Hydrodynamic analysis of core annular flow with a viscoplastic lubricant

Abstract

Core annular flow (CAF) with viscoplastic lubrication (VPL) is an attractive proposition for pipeline transportation of high viscous oil, slurries and suspensions. Past studies have performed stability analysis to show that the unyielded zone at the liquid-liquid interface stabilizes CAF by suppressing interfacial instabilities. However, an in-depth investigation of the flow hydrodynamics and the conditions which reduce the pumping power within stable CAF range using VPL has not been reported till date. Moreover, most of the studies have considered a Bingham Plastic liquid in the annulus. Only a single study (Usha & Sahu, 2019) is reported with Herschel-Bulkley (HB) liquid in the annulus that considers the entire annulus to be in the shear zone. Another experimental study (Huen et al., 2007) has demonstrated stable core annular flow with a shear thinning core and a HB annulus. In the present work, we analyze viscoplastically lubricated CAF for a Newtonian core where the yield stress annular liquid is described by the generalized HB model. The simplified analysis can predict CAF stability and is further explored to (i) assess the efficacy of VPL for stable energy-efficient oil transportation, and (ii) enhanced throughput without clogging during suspension transportation. The analysis, validated against data from literature, unravels the influence of rheological properties on flow hydrodynamics. We note that an annular liquid with low flow behavior index, $n$ and yield stress, ${\tau }_y$ lowers pumping power, but the yield stress should be sufficient to form a plug zone at the interface for suppressing instabilities and stabilizing CAF. For viscous oil, a phase diagram in dimensionless coordinates (Reynolds number of the oil core and Herschel-Bulkley number of the annular liquid, both expressed at the inlet conditions) suggests the range of operation where an available HB liquid can serve as an effective annular lubricant for energy-efficient transportation.