A thermodynamically mathematically matched model of the linear theory of poroelasticity is proposed for describing shale swelling with an aqueous electrolyte. In this case, it is assumed that shale behaves as an isotropic, ideal ionic membrane, and in this case, the swelling depends only on the full stress tensor and on the chemical potential of water in the pores of the rock. The diffusion equation for pressure was obtained from the equation of poroelasticity, in the presence of chemical effects. It is shown that the diffusion coefficient is inversely proportional to the porosity.
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Imomnazarov, B. X.; Imomnazarov, X. X.; and Khaydarov, Ilkhom
"About one mathematical model of swelling of the clay shay around cylindrical well,"
Scientific Journal of Samarkand University: Vol. 2020
, Article 43.
Available at: https://uzjournals.edu.uz/samdu/vol2020/iss1/43