Guo Abstract: Mathematical modeling of porous media flow for energy and environmental problems in Earth’s subsurface

Understanding and quantifying fluid flow in Earth’s subsurface plays a critical role in tackling several grand challenges of our time including climate change, energy security, and providing clean water resources for the world’s rapidly growing population. In this talk, I will give two specific examples of my research to illustrate the importance of mathematical modeling of fluid flow in the porous materials (e.g., rocks and soils) for solving emerging energy and environmental problems.

The first example is related to the recent shale gas boom in the US. Shale gas exists within rocks at the deep subsurface that consist of porous structures at nanometer scales. In such nanoporous materials, mechanics and thermodynamics of fluids can deviate significantly from their standard representations such as Naiver-Stokes flow. I will show how mathematical modeling at the microscopic scale in the nanometer range can help derive improved representations of the flux laws at macroscopic (i.e., continuum) scales that substantially improve our predictive capability of gas flow in shale rocks.

The second example is about an emerging contaminant, per- and polyfluoroalkyl substances (PFAS), in soils and groundwater that is causing an international crisis for our drinking water resources. Predicting the transport and migration of PFAS in soils and groundwater is critically important for better risk assessment and remediation strategies. I will present a mathematical model that incorporates the interaction between PFAS and the fluid-fluid interfaces (e.g., air and water) in soils. The model provides, for the first time, a mechanistic understanding of PFAS migration in soils wherein air and water coexist and form complex interfaces. Our model predictions are supported by a large body of field evidence at hundreds of PFAS-contaminated sites.