Methane in Subsurface: Mathematical Modeling and Computational Challenges

We discuss mathematical and computational models of two applications important for global climate and energy recovery involving the evolution of methane gas in the subsurface. In particular, we develop advanced models of adsorption occuring in coalbed methane recovery processes, and discuss the underlying conservation laws with non-standard terms. Next we describe the phase transitions relevant for modeling methane hydrates in subsea sediments where the major challenge comes from implementation of solubility constraints. For both applications we formulate the discretization schemes and outline the main challenges in convergence analysis and solver techniques. We also motivate the need for continuum and discrete models at porescale.