On the consistency of scale among experiments, theory, and simulation

James E Mcclure,Amanda L Dye,William G Gray,Cass T Miller

doi:10.5194/hess-21-1063-2017

Abstract

Abstract. As a tool for addressing problems of scale, we consider an evolving approach known as the thermodynamically constrained averaging theory (TCAT), which has broad applicability to hydrology. We consider the case of modeling of two-fluid-phase flow in porous media, and we focus on issues of scale as they relate to various measures of pressure, capillary pressure, and state equations needed to produce solvable models. 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. 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. 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 compute 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.

Highlights

Hydrologic systems are typically investigated using some combination of experimental, computational, and theoretical approaches
In the formulation that follows, we show how microscale pressures can be averaged in a variety of ways as well as the relationship of these averaged pressures to the true capillary pressure
We show that the ability to quantitatively analyze the internal structure of two-fluid porous medium systems has a profound impact on macroscale understanding

Summary

Introduction

Hydrologic systems are typically investigated using some combination of experimental, computational, and theoretical approaches. The macroscale is a scale for which a point is associated with some averaged properties of an averaging region comprising all phases, interfaces, and common curves present in the system Notions such as volume fraction and specific interfacial area arise when a system is represented at the macroscale in terms of averaged measures of the state of the system. Because of historical limitations on both computational and observational data, the macroscale has been the traditional scale at which models of natural porous media systems have been formulated and solved. Closure relations at this scale are needed to yield well-posed models. A precise coupling between these disparate length scales has usually been ignored

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