Methane in Subsurface: Mathematical Modeling and Computational Challenges

Abstract

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 implemen-tation 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. Key words. multiphase and multicomponent flow and transport, porous media, adsorption models, phase transitions, finite differences, methane hydrates, semi-smooth functions, semi-smooth Newton methods, hysteresis, coalbed methane, mean-field equi-librium models AMS(MOS) subject classifications. 76S05, 65M06, 65M22, 74N30, 76V05, 80A30, 65M75 1. Introduction. Methane is both a greenhouse gas and an energy resource. In this paper we discuss the challenges in computational model-ing of methane in two applications important for global climate and energy studies, namely Enhanced Coalbed Methane (ECBM) recovery, and mod-eling methane hydrate evolution in subsea sediments (MH). Coalbed methane is a form of natural gas extracted from coal beds. In recent decades it has become an important source of energy in the United States and other countries, and coal and methane are important energy resources exported from the US. In the ECBM technology, carbon dioxide and/or nitrogen or other gases are injected into unmineable coal seams to promote displacement and extraction of methane. Recent pilot projects in various countries evaluated ECBM as a potential carbon sequestration technology [140, 51, 148, 82, 135, 49, 46]. The technology appears promising but is associated with various uncertainties and hazards, not the least of which include incomplete understanding of the underlying processes and difficulties with carrying out experiments.