Simplified Formula for the Critical Entry Pressure and a Comprehensive Insight into the Critical Velocity of Dislodgment of a Droplet in Crossflow Filtration

Abstract

Produced water treatment remains a challenging issue for the oil production industry. Finding ways to effectively treat oily water systems without incurring higher operational costs is the struggle and focus of recent research work. The success in establishing a modeling approach to study the filtration of oily water systems is dependent upon our understanding of the fate of oil droplets at the membrane surface. It has been determined that four fates confront oil droplets at the membrane surface, namely, permeation, breakup, pinning, and rejection. Conditions for manifestation of any of these four fates depend on two operating conditions (transmembrane pressure and crossflow velocity) in comparison with two critical conditions (entry pressure and critical velocity of dislodgment). In this work, a new simplified formula for the critical entry pressure is introduced. It compares very well with the formula already existing in the literature. Furthermore, the complete model for the critical velocity of dislodgment in crossflow filtration is presented and highlighted. More investigations on the physical processes that are involved during the pinning of a droplet at a pore opening are presented. In addition, a thorough analysis of the forces that are involved during the permeation of a droplet that could lead to its breakup is presented. It is found that, once the droplet reaches the pore opening, the interfacial tension force and the pressure force continue to increase. Following the critical configuration, these forces continuously decline and the drag force due to the crossflow field, therefore, becomes sufficient to break up the droplet.