New insights for chemical-physical processes from analysis of observations using extreme value probability distributions

Abstract

Conventional extreme value (EV) theory has the Gumbel EV distribution as the theoretically correct distribution to represent the maximum depth of corrosion pits. It has long been used for prediction of the probability of leaks or major content losses in oil and gas and other pipelines subject to internal or external corrosion or both. This history is based largely on limited numbers of data, often laboratory data. Recent availability of very extensive field data, gathered in real-life long-term applications such as 'intelligent' pigging of pipelines shows much more complex statistics, not easily reconciled with classical theory. The paper shows that, properly interpreted, these data can be interpreted as consistent with the development of pit depth as a function changing of exposure period. Together with improved understanding of the interaction between physical-chemical processes and pit depth statistics the data also show that that pitting corrosion develops in a renewal process. This is not generally recognized in the corrosion literature and may account for the sometimes very large statistical uncertainty. Examples drawn from actual pipeline pigging data and from other sources are used to illustrate these points and to indicate the importance of understanding the physical phenomena for the practical prediction of the probability of exceedance. Some recent new developments for interpreting pit depth experimental data also are presented, indicating that the use of probability theory can have wider implications.