Modeling Particle-Size Distribution Dynamics during Precipitative Softening

Abstract

A population balance model was developed to simulate simultaneous precipitation and flocculation during precipitative softening. Rate coefficients for nucleation, crystal growth, and flocculation were extracted from experimental particle-size distribution (PSD) data based on changes in the total number and total volume of particles. Three models of flocculation were evaluated: rectilinear, curvilinear, and an empirical size-independent model. Model simulations were compared with experimental PSD data to test which model was most appropriate. The curvilinear precipitative flocculation model was superior when seeded precipitation occurred at moderate mixing intensities ( G=50–100 s−1 ) . However, the curvilinear model overpredicts the formation of very large particles and requires values of the collision efficiency greater than 1.0, suggesting a more complicated dependence of the PSD dynamics on mixing intensity and saturation ratio than presently included in the model. At higher mixing intensities ( G=300...