Summary
This paper reviews the state-of-the-art in casing/tubing structural reliability analysis, and the knowledge gained from it to date. Results are presented to show that, as previously suspected, burst design based on casing full of gas is over-conservative for noncritical wells. However, the risk-calibrated design criteria are strongly dependent on the design philosophy for underground blowout loads. It is demonstrated that well control is the largest single factor in reducing risk; gaps in current knowledge are identified, and recommendations made for future work.
Introduction
Quantitative risk analysis (QRA) of well casing/tubing systems has undergone rapid development in recent years. The more notable projects have included a risk comparison of steel and corrosion-resistant alloy completions;1 methodology and software development, including a pilot study;2 a design code calibration using working stress design;3,4 application of QRA methods to casing seat selection;5 development of reliability-based design criteria for HPHT wells;6 a design code calibration using load and resistance factor design (LRFD);7,8 and preparation of improved design equations for casing collapse.9
The first stage of development of the subject is largely complete, in that the analysis models and software tools are now reasonably mature, and initial results are available. A review of these results shows that QRA has, as hoped, given answers to many of the important questions remaining in the subject, such as cost benefit and the appropriate selection of design criteria. Equally, however, it has raised other questions that should have been asked at the beginning.
This paper is written from the fortunate position of being, at long last, wise with hindsight. It reviews:The state-of-the-art in well system QRA modeling.The knowledge gained from it to date.The questions which still need to be addressed.The development required to gain this knowledge.
The authors emphasise that, while a consensus is developing in many areas of the subject, the views expressed are theirs alone. They are largely based on in-house work carried out at WS Atkins during 1995-1997.
Well System QRA Models: The State of the Art
Risk Analysis and Structural Reliability.
"Quantitative risk analysis" has been used with different meanings by past authors, and it may be helpful to define exactly what is meant. Safety engineering (or risk analysis) answers the question "what is the total risk in the operation of the facility?" As such, it generally considers all the possible risks to the asset and its personnel (e.g., travel to and from the platform, equipment failure, operational errors, etc.), as determined by a hazard identification exercise.
The traditional approach is for the risk to be calculated using historical incidence data for each risk type, suitably adjusted for the given facility (e.g., number of wells, frequency of helicopter landings). The various risks, and the consequences of each risk event, are then combined to establish the total potential risk to life, risk to the asset, and so on. This process is called quantified risk assessment. Note this technique generally will not consider the effect of changes in design criteria, because it uses historical failure rate data.
Structural reliability can either answer the question "what should the design criteria be?," or establish the probability of failure of an existing design. It therefore only considers the risk of structural failure, which is usually a very small part of the whole. The risk is calculated by mapping the probability distribution functions (PDFs) of the various load and resistance variables to the predicted failure probability, using the ultimate limit state equations and mathematical techniques such as first/second order reliability method (FORM/SORM) or advanced Monte Carlo. A description of these techniques is beyond the scope of this paper, and the interested reader is referred to the literature.10–12
While the term QRA has been used to describe either technique, in this paper it primarily refers to structural reliability. However, recent work in structural reliability has highlighted the importance of mechanical reliability and human error risks,13 which are traditionally the preserve of safety engineers; and it is hoped that future work will address these wider issues.
Analysis Methods.
This section describes the various steps in a casing/tubing QRA. A consensus is developing in many areas, such as in the use of either FORM/SORM or advanced Monte Carlo to perform the probabilistic mappings. Where no consensus exists, the authors have described best current practice. While the treatment has been kept as simple as possible, some technical detail is unavoidable, and the reader interested primarily in the lessons learned may prefer to move directly to the next section.
Input Variables.
Field or test data is collected for each input variable, and the PDF type determined by plotting the raw frequency distributions onto probability scales. 10,12 The PDF parameters are then calculated,14 including sampling uncertainty if required.15,16
Load and Resistance ULS Equations.
The equations for the load and resistance ultimate limit states ("ULS equations") are chosen by comparison of predictions from the various candidate equations against field or full-scale test data (as applicable), for a statistically significant number of cases. In general, even the best predictive equation suffers from either mean point bias or underestimation of the output COV, or both. This is usually accounted for by treating the model uncertainty as a postmultiplicative random variable, whose PDF type and parameters are calculated during ULS equation selection.10,12
