A G-H scheme for back-calculation of breakage rate functions from batch grinding data

Abstract

Current methods for the estimation of breakage rate functions employ non-linear optimization techniques to back-calculate from the grinding data the parameters in an assumed functional representation of these grinding rate parameters. We present an alternate G-H scheme which can be executed by the simpler and faster linear least-squares techniques to provide satisfactory estimates of the individual grinding rate parameters without the imposition of any functional form. The proposed scheme is based on an approximate G-H solution to the discrete size grinding equation in which the lumped parameters G and H appear linearly and hence these can be readily computed. Moreover, the G-H solution is accurate enough to permit equating its time-derivative with that of the original grinding kinetics equation. The result is a set of linear algebraic equations from which breakage rate functions can be computed either sequentially, interval-by-interval, or simultaneously by the linear regression techniques. The G-H scheme has been tested extensively on both error-free computer-generated grinding data as well as experimental data. In the former case, the back-calculated breakage rate functions are in close agreement with the actual values, even when these values vary erratically with size. In the latter case, the simulated and predicted size distributions match the experimental distributions very closely.