Introduction of the Stream Function Concept to the analysis of hydrodynamic dispersion in porous media

Abstract

The stream function concept is introduced to the analysis of hydrodynamic dispersion in porous media. The governing partial differential equation for the stream function for two‐dimensional flow under steady state water and solute transport conditions in an isotropic porous medium is derived. For a uniform seepage velocity, the corresponding differential equation is obtained as a special case. The equation for axially symmetric solute transport case is also derived. It is shown that the isoconcentration curves and the hydrodynamic dispersion stream lines are not orthogonal to each other. For the uniform seepage velocity field case, general solutions are presented for concentration distribution and hydrodynamic dispersion stream function (HDSF) for strip sources having variable concentration distributions. Special solutions are presented for concentration, HDSF, and convective‐dispersive flux components for a strip source having constant concentration. The concept of hydrodynamic dispersion bounding streamline separating the solute transport zone from the other zones is also introduced. The methodology of the HDSF concepts and the solutions for some idealized cases can be applied for contaminant plume analysis, computer model validation, and other hydrogeological studies.