Modelling the formation, growth and coagulation of soot in a combustion system using a 2-D population balance model

A 2-D population balance model utilizing carbon mass and surface sites as internal variables was developed for soot formation during hydrocarbon decomposition reactions. The model provides particle properties such as composition and mean polyaromatic hydrocarbon size, enabling the incorporation of cyclization reactions, soot maturation, and a dynamic model of surface reactions. Accompanied by a reduced kinetic model for gas-phase species, this population balance model was then discretized using the fixed-pivot method, to provide predictions of the soot distribution as a function of position within a plug flow reactor. The model predictions of the particle size distribution functions resulting from high-temperature hydrocarbon pyrolysis within a PFTR system provide good comparison with experimental measurements under a variety of conditions. In addition to this, by tracking the changes in particle composition occurring through cyclization reactions, the point of carbon particle maturity could be determined, allowing subsequent predictions of the size distributions of the primary particles comprising soot aggregates. Through comparison with TEM and SEM imaging, these primary particle distributions were found to be accurate for the experimental conditions examined. While the implementation of the second internal variable describing particle composition was not found to provide substantial improvements to the prediction of the overall aggregate distribution from existing models, the additional computational cost that accompanies additional variables is justified in applications where morphological predictions of particle aggregates are of interest, in addition to their size distribution.