Research Article Numerical Study of the Collision and Coalescence of Water Droplets in an Electric Field The coalescence of binary water droplets in oil exposed to an external electric field is simulated using a model including both electrostatic and hydrodynamic sections. Available mathematical models for electric dipole-dipole force are pre- sented in the first part of the model. Volume of Fluid approach is applied in the second part of the model. The simulation results were in good agreement with the published experimental observations. The results indicated that an improve- ment in electrocoalescence speed could be achieved. It was also revealed that the skew angle of the electric field, the oil viscosity, and the initial drops distance influence the electrocoalescence. Moreover, a correlation was developed to predict electrocoalescence kinetic as a function of the participant parameters. Keywords: Binary droplets, Coalescence, Electrostatics, Hydrodynamics, Parametric study Received: September 06, 2012; revised: September 15, 2013; accepted: October 15, 2013 DOI: 10.1002/ceat.201200479 1 Introduction Separation of the emulsified water from crude oil is one of the most important steps in surface facilities [1]. It is generally conducted in several stages, consisting of flocculation, coales- cence, and settling in large vessels [2]. The sedimentation rate of the water droplets is controlled by the terminal velocity of the smallest drops. Therefore, the only way to speed up the separation process is to force small water droplets to coalesce into larger ones by applying electric field [3]. Coalescence of two droplets in a continuous fluid flow occurs in three steps [4]. When two droplets approach each other, high pressure is built up in the gap between them, while this pressure build-up causes the droplets to flatten. When the droplets are trying to drain the oil film, they lose the kinetic energy [5]. The separation process applied on water in oil (w/o) emulsions, where the electric field is used to assist mer- ging small water droplets into larger ones, is usually called electrocoalescence. The effects of the electrostatic field can be explained by body forces acting on water drops [6]. Brazier-Smith et al. [7] studied the influence of an electric field on two conductive droplets without considering viscous effects. Baygents et al. [8] completed the study of Brazier- Smith et al. [7] by considering viscous effects. Williams and Bailey [9] and Williams [10] have investigated coalescence rate of conducting drops in an external electric field both theoreti- cally and experimentally. Meon and Blass [11] have studied the coalescence of the drops on trickling films flowing off inclined plates. Later, the effects of hydrodynamic on two drop collision and coalescence under the effect of an electric field have been investigated for different drop motions [12, 13]. Jung and Sato [14] have used two different numerical methods of front- capturing and front-tracking to specify the interface of a single droplet. Mashayek et al. [15] used the spine-flux method (SFM) for the collision dynamic of two drops. Bjørklund [16] has used the level-set method in combination with the ghost- fluid method. Atten [17] has offered an analysis of the coales- cence process induced by the dipolar interaction between the droplets. Zhang et al. [18] have presented a theoretical model to predict the rate of binary drop collision. Simon and Bart [19] investigated the coalescence of drops caused by the random movement, experimentally. Gneist and Bart [20, 21] have studied electrostatic drop formation in liq- uid/liquid systems, using high frequency AC fields. Chiesa et al. [22–24] have presented a model essentially based on a Lagrangian framework for the drops. However, their model was dependent on tuning parameter of slip length and some closure sub-models to consider the fluid state of drop. Later, Melheim and Chiesa [25] have modified a new model, the cluster integration method, whose validity is more doubtful. Bresciani et al. [26] have studied droplet–droplet coalescence under the influence of an electric field through analytical solution. Chem. Eng. Technol. 2014, 37, No. 1, 27–35 © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.cet-journal.com Mehdi Mohammadi 1 Shahrokh Shahhosseini 1 Mahmoud Bayat 2 1 Process Simulation and Control Research Laboratory, Chemical Engineering College, Iran University of Science and Technology (IUST), Tehran, Iran. 2 Petroleum Refining and Processing Technology Development Division, Research Institute of Petroleum Industry (RIPI), Tehran, Iran. – Correspondence: Dr. Shahrokh Shahhosseini (shahrokh@iust.ac.ir), Process Simulation and Control Research Laboratory, Chemical Engineering College, Iran University of Science and Technology (IUST), Narmak 16765-163, Tehran, Iran. Coalescence 27