A new method to calculate the productivity of fractured horizontal gas wells considering non-Darcy flow in the fractures

• A new concept, named apparent equivalent wellbore radius, is introduced.
• A new equation for calculating the deliverability of a fractured horizontal gas well is derived.
• An iterative method for calculating the deliverability of a fractured horizontal gas well is presented.
• The new method considers non-Darcy effects in the fractures.

A multiply fractured horizontal well is one of the most effective methods for improving the productivity of low permeability reservoirs. There could be large errors when calculating the productivity of fractured horizontal gas wells if inertial non-Darcy flow in the fractures is not considered. However, there are few reports about the deliverability equation of fractured horizontal wells influenced by non-Darcy effects due to the difficulty in coupling non-Darcy flow in the fractures and radial Darcy flow in the reservoir.A new concept named apparent equivalent wellbore radius, which considers inertial non-Darcy flow in a fracture, is proposed. An iterative process is presented to calculate the productivity of fractured vertical gas wells using the new concept. Then, the iterative process is extended to calculate the productivity of multiply fractured horizontal gas wells using the advantage of the apparent equivalent wellbore radius, which conforms to the superposition principle. The results show that inertial non-Darcy effects could decrease well production greatly even in low permeability reservoirs (<1 mD) and reduce potential interference between hydraulic fractures.