A mathematical model of the electrical resistivity of a deformed rock
When (ρ1/ρ2 = 1, as the moisture content rises, the graph of ρ vs σav rapidly becomes linear; as the moisture content of coal rises, the inclinations, of the lines to the axis of σav decrease.
When ρ1/ρ2 ≪ 1, the resitivity depends very markedly on the moisture content. The presence of even very small amounts of water in the pores alters the conductivity of a rock by many orders of magnitude in comparison with that of the dry rock. In this case (when the moisture content is WS>0.5–0.6%), we can use Eq. (11), which gives a linear relation between ρ and σav.
For dry rocks the graph of ρ vs σav is nonlinear. A qualitative comparison between the curves in Fig. 2a-b and those obtained experimentally by Petukhov and Dal’nov  reveals that the model considered by us for a deformed porous medium gives a fair expression of the main laws accompanying the change in electrical conductivity of rocks during deformation. For the limitations mentioned above, the relation in Eq. (10) can be used to calculate ρ(σav) for any form of the function ɛv = ɛv(σav), expressing any rheological hypothesis corresponding to a real rock.
KeywordsPorous Medium Electrical Resistivity Coal Seam Water Saturation Lignite
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