APPROXIMATE ANALYTICAL SOLUTIONS FOR SOLUTE TRANSPORT IN 2-LAYER POROUS-MEDIA

Mathematical models for transport in layered media are important for i nvestigating how restricting layers affect rates of solute migration i n soil profiles; they may also improve the analysis of solute displace ment experiments. This study reports an (approximate) analytical solut ion for solute transport during steady-state flow in a two-layer mediu m requiring continuity of solute fluxes and resident concentrations at the interface. The solutions were derived with Laplace transformation s making use of the binomial theorem. Results based on this solution w ere found to be in relatively good agreement with those obtained using numerical inversion of the Laplace transform. An expression for the f lux-averaged concentration in the second layer was also obtained. Zero - and first-order approximations for the solute distribution in the se cond layer were derived for a thin first layer representing a water fi lm or crust on top of the medium. These thin-layer approximations did not perform as well as the 'binomial' solution, except for the first-o rder approximation when the Peclet number, P, of the first layer, was low (P < 5). Results of this study indicate that the ordering of two l ayers will affect the predicted breakthrough curves at the outlet of t he medium. The two-layer solution was used to illustrate the effects o f dispersion in the inlet or outlet reservoirs using previously publis hed data on apparatus-induced dispersion.