## Scientific Journal of Samarkand University

#### Abstract

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.

#### First Page

27

#### Last Page

30

#### References

- Haritonova G.V., Manucharov A.C., Chernomorchenko N.I., Zemlyanuxin V.N. Vliyaniye obmennix kationov Na i Mg na poverxnostnie svoystva glinistix // Pochvovedeniye. 2002. № 1. S. 87-92.
- Rice J.R., Cleary M.P. Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents // Rev. Geophys. Space Phys., 1976, v. 14, pp. 227-241.
- Sherwood J.D. Biotporoelasticity of a chemically active shale // Proc. R. Soc. bond., 1993, A 440, pp. 365-377.
- Sherwood J.D., Bailey L. Swelling of a shale around a cylindrical wellbore // Proc Royal SocLond A., 1994, v. 444, pp. 161–184.
- Imomnazarov B., Imomnazarov Kh
**.**Poroelasticity theory of chemically active clay shales // Bull. Nov. Comp. Center, Math.Model. inGeoph., 2017, No. 20., pp. 11-17. - Detournay E., Cheng A.H.-D. Poroelastic response of a borehole in a non-hydrostatic stress field // Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 1988, Vol. 25, No. 3, pp. 171-182.

#### Recommended Citation

Imomnazarov, B. X.; Imomnazarov, X. X.; and Khaydarov, Ilkhom
(2020)
"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