| A one-dimensional flow and transport model was developed to describe the movement of two fluid phases, gas and water, within a porous medium, and the transport of 226Ra and 222Rn within and between these two phases. Included in this model is the vegetative uptake of water and aqueous 226Ra and 222Rn that can be extracted from the soil via the transpiration stream. The mathematical model is formulated through a set of phase balance equations and a set of species balance equations. Mass exchange, sink terms and the dependence of physical properties upon phase composition couple the two sets of equations. Numerical solution of each set, with iteration between the sets, is carried out leading to a set-iterative compositional model. The Petrov-Galerkin finite element approach is used to allow for upstream weighting if required for a given simulation. Mass lumping improves solution convergence and stability behavior. The resulting numerical model was applied to eight problems and was found to produce accurate, mass conservative solutions when compared to published experimental and numerical results and theoretical column experiments. Additional validation of the model was achieved through the comparison of numerical solutions to experimental results from six mesocosm studies. |
