A novel binomial deliverability equation for fractured gas well considering non-Darcy effects

•A new concept named CTER is introduced.•CTER is short for conductive thickness between equivalent radii.•A novel binomial deliverability equation for fractured gas well is derived.•The novel equation considers non-Darcy effects in the fracture.

Hydraulic fracturing is one of the most effective methods to improve the productivity of low permeability reservoirs. Now, the effects of non-Darcy flow mainly caused by high velocity gas in hydraulic fracture are paid increasing attention to. But the binomial deliverability equation influenced by non-Darcy effects has never been seen in any paper for the difficulty in coupling linear flow model in the fracture and radial flow model in the reservoir.Based on equivalent radius models for hydraulic fracture, the authors put forward the concept of CTER, which is short for conductive thickness between equivalent radii. The value of equivalent radius for finite conductivity fracture is smaller than that of infinite conductivity fracture because of the existence of fracture conductivity. CTER whose permeability is equal to reservoir permeability is a theoretical radial conductive thickness existing between equivalent radius models for finite conductivity fracture and infinite conductivity fracture. By making use of CTER, we deduce the novel binomial deliverability equation with respect to the inertial non-Darcy effects in the fracture. With the help of the new concept and the new equation, it is found that non-Darcy effect caused by high flow rate of gas in the fracture influences high permeability reservoirs (>5 mD) more dramatically than those with low permeability (<1 mD).