Friction Factors for Turbulent Flow of Non-Newtonian Fluids in Coiled Tubing

Abstract

Abstract The applicability of Newtonian friction factor correlations for predicting friction pressure losses in turbulent coiled tubing (CT) flow of non-Newtonian fluids is investigated. All correlations presented are expressed in a simple and convenient form by separating the contribution of curvature effects of the reel and friction pressure losses in corresponding straight tubing. The primary advantage of separating reel effects from the straight tubing pressure losses is that the form of the friction factor correlation provides more generality and can be extended to both Newtonian and non-Newtonian fluids. Moreover, pipe roughness effects can be easily incorporated if necessary, and a single correlation can be used to predict friction pressure losses in both straight and reeled tubing. The correlations presented are valid for a wide range of generalized Reynolds numbers, and are applicable to most combinations of reel and tubing sizes available today. The results obtained from these proposed correlations are compared with published experimental data and very good agreement is obtained. Introduction In the past decade, coiled tubing (CT) has seen widespread utility in various applications such as solids washing, acidizing, drilling, cementing, well unloading, etc. as a means to transport fluids from the surface into the wellbore. Examples of fluids routinely pumped through the CT include water, acids, diesel, crude oil, gels, drilling mud, nitrogen, foams, and nitrified water. Broadly, these CT fluids can be classified as: compressible (fluid density is a strong function of pressure) or incompressible (pressure has a negligible effect on fluid density), and Newtonian (shear stress is linearly related to shear rate) or non-Newtonian (relationship between shear stress and shear rate is non-linear). In general, liquids are considered incompressible and can be either Newtonian or non-Newtonian in their fluid behavior. On the other hand, gases, foams, and multiphase fluids like nitrified water are compressible fluids and can also exhibit either Newtonian or non-Newtonian behavior. Thus, depending upon the fluid being pumped through the CT, horsepower requirements change, and have to be determined appropriately for proper design of CT operations. For a proper design, an accurate estimation of friction pressure loss is of great importance. Friction pressure losses in reeled tubing are greater than the corresponding friction pressure losses in straight tubing due to a secondary flow superimposed on the main flow through the CT. The extent to which this secondary flow affects the CT friction pressure losses largely depends upon the radius of curvature of the reel and internal diameter of the CT. In addition, since many fluids such as linear polymer gels and drilling mud exhibit non-Newtonian fluid behavior, their friction pressure losses are quite different from Newtonian fluids like water and diesel. Therefore, accurate quantification of the effects of curvature on friction pressure losses of such non-Newtonian flows through CT is particularly important.