Development of a reduced order model for bi-component granulation processes via laguerre polynomials

This paper presents a model reduction technique for obtaining low order models of wet granulation processes suited for model based control. The fluid bed granulation process is extensively employed by the pharmaceutical industry, in which a binder material is used to create bonds between powder drug particles and form granules. Performing a population balance study for these systems results in models that are usually too complex for control applications. The literature offers various reduced order models that approximate the size distribution dynamics of the process. However, these models either neglect the binder drops or incorporate simplified granulation rate expressions that are not realistic. This paper, in contrast, captures both the size and composition distribution dynamics of the granules and considers the physical and geometrical factors in determining the process rate. Using well known model reduction techniques such as orthogonal projections and the method of moments, we relate the bivariate particle distribution function to the dynamics of a finite number of probabilistic moments of the population. Finally, the accuracy of the model is demonstrated through comparing its predicted results with a constant number Monte Carlo simulation of the process.