The Dilemma of Scale

Ethan Coon

(page 2 of 3)

“This is one of the big challenges in trying to model real geological systems,” says David Moulton, an applied mathematician with the Mathematical Modeling and Analysis Group (or T-7) at Los Alamos, and Coon’s summer practicum adviser.  “We obviously can’t resolve everything, but we need to ensure that the approximations we introduce are useful.  The key is to create approximations that capture the influence of unresolved features well enough to advance our understanding of the system and inform policy decisions.”

For Moulton and Coon this means how to best extract an increasingly rare and valuable resource — oil.  In a new well, the oil is under pressure from the overlying rock and spurts out of the ground like a geyser. However, there’s still substantial oil left when the geyser stops.  How to get it out? Oil companies often pump in water or carbon dioxide to flush out the remaining oil.

“Being able to increase the efficiency of these oil reservoirs has numerous advantages.  It means more energy, it makes business sense, and it also minimizes the environmental impact of more drilling,” Coon says.

To do this, it’s critical to know how the oil and water flow in the rock, and that means understanding and modeling the fine-level details.

At Los Alamos, Moulton leads development of a state-of-the-art computational tool for improved modeling of flows through porous rock structures.

Example of multiscale basis function for single-phase saturated flow generated by MLUPS algorithm. Click image for larger version and more information

“Our Multilevel Upscaling (MLUPS) approach to modeling flow through heterogeneous media doesn’t make the jump to a coarse-scale model directly from the fine-scale one, as do most existing approaches,” Moulton says.  “Instead it uses a multi-resolution approach, building a hierarchy of models, each one a baby-step up from the previous one. And in this way it is more effective.”

When Coon arrived at Los Alamos, MLUPS was developed to the point it could model a single phase, or material, in a static state 15 times faster than the main competing technique.  Coon created an algorithm enabling MLUPS to simulate the flow of two materials over time — an ability that’s critical to simulating the interaction of oil and water in a reservoir.

In collaboration with Scott MacLachlan, a former Los Alamos summer student and (as of January 2008) an assistant professor at Tufts University, Coon also upgraded MLUPS so it incorporates mass conservation of the fluids, ensuring that the amount of material is the same at the start and end of a model run.  While not always critical in initial model development, mass conservation is essential to making technology that can be practically applied.

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