Population balance modelling of drum granulation of materials with wide size distribution

Abstract

A population balance model is developed to describe the drum granulation of feeds with a broad size distribution (e.g. recycled fertiliser granules). Granule growth by coalescence is modelled with a sequential two-stage kernel. The first stage of granulation falls within a non-inertial regime as defined by Ennis et al. ( Powder Technol., 65 (1991) 257–272), with growth occurring by random coalescence. The size distribution is observed to narrow and quickly reach an equilibrium size distribution. Further growth then occurs within a second inertial stage of granulation in which the granule size distribution broadens and requires a size-dependent kernel. This stage is much slower and granule deformation is important. Non-linear regression is used to fit the model to the experimental data of Adetayo et al. ( Chem Eng. Sci., 48 (1993) 3951–3961) for granulation of ammonium sulfate, mono-ammonium phosphate and di-ammonium phosphate for a range of moisture contents, granulation times and initial size distributions. The model accurately describes the shape of the granule size distributions over the full range of data. The extent of granulation occurring within the first stage is given by k 1 t 1; the extent of growth k 1 t 1 is proportional to the fractional liquid saturation of the granule, S sat, and increases with binder viscosity. Here, k 1 represents the rate constant for the first stage of growth and t 1 represents the time required to reach the final equilibrium size distribution for the first stage. Changes to the initial size distribution affect k 1 t 1 by changing granule porosity and, therefore, liquid saturation. A critical saturation, S crit, is necessary for the second stage of granulation to occur, leading to further growth. For S sat≤ S crit, a final equilibrium size distribution is reached before 5 min of granulation time. For S sat> S crit, granules are sufficiently deformable to continue growing for up to 25 min. S crit decreases with increasing binder viscosity. This model is suitable for use in dynamic simulation of granulation circuits where both moisture content and recycle size distribution may vary significantly with time.