Inclusion of shear rate effects in the kinetics of a discretized population balance model: Application to struvite precipitation.

The effect of mixing in the modelling of processes based on mass transfer phenomena is commonly ignored in wastewater treatment industry. In this contribution, the effect of the average shear rate in the nucleation and growth rates of struvite is analyzed by combining experimental data with simulation results obtained with a previously presented mass-based discretized population balance model. According to the obtained results, the effect of the average shear rate is identifiable for the selected data and mechanisms. Therefore, it should be considered when a detailed modelling of the process is needed. Consequently, in this contribution, the average shear rate has been decoupled from the kinetic constants. In addition, kinetic rates where it is explicitly included as a power law function have been proposed. The exponents in these power law functions for the primary homogeneous nucleation and growth are 1.3 and 0.3, respectively. Considering shear rate effects allowed to see in the simulation outputs experimentally observed effects: a faster pH decay and smaller particle distribution for increasing mixing intensities.

A New Mass-Based Discretized Population Balance Model for Precipitation Processes: Application to Struvite Precipitation.

Mathematical models describing precipitation processes in one step need to be upgraded. Particle size distribution is a crucial variable and its inclusion in the modelling libraries is necessary if the technology wants to be optimized through simulation. With this objective, a mass based population balance model is presented in this contribution. The model has been constructed using a stoichiometric matrix and a kinetic vector and using mass as the internal coordinate, as it is usually done in wastewater treatment modelling. Identifiability of the parameters of the model was evaluated using a sensitivity and a collinearity analysis for six simulation case studies of struvite precipitation. In addition, parameters in the model were calibrated to represent data from two batch tests in the laboratory. The results of the analysis showed that the identifiability of the parameters depends on the available experimental data and explored scenarios. Identifiability of the parameters could be the reason behind the shifting parameter values describing mechanisms of precipitation in the literature. This contribution helps to understand the possibilities and limitations that the population balance model approach offer.