Incomplete fluid–fluid displacement of yield stress fluids in near-horizontal pipes: Experiments and theory

Abstract

We present results of a primarily experimental study of buoyant miscible displacement flows of a yield stress fluid by a higher density Newtonian fluid along a long pipe, inclined at angles close to horizontal. We focus on the industrially interesting case where the yield stress is significantly larger than a typical viscous stress in the displacing fluid, but where buoyancy forces may be significant. We identify two distinct flow regimes: a central-type displacement regime and a slump-type regime for higher density ratios. In the central-type displacement flows, we find non-uniform static residual layers all around the pipe wall with long-wave variation along the pipe. In the slump-type displacement we generally detect two propagating displacement fronts. A fast front propagates in a thin layer near the bottom of the pipe. A much slower second front follows, displacing a thicker layer of the pipe but sometimes stopping altogether when buoyancy effects are reduced by spreading of the front. In the thin lower layer the flow rate is focused which results in large effective Reynolds numbers, moving into transitional regimes. These flows are frequently unsteady and the displacing fluid can channel through the yield stress fluid in an erratic fashion. We show that the two regimes are delineated by the value of the Archimedes numbers (equivalently, the Reynolds number divided by the densimetric Froude number), a parameter which is independent of the imposed flow rate. We present the phenomenology of the two flow regimes. In simplified configurations, we compare computational and analytical predictions of the flow behaviour (e.g. static layer thickness, axial velocity) with our experimental observations.