The development of multi-scale computational tools to model multiple hydraulic fractures propagating in complex media.

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The past decade has seen a significant change in the global energy landscape, largely due to a process commonly known as "fracking" that has made the extraction of hydrocarbons from shale gas reservoirs economically viable. This process has been enabled by a new technology that makes possible the generation of multiple hydraulic fractures (HFs) from horizontal wells. While fracking has been controversial, due to the risk of hydrocarbons leaking into groundwater, this novel technology can also be used to generate cleaner energy by creating fracture networks in geothermal reservoirs. Since the top 10 km of the earth's crust holds 50,000 times as much energy as all oil and gas reserves, this innovative technology also has huge potential for generating clean energy. To minimize the environmental risk of fracking and to optimize the placement of HF, it is necessary to have design tools that can simulate these new configurations of evolving HF. However, these important developments in HF technology have put field practice beyond current computer simulation tools. Existing tools are primarily focused on simulating the evolution of a single HF propagating in a piece-wise homogeneous elastic medium. What is now required is the capacity to simulate multiple HF that simultaneously propagate in complex solid media and interact with pre-existing joints and faults.***   Even the simplest mathematical model for a single HF propagating in a homogeneous elastic medium involves a coupled system of degenerate nonlinear integro-partial differential equations with a complex multi-scale structure. These equations also involve a singular free boundary problem, in which the front velocity can only be determined by evaluating a distinguished limit. This singular free boundary problem has limited HF simulators to the modeling of HF whose propagation is governed by a single physical process - typically the energy released when breaking the rock. In a recent significant breakthrough (Peirce & Detournay, 2008), we developed a robust and accurate numerical technique that uses the tip asymptotic solution obtained by local analysis to completely resolve this class of singular free boundary problem. We called this scheme the Implicit Level Set Algorithm (ILSA), which we have already used to solve a number of open problems. ***   This proposal outlines an ambitious research program that leverages the innovative ILSA scheme to further develop a novel set of computational tools that will enable engineers to optimize hydrocarbon production while minimizing the environmental impact of fracking. This program of research has already attracted the attention of industry and will provide new technology to petroleum engineers in the field. Establishing these robust design tools may result in regulatory requirements to design HF treatments to achieve maximal gas extraction using the least water. The potential impact for policy is considerable.**