Groundwater Pollutant Transport: Transforming Layered Models to Dynamical Systems

Chemical species such as tracers or dissolved pollutants disperse as they are advected by a fluid flowing within a permeable matrix. In many groundwater systems, the porous media have (near-horizontal) layered structures that have been determined by the geological processes which formed them. The advection-dispersion equations that model the transport then have coefficients that depend mainly on depth. In this study, the parameters that contribute to the coefficients in the partial differential equations are assumed constant within each layer, but can be different in each of the various layers. This allows aquifer systems with parallel-bedded structures to be modelled without having to resort to full numerical simulations. Anisotropy in permeability and in the dispersive length scales, as well as removal of the chemical by adsorption onto the matrix surface and movement into and/or out of dead-end pores, may all be incorporated. The resulting linear constantcoefficient pde’s are coupled by mass flux continuity requirements at the layer interfaces. In many cases, full or partial analytic solutions for the species concentration can be found, thereby saving computational effort. The use of integral transforms, Green’s functions and other techniques are used to solve the system of differential equations. First, the equations that describe the movement of the fluid and pollutant species are summarized. The modelling device of images is