Annular flow of non-Newtonian fluids remains a ubiquitous phenomenon in drilling operations but accurately estimating the frictional pressure loss with drill pipe rotation still poses a great challenge. Since annular frictional pressure losses increases the equivalent circulating density (ECD), it becomes imperative to accurately estimate the annular pressure loss in order to keep the ECD above the pore pressure and below the fracture gradient especially in deep offshore drilling where the pore pressure and fracture pressure are so close together.

When annular flows are encountered, a common practice is to calculate an effective diameter such that the flow behavior in a circular pipe would be roughly equivalent to the flow behavior in the annulus. This equivalent diameter definition replaces the diameter term in the friction factor, effective Reynolds number and Taylors number equations used for pipe flow thus resulting in different frictional pressure loss estimation. As a result, the selection of appropriate correlation for the respective fluids, flow regimes and putting into consideration pipe rotation has become important but has received very little attention.

In this study, the seven different equivalent diameter definitions used for estimating frictional pressure losses in an annulus were reviewed and theoretical analysis were performed on experimental data obtained from literatures to determine the effect of these definitions on wellbore hydraulics. Pressure loss ratios (PLR) which relates pressure loss with pipe rotation to pressure loss without pipe rotation weredevelopedfor each equivalent diameter definitionusing dimensional analysis techniques. These hydraulic models combined with conventional frictional pressure loss estimation were tested with experimental measurements to determine the model with an equivalent diameter definition that best predicts frictional pressure losses for power law fluids.

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