Kinetic investigations of struvite crystallisation in Poiseuille flow using discretised population balance methods

Abstract

Phosphorus is a non-renewable resource, essential for agriculture. Struvite crystallisation from wastewater offers an easy method of recovering up to 17% of global phosphorus losses. Reported struvite crystallisation kinetics vary significantly, resulting in large uncertainties in crystalliser design. Additionally, crystallisation models are rarely capable of describing particle size distribution, which is a key property of crystallisation kinetics, crystal packing and crystal dissolution rates. This thesis consisted of three major components: model development, experimental investigations and parameter estimation. As a precursor to model development, a review was conducted on struvite crystallization modelling and data from multiple kinetic investigations was analysed to identify trends and areas for targeted improvement. The large range in kinetic modelling techniques and results suggested the need for more detailed modelling, incorporating aggregation. On this basis, further investigations were conducted on population balances used to model aggregation processes. The volume average technique and a modified Hounslow technique were adopted for this work. Model testing showed that implementation of the cell average technique produced more accurate results but longer simulation times. The final approach used to analyse data in this work combined both models – using the cell average technique for nucleation and crystal growth analysis and the Galbraith modified Hounslow technique for the more computationally intensive aggregation investigations. A non-ideal thermodynamic model was used to describe the kinetic driving force for crystallization in the population balance model, which was then integrated into a continuum Poiseuille flow reactor model. Model tuning resulted in an acceptable level of output uncertainty. The key output of the modelling work was the development of a framework for nucleation, growth and aggregation investigation occurring in Poiseuille flow. In the experimental phase of this work, a lab-scale Poiseuille flow reactor was developed and used to investigate the impacts of feed mixing and supersaturation level on phosphorus recovery and particle size distribution. Sonication was successfully used to disrupt weakly bound aggregates providing insight into the aggregation process. Disrupted particles were relatively independent of operational conditions, showing that they continue to grow during the aggregation process. Vortex mixing was shown to have a significant influence on PSD and phosphorus recovery. A major output of the experimental work was the development of techniques for investigating aggregation, with potential for further application. The final major component of this work was to combine experimental results and the reactor model to regress kinetic parameters for nucleation growth and aggregation. The parameter estimation process was preceded by model sensitivity analysis. This allowed identification of (1) the most sensitive kinetic parameters, (2) how parameters affect outputs, (3) which parameters are correlated, and (4) how input variable uncertainty affected output variable uncertainty. Point 4 was used to inform uncertainty in the parameter regression process. Finally, parameter optimisation was conducted using a global, normalised, weighted objective function. Sonicated data provided nucleation and growth parameters which were then fixed to separately analyse non-sonicated data, providing aggregation parameters. The regressed parameters were close to those found by other population balance work on struvite – a significant result considering the large variation seen in the literature.