Modelling reactive pollutant transport in ground water: the case of two species
The locations of a significant number of industrial facilities, landfills and almost all mineral ore bodies are characterised by high in situ stresses and fractures and fissures act as flow paths for fluids underground. Regional scale fracture systems that transport pollution from spatially isolated source locations can cause mixing of chemical pollutants from different source origins due to fracture- fracture flux across two or more intersecting fractures, hence reactive transport. Alerts of groundwater contamination in response to multicomponent pollution transport have been investigated using a mathematical model of the hydrodynamic response of incompressible fluids such as groundwater flow. Fundamental to the model is the conservation of mass associated with the applied source strength and the concentration velocity field redistributions after source has released pollution, assuming the formation is homogenous. Solute distribution depends on the formation porosity and generally, fluids travel faster in fractures than in sedimentary formations. Different variations of the deterministic advection dispersion equation have been employed to predict coupled transport/reactive processes by substitution of a reaction term (retardation factor, etc..) which accounts for the changing concentration of the solid face components through time due to chemical reaction. However, fractured aquifers are inherently heterogeneous due to interconnecting fractures. The results in a non-homogenous mathematical formulation which difficult to solve analytically. As a result, most research endeavours have tended to depend on numerical solutions, increasingly made possible through advanced computational power. Even though it is questionable to what extend numerical models of groundwater reactive transport can be useful in making accurate quantitative predictions, it is still possible for a reactive model to predict the outcome of a particular chemical representation in an aquifer. Nevertheless, the linear, non-homogenous advection dispersion equation can still be solved analytical using the Green’s function method. In this thesis, we show how the advection-dispersion transport equation can be extended to account for geochemical reaction processes in a heterogeneous media. For the hypothetical case study, the system was made of a homogenous and a non-homogenous sub-component. The study’s methodological approach involved coupling of the homogenous transport phase with the non- homogenous system. The solution of the homogenous equation is obtained using Laplace transform and the exact solution of the new non-homogenous equation is obtained analytically using Laplace transform and the Green’s Function method. Both sub-models were solved numerically using the Crank-Nicolson discretization scheme and their stability conditions also established. For the proposed fracture flow system, the linear non-homogenous model was able to approximate the contribution of reactive transport processes in the system. Chemical reactions can attenuate the spread of a contaminant plume due to processes such as sorption and precipitation. The model presented in this thesis was able to predict fate of each species within the system. Mass transfer during and after the reaction resulted in the depletion of one source with respect to another, which the model showed positive results in capturing. The thesis concludes with a chapter on chemical equilibria which is the basis of kinetic modelling and the understanding of the progress of chemical reactions.