A Statistical Mechanics Framework for Immiscible Two-Phase Flow in Porous Media

Introduction

The flow of immiscible fluids in porous media is at the heart of a wide range of applications, some of which are central to humanity. Oil recovery has traditionally had such a role, but more recently, aquifer replenishment to maintain water supplies has become a field of increasing worldwide importance.

Complexity of Immiscible Multiphase Flow

Immiscible multiphase flow in porous media is a problem in hydrodynamics of extraordinary complexity. Not only does one have the intricacies of moving fluid interfaces, but the flow occurs within a pore space having a highly contorted geometry.

Length Scales in Porous Media

Porous media typically span orders of magnitude in length scales:

• The pore scale may be in the micrometer range or less.
• The macroscopic scale may be in the kilometer range.

Is there a way to find a description of the flow at these large scales from a knowledge of how the fluids behave at the pore scale?

Reformulating Statistical Mechanics

My claim is that there is. Statistical mechanics, which has been used to derive thermodynamics from the motion of molecules, can be reformulated to do the same for immiscible multiphase flow in porous media. This sounds like an impossible task as statistical mechanics demands equilibrium whereas the flow problem is driven. The approach I propose is based on information theory and hydrodynamics.

Objective

My objective is to develop a complete theory for immiscible multiphase flow in porous media at large scales based on a reformulation of statistical mechanics that encompasses the pore scale physics and which is simple enough to be useful in practical engineering applications.

Practical Implications

This will allow me to reproduce accurately the formation of viscous fingers when a less viscous fluid invades a more viscous fluid. This is a problem as important in field-scale modelling as it is difficult.

Broader Impact

This will be the first time a statistical mechanics framework for non-thermal, non-equilibrium systems has been developed. This has interest far beyond the realm of porous media.