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Fundamental to the description of flow in a porous medium is an understanding of Poiseuille flow in capillaries. For 1D incompressible laminar fluid flow within a capillary of radius rp, the average velocity v¯ is proportional to the pressure drop (Δp) per unit length and is

(4.1)

where μ is the shear viscosity (henceforth viscosity) and l is the capillary length. This result forms the basis of single-phase flow in porous media, which is best understood by considering the fundamental attributes of such a medium.

A porous medium is best described as an assembly of grains with voids in their midst. In a consolidated (cemented) medium, the voids may or may not be connected. Nevertheless, the ratio of the void volume to the total volume is the porosity. In any packed arrangement of grains, consolidated or otherwise, the porosity thus defined depends upon the total volume. It also depends on the initial point about which the porosity is computed. If the measured porosity is independent of the initial point, and does not vary beyond a particular volume called the representative volume or a macroscopic volume, then the medium is homogeneous and uniform according to the definition of Greenkorn (1983). An illustration of the concept is shown in Chapter 3, Fig. 3.3.

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