Density-stable yield-stress displacement flow of immiscible fluids in inclined pipes

Abstract

We experimentally study the displacement flow of a non-Newtonian yield-stress fluid by an immiscible Newtonian one in an inclined pipe. The pipe has a small diameter-to-length ratio. The less dense displacing fluid is placed above the denser displaced fluid i.e. a density-stable configuration. The displacing and displaced solutions are oil and water-based respectively. The flow between the Newtonian and non-Newtonian fluids has been studied over a wide range of controlling parameters, namely imposed flow rate, inclination angle, density difference, yield stress, viscosity, and surface tension. Compared to the previously studied miscible limit, we observe novel fracturing behavior at the interface between the two fluids; this fracture pattern is preserved in the non-Newtonian gel as the advancing oil flows through. Instead of both slump and center-type flows observed in the miscible case, we primarily observe center-type flows, which maintain similar flow profiles across mean imposed flow rates V^0 in the study. Similarly to the miscible case, the inclination angle β is not found to have an effect on the velocity of the advancing frontal region of the displacing fluid, V^f. The average thickness of the residual yield-stress layer in this study was found to be 0.14 of the radius, decreasing to 0.12 of the radius when higher viscosity oils are used as the displacing fluid. The residual layer thickness slightly increases with Reynolds number, Re, but shows no dependency on the density difference between the two fluids captured by the Atwood number, At. Finally, the unevenness in the yield-stress residual layer for immiscible fluids is found to be significantly less than that of the miscible case.