Analysis of Solute Transport in Column Tracer Studies

To pose mathematically tractable boundary conditions for finite porous media it is necessary to regard the representative elementary volume (REV) as infinitesimal. In so doing, continuity of macroscopic concentrations across boundaries is in general sacrificed to maintain flux continuity. The macroscopic concentration discontinuity can be rationalized by regarding influent and effluent concentrations as flux‐weighted mean values relative to the volume‐averaged resident concentrations ( C r ) in the porous medium near the boundaries. This concept leads logically to the definition of a flux concentration ( C f ) defined macroscopically as the ratio of the solute flux density to the fluid flux density. Flux concentrations obey a convection‐dispersion equation of identical form to that for resident concentrations and transformation of boundary conditions allows direct solution for C r or C f . Solutions are presented for C r and C f for one‐dimensional steady flow which assume back‐mixing at outflow boundaries to be negligible. The solutions are checked against measured effluent curves and resident concentration distributions of Br in a high dispersivity porous medium contrived to have an REV diam ( l ) of about 25 mm. The solution for C f accurately describes the breakthrough curve for a 190 mm long column and the solution for C r matches measured resident concentrations at locations further than l /2 from the boundaries. Solutions which assume equality of C r and C f at exit boundaries fail to describe the experimental data. The results indicate that fractured or aggregated porous media having continuous relatively large pores may be treated as simple continua if the flow region is several times larger than the REV.