An Improved Analysis of Axial Force Along Coiled Tubing in Inclined/Horizontal Wellbores

Abstract

Thm paper was prepared for presentabon at the 19S6 SPE Intemabonal ConfereM on Hcmzontat Well Technology held m Calgary, Canada, 18-20 Novem* 19% This papr was selected for presentawan by an SPE Prqrem Committee follovmg rewew of Inlormabcm cmtamed m an abstraci Submitted by the author(s) Contents of thm papw, as presented, have not been rewewed by ths %clely of Petroleum Engineers and are subject to wrractmn by the author(s) Th!s material, as presented, does not necessarily reflect any pmbon of Ihe Scuety of ptmleum Engineers ds oficars, or membars Papers presented at SPE meettngs are subject to publcatmn rewew by Edntortal Committees of the .?,c.aety of Petroleum Engineers Penn IssIcmto capy IS restricted to an abstraci of not more than 300 words IllustratIons may not be cop!ed The abstract should contain mnsp!cvous acknowledgment of where and by whom the paper was presented Whte Libfanan, SPE, P O. Box 833=, Rchardson, TX 75083 -3e3S, U S A fax 01-214-952-9435 AbstractThis 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.

A review of down-hole tubular string buckling in well engineering

“…To simplify Paslay's derivation, a sine function buckling shape is assumed and then Eq. (13) can be directly deduced with the energy method (Chen et al 1990;Miska et al 1996;Liu 1999), Gao et al (1998) obtained an identical solution with stability analyses on the approximate linear form of the buckling equation. The theoretical results are close to the Dellinger's experiments (Dellinger et al 1983), and the fitting formulas for horizontal wellbores from the experimental data are F crs ¼ 2:93EI 0:479 q 0:522 r À0:436 .…”

“…According to Wu, the critical helical buckling load is 2 ffiffi ffi 2 p À 1 times the critical sinusoidal buckling load. Miska et al (1996) assumed that the axial force increased linearly in the entire loading process and found that the critical helical buckling load was 2 ffiffi ffi 2 p times the critical sinusoidal buckling load. Miska et al (1996) also proved that the sinusoidal buckling configuration became unstable (b ¼ 1:875) before the tubular string changes to the helical buckling configuration.…”

“…Miska et al (1996) assumed that the axial force increased linearly in the entire loading process and found that the critical helical buckling load was 2 ffiffi ffi 2 p times the critical sinusoidal buckling load. Miska et al (1996) also proved that the sinusoidal buckling configuration became unstable (b ¼ 1:875) before the tubular string changes to the helical buckling configuration. Therefore, the tubular string may be in a sinusoidal or helical buckling state when the axial force satisfies 1:875\b\2 ffiffi ffi 2 p .…”

Post-buckling behaviour of a slender beam in a circular tube, under axial load

“…To illustrate the method a MATLAB program was elaborate and the following example was analyzed, [6,7,13] Figure 3 shows the dependence angle θ versus axial force, dependence found by the computer code. The Euler buckling force is 7.45 N (see figure 3a) and much higher force values were studied.…”

“…The problem is highly complicated because it involves a geometrical non-linearity to which the friction has to be added. Several theoretical models were proposed, all of them based on analytical models, some of them complicated, [1,2], or based on simplified (or even very simple) models using in general a variational approach, [3][4][5][6][7][8][9][10][11][12]. Experimental measurements were performed as well: some works are based only on experiments, [13,14], while in other works the experiments were meant to verify the theoretical models, [1,2,4,11,12].…”