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.
Highlights
Finite Element Methods (FEMs) are effective numerical techniques for solving the complex engineering problems
The Mixed Finite Element Methods (MFEMs) have succeeded in eliminating such instabilities [6, 7] as it may be extended to higher-order approximations as well as it is a locally
El-Amin et al [22] have used the MFEM with stability analysis to simulate the problem of natural gas transport in a low-permeability reservoir without considering fractures
Summary
Finite Element Methods (FEMs) are effective numerical techniques for solving the complex engineering problems. The Mixed Finite Element Methods (MFEMs) have succeeded in eliminating such instabilities [6, 7] as it may be extended to higher-order approximations as well as it is a locally. El-Amin et al [22] have used the MFEM with stability analysis to simulate the problem of natural gas transport in a low-permeability reservoir without considering fractures. We present a theoretical basis with proofs of the stability analysis of the MFEM (in Ref. [23]) including the necessary lemmas and theorem
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