Quantifying fate and transport of nitrate in saturated soil systems using fractional derivative model

Abstract

Natural soil systems usually exhibit complex properties such as fractal geometry, resulting in complex dynamics for the movement of solutes and colloids in soils, such as the well-documented non-Fickian or anomalous diffusion for contaminant transport in saturated soils. The development of robust mathematical models to simulate anomalous diffusion for reactive contaminants at all relevant scales presents a contemporary problem in computational hydrology. This study aims to develop and validate a novel fractional derivative, advection-dispersion-reaction equation (fADRE) with first order decay to quantify nitrate contaminants transport in various soil systems. As an essential nutrient for crop growth, nitrogen in various forms (i.e., fertilizers) is typically applied to agricultural plots but a certain fraction or excess that is converted to nitrate or nitrite will serve as a critical pollutant to surface-water and groundwater. Applications show that the fADRE model can consider both hydrological and biogeochemical processes describing the fate and transport of nitrate in saturated soil. Here “fate” is a commonly used terminology in hydrology to describe the transformation and destination of pollutants in surface and subsurface water systems. The model is tested and validated using the results from three independent studies including: (1) nitrate transport in natural soil columns collected from the North China Plain agricultural pollution zone, (2) nitrate leaching from aridisols and entisols soil columns, and (3) two bacteria (Escherichia coli and Klebsiella sp.) transport through saturated soil columns. The qualitative relationship between model parameters and the target system properties (including soil physical properties, experimental conditions, and nitrate/bacteria physical and chemical properties) is also explored in detail, as well as the impact of chemical reactions on nitrate transport and fate dynamics. Results show that the fADRE can be a reliable mathematical model to quantify non-Fickian and reactive transport of chemicals in various soil systems, and it can also be used to describe other biological degradation and decay processes in soil. Hence, the mathematical model proposed by this study may help provide valuable insight on the quantification of various biogeochemical dynamics in complex soil systems, but needs to be tested in real-world applications in the future.