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 the U.S. Strategic Petroleum Reserve (SPR), because entrainment of oil at the time during withdrawal poses a risk of contaminating the environment. Motivated to understand selective withdrawal in an SPR-like orientation, we performed experiments in order to investigate the critical submergence depth as a function of critical flow rate. For the experiments, a tube was positioned through a liquid-liquid interface that draws the lower liquid upward, avoiding entrainment of the upper fluid. Analysis of the normal stress balance across the interface produced a Weber number, utilizing dynamic pressure scaling, that predicted the transition to entrainment. Additionally, an inviscid flow analysis was performed assuming an ellipsoidal control volume surface that produced a linear relationship between the Weber number and the scaled critical submergence depth. This analytical model was validated using the experimental data, resulting in a robust model for predicting transition from selective withdrawal to entrainment.