Mathematical modelling of granola breakage during pipe pneumatic conveying

Granola is a baked aggregated food product which serves as a breakfast cereal or snack consisting of oats, cereals, nuts and honey. Particle breakage of aggregated granola can occur during conveying as product is transferred as part of the production process on its way to packaging. Such breakage occurs as a result of particle–particle and particle–wall collisions with the conveying equipment. In this work, a population balance model is developed to describe the breakage of granola as it is conveyed through a pneumatic conveying pipeline rig. The model incorporates the influence of conveying pressure, exposure time and pipeline geometry, and is also related to parameters associated with aggregate formation such as granulator mixing speed and time. The aggregates were formed in a high shear granulator subject to impeller agitation of 300 rpm for 9 min and were then propelled through a pipeline with a 90° bend at a number of different flow rates. Trials were carried out by applying compressed air at pressures of 200 kPa, 300 kPa and 400 kPa while the aggregates were subjected to a number of recycles through the rig. Modelling of this breakage process was achieved by constructing the population balance equations (PBEs) in the form of a mass balance on the granola aggregates. The solutions to the PBEs were obtained by means of discretization through the application of the Markov chain method. When the size range of the system was divided into an appropriate number of states, the Markov chain method for the population balances exhibited a reasonable approximation for predicting the particle size distribution (PSD) over time particularly during the initial rig cycles.