Toward a New Generation of Two-Fluid Flow Models Based on the Thermodynamically-Constrained Averaging Theory

Abstract

Traditional models of two-fluid flow through porous media at the macroscale have existed for nearly a century. These phenomenological models are not firmly connected to the microscale; thermodynamic constraints are not enforced; empirical closure relations are well known to be hysteretic; fluid pressures are typically assumed to be in a local equilibrium state with fluid saturations; and important quantities such as interfacial and curvilinear geometric extents, tensions, and curvatures, known to be important from microscale studies, do not explicitly appear in traditional macroscale models. Despite these shortcomings, the traditional model for two-fluid flow in porous media has been extensively studied to develop efficient numerical approximation methods, experimental and surrogate measure parameterization approaches, and convenient pre- and post-processing environments; and they have been applied in a large number of applications from a variety of fields. The thermodynamically constrained averaging theory (TCAT) was developed to overcome the limitations associated with traditional approaches, and we consider here issues associated with the closure of this new generation of models. It has been shown that a hysteretic-free state equation exists based upon integral geometry that relates changes in volume fractions, capillary pressure, interfacial areas, and the Euler characteristic. We show an analysis of how this state equation can be parameterized with a relatively small amount of data. We also formulate a state equation for resistance coefficients that we show to be hysteretic free, unlike traditional relative permeability models. Lastly, we comment on the open issues remaining for this new generation of models.

Towards Understanding Factors Affecting Arsenic, Chromium, and Vanadium Mobility in the Subsurface

“…Under such conditions, a mechanistic microscale model can provide an accurate description of the system [ 113 , 117 – 121 ]. However, natural subsurface systems of concern have length scales and media complexity that preclude the use of microscale models [ 111 – 113 , 116 , 117 , 133 , 134 ]. To produce mechanistic representations that are tractable, a larger scale representation, called the macroscale, must be used.…”

“…To produce mechanistic representations that are tractable, a larger scale representation, called the macroscale, must be used. At the macroscale, the mechanistic representation is based upon an averaged behavior of the underlying microscale representation of the system [ 111 – 113 , 116 , 117 , 119 , 133 , 134 ]. Such a representation can be approached with varying degrees of rigor ranging from phenomenological to detailed first-principles mathematical approaches for deriving such models.…”

“…Such a representation can be approached with varying degrees of rigor ranging from phenomenological to detailed first-principles mathematical approaches for deriving such models. Regardless of the rigor of the chosen approach, macroscale models require approximations of underlying microscale behavior that can introduce additional sources of error [ 114 , 116 , 117 , 133 , 135 – 137 ]. This error, referred to as modeling error, poses a challenge to macroscale modeling even if perfect knowledge of auxiliary conditions and model parameters exists.…”

“…Additional obstacles exist when the geochemical system of concern includes both a region above and below the water table. Such two-fluid flow problems come with their own model formulation issues [ 153 , 158 , 159 , 176 ], although recent advances suggest a new generation of macroscale models may resolve these deficiencies [ 133 , 181 – 183 ].…”