Physically-Based Particle Size Distribution Models of Urban Water Particulate Matter

A particle size distribution (PSD) of particulate matter (PM) is a primary metric to examine PM transport and fate, as well as PM-bound chemicals and pathogens in urban waters. To facilitate physical interpretation and data sharing, a series of concise analytical models are examined to reproduce unit operation (UO) influent and effluent PSD data and indices. The models are a (1) single-parameter exponential and two-parameter (2) gamma, (3) lognormal, and (4) Rosin-Rammler distributions. Two-parameter models provide physical interpretations for the central tendency of PM diameters, and shape as an index of PSD hetero-dispersivity. Goodness-of-fit is used to test models and PSDs. For influent data from two disparate areas, a paved source area and a larger watershed delivering unique PSDs, lognormal and gamma models provide consistent representation of influent and effluent complexity. In these areas, contrasting UOs (a clarification basin and a volumetric filter), subject to type I settling, scour, and filter PM elution, are differentiated based on flow, surface area, volume, and residence time. Surface overflow rate (SOR) as a common heuristic design tool for only type I settling is used to further test PSD models by simulating effluent PSDs for a scaled basin design. Lognormal and gamma models of SOR-generated effluent PSDs were not statistically different. In conclusion, two-parameter PSD models have physical interpretations and lower errors compared to an exponential model. Gamma and lognormal distributions are physically-based models that reproduce actual complex influent or effluent or through SOR as a tool for PSD transformation. Results indicate that PSD models and parameters can be applied to evaluate behavior of common UOs.