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Nonclassical Stochastic Methods in Subsurface Modeling, 20-9117

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Principal Investigator
Scott L. Painter
Point of Contact:
Alexander Sun

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.

Intelligent Systems, Advanced Computer and
Electronic Technology, and Automation Program
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