Modeling and simulation of mixing in water-in-oil emulsion flow through a valve-like element using a population balance model

• Multivariate population balance modeling was implemented in OpenFOAM.
• The population balance model was solved using the DQMoM-FC.
• Coalescence and breakage models were extended to inhomogeneous problems.
• Results for mean diameters are in agreement with the available experimental data.
• Simulation of a bivariate problem showed the importance of droplet dispersion.

Emulsion flows are very common in natural processes as well as in several engineering areas, such as in the process of desalting crude oil that occurs in refineries. This kind of flow is described as a polydispersed multiphase flow. In this work, we evaluated the behavior of water-in-oil emulsion flowing through a duct with an element used to mimic the effect of a globe valve. An Eulerian multi-fluid approach was employed by solving the population balance equation coupled with computational fluid dynamics. Coalescence and breakage models recently developed were extended to this inhomogeneous model. A bivariate population balance problem was also solved to demonstrate the mixing caused by the valve-like element. The simulated results showed good agreement with the available experimental data for the Sauter and DeBroukere mean diameters.