An alternative to the standard graphical presentation of CT operating limits is proposed in this paper to facilitate design of CT well interventions and to guide operational decisions in critical, at-risk procedures. Typical issues in intervention design include maximum safe overpull and maximum safe circulating and annular fluid pressures and the interplay between these parameters. However, CT job designers are sometimes unfamiliar with the interrelation between tension and fluid pressures. In particular, the relationship between surface weight and actual tubing stress is often overlooked. This interrelation can be explained and interpreted via the concepts of effective and real force. Based on a presentation of effective and real force, this paper proposes a graphical presentation of CT limits which references effective force, specifically surface weight. Using this modified stress graph, safe operating limits can be more clearly inferred from actual job parameters such as surface weight and pressure.


Yield, burst, and collapse limits for tubing and pipe have been subject to systematic theoretical analysis and empirical testing, which has resulted in a thorough understanding of many key operational parameters.1–5However, extensive availability of models and tools for limits evaluation and monitoring within the CT industry has not always translated into correct job design and execution in the field. There remains a need to unite theoretical concepts and tools within a more cohesive, simplified overall framework which can be easily applied in the field.

Practical issues may complicate application of theoretical results to real field situations. The field engineer in almost all real applications has access to only one force parameter, namely surface weight. Real-time data acquisition usually tracks CT operations at surface, where weight and pressure data are available. Although surface weight readings are often referenced to the traditional biaxial stress ellipse, weight and the axial force of the true stress state are distinct. Confusion sometimes arises regarding closed-ended and open-ended CT configurations. In general the inter-relationship between fluid pressures and tubing forces is not always obvious. These types of issues can be explained and resolved by correct interpretation of effective and real force results. In this paper an approach to CT limits is proposed in which surface weight is easily applied to the tubing limits problem. An interesting result is that surface turns out to be effective force.

Review of CT Limits Analysis

The most commonly accepted yield criterion in the CT industry for evaluating tubing limits is based on the distortion energy theory of failure, often referred to as the Von Mises yield criterion.1 To apply the Von Mises yield criterion, the three stress components, sa- axial stress, sr- radial stress, and sh- hoop stress, are incorporated into a single combined equivalent stress, sVM:

  • Equation 1

The basic equation for the Von Mises yield criterion may be modified to account for additional effects. When torque is applied to the tubing, the Von Mises yield criterion is modified to account for a torsional stress t. If tubing stiffness is included as provided by a stiff-string forces model, then an internal transverse shear stress term may be included. As a result the combined stress becomes:6

  • Equation 2


  • Equation 3


  • Equation 4

for torque T, normal wellbore contact for Fn, and external and internal cross-sectional areas A0and Ai.

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