Rock Heterogeneity and Fractures

Hydraulic fracturing has a wide range of applications. It is widely studied and modelled to better understand all the possible situations and foresee possible advantage in the industry. When it comes to modelling, the struggle of being able to simulate complex situation arises quickly. This work proposes a new volume control solver, using an indirect method and a hierarchical matrix, to reduce the size and time of computation. It allows to build much bigger meshes and proceed to more complex layout. The first application was a three layers case with a central layer (medium of injection) with a lower toughness. It put into question the Perkins, Kern and Nordgren’s model in toughness dominated propagation (PKN-K) and its assumptions while showing which parameters are driving the system. The propagation into a new layer seems to always happen, independently of the toughness ratio. The time required to enter the new mediumis however dependent of that value. The system, after a large amount of time, seems to behave like a radial crack in a homogeneous medium.