Thermodynamic modeling of water-in-oil emulsions: Implementation for two sizes of droplets

A thermodynamic model is proposed for predicting the phase behavior of water in crude oil emulsions while exposed to an external electric field. The model is based on the first order Barker-Henderson perturbation theory using appropriate expressions for interaction potential among water droplets. It is assumed that the emulsion contains two sizes of droplets in contrast to previous work which can handle same size droplets only. The deformation of the droplets during collision is also investigated, which according to results, may be neglected when at least one size of droplets is larger than 1 μm. However when all droplets are small, the deformation makes the emulsion more stable. This phenomenon affects the phase diagram in the whole range of volume fraction and should not be ignored. In order to make the model more realistic, the presence of inorganic salts in water droplets is also considered and the effect on phase diagram is quantified. Existence of electrolytes lowers polarizability of water droplets and decreases the effect of external electric field on saturation curve of the emulsion. Therefore, it leads to a higher value of electric field required to break the emulsion phase. The extra strength of the field required for water droplets containing 5 M NaCl is about 8%.