A refined semi-analytical model for hydraulic analysis of laminar power-law fluid flow in eccentric annuli

• A refined model for power-law fluid flow in eccentric annuli is proposed. • The hybrid method precisely locates the zero-shear-stress surface. • Directly links flow rate to pressure drop, solving a key engineering problem. • Validated against CFD and experimental data with excellent accuracy. • Quantifies the non-linear impact of eccentricity and flow index on pressure loss. Predicting laminar power-law fluid flow in eccentric annuli is crucial for managing wellbore pressure in complex drilling operations. This study presents a refined semi-analytical model that rigorously implements the concentric annular superposition principle. The core novelty lies in a hybrid numerical-analytical technique that employs hypergeometric functions and the bisection method to precisely locate the zero-shear-stress position within each discretized element, thereby overcoming the inaccuracies of previous approximation-based methods. This framework enables the direct and accurate calculation of key hydraulic parameters—including asymmetric velocity profiles, shear distributions, and frictional pressure drops—from given engineering flow rates. The model's high precision is demonstrated by reducing velocity continuity errors at the zero-shear interface to below 0.0007 m/s. Key findings confirm that peak velocity and shear occur on the wide-gap side, while increasing eccentricity significantly reduces frictional pressure gradients. Notably, at high eccentricities (ε > 0.4), the influence of the flow behavior index (n) becomes more pronounced, with fluids exhibiting higher n values showing lower frictional pressure gradients.