The basic law that describes the flow in porous materials is Darcy’s law. It describes a linear relationship between the velocity field u(m/s) and the gradient of the pressure p(Pa).

This is only valid for very low velocities or at low Reynolds numbers (Re < 10)

In case of relatively fast flow (Re > 10) or relatively high Knudsen numbers (Kn > 0.1) Darcy’s linear relation between velocity and pressure drop is no longer valid. Therefore, different Permeability Models have been introduced to capture these effects. A general form of the nonlinear relationship of pressure gradient to velocity can be written as

The flow regime through a packed bed may be identified from the Reynolds number of the bed. According to textbooks, for Reynolds numbers Re < 10 the flow can be described by Kozeny–Carman equation (Darcian flow). For 10 < Re < 1000, which is sometimes called the transitional regime, the flow is better described by the non-Darcian Ergun equation, and for Re > 1000 Ergun’s equation can be approximated by the Burke-Plummer equation for turbulent flows.