[Amath-seminars] Boeing lecture Today: Mary Wheeler

Joel Zylberberg joelzy at uw.edu
Thu Mar 13 08:53:49 PDT 2014

Reminder of Today's Boeing lecture by Mary Wheeler. See y'all there!

*Abstract: *Modeling of Coupled Flow and Mechanics in Fractured Porous Media

Thursday, March 13th, 2014, 4:00pm, Smith 205 <http://uw.edu/maps/?smi>

The coupling of flow and geomechanics in porous media is a major research
topic in energy and environmental modeling. Of specific interest is induced
hydraulic fracturing. Here fracking creates fractures from a wellbore
drilled into reservoir rock formations. In 2012, more than one million
fracturing jobs were performed on oil and gas wells in the United States
and this number continues to increase. Clearly there are economic
benefits of extracting vast amounts of formerly inaccessible hydrocarbons.
In addition, there are environmental benefits in producing natural gas.
Opponents to fracking point to environmental impacts such as contamination
of ground water, risks to air quality, migration of fracturing chemical and
surface contamination from spills to name a few. For this reason, hydraulic
fracturing is being heavily scrutinized resulting in the need for accurate
and robust mathematical and computational models for treating fluid
filled fractures surrounded by a poroelastic medium.

Even in the most basic formulation, hydraulic fracturing is complicated to
model since it involves the coupling of (1) mechanical deformation; (ii)
the flow of fluids within the fracture and in the reservoir; (iii) fracture
propagation. In this presentation we first discuss the modeling of coupled
flow and mechanics in a fixed fracture system. We then present an
incremental formulation of a phase field model for modeling
crack propagation with a fluid filled crack in a poroelastic medium that
was recently developed by Andro Mikelić, Mary F. Wheeler, and Thomas Wick.
This mathematical model represents a linear elasticity with fading elastic
moduli as the crack grows, which is coupled with an elliptic variational
inequality for the phase field variable. Computational results of benchmark
problems are provided that demonstrate the effectiveness of this approach
in treating fracture propagation.

Joel Zylberberg

Acting Assistant Professor
Department of Applied Mathematics
University of Washington
Seattle, WA


~ The neuroscience is theoretical, but the fun is real
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