Comparative Evaluation of Models for Non-Fickian Transport in Unsaturated Porous Media
DOI:
https://doi.org/10.69631/fx3kjg18Keywords:
Non-Fickian transport, Unsaturated porous media, Pore-network modelling, Mobile Immobile model, Multirate Mass Transfer model, Continuous Time Random Walk model, Direct EstimationAbstract
Understanding solute transport in unsaturated porous media is essential for a wide range of scientific and engineering applications. This study investigates non-Fickian transport in unsaturated porous media using pore-network modelling to simulate quasi-static two-phase flow and tracer trans-port. The pore-network model was first validated against experiments in glass bead packing. Then the validated model was used to simulate trans-port in three different hypothetical network structures with three different correlated pore-size distributions (characterized by correlation lengths), dif-ferent Péclet (Pe) numbers, and saturation values. Breakthrough curve (BTC) analysis reveals an expected shift from anomalous long-tailed behav-ior at low saturation to Fickian transport as saturation approaches unity.
The simulation results were interpreted using three continuum-scale approaches: Mobile-Immobile (MIM), Multirate Mass Transfer (MRMT), Continuous-Time Random Walk (CTRW), and their predictions were com-pared against each other and to direct estimations (DE) obtained from the pore-network simulations. Estimates of stagnant zone saturation from the MIM and MRMT models show strong sensitivity to saturation and flow con-ditions, at times yielding unrealistic values. Dispersion coefficients derived from the MIM and DE exhibit non-monotonic variation with saturation, con-sistent with both simulation trends and previously reported experimental observations, while the MRMT and CTRW models fail to capture this behav-ior. The DE analysis demonstrates that mass transfer coefficients vary with time, challenging the assumption of constant rates in the MIM and MRMT formulations. The findings underscore limitations of continuum-scale mod-els and emphasise the role of two-phase flow distributions, time-dependent mass transfer, and saturation-dependent dispersion in accurately predicting transport in unsaturated media.
WHY THIS PAPER MATTERSPredicting how dissolved substances move through partially saturated porous media is challenging because uneven flow can cause some material to move rapidly while some is retained for much longer. We use detailed pore-scale simulations to test whether commonly used larger-scale mod-els can reliably represent these underlying transport processes. Our results show that models can reproduce observed breakthrough behaviour while still producing parameters that do not accurately reflect the physical pro-cesses occurring within the pore space. This matters for improving predic-tions of solute and contaminant transport in environmental and engineering applications, including groundwater and subsurface systems.
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