Removal of a yield stress fluid by a heavier Newtonian fluid in a vertical pipe

Abstract

The present work aims to investigate, experimentally, analytically and computationally, the removal of a light yield stress fluid displaced by a slightly heavier Newtonian fluid, in a long vertical pipe. The fluids of interest are miscible and the displacement flow is downward. In general, the flow is controlled by at least four dimensionless numbers, and their combinations, namely the Newtonian Bingham number, 0 ≤ BN ≤ 18600, the viscosity ratio, 1 < m < 9723, the Newtonian Reynolds number, 13 ≤ ReN ≤ 2480, and the densimetric Froude number, 0.15 ≤ Fr ≤ ∞. In the definitions of BN, m and ReN, the displacing fluid’s constant viscosity is used as the viscosity scale. The experiments present a variety of different flow patterns, for which a number of regime classifications can be made. First, fully static residual wall layers are observed at BN ≳ 100 and moving residual layers are found below this transition value, which can be predicted by a simple analytical (lubrication type) model. Second, for displacement flows with BN < 100, the displacements can be divided into nearly-stable and unstable flow regimes, for which the transition occurs at a critical buoyancy number, χ=2ReN/Fr2≈120. Third, for fluid flows with BN ≳ 100, the residual layer patterns can be classified into three distinct sub-regimes, including corrugated, wavy and smooth regimes, as a function of ReN/(BN+m) and ReN/Fr. Fourth, to analyse secondary displacement front features, the experiments are phenomenologically classified into central and periphery displacements, for which the transition can be reasonably predicted by an appropriate analytical model. However, the long time displacing front velocities cannot be estimated by the analytical model. Finally, computational fluid dynamics simulations in a simpler channel geometry demonstrate that some of the complex displacement flow features may be predicted computationally.