Solutions and verification of a scale-dependent dispersion model

Area of Science:

• Environmental Science
• Geosciences
• Chemical Engineering

Background:

• Contaminant transport in porous media is crucial for environmental risk assessment.
• Existing models often assume constant dispersion, which may not accurately reflect real-world scenarios.
• Scale-dependent dispersion phenomena require advanced modeling approaches.

Purpose of the Study:

• To derive and validate analytical solutions for a one-dimensional scale-dependent dispersion model (SDM).
• To compare the predictive accuracy of the SDM against a conventional constant dispersion model (CDM).
• To assess the performance of both models under conditions of linear sorption and first-order degradation.

Main Methods:

• Analytical solutions were derived for the SDM, incorporating linear equilibrium sorption and first-order degradation.
• The SDM's pulse source solution was experimentally verified using tritium data from a homogenous pea-gravel column.
• Model performance was evaluated by comparing predictions with experimental data and calibrating model parameters.

Main Results:

• The SDM provided satisfactory concentration predictions across multiple sampling locations.
• The CDM only fitted experimental data well at a single location.
• Both models, when calibrated, showed equally good fits and indicated a linear increase in dispersivity with distance.

Conclusions:

• The scale-dependent dispersion model (SDM) offers superior accuracy for contaminant transport predictions compared to the constant dispersion model (CDM).
• The SDM's accuracy is expected to improve with increasing transport distance.
• The study highlights the importance of considering scale-dependent dispersion in environmental modeling.