HR: 13:40h
AN: H13J-01    [Abstracts]
TI: Numerical Simulation of Planar Fluid-Driven Fractures
AU: * Detournay, E
EM: detou001@umn.edu
AF: University of Minnesota, Department of Civil Engineering 500 Pillsbury Drive SE, Minneapolis, MN 55455, United States
AU: Peirce, A
EM: peirce@math.ubc.ca
AF: The University of British Columbia, Department of Mathematics #121-1984 Mathematics Road, Vancouver, B.C V6T 1Z2, Canada
AB: Fluid-driven fractures are a class of tensile fractures that propagate in prestressed solid media due to internal pressurization by an injected viscous fluid. There are numerous examples of such fractures occurring in natural geological processes. The numerical simulation of fluid-driven fractures remains a particularly challenging computational problem, despite significant progress made since the first algorithms were developed in the 1970's. The major challenges stem from the dependence of the near-tip asymptotic form of the fracture width on the dominant physical process governing the propagation of the fracture and from the a priori unknown boundary of the fracture footprint. In this talk we describe a novel algorithm that is based on an implicit level set method to locate the free boundary. The algorithm exploits the applicable local tip asymptote to locate the unknown fracture front. The algorithm does not rely on the calculation of the normal front velocity from the pressure gradient field, which is typically singular at the tip. In fact, the implicit algorithm is able to provide accurate estimates of the normal velocity of the front by solving an appropriate nonlinear equation within each element of a small set of elements close to the fracture front. We provide numerous examples that demonstrate the robustness, efficiency, and accuracy of the algorithm for fractures that propagate in a variety of regimes: toughness dominated, viscosity dominated, and leak-off dominated.
DE: 1829 Groundwater hydrology
DE: 5104 Fracture and flow
DE: 8010 Fractures and faults
DE: 8020 Mechanics, theory, and modeling
DE: 8045 Role of fluids
SC: Hydrology [H]
MN: 2007 Fall Meeting