Water/oil separation modeling by population balance equations - solution of the probability density function

We discuss a model derived from the Williams population balance equations, written in mixture\ud form, to represent water-in-oil emulsions undergoing separation by gravity. The model includes\ud the treatment of the disperse phase, represented by a discrete distribution function at each material point,\ud leading to the solution of the Population Balance Equations. This approach allows for a better representation\ud of the physics of emulsions, providing a general framework to include phenomena such as inter-drop\ud coalescence, coalescence with the homophase and the presence of dense-packed layers. The goal is to\ud devise a solver for the complete system of equations (including momentum and mass conservation), so\ud as to push forward the state of the art in the area, which nowadays relies mainly on one-dimensional\ud kinematic separation models. Such an advanced solver is necessary to model the complete flow within\ud separators of arbitrary geometries. This work includes a first description and discussion of the polydisperse\ud model and the selection of a fast and accurate method for the solution of the system of one\ud dimensional hyperbolic equations resulting from the treatment of the disperse phase.Centro de Matemática e Estatística Aplicadas à Indústria (CEPID-CeMEAI)FAPESP (concessão No. 2012/14481-8)CONICETUniversidad Nacional del Litora