Population Balance Model for Batch Gravity Separation of Crude Oil and Water Emulsions. Part I: Model Formulation

A population balance model for the separation of emulsions in a batch gravity settler is presented. Within the context of the model development, possible methodologies were elucidated for incorporating a) the physical properties of the bulk liquids, b) the physical properties of the phase interface, and c) the presence and functioning of interfacially active compounds. The model presented explicitly accounts for interfacial coalescence and the deformation of the emulsion zone due to the dynamic growth of the resolved dispersed phase; interfacial coalescence is modeled in terms of physically meaningful film drainage models and an approach for incorporating the accumulated buoyancy force in the dense packed layer is also discussed. Hydrodynamically hindered sedimentation is also considered in the model. The model is well suited to predict experimental batch settling data, especially data obtained from low-frequency NMR measurements of emulsion destabilization. The model predicts the evolution of the volume fraction of the dispersed phase at any axial position and time in the separator. Furthermore, the model predicts the location of the resolved dispersed phase interface as a function of time. Additionally, for any axial position and time in the settler, the model predicts the evolution of the average number density of droplets, the average volume/radius of droplets, the standard deviation of the droplet volume/radius, and the rate of growth of the droplets. The model is compared directly with experimental data for crude oil separations in Part II of this article.