Friction Pressure Losses of Fluids Flowing in Circular Conduits
Authors: Ahmed Kamel Ahmed Hosny , Shaqlaih Ali S. 
Published: April 2012

Abstract
Fluids are pumped through circular conduits in various operations in thepetroleum industry. These fluids may be Newtonian or non-Newtonian, clean orproppant-laden, polymer-based or surfactant-based, single-phase or multi-phase, drag-reducing, etc. They are pumped through straight and coiled tubing as wellas through annuli under laminar or turbulent flow conditions. Calculation offriction pressure losses for these circumstances is very crucial and vital forthe success of the operation.
A simple Darcy-Weisbach equation is widely used to calculate friction pressurelosses in pipes. However, a unique term, Fanning friction factor, has to bedetermined. Enormous numbers of correlations are available to determine thefriction factor. These correlations vary in complexity and applicability andhave their own limitations. In addition, several parameters included in thecorrelations have to be identified and they vary from one correlation toanother. What is the suitable correlation? That is the question. Estimating theFanning friction factor is not an easy task and very confusing. Inaccurateestimation may lead to erroneous results and thus, failure of operations.
This paper is a more insight and comprehensive review of the Fanning frictionfactor correlations and presents how to select the most suitable one forspecific conditions. It discusses the parameters involved in the frictionfactor calculation and how to define it. The authors compare and question theapplicability, accuracy, and limitations of each correlation to propose themost accurate ones. An innovative code, based on the most widely and accuratecorrelations, is proposed to predict the Fanning friction factor. It is a userfriendly and step-by-step code that overcomes the complexity faced by theprofessional in the oil industry to calculate friction pressure losses. Inconclusion, this paper summarizes the state-of-the-art in the field of fluidhydraulics in the oil and gas industry.

Introduction
In the petroleum industry processes, variety of fluids are pumped throughstraight and coiled tubing during operations such as hydraulic fracturing, acidizing, wellbore cleanup, cementing and drilling which usually are executedunder turbulent flow conditions. Accurate prediction of friction pressurelosses when pumping these fluids has remained a challenge, mainly due to thelack of adequate friction loss correlations and proper understanding of thecomplex flow phenomena of fluids (especially non-Newtonian fluids in coiledtubing). The classical Darcy-Weisbach equation has been used for predictingfriction pressure losses. It is a simple equation to be used. Yet, a verycrucial and confusing term has to be determined. It is the friction factor. Friction factor is not a constant and it depends on various parameters relatedto pipe specifications, fluid behavior, and flow regime. It is important torecall that the friction factor originally defined by Blasius is four times theFanning friction factor. This article focuses on the Fanning friction factor,f.

Straight and Coiled Tubing.
The oil and gas industry has beenextensively utilizing coiled tubing, CT due to its numerous advantages overconventional straight tubing. However, centrifugal forces result from CTcurvature yield secondary flow, which increases friction pressure losses. Moreover, the small diameter of CT yields excessive friction pressure losseswhich often limit the maximum obtainable fluid flow rate in most CToperations.
The friction pressure losses in CT have a major impact on success of the job ifit has not been taken into account. Friction in coiled tubing has been shown tobe up to 200 % higher than it for the same fluid in straight tubing. As thecurvature ratio increases, friction pressure losses increase as well.