(658f) A Population Balance Model for Calculation of Total Evaporation Rate during Fluid Bed Granulation or Coating

It is known that the granule moisture is a critical property of particles during fluid bed granulation (FBG) or fluid bed coating (FBC) processes. It is an important attribute for the quality of coating and has a strong impact on the granule growth. The granule moisture is usually measured by taking samples and gravimetrically evaluating the moisture (e.g. in terms of LOD = Loss on Drying). Relatively newer NIR method can measure the same quantity continuously [1].

Mathematical models of different complexity have been developed and used for simulation of FBG processes. The models use different expressions for calculation of the evaporation rate of water present in the sprayed binder [1 -3]. The models assume presence of a continuous film on the granule surface and the evaporation rate is then calculated by standard expressions for the mass and heat transfer coefficients. Most procedures employ either the Antoine equation or the experimentally measured sorption equilibria for calculation of the equilibrium moisture content at the particle surface [3]. Based on our experience with employing the above methods for different FBG and FBC systems it is challenging to find a meaningful correlation between the parameters of the evaporation rate expressions and process conditions [1, 2].

A total mass and heat balances (TMHB) model employing the above expressions was developed and presented before [1, 2]. In this contribution a different approach for calculation of total evaporation rate is proposed and tested. The approach assumes that the total evaporation rate is a summation of evaporation rates of individual droplets of different sizes deposited on the particle surface. This assumption is justified by the fact that many FBG and particularly FBC processes are run at dry conditions and the particle LOD is typically between 1% -6%. So, it is unlikely to have a continuous wet layer of the binder solution on the particle surface. A new population balance (NPB) model (based on volume approach) calculating the total evaporation rate as summation of evaporation rates of shrinking and drying droplets was developed by using Direct Quadrature Method of Moments (DQMOM). The method is simple and fast (by adding only 4-6 ordinary differential equations for the PSD moments tracking) and calculates the total evaporation rate as a change of the first moment (volume) of the PSD of all droplets delivered into the system. During the presentation we will share simulation results and comparison of models of different complexity (1D or 2D) and also comparison with experimental results. The TMHB model and the DQMOM model (NPB) are then combined with another population balance (PB) model calculating the granule growth [3]. The PB model employs the granule moisture calculated by the TMHB+ NPB combination for calculation of the agglomeration kernel. In summary, the combined model predicts granule moisture, temperature and PSD from the process conditions [3].

References:

[1] Rajniak, P. et al.: Development of a mechanistic model for fluid bed granulation. AIChE Annual Meeting, 2015, Salt Lake City.

 [1] Ricart, B. and P. Rajniak: Experimental and theoretical study of simultaneous agglomeration and drying in fluidized bed granulator. AIChE Annual Meeting, 2013, San Francisco.

[3] Peglow, M. et al.: A generic population balance model for simultaneous agglomeration and drying in fluidized bed. Chem. Eng. Sci. 62 (2007) 513 â?? 532.