Quantification of oil droplet shearing in produced water treatment facilities is a crucial aspect of operations for the oil and gas industry. In this paper, a detail mathematical modeling of droplet breakage and coalescence using a Population Balance Method (PBM) is addressed. The PBM models the dynamics of droplet size distribution due continuous interactions between individual droplets (such as coalescence and breakup). An understanding of the PBM in regards to the conservation of mass of dispersed droplets is also developed. A stand-alone PBM is used for calculating coalescence and breakage rates in a system having homogeneous mixture and constant turbulent energy dissipation. A coupled computational fluid dynamics-PBM approach is also implemented in a hydrocyclone to examine the local rates of droplet breakup and coalescence. Effects of the turbulent intensity and the interfacial tension of an oil-water mixture and the volume fraction of the dispersed phase on the time evolution of volume fraction distribution and Sauter mean diameter are examined. Results show that, for typical fluid properties associated with produced water, droplet-droplet coalescence is dominant over droplet breakage when the turbulent energy dissipation (ε) is small; the opposite is found for regions associated with high energy dissipation. In a hydrocyclone, the rate of droplets shearing is significant near the entry and at the inlet chamber; this rate decreases downstream. The research outcomes based on the stand-alone PBM and coupled CFD-PBM approaches allow us to identify and redesign the critical part of the water treating facilities to minimize shearing of dispersed droplets.

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