Tan Bui-Thanh, an assistant professor in the Department of Aerospace Engineering and Engineering Mechanics, has received three research grants this year from industry and research organizations alike to study efficient methods for solving challenging inverse problems.

The grants come from the National Science Foundation; Computer Modeling Group Ltd., or CMG, a company that makes software for simulating oil and gas reservoirs; and the King Abdullah University of Science and Technology (KAUST). Each grant supports inverse problem solving applications in oil and gas exploration and recovery, an area of research that’s of increasing societal importance, Bui-Thanh said.

“Energy demand is ever increasing,” Bui-Thanh said. “In parallel to efforts of finding other sources of energy, we need to discover new oil reservoirs and find ways to recover the significant amount of residual oil in existing reservoirs.”

Inverse methods are problem-solving techniques that use mathematical models, typically partial differential equations, along with observational data of a physical phenomenon or environment to make inferences about features relating to that particular phenomenon or environment. A familiar example of an inverse problem solution is the image created by an ultrasound machine, Bui-Thanh said.

“The sound waves transmit through the body and bounce back, and from the echoing waves you can make inferences about something you don’t see inside the body,” Bui-Thanh said.

Instead of imaging part of the body, Bui-Thanh’s research involves imaging parts of the Earth—a problem that’s much larger in scale than a medical ultrasound. The research involves analyzing large amounts of observational data together with big mathematical models to image the earth’s interior, and then determining the uncertainty present in the image. Bui-Thanh said that calculating uncertainty is a vital part of the process because imperfections in the data always exist and need to be accounted for to understand the accuracy of the inverse problem solution.

“Seismic inversion and reservoir history matching involve lots of data—some would say “big data”—noisy data,” Bui-Thanh said. “We don’t only give a solution, but also the estimated uncertainty.”

The National Science Foundation grant supports research into reservoir simulation, and software processing on high performance computers. Specifically, Bui-Thanh is focusing on developing the Weak Galerkin and Hybridized Discontinuous Galerkin Methods, types of finite element analysis, to boost the problem-solving speed by improving how unknowns are reduced and distributed across computers with potentially thousands of processing cores.

For the CMG grant, the focus is on developing methods that can estimate how much residual oil is left in a reservoir that’s already been tapped. Bui-Thanh is collaborating on the project with Quoc Nguyen, an associate professor in UT Austin’s Department of Petroleum and Geosystems Engineering. While Nguyen is developing methods to extract residual resources, Bui-Thanh is working on a physics-based math model to quantify how much leftover oil a reservoir can be expected to hold. With enhanced recovery techniques able to produce 30 to 60 percent of the original amount of oil held in a reservoir, the amount of oil left in a reservoir can be significant.

For the KAUST grant, the research supports mathematical analysis that can help distinguish a valuable reservoir from a dud. The work involves developing efficient methods for jointly analyzing seismic data (which is good at detecting reservoirs in rock formations) and electromagnetic data (which is good at distinguishing oil reservoirs from salt water reservoirs). Collaborating with Bui-Thanh is Omar Ghattas, the director of the Center for Computational Geosciences and Optimization at UT Austin’s Institute for Computational Engineering and Sciences, and scientists from KAUST and New York University.

All three research projects began this year and are currently in progress, Bui-Thanh said. He believes that inverse modeling’s ability to turn “big data” into actionable information to recover unreachable objects through big mathematical models makes the method valuable in the areas of energy exploration and production.