Productivity equation of fractured horizontal well in a water-bearing tight gas reservoir with low-velocity non-Darcy flow

• Productivity equation of horizontal fractured well in tight gas reservoir is got.
• The influence of TPG on the volumetric flow rate is great and cannot be neglected.
• With the increase of the number of fracture, the total production increases slowly.

Based on the features of tight gas reservoirs and considering the existence of threshold pressure gradient (TPG), a new mathematical model was established for low-velocity non-Darcy flow in water-bearing tight gas reservoirs. Calculation method of control areas is also presented. Productivity equations of vertical fractured well and horizontal fractured well in tight gas reservoirs are obtained with TPG. Influential factors were analyzed to provide theoretical basis for the effective development of tight gas reservoirs. According to the numerical results, with the increase of pressure drawdown, both the volumetric flow rate of gas well and control area grow first and then gradually becomes stable. The influence of TPG on the volumetric flow rate of gas well is great and cannot be neglected. For fractured horizontal well, gas well production increases with the increase of flow conductivity capacity and half-length of hydraulic fractures. For certain length of the borehole, when the fracture spacing increases and the number of the fractures decreases, the control area and the volume flow rate of the gas well decreases. Consequently, there is an optimum allocation among drawdown pressure, fracture half-length, fracture conductivity and fracture spacing to achieve maximum production.