A novel criterion based on slip ratio to assess the flow behavior of W/O emulsions within centrifugal pumps

•A criterion to analyze emulsion flow behavior under centrifugal field was proposed.•A new model to estimate the Sauter mean diameter within centrifugal pump.•The drag reduction phenomenon within centrifugal pump was observed. Water-in-oil emulsions usually present complex rheological behavior that depends on the physicochemical properties of both phases, the presence of surfactants, and the flow conditions. Thereby, this paper aims to propose a criterion to characterize the rheological behavior of stable and unstable water-in-oil emulsions within the centrifugal pumps. This criterion is based on the slip ratio between the dispersed and continuous phases. For this, the droplet size distribution was measured at the ESP outlet and the slip ratio was estimated based on the centrifugal buoyancy-induced flow. A new model was proposed to determine the Sauter mean diameter for different systems of the water-in-oil emulsion flows within the ESP based on operational conditions, which presents good agreement with the experimental data (12.6% of error). Finally, a new dimensionless number parameter named Slip Relevance number was proposed to separate the different emulsion flow behaviors within the ESP and its critical value was obtained.