Modeling of Demulsification Process of Crude Oil Emulsions from Wastewater of Desalination Plant

The crude oil contains various contaminants including water, gas and sediments which should be removed in desalination unit. In addition, the wastewater from desalination unit should be refined to remove the oil droplets. In this work, a mathematical model was presented for demulsification process of crude oil emulsions from wastewater of desalination plant. A nonlinear hyperbolic integral differential equation was obtained by population balance method. The population balance integral equation terms were simplified using fixed pivot method and a system of partial differential equation (PDE) were obtained. The partial equations were converted into systems of ordinary differential equations (ODE) using the method of line. The ODEs were solved by the application of MATLAB Software. The profile of volumetric distribution of oil droplets, mean droplet diameter (D4,3), and oil separation rate along the height of the system at different times were reported. The accuracy of the model was examined by comparing with experimental data of water dispersion in oil system obtained from literature. Then, the model was applied to predict the oil in water systems and the effects of viscosity and density crude oil on separation of dispersed phase and mean droplet diameter (D4,3) were investigated. Finally, adjustable coefficients in the equations were estimated. The results showed that, by reducing the density of crude oil the settling velocity increases. Furthermore, the decreasing in crude oil viscosity will lead to increase the frequency collision droplets and oil separation.