ANALYTICAL SOLUTION OF SOLUTE TRANSPORT IN TWO DIMENSIONAL MULTI-LAYER AQUIFER SYSTEMS

This article presents an analytical solution of two-dimensional solute transport in two-layer aquifer systems with unidirectional flow using third type boundary condition (Cauchy boundary) at the inlet location of the system. The solutions may be used for predicting solute concentrations in homogeneous media, verifications of more comprehensive numerical models, and laboratory or field determination of solute transport parameters.

Advection, longitudinal and vertical dispersion, first order irreversible decay, and linear sorption are included for both layers. This study solves transport equations in both layers simultaneously and maintains continuities of concentration and mass flux at the two layers interface. General solutions were derived for an arbitrary solute input with the help of Laplace transform.

Transport equations are first solved in Laplace domain, and solutions are then inverted numerically to yield solutions at real time domain. The solutions were developed for three different cases; conservative case, reaction case, and reaction & retardation case. Concentration profiles in both layers are obtained and mass transported to each layer has been calculated in each case as well.