arXiv subjects

Vittorio Di Federico

Publications and source records attributed to Vittorio Di Federico.

2 recordsLinked to original sources

arXiv2026

Stochastic Modeling and Upscaling of Hydrodynamic Transport in Geological Fractures

Characterizing hydrodynamic transport in fractured rocks is essential for carbon storage and geothermal energy production. Multiscale heterogeneities lead to anomalous solute transport, featuring breakthrough curve (BTC) tailing and nonlinear growth of plume spatial moments. We focus on purely advective transport within synthetic geological fractures with prescribed relative closure $σ_a/\langle a \rangle$ and correlation length $L_\mathrm{c}$. We adopt a stochastic approach with multiple fracture realizations for each set of geometric parameters. Steady-state depth-averaged Stokes flow is solved under the lubrication approximation. Flow heterogeneity is organized over the correlation length $L_\mathrm{c}$. The ensemble-averaged velocity PDFs are insensitive to $L_\mathrm{c}$ but strongly influenced by $σ_a/\langle a \rangle$, particularly their low-velocity power-law scaling. A time-domain random walk (TDRW) simulation is used to compute plume spatial moments and outlet BTCs. The mean longitudinal plume position scales linearly with time at both early and late stages. The variance shows ballistic scaling at early times and a late-time behavior controlled by the low-velocity power law of the velocity PDF, with exponent $α$ strongly influenced by $σ_a/\langle a \rangle$. The properties of the BTCs are also controlled by $α$, including the broadening of the peak as $σ_a/\langle a \rangle$ increases, and the scaling of the power-law tails. Advective transport is also modeled using a one-dimensional continuous-time random walk (CTRW) that relies only on the velocity PDF, flow tortuosity, and flow correlation length. The CTRW reproduces the TDRW results and provides analytical predictions for the asymptotic transport scalings.

physics.flu-dyn↗

arXiv2026

Effects of Wall Roughness on Coupled Flow and Heat Transport in Fractured Media

Heat transfer in fractured media is governed by the interplay between advective transport along rough-walled fractures and conductive transport, both within the fractures and in the surrounding low-permeability matrix. Flow localization induced by aperture heterogeneity, combined with matrix conduction, gives rise to anomalous thermal behavior. To capture these effects, we develop a stochastic modeling framework that couples a time-domain random walk (TDRW) representation of advective and conductive transport in the fractures with a semi-analytical model of conductive heat exchange with the matrix. Matrix trapping times follow a Lévy-Smirnov distribution derived from first-passage theory, capturing the heavy-tailed dynamics typical of fractured systems. Heat flux at the fracture-matrix interface is computed via a nonlocal convolution integral based on Duhamel's principle, accounting for thermal memory effects. The model is validated against analytical benchmarks and finite-element simulations. Monte Carlo simulations over stochastic aperture fields quantify the influence of fracture closure, correlation length, and Péclet number. Results reveal a transition from superdiffusive to subdiffusive regimes, driven by the competition between advective transport along preferential paths, dispersion induced by aperture variability, and matrix-driven heat conduction. In the long-time regime, heat exchange exhibits a characteristic $t^{-1/2}$ decay. At early times, limited thermal penetration into the matrix leads to weaker interfacial fluxes, underscoring the role of matrix thermal inertia. The proposed framework enables physically consistent and computationally efficient simulations of thermal transport in complex fractured systems, with implications for geothermal energy, subsurface thermal storage, and engineered heat exchange in low-permeability environments.

physics.geo-ph↗