Darcy's law can not describe fluid flow accurately when the flow rate is high. In most cases in the recovery process, fluid flow is governed by Darcy's law. But when the flow rate is very high, for an instance, near the wellbore, Darcy's law is inadequate to describe fluid flow.
In 1901, Forchheimer put forward a classical equation, known as the Forchheimer equation, to make up the deficiency encountered by Darcy's law at high flow rates. He added a non-Darcy term into the Darcy flow equation. The non-Darcy term is the multiplication of the non-Darcy coefficient, fluid density, and the second power of velocity. One of the most important aspects in determining the non-Darcy effect is to estimate the non-Darcy coefficient as accurately as possible.
In this paper, theoretical and empirical correlations of the non-Darcy coefficient in one-phase and multi-phase cases in the literature are reviewed. Most researchers have agreed that the non-Darcy effect is not due to turbulence but to inertial effect. The non-Darcy coefficient in wells is usually determined by analysis of multi-rate pressure test results, but such data are not available in many cases. So, people have to use correlations obtained from the literature. This paper summarizes many correlations in the literature, and will provide a good reference for those who are interested in the investigation of the non-Darcy effect in the recovery process.