Bending Torque and Strain Energy in Reeling Coiled Tubing

Abstract

Summary In this paper, formulas for determining torque and strain energy in reeling coiled tubing are derived. The general formula for calculating torque is simplified by using fully plastic deformation replacing elastoplastic deformation. The simplified torque is within 0.25% relative error as compared to the torque formula obtained by using elastoplastic assumption. Most of the strain energy in reeling coiled tubing is dissipated (converted into heat). Only a small part of the total strain energy is recovered. The recovered energy is the elastic energy that is stored during reeling. The stored elastic energy typically accounts for 5% to 15% of the total strain energy in reeling, depending upon tubing and spool sizes as well as tubing material mechanical properties. Introduction Coiled tubing (CT) is a technology that is attracting a lot of attention in the oil and gas industry. Coiled tubing is a high strength, low alloy carbon steel (Young's modulus ~ 29,000,000 psi and yield strength ~ 70,000 - 90,000 psi) tubular product manufactured in a continuous string, typically extending 3,000 to 25,000 feet in length. Traditionally, operators used pipes averaging 30 feet in length joined together section by section and supported by a derrick to service wells. With CT, a continuous length of tubing wrapped in a spool with core diameter of 240 inches or less is reeled in and out of wells like fishing line. While the average diameter of conventional drill pipe ranges from 1.625 inch to 6.625 inch. coiled tubing can be manufactured in sizes from 1 inch to 6.625 inch in diameter with wall thickness from 0.080 inch to 0.30 inch. Because of the economic advantage and operational efficiency as compared to conventional technology, CT has gained wider acceptance in the oil and gas industry.1 Coiled tubing is manufactured in a tube mill from flat steel strip (typically 3,000 feet in length) that is rolled and welded by high frequency induction without the addition of filler metal. Coiled tubing as long as desired by users can be made by welding length of pre-inspected flat strip together prior to forming the tube in the mill. The string undergoes extensive radiographic and electromagnetic examination in both the tube and strip form. The stress induced by the mechanical deformation in the forming process is relived using an in-line full-body induction heat treatment on the mill. Sometimes tapered strings of CT (constant OD with varying wall thickness) are manufactured in order to increase the optimal performance while minimizing the total weight of the string. After the tubing is milled, it is reeled onto a spool, and hydraulically tested before it is shipped for use. Coiled tubing is now increasingly used in the oil and gas industry. Safety and reliability are the major concerns for the coiled tubing operators. There are many factors that determine the life of a given CT: corrosion; flexural bending; internal (or external) pressure and tension (or compression); and mechanical damage due to improper use. While fatigue, collapse, and buckling problems are well studied2, the basic mechanical properties such as bending torque and strain energy are less documented. The understanding of the bending torque is important in choosing the spool sizes as well as reeling motors. The understanding of the strain energy, especially the recoverable elastic energy, is important for safety in using coiled tubing. In this paper, we derive formulas for determining bending torque and strain energy in reeling coiled tubing. Our calculations show that the plastic bending moment accounts more than 99% of the total bending torque in reeling coiled tubing. The elastic bending moment is less than 1 % of the total bending torque. Thus, one can safely treat the bending of coiled tubing in a typical core or guide arch as perfectly plastic deformation. Most of the strain energy in reeling coiled tubing is dissipated, but the stored elastic energy is significant, constituting about 10% or so of the total strain energy, depending on the tubing sizes, core or guide arch dimensions, and mechanical properties.

Research on the Analysis of Coiled Tubing Fatigue Life

“…Cross section stress distributes [3]. Under the actions of a tension bending combination, the cross section mechanics model of coiled tubing on the reel for calculating the moment and axial force is established by using elastic-plastic mechanics method.…”