Effect of spatial correlation on the failure probability of pipelines under corrosion David De Leon * , Oscar Flores Macı ´as Instituto Mexicano Del Petro ´leo, Eje Central No. 152, D.F., Me ´xico Received 4 January 2003; revised 5 July 2004; accepted 6 July 2004 Abstract Corrosion in pipelines has been probabilistically modeled. However, the potential effect of spatial correlation of corrosion defects, in several segments of a pipeline, on its failure probability has not received much attention. In this paper, several degrees of spatial correlation are assumed for the corrosion in determined segments of a pipeline and their effects on the global reliability are examined. The pipeline is assumed to be a series system. The failure mode is considered to be controlled by the stresses due to internal pressure and the presence of corrosion. Component reliability is calculated by First Order Second Moment approximations. First order bounds are used to define the limits for the global failure probability by assuming first, either no correlation (independent pipeline segments) and, secondly, perfect correlation between segments. Then, second order bounds are estimated to improve the calculation of the failure probability by including the correlation coefficients mentioned above. The correlation degree between failure modes at two pipeline segments increases with the degree of correlation of the corrosion initial depths located at these segments. Also, for a correlation coefficient between corrosion depths larger than 0.6, its contribution to the correlation between failure modes becomes significant and, therefore, should be accounted for. When the specific correlation degree between corrosion defects at adjacent pipeline segments is considered in the calculation of an example pipeline failure probability, this probability is narrowly bounded between 0.58 and 0.59, as compared to the usual practice where this correlation is assumed to be either 0 or 1 for which the failure probability is bounded between 0.49 and 0.79. The formulation may be used to set optimal maintenance schedules for pipelines under corrosion. q 2004 Elsevier Ltd. All rights reserved. Keywords: Spatial correlation; Corrosion; Probability of failure; Monte Carlo simulation; Pipeline reliability 1. Introduction The use of pipelines is, to some extent, the most economical way to transport hydrocarbons. In Mexico, there are 55,000 km of land gas and oil pipelines. Pipeline managers require assessments of integrity and safety in order to make appropriate decisions regarding the allocation of funds for maintenance and operation. Limited resources require rational and sound criteria for realistic assessment directed towards their best utilization. Over time, this assessment is resorting more to the use of structural reliability techniques [1–4]. Pipelines, as other structures, deteriorate over time. In particular, an important failure or damage mode in steel pipelines is corrosion. For this reason, a careful analysis with suitable models should be exercised to understand and prevent or control the mechanism of corrosion damage in a pipeline [5]. Corrosion effects have been included in the reliability analysis of steel structural components [6]. The corresponding evaluations in the literature do not include, so far, the effect of several pipeline segments, and the feasible correlation of the spatial occurrence of corrosion defects over several segments of the whole pipeline. 0308-0161/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2004.07.018 International Journal of Pressure Vessels and Piping 82 (2005) 123–128 www.elsevier.com/locate/ijpvp * Corresponding author. Address: Col. Copilco-Universidad, Copilco 300, Bldg. 9, apt. 4, Del. Coyoacan 04360, Mexico. Tel.: C52-9175-7868; fax: C52-9175-7864. E-mail address: dleon@imp.mx (D. De Leon).