Modeling and measurement of granule attrition during pneumatic conveying in a laboratory scale system

A methodology combining theoretical and experimental techniques for characterizing and predicting the friability of granules in a laboratory scale pneumatic conveying systems is developed. Models of increasing mathematical complexity are used for analysis of experimental data. Firstly, a two-dimensional (2-D) computational fluid dynamics (CFD) model of the gas–solid flow within the Malvern Mastersizer laser diffraction equipment is developed to simulate impact of different inlet jet pressures on the flow properties and to calculate average velocity and average volume fraction of particles in the equipment. Secondly, a simple maximum-gradient population balance (MG-PB) mathematical model of breakage is developed. The model is solved using the Quadrature Method of Moments (QMOM) and used for evaluation of experimental data from the Malvern equipment. Different semi-empirical expressions for the breakage kernels and for the daughter distribution functions are tested. Multiple breakage distribution functions are needed to get satisfactory agreement with experimental data. Finally, a CFD-PB model combining CFD and QMOM methodologies is developed. The combined model employs different binary fragment distribution functions and a kernel with the breakage rate proportional to the characteristic particle size and to the square of the impact velocity between a particle and the equipment wall. Simulation results are compared with attrition experimental data indicating that the model is able to capture the qualitative trends and quantitatively predict the Sauter mean diameter d32 at the outlet. However, the lower moments, in particular m0 and m1 are under predicted by the model. Based also on the MG-PB model results, it is our hypothesis that chipping, or breakage of particles in multiple fragments results in higher m0 and m1 than predicted. Further improvements of the model are proposed to incorporate multiple breakage effects. It is assumed that analogous physically based models combining properties of the gas–solid flow with the PB models can be employed to predict attrition and breakage in large-scale pneumatic conveying systems.

Graphical abstractAttrition (decrease of Sauter mean diameter) of fragile granules flowing in a laser diffraction particle size analyzer is directly measured at different flow conditions (inlet pressure) in the analyzer. A mathematical model combining CFD with population balancing is used for fitting to experimental data. Parameters of a physically based breakage kernel employing the impact velocity between a particle and the equipment wall are evaluated. Analogous models can be used for prediction of attrition in large-scale pneumatic conveying systems.Figure optionsDownload full-size imageDownload as PowerPoint slide