On the Potential Errors in SoluteTransport Modeling In Aquifers

Historically, solute transport modeling in groundwater has started after the 1950s by adapting Fick's diffusive flux equation with some modifications to represent the effects of dispersion. Although a lot has been achieved since the 1950s, still there are controversial issues regarding the dispersion coefficients or dispersivities and boundary conditions. The effects of different boundary conditions on the accuracy of solute transport predictions have not been recognized until the late 1970s. More specifically, more than three decades ago, the importance of the flux-type boundary conditions  was recognized and it has been proven that the constant concentration  boundary condition violates the mass balance constraints at the source locations depending on the solute transport and hydrogeologic parameters; whereas the flux-type boundary conditions exactly satisfy the mass balance constraint. Despite these facts, still the usage of the flux-type boundary condition and the associated solutions are not as widespread as the constant concentration source solutions in practice. In this study, a comparative evaluation of the flux-type and constant concentration-type solutions will be presented by using two different two-dimensional analytical solute transport solutions based on the flux-type and constant concentration source conditions. Based on the aforementioned facts, the practical ramifications of the flux-type and constant concentration-type source solutions will be presented with practical applications and recommendations will be made accordingly.