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Upstream Dispersion in Solute Transport Models: A Simple Evaluation and Reduction Methodology
D J Irvine, A D Werner1, Y Ye2
1College of Science and Engineering, and National Centre for Groundwater Research and Training, Flinders University, Adelaide, Australia.
This study provides analytical solutions to quantify upstream dispersion, an artifact in groundwater solute transport models. The findings offer methods to estimate and minimize this phenomenon in advection-dispersion equation applications.
Area of Science:
- Environmental Science
- Hydrogeology
- Geochemistry
Background:
- Upstream dispersion is an artifact in solute transport models, causing artificial solute movement against groundwater flow.
- This phenomenon is particularly problematic in advection-dispersion equation (ADE) applications with increasing solute concentrations.
- Understanding and quantifying upstream dispersion is crucial for accurate environmental modeling.
Purpose of the Study:
- To develop analytical solutions for quantifying the length scale of upstream dispersion.
- To provide simple formulae for estimating upstream dispersion distance under idealized conditions.
- To demonstrate methods for minimizing upstream dispersion by modifying model parameters.
Main Methods:
- Derivation of analytical solutions for upstream dispersion.
- Formulation of simple equations to estimate upstream dispersion distance.
- Application of the analytical solution to hypothetical scenarios and existing case studies.
Main Results:
- Analytical solutions were derived to quantify upstream dispersion length scales.
- Under steady-state, homogeneous conditions, upstream dispersion is primarily a function of longitudinal dispersivity.
- The study highlights the relevance of this ADE anomaly in common groundwater transport problems.
Conclusions:
- The developed analytical solutions effectively quantify upstream dispersion.
- The findings provide practical tools for researchers and modelers to address this artifact.
- Modifying dispersion parameters based on these solutions can minimize upstream dispersion, improving model accuracy.
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