Modeling, analysis and simulation: methane hydrate in the subsurface

"If you never heard of methane hydrate, this might be good news". Methane hydrate is an ice-like crystalline substance made of water molecules encasing a molecule of methane, abundantly present in marine and Arctic sediments whenever pressure is high enough and temperature is low enough. Its presence is a “smoking gun” in climate science due to a possibility of release of methane gas into the atmosphere. On human time scales, methane hydrate is also an environmental hazard as well as a potential energy resource. In our work we considered a comprehensive PDE model for hydrate evolution which is a complex coupled system of 4 nonlinear equations coupled by thermodynamics constraints. To make progress towards the understanding of its mathematical structure, we must simplify the model, but the simplifications must be modest enough to keep the model relevant, mathematics interesting enough, and to allow for simulation of realistic case scenarios. In the talk we will present results of this compromise, and discuss the well-posedness of the model as well as numerical stability of finite volume schemes.