An experimental study has been conducted to investigate the effects of eccentricity on friction pressure loss calculations for drilling and stimulation fluids. Reynolds number in the range of 800 to 100,000 allowed the analysis of friction pressure losses of non-Newtonian fluids in both concentric and eccentric annuli in laminar and turbulent flow regimes.

Analysis of Fanning friction factors as a function of generalized Reynolds number showed that the effects of eccentricity are significant when annular friction pressure losses are estimated. The results demonstrated that the annular pressure losses in a fully eccentric annulus can be as low as 40% of the value in concentric annulus. It was observed that the effect of eccentricity is more evident as the fluid concentration increases. From experimental data obtained in this study, new correlations are proposed to calculate friction pressure losses in concentric and eccentric annuli for laminar and turbulent flow regimes. Though not ideal, these new correlations estimate friction losses in annuli much closer than the previously published equations.


While the problem of fluid flow in concentric annulus has received much attention in the past, only in the last two decades an interest has started for the same problem in an eccentric annulus. If the annular space is concentric, the flow can be analyzed without much difficulty. But if the annular space is eccentric; i.e., the axes of the inner and outer tubes do not coincide with each other, a great deal effort is required. Unfortunately the latter case represents the majority of realistic situations, especially in a deviated well-bore where the drill pipe has a strong tendency to offset toward the low side because of gravitational effects.

The determination of the annular flow performance of Non-Newtonian fluids is quite important in the planning and design of the hydraulics program of a well because significant pressure losses can develop in the constrained space. The knowledge of rheological data and methods of predicting pressure losses are the key points to calculate proper pump rates and avoid any obstacle in a normal operation of oil production.

Traditionally, friction pressure calculations are useful in determining horsepower requirements, bottomhole treating pressure, and maximum wellhead pressure. An accurate prediction of the friction losses is very important from the economic point of view. Optimizing the friction pressure loss calculations through the well bore annulus allows making an appropriate evaluation of the wellbore hydraulics, which is essential to reduce the problems and avoid high costs of operation.

The purpose of this study is to investigate the effects of pipe eccentricity on friction pressure loss calculations for the flow of Newtonian and non-Newtonian fluids through concentric and fully eccentric annuli. The paper examines the effect of gel concentration on friction pressure losses for concentric and eccentric annuli. From data gathered by pumping various drilling and stimulation fluids through rough annuli, practical engineering correlations for Newtonian and Non-Newtonian fluids in laminar and turbulent flow regimes are developed. The results show that friction pressure losses in eccentric annuli can be considerably overestimated if the eccentricity effects are not taken into consideration.


A great number of studies are available on estimating friction pressure losses in laminar and turbulent flow of Newtonian and non-Newtonian fluids in concentric annuli. However, very little has been accomplished for the estimation of friction losses in laminar and turbulent flow of Newtonian and non-Newtonian fluids through eccentric annuli.

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