On the Consistency of Scale Among Experiments, Theory, and
Simulation
Abstract. The career of Professor Eric F. Wood has focused on the resolution of problems of scale in hydrologic systems. Within this context, we consider an evolving approach known as the thermodynamically constrained averaging theory (TCAT), which has broad applicability to hydrology. Specifically, we consider the case of modeling of two-fluid-phase flow in porous media. Two-fluid flow processes in the subsurface are fundamentally important for a wide range of hydrologic processes, including the transport of water and air in the vadose zone and geological carbon sequestration. Mathematical models that describe these complex processes have long relied on empirical approaches that neglect important aspects of the system behavior. New data sources make it possible to access the true geometry of geologic materials and directly measure previously inaccessible quantities. This information can be exploited to support a new generation of theoretical models that are constructed based on rigorous multiscale principles for thermodynamics and continuum mechanics. The challenges to constructing a mature model are shown to involve issues of scale, consistency requirements, appropriate representation of operative physical mechanisms at the target scale of the model, and a robust structure to support model evaluation, validation, and refinement. We apply TCAT to perform physics-based data assimilation to understand how the internal behavior influences the macroscale state of two-fluid porous medium systems. Examples of a microfluidic experimental method and a lattice Boltzmann simulation method are used to examine a key deficiency associated with standard approaches. In a hydrologic process such as evaporation, the water content will ultimately be reduced below the irreducible wetting phase saturation determined from experiments. This is problematic since the derived closure relationships cannot predict the associated capillary pressures for these states. In this work, we demonstrate that the irreducible wetting-phase saturation is an artifact of the experimental design, caused by the fact that the boundary pressure difference does not approximate the true capillary pressure. Using averaging methods, we measure the true capillary pressure for fluid configurations at and below the irreducible wetting phase saturation. Results of our analysis include a state function for the capillary pressure expressed as a function of fluid saturation and interfacial area.