4
Estimating the Risk of Pipeline Failure Due to Corrosion
M. NESSIM
C-FER Technologies Inc., Edmonton Alberta, Canada
A. INTRODUCTION Metal loss corrosion is one of the major causes of pipeline failures. For example, failure statistics collected by the U.S. Department of Transportation indicate that 17% of reportable gas pipeline failures and 27% of reportable liquid pipeline failures are caused by corrosion [I]. In Alberta, where there is a large percentage of gathering pipelines and consequently more significant internal corrosion problems [2], corrosion accounts for approximately 40% of all pipeline failures. As the pipeline network ages, it is important to understand the risk of failure due to corrosion and take appropriate measures to keep it at tolerable levels. Risk is defined in the Concise Oxford Dictionary as "the chance of loss", which captures the two main components of risk, namely, an uncertain event (chance) that can cause adverse consequences (loss). In the context of pipeline corrosion, risk, /?, can be defined as the probability of a corrosion-caused failure, P, multiplied by a measure of the failure consequences, C (i.e., R = PC). There is a significant body of literature dealing with pipeline failure risks due to corrosion [31O]. Existing approaches can be classified as either qualitative or quantitative methods. Qualitative methods provide approximate rankings of pipeline segments with respect to the risk of failure. These rankings are based on combining subjective scores assigned to each attribute that affects the risk of corrosion (e.g., age, operating temperature, cathodic protection, and soil corrosivity). Quantitative risk assessment methods on the other hand attempt to provide actual estimates of the probability and consequences of failure, based on historical data and analytical models. As such, they require a more significant effort to implement, however, they have the potential to provide more objective and reliable results. The objective of this chapter is to describe an approach for estimating the risk of pipeline failure due to corrosion, and for making efficient maintenance decisions to control corrosion-related problems. Although the focus is on pipeline corrosion, the overall framework and many of the concepts are applicable to other systems such as downhole casing, boilers, and pressure vessels.
B. CHARACTERIZING PIPELINE CORROSION Figure 1 shows a sketch of a typical external corrosion defect, which usually consists of a number of individual pits that grow until they join together into a single feature. The parameters used to
Uhlig's Corrosion Handbook, Second Edition, Edited By R. Winston Revie. ISBN 0-471-15777-5 ? 2000 John Wiley & Sons, Inc.
Length
Area = Average Depth x Length Maximum Depth
Pipe Wall Thickness
FIGURE 1. Geometry of a corrosion defect.
characterize a corrosion feature are shown on the figure. They may include defect length (defined as the maximum length of the corrosion feature along the pipe axis) and defect depth (which can be characterized by either the maximum depth, or the average depth along the deepest route through the feature). There are several inspection technologies that can be used to provide direct or indirect information on pipeline corrosion defects. These include Coating damage survey methods such as Pearson surveys, current attenuation surveys, close interval potential surveys (CIPS) and the dc voltage gradient (DCVG) survey technique. These methods detect coating damage and provide an indication of the severity (or size) of damage. Differences between these methods relate to the physical principles used, and the type of information and interpretation required. Some survey methods produce additional information (beyond coating damage indications) that is relevant to corrosion. The CIPS, for example, determine the effectiveness of cathodic protection, whereas DCVG surveys provide an indication of whether or not corrosion is active at a given location. Harvey [11] gives a summary of the capabilities and limitations of different coating damage survey methods. Low-resolution or high-resolution in-line inspection tools. Low-resolution tools generally provide the location of metal loss corrosion defects and a coarse estimate of the maximum defect depth (e.g., <30%, 30-50%, and >50% of the pipe wall thickness). High-resolution inspection tools provide information on the number, location, and geometry of defects (including estimates of defect length, width, and average or maximum defect depth). Some inspection vendors offer an incremental approach in which low-resolution data is provided, with the option of an information upgrade that provides high-resolution inspection data. Regardless of how sophisticated a certain inspection method is, there are always accuracy limitations associated with the information provided. C. PRESSURE RESISTANCE OF CORRODED PIPELINES The degree of reduction in the pressure capacity of a pipeline at a corrosion defect depends on the defect size (specifically, depth, and length). The pipe resistance, /?, can be calculated as a function of
defect geometry, pipe geometry, and material yield strength using the following relationship [12]:
?>-?'№K+
c
(Ib)
M(T) = y 1 + 0.6275^f - 0.003375^f
where Tis the wall thickness, D is the pipe diameter, S is the yield strength, M(T) is a geometric factor (called the Folias factor) that accounts for bulging of the pipe before failure, L is the defect length, C is a model uncertainty factor (see below), and T is time. It is noted that the resistance is a function of time since both defect depth and length are treated as functions of time to account for defect growth:
H(T)= H(O)+ T G* L(T) -L(O) + T G1 (2a) (2b)
where H(Q) and L(O) represent the defect depth and length at present and Gh and G/ are the defect depth and length growth rates. Equation (1) is based on a semiempirical relationship that was developed in the early 1970s [13,14]. Figure 2 shows the results of this model plotted against the results of burst tests carried out on corroded pipe taken out of service [15]. This figure indicates that there is some uncertainty associated with the results of the model, hence the model uncertainty factor C in Eq. (1). Regression analysis of the data in Figure 2 shows that C has an average value of 1.38 MPa. Example 1: Consider a 914-mm OD X60 pipeline with a wall thickness of 8.74mm and an operating pressure of 5.7 MPa. Assume that the line has a corrosion feature with a length of 75 mm and an average depth of 1.5 mm. Also assume that defect depth and length have growth rates of 0.35 and 1.0 mm/year, respectively. Figure 3 shows the resistance of this corrosion defect as a function of time as calculated from Eqs. (2) and (3). Figure 3 shows that, if not repaired, this feature will fail after 17 years.
Calculated Burst Pressure (MPa)
FIGURE 2. Burst test versus corrosion model results.
Load / Resistance (MPa)
Resistance Load
Time (years) FIGURE 3. Resistance at a single corrosion defect as a function of time (Example 1).
D. PROBABILITY OF FAILURE DUE TO CORROSION As demonstrated in Section C, a corrosion failure occurs when the pressure resistance at the defect drops below the maximum operating pressure (see Fig. 3). Because of the uncertainties associated with defect sizes, growth rates, pipe material yield strength, and model error, there is some uncertainty regarding the calculated value the time-to-failure for a specific corrosion defect. The time to failure is therefore best characterized in probabilistic terms. The probability of failure on or before time T, /?/(T), is equal to the probability that the resistance, R(i), will drop below the applied pressure, A. This can be expressed as follows: pf(i) = p[R(i) <A}= p[R(i) - A < O] (3)
Substituting the value of R(i) from Eqs. (1) and (2) gives the probability of failure as the probability of occurrence of a particular combination of pipeline and defect attributes (viz., diameter wall thickness, yield strength, defect dimensions, and growth rates) that lead to a lower resistance than the applied pressure. There are a number of standard methods that can be used to calculate this probability from the probability distributions of the basic pipeline and defect attributes [16, 17]. It is also possible to calculate the probability of failure during a given time interval (TI to T2), given that the pipeline survives to the beginning of this interval from Eg. (5) [18]:
x*. <?<??>-"^y
<>
4
If the time interval is taken as 1 year, Eq. [4] gives the annual probability of failure as a function of time. Finally, if it is assumed that failures at individual corrosion features are independent events, the probability of failure per kilometer of pipe can be calculated by multiplying the probability of failure per defect by the number of defects per kilometer. Example 2: Assume that the pipeline in example 1 has an average of 2.5 corrosion defects per kilometer and that the pipeline and defect attributes used in Eqs. (1) and (2) are as given in Table 1. Figure 4 gives the annual probability of failure as a function of time [as calculated from Eqs. (3) and (4)] for this pipeline.
TABLE 1. Probability Distributions of Input Parameters (Example 2) Parameter Yield strength Pipe wall thickness Pipe diameter Model error — A Model error — B Defect depth Defect length Depth growth rate Length growth rate Mean Value
COV (%) 3.5 1.0 0.06 O 110 45 40 O O
Distribution Type Normal Normal Normal Fixed Normal Log normal Log normal Fixed Fixed
Data Source Mill data Mill data Mill data Regression analysis Regression analysis Assumed Assumed Shannon and Argent (1989) Assumed
461 MPa 8.74mm 914mm 1.0 1.38 1.8mm 120mm 0.1 mm/year 5 mm/year
Time (years) FIGURE 4. Probability of failure as a function of time for pipeline in example 2.
E. IMPACT OF MAINTENANCE ON RELIABILITY 1. Characterization of Inspection Accuracy 1.1. Detection Power An inspection method is not guaranteed to detect all defects and therefore there is a chance that an existing defect will be missed. The probability of detecting a specific defect can be characterized as a function of defect size; the larger the defect, the higher the probability that it will be detected. Rodriguez and Provan [19] suggested the following characterization of the probability of detection: P^l* = 1-?-?* (5)
where pd\h is the probability of detection for a defect with size h, and q is a constant that determines the overall power of the detection method. 1.2. Sizing Accuracy There is also a random measurement error, E, associated with defect sizes estimated from in-line inspection. Measurement errors are usually modeled by a normal distri-
bution. The mean value of E is equal to the systematic bias of the measurement (or zero if there is no bias) and the standard deviation represents the random error component. These parameters can be obtained from vendor specifications or from verification excavation data [2O]. 2. Effect of Inspection and Repair on Defect Size The process of inspection and repair improves the pipeline condition by modifying the probability distributions of defect size and defect frequency. The degree of modification depends on the accuracy of the inspection method and the threshold used for repair. Figure 5 illustrates the steps involved in characterizing the remaining defects after inspection. Initially, the inspection divides the population of original defects into detected and undetected defects. Since larger defects are more likely to be detected (see Section E.I), detected defects are likely to be larger on average than the original defects. Similarly, undetected defects will be smaller on average than the original defects. This is illustrated in Figure 6 [21], which shows that the size distribution is shifted to the right for detected defects and to the left for undetected defects. The inspection tool used in developing the plots in Figure 6 is assumed to have a detection constant q = 0.4 [see Eq. (6)]. The inspection tool will provide a measured size of detected defects, which will be somewhat different from the actual size because of tool accuracy limitations. A repair criterion will typically be applied to each detected defect to identify ones that require repair. The repair criterion may be based on the measured defect depth or the calculated failure pressure (from the measured defect depth and length) at the defect location. The population of remaining defects will then consist of defects that did not meet the repair criterion. Because the repair decision is based on the measured (rather than the actual) defect size, some critical defects may have been undersized by the inspection tool, and will therefore be left not repaired.
Size of original defects Inspection detection power
Size of detected defects Inspection sizing accurracy Size of undetected defects Measured size of detected defects
Repair criterion
Size of remaining detected defects
Size of all remaining defects
FIGURE 5. Modeling the impact of inspection and repair on corrosion defect population.
Original Detected Undetected Probability
Defect Size (mm)
FIGURE 6. Size distributions of original, detected, and undetected defects.
TABLE 2. Measurement Error Parameters for a Typical High-resolution In-line Inspection Tool Parameter Defect depth measurement error Defect length measurement error Average (mm)
O 15
Standard Deviation (mm)
0.68 27
Distribution Type Normal Normal
Detected 1.25 MAOP 1.5 MAOP Probability
Defect Depth (mm) FIGURE 7. Probability distributions of defect size before and after repair. The population of remaining defects can be obtained by combining undetected defects with defects that were detected but not repaired. Figure 7 shows a comparison between the size distributions of an original defect population and the corresponding population of defects remaining after inspection and repair of all defects with a failure pressure <1.25 and 1.5 of the maximum allowable operating pressure (MAOP). The measurement error parameters for the inspection tool used are assumed to be as shown in Table 2. The figure shows that the inspection and repair shifts the
defect size to the left (lower values). The average number of defects per kilometer remaining after repair can be obtained by subtracting the number of defects that are detected and repaired from the original average number of defects per kilometer. Details of the calculations used to produce the results in this section are given by Nessim and Pandey [21].
F. APPLICATION TO MAINTENANCE PLANNING 1. Problem Definition Consider the gas pipeline used in Examples 1 and 2 (914-mm OD X60 with a wall thickness of 8.74 mm and an operating pressure of 5.7 MPa) with the corrosion defect population given in Table 1. Assume that the pipeline is being considered for a high-resolution in-line inspection with the tool characterized in Table 2. A maintenance plan in this case involves answering the following questions: 1. What is the optimal time interval to first inspection of the pipeline? 2. Once the first inspection is performed, what are the optimal repair criterion and interval to next inspection? 2. Time to First Inspection The annual failure probability for this pipeline in its initial state is plotted in Figure 4. The time to first inspection can be estimated from this figure by defining a maximum allowable probability of failure and finding the time at which this probability will be exceeded. Figure 4 shows that if the maximum allowable probability were 10~3/km.year, the inspection would be required after 3 years. It is also possible to base the decision on a cost optimization analysis. The expected total annual cost, c,, for each choice can be calculated from Ct =PfCf + (Ci + nrcr} [ ^ _ ( 1 M + M p J
(7)
in which the first term is the expected annual failure cost calculated as the annual probability of failure, pf, multiplied by the cost of failure c/in present day currency; and the second term is the total maintenance cost per kilometer amortized over the time to next inspection. The total maintenance cost is calculated as the sum of the inspection cost per kilometer, ct, and the average number of repairs per kilometer, nr, multiplied by the cost per repair, cr. This cost is amortized over the interval to next inspection T/, based on a real interest rate of u. If we assume that the cost of failure is $1 million, the inspection cost is $4000/km, the cost of repair is $5000 per defect and the real interest rate is 5%, the total expected cost will be as shown in Figure 8. This figure plots the results for the status quo and for an inspection followed by repair of all defects with a failure pressure less than 1.25 MAOP. The minimum cost associated with the inspection option is $1.8 million, corresponding to an inspection interval of ~7 years. The cost associated with the status quo is less than $1.8 million for the first 9 years. This means that the optimal solution is to carry out the inspection after 9 years. 3. Inspection Interval and Repair Criterion It is now assumed that the inspection has been carried out after 9 years, and that an average number of 1.3 defects per kilometer is found, with the depth and length distributions given in Table 3. The
No inspection
Inspection with repair at 1.25 MAOP
Time to Next Inspection (Years) FIGURE 8. Total annual costs for the inspection and no inspection options. TABLE 3. Corrosion Parameters Obtained from an Inspection Parameter Defect depth Defect length Number of detected flaws Average 2.5mm 120mm 1.3 per km
COV (%) 60 50 O
Distribution Type Log normal Log normal Fixed
maintenance planner wishes to choose a repair criterion and an interval to next inspection. Figure 9 can be used to make this decision on the basis of the maximum allowable failure probability. It shows that a repair criterion of 1 .25 MAOP is inadequate to meet a target annual failure probability of 10~3. A repair criterion of 1.5 MAOP would lead to an acceptable probability of failure for the next 15 years. Based on this a repair criterion of 1 .5 MAOP should be used and the next inspection should be carried out after 15 years. The cost optimization calculations lead to the results in Figure 10. The lowest cost is associated with a repair criterion of 1.5 MAOP and an interval to next inspection of 14 years.
Annual Probability of Failure per km
No repair 1.25 MAOP 1.5 MAOP
Time to Next Inspection (years) FIGURE 9. Annual probability of failure for three different repair criteria.
Annual Cost ($1000/km)
No repair 1.25 MAOP 1.5 MAOP
Time to Next Inspection (years) FIGURE 10. Total annual cost for three different repair criteria.
G. SUMMARY This chapter describes a framework for risk-based assessment of pipeline corrosion risk, and demonstrates maintenance planning with a risk-based approach. The examples developed serve to demonstrate the benefits associated with risk-based planning: 1. Consistent safety levels. Minimum safety targets can be set and actions taken to ensure that they are met across a whole system. 2. Optimal balance between maintenance costs and failure risks. Maintenance plans that achieve safety goals at a minimum possible cost can be defined. This can result in significant savings in overall operating costs. 3. Documentation of rationale behind decisions. The analysis process provides the reasoning and documentation needed to communicate prudent risk management.
H. REFERENCES
1. AGA, An Analysis of Reportable Incidents for Natural Gas Transmission and Gathering Lines—June 19941990. NG-18 Report No. 200, prepared by Battelle Memorial Research Institute for the Line Pipe Research Supervisory Committee of the American Gas Association, 1992 Arlington, VA. 2. Alberta Energy and Utilities Board, Pipeline Performance in Alberta 1980-1997, EUB Report 98-G, 1998, Calgary, Alberta, Canada, p. 12. 3. M. A. Nessim and M. J. Stephens, Optimization of Pipeline Integrity Maintenance Based on Quantitative Risk Analysis. Proceedings of the Pipeline Reliability Conference, Houston, TX, 1995. 4. W. K. Muhlbauer, Pipeline Risk Management Manual. Gulf Publishing Company, Houston, TX, 1992. 5. M. Urednicek, R. I. Coote, and R. Courts, Optimizing Rehabilitation Process with Risk Assessment and Inspection. Proceedings of the CANMET International Conference on Pipeline Reliability, Calgary, June II12-1 to 11-12-14, Gulf Publishing, Houston, TX, 1992. 6. T. B. Morrison and R. G. Worthingham, Reliability of High Pressure Line Pipe Under External Corrosion. Proceedings of the Eleventh International Conference on Offshore Mechanics and Arctic Engineering, Vol. VB, Pipeline Technology, Calgary, Alberta, Canada, 1992. 7. G. D. Fernehough, The Control of Risk in Gas Transmission Pipeline. Institution of Chemical Engineers, Symposium, No. 93, 25-44, 1985, Manchester, England.
8. R. T. Hill, Pipeline Risk Analysis. Institution of Chemical Engineers Symposium Series, No. 130, 637-670, 1992, Manchester, England. 9. R. B. Kulkarni and J. E. Conroy, Development of a Pipeline Inspection and Maintenance Optimization System (Phase I). Gas Research Institute Contract No. 5091-271-2086, 1991, Chicago, IL. 10. J. F. Kiefner, P. H. Vieth, J. E. Orban, and P. I. Feder, Methods for Prioritizing Pipeline Maintenance and Rehabilitation. Final Report on Project PR3-919 to the American Gas Association, 1990, Arlington, VA. 11. D. W. Harvey, Materials Performance, 33 (8), August, 22-27, 1994. 12. M. Brown, M. Nessim, and H. Greaves, Pipeline Defect Assessment: Deterministic and Probabilistic Considerations. Second International Conference on Pipeline Technology, Ostend, Belgium, September 1995. 13. J. F. Kiefner, W. A. Maxey, R. J. Eiber, and A. R. Duffy, Failure Stress Levels of Flaws in Pressurized Cylinders. Progress in Flaw Growth and Fracture Touchness Testing, ASTM STP 536, American Society for Testing and Materials, 461-481, 1973, Philadelphia, PA. 14. R. W. E. Shannon, Inter. J. Pressure Vessel Piping, 2, p. 243 (1974). 15. J. F. Kiefner and P. H. Vieth, Project PR 3-805: A Modified Criterion for Evaluating the Remaining Strength of Corroded Pipe. A Report for the Pipeline Corrosion Supervisory Committee of the Pipeline Research Committee of the American Gas Association, 1989, Arlington, VA. 16. A. H-S. Ang and W. H. Tang, Probability Concepts in Engineering Planning and Design—Volume II: Decision, Risk and Reliability. Wiley, New York, 1984. 17. H. O. Madsen, S. Krenk, and N. C. Lind, Method of Structural Safety. Prentice-Hall, Englewood Cliffs, NJ, 1986. 18. Reference 17, p. 287. 19. E. S. Rodriguez HI and J. W. Provan, Corrosion, 45(3), 193 (1989). 20. G. Avrin and R. I. Coote, On Line Inspection and Analysis for Integrity. Pacific Coast Gas Association, Transmission Conference, Salt Lake City, UT, 1987. 21. M. A. Nessim and M. D. Pandey, Reliability Based Planning of Inspection and Maintenance of Pipeline Integrity. C-FER Report 95036, 1996, Edmonton, Alberta, Canada.