Semi-Infinite Hydraulic Fracture Driven by a Sequence of Power-Law Fluids

Abstract

Hydraulic fracturing technology most often involves multiple fluids with different properties to achieve desired treatments. This study examines the effects of multiple sequential fluids on the stress, strain, and deformation fields in the near-tip region of a semi-infinite fracture. It is assumed that the immiscible displacement of multiple power-law fluids is separated by stable boundaries. The fracture opening of a steadily propagating hydraulic fracture is computed by solving the elasticity and lubrication equations. The numerical solution correctly captures the well-known asymptotic behavior at the crack tip for multiple fluids. Specifically, the multiple-fluids solution asymptotically approaches the solution for the first fluid in the immediate vicinity of the tip and approaches the solution corresponding to the last fluid far from the tip. In the transition region, the behavior depends on the presence of additional fluids and the locations of their respective boundaries. Illustrative results for multiple fluids with different properties and boundary locations are included.