Predicting transition from selective withdrawal to entrainment in two fluid stratified systems

Selective withdrawal is a desired phenomenon in transferring oil from large caverns in US Strategic petroleum reserve, because entrainment of oil at the time during withdrawal poses a risk of contaminating the environment. In order to predict a critical submergence depth at a critical flow rate, a selective withdrawal experiment at a high Reynolds Number was conducted. A tube was positioned through a liquid-liquid interface that draws the lower liquid upwards. Analysis of the normal stress balance across the interface produced a Weber number, utilizing dynamic pressure scaling, that predicted the transition to entrainment. An inviscid flow analysis, using Bernoulli's principle, assuming an ellipsoidal control volume surface for the iso-velocity profile produced a linear relationship between the Weber number and the scaled critical submergence depth. The analytical model was validated using the experimental data resulting in a robust model for predicting transition from selective withdrawal to entrainment.