A new model is developed that calculates the productivity of a hydraulically fractured well, including the effect of fracture-face damage caused by fluid leakoff. Results of the new model are compared with three previous models (McGuire and Sikora 1960; Prats 1961; Binder and Raymond 1967). The existing models assume either elliptical or radial flow around the well, with permeability varying azimuthally. Significant differences in the calculated well productivity indicate that earlier assumptions made regarding the flow geometry can lead to significant overestimates of well productivity index (PI). Agreement with the analytical solution of Prats (1961) is achieved for finite-conductivity fractures and no fracture damage. It is shown that the use of either McGuire's model (McGuire and Sikora 1960) or Raymond's model (Binder and Raymond 1967) to estimate improvement in well PI in fractured wells can lead to a significant overestimation of the well PI. The new model provides a useful tool to quickly calculate the productivity of wells that have both a finite-conductivity fracture and damage in the invaded zone. The simple and discrete nature of the model makes it ideal for implementation in spreadsheets and to connect to fracture-performance models.

Cleanup of the damage in the invaded zone depends on the capillary properties of the formation and the drawdown pressure applied across the damaged zone during production. If capillary forces are small and drawdown pressure is high, the water will be recovered, resulting in negligible damage. It is found that the invaded zone will cause significant damage when the permeability of the damaged zone is reduced by more than 90%. For low-permeability, depleted formations where water recovery is poor, the fracturing fluid should be energized with a gas component so that the relative permeability damage to gas inflow can be minimized.