Dynamic Analysis Of Grinding Using The Population Balance Model

The dynamic behavior of batch mill, CSTR mill, and a closed grinding network consisting of a mill, sump, and cyclone was analyzed using the dynamic population balance model (PBM). The dynamic solution of the PBM of a batch, CSTR and a closed grinding network consisting of a mill, sump, and cyclone forms the basis of the dynamic analysis presented here. Two numerical dynamic solution approaches were used. These are: 1) providing additional constraints on breakage selection functions or 2) performing the Arbiter-Bhrany (or other) normalization of the selection functions. Actual experimental anthracite batch grinding data was used to obtain the functionality of the batch dynamic mill selection and breakage functions for a real physical system. The Levenberg-Marquardt algorithm for systems of constrained non-linear equations is used to solve the batch dynamic PBM grinding equations to obtain the grinding selection and breakage rate functions. The mill, sump and hydrocyclone were modeled as a CSTR operating at various retention times. Batch dynamic PBM data was used to provide the mill kinetic and breakage selection function data. Different dynamic solutions were obtained depending on the numerical approach used. Each solution approach to a dynamic PBM with transport, while giving the same prediction for a single batch grinding time, gives different solutions or predictions for mill composition for other grinding times. This fact makes dynamic nodal analysis and control problematic. The fact that the constraint solution approach gives a solution may suggest that normalization for closed networks is not necessary. Differences in solutions to the PBM cannot be excused away by inaccuracies in the data used to model the grinding phenomenon.