Geokolloqium, Prof. David C. Mays

- GEOWISSENSCHAFTLICHES KOLLOQUIUM -

Chaotic Advection in Porous Media: Dimensionality, Scaling, and Engineering

Prof. David C. Mays
University of Colorado Denver

The growing body of literature exploring chaotic advection in porous media has provided new insights into solute transport, mixing, and reaction in two-dimensional (2D) and 3D geometries and spanning the micrometer scale of pores to the 10-meter scale of groundwater remediation field sites. Chaotic advection refers to chaos in laminar flows manifesting unpredictability from sensitive dependence on initial conditions, popularly known as the butterfly effect. This unpredictability results, not from inertial terms in the Navier-Stokes equations nor from random heterogeneity in the porous media, but from the nonlinear structure of the dynamic system itself, in which solute plumes are stretched and folded, popularly known as the baker's transformation. The analysis of such flows depends on Lagrangian tools including Lyapunov exponents to quantify the butterfly effect and Poincaré sections to visualize the flow morphology. The literature features three principal applications to date, namely (1) ubiquitous chaotic advection at the pore scale, (2) naturally
occurring chaotic advection at the Darcy scale, and (3) engineered chaotic advection, a subset of engineered injection and extraction (EIE). Among these applications, EIE has attracted the most attention so far, including theoretical developments, laboratory experiments, and one field test, with contributions from groups in Australia, Canada, Germany, India, Spain, and the United States. Chaotic advection in porous media holds promise for understanding natural processes, such as carbon and nutrient cycling, and engineered processes, such as groundwater remediation and in situ leach mining. If one accepts the premise that the rich complexity of biogeochemistry in subsurface environments is often transport-limited, then chaotic advection offers a conceptual framework to rethink flow as a tuning knob that might be adjusted to overcome that limitation.