstranger@list.ru, ORCID ID: 0000-0001-8156-4972.

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