Theoretical and numerical modeling of electric conductance of rocks with coupling pores

The study focuses on electric conductance of two-dimensional and three-dimensional two-component medium containing intersecting inclusions. The conductance was calculated for two limit cases–perfect conductive inclusions and insulating inclusions. Using the method of single inclusion addition, expressions are obtained for the conductance in such media. In 2D case, the conductance in the medium with circular inclusions is obtained, in 3D cases, the conductance in the medium with spherical inclusions, which totally conforms with the real-life structure of porous rocks, is obtained. The dependences underwent check-up via modeling of the conductance in two-component rocks in COMSOL Multiphysics. The agreement of the numerical results with the dependences and with the predictions of the effective medium method was tested. In the two-dimensional case, the method of single inclusion addition had a distinct advantage over the method of effective medium both for perfect conductive and isolating circular inclusions. In the three-dimensional case, the effective medium method is preferable for the spherical inclusions, while both methods are usable for the isolating inclusions. The proposed method also allows indication of the connection between the shape of inclusions and the exponent in the Dakhnov–Archie equation used to estimate rock porosity. 

Sizin P. E. Theoretical and numerical modeling of electric conductance of rocks with coupling pores. MIAB. Mining Inf. Anal. Bull. 2026;(12):48-60. [In Russ]. DOI: 10.25018/0236_1493_2026_12_0_48.

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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