An Improved Analysis of Axial Force Along Coiled Tubing in Inclined/Horizontal Wellbores
Authors: Miska Stefan , Qiu Weiyong , Volk Len , Cunha J.C. 
Published: December 2007

Abstract
This paper presents an improved mathematical model for the axial force calculations along coiled tubing (CT) while drilling in inclined and horizontal wellbores. This new mathematical model is more general as it includes three types of coiled tubing configurations: straight, postbuckling "snaking", and helical. The equations for predicting the axial force under "snaking" configuration are believed to be presented for the first time. The "snaking" configuration of CT is of practical importance as it is a stable configuration for a wide range of axial loads. Several numerical case studies are provided to show the usefulness of the proposed axial force transfer model. The influences of friction, coiled tubing and wellbore size on the axial force predictions are described and presented in graphical form. Finally. a number of laboratory experimental results validate the proposed axial force transfer model as long as the effect of residual bending is not significant.

Introduction
While drilling represents a small fraction of the many uses of coiled tubing, it is by far the most exciting and promising application owing to the increase safety under-balanced drilling and continuous tripping operations. Drilling under-balanced helps prevent damage to the formation, reduces the likelihood of differential sticking and may result in faster penetration rates if adequate weight on bit (WOB) and RPM are used. In fact, coiled tubing is capable of performing numerous drilling jobs, such as:–Drilling under-balanced with gas lift, foam, or liquid.–Drilling through tubing (typically, 3-1/2 in, and 4-1/2 in.). - Coring.–Setting whipstock and cutting casing windows.–Setting tool wireline telemetry.–Air/mist drilling.–Off-pad drilling.–Running liners and hangers.–Underreaming.
The dramatically increasing applications of coiled tubing drilling require much more precise modeling of the buckling behavior of coiled tubing and the axial force transfer under wellbore conditions. A good axial force transfer model is important for the following practical applications:–Design of the best wellpath (configuration).–Selection of wellbore and CT dimensions.–Evaluation of stresses and corresponding strains (CT elongation/shortening).–Prediction of WOB, bit wear, rate of drilling and anticipated cost per foot.–Prediction of "lock-up" occurrence.–Directional control.

Review of Axial Force Transfer Modeling
A number of papers have discussed how to predict the axial force profile in directional wellbores. In the conventional approach, drillpipe has been considered as a cable (soft models). In 1983, Johancsik et al. presented a drag model to predict the axial force profile of a wellbore. While their soft string model is quite reasonable for drillpipe under tension its practical usefulness is limited for CT as it does not consider the possibility of pipe buckling.
In 1993, Wu and Juvkam-Wold studied the frictional drag of helical buckled pipes in extended reach and horizontal wells. The differential equation for static axial force balance (as depicted in Fig. 1) is given by:
(1)
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