Theoretical stability analysis of mixed finite element model of shale-gas flow with geomechanical effect

Abstract

In this work, we introduce a theoretical foundation of the stability analysis of the mixed finite element solution to the problem of shale-gas transport in fractured porous media with geomechanical effects. The differential system was solved numerically by the Mixed Finite Element Method (MFEM). The results include seven lemmas and a theorem with rigorous mathematical proofs. The stability analysis presents the boundedness condition of the MFE solution.

Editorial: Advanced modeling and simulation of flow in subsurface reservoirs with fractures and wells for a sustainable industry

“…The results indicated that the gas effective permeability increases in a less complex and more discrete pore network. El-Amin et al [10] introduced a theoretical foundation of the stability analysis of the mixed finite element solution to the problem of shale-gas transport in fractured porous media with geomechanical effects, in which the differential system was solved by the Mixed Finite Element Method (MFEM).…”