Mathematical modelling of wastewater treatment processes for the removal of emerging pollutants - Acheampong, Edward (2020)
The presence of emerging pollutants such as pharmaceutical and related bioactive compounds (BACs) in the aquatic environment are of great concern since they pose a risk to aquatic organisms and the ecosystems even at small (ng/L) concentrations. Many wastewater treatment plants (WWTPs) were never designed to remove these pollutants (BACs), and so are major routes through which BACs enter the water environment. However, knowledge of the fate and behaviour of these BACs is still limited. Because all water is reused, and is a scarce resource, there is an impetus for further understanding of BACs dynamics in WWTPs to ensure informed sustainable wastewater treatment policies are geared towards producing treated wastewater effluent of appropriate quality (i.e., effluent BACs concentrations satisfying predicted no effect concentration (PNEC)). Mathematical modelling plays a prominent part in environmental studies since it saves time and the cost of repeatedly designing new experiments by offering the opportunity to alternatively deepen knowledge of complex mechanisms via computer simulation evaluations. For these reasons, in this thesis, we develop mathematical and statistical models, and computer simulations to investigate the dynamics and mechanisms of BACs treatment by WWTPs in combination with real full-scale WWTP data. More importantly, the aim is to gain insight into BAC processing by the activated sludge process technology of WWTPs as well as the quantification of uncertainties surrounding the removal efficiency of the WWTP. We also suggest practical interpretation of the removal efficiency in relation to the rate of consumption and production of pollutants (BACs) by the WWTP. In the mathematical models, we explore for the first time two pathways to BACs sequestration, namely, from the liquid and adsorbed phase. We develop deterministic and stochastic systems of ordinary differential equations to model and compare the effectiveness to the treatment of a case study pharmaceutical, 17α-ethinlyestradiol (EE2) in a bioreactor, with particular focus on determining the nature of the experimentally measured BAC concentration in the solid phase. We demonstrate good agreement between the data and the proposal model with results suggesting that the measured EE2 concentration in the solid phase is the sequestered EE2 concentration in the model rather than adsorbed EE2 concentration. Moreover, sensitivity analysis was performed for the purposes of investigating the impact of parameters on the model outputs and overall relative sensitivity of model outputs was between +1 to -2.5, where values above 2 in absolute terms were considered highly sensitivity. Two estimation approaches, nonlinear least squares and non-parametric were used to estimate ODE model parameters whilst for SDE model, simulated maximum likelihood methodology was used. Using nonlinear least squares (NLS) and nonparametric bootstrap methodologies, the impact of the normality assumption on estimates of model parameters was examined. The results show the effect on the covariance structure of the model parameters. Another topic of this thesis concerns the modelling based on limited empirical data, which is often the case for environmental studies making it difficult to fit data to existing complex wastewater models. We proposed a stochastic first-order differential equation which treats the WWTP as a single unit process and is capable of describing the evolution of BAC concentrations in the effluent, which has been demonstrated for three BACs. A modification to the proposed model was made to study another type dataset that is sporadic in time, which led to the development of a classification rule for the removal efficiency of the WWTP based on a simple linear regression model. This is the first time to the best of our knowledge an alternative method for calculating removal efficiency have been proposed. The parameters of the regression model pave the way for interpreting the removal efficiency of the WWTP in relation to the overall rate of consumption and production of pollutants (BACs), which is a novel aspect of the proposed modelling approach. Finally, we have also investigated correlation between BACs concentration. This approach is motivated by the complex behaviour of BACs during wastewater treatment. The insight into the correlation within and between influent and effluent BACs of WWTP will reduce the cost involved in BACs studies. Thus, measurements will not be required for all BACs concentration since certain BACs may be used as indicators for others. Furthermore, the determination of hydraulic retention time (HRT) across the WWTP via correlation analysis suggests that HRT for each BAC may be different and that HRT is not a fixed parameter but variable which lies in a range. So when correlating influent and effluent, it is valuable to know the HRT of the WWTP and the range HRT will have. Also, for the first time to the best of our knowledge, a multivariate exploratory tool, JIVE was used to analyse the WWTP data. The results confirm that variations in influent BACs concentrations are unrelated to effluent variations but are a results of variations in the load coming from household, industry, etc.