Analysis of a constant height hydraulic fracture driven by a power-law fluid

The focus of this study is to analyze a parametric space for the problem of a constant height hydraulic fracture driven by a power-law fluid. The interplay of physical mechanisms related to toughness, fluid resistance, and leak-off is considered, but the model is restricted to local elasticity for simplicity. The problem of a semi-infinite constant height fracture is first analyzed: limiting solutions are obtained analytically and their locations inside the dimensionless parametric space are obtained. Then, the problem of a finite constant height fracture is investigated. Similarly, limiting vertex solutions are first outlined and then their locations in the parametric space are quantified. Results demonstrate that the effect of the power-law factor is relatively mild, as it does not significantly distort the parametric spaces. At the same time, there are quantitative differences, which are also determined by the obtained results. Numerical examples highlighting the effect of fracture regime on morphology of multiple fractures are presented at the end.