Abstract: 
We investigate the impact of nonlinearity of high and low velocity flows on the well productivity index (PI). Experimental data shows the departure from the linear Darcy relation for high and low velocities. Highvelocity (postDarcy) flow occurring near wells and fractures is described by Forchheimer equations and is relatively wellstudied. While low velocity flow receives much less attention, there is multiple evidence suggesting the existence of preDarcy effects for slow flows far away from the well. This flow is modeled via preDarcy equation. We combine all three flow regimes, preDarcy, Darcy and postDarcy, under one mathematical formulation subjected to certain critical transitional velocities. This allows to use our previously developed framework to obtain the analytical formulas for the PI for the cylindrical reservoir. We study the impact of nonDarcy effect on the PI depending on the wellflux and the parameters of the equations. 
