Abstract
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•A new model is developed to predict the decline in permeate flux when filtering produced water.•This model accounts for clustering and coalescence of oil droplets at membrane surface.•Two parameters are obtained in the derived flux declining formula.•These parameters are dependent on the membrane system and the operating conditions.•They are obtained by fitting experimental data.
In this work, a new model to predict the decline in permeation flux with time during the filtration of oily water systems using polymeric-type membranes is introduced. This model accounts for the different fates associated with the behavior of oil droplets when they pin over the membrane surface. Two mechanisms have been proposed, in the first, the accumulation of pinned oil droplets that are neither permeated nor detached has been assumed to block pore openings and reduce the pores available for filtration. The decline in the available pore openings has been used to correlate the decline in permeation flux. This has been the focus of our previous work. In this work, we extend this model to account for the more general scenario contributing to the problem of fouling in oily water filtrations. This mechanism is generally attributed to the coalescence and clustering of oil droplets with pinned droplets to make larger size oil chunks or laminates that, likewise, reduce the area of the membrane available for filtration. In this model, the details of the fates of individual oil droplets are irrelevant due to the dynamic process that changes the shape, size and orientation of oil droplets. Instead a coarser framework is constructed in which the oil, the water and the membrane are dealt with as three separate continua rather than the multitude of continua of both the oil and membrane that was required in the previous framework. A mathematical model is developed to predict the permeation flux with time. The model involves two parameters that are essentially lumping several dependence relationships for the particularity of the oil-water-membrane system. These two parameters may be obtained through fitting exercise with experimental data. An experimental setup is constructed to provide fitting with the developed model. Comparisons with the experimental data as well as with the available data in literature, show very good match which builds confidence in the modeling approach.