Probabilistic estimation of remaining life of a pipeline in the presence of active corrosion defects

A methodology is presented for the assessment of remaining life of a pressurised pipeline containing active corrosion defects. A probabilistic approach is adopted to this methodology and the associated variables are represented by normal or non-normal probabilistic distributions. A failure pressure model based on fracture mechanics is adopted for the assessment of pipeline failure pressure and linear idealisation of the long-term corrosion growth rate is carried out. Because of the presence of nonlinearity in the limit state function and also of the presence of non-normal variables, the Level II advanced first order second moment iterative method is employed for carrying out reliability analyses. The methodology is applied to an example pipeline and the remaining useful life of this pipeline is assessed. Relative contribution of the random variables and the sensitivity of the reliability index to the change in variance of the random variables is also investigated.     

Effect of spatial correlation on the failure probability of pipelines under corrosion

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.     

System reliability of corroding pipelines

A methodology is presented in this paper to evaluate the time-dependent system reliability of a pipeline segment that contains multiple active corrosion defects and is subjected to stochastic internal pressure loading. The pipeline segment is modeled as a series system with three distinctive failure modes due to corrosion, namely small leak, large leak and rupture. The internal pressure is characterized as a simple discrete stochastic process that consists of a sequence of independent and identically distributed random variables each acting over a period of one year. The magnitude of a given sequence follows the annual maximum pressure distribution. The methodology is illustrated through a hypothetical example. Furthermore, the impact of the spatial variability of the pressure loading and pipe resistances associated with different defects on the system reliability is investigated. The analysis results suggest that the spatial variability of pipe properties has a negligible impact on the system reliability. On the other hand, the spatial variability of the internal pressure, initial defect sizes and defect growth rates can have a significant impact on the system reliability.     

Reliability estimation of pressurised pipelines subject to localised corrosion defects

This paper describes a probabilistic method for the assessment of the suitability of corroded pipelines under pressure loading. The method takes into account the uncertainties of the variables that influence suitability. The paper starts with a review of the various available techniques for the assessment of failure pressure of corroded pipelines and then develops a probabilistic limit state model from the available deterministic failure equations. The advanced first-order second moment method is then employed to estimate reliability. This approach is then applied to some typical examples. The results are presented in graphical form.     

Evaluation of the effect of corrosion defects on the structural integrity of X52 gas pipelines using the SINTAP procedure and notch theory

The notch stress intensity factor concept and the structural integrity assessment procedure for European industry (SINTAP) structural integrity procedure are used to assess gas pipeline integrity using deterministic and probabilistic methods. These pipes have external longitudinal semi-elliptical corrosion defects. Stress concentration at a defect tip is investigated via elastic–plastic finite element method analysis. The notch stress intensity concept is implemented into the SINTAP procedure and a notch-based failure assessment diagram is proposed. The safety factor and security factor are calculated through the SINTAP basic level.     

The relationship between load factors and failure probabilities determined from a full elastic-plastic probabilistic fracture mechanics analysis

The premise of assessing defects from an estimate of the failure probability, rather than from an estimate of the minimum load to cause failure, is discussed.A procedure is presented for incorporating a full elastic-plastic failure analysis into probabilistic fracture mechanics. This is based on the failure avoidance diagram developed by Milne et al.² and the probability of fracture for any assessment point on the diagram.Numerical examples are presented where failure probabilities are compared with the load factors necessary to elevate the assessment point onto the failure avoidance curve. Both absolute and time-dependent failure probabilities are considered. In general, constant load factors do not correspond to constant failure probabilities. The relationship between the two factors depends on the distribution of materials parameters used. General applications for the consideration of a probabilistic assessment of defects are discussed.     

Ultrasonic inspection for long defects in thick steel components

A model calculation is presented to demonstrate that very long defects should play a negligible role in the assessment of the failure of pressure vessels of pressurised water reactors. The calculations are of the probability that very long defects could remain in the vessel undetected if ultrasonic inspection of the vessel is undertaken with 45° shear-wave pulse-echo and Tandem techniques to a standard at least as good as achieved in the PISC round robin trials. The probability calculated is that of incorrectly accepting referable defects, and hence is relevant to probabilistic analysis of pressure vessel failure. It is, therefore, correctly more conservative than functions concerned with the capability of ultrasonic detection only, since the aim is to provide results which are pessimistic estimates of the failure frequency. A full probabilistic fracture mechanics assessment is not made since we show that the chance of incorrectly accepting a very long defect (12 mm × 80 mm) in a plate 219 mm thick would be about 10⁻⁴ or less provided an ultrasonic scan pitch of 10 mm or less is used and the estimate of ultrasonic reliability is taken to be that due to team-to-team variation. However, this value is believed to lie below that determined by other considerations, such as human error. We conclude that the chance of accepting unacceptable, very long, defects is limited by these other sources of error. Hence the contribution of very long defects to pressure vessel failure will be very small.     

Prediction of remaining strength of corroded pressurised pipelines

In this paper a deterministic model is developed which can be used to evaluate the remaining strength of corroded steel pipeline over time. This model also can be used to evaluate the maximum allowable failure pressure of corroded pipelines. The motivation for the development of the model is that during in-service conditions the strength of pressurised pipelines may be impaired, for example, from the failure of the protective coatings, paint surfaces or cathodic protection or as a result of externally applied mechanical damage or as a result of ageing (e.g. fatigue). Any of these may lead to the initiation of corrosion at the damaged area if it is not repaired. Once initiated, corrosion increases gradually both in extent and depth with increased exposure period. This results in the reduction of the remaining strength and hence a reduction in the carrying capacity of a pipeline. It also creates uncertainty about the future capacity. The proposed model is related to accepted methods for estimating the remaining strength of pipelines, but uses a simple corrosion model to estimate future remaining life. A sensitivity analysis can be used to investigate the effect of corrosion parameters on the pipeline carrying capacity. A simple example is given to illustrate the approach.     

A study on the reliability assessment methodology for pressure piping containing circumferential defects: I: computation method of failure probability of welded joint containing circumferential defects

When the reliability of a pressure piping needs to be assessed, every welded joint containing defects should first be analyzed. This paper describes a computational method of failure probability of a welded joint containing circumferential defects; the uncertainties of variables, relation of random variables and three possible failure modes of the pipe are considered. Then a new probability limit state model is set up, and the Monte-Carlo simulation method is employed to compute the failure probability of welded joint. In the end, a typical example of this approach is presented.     

Failure pressure analysis of hydrogen storage pipeline under low temperature and high pressure

Low temperature and high pressure line pipes are widely used in hydrogen storage, air separation plant, liquefied natural gas (LNG) transportation etc. The material properties of pipes at low temperature are different from those at room temperature. If the medium in the pipe is corrosive, it will cause the pipe wall thickness to decrease. However, the failure pressure of the corroded hydrogen storage pipeline at extremely low temperature is lacking of adequate understanding. In this paper, we provided a novel failure pressure equation of the mild steel line pipe with corrosion defects at extremely low temperature. Firstly, a mechanical model of the line pipe with corrosion defects is established. And then, an analytical solution of the mechanical model is obtained based on elastic theory. Next, a failure pressure equation of the corroded hydrogen storage pipeline at extremely low temperature is developed. In the end, the accuracy of the failure pressure equation is verified by comparing with finite element method (FEM). The results suggest that the calculated value of the failure pressure equation is consistent with that of FEM. This paper provides a theoretical basis for the safety assessment of low temperature hydrogen storage pipeline. The new equation presented in this paper can provide useful guidance for the design of low temperature and high pressure pipelines.     

A probabilistic structure life prediction system for container ship repair and inspection

A probabilistic fracture mechanics code has been developed to assess the impact of welding procedure, inspection frequency, and flaw detection/rejection criteria, on the reliability of butt weld joints in container ship deck doubler plates. A fatigue loading stress spectrum was developed based on statistical sea state data and a structural model of a ship. An initial flaw size distribution was developed from ultrasonic inspection results of deck doubler butt welds. Other random variables included fracture toughness and inspection detection of weld defects. Probability distributions of the input random variables were applied through Monte Carlo simulation to a deterministic fracture mechanics model for fatigue crack growth. This paper describes the development and application of the analysis program.     

On the application of probabilistic fracture mechanics to the reliability and inspection of pressure vessels

A probabilistic fracture mechanics model was developed to analyse the failure probability of a typical high power density reactor pressure vessel. The major causes for the nuclear reactor pressure vessel failure include fatigue, corrosion fatigue and brittle failure. All these causes are greatly affected by the stress loading conditions, material properties (aged by neutron damage), and defects embedded in the structure. Both an analytical first-order second-moment approximation and a hybrid methodology were employed in this study. In addition to the static scatter of the pre-existing cracks and material properties, a random walk model based on the operating history was introduced to represent the random occurrence of the abnormal transient stresses. The failure mode is defined as the brittle failure caused by a critical crack, meaning the stress intensity factor around a critical crack exceeding the fracture toughness of the pressure vessel material. Through a sample study on a typical high power density nuclear power plant, it was found that the vessel failure probability is about 4 × 10⁻⁴ at the 40th year of operation and the failure rate is in the order of 5 × 10⁻⁶ per vessel per year, which had reasonable agreement with the value of 10⁻⁴−10⁻⁶ as reported based on real-world statistics. In addition to the failure probability caused by fatigue crack growth, the reliability of a Low Temperature Overpressure incident was also evaluated.     

Risk assessment for pipelines with active defects based on artificial intelligence methods

The paper provides another insight into the pipeline risk assessment for in-service pressure piping containing defects. Beside of the traditional analytical approximation methods or sampling-based methods safety index and failure probability of pressure piping containing defects will be obtained based on a novel type of support vector machine developed in a minimax manner. The safety index or failure probability is carried out based on a binary classification approach. The procedure named classification reliability procedure, involving a link between artificial intelligence and reliability methods was developed as a user-friendly computer program in MATLAB language. To reveal the capacity of the proposed procedure two comparative numerical examples replicating a previous related work and predicting the failure probabilities of pressured pipeline with defects were presented.     

Prediction of the failure pressure for complex corrosion defects

A new method for predicting the failure pressure of corrosion defects in pipelines has been developed. The failure pressure of a plain pipe represents an upper limit for the failure pressure of a pipe with a corrosion defect. The failure pressure of a uniform depth, infinitely long groove, where the depth is equal to the maximum depth of the corrosion defect, represents a lower limit for the failure pressure of a pipe with a natural corrosion defect. The predicted failure pressure can be calculated from these limits using the weighted depth difference (WDD) method, which accounts for the defect geometry and any interaction with adjacent defects. The WDD method has been validated using the results of 40 burst tests of pipe sections containing real corrosion defects. The results indicate that this method provides more accurate burst pressure predictions than the currently accepted corrosion defect assessment procedures.     

Reliability simulation of solar concentrator receiver

The reliability of solar concentrator is investigated using finite element (FE) modelling. An FE model of the receiver absorber is built and simulated using latin hypercube sampling. A transient thermal structural simulation is conducted, and the maximum thermal stress affecting the absorber is determined. Based on the failure criterion, the most effective parameters are determined and assigned as random variables. A stochastic simulation is performed resulting in a probability density function (PDF) of the thermal stress-life. The PDF is used to estimate the reliability of the absorber. Different designs and materials of the absorber tubes are investigated. Consequently, methods to improve the reliability of the absorber are identified.     

Reliability of pipelines with corrosion defects

This paper aims at assessing the reliability of pipelines with corrosion defects subjected to internal pressure using the first-order reliability method (FORM). The limit-state function is defined based on the results of a series of small-scale experiments and three-dimensional non-linear finite element analysis of the burst pressure of intact and corroded pipelines. A sensitivity analysis is performed for different levels of corrosion damage to identify the influence of the various parameters in the probability of burst collapse of corroded and intact pipes. The Monte Carlo simulation method is used to assess the uncertainty of the estimates of the burst pressure of corroded pipelines. The results of the reliability, sensitivity and uncertainty analysis are compared with results obtained from codes currently used in practice.     

Methodology for improving the reliability of biomass energy potential estimation

This paper presents a novel approach to address uncertainty and improve reliability of the estimation of the biomass energy potential at a country level, particularly suitable for situations when quality and availability of data are limited. The proposed methodology improves the prediction reliability by following four steps: 1) using a simple accounting framework, 2) using a robust selection of probability density functions, 3) using a probabilistic propagation of uncertainty and 4) using sensitivity analysis to identify key variables contributing to uncertainty as well as a root cause analysis and a set of sub-models to improve estimation of key variables.The application of the methodology to the energy scenario in Colombia shows that the improved estimation of the theoretical energy potential has an almost identical mean value compared to the preliminary estimate, but the uncertainty is significantly lower (less than 50%). Moreover, the mean value of the technical energy potential obtained through the methodology is 25% lower than the preliminary potential and the uncertainty reduces by one third.     

Theoretical and experimental evaluation of the limit state of transit gas pipelines having corrosion defects

The limit carrying capacity of gas pipelines having corrosion defects were evaluated by means of an improved FEM analysis, together with the ANSI/ASME defect judgement and an experimental verification. When compared with our past presentation at the proceedings of the CAPE'93 Colloquium (dealing with reproduced defects), this paper evaluates the remaining lifetime of a pipeline having natural faults. The new improved analysis includes geometrical nonlinearities leading to a modification of limit state parameters and thus matching better with actuality. This presented work was initiated by the firm of Trans-Gas in Prague after having had a pipeline inspected proving some parts of it as being heavily corroded. The task in hand was to determine the remaining pipeline lifetime with the view to at least a two-year period.     

在役钢筋混凝土渡槽非概率时变可靠度分析

针对渡槽碳化概率可靠度分析需要大尺度的样本空间及统计变量特征难以获取等问题,基于区间模型非概率可靠度理论与混凝土碳化理论,提出了在役钢筋混凝土渡槽碳化的非概率时变可靠度计算方法,通过实例分析并与规范做比较,验证了计算模型的正确性。分别采用所提计算方法和Monte-Carlo概率可靠度法对既有渡槽结构进行可靠度计算。结果表明,非概率可靠度指标计算值较概率可靠度指标计算值小,该方法会使渡槽结构留有一定的冗余度;所提计算模型能简便有效地对渡槽结构做出碳化耐久性分析,弥补了概率可靠度分析的不足,研究结果对工程实践具有一定的指导意义。     

The determination of cost-effective NDE inspection schedules for structures containing defects based on probabilistic fracture mechanics

Modern fracture mechanics analysis techniques can confidently estimate critical defect sizes, but due to certain parameters, such as defect size and occurrences, material properties, as well as loading, being statistically distributed, a probabilistic approach must often be adopted. A robust analytical method has been developed, which incorporates two-dimensional defect size distributions, detection probabilities, elastic-plastic critical defect size estimations, as well as fatigue crack growth analysis, to estimate the probability of fracture failure of structures containing defects. It is argued that the probability of failure as an output of an integrity assessment is directly relatable to cost factors and based on this relationship, a powerful procedure is presented to establish cost-effective fracture control meaures such as inspection schedules. The procedure is based on the premise that the probability of failure multiplied by the cost of failure yields a cost, termed the probable cost of failure, which gives an indication of how much money should be spent on fracture control. A cost-effective fracture control measure is then defined as a measure which would cost less to implement than the amount of money saved in probable failure expenses due to the introduction of the measure. The application of this principle is illustrated with a case study.