Nucleation and crystal growth kinetic parameter optimization of a continuous Poiseuille flow struvite crystallizer using a discretized population balance and dynamic fluid model

Struvite crystallization is an important process in recovering phosphorus from waste streams, but kinetic parameters involve significant uncertainty. In this research a model is developed which includes population balance, fluid flow equations, and kinetic relations. Power law rate coefficients for struvite nucleation (k(nuc) = 7.509 x 10(7) L-1.min(-1)) and growth (k(g) = 16.72 mu m.min(-1)) are optimised by combining a Poiseuille flow reactor model (PFR) and experimental data for phosphorus concentration and particle size distribution (PSD) at the reactor outlet. Nucleation and crystal growth rates were optimized using both filtered and sonicated PSD samples. The model incorporated three key aspects: non-ideal thermodynamics; Poiseuille fluid flow (including advection, diffusion and reaction); and a discretized population balance model (PBM). Sensitivity analysis using deltas (min/max) showed diffusion effects to be negligible and indicated that power law rate constants for both nucleation and growth were more influential on PSD and phosphorus concentration than the associated rate orders. Optimized parameters agreed reasonably well with a previous study conducted by our group under different conditions, using a different model, providing confidence in results. The optimized nucleation rate, k(nuc), was only 12% lower than that found using a similar model for a seeded system, where secondary nucleation is dominant. Additionally, a primary nucleation model provided a poor fit to experimental data. These two factors indicate that secondary nucleation is an influential mechanism. A 2nd order growth model provided a better fit to data than a previously suggested 5th order growth model. The optimized growth rate coefficient, k(g), was higher than in any previous studies, an effect attributed to sonication, which eliminated aggregates.