An investigation on the fractional derivative model in characterizing sodium chloride transport in a single fracture⋆

Abstract

Contaminant transport in a single fracture cannot be reliably captured by the classical advection-dispersion equation model, due to the heterogeneity nature of the fracture. This study applied a time fractional advection-dispersion equation (ADE) model to quantify chloride ion transport in a single fracture observed in the lab. We further explored the solute transport characteristics by comparing them with the simulation results using a classical ADE model and a space-time fractional ADE model. Comparison results show that the time fractional derivative model is better than the classical ADE model in describing the blocking process of solute transport in the fracture (the tailing phenomenon of the breakthrough curve or BTC). The space-time fractional ADE model is not needed to describe the observed BTC, because only time evolution of solute concentration is considered in this case. Experimental analysis also indicates that the order of the time fractional derivative increases with the fracture aperture, and sub-diffusion is enhanced by a slower flow velocity.