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

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