Accurate Predictions of Velocity Profiles and Frictional Pressure Losses in Annular YPL-Fluid Flow

Eccentricity of the annulus can greatly affect the velocity profile, especially in extended-reach wells and slimholes. While frictional pressure losses in concentric and fully eccentric annuli have been studied before, this paper focuses on the effect of arbitrary eccentricities on velocity profile and corresponding influence on frictional pressure losses. In this study, axial flow of yield-power-law (YPL) fluids in eccentric annuli for a 2D steady-state flow has been investigated numerically and verified against experiments. A boundary-fitted coordinate system is used to discretize the flow equations and generate the mesh network. Fluid-flow equations were solved adopting an iterative method. The results of simulation include the effects of fluid rheology, flow rate, annulus dimensions, and eccentricity on velocity profile and frictional pressure losses in the annulus. Numerical results were compared with the available extensive experimental investigations on the flow of a variety of drilling fluids that have a strong shear-thinning property and high yield stress (e.g., polymer-based and bentonite fluids). The tests were implemented over a wide range of flow rates using a flow loop that is equipped with a pipe viscometer and several annular test sections with various sizes and eccentricities. Field observations, experimental data, and the analytical approach in this study indicate that increasing eccentricity lowers frictional pressure drop in the annulus. A good agreement was observed between the numerical-simulation results and experimental measurements. Comparison of the present and past studies with analytical solutions of Newtonian fluids in an eccentric annulus shows that the current study provides more-accurate results. Detailed numerical simulation and the equations that are presented in this study can be used by investigators. The application of the Cartesian and boundary-fitted coordinate systems and algebraic correlations for geometry transformations are presented. Moreover, the exact method of flow-rate calculation based on the velocities at each gridpoint is shown in the provided details. The application of findings in this study includes more-accurate predictions of velocity profile and frictional pressure loss in the annulus, which lead to better predictions of barite sag, cuttings transport, equivalent circulating density, and mud cement displacement in special cases of cementing operations.