Population balance model for mixing in continuous flow systems

A population balance model is developed for describing macromixing–micromixing hierarchy of continuous flow systems based on the concept of interactive populations of fluid elements. Macromixing is represented as motion of fluid elements in the physical space described by convection–dispersion models while micromixing is described as motion in the composition space induced by randomised mass exchange interactions of fluid elements. A generalised coalescence/redispersion model is formulated, characterised by the intensity of coalescence/re-dispersion interactions and a set of random variables describing the transfer rates of species between the fluid elements. The model allows defining different micromixing rates for different species.The axial dispersion-coalescence/redispersion (ADCR) model, formulated as a special case of the general population balance model describes macromixing–micromixing hierarchy for multicomponent processes in chemical reactors. An infinite system of moment equations is derived for the joint moments of concentrations of species which is closed by applying a cumulant-neglect closure for higher order chemical reactions. Verification of the ADCR model carried out by comparing the computational results of the second-order moment equation reduction with Vassilatos’ experimental data in the case of a tubular reactor with bimolecular quasilinear chemical reaction shows good correspondence. The properties of macromixing–micromixing interactions are examined by numerical experiments using the second-order moment equation reduction. Predictions of the model in maximally micromixed states provide excellent qualitative and quantitative agreement with the results of the continuum balance equation model, and appears to be a good tool for direct modelling of macromixing–micromixing hierarchy in chemical reactors.