From Local Mixing to Macrodispersion: A Sigmoid Approach to Modelling Scale-Dependent Contaminant Transport

Understanding and predicting contaminant migration in heterogeneous aquifers remains a central challenge for groundwater protection and remediation. Accurately predicting the fate and transport of reactive contaminants is hindered by subsurface heterogeneity, scale-dependent dispersion, and complex reaction chains, all of which control plume architecture and thus remediation performance. This study advances current transport theory by introducing a novel sigmoid dispersivity model that provides a bounded, physically meaningful transition from local-scale pore mixing to field-scale macrodispersion. Focusing on a five-species chlorinated solvent (CS) decay chain, the approach is implemented using a two-dimensional advection-dispersion equation solved by an implicit finite difference scheme. The proposed model uniquely introduces an effective dispersivity function that dynamically represents concentration distributions, apprehending non-linear retardation, first-order decay, and pre-asymptotic spreading patterns more accurately than conventional analytical solutions. A comparative evaluation against four widely used dispersivity models demonstrates that the sigmoid model more accurately captures plume skewness, early-time breakthrough behaviour, and long-distance tailing, verified through spatial-moment analysis. Crucially, the results uncover a significant coupled effect where the dispersion of a parent plume exerts a strong control on the mobility and risk footprint of daughter products, a theoretical insight with profound implications for field applications. By improving the upscaling transport parameters across scales, this model provides a robust tool for improved aquifer characterisation, improved vulnerability assessment, and a strong basis for optimised remediation schemes for persistent groundwater contaminants. Moreover, it directly contributes to bridging theoretical developments in transport modelling with practical field applications, offering a promising tool for risk management and long-term groundwater sustainability.