Chapter 7 - Applications of Darcy’s Law

Abstract

This chapter describes the characteristics of the flow of fluids through porous geological materials. Darcy's law and its derivatives are used to describe the flow of compressible and incompressible fluids through porous rocks. The simplest case of fluid flow through porous media is the linear flow of a single-phase fluid under a constant pressure gradient, which is known as linear steady-state flow. When two fluids are present in a porous medium, steady-state flow occurs under a constant pressure gradient only when the fluid saturations remain constant. If the saturations change with respect to time, the flow of fluids is characterized as unsteady-state flow. Steady-state and pseudosteady-state flow rate equations, based on Darcy's law for linear and radial flow of compressible and incompressible fluids, can be used to predict the production performance of porous and permeable flow systems of simple geometry. Natural reservoir systems do not ordinarily conform to any simple geometrical shape. The two most practical geometries are the linear flow and the radial flow systems. In the linear system, the flow occurs through a constant cross-sectional area and the flow lines are parallel and in the radial system, the flow occurs between two concentric cylindrical surfaces, the well being the inner cylinder and the reservoir boundary the outer cylinder.