One-Dimensional Modelling of Reactive Pollutant Transport in Groundwater

Abstract

The locations of a significant number of industrial facilities, landfills, and almost all mineral ore bodies are characterized by high in situ stresses and fractures, which act as flow paths for fluids underground. Toxic chemical transport is one of the main reasons for loss in groundwater quality and reactive transport modelling is an important tool necessary for predicting and controlling their fate. Modelling reactive transport has largely been achieved using the hydrodynamic transport equation, with an additional reaction and/or decay term. To date, however, most approaches to modelling reactive transport often consider an already existing mixture (multi-phase and/or multi-species) undergoing such transport in homogeneous media. The motivation of this research is to use the transport solutions of two single-phase species in homogeneous media to describe the reactive transport of two species before and after mixing, due to formation heterogeneity. This practical scenario can be observed where regional-scale fracture systems transporting pollution from spatially isolated source locations cause the mixing of chemical pollutants from different source origins due to fracture–fracture flux across two or more intersecting fractures. Here, the authors present a framework for determining the exact solution of the reactive groundwater transport model by the coupling of the homogeneous and non-homogeneous model sub-components. The solution of the homogeneous sub-component is obtained using the Laplace transform. The exact solution of the proposed non-homogeneous equation is obtained analytically using Green’s function method. Further, the two equations are numerically discretized using the Crank–Nicolson scheme and their stability conditions are also established. Instead of presenting the specific solution of a particular case study scenario, a general model to approximate the contribution of reactive processes in the system is presented. It is found that the fate and contribution of each species within the system is captured by the model for which the reaction kinetics and equilibrium partitioning between liquid and solid phases are all assumed to be linear first order.