This paper reviewed briefly and systematically the classical Darcy flow and its extended formulations known as Forchheimer , Brinkman or Forchheimer Brinkman extended Darcy flow.

A new skin factor model for open hole completion of horizontal wells under Non-Darcy flow;

Consolidation computation of aquitard considering non-Darcy flow;

New deliverability equation for gas wells with high velocity non-Darcy flow;

The result shows that waterflood frontal movement of non Darcy flow is fast, resulting in earlier water breakthrough; the higher the injection rate, the faster the frontal movement, and the earlier the breakthrough.

Amathematical model for Non Darcy flow of two phase fluid through anisotropic double porosity media with a vertically fractured well working is established.

During the process of the deviation,it considers the effect of non Darcy flow and the anisotrophy of gas layers on the productivity of horizontal wells.

According to the concept of equivalent hydraulic conductivity K L and the unified governing equation of karst triple void media which coupled darcy flow with non darcy flow, a karst tube fissure pore triple media model is constructed to simulate karst aquifer system in Beishan area in Guangxi province.