Abstract:

Hydrodynamic transport in fractured rocks is typically anomalous, with heavy-tailed breakthrough curves and nonlinear growth of plume moments. This talk shows how this behavior emerges from heterogeneity across scales and how it can be upscaled. Geological fracture walls are rough over many scales, a legacy of fracturing, shear and weathering, and are mismatched below a correlation length.

The resulting aperture heterogeneity channels flow into a few preferential paths surrounded by quasi-stagnant regions. Fast channels cause early arrivals, while slow regions cause long tails and anomalous plume spreading. Both effects are controlled by low-velocity statistics, and hence by fracture closure. In fracture networks, connectivity and aperture variability play the same role. They focus flow onto a sparse backbone, while poorly connected or low-transmissivity branches trap particles. Aperture variability alone makes transport non-Fickian, whereas fracture density matters little.

At both scales, the hidden structure of transport lies in intermittent Lagrangian velocities: fast excursions alternate with long slow episodes that control late-time spreading. We upscale transport with a continuous-time random walk driven by an Ornstein–Uhlenbeck velocity process. The model condenses the flow into three quantities derived from flow alone: the velocity distribution, the tortuosity and a correlation length. It reproduces particle tracking, predicts asymptotic scalings and reveals the limits of a single-scale closure.