Modelling solute transport in homogeneous and heterogeneous porous media using spatial fractional advection-dispersion equation

Abstract

This paper compared the abilities of advection-dispersion equation (ADE) and spatial fractional advection-dispersion equation (sFADE) to describe the migration of a non-reactive contaminant in homogeneous and heterogeneous soils. To this end, laboratory tests were conducted in a sandbox sizing 2.5 × 0.1 × 0.6 m (length × width × height). After performing a parametric sensitivity analysis, parameters of sFADE and ADE were individually estimated using the inverse problem method at each distance. The dependency of estimated parameters on distance was examined. The estimated parameters at 30 cm were used to predict breakthrough curves (BTCs) at subsequent distances. The results of sensitivity analysis indicated that average pore-water velocity and dispersion coefficient were, respectively, the most and least sensitive parameters in both mathematical models. The values of fractional differentiation orders (α) for sFADE were smaller than 2 in both soils. The scale-dependency of the dispersion coefficients of ADE and sFADE was observed in both soils. However, the application of sFADE to describe solute transport reduced the scale effect on the dispersion coefficient, especially in the heterogeneous soil. For the homogeneous soil, the predicting results of ADE and sFADE were nearly similar, while for the heterogeneous soil, the predicting results of sFADE were more satisfactory in comparison with those of ADE, especially when the transport distance increased. Compared to ADE, the sFADE simulated somewhat better the tailing parts of BTCs and showed the earlier arrival of tracer. Overall, the solute transport, especially in the heterogeneous soil, was non-Fickian and the sFADE somewhat better described non-Fickian transport.

Keywords

• fractional differentiation order
• fractional dispersion coefficient
• non-fickian transport
• scale effect