Wells are becoming more challenging and casing designers are faced with increasing design pressures. Deep hydrocarbon targets lead to requirements for the casing to resist collapse under external pressure while significant internal pressure and axial compression or tension may exist at the same time.

This paper describes the development, and its evaluation, of a new collapse strength equation for oil country tubular goods (OCTG). It is based on a generalization of a model previously proposed by Tamano et al.1. The new model is evaluated through comparisons with both finite element analyses and test data. It is more accurate in dealing with combined internal pressure, external pressure and axial load than, for example, the model currently provided in API Bulletin 5C32.

The joint API/ISO SC5 Work Group 2B tasked with modernizing the API 5C3 property equations has evaluated a number of collapse models available in the literature on their performance against several different collapse databases. As a result the model presented here is recommended for developing collapse ratings in the new ISO 10400 standard.


The design collapse strength equations currently used in the industry and provided in API Bulletin 5C32 give a highly non-uniform failure probability over diameter, weight and grade for downhole well tubulars3. In addition, the API 5C3 average collapse strength equations are relatively poor predictors of true collapse and hence no compelling case exists to use these equations for qualifying high collapse pipe and other proprietary products. Furthermore, designing deep wells is becoming more challenging due to requirements for the casing to resist collapse under external pressure while significant internal pressure and axial compression or tension may exist at the same time. This highlighted the need for revisiting the method to account for combined loading in collapse.

The situation may be improved if more accurate collapse prediction formulas could be developed that capture adequately the physics of collapse failure, and include more explicitly the effect of imperfections. Because the collapse failure mechanism is an instability phenomenon - i.e. the transition from an essentially round pipe to a pipe that starts to ovalize and flatten with the external pressure capacity reaching a maximum can happen very quickly - it is not feasible to expect a simple equation to capture this failure mechanism very accurately. However, theoretical analyses, detailed finite-element analyses and numerous collapse tests have provided a wealth of insight that has guided the development of approximate collapse equations that capture collapse failure to a satisfactory degree.

Like other currently available models the model presented in this paper consists of a number of interlinked concepts:

  1. An equation for elastic collapse of a perfect pipe, relevant for very thin pipe

  2. An equation for through-wall yield collapse of a perfect pipe, relevant for very thick pipe

  3. An equation providing a transition between elastic collapse and yield collapse, thus predicting the collapse strength for all relevant pipe sizes, weights and grades.

  4. Factors to incorporate the effect of imperfections such as ovality, stress-strain curve shape, residual stress and eccentricity

An additional objective of this paper is to address the effect of combined loading. API 5C3 describes a conservative method to account for axial load and internal pressure, focused on use with its lower bound design strength equations. However, deriving risk-based collapse ratings require an Ultimate Limit State (ULS) model that more accurately predicts the actual (50-percentile) collapse strength. In particular for heavy-walled pipe, the effect of internal pressure on collapse derived from first principles shows interesting differences with the API 5C3 formulation. For very deep wells the new approach to combined loading can have significant economic implications.

In the following sections, firstly collapse of ideal pipe is addressed, providing formulas for elastic collapse and yield collapse under combined loading (section 2). The new general formula predicting collapse for all relevant pipe sizes, weights and grades and including the effect of imperfections is presented in section 3. Section 4 provides additional observations about the new equation and compares it with some well-known existing equations. Section 5 addresses its performance against finite-element analyses and tests. The paper ends with a number of conclusions.

This content is only available via PDF.
You can access this article if you purchase or spend a download.