Stochastic Uncertainty Quantification Approaches for Large Scale Subsurface Problems

Graduate SeminarStochastic Uncertainty Quantification
Approaches for Large Scale Subsurface
ProblemsProfessor Dongxiao Zhang
Petroleum and Geological Engineering
The University of OklahomaAbstract
Prediction of subsurface flow and transport is subject to uncertainties, which can
result from the heterogeneity of the media and our incomplete knowledge about
their properties. Such uncertainties render the model parameters random and the
equations describing flow and transport in the media stochastic. Monte Carlo
simulation method (MCS) is the most common and conceptually straightforward
approach. However, it requires large computational efforts, especially for large scale
problems. Recently, a number of alternative stochastic approaches have been
developed to quantifying prediction uncertainties. This talk discusses four
representative methods: The moment equation method (ME); the Galerkin
polynomial chaos expansion method (PCE); the Karhunen-Loeve based moment
equation method (KLME); and the probabilistic collocation method (PCM). The
efficiency of these methods depends on how the random (probability) space is
approximated. Detailed theoretical analyses and numerical computations are
performed to compare these methods against MCS in terms of accuracy, efficiency,
validity range, and compatibility with existing deterministic simulators. It is found that
the KLME, PCE and PCM are generally more efficient than the MCS and the ME for
larger-scale problems. The expansions in representing the dependent random fields
and the ways for evaluating the expansion coefficients distinguish among the KLME,
PCE and PCM.Friday, February 23, 2007
Seminar at 11:15 a.m.
HED 116The Scientific Community is cordially invited.

Location: Hedco Pertroleum and Chemical Engineering Building (HED) - 116

Audiences: Everyone Is Invited

Contact: Petra Pearce