A New Way to Compute Annular Friction Loss

Abstract

Laminar flow of non-Newtonian fluids through an annular space is frequently encountered in drilling fluid circulation, cementing, formation fracturing, and water and sand control. Theoretical solutions for various models (Bingham plastic, Power-law, Reiner-Ravlin, Rabinowitsch) describing the behavior of non-Newtonian fluids have been published. However, data have not been released to substantiate the results. Therefore the development of a new equation to compute friction losses in an annular space - and a comparison of the results with those of other equations derived by different approaches - is important. The nature of non-Newtonian fluids remains controversial. Some authorities believe that the Bingham plastic model best describes all non-Newtonian fluids. Others disagree and think that most non-Newtonian fluids are best described by the Power-law model. Regardless of controversy, the Bingham plastic model is encountered rarely. This model applies more exactly in high-solids drilling fluids. Popularity of saltsaturated and low-solids drilling fluids, oil emulsion, inverted emulsion and oil base muds - as well as aqueous gels and gelled crude oils for hydraulic fracturing - has emphasized a need for the Power-law model. Further controversy arose when some authorities proposed that the equation for flow of Bingham plastic fluid in a cylindrical pipe could be replaced in the equation by the hydraulic radius to describe flow in the annulus. Others pointed out that even for a simple Newtonian fluid, the substitution of the hydraulic radius in the cylindrical pipe equation would produce erratic results.