Failure probability calculation model applied to gas pipelines

Abstract

This article presents an application for failure probability in long-pipeline gas systems through the development of trend curves over time for the attributes of corrosion wear, which are related to the length, width, and depth of the defect. In addition, Risk-Based Inspection (RBI) is applied in the most favorable numerical failure values according to the location of the defect, with the aim of analyzing the structural reliability and the expected useful life of the gas pipeline. To do this, it was necessary to use the data provided by pig readings in 2008, 2012 and 2018 by an instrumented pig, type Magnetic Flux Leakage (MFL), inspecting a gas pipeline with the finality to measure wall thickness. The 56 km long and 18 in diameter pipeline is partly onshore and partly offshore. Also, the pipeline anomalies are standardized according to the standards established in POF (2016). It is important to emphasize that the methodology described in this article can be used in the industry where the prevention of leakage incidents, the predictability of maintenance, and the elaboration of the respective inspection plans are required, since it has been theoretically possible to calculate the probability of failure in time beyond the respective impact on risk for the operational variables presented.

Keywords:
smart pigs; RBI; structural reliability; failure probability; gas pipelines.

1. Introduction

Land and sea pipeline systems are utilized for the transportation of natural gas, crude oil, and derivatives. The implementation of periodic assessments utilizing predictive maintenance is of critical importance for the purpose of ensuring the safety and operability of the built infrastructure.

The most recent research, as presented in Filho et al. (2014), indicates that corrosion defects in oil and gas pipelines can potentially compromise the safety of these structures. Moreover, Nicoletti et al. (2010) posit that inspection aimed at verifying metal loss represented by corrosion provides valuable data for the assessment of pipeline integrity.

One of the procedures for conducting an inspection of pipelines is to pass an instrumented pig, which is equipped with a Magnetic Flux Leakage (MFL) tool. As reported in Pandey (1998), the loss of metal due to corrosion, whether internal or external, results in a disturbance in the magnetic field, which is proportional to the volume of material removed.

The MFL tools apply the flux leakage principle, which involves the use of a magnetization system that employs a magnetic field along the length of the tubing as the tool moves through the line. The defects result in the corruption of the applied field, which in turn produces flow leakage. Sensors positioned on the pig's body are employed to quantify flow leakage, with the system recording and storing this data. Subsequently, the measurements undergo analysis to estimate the geometric defect and severity (Thom, 2003).

The application of algorithms enables the determination of the probability of failure, as well as the risk of failure and structural reliability. In this context, the length, width, and depth of the defect, which represent the loss of thickness of the pipeline, are employed in accordance with the precision of the instrumented pig.

Firstly, the conventional method entails calculating the probability of failure over time based on a Weibull distribution function. This is achieved by determining the shape parameter β and scale parameter η, which allows for the identification of the most and least favorable wear positions in the gas pipeline.

This methodology enables the acquisition of input data for risk-based inspection (RBI), which is employed to estimate the risk by means of failure pressure analysis models. These models are utilized to calculate the remaining resistance of pipelines that are subject to corrosion in accordance with the standards Modified B31G, Shell 92, and DNV-99. This is accomplished through the utilization of the Monte Carlo method. As reported in Abubakirova et al. (2020), the RBI is a method that is becoming increasingly popular and reliable for the evaluation and development of inspection plans.

Figure 1 provides a concise overview of the flow diagram utilized in the failure probability calculation model applied to gas pipelines.

Figure 1
Flow diagram utilized in the failure probability calculation model applied to gas pipelines.

A subsequent review of more recent bibliographic references revealed that Amaya et al. (2019) discusses the selection of reliability models in corroded pipelines for future intervention strategies. Furthermore, Zelmati et al. (2022) presents a study that is related to the corrosion rate during the evaluation of the remaining useful life of pipes at the end of their useful life. This study proves to be fundamental for calculating the interval between two consecutive inspections.

2. Theoretical concepts

2.1 Oil and gas pipelines

The transport of high volumes of oil and its derivatives (oil pipelines) and natural gas (gas pipelines) over extended distances for several years is a fundamental aspect of the energy industry. This is achieved through the use of pipelines, with the objective of ensuring both the safety and reliability of the process. In practice, pipelines are classified according to their location: underground (buried), aerial (visible), and submarine (submerged).

Pipelines of this nature are typically constructed from steel, which is renowned for its strength and durability. They may be welded or flanged, and may be coated, depending on the environmental conditions and variables, the purpose of the pipeline, and the product to be transported.

Pipeline systems must be designed to accommodate and be compatible with the corrosion control practices described in ISO 13703 (2000), as well as the recommendations for respective corrosion-resistant materials and mitigation methods.

2.2 Corrosion in onshore and offshore pipelines

As elucidated in Bhandari et al. (2015), corrosion is a significant contributor to the deterioration of both onshore and offshore infrastructures. It has a profound impact on the useful life of process equipment and pipes, leading to potential structural failure, leaks and environmental pollution. Corrosion pits, in particular, have been identified as a particularly hazardous form of corrosion. They are considered to be one of the most common causes of incidents and accidents related to corrosion.

The types of anomalies identified by the instrumented pig during the scanning of onshore and offshore pipelines in accordance with the definition of the anomaly dimension class for the MFL provided in POF (2016) are as follows: axial grooving (AXGR), axial slotting (AXSL), circumferential grooving (CIGR), circumferential slotting (CISL), general (GENE), pinhole (PINH) and pitting (PITT).

This article will address and analyze the quantity of defects linked to the corrosion of the pipeline.

2.3 Pipeline pigging operations

In order to guarantee the security of operations within pipeline networks, periodic assessments are conducted utilizing the Magnetic Flux Leakage (MFL) pig, which is a type of instrumented pig tool introduced into the pipeline and moves along the entire length of the pipeline at a constant velocity.

The MFL tool is based on the principle of magnetic flux leakage to verify the structural integrity of the line. The apparatus applies a magnetic field along the circumference and length of the pipeline as the tool traverses the pipe. Defects in the pipeline result in the corruption of the applied field, which in turn causes flow leakage.

The sensors distributed on the external surface of the instrumented pig are employed to measure the spectrum, with the system subsequently recording and storing these nonconformities. Subsequently, the measurements are subjected to analysis with the objective of estimating the geometric defect, its severity, and its location.

2.4 Monte Carlo method

The Monte Carlo method is a technique used to produce numerical results without performing physical tests. Previous test results or other information can be used to establish the probability distribution of important parameters in the problem.

It is a highly effective tool, frequently employed in the analysis of random phenomena, utilizing mathematical modeling in conjunction with computer programming. In a problem involving random variables, the expected output is statistical or probabilistic information. In the Monte Carlo method, the input variables are represented by a set of deterministic numbers.

In structural reliability analysis, this technique entails the generation of a convenient number of independent artificial samples from the joint probability density function of the random variables. For each of these samples, the limit state function is evaluated. If the result is less than or equal to zero, a failure is counted.

Although this technique is relatively straightforward and provides confidence measures in relation to the probability being evaluated, it does present several difficulties in its use. One of the difficulties is the number of evaluations of the limit state function. The probability of failure in structural problems is low, and if the coefficient of variation in the estimator is approximately 10%, the number of necessary analyses must be considerable (Ferreira, 2020). In this study, the results were obtained for a sample size of 10⁷ computational simulations.

The Monte Carlo method is employed in the estimation of structural reliability in pipelines. This involves the following steps: the selection of a pipeline section, the prior collection of operation and failure data through non-destructive tests (NDT), and the calculation of the probability of failure using standardized and normative RBI models.

2.5 Reliability function for the Weibull distribution

In the context of risk rates as a function of time, failure events that are not constant can be most effectively represented by the Weibull distribution (Krishnasamy et al., 2005).

In the present study, the characteristics and universe of failure data indicate that the distribution exhibited asymmetric behavior for different components of the system under investigation. Therefore, the Weibull distribution was adopted, which is suitable for more generic failure treatment due to its versatility for representing events of different failures.

The cumulative probability of failure over time is presented in Equation 1, where parameter η represents the characteristic life (scale parameter), and β the shape parameter of the failure model (Thom et al., 2014).

(1) $$F(t)={\int }_{-\mathrm{\infty }}^{t}f(t)dt=1-e^{-(t//\eta {)}^{\beta }}$$

The Weibull distribution is capable of representing stretches of data, such as those presented in the failure rate curve, which is commonly referred to as the bathtub curve in practice. In its most general case, the Weibull distribution has three parameters. The function is represented in the sequence as follows:

(2) $$f(t)=\frac{\beta }{\eta }{\left(\frac{t-\gamma }{\eta }\right)}^{\beta -1}{e}^{-{\left(\frac{t-\gamma }{\eta }\right)}^{\beta }}$$

(3) $$f(t)=0,\text{if}t\le \gamma$$

The parameters β and η are greater than 0. In most cases, the location parameter γ, which is related to the initial or minimum life of the component, is often ignored in analyses related to maintenance. The shape parameter β exerts a significant influence on both the failure rate and the time elapsed until failure (Kardec and Nascif, 1999).

In considering Equation 2, it is possible to observe the various behaviors that the Weibull distribution can assume when the value of η is maintained constant and the value of β varies. This is accompanied by the correlating values in the bathtub curve, which can be summarized as follows:

• • 0 < β < 1 => Period of infant mortality;

• • β = 1 => Useful life period;

• • β > 1 => Wear period.

In this manner, the probability of a component failing within a specified operating time interval can be calculated based on the aforementioned parameters. This allows for the estimation of potential failure risks within the specified interval.

2.6 Pipeline integrity management: Risk-Based Inspection

The pipelines have been designed with the intention of ensuring the safe operation and transportation of fluids. In service, they will be exposed to risks of failure that may not have been anticipated. For instance, the pipeline may deteriorate over time due to corrosion or fatigue. Additionally, operating conditions may vary due to changes in the composition of transported products or the addition of new routes. Consequently, the pipeline may be subjected to more rigorous operational conditions associated with the transported load (fluids), due to augmented internal pressure and/or temperature, fatigue or deformation induced by curvature, external impacts, and so forth.

In order to minimize and alleviate the risk potential and the economic potential of failures and environmental consequences, operators implement an inspection and maintenance program. For instance, a program designed to mitigate the risk of internal corrosion may include online product monitoring, internal inspection using smart pigs to detect and monitor corrosion, and the use of inhibitors (anodes or cathodes) to regulate internal corrosion.

The Risk-Based Inspection (RBI) methodology allows for the prioritization of areas at greatest risk of collapse in a structure, thereby facilitating the identification of preventive or corrective maintenance actions. The RBI strategy can be applied to both oil and gas pipelines and static equipment in onshore and offshore areas throughout their entire useful life (Thom, 2018).

2.7 Failure pressure

The probabilistic numerical analysis employs the Monte Carlo method, which necessitates statistical data on the material properties and information regarding the physical integrity of the gas pipeline (Madsen et al., 1986). In this study, the failure function or limit state function g(t) is defined as the difference between the failure pressure P_f and the operating pressure in the gas pipeline P_op.

(4) $$g(t)=P_f-P_{op}$$

Three distinct failure pressure models are employed in order to ascertain the probability of failure (Caleyo et al., 2002):

a) Modified B31G

(5) $$p_f=\frac{2({\sigma }_{\mathrm{e}}+68.95)e}{D}\left[\frac{1-0.85\frac{d(T)}{e}}{1-0.85\frac{d(T)}{e}{M}^{-1}}\right]$$

b) Shell 92

(6) $$p_f=\frac{1.8{\sigma }_{r}e}{D}\left[\frac{1-\frac{d(T)}{e}}{1-\frac{d(T)}{e}{M}^{-1}}\right]$$

c) DNV-99

(7) $$p_f=\frac{2{\sigma }_{r}e}{D-e}\left[\frac{1-\frac{d(T)}{e}}{1-\frac{d(T)}{e}{M}^{-1}}\right]$$

in these equations the following variables are employed: corrosion depth d(T), Folias factor M, yield stress σ_e, tensile strength σ_r, wall thickness e, and external diameter of the duct D. The depth of the corrosion defect is determined by

(8) $$d(T)=d_0+\left[(V_r+er)(T-T_0)\right]$$

the initial depth of the defect (d₀), the radial corrosion rate (V_r), the corrosion rate error (er), and the time of the last inspection (T₀) constitute the variables under consideration.

3. Materials and methods

The structural reliability of gas pipelines is estimated through three readings obtained by field operations through the passage of the MFL-type instrumented pig. These readings collect the attributes of length, width, and depth of the defect (loss of thickness), which are then used to verify the behavior of the pipeline at risk of failure. In the interaction between these defects, the use of the ASME B31G (1991) standard is required.

3.1 Data used

The material utilized in the duct was API 5L X60, exhibiting a yield stress of 60,000 psi and rupture stress of 70,000 psi. Its diameter was 18 inches, with a thickness of approximately 9/16 inch. The maximum allowable operating pressure (MAOP) was 68 kg/cm².

Despite the evidence of obstacles along the pipeline networks, such as derivations, curves, valves, tees, amendments, as well as the position of galvanic anodes, their locations and dimensions are not provided to us. Consequently, it is not possible to correlate the concentration of internal or external corrosion in the installation region.

In this study, pigging readings from 2008 (1,288 data points), 2012 (2,668 data points), and 2018 (2,253 data points) were utilized in a 56-kilometer-long sea and land gas pipeline. As previously stated, the pigging process captures data regarding the length, width, and depth of the defect (hereafter referred to as "attributes") as it traverses the interior of the gas pipeline.

To perform the trend analysis, it is necessary to arrange the data in accordance with the evolution of wear increments over time of the attributes involved, which are linked to metal loss due to corrosion.

The use of the Python language enabled the organization and grouping of data, thus facilitating the subsequent data analysis.

3.2 Interface with the Python language

In order to facilitate the analysis of data captured by the pig, an algorithm was developed in the Python programming language. The selection of Python as the application language was based on its versatility, speed of development, and the availability of additional libraries to assist in program development.

The program operates from the operating system terminal and accepts input data in Excel format, which was collected by the instrumented pig. In addition, it accepts a series of additional parameters that determine the resulting output data.

Table 1 depicts the behavior and distribution of the data following the respective treatment. It can be observed that the loss of thickness is expressed as a percentage. In accordance with the POF (2016) standard, a pipeline is condemned for operation when the loss of thickness exceeds 80%. This standard aims for intervention and corrective maintenance.

Table 1
Data sample adjusted and organized using the Python programming language

2008				2012				2018
Longitudinal Distance [m]	Thickness Loss (%)	Corrosion Defect Length L [mm]	Corrosion Defect Width W [mm]	Longitudinal Distance [m]	Thickness Loss (%)	Corrosion Defect Length L [mm]	Corrosion Defect Width W [mm]	Longitudinal Distance [m]	Thickness Loss (%)	Corrosion Defect Length L [mm]	Corrosion Defect Width W [mm]
12,846.86	10	18	17	12,846.15	10	20	18	12,829.06	27	35	19
12,848.94	10	12	18	12,848.69	10	12	18	12,848.70	12	14	20
12,850.84	10	17	18	12,850.68	11	21	18	12,850.85	20	37	26
12,859.93	11	16	18	12,866.00	11	25	18	12,862.81	19	44	38
12,967.69	11	17	17	12,978.84	15	34	18	12,995.65	18	43	34
38,735.76	10	12	18	38,708.77	10	12	18	38,677.94	17	13	20
38,734.18	10	15	17	38,693.14	10	21	18	38,678.05	21	31	29
38,749.53	10	16	17	38,750.86	10	18	18	38,750.60	23	35	34
38,768.09	10	15	18	38,774.75	10	16	18	38,774.47	20	34	36
38,808.68	12	16	17	38,823.03	12	16	18	38,822.99	25	32	20

3.3 Activity sequencing

Once the presented result was obtained, the correspondence between the events raised by the pig and the appropriate data was performed by means of checks carried out in different inspection years, in accordance with the following steps:

a) A region of tolerance for the pig reading is calculated in relation to the reference year (in this case 2018, as it is the most recent inspection) using the current reading position (Longitudinal distance) multiplied by the instrument precision (0.25%), as indicated in the equipment manual.

b) Consequently, the position readings conducted in years disparate from the reference year must be within the region previously demonstrated and have the same classification as the failure event presented.

c) To calculate the parameters of the Weibull distribution (β and η), which are related to the concepts presented in Section 2;

d) Subsequently, the probability of failures is calculated using the conventional method, as outlined in Equation 1.

e) In the case of the RBI calculations, in addition to the standardized standards Modified B31G, Shell 92 and DNV-99, the limit state function predicted in Equation 4 was also used to calculate the probability of failures by the Monte Carlo method, by comparing the failure pressure and the operating pressure.

4. Results

4.1 Probability of failure determined with three pipeline pigging operations

Following the optimization and organization of the data based on the three readings of the MFL pigs (2008-2012-2018), in accordance with the type of attribute, with the values of material loss over time, with the location of the defect, and with the precision of the instrumented pig, it was possible to generate the results presented in Figures 2, 3, and 4. The figures illustrate the probability of failure over a period of 100 years of operation for the length, width, and thickness of corrosion, respectively.

Figure 2
Probability of failure arising from the length of the defect.

Figure 3
Probability of failure arising from the width of the defect.

Figure 4
Probability of failure arising from the loss of thickness of the pipeline.

The aforementioned figures illustrate the probability of failure, as indicated by the red curves, in relation to the cited useful life expectancy. Conversely, the green curve illustrates the least favorable scenarios with regard to metal loss over time. In gray, we present the other and various possible combinations where we had increasing values of the studied attribute.

After 20 years, which is extended up until 100 years, the curves indicating the more favorable (red) and less favorable (green) wear patterns become increasingly distinct. This phenomenon can be interpreted as a corrosion process that is evolving in the pipeline, which suggests a progressive deterioration in its integrity.

This technical survey is of great importance, as it estimates the useful life of the infrastructure and identifies the points most vulnerable to collapse over time.

In the MFL pig position of 12,742.96 m, the most favorable conditions for material loss in terms of length (Figure 2), depth (Figure 4), and the average width of the corrosion pit (Figure 3), were identified. These values serve as input data for the RBI procedure.

4.2 Probability of failure determined with two pipeline pigging operations

In order to expand the quantity of data employed and observe the behavior of the resulting curves, two consecutive MFL pig inspections were conducted (2008-2012, 2012-2018 and 2008-2018). These inspections were conducted in accordance with the previously mentioned technical guidance.

The results are presented in Figures 5, 6, and 7, which illustrate the probability of failure over a 100 years operational period for the length, width, and thickness of corrosion, respectively.

Figure 5
Probability of failure arising from the length of the defect.

Figure 6
Probability of failure arising from the width of the defect.

Figure 7
Probability of failure arising from loss of thickness of the pipeline.

In the MFL pig position of 12,784.70 m and 103.44 m, the most favorable conditions for metallic loss in terms of length (Figure 5), depth (Figure 7), and the average width of the corrosion pit (Figure 6), were identified. These values serve as input data for the RBI procedure.

4.3 Application of Risk-Based Inspection (RBI)

As previously noted, the most favorable values at the wear location points for the attributes of length and depth of the defect, as well as the average width of the corrosion pit, serve as the input data for RBI in three and two pig inspections.

In this manner, the standardized routines Modified B31G, Shell 92, and DNV-99 are employed to calculate the results presented in Table 3 at one-year intervals. The probability of failure is determined until the final time of 20 years.

Table 2
Parameters in the Weibull distribution.

Attribute	Predictive maintenance		Defect location (m)		Weibull distribution		Probability of failure (%)
	Three pigging	Two pigging	More favorable	Less favorable	β	η	100 years
Length	x		12,742.96		1.41	29.53	99.63
				12,967.69	0.91	69.60	75.05
Width	x		12,846.42		1.35	43.71	95.25
				12,742.96	0.91	63.86	77.80
Loss of thickness	x		12,742.96		1.41	24.61	99.93
				12,710.81	0.93	38.21	91.38
Length		x	12,784.70		1.44	22.48	99.98
				56,144.60	0.99	87.28	68.14
Width		x	12,771.99		1.44	33.72	99.16
				12,785.41	1.28	123.57	53.37
Loss of thickness		x	103.44		1.44	18.73	100.00
				12,850.18	0.73	34.30	88.80

Table 3
Impact on safety risk.

Probability of failure (%)
		Three pigging				Two pigging
Year	Shell 92	Modified B31G	DNV-99	Impact on risk	Shell 92	Modified B31G	DNV-99	Impact on risk
1 to 9	0.00	0.00	0.00		0.00	0.00	0.00
10	0.00	0.00	0.00		0.01	0.00	0.00	High
11	0.31	0.06	0.14	High	0.34	0.07	0.15	High
12	1.62	0.64	0.70	High	1.66	0.66	0.71	High
13	3.48	1.93	1.46	High	3.49	1.94	1.47	High
14	5.26	3.49	2.20	High	5.27	3.51	2.20	High
15	6.76	5.02	2.82	High	6.75	5.02	2.81	High
16	8.03	6.40	3.34	High	8.02	6.38	3.34	High
17	9.08	7.55	3.80	High	9.08	7.52	3.79	High
18	9.97	8.57	4.17	High	9.96	8.55	4.18	High
19	10.71	9.43	4.51	High	10.71	9.42	4.51	High
20	11.40	10.20	4.82	High	11.38	10.19	4.81	High

In the Risk-Based Inspection (RBI) analysis for the pipe, it is observed that up to 10 years, the three standards present values close to zero for the probability of failure. Moving forward, the Shell 92 failure pressure analysis model presents more cautious results that require attention.

Accordingly, the theoretical and mathematical modeling presented indicate that, even when considering a user inspection every five years or a mandatory inspection every ten years, the 56 km pipeline would remain capable of withstanding the respective operating pressure, despite the evolution of loss of material by corrosion over time.

5. Discussion

5.1 Weibull distribution parameters

Table 2 presents some values of the shape parameter (β) of the failure model in the Weibull distribution above 1. This indicates that the component is in the aging zone of the bathtub curve. Consequently, the probability of failure is high.

However, when the characteristic life (η - scale parameter) in the Weibull distribution is relatively high in comparison to the others, it results in a favorable trend in the probability of pipeline failure.

5.2 Impact on risk

In the Risk-Based Inspection (RBI) analysis for the gas pipeline, it is observed that the Shell 92 failure pressure analysis model presents more conservative results.

Table 3 also illustrates the range of failure probabilities and their associated consequences, as outlined by Mokhtar et al. (2009). It can be observed that the risk is considered to be higher after 11 years of use for three pigging and 10 years of use for two pigging.

6. Conclusions

In this study, a real database of in-pipe inspection with MFL pigs was employed to develop and validate structural reliability tools for assessing the probability of failures using the conventional method and the Monte Carlo method. The objective was to establish an inspection program for long-distance gas pipeline systems based on quantitative risk assessment.

It is recommended that, for reasons of safety, the pipeline be inspected at the most critical levels in the event of defects with different time intervals. In this regard, it is prudent to consult the technical guidance in POF (2016) in relation to the other positions. Furthermore, it is necessary to conduct a more thorough examination of the cause of non-measurement in sections of the pipeline system that are being inspected.

The results indicate that the duct has a relatively long useful life (60 years until wall collapse) due to the high values of the diameter and thickness of the duct wall. This is a duct with a very conservative dimension. These results are in accordance with numerical studies of the sensitivity of random variables, whose objective is to verify the greater or lesser influence of these variables on the failure of a pipeline. The existing literature indicates that the depth of the defect, the internal pressure of the fluid, the diameter, and the thickness of the pipeline wall have a significant impact on the probability of pipeline failure.

Moreover, the probability of failure over time when employing two MFL pigging operations was found to be comparable to that of the previous operation. In this case, the use of fewer inspection processes could result in a reduction in predictive maintenance costs.

Furthermore, it is often challenging to conduct a reliability assessment based on failure data due to the lack of observed or recorded failures in history. In such instances, the inspection data typically represents a collection of information regarding the degradation of the pipeline. The data provides insights into the corrosion of the pipeline within the selected period, which can be used to inform the reliability assessment.

As future studies are conducted, it is recommended that a cost-benefit analysis be conducted to verify whether it is possible to reduce pigging operations while maintaining the same or equivalent technical and operational result.

Acknowledgements

The authors are grateful to UFES (Universidade Federal do Espírito Santo) and PETROBRAS (Petróleo Brasileiro S/A) for the support and efforts provided in this initiative. Teacher Oldrich Joel Romero extends his gratitude to the FAPES - Fundação de Amparo à Pesquisa e Inovação do Espírito Santo for their financial support, as evidenced by Fapes Notice N^o 6/2021 - Capixaba Researcher Scholarship, TO 356/2022.

References

• ABDALLA FILHO, J. E; MACHADO, R.; BERTIN, R.; VALENTINI, M. On the failure pressure of pipelines containing wall reduction and isolated pit corrosion defects. Computers and Structures, Elsevier Ltd. 132, p. 22-33, 2014.
• ABUBAKIROVA, R.; YANGA, M.; KHAKZAD, N. A risk-based approach to determination of optimal inspection intervals for buried oil pipelines. Process Safety and Environmental Protection, Elsevier B.V, 134, p. 95-107, 2020.
• AHAMMED, M. Probabilistic estimation of remaining life of a pipeline in the presence of active defects. International Journal of Pressure Vessels and Piping, v. 75, p. 321-329, 1998.
• AMAYA, R.; SANCHEZ-SILVA, M.; BASTIDAS-ARTEAGAC, E.; SCHOEFSC, F.; MUNOZ, F. Reliability assessments of corroded pipelines based on internal pressure: a review. Engineering Failure Analysis, Jan. 2019.
• AMERICAN SOCIETY OF MECHANICAL ENGINEERS. ASME B31G: manual for determining the remaining strength of corroded pipelines, 1991.
• AMERICAN SOCIETY OF MECHANICAL ENGINEERS. ASME B31.8S: managing system integrity of gas pipelines, 2004.
• ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS. ABNT NBR ISO 15649: tubulação para a indústria de petróleo e gás natural. Rio de Janeiro: ABNT, 2004.
• BHANDARI, J.; KHAN F.; ABBASSI R.; GARANIYA, V; OJEDA R. Modeling of pitting corrosion in marine and offshore steel structures: a technical review. Journal of Loss Prevention in the Process Industries, Elsevier Ltd., 37 p. 39-62, 2015.
• CALEYO, F.; GONZALEZ, J.; HALLEN, J. A study on the reliability assessment methodology for pipelines with active corrosion defects. International Journal of Pressure Vessels and Piping, Elsevier Science Ltd., 79, p. 77-86, 2002.
• FERREIRA, E. Análise de confiabilidade: método SORM DG. Dodo Books Indian Ocean Ltd. Chisinau, 2020. (Novas Edições Acadêmicas).
• INTERNATIONAL ORGANIZATION FOR STANDARDIZATION. ISO 13703: petroleum and natural gas industries - design and installation of piping systems on offshore production platforms. ISO 13703:2000(E)., 2000.
• KARDEC, A.; NASCIF, J. Manutenção: função estratégica. Rio de Janeiro: Qualitymark Editora Ltda., 1999.
• KRISHNASAMY, L.; KHAN, F.; HADDARA M. Development of risk-based maintenance (RBM) strategy for a power-generating plant. Journal of Loss Prevention in the Process Industries, 18, p. 69-81, 2005.
• MADSEN, H.; KRENK, S.; LIND, N. Method of structural safety. New Jersey: Prentice-Hall, 1986.
• MOKHTAR, A.; ISMAIL, M.; MUHAMMAD, M. Comparative study between degradation analysis and first order reliability method for assessing piping reliability for Risk-Based Inspection. International Journal of Engineering & Technology IJET-IJENS, v. 09, n.10, 2009.
• MUHLBAUER, W. Pipeline risk management manual: ideas, techniques, and resources. 3. ed. Elsevier, Jan. 2004.
• NICOLETTI, E.; SOUZA, R.; OLIVIER, J. External corrosion Growth on an Ageing Pipeline: a case study. In: INTERCORR ABRACO, Fortaleza, maio 2010. INTERCORR2010_272.
• PANDEY, M. Probabilistic models for condition assessment of oil and gas pipelines. NDT&E International, v. 31, n. 5, p. 349-358, 1998.
• PIPELINE OPERATORS’ FORUM. POF 2016. Specifications and requirements for in-line inspection of pipelines. Version 2016.
• THOM, F. Cálculo da confiabilidade de tubulações de óleo e gás baseado em amostragem por hipercubo latino e estratificada. Dissertação (Mestrado em Engenharia Mecânica) - Universidade Federal do Espírito Santo, Vitória, 2003.
• THOM, F. Modelo de cálculo de risco dinâmico aplicado a compressores de gás. 2018, 299f. Tese (Doutorado em Engenharia Civil) - Escola de Minas, Universidade Federal do Ouro Preto, Ouro Preto, 2018.
• THOM, F.; SISQUINI, G.; FREITAS, M. Inspeção baseada no risco (IBR) aplicado a dutos de petróleo e gás: estudo de caso. In: CONGRESSO BRASILEIRO DE MANUTENÇÃO E GESTÃO DE ATIVOS - ABRAMAN, 29. Anais [...]. Santos, p. 1-16, 2014.
• THOM, F.; SISQUINI, G.; JESUS, M.; OLDRICH, J. Aplicação da inspeção com pig do tipo MFL na determinação da probabilidade de falha de gasodutos. CONEMI - CONGRESSO INTERNACIONAL DE ENGENHARIA MECÂNICA E INDUSTRIAL, 23. Anais [...]. Vitória, 2023.
• THOM, F.; ZOGHBI, J.; FREITAS, M.; SISQUINI, G. Dynamic risk calculation model applied to gas compressors. REM - International Engineering Journal, Ouro Preto, v. 73, n. 1, p. 33-41, jan./mar. 2020.
• ZELMATI, D.; BOULEDROUA, O.; GHELLOUDJ, O.; AMIRAT, A.; DJUKIC, M. A probabilistic approach to estimate the remaining life and reliability of corroded pipelines. Journal of Natural Gas Science and Engineering, Elsevier Ltd. 99, 104387, 2022.
• ZHAOYANG, T.; JIANFENG, L.; ZONGZHI, W.; JIANHU, Z.; WEIFENG, H. An evaluation of maintenance strategy using risk-based inspection. Safety Science, 49, 852-860, 2011.

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Publication Dates

• Publication in this collection
  13 Jan 2025
• Date of issue
  2025

History

• Received
  25 Mar 2024
• Accepted
  12 June 2024