Summary
A comprehensive theoretical analysis of turbulent flow of a power-law fluid
in coiled tubing was conducted with the approach of boundary layer
approximation. Equations of momentum integrals for the boundary layer flow were
derived and solved numerically. Based on the results of the numerical analysis,
a new friction-factor correlation was developed which is applicable to a wide
range of flow behavior index of power-law fluid model. The new correlation was
verified by comparing it with the published Ito correlation for the special
case of Newtonian fluid. For non-Newtonian fluids, there is also a close
agreement between the new correlation and the experimental data from recent
full-scale coiled tubing flow experiments.
Introduction
Many fluids that are pumped through coiled tubing are typically
non-Newtonian fluids, such as polymer gels or drilling muds. Understanding
their flow behavior and being able to accurately predict frictional pressure
through coiled tubing are essential for better operations design. A recent
literature review (Zhou and Shah 2004) indicates that though there are numerous
studies on the flow of Newtonian fluids in coiled pipes, there is, however,
very little information with regard to the corresponding flow of non-Newtonian
fluids.
Among the various approaches of investigating fluid flow in coiled pipes,
there is one important method called boundary layer approximation analysis. It
is especially useful for high-Dean (1927, 1928) number flows where the effect
of secondary flow is largely confined in a thin boundary layer adjacent to the
pipe wall (Dean number is commonly defined as: (equation). According to this
approach, the tubing cross-section can be divided into two regions: the central
inviscid core, and the thin viscous boundary layer. This leads to much
simplified flow equations for high-Dean number flows in curved geometry. This
approach has been used by a number of researchers, for example, by Adler
(1934), Barua (1963), Mori and Nakayama (1965), and Ito (1959, 1969) for
Newtonian fluids, and by Mashelkar and Devarajan (1976, 1977) for non-Newtonian
fluids.
In a previous attempt, Zhou and Shah (2007) applied the method of boundary
layer approximation to solve the laminar flow problem of a power-law fluid in
coiled tubing and obtained an empirical friction-factor correlation based on
the theoretical analysis and numerical solutions. In the present study, we take
the same analysis approach but consider the turbulent flow of a power-law fluid
in coiled tubing. A friction-factor correlation for turbulent flow in coiled
tubing is developed, and its validity is evaluated with a published correlation
(Ito 1959) and recent full-scale experimental data.
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
9 February 2004
- Revised manuscript received:
5 August 2007
- Manuscript approved:
17 August 2007
- Version of record:
20 December 2007
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