Stochastic modelling and upscaling of hydrodynamic transport in geological fractures
Abstract
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 / a and correlation length L 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 c . The ensemble-averaged velocity probability density functions (PDFs) are insensitive to L c but strongly influenced by σ a / a , 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 behaviour controlled by the low-velocity power law of the velocity PDF, with exponent α strongly influenced by σ a / a . The properties of the BTCs are also controlled by α, including the broadening of the peak as σ a / a increases, and the scaling of the powerlaw tails. Advective transport is also modelled using a one-dimensional continuous-time random walk (CTRW) that relies only on the velocity PDF, flow tortuosity and flow;
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BibTeX
@article{lenci2026stochastic,
title = {{Stochastic modelling and upscaling of hydrodynamic transport in geological fractures}},
author = {Alessandro Lenci and Yves Méheust and Marco Dentz and Vittorio Di Federico},
journal = {Journal of Fluid Mechanics},
year = {2026},
month = sep,
doi = {10.1017/jfm.2026.11831},
url = {https://insu.hal.science/insu-05754326v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Stochastic modelling and upscaling of hydrodynamic transport in geological fractures
AU - Alessandro Lenci
AU - Yves Méheust
AU - Marco Dentz
AU - Vittorio Di Federico
PY - 2026
DA - 2026/09/18
JO - Journal of Fluid Mechanics
DO - 10.1017/jfm.2026.11831
UR - https://insu.hal.science/insu-05754326v1
AB - 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 / a and correlation length L 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 c . The ensemble-averaged velocity probability density functions (PDFs) are insensitive to L c but strongly influenced by σ a / a , 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 behaviour controlled by the low-velocity power law of the velocity PDF, with exponent α strongly influenced by σ a / a . The properties of the BTCs are also controlled by α, including the broadening of the peak as σ a / a increases, and the scaling of the powerlaw tails. Advective transport is also modelled using a one-dimensional continuous-time random walk (CTRW) that relies only on the velocity PDF, flow tortuosity and flow;
SN - 0022-1120
SN - 1469-7645
ER -