Computational science is a field obsessed with convergence, where equations are scripted to result in real-world numbers that minimize risk and chance as much as possible.
With that in mind, it’s a bit ironic that Mary Wheeler, the director of the ICES Center for Subsurface Modeling, became a mathematician and computational scientist because of an accidental encounter.
“My roommate in college was taking a numerical analysis course and I would see her working on those problems and I thought ‘that’s interesting.’ And that’s how I first got involved,” said Wheeler, who was enrolled in the late 1950s at The University of Texas as a government major. “It happened by circumstance.”
That exposure ignited chain of events, starting with Wheeler adding a math major to her undergraduate studies, which would lead her to pursue a career in mathematics. Although her start in the field may have been a chance affair, Wheeler is now purposefully driving her chosen field forward as a world-renown researcher in subsurface modeling.
Wheeler has published over 250 research papers, and has made advancements in developing algorithms for modeling subsurface flow in a variety of contexts, from reservoirs of oil and gas beneath the earth’s surface to blood flow beneath the human integument.
Now, her achievements have been recognized with the John von Neumann Medal, the highest award bestowed by the Unites States Association for Computational Mechanics. She is the first woman to receive the medal in its 23-year history. The award honors individuals who have made “outstanding, sustained contributions in the field of computational mechanics generally over periods representing substantial portions of their professional careers.”
John von Neumann, the award’s namesake, was a 20th century scientist and mathematician whose fundamental contributions to computer science, applied mathematics, and physics—as well as his ability to astound his colleagues with his feats of mental math—put him in the pantheon of scientific greats.
“It’s a very prestigious award. And I’d like to say, I’m excited because von Neumann has been one of my heroes in science,” said Wheeler. “He appreciated the importance of these problems.”
It’s not rare to hear mathematicians use the word “elegance” to describe the intrinsic beauty of a well-constructed theorem, even if it’s not being applied to any “real-world” problem. Some mathematicians prefer to work with pure mathematics and focus on elegance over application.
Wheeler is not one of them.
“One of the things I noticed as a graduate student was that there were a lot of people in math who weren’t really interested in physical problems. And that always bothered me,” said Wheeler. “Because I think it is interesting to do a problem just for curiosity. But it is exciting to see how you can apply it.”
The homepage to her personal website echoes this sentiment with a bolded, mission-statement at the top of the page.
"I really enjoy developing efficient and accurate solutions to real-world problems, while maintaining a solid theoretical base."
But the best way to see Wheeler’s approach to mathematics and computational science is to examine her range of research projects and published papers spanning more than 50 years. Her research is united by the common topic of subsurface modeling, where the biggest funders come from the oil and gas industry, but the applications range much further than what an oil drill bit can reach.
“Your body is a subsurface and bones and breasts are a porous media. And the same mathematical models we do for geological subsurface also apply to the subsurface of the body,” said Wheeler. “This is not just a one-shot deal. Mathematics is the language of sciences and how you communicate results. And with this language, you can communicate it across different disciplines.”
In the past, Wheeler has applied a mathematical lens towards understanding topics like ground subsidence, where subsurface changes cause the Earth’s surface to cave-in or shift, blood vessel formation, and contaminant transport in ground water.
Her most recent research aligns closely with issues on the forefront of the energy industry—how to safely extract oil and gas from the ground and how to store the greenhouse gas by-products that are released when those substances are combusted.
A model that Wheeler is developing shows how fractures induced in rock during the hydraulic fracturing process propagate and how fluids like water, chemicals and natural gas flow through the fractures.
“One of the issues is how do you connect [hydraulic fracturing] models with a fluid simulator. And that’s not really being done right now [by other researchers],” said Wheeler.
Having a better idea how fractures spread in a rock, and liquids through them, is important to informing fracturing methods that don’t disturb groundwater—an especially valuable resource in Texas, where some cities’, including San Antonio’s, water supply is almost completely dependent on ground water wells.
Another model of Wheeler’s is simulating how rock can be used as a holding tank. The thinking here is to store CO2 gas in saline aquifers under the earth’s surface, keeping the gas out of the atmosphere where it could contribute to the greenhouse effect, and out of the ocean where the gas contributes to ocean acidification.
“The idea is that if we stop the gas now, we can eliminate some of these greenhouse gasses to buy time until people can use solar, or come up with other approaches of energy,” said Wheeler. “We’ve seen that geomechanics needs to be incorporated into these carbon sequestration problems.”
“It’s these issues of trying to tie environmental concerns with production,” said Wheeler. “You want it to be environmentally prudent.”
Wheeler and her research team have developed algorithms to combine geomechanics physics with fluid models. Each step of the combined model has hundreds of millions of unknown values, said Wheeler. But by developing a mathematical technique called figurative coupling, Wheeler and her team have been able to achieve convergence, or values that can be applied to real world problems.
“The technique is really nice for these problems because they are computationally intensive and this approach seems to converge quite fast and it’s very robust,” said Wheeler.
Developing “new mathematics”—algorithms and analytic techniques that have never been used before—is what Wheeler and her research team must do to approximate sub-surface simulations that mirror reality, that understand the interaction of various processes to create an over-arching effect.
It’s an immense change from what Wheeler studied as a mathematics graduate student at Rice University in the 1970s. Then, physics problems could only be approached in one dimension, with 10 data elements, and computer code was written on paper punch cards. Now, Wheeler says, problems take into account three dimensions, may have over a billion data elements, and are solved on supercomputers that can analyze quadrillion operations per second. The problems also include the mathematical subtleties of phase changes, mass transfer, as well as chemical, mechanical and thermal reactions.
“I have been lucky that this has been a golden age for computation,” said Wheeler.
“I’ve had an interesting career and I’ve enjoyed it very much,” said Wheeler. “But I never dreamed that I would be here.”
Wheeler entered the field of applied mathematics when women were practically non-existent in it.
As an undergraduate at UT she recalls entering the engineering building and having a professor in a hallway ask her, “And whom do you belong to?”
Now, she holds the University of Texas at Austin’s Ernest and Virginia Cockrell Chair and is a professor in the departments of aerospace engineering and engineering mechanics, and petroleum and geosystems engineering. Before joining UT, she was the Noah Harding Professor in engineering at Rice University.
“My family certainly encouraged me,” said Wheeler. “My mother, my husband, both were very encouraging, because certainly there weren’t very many women at that time,” said Wheeler about her start in applied mathematics.
“It wasn’t uncommon to go to an applied math or finite element meeting and go to a dinner where there were 40 men and I was the only woman”
Personal drive and family support aided Wheeler throughout her career. But Wheeler attributes luck as the force that started at all.
After all, if it would not have been for a fateful roommate pairing, it’s likely that Wheeler’s career path may have gone in a completely different direction. She would have not spent decades advancing the field of applied mathematics, and mentoring dozens of graduate students who have gone on to forge their own careers. She would not have been awarded the John von Neumann medal.
Wheeler says she hopes future students of applied mathematics won’t have to be as “lucky” as she was.
“[The start of my career] just happened by circumstance, I fell into it. And people shouldn’t just fall into it,” said Wheeler, who makes a point to participate in outreach efforts toward high school students, the most recent sponsored by the Bureau of Economic Geology. “They should have exposure to it. And that’s why I’m interested in [outreach to] these small Texas towns, so at least students can be exposed to these opportunities.”
Article by Monica Kortsha