Hydraulic fracture modeling: past, present, and promising

Mathematical modeling can provide an important window on the field application of hydraulic fractures to energy extraction and storage. In this presentation, I will outline some of the hydraulic fracture modeling projects with which I have been involved, including: (i) efficient ways to model planar hydraulic fractures in multilayer elastic media; (ii) the development of the Implicit Level Set Algorithm (ILSA) that can incorporate multiscale tip asymptotics and locate the fracture free boundary on a coarse mesh; (iii) the combination of the Extended Kalman Filter (EKF) with a hydraulic fracture model to invert tilt meter measurements; and (iv) the modeling and asymptotics of leak-off driven recession of the closure front, culminating in the Sunset Solution. I will demonstrate how these latter two projects, which build on a long history of hydraulic fracture modeling, have the potential for real-time monitoring and measurement in field applications.