Hydrodynamic Dispersion in Geological Fractures

This presentation was delivered at the 25th Computational Methods in Water Resources (CMWR 2024) conference, held from September 30 to October 3, 2024, at the University of Arizona in Tucson, USA. The work addresses hydrodynamic dispersion in geological fractures, with a focus on the impact of wall roughness and spatial correlation on flow organization and anomalous transport behaviors. Flow is simulated in synthetic aperture fields generated as isotropic self-affine topographies, using a finite volume solver for the Reynolds equation under the lubrication approximation. The results highlight the emergence of superdiffusive transport due to contact zones and strong velocity heterogeneity, with macrodispersion evolving from early ballistic behavior to a plateau that is rarely reached in geologically realistic domains. To upscale these dynamics, a Lagrangian framework is employed in which particle velocities are modeled as a stationary Gauss-Markov (Ornstein-Uhlenbeck) process. This leads to a stochastic continuous time random walk (CTRW) model where particle transition times are derived from the velocity process. The upscaled model captures key transport features such as breakthrough tailing and anomalous dispersion, using only the Eulerian velocity distribution, flow tortuosity, and a characteristic length scale—without requiring full spatial resolution of the flow field. The study is part of the MSCA-funded GEONEAT project and contributes to the development of efficient upscaling strategies for transport modeling in rough-walled fractures.