Identifying the residence time distributions of urban drainage structures from solute transport data using maximum entropy deconvolution

Solute transport, the processes of water carrying particles through flow, is affected by the bulk mixing that the flow experiences. Improved understanding of solute transport can therefore lead to improved understanding of bulk mixing processes. The Residence Time Distribution (RTD) is a non-parametric model that more fully describes solute transport than traditional models, and therefore can provide additional insight into the underlying mixing processes. As a predictive model, a downstream concentration profile can be expressed as the convolution of an upstream concentration profile with an RTD. Maximum entropy deconvolution is an optimisation method that can be used to reverse the convolution process and obtain an RTD from paired experimental upstream/downstream concentration profiles. This thesis focuses on the application of maximum entropy deconvolution to solute transport. As maximum entropy deconvolution is a relatively new method as applied to solute transport data, it has been tested thoroughly. An initial investigation of the effects of outlet angle on short-circuiting (as a mixing process) in surcharged manholes was undertaken to guide further work on maximum entropy deconvolution. Maximum entropy deconvolution was found to make repeated comparisons between recorded and predicted data through a constraint function. A study evaluating 12 potential correlation measures was undertaken, finding 8 measures potentially suitable for inclusion in maximum entropy deconvolution as a constraint function. 3 correlation measures were found to be additionally suitable for independent model evaluation. Several other configuration settings to maximum entropy deconvolution (number and distribution of sample points, and number of iterations) were also found to impact on the deconvolved RTD. These were examined with different types of input data (e.g. storage tank vs manhole) in order to determine a robust combination of settings for all data types. Two novel extensions to maximum entropy deconvolution are proposed and examined. The first novel extension involves changing interpolation function and number of sample points to give a smoother RTD. The smoother shape is more realistic and allows for easier interpretation of the RTD. The use of alternative interpolation functions also reduces the impact of over-sampling. The second novel extension is the deconvolution of raw data, i.e. data without pre-processing, reducing potential sources for error and making deconvolution easier to apply. Synthetic raw data was examined to produce guidelines for raw data quality. When the quality limits are exceeded, some minimal pre-processing then becomes necessary. A large data set, covering both benched and unbenched manholes with 0°, 30°, 60°, and 90° outlet angles at a range of surcharge depths and flow rates, has been re-analysed (as raw data) with deconvolution. The data was previously analysed with Advection Dispersion Equation and Aggregated Dead Zone models. 6 characteristic RTD shapes were observed, from which different flow fields have been inferred. Deconvolved RTDs are shown to provide new insight into mixing processes occurring.