Elsevier

Ocean Engineering

Volume 226, 15 April 2021, 108852
Ocean Engineering

Microbiologically influenced corrosion (MIC) management using Bayesian inference

https://doi.org/10.1016/j.oceaneng.2021.108852Get rights and content

Highlights

  • A new microbiologically influenced corrosion management (MIC) methodology is presented.

  • The methodology built using Continuous Bayesian Network technique with Hierarchical Bayesian Analysis.

  • The methodology provides the precise failure probability and MIC rate.

  • The application of the methodology is demonstrated on a subsea pipeline.

Abstract

Microbiologically influenced corrosion (MIC) is a complex phenomenon that occurs when a microbial community is involved in the degradation of an asset (e.g. pipelines). It is widely recognized as a significant cause of hazardous hydrocarbon release and subsequently, fires, explosions, and economic and environmental impacts. This paper presents a new MIC management methodology. The proposed methodology assists in accurately monitoring MIC activity and accordingly develop strategies to manage it. The MIC monitoring and management activities are achieved using Continuous Bayesian Network (CBN) technique with Hierarchical Bayesian Analysis (HBA). The integration of HBA and CBN helps overcome the Bayesian network's discrete value limitations (BN) and source-to-source uncertainty for each node in the network. The methodology can provide the precise value of parameters, such as failure probability and MIC occurrence rate which are verified using observed data. The application of the methodology is demonstrated on a subsea pipeline. The study provides a better understanding of the influencing factors of MIC rate and failure probability. This assists in developing effective MIC management strategies.

Introduction

Microbiologically influenced corrosion (MIC), also known as biocorrosion, is a significant threat to asset integrity in most industries especially in oil and gas industrial sectors (Taleb-Berrouane et al., 2018; Technol and Gu, 2012; Xu et al., 2016). Because of their activities based on metabolites MIC is caused by microbial biofilms, where their activities reflect in reservoir souring and asset deterioration (Gu et al., 2019; Ibrahim et al., 2018). As industrial assets age, MIC becomes a common risk factor leading to an accident (e.g. fluid flooding, leakage, rupture, etc). Besides, MIC has been extensively reported as annually causing the loss of billions of dollars in the US (Walsh et al., 1993). MIC has been attributed to approximately 10% of corrosion cases in the UK (Romero et al., 2000), the largest, Prudhoe Bay's oil spill occurred due to MIC in 2006 (Ibrahim et al., 2018), and Alaskan pipeline leakage was caused by microbial activities.

Staying with the aforementioned introduction, performing MIC management is therefore vital, whereby operators can use quantitative, semi-quantitative, and qualitative models to support decision making to manage corrosion. MIC management, underlying the idea of corrosion management approaches, should employ the key factors of recently introduced corrosion management systems (CMS) (Morshed, 2011) to make sure that all required MIC preventives, control and mitigative actions are performed in a sustainable, well-established, and effective manner (Lund et al., 2017; Skovhus et al., 2018). Three main steps need to be considered in any corrosion management approach: (i) understanding the MIC threat mechanism and how it affects the assets, (ii) recognizing and performing an appropriate management practice, and (iii) monitoring the management practices to examine whether the practices are effective or need further modifications (Lund et al., 2017; Skovhus et al., 2016). These steps are taken into account based on CMS procedures on a daily, weekly, monthly, and annual basis. Thus, corrosion management in general, and MIC specifically, can be viewed as a supporting program, in which management practice is presented and facilitated. It should be highlighted that MIC management in an ongoing and continuous process since MIC is known as an asset integrity threat, which further increases the operational risk. Therefore, MIC management has to follow the ISO 31000 (“ISO 31000: Risk Management,” 2009) framework on risk management.

There are a considerable number of corrosion management programs based on the reliability/availability of assets proposed by both the academic and industrial sectors over the past few decades. These management programs are typically categorized into different classes, namely: (i) calculating the failure probability of asset (pipeline) over a period (before and after launching in-line inspection and cleaning tools), (ii) repairing the defect if required, (iii) optimizing the periodic schedule of in-line inspection tools to determine the defects and corresponding sizes of the defects, (iv) manipulating operational parameters, (v) using chemical compounds (e.g. inhibitors and biocides), (vi) applying coating and cathodic protection, and combination of the classes (Gomes et al., 2013; Gomes and Beck, 2014; Javaherdashti and Alasvand, 2019a; Teixeira et al., 2008; Zhang and Zhou, 2014; Zhao et al., 2009; Zhou, 2010, 2011).

The pit depth growth models play an important role in proposing a corrosion management practice, to approximate the failure probability of the pipeline as a function of time, predicting the remaining strength of the pipeline, as well as examining the defect's location and determining the efficiency of each management practice. This is why utilizing the data collected from pipeline history over time is essential for the industry to develop a pit depth growth model in a much more realistic way. In literature, pit depth growth models can be developed by using conservative and non-conservative techniques. The latter may lead to critical defects being overlooked by the management practice and increase the occurrence of serious consequences. On the other hand, the conservative pit depth growth models will increase the uncertainty of management practice (Zhang et al., 2014). Developing a mechanistic model for pit depth growth models is an intrinsically complex process as it may include two types of variables, namely temporal and spatial. The temporal variables are defined as the pit depth growth path of a defect that varies over time, while the spatial variables are defined as the pit depth growth path of more than one defect. However, all variables may be correlated. The probabilistic pit depth growth model is widely used in the literature as random variables and stochastic-based models. It simply means that the pit depth growth is considered to follow a linear or power-law function of time (Ahammed, 1998; Ahammed and Melchers, 1996; Teixeira et al., 2008; Zhang and Zhou, 2014; Zhou, 2010, 2011). As an example, the growth of a corrosion defect is characterized by utilizing the Markov process and a gamma distribution with a shape and scale parameter as time-variant and time-invariant, respectively (Noortwijk, 2009; Noortwijk et al., 2007; Pandey et al., 2009). A gamma process is employed to characterize corrosion growth of the multiple defect (Maes and Dann, 2007). A non-homogenous Markov process is used for pit growth according to the experimental data for Aluminum (Maes and Dann, 2007). A non-homogenous Markov process is also used by (Caleyo et al., 2009; Valor and Caleyo, 2007) to characterize the pitting corrosion, in which Weibull distribution is assumed for corrosion initiation time. A power-law function of time is considered to model the parameters in transition probability. In another study, the time-dependent transition intensities were examined by collecting the pipeline defect information with in-line inspection tools (Hong, 1999). However, there are significant challenges associated with modeling the pit growth by adopting Markov process-based models: (i) selecting a transition probability function and the sufficient numbers of damage state, (ii) using data from in-line inspection tools introduces the uncertainties as well as errors, and (iii) facing the spatial correlation between the defects.

This is why the Bayesian-based methodologies are robust and powerful tools, utilizing data for pit depth growth modeling. As an example, hierarchical Bayesian methodology and dynamic Bayesian networks, by incorporating new data, have been used to analyze the deterioration mechanistic model of corrosion and updating the parameters in the model (Palencia et al., 2019; Teixeira et al., 2019; Xiang and Zhou, 2018; Zhang and Weng, 2020). The hierarchical Bayesian analysis (HBA) is utilized to model the pit growth in the pipeline (Zhang et al., 2014). Researchers used a non-homogenous gamma process to derive the probability distribution for the parameters within multiple defects. In another study, Al-Amin et al. (2014) developed a pit depth growth model for a specific defect using HBA based on the data obtained from the in-line inspection tools. A hierarchical Bayesian framework was developed by Qin et al. (2015) to model defect generation and growth of metal deterioration in oil and gas steel pipelines. Pesinis and Tee (2018) proposed a framework to estimate corrosion-based failure probabilities of underground natural gas pipelines and corrosion growth defects by using a hierarchical Bayesian model. A hierarchical Bayesian model based on a non-homogeneous gamma process is proposed considering the operational conditions of a pipeline over a period of time (Groth, 2019). Zhang and Wang (Zhang and Weng, 2020) used a Bayesian network (BN) to construct a knowledge-based model by analyzing the failure probability and leakage size of corrosion for an underground gas pipeline.

However, in all aforementioned studies, there is a lack of comprehensive pit depth growth modelling considering both model and data uncertainties, which further helps on-site operators to make decisions by proposing a management practice. Therefore, to deal with the lack of previous studies, CBN along with HBA can be used. CBN which can be considered as an extension of typical BN (Song et al., 2017) is a powerful tool and can handle model uncertainty using adaptive models. In addition, CBN, by utilizing continuous nodes, can better reflect those variables that change continuously in nature. CBN and its extensions have been broadly used such as, but not limited to the field of safety, reliability, and risk management (Hossain et al., 2019; Kabir et al, 2018, 2020; Khakzad et al., 2013; Misuri et al., 2018). HBA is also a robust technique to deal with different sources of information known as data uncertainty. In safety, reliability, and risk management domains, the existing data is generally inadequate to conduct analysis, especially modeling the pit depth growth, where improper modeling causes pipeline failure. Thus, to obtain acceptable results to support decision making, HBA utilizes and then aggregates a wide range of information. In addition, in recent years, the availability of Markov Chain Monte Carlo (MCMC) using a sampling application can help decision-makers to fully track performing HBA (Kelly and Smith, 2009; Khakzad et al., 2014b; Siu and Kelly, 1998; Yang et al., 2012).

The contribution of this study is threefold. The first contribution is in providing CBN along with HBA in one methodology framework for MIC management. Thus, the proposed framework takes into account both model and data uncertainty. Second is in developing a new mechanistic model for pit depth growth under the influence of MIC, and third is using the Bayesian-based model over a period of time to propose the optimum and best management practices.

The organization of the paper is presented as follows. In Sections 2 Methodology, 3 Application to a case study, the preliminaries of CBN and HBA are explained, respectively. In Section 4, a framework is proposed to manage MIC considering both types of model and data uncertainties. In Section 5, a corroded pipeline is studied as a case study to demonstrate the application of the developed methodology. In the final section a conclusion, challenges of the current study, and direction for upcoming research are provided.

The BN has enough capacity to analyze the behavior of each node over time given new data, making it one of the most powerful and robust tools. Common BN-based approaches have been widely used in different engineering domains such as, but not limited to (Abimbola et al., 2016; Adesina et al., 2020; Arzaghi et al., 2018; Noroozi et al., 2013; Taleb-Berrouane et al., 2020; Yazdi et al., 2020; Zarei et al., 2019; Zinetullina et al., 2019). BN-based approaches can employ different types of input data (objective or subjective) to estimate the probability centered event by reducing the model uncertainty with consideration of interdependency between all the participating nodes. However, the common BN-based models ignore the preciseness and modeling flexibility since the discrete nodes are used in the models. In other words, the common BN-based approaches consider the continuous nature of causal factors in the network as discrete variables. Therefore, these types of estimations provides uncertainty during the analysis process (Adumene et al, 2020a, 2020b, 2020c; Bhandari et al., 2015; Xia et al., 2018; Yazdi et al., 2019; Zarei et al., 2020). In real-world applications, there are often variables that continuously change over time and therefore cannot be modeled using common BN-based models with discrete variables. Such is the case for MIC.

To deal with the abovementioned drawbacks, the common BN-based approaches can be further developed as a CBN considering the continuous causal factors. In CBN, the nodes of the models can be represented as a combination of discrete and continuous variables. To see how CBN can be constructed from a common BN-based model, Guozheng et al. (Song et al., 2017) proposed a framework to convert BN into the CBN. According to this study, two significant changes are required so that the parental nodes can quantitatively signify the child nodes. First of all, all nodes with a continuous nature in BN-based modes must be defined by employing measurable variables. Next, the child nodes' value in CBN needs to be represented as a function of the parental nodes’ value. This simply means that the conditional probability tables (CPTs) in the common BN-based models are transferred into the conditional probability distributions or mathematical functions that represent the relationships between the value of the child and parental nodes.

In CBN, the computation of posterior distribution becomes much more complex and therefore the analytical methods or Monto Carlo simulations cannot compute the posterior distributions. Markov Chain Monto Carlo (MCMC) is a robust tool and has high level capacity to compute the complicated posterior distribution with high dimensions. To elaborate, MCMC has two main parts (i) Monto Carlo, and (ii) Markov Chain. Monto Carlo refers to a method that relies on the generation of random numbers and Markov Chain refers to a sequence of numbers in which each number depends on the previous number in the sequence. However, Monto Carlo simulations fail to sample from the complicated distribution which has different types of dependent variables. To handle this issue, Markov Chain is used to assist Monto Carlo, and therefore MCMC is utilized. To obtain more details about MCMC and its algorithms one can refer to (Gilks, 1996).

Simply put, Bayesian analysis is one of the main elements of the Bayesian methods that deal with the unknown parameters of a mechanistic process as random variables instead of using deterministic values. The Bayesian analysis makes use of prior knowledge about the mechanistic process' parameters which may be derived from expert opinion, past experience, and information from previous research studies. Subsequently, the prior knowledge is adjusted based on the newly observed data to update the opinions about the parameters of a mechanistic model. Furthermore, the updated belief can then be considered as the prior distribution for updating in the future as the new data becomes obtainable. Thus, by repeating this process, the data uncertainty about the parameters of the mechanistic model is reduced. Hierarchical Bayesian Analysis (HBA) (Banerjee et al., 2014) is a unique case of the Bayesian methods, in which the prior distribution is disjointed into the conditional distribution sequentially (Robert, 2007). HBA is a powerful tool for making statistical inferences about the parameters of the mechanistic model in which there are complicated interactions between the parameters. In addition, HBA is principally appropriate for population, where the model's parameters described as a sample in the population are measured to be associated with the parameters for another sample from the same population (Al-Amin et al., 2014; Demichelis et al., 2006).

Let it be assumed that there is a population of n random variable, Yi(1=1,2,3,,n) which can describe similar mechanistic processes. Consider that there is a set of unknown parameters where θi denotes the probability distribution of a random variable Yi. The prior distribution p(θi|ω)can be assigned to θi, in which p(θi|ω) signifies the PDF of θi and is conditioned on the known parameters ω, and are considered to be common to the population of Yi. Moreover, let it be us assumed that yi denotes a set of observed data for Yi. The updated opinion of θi can be obtained using Bayes’ theorem (Fenton and Neil, 2013) by combining the prior distribution and the observed data in the following Equation:p(θi|yi)=L(yi|θi)×p(θi|ω)p(yi)L(yi|θi) is the known likelihood function is based on the information provided by the data, which is conditional on θi. Besides, the entity p(θi|ω) is called the posterior distribution, which reflects the combination information of prior information and obtained new data. The quantity p(yi) is the normalizing constant which confirms that the left-hand side of Equation (1) is a probability distribution. The p(θi|yi) integrates to be unity and is known as the marginal likelihood, which can further be determined by integrating the numerator on the right-hand side of Equation (1), regarded as θi.Therefore, the following Equation can be derived:p(yi)=L(yi|θi)×p(θi|ω)dθi

Keeping the normalization constant in mind, using proportionality symbol (), Equation (1) can be rewritten as:p(θi|yi)L(yi|θi)×p(θi|ω)

The abovementioned explanations are based on standard Bayesian formulations, where it is assigned a prior distribution into the parameterθi by controlling the distributionYi. However, the standard Bayesian formulations can be further developed by considering that the parameter ω which controls the distribution of θi is a random variable as well, by assigning the prior distribution, p(ω|ψ), into the ω. According to this extension, thep(ω|ψ) is named as hyper-prior and ψ in named as hyper-parameter (Banerjee et al., 2014; Robert, 2007). In addition, the hyper-parameter can be known and can present the prior belief about ψ. In practice, ω can be also be treated as random variables and proceed to the next level of hierarchy. As can be seen from Fig. 1 (modified after (Banerjee et al., 2014)), the simple graphical structure of a common HBN of extended Bayesian model is provided. Therefore, the extended Bayesian model can be summarized as follows:

  • i.

    Likelihood of data: L(yi|θi) ,

  • ii.

    First stage of prior:p(θi|ω) ,

  • iii.

    Second stage of prior:p(ω|ψ),

  • iv.

    Posterior distribution of θi:p(θi|yi)L(yi|θi)p(θi|ω) ,

  • v.

    Posterior distribution of ω:p(ω|θi)L(θ1,θ2,,θn|ω)p(ω|ψ).

In such cases, HBA can be defined in four levels, due to the fact that level one is based on inspection data, i.e., the defect depths described by inspections which are connected to measurement uncertainties, level two highlights the auxiliary variables, including the actual depths at the times of inspections and increments of the actual depths between two consecutive inspections, level two also makes the likelihood function for the measured depth mathematically tractable and facilitates the Bayesian updating, in level three the parameters for level two are provided (e.g., the parameters in gamma distributions), and finally in level four hyperparameters assist in finding out the parameters in level three. It should be added that based on the type of decision making problem, the level can be increased or shortened. By studying the literature and with the support of decision-makers such as, but not limited to (Al-Amin et al., 2014; El-gheriani et al., 2016; El-Gheriani et al., 2017; Khakzad et al., 2014a, 2014b), and to the best of the authors’ understanding, some of the merits of HBA compared to other statistical models can be highlighted as following:

  • (i)

    HBA enables one to deal with the source to source uncertainties by utilizing the hierarchical prior assignment. Thus, the feature of HBA makes a robust estimation of the parameters, in which the posterior results are based on the average from different possible prior options (Robert, 2007).

  • (ii)

    HBA using the conditional hierarchical priors can better describe the spatiotemporally (space-time) correlated data (Congdon, 2020).

  • (iii)

    The computations of the Bayesian model are commonly simplified by the hierarchical structure within posterior distribution simplification. This results from priors' decomposition. Thus, different sampling algorithms can be employed to update the parameters (Banerjee et al., 2014; Congdon, 2020; Robert, 2007).

  • (iv)

    In HBA, a specific group or singular parameter can derive information from the equivalent of the parameters(Ntzoufras, 2011). Thus, the level of singular inference can be obtained as precisely as possible and shows its merits when the observed data and sample size are small. To characterize the pit depth for a single MIC defect of a subsea pipeline, HBA using inferences is practically advantageous, since the information that is linked to give defect is commonly limited.

The mean, standard deviation, and other probabilistic characteristics of random variables, which are entered in HBA can be determined by integrating and combining the posterior distribution. However, there is a lack of close form solutions to obtain the posterior distribution when the Bayesian Network has high dimensions and is complex. Therefore, similar to the CBN mentioned in Preliminary 2, the difficulties can be handled using MCMC techniques. In the MCMC methods, a Markov chain is initially constructed to consider the start values of the parameters, and subsequently converges to the posterior distribution which is actual target density. It should be added that the sample is dependent on the start value; therefore, the influence of the start value needs to be reduced by ignoring the first part of the sample. This period is referred to as the burning-in period. The burning-in period is the time it takes the chains to be stabilized, which means therefore that there is not up and down drifting over time by ignoring the sample in the burning-in period. Afterward, the sample can be used for Bayesian inference of the parameters. There are some important algorithms that are commonly utilized to perform an MCMC, such as, but not limited to “Metropolis random walk Hastings”, “Slice sampling”, and “Gibbs's sampling”. To get more details about MCMC methods and corresponding algorithms, one can refer to the following references (Banerjee et al., 2014; Congdon, 2020; Ntzoufras, 2011; Robert, 2007).

Section snippets

Methodology

It is important to predict the rate of MIC as well as pit depth growth in the early stage of subsea pipeline development to provide appropriate management practice(s), which can prevent, mitigate, and control the occurrence of pipeline failure caused by MIC. However, MIC management is a challenging task for decision-makers due to a lack of information in probabilistic risk analysis. The rate of MIC and pit depth growth can be estimated by utilizing modeling techniques such as Bayesian network.

Application to a case study

The proposed methodology is applied to an APL 5L grade X42 subsea hydrocarbon transition pipeline which is highly suspect of internal MIC and is required to be in operational condition for at least 40 years. The pipeline carries co-mingled fluids from a different number of subsea resources.

According to the first step of the developed methodology, the mechanistic model of maximum pit depth growth influence by MIC appears in Fig. 4. The mechanistic model of MIC is drawn with consideration to (i)

Conclusions

This paper presents individual pit depth growth characterization using a Bayesian model. The pit depth growth of an active corrosion defect influenced by MIC was considered to observe a power-law path. The power-law function parameters are obtained using HBA based on the different effective operational and environmental factors, and material properties. The MCMC method was utilized to perform the Bayesian updating and statistical inferences of the model parameters.

The application of the

CRediT authorship contribution statement

Mohammad Yazdi: Conceptualization, Methodology, Formal analysis, Investigation, Writing – original draft, Writing – review & editing. Faisal Khan: Conceptualization, Methodology, Writing – review & editing, Supervision, Project administration, Funding acquisition. Rouzbeh Abbassi: Conceptualization, Methodology, Writing – review & editing, Supervision.

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.

Acknowledgements

The authors acknowledge the financial support provided by Genome Canada and their supporting partners, and the Canada Research Chair (CRC) Tier I Program in Offshore Safety and Risk Engineering.

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