# Technical Report 78, c4e-Preprint Series, Cambridge

## Statistical approximation of the inverse problem in multivariate population balance modelling

ref: Technical Report 78, c4e-Preprint Series, Cambridge

Associated Theme: Particle Processes

This paper deals with the estimation of model parameters and their uncertainties encountered in granulation modelling. A multivariate, detailed population balance model of a high shear granulation process is locally approximated by first and second order response surfaces, allowing a fast computation of the model response. The response surfaces are used in three different objective functionsâ€”moment matching, expected least squares and expected weighted least squaresâ€”in order to estimate ranges for the rate constants for particle coalescence, particle compaction, particle breakage, and reaction, which appear as free parameters in the granulation model. Firstly, second order response surfaces for the population balance model are constructed and used as approximation of the model in the objective functions for the numerical solution of the inverse problem. Secondly, the choice of objective function is investigated. It is found that the uncertainties of the model predictions differ for the three objective functions only slightly. The estimates for the intervals of the model parameters either overlap or are very close. However, the moment matching objective function is recommended because the number of estimated parameters and experimental data sets can be chosen independently.

Material from this preprint has been published in: Industrial and Engineering Chemistry Research 49, 428-438, (2010)

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