Modeling of laminar flow in an eccentric elliptical annulus for YPL fluid

Abstract The precise and convenient calculation of bottom hole pressure can provide a guarantee for safe drilling. Most of the existing models for determining the downhole pressure or annular pressure gradient (PG) are applied only to the circular wellbore. Due to the nonuniform in situ stress and the anisotropism of formation rock, the borehole formed by rotary drilling is the closest to the ellipse, that is, the irregular circular borehole. Therefore, it is of importance to research YPL fluid flow through the eccentric elliptical annulus (EEA) for the accurate prediction of bottom hole pressure. In this paper, a numerical model for determining the PG of YPL fluid flow in the EEA is developed on the basis of fluid mechanics. Then, through parameter studies, a new regression model (RM) of the pressure ratio in the EEA is established. The commercial software ANSYS was used to research the laminar flow of yield-power-law fluids through the EEA, and the simulation results are used to verify the numerical model and new regression model. The main conclusions are as follows. (1) The PG increases quasi-linearly or linearly with the mean velocity, fluid consistency index and yield stress and hardly changes with the azimuth of the inner pipe center. The PG decreases with a / b ( η ) and eccentricity ( e ) when the mean velocity is constant. (2) The new regression model is valid for the ranges 0.2≤ K d  ≤ 0.8, 0≤ e  ≤ 0.95, 0.2 ≤  n  ≤ 1.0, and 1.0≤ η  ≤ 1.2 and shows excellent agreement with existing model and computational fluid dynamics (CFD) simulations, within ±5% error bars. (3) The maximum velocity first increases and then decreases with e . The results of axial velocity and PG using CFD software are found to be in excellent agreement with the numerical model solutions. (4) Predicting the PG in the EEA using the new regression model has high precision and without complicated numerical computation.