Analytical solutions for convective‐dispersive transport in confined aquifers with different initial and boundary conditions

Abstract

Analytical solutions of the general one‐ dimensional solute transport model for confined aquifers, applied to specific scenarios, are obtained. The mathematical formulation that is solved includes, in addition to the usual convection/dispersion formulation, (1) distributed first‐order loss, e.g., by metabolism, chemical reaction or irreversible dissolution; (2) linear equilibrium sorption rules; (3) a single, constantly emitting, source of finite length, which can be placed anywhere on the right half line and can be of any reasonable width; (4) mass conserving boundary conditions which include a highly tailorable time distribution of chemical concentration at the inlet boundary; and (5) a highly tailorable initial distribution on [0, ∞). The model constitutes an extension and generalization of the existing literature. Five transport and fate scenarios are presented as follows: (1) a compound initially distributed in stair step fashion, (2) a constant source, (3) a constant rate of entry at the inlet boundary, (4) an inlet boundary concentration that is decaying with time, and (5) conditions 1, 2, 3, and 4 specified at the same time.