Chapter 14: Single-Phase Permeability

The capacity to flow fluids is one of the most important properties of reservoir rocks. As a result, extensive research has been applied to describe and understand the permeability of rocks to fluid flow. In this chapter, only single-phase or absolute permeability will be considered. Multiphase relative permeabilities must be derived using relations described in the chapter on relative permeability and capillary pressure.

Permeability ( k ) is a rock property relating the flow per unit area to the hydraulic gradient by Darcy’s law,

where p is pressure, ρ is fluid density, g is gravitational acceleration, z is elevation, and μ is the dynamic viscosity. The ratio q/A has the units of velocity and is sometimes referred to as the “Darcy velocity” to distinguish it from the localized velocity of flow within pore channels. The natural unit of k is length squared; however, petroleum usage casts Eq. 14.1 in mixed units, so that the unit of k is the darcy, which is defined as the permeability of a porous medium filled with a single-phase fluid of 1-cp viscosity flowing at a rate of 1 cm ³ /s per cross-sectional area of 1 cm ² under a gradient of 1 atm pressure per 1 cm. ¹  Reservoir rocks are usually characterized in millidarcies (md), a unit that is 1/1000 of a darcy. Conversion factors are 1 darcy = 0.9869×10 ^-12 m ² or 1 md = 0.9869×10 ^-11 cm ² . Bass ²  noted that Darcy’s law holds only for viscous flow and that the medium must be 100% saturated with the flowing fluid when the determination of permeability is made. Furthermore, the medium and the fluid must not react by chemical reaction, absorption, or adsorption; otherwise, the permeability changes as the fluid flows through the sample. Darcy’s law ( Eq. 14.1 ) has many practical applications, including determination of permeability in the laboratory and wellbore.