With the evolution of long, deep and hot wells, the design margins have become very small. This motivated the presented study and prompted the investigation for a precise well design model for burst and collapse. Although most well designs are based on one- and two-dimensional mechanics, more recent design packages include a three-dimensional version as well. It will be shown that these models are accurate only for certain conditions.

This paper presents an exact solution to the three-dimensional well design problem. Field examples demonstrate the accuracy of the new and conventional design models. The new model calculates design factors that are exact, thereby offering a tool for optimized well design. The presented theory is based on the von Mises yield criterion and the Lamé thick-walled solution for the pipe.


There are a wide variety of models and techniques available to estimate burst and collapse pressures of pipe used for drilling, completion and well intervention. The results obtained using the different methods are not always easy to compare since the underlying theory differs. In this study we present a threedimensional (3D) model that is exact.

The early approach was to simplify the design equations for burst and collapse by neglecting the effects of radial stress and axial load. This is called uniaxial well design. Radial stress is usually small compared to hoop stress in tubulars with high pressure-differentials and it is always compressive. Neglecting axial load, on the other hand, could introduce large errors in the design.

For burst calculations, the uniaxial Barlow equation1 is still quite popular because of its simplicity. This equation is derived assuming a thin-walled pipe with zero outside pressure. The pipe will burst when the hoop stress reaches the yield strength. The major shortcoming of the Barlow formula is the omission of axial load effects. For a pipe without axial loads, the equation is fairly accurate for large diameter to thickness ratios. It works well for a casing string, but is in error for small-diameter pipes.

By neglecting radial pipe stress, a two-dimensional (2D) load diagram results with the shape of an ellipse. Studying this, one observes that axial tension lowers the pipe collapse resistance and axial compression makes the pipe weak in burst. Reversing the conditions, the opposite is true. In the biaxial approach, the axial effects are honored while the less important radial stress is neglected. Biaxial stress analysis of well tubulars is an improvement compared to uniaxial theory.

Triaxial Design

Well tubulars may be subjected to a variety of loads during installation and service. Tensile and compressive axial stresses are produced by axial loads and bending of the pipe. Pressure inside and outside of the tubular gives rise to radial and hoop stresses. Pipe may also experience shear stresses if torque is applied. In this paper we consider axial loads and pressure effects only. Tensile stress is positive and a negative sign indicates compression throughout the paper.

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