Models of multi-phase flow in porous media typically include an equilibrium constitutive relationship between capillary pressure (Pc) and saturation (S). Use of an equilibrium relationship implies that time scales of dynamics between those variables are short (fast) relative to time scales associated with other system dynamics. Practical guidance in the soil science literature regarding time scales for equilibrium between Pc and S indicates that an equilibrium relationship may not be justified. An alternative formulation has been developed in which a dynamic, time-dependent relationship between Pc and S is introduced. Initial investigations of data reported in the literature indicate that dynamics in the Pc-S relationship exist, and associated analysis shows that those dynamics can be captured within this dynamic formulation. While this formulation is promising, there are a number of significant aspects that need to be investigated, from the fundamental nature of the underlying dynamics, to the ways in which the dynamics change as a function of spatial averaging scale and degree of heterogeneity. To address the nature of these dynamics, three hypotheses are posed, which form the basis for the proposed work: Hypothesis 1: Viscous Effects at the Pore Scale lead to a Dynamic Capillary Pressure. Hypothesis 2: Dynamic Capillary Pressure effects are progressively more important as averaging length scale increases and as the degree of subscale heterogeneity increases. Hypothesis 3: The dynamic coefficient in the new formulation is not constant but a well-defined function of saturation Sw. These hypotheses will be tested using computational models of multiphase flow across a range of length scales. If these hypotheses are true, then the way that two-phase flow problems have been described and modeled for more than 50 years will need to be modified, with a fundamentally new parameter introduced, and a concomitant new way of thinking about these systems. This project will have broader impacts beyond the specific porous media research. In addition to usual development of graduate students, the project will include collaborations with colleagues at the University of Bergen (Norway) and the Technical University of Delft (Netherlands), including exchanges of graduate students between those institutions and Princeton University. In addition, an international workshop will be convened at Princeton during the third year of the project, to discuss the specific topic of new constitutive relationships for multi-phase flow with a focus on dynamic capillary pressure.
