L. Alfonso

Criteria for performance assessment and calibration of in-line inspections of oil and gas pipelines

Oil and gas pipeline operators routinely use magnetic flux leakage (MFL) and ultrasonic (UT) in-line inspection (ILI) to detect, locate and size metal losses caused by corrosion. As a preliminary step in fitness-for-service evaluations, the quality of the ILI is assessed through statistical comparison of the ILI data with data gathered in the field at dig sites. This work presents generalized criteria for the performance assessment and calibration of MFL and UT ILI tools from field measurements. The proposed criteria are capable of accounting for the measurement errors of both the ILI tool and the field instrument. The performance assessment of the ILI run is based on the determination of the minimum number of unsuccessful field verifications required to reject the ILI at a given significance level. The calibration of the ILI data uses new, simplified, error-in-variables methods to estimate the true size of the corrosion metal losses reported by the ILI tool. The proposed methodology also allows for determination of the errors associated with the estimation of the true defect depths. This information is of utmost importance in conducting reliability and risk assessments of pipelines based on either the probability distribution properties of the pipeline defect population, or the probability of failure of each individual defect in the pipeline. The proposed criteria are tested using Monte Carlo simulations and a real-life case study is presented to illustrate their application.

Markov Chain Models for the Stochastic Modeling of Pitting Corrosion

The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth) Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorovs forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorovs system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.

Statistical Analysis of Pitting Corrosion Field Data and Their Use for Realistic Reliability Estimations in Non-Piggable Pipeline Systems

The reliability and risk of non-piggable, corroding oil and gas pipelines can be estimated from historical failure data and through reliability models based on the assumed or measured number of corrosion defects and defect size distribution. In this work, an extensive field survey carried out in an upstream gathering pipeline system in Southern Mexico is presented. It has helped determine realistic values for the number of corrosion defects per kilometer (defect density) and obtain a better description of the corrosion defect size distributions in this system. To illustrate the impact that these new corrosion data can have on pipeline risk management, a reliability study is also presented where the field-gathered corrosion data have been used as input to a reliability framework for the estimation of the failure index of non-piggable pipelines and pipeline systems when different amounts of corrosion data are available.

Application of Extreme Value Statistics to the Prediction of Maximum Pit Depth in Non-Piggable, Buried Pipelines

Currently, the reliability of non-piggable pipelines is mainly assessed either from historical failure data or from the results of direct assessment evaluations. When external, localized corrosion is the main threat to the pipeline integrity, the most important factor in assessing the reliability of a pipeline segment is the distribution of maximum pit depths. This distribution cannot be directly derived from historical failure data, nor from the information obtained from external corrosion direct assessment. In contrast, the statistical modeling of extreme values could be used to predict the distribution of pit depth maxima in a pipeline from a relatively small number of maximum pit depths measured at excavation sites along its length. Despite of the large number of works aimed at the application of the extreme value statistics, there is a lack of studies devoted to the applicability of the method for prediction of the maximum pit depth for the pit densities and pit spatial patterns typical of long buried pipelines. In this work, Monte Carlo simulations were conducted in order to assess the statistical errors associated with the prediction of the maximum pit depth for a wide range of the number and size of the inspection areas, pits per unit area and pit spatial patterns. As a result, the optimum area of inspection is proposed. The Monte Carlo numerical experiments were run by using synthetic and real corrosion data acquired by magnetic flux leakage and ultrasonic in-line inspection (ILI) tools, an approach that has not been reported in previous studies. The ILI data was sampled using standard methods of extreme value analysis, and the predicted maximum pit depth was compared with that reported by the in-line inspection. Monte Carlo simulations with synthetic and real corrosion data have allowed assessing the influence of the number and size of the inspected areas on the accuracy of predictions when pits distribute homogeneously and non-homogeneously in the pipeline. It is shown that, when the distribution of pits is homogeneous, the accuracy in the maximum pit depth prediction using the proposed method is similar to the measurement errors associated with magnetic flux leakage ILI tools.Copyright

On the scaling of the distribution of daily price fluctuations in the Mexican financial market index

In this paper, a statistical analysis of log-return fluctuations of the IPC, the Mexican Stock Market Index is presented. A sample of daily data covering the period from 04/09/2000–04/09/2010 was analyzed, and fitted to different distributions. Tests of the goodness of fit were performed in order to quantitatively asses the quality of the estimation. Special attention was paid to the impact of the size of the sample on the estimated decay of the distributions tail. In this study a forceful rejection of normality was obtained. On the other hand, the null hypothesis that the log-fluctuations are fitted to a α-stable Levy distribution cannot be rejected at the 5% significance level.

On the Applicability of Extreme Value Statistics in the Prediction of Maximum Pit Depth in Heavily Corroded Non-Piggable Buried Pipelines

There exists a large number of works aimed at the application of Extreme Value Statistics to corrosion. However, there is a lack of studies devoted to the applicability of the Gumbel method to the prediction of maximum pitting-corrosion depth. This is especially true for works considering the typical pit densities and spatial patterns in long, underground pipelines. In the presence of spatial pit clustering, estimations could deteriorate, raising the need to increase the total inspection area in order to obtain the desired accuracy for the estimated maximum pit depth. In most practical situations, pit-depth samples collected along a pipeline belong to distinguishable groups, due to differences in corrosion environments. For example, it is quite probable that samples collected from the pipeline’s upper and lower external surfaces will differ and represent different pit populations. In that case, maximum pit-depth estimations should be made separately for these two quite different populations. Therefore, a good strategy to improve maximum pit-depth estimations is critically dependent upon a careful selection of the inspection area used for the extreme value analysis. The goal should be to obtain sampling sections that contain a pit population as homogenous as possible with regard to corrosion conditions. In this study, the aforementioned strategy is carefully tested by comparing extreme-value-oriented Monte Carlo simulations of maximum pit depth with the results of inline inspections. It was found that the variance to mean ratio, a measure of randomness, and the mean squared error of the maximum pit-depth estimations were considerably reduced, compared with the errors obtained for the entire pipeline area, when the inspection areas were selected based on corrosion-condition homogeneity.Copyright

A Monte Carlo Framework to Simulate Multicomponent Droplet Growth by Stochastic Coalescence

The accurate modeling of the interactions between aerosols and cloud droplets for a multicomponent system is a very difficult task in cloud modeling, since to express a variety of properties of the hydrometeors (such as the masses of water and soluble materials inside droplets) there is a need for multi-dimensional size distributions. The aerosol distribution becomes important as the cloud drops evaporate and the solutes are recycled into aerosols that can serve as cloud condensation nuclei (CCN): the larger the mass of a hygroscopic aerosol, the lower the supersaturation needed to form a cloud droplet. In the marine environment, the aerosol recycling process is believed to be the major mechanism responsible for the bimodal shape of the aerosol size distributions (Flossmann, 1994; Feingold and Kreidenweiss, 1996). The heterogeneous chemical reactions, which add nonvolatile solute to each cloud droplet, strongly depend on the salt content and pH of the droplet (Alfonso and Raga, 2004). Since aerosols also have a significant influence on cloud microphysics and cloud radiative properties, it is necessary to simulate aerosol processes realistically and with adequate accuracy. The usual approach adopted in detailed cloud microphysical modeling is to describe the aerosols and drops in two separate one-dimensional size distributions. Within this approach, only the average aerosol mass contained in drops of certain size is known, and it is not possible to accurately track the aerosol mass distribution within cloud droplets (Jacobson, 1999). For the deterministic case (based on the solution of the kinetic collection or stochastic collection equation), the aerosol processing due to collision-coalescence was addressed by Bott (2000) by extending his previous model (Bott, 1998) to two-dimensional distributions. Within this framework each particle is characterized both by the mass of its dry aerosol nucleus and by its water mass. By adopting this framework, there is no need to parameterize the activation process. Nevertheless, in real situations, there are several types of aerosols that act as CCN, and form an internal or an external mixture. Thus, the number of components of the system can be larger than two. The solution of the kinetic collection equation when the number of

On the Use of the Generalized Lambda Distribution and Parametric Bootstrap Method in the Prediction of Maximum Pit Depths: Comparison With Experimental Pipeline Data

The approach proposed by Najjar and coworkers for the prediction of maximum pit depth is applied and validated through direct comparison with real pipeline steel pitting corrosion data. This methodology combines the Generalized Lambda Distribution (GLD) and the Bootstrap Method (BM) in order to estimate both the maximum pit depth and confidence intervals associated with the estimation. Samples are drawn from real-life pitting corrosion data and the GLD is used to obtain modeled pit depth distributions emulating the experimental ones. In order to estimate the maximum pit depth over an N-times larger area, simulated distributions, N-times larger than the experimental ones, are generated 104 times. The deepest pit depth is extracted from each simulated bootstrap sample to obtain a dataset of 104 extreme pit-depth values. An estimate of the maximum pit depth for the N-times larger surface can be obtained from this dataset by calculating the average of the 104 extreme values. The uncertainty in the estimation is derived from the 95% confidence interval of the bootstrap estimate. In this report, the results of the application of the GLD-BM framework are compared with extreme pit depth values observed in real pitting corrosion data. The agreement between the estimated and actual maximum pit depths points to the applicability of the GLD-BM as an alternative in estimating the maximum pit depth when only a small number of samples are available. The main advantage of the combined methodology over the Gumbel method is its great simplicity, since fast and reliable estimations can be made with at least only two experimental samples.© 2010 ASME