In wastewater treatment, there is an increasing focus on nutrient and energy recovery and a reduction in energy consumption to counter climate change. Because of this, integrated mathematical modelling platforms are required to support plant-wide developments making use of emerging, resilient and environmental-friendly technologies. A reliable model description of a wastewater treatment plant should include both biology and physico-chemistry. However, existing standard models used across the wastewater sector have a biological focus with over-simplified descriptions of important physico-chemistry, especially with minerals precipitation which is a very important class of physicochemical reactions.
As part of development of a more widely applicable physicochemical framework, this thesis sought to identify a suitable minerals precipitation modelling approach that could give reasonable results in mainstream use with wastewater treatment. This research aim was approached in three steps. Firstly a review of available modelling approaches suggested a simple equilibrium kinetic-based modelling approach could be feasible. This approach was then validated in a simple system of calcite in synthetic solutions using pH titration experiments with the reliable Constant Composition Method (CCM). Further statistical analysis focused on clarifying key environmental factors that influence calcite precipitation to determine whether these are necessary to include in a model. Secondly, the proposed model approach was further tested on different types of wastewater and for multiple parallel precipitation reactions. Experiments included dynamic titration or aeration with synthetic wastewater and real wastewater. Thirdly, the general physicochemical modelling approach was implemented in a plant-wide platform together with standard biological models, namely activated sludge model No 2 (ASM2d) and Anaerobic Digestion Model No. 1 (ADM1). The plant-wide model evaluation compared simulations with real data from a full-scale wastewater treatment plant, and used steady-state, dynamic and scenario analyses to test the model performance.
Experimental evidence for calcite precipitating in synthetic aqueous solutions, suggested that minerals precipitation kinetics could be reliably described with a 1st order dependency on mineral solid state Xcryst and a 2nd or 3rd order dependency on supersaturation. This results in a kinetic rate law for each mineral with a single adjustable kinetic rate parameter (kcryst). Such a kinetic rate law has the major advantages of not requiring detailed analysis of mineral surface area present in a wastewater (usually impossible to reliably measure or track), while still being able to model nucleation induction where very low seed concentrations exist. The model approach was observed to be more tolerant to a fast precipitation rate coefficient (kcryst = 0.23 h-1), which implied that a modeller could select an arbitrarily high kinetic rate coefficient (kcryst>0.23 h-1) where inadequate process data is available to estimate kcryst values. The equilibrium part of the model is fully resolved by well-established aqueous electrolyte equilibrium thermodynamics, and thus did not require any adjustment of model parameters. Model analysis of the rate of calcite precipitation indicated that supersaturation and temperature had strong effects and should be included in a kinetic rate law. Magnesium impurity had a moderate effect and so model correction for this may be optional. Ionic strength and pH only impacted on equilibrium.
Further testing for multi-species systems in real wastewater indicated that precipitation was dominated by the mineral struvite, forming together with varied and minor amounts of calcium phosphate and some calcium carbonate. Kinetic rate coefficients (kcryst), which were statistically fitted, were generally in the range 0.35-11.6 h-1 with 95% confidence intervals of 10-80% relative. The results confirmed that the baseline model approach provided a statistically good fit of measured pH, dissolved calcium, magnesium, total inorganic carbon and phosphate. With this application, the precipitation modelling approach offered the advantage of only requiring a minimal number of empirical fitted parameters (kcryst values), resulting in improved model statistics and identifiability. Confidence regions for kinetic rate coefficients were often asymmetric with model-data residuals increasing more gradually with larger coefficient values. These observations again suggested that large kinetic coefficients could be used when actual measured data are lacking for particular precipitate-matrix combinations. Correlation between kinetic rate coefficients of different minerals was low, indicating that parameter values for individual minerals could be independently fitted (keeping other model parameters constant).
The present thesis has also developed and validated application of a plant-wide model with minerals precipitation. With default rate kinetic and stoichiometric parameters, a good general agreement was obtained between a full-scale experimental dataset and simulated results for different water and sludge streams around a wastewater treatment plant under steady-state conditions. Dynamic simulations indicated that a plant-wide model can be important and extremely useful for prototyping nutrient recovery.
The overall findings of this thesis suggested that a reliable description of minerals precipitation could be obtained, using a common equilibrium-kinetic approach with an arbitrarily fast mineral precipitation rate parameter and 1st order dependency on mineral state. The thesis also evaluated alternative approaches to identification of minerals, and clarified model behaviour in terms parameter confidence regions and correlation.