A process-based method of estimating exponential decay parameters for particulate removal in a gravel trench

Observed reductions in pollutant concentrations through stormwater treatment devices commonly display the characteristic form of exponential decay, in which the rate of decrease of pollutant concentration with distance is proportional to the concentration. The observation of an apparently irreducible or background pollutant concentration, C*, in many devices has led to development of the two-parameter "k-C*" model. It is known that this model is too simplistic because the parameters k and C* are not constant but can vary greatly with pollutant concentration and hydraulic conditions. This paper presents an alternative exponential decay model for filtration of particulate pollutants, which is based on simple mathematical descriptions of key removal processes. The model delivers a process-based method for estimating the exponential decay constant. Moreover, the need to specify a background concentration is eliminated. To test the theory, the model is applied to the removal of clay and silica particles from horizontal flow through an experimental gravel trench. Particle concentrations were measured at nine locations along a 7.2 m long flume. The model agrees very well with the observed change in suspended solids concentration for the two pollutant materials and the range of flow rates tested. A single model parameter, notionally representing the "stickiness" of pollutant particles, is required for different pollutant materials.