Three-Dimensional Analytical Modeling of Diffusion-Limited Solute Transport.
Abstract
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 advective/dispersive 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 advective/dispersive 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 advective/dispersive transport, and with the moments of a model that assumes a first order rate law governs mass transfer between the mobile and immobile regions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1986
- Accession Number
- ADA171258
Entities
People
- Mark N. Goltz
Organizations
- Air Force Institute of Technology