Asymptotic and numerical analysis of hydraulic fractures

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Hydraulic fractures (HF) are brittle fractures that propagate in rock due to the injection of a viscous fluid. HF are deliberately created in oil and gas reservoirs to improve the connection between the extraction borehole and the rest of the reservoir. They are also used to pre-fracture ore-bodies in mining; to create fracture networks in geothermal reservoirs; and to dispose of waste. They will also be used in the sequestration of CO2. Unfortunately, propagating HF can perforate the impermeable layers that provide containment to the oil, waste, or CO2, leading to loss of hydrocarbons and severe environmental damage. It is thus crucial to have analysis tools to predict, monitor, and control the growth of HF. The objective of the proposed research is to develop asymptotic solutions and numerical algorithms for the accurate and efficient modeling and monitoring of HF propagation. The mathematical models for HF typically consist of a system of integro-partial differential equations together with boundary and propagation conditions that determine the location of the moving fracture boundaries. In this proposal, I outline a program of research that will build on the key developments that we have recently achieved in the asymptotic analysis and computational modeling of planar HF. In particular, I will develop a robust algorithm that will be able to model the propagation and recession of a planar HF through layered sedimentary rock. In addition, I plan a new initiative to develop computational tools to model the propagation of HF through networks of pre-existing fractures, which is important for the extraction of oil from deposits in shales. I also plan to use these accurate computational models to develop and calibrate models with reduced computational requirements. These reduced models will then be coupled with the Kalman Filter in order to monitor propagating HF by inverting the deformations that they induce in the rock.