Semi-analytical modeling and physical insights into eccentric annular flow of Herschel–Bulkley fluids

Eccentricity in annular flow has a strong influence on pressure drop, particularly for non-Newtonian fluids such as Herschel–Bulkley (HB) fluids that are widely used in drilling and energy applications. Although this problem has been studied before, many existing approaches are difficult to reproduce, or do not isolate the specific role of eccentricity. In this work, we develop a semi-analytical model that combines the continuity and momentum equations with the HB rheological law to predict pressure drop in eccentric annuli. The model provides a compact expression for flowrate that captures how eccentricity, fluid properties, and geometry interact to determine flow resistance. Validation is carried out using laboratory-scale flow-loop experiments and comparison with published data, showing good agreement across a range of conditions. A sensitivity study further clarifies the relative influence of yield stress, consistency index, and flow behavior index on pressure drop. The results highlight general physical trends in annular flow of yield-stress fluids, offering a reproducible and lightweight alternative while retaining strong physical insight.