Non-equilibrium Statistical Mechanics of Two-Phase Flow in Porous Media

Abstract

The world that we live in is a consortium of fluid-solid interactions. The field of two-phase flow in porous materials poses interesting questions regarding such interactions. In this project, we develop a statistical mechanical and non-equilibrium thermodynamical formalism to describe the flow of immiscible fluids in porous media such as rocks or sand.

A key concept underpinning this work is the configuration probability, also known as the ensemble distribution. It is the probability that a fluid bubble has a certain position in the space of interest. The knowledge of the configuration probability allows us to construct a very efficient Metropolis Monte Carlo algorithm to evolve the two-phase flow system to steady-state.

Central to two-phase flow problems is the relative permeability formalism, which describes the behavior of two immsicible fluids that are competing for the void space in a porous material. We question the assumptions upon which this formalism is based and derive new equations that are analogous to thermodynamic relations such as the Gibbs Duhem equation.

Finally, as a concrete example of industrial applications of non-equilibrium thermodynamics, we investigate the capacity of thermoelectric generators to produce power from a transient environment of a silicon production plant operating at very high temperatures.