KDI: Multiscale Modeling and Simulation in Scientific Inference: Hierarchical Methods for Parameter Estimation in Porous Flow

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Trangenstein9873275The investigator and his colleagues develop new spatial models and numerical methods for flow in porous media. Conventional simulation models for these problems require very high-dimensional parameters as inputs, yet the determination of these parameters is radically ill-posed. Reliable and relevant additional data sources are scarce. The problem is multi-scaled, since fine-scale variations in the defining parameters can have key large-scale effects. Hence this project will develop models and numerical methods on a hierarchy of scales. However, the relationship between different scale sub-models goes beyond simple averaging. The investigators develop statistical models, methodology and computation for data synthesis and high-dimensional inference and predictions. Computations for fluid flow incorporate hierarchical simulation involving adaptive mesh refinement and streamtube methods. The large size of the computations requires distributed computing and the construction of a network of workstations running custom software. The methods are validated against new analytical work in stochastic partial differential equations. Finally, the resulting methodology is applied to field studies of contaminant cleanup involving surfactants and to oil production problems.Uncertainty in porous flow has a large impact on society and the economy. For example, the cost of discovery and efficient production of petroleum affects the cost of transportation and energy production. Also the cost of location and removal of contaminants from ground water affects the cost and quality of safe water resources. One goal of this project is to develop new statistical and computational methods to assess and reduce the uncertainty in modeling flow in porous media. This goal requires new research into modeling, uncertainty, computation and data measurement. To address this wide range of issues, this project involves a collaboration of applied mathematicians, statisticians and engineers. As a result, this project is directed toward the Knowledge and Distributed Intelligence area of interest at NSF, and especially the New Computational Challenges aspect of this initiative. In order to assign confidence to computer simulations, the statisticians in this project develop concepts, models and methods to integrate data and to incorporate and measure uncertainty. Together, the statisticians, applied mathematicians and engineers use a variety of sophisticated analytical and numerical techniques to reduce the size and cost of the computations. The engineers apply the resulting methods to various field studies, and communicate the results to their industrial affiliates. Even with these new concepts and algorithms, the size of the computations is so large that many computers have to work on the problem simultaneously. The applied mathematicians build a network of workstations using fast communication boards to perform these large calculations, and dedicate this machine to these calculations and to student instruction.