Аннотация:We consider the displacement of non-Newtonian fluids in a hydraulic fracture, with application to overflush at the end of stimulation. The practice of overflushing is common for horizontal wells drilled in unconventional formations. It ensures well cleanup, but it may damage the overall fracture performance due to a combination of factors: creation of unsupported cavities by disaplcement, fracture closure takes long enough resulting in redistribution, with the overflushing fluid rising to the top of the fracture and the slurry-laden fluid falling to the bottom, leaving a significant portion of the near-wellbore area unpropped and closing off access to the top of the reservoir. A modeling approach was chosen to gain insight in the overflushing process, which, from the fluid mechanics point of view, is a displacement of a Hershel-Bulkley fluid by a power law fluid in a Hele-Shaw cell, leading to the development of a Saffman-Taylor instability at the interface between the fluids. A novel numerical model, which takes into account the yield-stress behavior of the slurry, was thus developed using the lubrication approximation. Bounds for safe overflushing are proposed, which are a lot more restrictive in case of slickwater fluids.