On the Use of First- and Third-Type Boundary Conditions in Solute Transport Modeling and Degradation Studies

Models for solute transport in groundwater historically have relied nearly exclusively on the use of first-type (given concentration) inlet or source conditions. The disadvantages of first-type inlet solutions were largely ignored until the late 1970s. Several studies in soil physics and groundwater hydrology during the past three decades have stressed the importance of third-type (given flux) inlet solutions in preserving mass across the inlet boundary condition.  These studies showed that first-type source solutions violate mass balance across the inlet location depending upon the prevailing solute transport and hydrogeologic parameter values.  Third-type solutions on the other hand exactly satisfy relevant mass balance constraints (Kreft and Zuber, 1978; van Genuchten and Parker, 1984; Parker and van Genuchten, 1984; Batu and van Genuchten, 1990; Batu, 2010). Despite these studies, many or most solute transport modeling applications still rely on first-type solutions. This also includes methods for determining the degradation rate from experimental data.  In this study we show by example the type of errors being made when experimental degradation data are being analyzed using first-type solutions rather than the formally more correct third-type source solutions.