The role of interfacial areas in two-phase flow in porous media : bridging scales and coupling models
Jennifer Niessner · OPUS Publication Server of the University of Stuttgart (University of Stuttgart) · 2010
This habilitation deals with a thermodynamically consistent modeling of two-phase flow in porous media which is extremely relevant for the understanding, the prediction, and optimization of the processes in many environmental, technical, and biological systems. Among these are the storage of carbon dioxide in the subsurface, methane migration from abandoned coal mines, the migration of radioactive gases from nuclear waste disposal sites (environmental systems), the processes in fuel cells and heat exchangers (technical systems) or the interaction between blood vessels and interstitial space (biological systems) which is very important for cancer therapy. The presented thermodynamically consistent model of two-phase flow in porous media is the first to numerically account for the extremely important role of phase-interfacial areas. This is put into practice through use of a rational thermodynamics approach by Hassanizadeh and Gray [1990] which not only includes interfaces as parameter in the equations, but additionally as entities allowing the formulation of conservation equations for interfaces. To be exact, conservation equations of mass, momentum, energy, and entropy are formulated on the pore scale for phases and interfaces and volume-averaged to the macro scale. The entropy productions of the entropy conservation equations are used to formulate the second law of thermodynamics. A speciality of the approach is the fact that thus, constitutive relationships do not need to be empirically formulated, but can be obtained by exploiting the residual entropy inequality. The aim of this work is to make the thermodynamically consistent and physically-based model accessible to numerical modeling allowing to represent effects which could otherwise not (or only using completely empirical approaches) be described. Among these are capillary hysteresis as well as the kinetics of mass and energy transfer between phases as these transfer processes take place across interfaces and thus, are highly dependent on them. Based on indicators and dimensionless quantities, the integration of the interfacial-area-based model into a multi-scale multi-physics framework is shown. This allows for the solution of the physically-based and thermodynamically consistent model whenever this is necessary and the solution of the empirical, but less costly, classical model wherever and whenever the physical situation allows. With such an approach, computing times and the amount of data needed can be drastically reduced.