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 0.1) Darcy’s linear relation between velocity and pressure drop is no longer valid.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.