Nonclassical Stochastic Methods in
Subsurface Modeling, 20-9117
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Scott L. Painter
Point of Contact:
Inclusive Dates: 01/15/99 - Current
Background - The physical properties
controlling mass and energy transport can vary greatly from point to point within the
subsurface. In typical applications, these properties are sparsely sampled, leading to
large uncertainties in predictions of fluid or contaminant movement. In recent years,
groundwater hydrologists and petroleum engineers have acknowledged this unavoidable
uncertainty and are adopting probabilistic frameworks for making predictions. These
probabilistic approaches require realistic mathematical models for subsurface
heterogeneity. However, subsurface properties are characterized by complex multiscaled
spatial fluctuations that are known to be inconsistent with classical statistical models
for spatially distributed systems. More realistic alternatives to classical stochastic
models for subsurface heterogeneity are needed.
Approach - This project is developing new
stochastic subsurface modeling tools based on contemporary mathematical descriptions of
nonlinear variability in complex systems. Emphasis is on fractal scaling models and other
approaches that capture long-range spatial dependence and extreme variability. Existing
and newly developed fractal models are being evaluated with outcrop and borehole data.
Practical simulation tools based on these models are being developed.
Accomplishments - A new fractal scaling model
based on a superposition of an infinite number of Gaussian models was developed. The
resulting model is being tested against large sets of outcrop and borehole data.
Preliminary indications are that the model reproduces important features of these data,
including long-range spatial dependence, highly non-Gaussian distributions, and clustered
volatility (intermittency). Accurate stochastic simulation algorithms based on the new
approach were developed; software implementation is underway. Simulation studies examining
the consequences for contaminant migration are in progress.
Advanced Computer and
Electronic Technology, and Automation Program
1999 IR&D Home