The use of deconvolution techniques to identify the fundamental mixing characteristics of urban drainage structures

Abstract

Mixing and dispersion processes affect the timing and concentration of contaminants transported within urban drainage systems. Hence, methods of characterising the mixing effects of specific hydraulic structures are of interest to drainage network modellers. Previous research, focusing on surcharged manholes, utilised the first-order Advection-Dispersion Equation (ADE) and Aggregated Dead Zone (ADZ) models to characterise dispersion. However, although systematic variations in travel time as a function of discharge and surcharge depth have been identified, the first order ADE and ADZ models do not provide particularly good fits to observed manhole data, which means that the derived parameter values are not independent of the upstream temporal concentration profile. An alternative, more robust, approach utilises the system's Cumulative Residence Time Distribution (CRTD), and the solute transport characteristics of a surcharged manhole have been shown to be characterised by just two dimensionless CRTDs, one for pre- and the other for post-threshold surcharge depths. Although CRTDs corresponding to instantaneous upstream injections can easily be generated using Computational Fluid Dynamics (CFD) models, the identification of CRTD characteristics from non-instantaneous and noisy laboratory data sets has been hampered by practical difficulties. This paper shows how a deconvolution approach derived from systems theory may be applied to identify the CRTDs associated with urban drainage structures.

On the potential of on-line free-surface constructed wetlands for attenuating pesticide losses from agricultural land to surface waters

“…We employed two approaches to modelling solute behaviour in the studied wetlands: (1) the Aggregated Dead Zone (ADZ) model of Beer and Young (1983) and (2) maximum entropy deconvolution (Sonnenwald et al, 2015) to determine solute Residence Time Distributions (RTDs) for each system under different conditions. The "non-parametric" (empirical) RTD is the theoretical distribution of solute in a system in response to an instantaneous input (Levenspiel, 1972) and makes no a priori assumptions about how the system operates (Stovin et al 2010).…”

Residence Time Distributions for Turbulent, Critical, and Laminar Pipe Flow

“…Danckwerts, 1953) Recent work has investigated techniques for recovering the RTD numerically through identification of the impulse response function required to transform a measured upstream proÞle into a measured downstream proÞle. Stovin et al (2010) and Guymer and Stovin (2011) used deconvolution (see later section) to recover RTDs from laboratory data from a surcharged manhole. In this case, the mixing processes of interest were generated by the manhole geometry and associated ßow-Þelds.…”

“…Of the six approaches, they concluded that the best in terms of overall performance was 'maximum entropy deconvolution', developed by Skilling and Bryan (1982). Stovin et al (2010) and Guymer and Stovin (2011) successfully applied maximum entropy deconvolution to data from tracer studies within surcharged manholes. Sonnenwald et al (2014) further investigated maximum entropy deconvolution and found it to be applicable to a wide range of field and laboratory solute transport data.…”

Applications of the concept of river tracer data similarity

“…Interestingly, the study of similarities and differences between nondimensional tracer residence time distributions has been mooted as a way of identifying flow regimes in urban drainage structures (Stovin et al . , ). It is not clear if there is any link between these nondimensional residence time distributions and the nondimensional profiles under study in the current paper.…”