Milling is one of the more common, deceptively simple but inherently complex unit operations in use in the process industry in general and the pharmaceutical industry in particular. The particle size distribution produced in milling is the result of a convoluted interplay between the material properties, the configuration of the milling equipment and mill specific operating parameters, which jointly give rise to specific breakage mechanisms. Consequently, the prediction of breakage behavior becomes difficult. Population balance modeling offers a suitable approach to address some of these problem features. It has been shown that certain forms of linear as well as nonlinear breakage behavior exhibit interesting scaling behavior, which is amenable to model extraction through inverse problem approach proposed by Sathyagal et al (1995). It is this methodology that has been implemented along with the nonlinear milling analysis of Bilgili and Scarlett (2005) and Nere et al. (2008) for model identification and subsequently, its verification.

We present the experimentally characterized dynamic evolution of the particle size distributions for two lab scale quadro comills, namely Quadro U5 and Quadro 197. Three types of roller compacted granules of Acetaminophen, Ibuprofen and Tolmetin with MCC and SiO2 as excipients were used for the milling experiments. Both the mills were operated in batch mode, a requisite to generating the data for inverse problem. The operating parameters such as the impeller speed and the batch sizes were chosen to gather dynamic data. The data thus generated is subjected to the inverse problem approach to extract the models for both the breakage rates and daughter size distributions. These models are validated by comparing the forward simulation of the population balance equation with experimental measurements.

Furthermore, an attempt will be reported to unify the extracted milling models to account for the effects of various operating parameters using an artificial neural network approach. The overall aim of the present work is to develop a general framework integrating population balances with artificial neural networks with the aim of providing a flexible and practical approach for the development of hybrid models for milling model.

Reference

1. Sathyagal, A. N., Ramkrishna, D., and Narsimhan, G. Solutions of Inverse Problems in Population Balances II. Particle Break-Up. Comput. Chem. Eng. 19, (1995), 437.

2. Bilgili, E. and Scarlett, B. Population balance modeling of non-linear effects in milling processes, Powder Technology 153, (2005), 59– 71.

3. Nere, N. K. McCann, R., Morris, K. and D. Ramkrishna. On the Modeling of Milling in Pharmaceutical Industry. AIChE Annual meeting, Philadelphia, PA , November 2008.