Computer simulation of hydraulic fractures

We provide a brief historical background of the development of hydraulic fracturing models for use in the petroleum and other industries. We discuss scaling laws and the propagation regimes that control the growth of hydraulic fractures from the laboratory to the field scale. We introduce the mathematical equations and boundary conditions that govern the hydraulic fracturing process, and discuss numerical implementation issues including: tracking of the fracture footprint, the control of the growth of the hydraulic fracture as a function of time, coupling of the equations, and time-stepping schemes. We demonstrate the complexity of hydraulic fracturing by means of an application example based on real data. Finally, we highlight some key areas of research that need to be addressed in order to improve current models.