Principles of Single-Phase Flow Through Porous Media

Porous media are both permeable and dispersive to a traversing fluid. Flow of a single-phase fluid in porous media is not only of practical interest but also of fundamental significance in characterizing the porous media. In this chapter, the characteristics of porous media are introduced from both fundamental and application points of view. A continuum approach is used. The volume-averaged equations are used to describe the flow, where the momentum dispersion has been neglected. The relations between Darcy's law-Brinkmans equation and the volume-averaged Navier-Stokes equation are described. The Forchheimer hypothesis, Ergun equation, and Liu-Afacan-Masliyah equation are briefly described in terms of coupling of the viscous and inertial effects on the single-phase flow in porous media. Discussions are provided on the concept and modeling of areal porosity, tortuosity, permeability, and shear factor. A curved passage model is discussed in terms of the shear factor and pressure-drop modeling for flow through porous media. Bounding wall effects are discussed through a simple approach. Examples of flow simulations in porous media (i.e., slightly compressible flow in oil reservoirs and incompressible flow in fixed beds) are provided.