The increasing demands for oil, water, and food produced in an environmentally sound manner have placed emphasis on the manner of their production, a major part of which is concerned with flow through porous media.

The movement of materials through porous media is of interest in many disciplines: in chemical engineering—adsorption, chromatography, filtration, flow in packed columns, ion exchange, reactor-engineering; in petroleum engineering—displacement of oil with gas, water and miscible solvents including surface-active agent solutions and description of reservoirs; in hydrology—movement of trace pollutants in water systems, recovery of water for drinking and irrigation, salt water encorachment into fresh water reservoirs; in soil physics—movement of water, nutrients, and pollutants into plants; in biophysics—life processes such as flow in the lung and the kidney.

This paper reviews the fundamentals of steady flow through porous media: it discusses the pseudotransport coefficients permeability, capillary pressure, and dispersion and relates these coefficients to the geometry of porous media. It also discusses single-fluid flow, multifluid immiscible flow, and multifluid miscible flow including the effects of heterogeneity, nonuniformity, and anisotropy of media.