Well-Posedness of a fully coupled thermo-chemo-poroelastic system with applications to petroleum rock mechanics
White, Luther W.
Texas State University, Department of Mathematics
We consider a system of fully coupled parabolic and elliptic equations constituting the general model of chemical thermo-poroelasticity for a fluid-saturated porous media. The main result of this paper is the developed well-posedness theory for the corresponding initial-boundary problem arising from petroleum rock mechanics applications. Using the proposed pseudo-decoupling method, we establish, subject to some natural assumptions imposed on matrices of diffusion coefficients, the existence, uniqueness, and continuous dependence on initial and boundary data of a weak solution to the problem. Numerical experiments confirm the applicability of the obtained well-posedness results for thermo-chemo-poroelastic models with real-data parameters.
Parabolic-elliptic system, Poroelasticity, Thermo-poroelasticity, Thermo-chemo-poroelasticity, Existence, Uniqueness, Well-posedness
Malysheva, T., & White, L. W. (2017). Well-Posedness of a fully coupled thermo-chemo-poroelastic system with applications to petroleum rock mechanics. <i>Electronic Journal of Differential Equations, 2017</i>(137), pp. 1-22.
Attribution 4.0 International