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Fluid-driven fracture
Hydraulic fractures represent a particular class of tensile fractures that propagate in rock as a result of internal pressurization by an injected viscous fluid. Hydraulic fractures are engineered most commonly for the stimulation of hydrocarbon-bearing rock strata to increase production of oil and gas wells. Scaling considerations have provided
a framework to classify the different growth regimes and to identify the relevant regime for hydraulic fracturing treatments. Analysis is based on explicitly recognizing that the evolution of a hydraulic fracture is characterized by multiple time scales, with the time scales being associated with the transition between two particular regimes of propagation. The multi- scale nature of the tip asymptotics that arise as a result of competing physical processes in a fluid-driven fracture has also been mapped. These asymptotic solutions have led to the derivation
of rigorous reference solutions and to the development of robust numerical algorithms to simulate the growth of these fractures. [49–52]
