This image illustrates the irregular spreading behavior of a contaminant plume in the subsurface environment. This seemingly erratic spreading is attributed to the spatial variability of the aquifer’s hydraulic properties over a multitude of length scales. Darker shades of blue indicate a higher concentration of a contaminant whereas lighter shades of blue represent lower concentrations. This image was generated using high-resolution numerical simulations. Image/Felipe de Barros and ALESSANDRA BONAZZI.
Flowing rivers, icy mountain lakes, crystalline reservoirs – we like to think that our water comes straight from these sources. In reality, approximately 38% of drinking water in the United States comes from underground aquifers – layers of permeable rock and sediment that serve as a “sponge” storing large quantities of water.
As rain and snowmelt seeps into the cracks and crevices beneath the land’s surface, the supply is continually renewed. Groundwater is therefore a crucial part of our hydrology infrastructure, and it’s also used extensively for agriculture and industry. But here’s the conundrum. Those very processes release toxic chemicals back into the aquifers, and the spread of these contaminants is notoriously difficult to predict and prevent.
In recent years, two professors working across different departments at USC Viterbi have formed a collaboration on the basis of shared fascination with the puzzle of contaminant flow.
Felipe de Barros, associate professor at USC Sonny Astani Department of Civil and Environmental Engineering.
Felipe de Barros, an associate professor at USC Sonny Astani Department of Civil and Environmental Engineering, applies his expertise in environmental fluid mechanics to develop models for simulating and predicting the behavior of large-scale hydrogeological systems for the purpose of risk analysis. Muhammad Sahimi, a professor in the USC Mork Family Department of Chemical Engineering and Materials Science and N.I.O.C. Chair in Petroleum Engineering, is recognized as a global leader in porous media science. While de Barros focuses on improving uncertainty quantification in hydrogeological models, Sahimi applies advanced machine learning techniques to produce models of unparalleled accuracy. Their two areas of expertise are distinct but complementary; de Barros – as a mid-career researcher – considers Sahimi to be one of his most important mentors.
“Our goal is to discover a widely applicable methodology and mathematical framework that enables us to quantify and predict the spreading of these core chemicals,” explained de Barros. “That’s very important. If an aquifer is contaminated, decision makers need to know exactly where to install wells to monitor the water quality and take immediate action.”
The cleaning (“remediation”) of contaminated aquifers costs the US millions of dollars each year, and the presence of chemicals in our water system has a direct impact on human health. It’s clear that we are in urgent need of better computational tools for understanding flow and transport processes, and Sahimi and de Barros believe that that the answer involves combining machine learning with physics-based models.
The tricky part of the challenge arises from the fact that geological media is extremely heterogenous. The properties and combinations of the different layers of matter – whether sand, rock, or soil – vary greatly according to location, meaning that the rate and direction of groundwater flow is almost impossible to track via a catch-all, abstract model.
As a result, the issue of predicting a build-up in underground contaminants has become a something of a notorious problem in the fields of hydrology and percolation theory. In fact, it sparked a 40-year debate about the most accurate and applicable model – the equation that would crack the code of how contaminants spread in different contexts.
In 2023, the two professors achieved the first major breakthrough of their collaboration, working alongside Sami Masri, professor of civil and environmental engineering, and Jinwoo Im, a former PhD student in de Barros’ lab. Their paper published in the journal Physical Review E, “Data-driven discovery of the governing equations for transport in heterogeneous media by symbolic regression and stochastic optimization,” effectively mediated between all prior approaches to arrive at an optimal answer.
“The vast increase of available data has meant we’ve been able to make unprecedented leaps forward in the predictive capabilities of these models,” said Sahimi. “The beauty of the solution is that it simultaneously reveals the most accurate model, while also distinguishing which of the prior theories were wrong, and which were right.”
Muhammad Sahimi, professor in the USC Mork Family Department of Chemical Engineering and Materials Science and N.I.O.C. Chair in Petroleum Engineering.
The success of the paper laid the foundations for the next stage of their research, supported by a significant grant from the National Science Foundation (NSF). With a highly effective mathematical framework as a starting point, Sahimi and de Barros can now apply their thinking to real-world problems specific to hydrology.
“The findings we previously published have provided a stepping stone for what’s to come,” said de Barros. “Now we’ll be tackling problems at a far larger scale, in the context of heterogeneities which vary by much greater orders of magnitude. We’ll be exploring several different scenarios, as well as applying data from on-site research.”
As part of this next stage, the two professors will be expanding their unique “grey box” approach to machine learning.
“You’ve probably heard of black box models, where you plug in the data and an algorithm generates a prediction. It’s a closed system – you don’t know what kind of “magic” is happening in there,” said Sahimi. “We believe it’s important to ensure a level of transparency, and that comes from refining the data analysis through physics-informed decisions. We’re not just tuning parameters up and down to arrive at a computation-generated result. There’s much more to it.”
It’s an attitude that characterizes the engineer mindset – never satisfied with answers that aren’t grounded in the realities of Earth systems and physical processes. Ultimately, as much as they love the math, it’s the impact on human and planetary health that motivates Sahimi and de Barros to tackle one of the most intractable puzzles in environmental engineering and hydrological sciences.
“You might not be able to ‘see’ groundwater at the level day-to-day life, but it’s part of the flow that sustains us,” said de Barros. “We’re committed to guaranteeing access to clean water for generations to come.”
Published on October 23rd, 2024
Last updated on November 4th, 2024
