For flows in porous media with Reynolds numbers greater than about 1 to 10, inertial effects can also become significant. Sometimes an inertial term is added to the Darcy's equation, known as Forchheimer term. This term is able to account for the non-linear behavior of the pressure difference vs flow data.
where the additional term  is known as inertial permeability, in units of length .
The flow in the middle of a sandstone reservoir is so slow that Forchheimers equation is usually not needed, but the gas flow into a gas production well may be high enough to justify use of Forchheimers equation. In this case, the inflow performance calculations for the well, not the grid cell of the 3D model, is based on the Forchheimer equation. The effect of this is that an additional rate-dependent skin appears in the inflow performance formula.
Some carbonate reservoirs have many fractures, and Darcys equation for multiphase flow is generalized in order to govern both flow in fractures and flow in the matrix (i.e. the traditional porous rock). The irregular surface of the fracture walls and high flow rate in the fractures may justify the use of Forchheimers equation.