Flux‐Averaged and Volume‐Averaged Concentrations in Continuum Approaches to Solute Transport

Abstract

Transformations between volume‐averaged pore fluid concentrations and flux‐averaged concentrations are presented which show that both modes of concentration obey convective‐dispersive transport equations of identical mathematical form for nonreactive solutes. The pertinent boundary conditions for the two modes, however, do not transform identically. Solutions of the convection‐dispersion equation for a semi‐infinite system during steady flow subject to a first‐type inlet boundary condition is shown to yield flux concentrations, while solutions subject to a third‐type boundary condition yield volume‐averaged concentrations. These solutions may be applied with reasonable impunity to finite as well as semi‐infinite media if back mixing at the exit is precluded. Implications of the distinction between resident and flux concentrations to laboratory and field studies of solute transport are discussed. It is suggested that perceived limitations of the convection‐dispersion model for media with large variations in pore water velocities may in certain cases be attributable to a failure to distinguish between volume‐averaged and flux‐averaged concentrations.