Upstream Dispersion in Solute Transport Models: A Simple Evaluation and Reduction Methodology

D. J. Irvine, A. D. Werner, Y. Ye, A. Jazayeri

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
34 Downloads (Pure)


This article outlines analytical solutions to quantify the length scale associated with “upstream dispersion,” the artificial movement of solutes in the opposite direction to groundwater flow, in solute transport models. Upstream dispersion is an unwanted artifact in common applications of the advection-dispersion equation (ADE) in problems involving groundwater flow in the direction of increasing solute concentrations. Simple formulae for estimating the one-dimensional distance of upstream dispersion are provided. These show that under idealized conditions (i.e., steady-state flow and transport, and a homogeneous aquifer), upstream dispersion may be a function of only longitudinal dispersivity. The scale of upstream dispersion in a selection of previously presented situations is approximated to highlight the utility of the presented formulae and the relevance of this ADE anomaly in common transport problems. Additionally, the analytical solution is applied in a hypothetical scenario to guide the modification of dispersion parameters to minimize upstream dispersion.

Original languageEnglish
Pages (from-to)287-291
Number of pages5
Issue number2
Early online date4 Aug 2020
Publication statusPublished - 1 Mar 2021


  • upstream dispersion
  • solute transport models
  • 1D analytical solutions
  • advection-dispersion equation (ADE)
  • steady-state fresh groundwater flow


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