On the Errors Associated with Two-Dimensional Stochastic Solute Transport Models

Abstract

Many subsurface solute transport studies employ numerical modeling techniques to estimate solute arrival times. Simplifying assumptions must be made to define the modeling domain within a mathematical framework. One common assumption is that the vertical flow is negligible such that the flow field can be simulated with a two-dimensional model. Reducing the vertical dimension reduces the number of flow paths that a solute can take. In a heterogenous medium, artificially removing the 3rd dimension may lead to erroneous results. We investigate the error in the simulated solute breakthrough associated with a two-dimensional model. We also use a stochastic solution of solute arrival time to derive a transform of a two-dimensional ln (k) field so that solute transport more closely resembles three-dimensional transport behavior. The moment equations for two- and three-dimensional domains were solved simultaneously to calculate this transform. The results indicate that the removal of the vertical variability (3D → 2D) introduces a 5–10% error in the predicted solute breakthrough. The error tends to increase with increased hydraulic conductivity variance. Numerical experiments confirm that the transform developed herein decreases the relative error of particle breakthrough curves.