Quantifying colloid fate and transport through dense vegetation and soil systems using a particle-plugging tempered fractional-derivative model

Abstract

Colloid contaminants are widely distributed in surface runoff from crop land and can be effectively removed by vegetative filter strips (VFS), whose quantification however proves difficult. Standard mechanism-based models contain many unknown parameters with intrinsic uncertainty, limiting their applicability and potential extension for other environmental conditions and colloid contaminant types. To remedy this limitation and capture the complex dynamics of colloids through the soil-vegetation system, this study proposes a parsimonious, particle-plugging tempered fractional advection-dispersion eq. (P-TFADE) with a few empirical parameters, which is built upon the promising fractional calculus engine. The P-TFADE model extends the promising tempered fractional derivative model by incorporating a plugging term, which is then proved to be able to capture both the plugging dynamics and tailing behavior of colloids under various hydrologic and geochemical conditions. Applications also show that the two critical parameters in the P-TFADE model, the time index (α) and plugging coefficient (Kp), can efficiently characterize the impact of the flowrate and ionic condition on transport of different sized colloids observed in our laboratory. In addition, the vegetation type determines the overall structure of the soil-vegetation system, whose impact on the colloid removal efficiency can be quantified by adding a parameter λ in the physical model. Therefore, the novel P-TFADE model can reduce the model uncertainty and help us further understand the nature of colloid dynamics through dense vegetation and soil systems.

Keywords: Colloid transport; Plugging process; Removal efficiency; Soil-vegetation system; Tailing behavior; Tempered fractional model.