A new mathematical model of continuous gravitational separation with coalescence of liquid-liquid emulsions

Abstract

A model for a continuous gravitational separation process of a liquid-liquid dispersion is presented, which is formulated as a population balance equation (PBE) that describes the coalescence and the hindered polydisperse sedimentation of droplets. This is important because this separation process is critical in the operation of many industries as discussed later. This study is based on previous findings by Garcia and Betancourt (2019) where a formulation for a batch process was presented. This analysis shows the improvements and differences between the model presented in this study and the formulation by Garcia and Betancourt (2019). The modeling framework comes from the Kynch’s theory that has been employed to model solid particle sedimentation processes; however, in this case the principles are applied to an organic phase-aqueous phase liquid mixture. For the numerical solution of the model, the PBE is discretized in terms of droplet volume. Since the population balance model is subject to mass loss due to droplet coalescence, we propose a formula to compute the source term of the largest droplet class. Model validation used experimental data from literature for a continuous process. Numerical results explored the variation of parameters such as feed flowrate, feed oil volume fraction and the standard deviation of the initial and feed droplet volumes.