Non Darcy flow - Forchheimer equation

 Darcy’s Law is only valid for slow flow, where the flow is mostly laminar — in other words where water molecules pass through in straight lines, rather than creating turbulence that interferes with the flow.

Reynolds number:

 The Reynolds number is a measure that predicts if flow in a liquid will be laminar or turbulent — higher numbers indicate a higher likelihood of turbulent flow. Less viscous and faster moving liquids have higher Reynolds numbers — so water flowing quickly through an espresso puck has a higher Reynolds number than oil seeping through bedrock. 

At Reynolds numbers above 10, the turbulence becomes significant enough that Darcy’s Law is no longer accurate. When this happens, we need to introduce a correction to the equation — known as the Forchheimer term

Turbulence:

Ted Lingle coffee brewing handbook on turbulence (agitation)

ANSYS: How to define turbulence flow equation in CFD

Reference 

BaristaHustle

SlideShare - single phase flow 

SlideShare 

Researchgate 

Sensitivity aspect 

Comsol