The Essential Role of REV Analysis Specific to Solute Transport in Homogeneous Porous Media and Its Implications for Flow-Dependent Dispersion Coefficients

Abstract

This study investigated the Representative Elementary Volume (REV) for solute transport using pore-scale computational simulations and laboratory column experiments in homogeneous media up to 1.83 m long. Non-Fickian tailing was observed at transport distances shorter than the solute transport REV, becoming more pronounced with increasing Peclet number (Pe). Non-Fickian ‘tails’ transitioned to Fickian ‘Gaussian’ characteristics between 1 and 1.83 m. The apparent dispersion coefficient converged towards a steady hydrodynamic dispersion coefficient between 1 and 1.5 m, both signifying the emergence of pore-scale solute transport physics into a continuum and defining the solute transport REV, rather than the ‘scale effect’. This challenges the assumption that Darcy’s law, with its much smaller REV (2.8 cm), is adequate for defining the continuum for solute transport. When the transport length was shorter than the solute transport REV, there was an overestimation of the Pe-dependent dispersion coefficient due to solute stretching from non-Fickian tailing, leading to nonlinear relationships. As the transport length approached the solute transport REV, the nonlinear Pe-dependence converged towards a linear relationship, conforming with hydrodynamic dispersion theory in the mechanical transport regime. Similarly, the longitudinal dispersivity coefficient showed Pe dependence until the transport reached the solute transport REV, beyond which it became Pe-independent, confirming theoretical expectations once again. These findings suggest a need to reconsider previously proposed exponents that did not account for the REV specific to solute transport. The differences observed between computational simulations and laboratory experiments, such as the persistent memory of subtle tails in simulations, suggest areas for future research. However, this study sets a benchmark for the methodology of estimating dispersion and dispersivity coefficients, including their Pe dependencies, in accordance with theoretical expectations through REV analysis specific to solute transport.