One-Dimensional Mixing Model for Surcharged Manholes

Abstract

Mixing and dispersion processes affect the timing and concentration of contaminants transported within urban drainage systems. Hence, methods of characterizing the mixing effects of specific hydraulic structures are of interest to drainage network modelers. Previous research, focusing on surcharged manholes, used the first-order advection-dispersion equation (ADE) and aggregated dead zone (ADZ) models to characterize dispersion. However, although systematic variations in travel time as a function of discharge and surcharge depth were identified, the ADE and ADZ models did not provide particularly good fits to observed manhole mixing data, which meant that the derived parameter values were not independent of the upstream temporal concentration profile, and no rules for predicting parameter values based on manhole size and configuration were provided. An alternative, more robust, method is described by using the system’s cumulative residence time distribution (CRTD). This paper shows how a deconvolution approach derived from systems theory may be applied to identify, from laboratory data, the CRTDs associated with surcharged manholes. Archive laboratory data are reanalyzed to demonstrate that the solute transport characteristics of a surcharged manhole with straight-through inflow and outlet pipes over a range of flow rates and surcharge depths may be modeled using just two dimensionless CRTDs, one for prethreshold and the other for postthreshold surcharge depths. The model combines the derived manhole CRTDs with a standard (Gaussian) pipe dispersion model to provide temporal solute concentration profiles that are independent of both scale and the ratio of the pipe and manhole diameters.