Comparative Evaluation of Models for Non-FickianTransport in Unsaturated Porous Media

Abstract

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 transport. The pore-network model was first validated against experiments in glass bead packing. Then the validated model was used to simulate transport in three different hypothetical network structures with three different correlated pore-size distributions (characterised by correlation lengths), different Peclet (Pe) numbers, and saturation values. Breakthrough curve (BTC) analysis reveals an expected shift from anomalous long-tailed behaviour 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 compared 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 conditions, at times yielding unrealistic values. Dispersion coefficients derived from the MIM and DE exhibit non-monotonic variation with saturation, consistent with both simulation trends and previously reported experimental observations, while the MRMT and CTRW models fail to capture this behaviour. 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 models and emphasise the role of two-phase flow distributions, time-dependent mass transfer, and saturation-dependent dispersion in accurately predicting transport in unsaturated media.