Regression modeling for laminar flow of herschel–barkley fluids in the concentric elliptical annulus

Abstract Deep fractured formations have poor pressure-bearing capacity and a narrow safety drilling fluids density window, leading to high risk of well control. Accurate prediction annulus pressure drop is great significance the safe deep formations. Conventional predictions are mostly based on regular circular but elliptical easily formed due rock structure, mechanical properties heterogeneity ground stress. In order accurately conveniently predict Herschel–Barkley (H–B) laminar flow in concentric wellbore (CAEW), an analytical model assumption narrow-slot was established solved by considering core this paper. We found that pattern index, proportion inner outer diameter major minor axes were main influencing factors through analysis. On basis, new method for predicting H-B CAEW established. It regression excellent agreement with numerical models, most error bars within ± 10%, indicating could dimensionless gradient without complex mathematic method.