Incorporating experimental uncertainties into multivariate granulation modelling

Braumann, Andreas; Kraft, Markus

doi:10.1016/j.ces.2009.09.063

Cited by 29 publications

(25 citation statements)

References 32 publications

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“…This method takes also the propagation of uncertainties into account and estimates confidence intervals for the determined parameters. Braumann et al [22,23] have used this method to estimate the parameters in a multivariate population balance model and studied the influence of different objective functions.…”

Section: Introductionmentioning

confidence: 99%

Developing the PAH-PP soot particle model using process informatics and uncertainty propagation

Sander

Patterson

Braumann

et al. 2011

Proceedings of the Combustion Institute

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Section: Introductionmentioning

confidence: 99%

Developing the PAH-PP soot particle model using process informatics and uncertainty propagation

Sander

Patterson

Braumann

et al. 2011

Proceedings of the Combustion Institute

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“…Furthermore, two other objective functions for the parameter estimation are studied. This so-called expected least-squares and expected weighted least-squares objective functions yield estimates for the unknown model parameters are not too different from the (23) estimates using the moment matching objective function. However, the uncertainties in the model predictions are smaller than the one resulting from the moment matching function.…”

Section: Discussionmentioning

confidence: 98%

Statistical Approximation of the Inverse Problem in Multivariate Population Balance Modeling

Braumann

Man

Kraft

2009

Ind. Eng. Chem. Res.

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This paper deals with the estimation of model parameters and their uncertainties encountered in granulation modeling. The outcome of a multivariate, detailed population balance model of a high shear granulation process is locally approximated in the parameter space by first and second order response surfaces, allowing a fast computation of the model response. The response surfaces are used in three different objective functionssmoment matching, expected least-squares, and expected weighted least-squaressin 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. First, second-order response surfaces for the population balance model are constructed and used as approximations of the model in the objective functions for the numerical solution of the inverse problem. Second, 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. IntroductionGranulation is an important and widely used process in many industries. In order to improve the process, e.g. produce a product which is cheaper and/or closer to the required specification, the process needs to be better understood, for instance, through additional experiments and/or modeling of the process. Detailed modeling of the granulation processes, such as by population balances, captures the complex structure of the granules and the various transformations in a granulator such as nucleation, coalescence, and breakage, to name but a few, thereby aiming to bridge between the micro-and macroscales. The rates with which these processes occur are normally not known and have to be estimated using experimental results.This so-called "inverse problem" is encountered in virtually all modeling applications. Ramkrishna and Mahoney 1 emphasize the importance of the inverse problem in population balance modeling. Population balance models are not only used in granulation, 2-7 but also in other fields such as precipitation and crystallization, 8-10 combustion, 11-14 polymerization, 15,16 and modeling of biological systems. 17 In terms of parameter estimation, rates, such as the growth rate in a precipitation 18 or the aggregation rate in a granulation process, 19 are very often the center of interest. This parameter identification can be performed in different ways. For instance, Vikhansky and Kraft 20 developed a stochastic algorithm that can be used to calculate the sensitivities of the parameters of a population balance for coagulation only processes. On the basis of this method, they solve the inverse problem for a liquid-liquid extractor. 21 Following a technique developed by Sheen et al. 22 for par...

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“…However, an alternative way of retrieving the 7 kernels based on experimental data is to solve the inverse problem [51,52]. Braumann and Kraft studied the 8 inverse problem occurring in a multidimensional population balance model describing granulation employing 9 linear response surfaces [39] and second order response surfaces [53]. There are different collision frequency 10 functions for kernels available in the literature based on theoretical, empirical and experimental calculations 11 and observations (Table 6).…”

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confidence: 99%

“…PBEs incorporating the effect of such parameters are now frequently being developed [21,[37][38][39][40][41]. A multi-…”

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confidence: 99%

See 1 more Smart Citation

Model-based analysis of high shear wet granulation from batch to continuous processes in pharmaceutical production – A critical review

Kumar

Gernaey

Beer

et al. 2013

European Journal of Pharmaceutics and Biopharmaceutics

109

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The manufacturing of pharmaceutical dosage forms, which has traditionally been a batch-wise process, is now also transformed into a series of continuous operations. Some operations such as tabletting and milling are already performed in continuous mode, while the adaptation towards a complete continuous production line is still hampered by complex steps such as granulation and drying which are considered to be too inflexible to handle potential product change-overs. Granulation is necessary in order to achieve good flowability properties and better control of drug content uniformity. This paper reviews modelling and supporting measurement tools for the high shear wet granulation (HSWG) process, which is an important granulation technique due to the inherent benefits and the suitability of this unit operation for the desired switch to continuous mode. For gaining improved insight of the complete system, particle-level mechanisms are required to be better understood, and linked with an appropriate meso-or macro-scale model. A brief review has been provided to understand the mechanisms of the granulation process at micro or particle-level such as those involving wetting and nucleation, aggregation, breakage and consolidation. Further, population balance modelling (PBM) and the discrete element method (DEM), which are the current state-of-the-art methods for granulation modelling at micro-to meso-scale, are discussed. The DEM approach has a major role to play in future research as it bridges the gap between micro-and meso-scales. Furthermore, interesting developments in the measurement technologies are discussed with a focus towards inline measurements of the granulation process to obtain experimental data which are required for developing good models. Based on the current state of the developments, the review focuses on the twin screw granulator as a device for * Email address: ingmar.nopens@ugent.be, Tel.: +32 (0)9 264 61 96; fax: +32 (0) continuous HSWG and attempts to critically evaluate the current process. As a result, a set of open research questions are identified. These questions need to be answered in the future in order to fill the knowledge gap that currently exists both at micro-and macro-scale, and which is currently limiting the further development of the process to its full potential in pharmaceutical applications.

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Incorporating experimental uncertainties into multivariate granulation modelling

Cited by 29 publications

References 32 publications

Developing the PAH-PP soot particle model using process informatics and uncertainty propagation

Developing the PAH-PP soot particle model using process informatics and uncertainty propagation

Statistical Approximation of the Inverse Problem in Multivariate Population Balance Modeling

Model-based analysis of high shear wet granulation from batch to continuous processes in pharmaceutical production – A critical review

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