Closure and Numerical Simulation of a New Class of Multiphase Flow and Transport Models.

Abstract: Abstract. Multiphase flows in porous media occur in a variety of phenomena in science and engineering, with applications ranging from biomedicine to oil recovery systems in petroleum engineering. Mathematical models are essential for enhancing our predictive capabilities in the study of such systems. A subset of models commonly used to describe transport phenomena in subsurface systems suffer from several limitations in achieving this goal. For example, classical models are typically posed in terms of quantities that are not systematically linked to well defined quantities at smaller scales; they are typically closed with ad hoc nonlinear, hysteretic closure relations expressing the interdependence among fluid pressures and saturations; and these models do not include explicit account for such factors as contact angles, interfacial areas, and curvatures, which would be expected from the consideration of the microscale physics of such systems. These shortcomings have inspired an approach based on a thermodynamically constrained averaging theory, to derive multiphase flow and transport models which follow more directly from fundamental physical principles. Results are accumulating that show that the new approach can resolve some of the shortcomings with traditional models. We examine the form of the new models, and we use the results of lattice-Boltzmann simulations to guide the formulation of closure relations that explicitly include interfacial areas. Our goal is to produce well-posed, closed models of multiphase systems and to compare these models with traditional formulations and experimental results. Toward this goal, we examine and analyze certain distinguished limits and present results from computational simulations that support this new class of models. Once established, we plan to tailor numerical tools to the mathematical structure of our new class of models for large scale problems, thus bridging the scale gap between lattice-Boltzman simulations and in-field applications.