Non-Newtonian Flow in Eccentric Annuli

A common assumption for annular flow used in the petroleum industry is that the inner pipe is concentrically located inside the flow geometry; however, this is rarely the case, even in slightly deviated wells. Considering the increasing number of directional and horizontal wells, the flow behavior of drilling fluids and cement slurries in eccentric annuli is becoming particularly important. In this paper, the governing equation of laminar flow is numerically solved using a finite differences technique to obtain velocity and viscosity profiles of yield-power law fluids (including Bingham plastic and power law fluids). Later, the velocity profile is integrated to obtain flow rate. Results show that the velocity profile is substantially altered in the annulus when the inner pipe is no longer concentric. Stagnant regions of flow were calculated in the low side of the hole. Viscosity profiles predicted for an eccentric annulus show how misleading the widely used single-value apparent viscosity term can be for non-Newtonian fluids. Profiles of velocity and viscosity in concentric and varying eccentric annuli are presented in 3-D and 2-D contour plots for a better visualization of annular flow. Frictional pressure loss gradient versus flow rate relationship data for power law fluids is generated using the computer program. Later, this data is fitted to obtain a simple equation utilizing regressional analysis, allowing for a quick calculation of friction pressure losses in eccentric annuli. For a given flow rate, frictional pressure loss is reduced as the inner pipe becomes eccentric. In most cases, about a 50-percent reduction in frictional pressure loss is predicted when the inner pipe lies on the low side.