Sufficient conditions for Hadamard well-posedness of a coupled thermo-chemo-poroelastic system

Abstract

This article addresses the well-posedness of a coupled parabolic-elliptic system modeling fully coupled thermal, chemical, hydraulic, and mechanical processes in porous formations that impact drilling and borehole stability. The underlying thermo-chemo-poroelastic model is a system of time-dependent parabolic equations describing thermal, solute, and fluid diffusions coupled with Navier-type elliptic equations that attempt to capture the elastic behavior of rock around a borehole. An existence and uniqueness theory for a corresponding initial-boundary value problem is an open problem in the field. We give sufficient conditions for the well-posedness in the sense of Hadamard of a weak solution to a fully coupled parabolic-elliptic initial-boundary value problem describing homogeneous and isotropic media.

Keywords

• Parabolic-elliptic system
• poroelasticity
• thermo-poroelasticity,
• thermo-chemo-poroelasticity
• Hadamard well-posedness