Damköhler number distributions and constituent removal in treatment wetlands

Abstract

Using hypothetical wetland simulations and data from the literature, Kadlec [Eco. Eng. 15 (2000) 105] recently demonstrated that plug-flow models commonly used to quantify treatment wetland performance fail to describe conditions other than those under which calibration data are collected. Parameters of these models (removal rate constants ( k) and background concentrations ( C*)) demonstrate apparent dependence on inlet concentration and hydraulic loading rate which is not alleviated by including dispersion to address non-ideal flow. The phenomenon can be understood as resulting from an interdependence between k and local flow velocity, due to the functional dependence of each on drag-inducing surfaces (and attached biofilms) associated with submerged vegetation and litter. This paper presents a simple method, based on theoretical considerations, for determining C* using inlet–outlet data, independent of the degree of mixing or the nature of the removal processes. This paper also expands upon the hypothetical multi-channel example to suggest a modeling approach in which a wetland is treated conceptually as an ensemble of parallel, non-interacting stream tubes in plug-flow, characterized by a continuous distribution of Damköhler numbers. The Damköhler number distribution (DND) can be estimated from the residence time distribution (RTD) under the assumption of uniform flow path length. For such a wetland, under steady state conditions and with constant inlet concentration, the fraction of a removable pollutant remaining as a function of normalized distance from inlet to outlet is given by the Laplace transform of the DND. Similarly, the DND can be derived from the inverse Laplace transform of the normalized concentration versus normalized distance curve. Given both an RTD and a DND, it is possible to investigate the relationship between k and residence time, and the mechanistic nature of the removal process. Employing these concepts makes it possible to generate an expression for normalized concentration as a function of fractional distance that is unaffected by changes in inlet concentration, and inherently takes into account changes in hydraulic loading rate.