Three-Dimensional Analytical Modeling of Diffusion-Limited Solute Transport.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
Pagination or Media Count:
Work conducted using laboratory soil columns has shown that diffusion into regions of immobile water can have a large effect on solute transport through porous media. This study focuses on the development, analysis, and application of an analytical model which incorporates the diffusion mechanism into the traditional three dimensional advectivedispersive solute transport equation. By consecutively applying the Laplace transform in time and the Fourier transform in space, analytical solutions are derived for the coupled partial differential equations which describe three dimensional advectivedispersive transport through regions of mobile water and Fickian diffusion through immobile water regions of simple geometry spherical, cylindrical, and layered. To assist in the analysis of the models, a modified form of Aris method of moments is presented, which permits the calculation of the spatial and temporal moments of the three-dimensional diffusion models, without having to invert the Laplace or Fourier transformed solutions. Using this method, the moments of the diffusion models are compared with one another, with the moments of a model that assumes equilibrium advectivedispersive transport, and with the moments of a model that assumes a first order rate law governs mass transfer between the mobile and immobile regions.
- Hydrology, Limnology and Potamology