Collections > Master's Papers > Gillings School of Public Health > A Beginner's Guide to the Understanding of Integral Continuum Approaches Applied to the Formulation of Flow and Transport Equation in Porous Media Systems

Standard approaches exist in many fields of science and engineering for the description of multiphase flow and transport phenomena in porous media; we focus on multiphase subsurface systems in this work. The common approach to the formulation of balance equations for such systems is limited by several inconsistencies and approximations that affect the accuracy of these formulations in a manner and to an extent that is not well understood. The constitutive relations traditionally applied have evolved under restrictive assumptions and conditions yet are routinely applied to systems that are much different. Additionally, paradoxes exist in the commonly applied constitutive relations. The integral continuum approach yields a complete formal averaging formulation of mass, momentum, and energy balance laws for volumes, interfaces, and contact lines. This formulation can be constrained by entropy balance relations to yield a more complete and thermodynamically consistent description of multiphase flow and transport phenomena than is available through standard approaches. In this work, we:(1) review the standard approach for modeling multiphase flow and transport, noting inconsistencies and limitations; (2) outline the integral continuum approach at the microscale and macroscale; (4) compare and contrast the balance equations resulting from the approaches; (5) derive integral continuum balance equations, formally averaged from th emicroscale to the macroscale, for volumes, interfaces, and contact lines; (6) apply the integral continuum balance equations to a two fluid-phase subsurface system; (7) constrain the application thermodynamically utilizing the methodology of Coleman and Noll [1963]; and (8) comment on the unresolved issues facing the application of integral continuum approaches, noting promising approaches for the resolution of these issues.