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.

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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

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Air Force
  • Boltzmann Equation
  • Chemical Synthesis
  • Chemistry
  • Computational Science
  • Differential Equations
  • Environmental Pollutants
  • Environmental Protection
  • Fluids
  • Groundwater
  • Human Behavior
  • Mass Transfer
  • Organic Compounds
  • Partial Differential Equations
  • Three Dimensional
  • Two Dimensional
  • Water Resources

Readers

  • Calculus or Mathematical Analysis
  • Electrochemical Engineering/ Fuel Cell Technologies
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space