A team of Duke mathematicians, statisticians and engineers will collaborate to study the intricate and little-understood complexities of how liquids flow through porous media such as geological formations, thanks to a $2.3 million grant from the National Science Foundation. The project will involve Duke faculty and postdoctoral fellows using a new dedicated network of fast workstations connected by high-speed links.
Although the researchers will develop fundamental new modeling and computational methods, the project also will contribute to such practical applications as increasing the efficiency of oil production and using chemicals to remove pollutants from groundwater.
"We are extremely gratified that the NSF has provided funding for this important basic research," said Professor of Mathematics John Trangenstein, principal investigator for the project. "This grant will enable a highly productive interdisciplinary collaboration among applied mathematicians, statisticians and engineers that will yield new insights into this important topic. The grant will also encourage the formation of such partnerships in the future to meet such major computational and modeling challenges."
"This is such an impressive grant," said Rep. David Price, D-N.C., congressman from Duke's district and member of the House Appropriations Committee. "The selection process was extremely competitive, and the Duke proposal was judged to be one of the best. I am proud to be a strong supporter of the National Science Foundation."
The new NSF-sponsored project will aim at developing new statistical and computational methods to assess and reduce the uncertainty in modeling flow in porous media, Trangenstein said.
Such modeling in which the scientists and engineers construct mathematical simulations inside a computer is extremely complex. For example, such porous media as underground geological formations can be highly heterogenous and can interact with a flowing liquid both physically and chemically.
Also, said Trangenstein, variations in such factors at microscopic scales can have important large-scale effects. Thus, he said, the research team will develop models and numerical methods on a hierarchy of scales.
Reaching their research goals will require the Duke researchers to seek new basic insights into mathematical modeling, uncertainty, computation and data measurement. Addressing such a wide range of issues demands a collaboration among disciplines, Trangenstein said.
For example, the project's statisticians David Higdon, Peter Mueller and Michael West will develop concepts, models and methods to integrate data and to incorporate and measure uncertainty, he said.
Importantly, the mathematicians also will work to reduce the size and computational cost of the simulations, to make them more useful, both scientifically and practically.
To test the mathematical models, the engineers will apply the resulting methods to various field studies, and will work with industry to help apply the methods to practical problems. Engineers participating in the project include Duke civil engineer Zbigniew Kabala, Gary Pope at the University of Texas and Akhil Datta-Gupta at Texas A&M.
The huge computational demands of such mathematical models will require the power of many computers working simultaneously on related parts of the big problem, Trangenstein said. Thus, the NSF grant will fund construction, by Duke mathematician William Allard and Duke computer scientists Jeffrey Chase and Alvin Lebeck, of a network of computer workstations linked by fast communication boards.
This project also will serve the instructional interests of Duke and NSF by training selected students in large-scale distributed computing on the new machine, Trangenstein said.