Filtration of emulsions is an important operation in multiple processes of chemical, environmental, and petroleum engineering. The primary concern of the present study is cleaning of water produced from a petroleum reservoir. The produced water is filtered from the oil droplets before being dumped into the sea or reinjected into the reservoir. Efficiency of filtration is determined, in particular, by the droplet size distribution and interfacial properties. We have developed a new population balance model of emulsion filtration, based on the Boltzmann–Smoluchowski approach. The model accounts for the droplet size distribution, as well as for the different mechanisms of the droplet capture: attachment to the surface and straining in the pore constrictions. The model can not only be applied to filtering of the produced water, but also to more general emulsion processing. It is capable of reproducing experimental data on the droplet production history and dynamic permeability decline. The sensitivity study indicates low sensitivity of the permeability decline curves to the model parameters. The production histories or other kinds of experimental data are necessary to discriminate between the different parametrizations of the model.
Papine-Paktoris et al. (Sun,) studied this question.