Fluid Flow in Coiled Tubing: A Literature Review and Experimental Investigation
Authors: Zhou Y. , Shah S. 
Published: March 2010

Abstract
This paper presents a comprehensive review of the theoretical and experimental studies of steady, fully-developed flow of Newtonian and non-Newtonian fluids in coiled tubing. The flow mechanisms and characteristics of secondary flow and its effect on the flow resistance have been discussed. Available friction factor correlations have been analyzed and evaluated for accuracy and applicability. Compared with its counterpart of Newtonian fluid, the flow of non-Newtonian fluid in coiled pipes has remained much less studied. The paper also briefly describes the recent development of full-scale experimental investigations on the frictional pressure losses of various fluids in coiled tubing.

Introduction
Coiled tubing (CT) has been used in well drilling, completion, stimulation, wellbore cleanout, and other operations in the petroleum industry(1). Accurate prediction of frictional pressure losses when pumping fluids through coiled tubing has remained a challenge in hydraulics design, mainly due to the lack of adequate friction loss correlations and proper understanding of the complex flow phenomena of fluids (especially non-Newtonian fluids) in coiled tubing. Because of the effect of centrifugal forces, secondary flow occurs when a fluid flows through a coiled tubing. It is a known fact that flow in coiled tubing encounters more pressure losses than in straight tubing. It is believed that secondary flow causes the excessive friction losses. Since the classic work of Dean(2, 3), the flow of Newtonian fluids in coiled pipes has been extensively studied; in contrast, the flow of non-Newtonian fluid in coiled pipes has remained relatively unstudied.
The objective of this paper is to review both theoretical and experimental studies on the flow of Newtonian and non-Newtonian fluids in coiled pipes. The mathematical formulation and the general characteristics of the secondary flow are first introduced in order to prepare for discussion of various theoretical studies. The available friction factor correlations will be compared and evaluated for their accuracy and applicability.
A recent increase of coiled tubing applications has been driving the research activities of coiled tubing hydraulics using full-scale experimental facilities. This paper will also present recent developments in those experimental investigations.
It is hoped that this comprehensive review and the experimental results will provide valuable information for those interested in the application and research of coiled tubing hydraulics.

Newtonian Fluid
Governing Equations
Figure 1 shows the toroidal coordinate system that has been used in studying fluid flow in coiled pipes. We denote the radius of the pipe by a, and the radius of the coil as R. C is the centre of the pipe cross section, and θ is the angle that the cross-section makes with a fixed axial plane. OZ is the axis of the coil. Assume the flow is in the direction of increasing θ under a driving pressure gradient. The velocity components u, v, and w are in the directions of r, α, and θ, respectively.
The equations of momentum and continuity(2, 3) are:Equation (1) Available In Full Paper.Equation (2) Available In Full Paper.FIGURE 1: Toroidal coordinate system. Available in Full Paper.Equation (3) Available In Full Paper.