Modeling two-fluid-phase flow and species transport in porous media

- Rigorous modeling framework for two-phase porous medium systems is provided.
- Complete set of macroscale conservation equations and closure relations is specified.
- Macroscale models are consistent across scales and with second law of thermodynamics.

SummaryThe thermodynamically constrained averaging theory (TCAT) is used to formulate a modeling framework for mechanistic models of species transport in multiphase porous medium systems containing two fluid phases and a solid phase. Primary restrictions guide the selection of entities and the set of conservation and balance equations needed to formulate an augmented entropy inequality (EI). Classical irreversible thermodynamics is upscaled from the microscale to the macroscale and used to provide a connection among material derivatives that arise from the conservation and balance equations under near-equilibrium conditions. An essentially exact constrained EI (CEI) is derived to approach the force-flux form of the EI that is desired. A set of approximations is applied to the CEI to produce a non-unique simplified EI (SEI), which is in the strict force-flux form needed to guide the formulation of closure relations.Sets of secondary restrictions are applied to the general SEI to form simpler subsets of the general SEI that apply for the local thermal equilibrium and isothermal cases. The SEI is then used to constrain the permissible form of the closure relations and to formulate a set of low-order closure relations. A specific model instance is formulated in closed form by specifying a complete set of conservation equations and closure relations. Many other model instances can be derived from the general modeling framework presented, and these potential extensions are discussed.