External corrosion pitting depth prediction using Bayesian spectral analysis on bare oil and gas pipelines

https://doi.org/10.1016/j.ijpvp.2020.104224Get rights and content

Highlights

  • Environmental and soil factors are used to predict the external corrosion pit depth.

  • The effects of continuous factors is represented as nonlinear penalized splines.

  • A sensitivity analysis reveals the relative contribution of the considered factors.

  • The pit depth evolution over time can be represented as a bimodal process.

  • The final additive model performance is high.

Abstract

Corrosion of buried pipes is complex and difficult to model without considering corrosiveness of the soil. To estimate the external corrosion of buried and aged oil and gas pipelines, a Bayesian spectral analysis regression is proposed. The depth of the corrosion pit progression on a bare metallic pipe is linked to the soil factors that are assumed to influence its rate. The time the pipe is exposed to these factors and the annual precipitations are added to the selected soil influencing factors. The relationship between the identified factors (covariates) and the depth of the corrosion pit (response variable) is expressed as a semiparametric. Thus, the complex electrochemical process of corrosion is represented mathematically. The proposed approach is applied to the data published online by the National Institute of Standard and Technology in the US. The results allow a better quantification of the uncertainty in the predictions for each factor and an improvement in the performance of statistical prediction models of external depth of the corrosion pit.

Introduction

Oil and gas pipelines are expected to function reliably and provide continuous service. However, the pipelines are exposed to various environmental and operational deleterious factors that may compromise their integrity [1], [2], [3], [4]. External corrosion is the main contributing factor to leakage [5], [6]. In Canada, from 2008 to 2019, the National Energy Board registered 1,305 oil and gas pipelines incidents among which 177 were due to corrosion [7]. Localized corrosion (mainly the pitting corrosion) is critical and challenging to be detected [8], [9]. Furthermore, pitting corrosion can lead to more severe corrosion modes, such as stress corrosion cracking, fatigue corrosion and intergranular corrosion [10].

A summary of the different factors affecting the corrosion process are summarized in Table 1. Castaneda [1] listed 8 soil factors including the type of soil, the water content, the degree of aeration, the pH, the redox potential, the soil resistivity, the salt contents (e.g. sulfates, chlorides) and the microbiological activities as the most influential factors impacting the corrosivity of the soil on metallic pipes. Xie [11] analyzed the effect of the sulfate reduction bacteria on the appearance and the development of stress cracking corrosion on X80 pipelines. These critical soil factors are incorporated into external corrosion model to characterize the position and the rate of the loss of the metal.

In general, environmental factors are not always available to allow a better representation of their effect on the soil corrosivity. Furthermore, the way they affect the soil corrosivity is complex and not explicitly known. Bare pipelines and those where the mitigation strategies have failed are the most affected by the environmental soil conditions.

Corrosion control strategies extend the useful life of the pipeline but cannot prevent the occurrence of external localized corrosion [14]. The useful life of the pipelines is affected when the mitigation strategies fails (e.g. coating disbandment) and the pipeline is in direct contact with aggressive environment [3], [6]. External corrosion models for oil and gas pipelines have become important tools in the implementation of the current preventative technologies (passive and active protections) and are used to support analyses of the information acquired from each survey or inspection [15]. The occurrence of new localized corrosion pitting is stochastic in nature and difficult to replicate using mathematical formulations. In practice, more attention is given to study the growth of existing localized corrosion rather than the initiation of new ones [5].

Several studies modeled localized corrosion as a time dependent stochastic damage process [4], [6], [16], [17], [18]. Deterministic models considered include single value corrosion rate [9], linear corrosion rate [19] and nonlinear corrosion rate [20]. These approaches do not consider the stochastic nature of the corrosion nor the soil factors that can affect the corrosion rate. On the probabilistic side, the power law function defined as a function of time was proposed by Romanoff [12] and fundamental contribution to understand corrosion of pipes. The exponent is assumed to be positive and less than one. A summary of the different depth of the corrosion pit modeling is given in Table 2. In these models, the power law approach is conserved as basic modeling approach with the addition of the soil factors to account for the corrosion environment.

Soil factors have been proposed to be included in the depth of the corrosion pit by Mughabghab and Sullivan [21]. Inspired by Romanoff [12], Some other studies included two multilinear regressions for the coefficient and the exponent in the power law formulation [6], [17], [21], [23]. In addition, they proposed to include the initiation time of the localized corrosion. Melchers et al. [15] reported a multiphase phenomenological model describing the behavior of the pitting with regards to the time covariate. Norahzilan et al. [22] expressed the relationships between the soil factors (e.g. moisture content, clay content and plasticity index) and the corrosion rate as a linear regression. Ricker et al. [3] used the NIST data and applied a linear regression to evaluate the effect of corrosion on metallic pipes pitting. Caleyo et al. [24] proposed a Bayesian methodology for the analysis of external corrosion data. Their model included also the detection and measurement errors. Wang et al. [4] addressed the spatial correlation of the external corrosion by introducing a hidden Markov random field model that consider the soil properties and the location of defects provided by inline inspections. Evolution of the deterioration shows importance of the power law approach. In addition, the soil variables were assumed to have a log-linear or simply a linear dependence with the maximum pit depth that is simplistic and may not capture complexity of the physical process. Melchers and Petterson [25] reanalyzed the data presented in Romanoff’s report at the National Bureau of Standard and they proposed bimodal approach. They showed that the power law and the linear function are not consistent with the data.

In developing the predictive model, an unsupervised approach is required to learn from data without fixing a general equation term as in power law or linear function. In addition, it is important to consider the stochastic nature of the pit growth through a Bayesian perspective. Several approaches are used to compute the coefficients in a semi-parametric equation, e.g. direct maximization of the likelihood function [26], iterative re-weighted least squares [27] and support vector machines coupled with the optimization of hyperparameters [28]. Chinedu [29] used blackbox regression based on parametric subspace clustering to account for the nonlinear relationship between the defect depth and the operational factors. The confidence bands for the non-parametric parts are indirectly analyzed through the standard error produced by the variance–covariance matrix and the parametric terms are estimated through hypothesis test. This procedure is expensive and could lead to large errors if not much data is recorded for a regressors in the additive model. The Bayesian spectral analysis allows the estimation of the posteriors with increased accuracy and reduced computational effort. The Bayesian spectral analysis model using Gaussian priors aims at developing semi-parametric models with Bayesian shape-restricted function estimation for generalized additive models that can handle the monotonicity, convexity, S-shaped and the U-shaped functions [30], [31].

This study proposes a new Bayesian spectral analysis regression (BSAR) model to evaluate the depth of the corrosion pitting on bare pipelines buried in soil of known characteristics. The BSAR allows a semi-parametric representation of the relationship between the soil factors and the depth of the corrosion pitting. The nonlinear functions are included in the model to capture the nonlinear relationship between the soil factors and the corrosion pit depth. Moreover, the additive property of the BSAR allows to build individual accurate predictive models that are summed to build the final prediction (in this case the corrosion pith depth). The result is examined using the coefficient of determination and the Root mean square error. The comparison of these performance tools between the proposed approach and the approach presented in Velasquez shows significant improvement.

Section snippets

Proposed framework

The proposed methodology starts with data collection and processing (see Fig. 1). Data analysis is performed in order to decide on the missing information. All entries with missing information are removed from the database and the covariates are classified into categorical (discrete) and continuous variables. The complexity of the influence of the selected factors on the pit depth growth is captured by allowing the continuous covariates to have a nonlinear effect to the response depth of the

Results and discussion

From the characteristics of the soil (Table 1) at each burial site and the observed depth of the corrosion pitting, the BSAR is developed for assessment of the depth of the corrosion pit. For each function fk defined in Eq. (2), the restriction in the shape is defined as free. The BSAR parameters (e.g. the number of basis functions and hyperparameters) are iteratively turned on to enhance the predictions output and maximize the correlation between the prediction and the observations.

Factors

Conclusion

Localized external corrosion in oil and gas pipelines is a major cause of the loss of confinement that have been reported over the last decades. Different types of deterioration models exist and the most promising are the statistical models that consider the cause–effect relationship between the environment where the pipelines is buried and the pipeline wall thickness. This study improves the prediction of external corrosion pit depth through nonlinear representation of individual effects of

CRediT authorship contribution statement

Ngandu Balekelayi: Conceptualization, Methodology, Investigation, Formal analysis, Writing - original draft. Solomon Tesfamariam: Supervision, Conceptualization, Resources, Funding acquisition, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors acknowledge the financial support through The BC Oil and Gas Research and Innovation Society (BC OGRIS) and MITACS .

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