On one thermodynamically consistent model of clay shale swelling

  • Imomnazarov Bunyod Kh., buned11998.07@mail.ru Novosibirsk State University, 1 Pirogov Street, Novosibirsk 630090, Russia
  • Khaydarov Ilkhom Q., khaydarov_iq@rambler.ru Chirchiq State Pedagogical Institute of Tashkent Region, 104 Amir Temur Street, Chirchiq 111700, Uzbekistan
  • Imomnazarov Kholmatzhon Kh., imom@omzg.sscc.ru Novosibirsk State University, 1 Pirogov Street, Novosibirsk 630090, Russia
Keywords: porous medium, saturated fluid, elastic parameters, stress tensor, partial density, Darcy law, chemical potential


A modified version of the linear poroelasticity theory described by three elastic parameters is applied to the mathematical modeling of shale swelling with an aqueous electrolyte. It is assumed that the shale behaves as an isotropic ideal ionic membrane, and in this case, swelling depends only on the total stress and on the chemical water potential in pores of the rock. A formula is obtained for the Poisson coefficient in terms of three elastic parameters, the physical densities of the saturated fluid of the porous medium, and the porosity coefficient. It is shown that the diffusion coefficient is a function of the coefficient of interfacial friction (permeability) and is inversely proportional to the coefficient of porosity. The formulas for the flat strain analysis around the wellbore were obtained.


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How to Cite
Imomnazarov, B., Khaydarov, I. and Imomnazarov, K. (2020) “On one thermodynamically consistent model of clay shale swelling”, Mathematical notes of NEFU, 27(2), pp. 93-104. doi: https://doi.org/10.25587/SVFU.2020.43.24.006.
Mathematical Modeling