Parameter estimation in a multidimensional granulation model Andreas Braumann a , Markus Kraft a, ⁎, Paul R. Mort b a Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge, CB2 3RA, UK b Procter and Gamble Co., ITC, 5299 Spring Grove Avenue, Cincinnati, OH 45217, USA abstract article info Article history: Received 12 May 2008 Received in revised form 15 April 2009 Accepted 11 September 2009 Available online 21 September 2009 Keywords: Granulation Agglomeration Modelling Multidimensional population balance Response surface methodology A new multidimensional model for wet granulation is presented, which includes particle coalescence, compaction, reaction, penetration, and breakage. In the model, particles are assumed to be spherical and consist of two kinds of solid, two kinds of liquid, and pore volume. The model is tested against experimental results (Simmons, Turton and Mort. Proceedings of Fifth World Congress on Particle Technology, paper 9d, 2006) from the granulation of sugar particles with different PEG based binders in a bench scale mixer, being carried out for different impeller speeds, binder compositions and process durations. The unknown rate constants for coalescence, compaction, reaction, and breakage were fitted to the experiments and the sensitivities of the mass of agglomerates were calculated with respect to these parameters. This is done by employing experimental design and a response surface technique. The simulations with the established set of parameters show that the model predicts the trends, not only in time, but also for crucial process conditions such as impeller speed and the binder composition. As such it is found that more viscous binder promotes the formation of porous particle ensembles. Furthermore, the statistics of the different events such as collisions, coalescence and breakage reveal for instance that successful coalescence events outnumber the breakage events by a factor of up to three for low impeller speeds. © 2009 Elsevier B.V. All rights reserved. 1. Introduction The processes of granulation and agglomeration have been performed on industrial scales for decades, and yet the understanding of both processes remains incomplete. The manufacturing of granules is of considerable significance in many industries e.g., in the production of fertilizers, washing powders, and pharmaceuticals. The creation of granules as particulate material which has to fulfil specific quality requirements can be achieved either via dry or wet granulation (e.g., in fluidized beds, rotating drums or high shear mixers [1]). In the last case the solid–liquid-ratio plays a crucial role as the liquid acts as mediator between the solid particles and promotes the growth of the granules. So called regime maps have been established in various studies [2–4]. Although these maps are able to accurately describe what can be observed in a granulator (crumbling, steady growth, etc.) under different conditions, they fail to adequately answer many questions about the underlying mechanisms. If a granule is observed on the microlevel, several subprocesses can be distinguished, with coalescence and breakage being considered as the most important ones which govern the granulation process [5]. Since liquid is part of the system as well, it is important how the liquid (binder) is added, whether it is sprayed into the vessel [6] or put in as a paste (melt binder) [7]. The growth process of the granules is then influenced by the spreading, i.e., the distribution of the binder. Spreading is, among other factors, governed by the droplet size, spray rate, powder bed movements and penetration of the liquid [8,9]. Coalescence of the particles results in the growth of the granules. The process is also called layering in the case where small particles coalesce with (much) larger particles. This will be the dominating growth process when the droplet sizes are rather small compared to the particle size. The interaction of all of these processes will determine the behaviour of the system and the outcome of the granulation process. The linking of the different subprocesses is sketched in Fig. 1. Through the addition of binder the particles are wetted. After picking up some binder the particles start to coalesce/ grow. Due to impacts experienced in the equipment (e.g., from the impeller) the particles will then undergo consolidation (also known as compaction). Depending on the material properties and the process conditions, breakage of the granules will occur, causing them to disintegrate. However, the breakage of the wet particles also leads to the dispersion of the binder, so that the liquid component is spread throughout the particle ensemble enabling further coalescence events. Although coalescence and breakage are antagonistic process- es, both are necessary to drive the granulation process. The key question is then: which ratio of coalescence to breakage events is most beneficial to the overall process? All of the influences mentioned above have an impact on the performance of the granulation processes, and it would therefore be beneficial to have a more complete understanding of the process in ⁎ Corresponding author. Tel.: +44 1223 762784; fax: +44 1223 334796. E-mail address: mk306@cam.ac.uk (M. Kraft). 0032-5910/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2009.09.014 This is the Computational Modelling Group's latest internal version. Please download the official version from http://dx.doi.org/10.1016/j.powtec.2009.09.014