Flow of Drilling Fluids Through Eccentric Annuli

Abstract

The eccentric annular flow of power-law and Bingham plastic fluids is analysed in this paper using a new method in which an eccentric annulus is represented by infinite concentric annuli with variable outer radii. For the case of power-law fluids, ana1ytical solutions of the shear stress and velocity profiles have been obtained which are valid over the entire eccentric annulus. For Bingham plastic fluids, the profiles have been obtained at the minimum and maximum dimension positions of the eccentric annulus, which are -considered to be the important positions for the analysis of cuttings transport in an inclined eccentric drilling annulus. The results show that the local velocity and shear stress have greater magnitude in the enlarged region of an eccentric annulus than in the reduced region. In addition, like the case of concentric annular flow, the present analysis indicates that the profiles of the velocity and the magnitude of the shear stress in an eccentric annulus are not symmetric in the radial direction. Previous studies gave either unrealistic symmetric profiles or very complicated solutions. Based on the above analysis, the effect of the eccentricity of a drilling annulus on cuttings transport is evaluated. The results of this analysis will aid in the design of drilling programmes, particularly for deviated wells, to ensure efficient transport of drilled cuttings. Introduction Drilling engineers deal routinely with the flow of drilling fluids which are non-Newtonian in rheological behaviour, in the annular space between the drillpipe and the casing or wellbore. Traditionally, the assumption is made that the drillpipe is placed concentrically in the casing or wellbore when the annular flow and the behaviour of the transported drilled cuttings is analysed. In reality, however, the drillpipe is usually positioned eccentrically, especially in deviated wells where the drillpipe has a strong tendency to lie against the low side of the hole. A number of studies have been reported for the flow of non-Newtonian fluids through eccentric annuli. Heyda, Redberger and Charles, Mitsuishi and Aoyagi, and Guckes approached the problem by using bipolar co-ordinates to define the eccentric annular geometry and developed methods for the calculation of the velocity profile which involve extensive numerical iterative computation. Vaughn and Iyoho and Azar treated an eccentric annulus as a slot with variable height and developed the analytical models of the velocity profile for power-law fluids. However, because their models are in essence the modified model for flow between parallel plates, unrealistic symmetric velocity and linear shear stress profiles result. In this paper, the annular flow of drilling fluids is analysed based on the eccentric annular geometry using a new method which treats an eccentric annulus as an infinite concentric annuli with variable outer radii. The two most commonly used rheological models i.e. power-law and Bingham plastic models, are used in the analysis to define the rheological behaviour of the drilling fluids. Then, based on the above analysis, the effect of the pipe/hole eccentricity on cuttings transport is evaluated.

Non-Newtonian Flow in Eccentric Annuli

“…Since the fluids of petroleum engineering are typically non-Newtonian in behavior, the studies of nonNewtonian fluid flow in eccentric annuli followed. Unfortunately, a number of investigators have built their eccentric annular flow studies on an equation of flow which is valid for a concentric annulus only and, therefore, have failed to obtain Contributed by the Petroleum Division and presented at the Thirteenth Annual Energy-Sources Technology Conference and Exhibition, New Orleans, Louisiana, January 14-18, 1990 accurate results (Vaughn, 1965;Iyoho and Azar, 1981;Luo and Peden, 1987;Uner et al, 1989). However, Guckes (1975 numerically solved the equation of flow for the eccentric annulus and obtained a flow rate versus frictional pressure loss gradient relationship for the power law and the Bingham plastic-type non-Newtonian fluids for a limited range of eccentricities.…”

Frictional pressure loss of drilling fluids in a fully eccentric annulus

“…Theoretical models that are based on introducing geometric parameters, such as Pipe Equivalent, generally delivered a poor result by greatly under-estimating the eccentricity effect. However, the Corrected Narrow Slot approach showed acceptable accuracy with comparison to other more sophisticated and M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 9 computationally expensive CFD models (Luo and Peden, 1990;Hashemian Adariani, 2005) for the presented geometry.…”

“…However, results obtained from the Corrected Narrow Slot approach show reasonable accuracy for the presented geometry and in several cases performed even better than the simplified CFD models for eccentric annuli such as the models by Luo and Peden (1990) or Hashemian Adariani (2005). Theoretical models that are developed based on introducing geometric parameters such as the Pipe Equivalent approach (Ahmed et al, 2006) or the model by Sestak et al (2001) yielded very poor predictions and greatly underestimated the effect of eccentricity on pressure loss in a fully eccentric annulus.…”

“…Luo and Peden (1990) provided a practical approximation for the flow through eccentric annuli. The eccentric annulus was treated by suggesting it is composed of infinite concentric annuli with variable outer radii.…”

“…Proposed model in this study is compared with the experimental data (Erge, 2013) as well as other widely used theoretical and numerical models, including: Narrow Slot (Appendix B), corrected Narrow Slot (Appendix B), Luo and Peden (1990) (Ahmed et al, 2006) andHashemian Adariani (2005). Since, the Narrow Slot approximation does not consider the effect of pipe eccentricity, the obtained pressure loss from this approach is corrected by Eq.…”