Fundamentals of Fluid Flow in Porous Media
Homogeneous usually means describing a material or system that has the same properties at every point in space; in other words, uniform without irregularities. It also describes a substance or an object whose properties do not vary with position. To apply this term on a porous medium we should define a “macroscopic system”. A few sand grains cemented together constitute a microscopic rather than macroscopic porous medium. The properties of a microscopic sample are not expected to be representative of the macroscopic porous medium from which it was removed.
Let us suppose that a macroscopic pore structure parameter such as porosity or permeability is determined in a series of samples of increasing size, taking from a large porous sample, and the result is plotted against the sample’s size. It could be seen that initially the calculated properties change with sample size and there are some fluctuations in the results with increasing sample size. With increasing sample size the amplitude of these fluctuations decreases and gradually diminishes until finally a smooth line is obtained after a certain sample size (Figure 2‑1). By definition “the sample said to be macroscopically representative whenever the macroscopic measured property (such as porosity and permeability) is not fluctuating any more when including more material around the initial sampling point, but its variation can be represented by a smooth line”