Estimation of batch precipitation kinetics by a simplified differential method

Abstract

This research note describes a method based on a discretized population balance to estimate the rates of growth, agglomeration, and nucleation from experimental batch crystal-size distribution (CSD) data. This so-called inverse problem is posed as a nonlinear optimization, where an objective function based on the difference between the experimental and model-predicted values is minimized with respect to the kinetic parameters. It is shown that in the case when the objective function is formulated in terms of the time derivatives of the measured variables, the original problem can be reduced into three smaller subproblems that can be rapidly solved. The method is illustrated using data from a batch aluminum trihydroxide precipitation experiment. The validity of the estimates is evaluated by comparing the experimental CSD with that obtained from the simulation using the estimated kinetics. Estimates from the method are also compared to the estimates obtained using the differential technique of Bramley et al. (1996).