We now take a break from the theoretical developments of the previous chapters and consider applications of lattice gases to the study of complex flows through complex geometries. Our complex geometry is one of the most complicated nature has to offer—a porous rock. The flows we consider are either those of a simple fluid, such as water, or an immiscible two-fluid mixture, such as water and oil. The problems we shall illustrate are not only of intrinsic interest for physics but have applications in fields as diverse as hydrology, oil recovery, and biology, to name just a few.

Our objectives in this chapter are twofold. First, we wish to indicate the level of accuracy that one may expect from these kinds of flow simulations. Second, we wish to show what we can learn from such work. We begin with a brief introduction to the subject.

Geometric complexity

All rocks found on the earth's surface are porous, but those rocks that we call sandstones are usually more porous than others. Sandstones are formed from random assemblages of sand grains that are cemented together over geologic time. Fluids such as oil or water may then become trapped in the pore space between the cemented sand grains. There may be an economic interest in extracting these fluids, or, equally possible in modern times, we may wish to predict the rate at which some contaminant such as radioactive waste could migrate through such a medium.