Advective solute transport through porous media along streamlines

Abstract

Transforming the standard solute transport models into one-dimensional ones along streamlines by excluding from them diffusive and dispersive components and direct including in simulation procedures the mechanical dispersion, the predominate factor defining solute transport in day-to-day applications, permit reducing these models to ordinary differential equations of the first order, making simulations less cumbersome and more flexible and permitting analytical solutions under about any practical conditions. The models of solute transport along flux tubes and streamlines are discussed in numerous publications. Most of those models, if not all, are one-dimensional copies of the mass conservation law and do not take in consideration streamline specificity: the absence of sinks and source within flux tubes to which the streamlines belong. This makes the obtained equations either inadequate or unnecessary oversimplified by assuming the pore water velocity constant along the streamlines. The development of the solute transport equations along streamlines taking in account the above mentioned specificity is presented in Appendix 1. Appendix 2 contains development of analytical solutions to the corresponding models for spatially varying actual pore water velocities, arbitrary initial and boundary conditions, linear and non-linear (Freundlich and Langmuir isotherms) interaction of solutes with the surroundings. Calculating concentration at given points and instants, the concentrations for the involved streamlines must be summarized accordingly to mechanical dispersion. The method of weighted summarizing is suggested. The approach is illustrated by field examples.