Model reduction for prediction of silver halide precipitation

Abstract

A fully mechanistic model was developed to simulate the turbulent mixing and precipitation of silver bromide in a semi-batch reactor. Instantaneous primary nucleation, multiple species thermodynamic equilibria, size-dependent growth kinetics, crystal population balances and accurate modeling of turbulent flow in a stirred tank are fully coupled in a multi-scale, Eulerian–Lagrangian approach. Several significant advances are achieved in the course of the model development. First, a novel symmetric geometric length scale is developed to allow resolution of the scales of nucleation, growth, and dissolution in a single model. This significantly improves the model's ability to predict the crystal size distribution, and eliminates a severe numerical instability in the population balance equations. Second, the multi-species equilibria are accurately represented by a linear equation over most of the range of interest. Third, nucleation occurs primarily in the feed plume, while growth occurs primarily in the bulk, although the two processes remain coupled through the mixing model and the population balances. Seeded and unseeded precipitation experiments were conducted to allow model validation. A comparison of the model predictions with the experimental crystal size distributions shows excellent agreement. The model is also able to isolate a weakness in the growth model in the Gibbs–Thompson controlled range, between the lower limit of the experimentally available data and the size of the nuclei. The validated model provides several insights into the precipitation process, and is suitable for further examining mixing effects on the precipitation process.