Model helps prevent failures from pressure-induced fatigue

HYDROSTATIC TESTING-Conclusion

Liquid pipeline service failures have occurred because of pressure-cycle-induced fatigue crack growth of defects.¹ Our own familiarity with this phenomenon suggests that it may be more common than the public record reveals.

Such failures have also been prevented, however, by preemptive responses by pipeline operators worldwide.

This final of two articles on hydrostatic testing presents a technique that has assisted operators in addressing and controlling pressure-cycle-induced fatigue crack growth.

Part 1 of this series (OGJ, July 31, 2000, p. 54) presented findings related to the use of hydrostatic testing to verify pipeline integrity.

Crack growth

As constructed, pipelines may contain defects or imperfections from the pipe-manufacturing process, transit fatigue, or construction flaws. If severe, these defects will not survive the initial preservice hydrostatic test and will be eliminated.

If they are not severe enough to fail in the test, they will remain in the pipeline and may become enlarged by pressure-cycle-induced fatigue. This situation is illustrated schematically in Fig. 1a by the failure-pressure-vs.-crack-size relationship.

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Fig. 1a shows that no flaw larger than a_T can survive the initial test. The test establishes an initial safety margin because flaws must be larger than a_T (as large as a_S) to fail at the maximum operating pressure (MOP).

If a mechanism exists for flaws to grow in service, the margin will be eroded and, as shown in Fig. 1b, after a time (t₁), an existing flaw of size a_T may grow to a size a_S. At that point, a service failure at the MOP becomes possible.

If this situation is anticipated, however, and if the rate of crack growth is predictable, a pipeline operator can make a timely intervention before the size a_S is reached.

By conducting a current hydrostatic test, the operator can either remove those flaws that now have sizes larger than a_T or at least prove that they do not exist. The maximum remaining defect size is then reset to a_T.

Pressure cycles

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Fig. 2 shows a typical 15-month service pressure spectrum for a liquid pipeline. Literally hundreds of large variations in pressure occur as various pumping schemes are used to meet shippers' requirements and take advantage of varying electric-power rates between daytime and nighttime.

Variations in pressure cause variations in hoop stress, and if a longitudinally oriented crack is present, the variation in stress can cause the crack to grow. An accompanying box presents the mathematically defined term "stress-intensity factor," which is the crack-driving force.

As "K" is proportional to S, DK is proportional to DS. In other words, fluctuating stress causes K to fluctuate, and a fluctuating K represents the factor that will cause a crack to grow.

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Notice that K is a function of crack size "a" as well as a function of S. In fact, the log of the rate of crack growth, da/dN, has been shown to be proportional to the log DK (Fig. 3). This results in an equation for da/dN.

By solving for dN and integrating, one can predict the number of cycles required to grow the crack from an initial size a_T established by a test to the size a_S that will fail at the MOP.

This relationship is often called the "Paris" law after the person who first proposed it. It is a form of linear-elastic fracture mechanics.

Model

Crack-growth models can be used to evaluate the effect of pressure-cycle-induced growth on the possibly remaining flaws in a pipeline. One such model, referred to as RETEST,² is based on linear-elastic fracture-mechanics (LEFM) principles and assumes that a family of "initial" defects is present in the pipe.

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As a first step in a RETEST analysis, the user establishes the sizes of both the initial and the final defects. The initial defects (or cracks) are assumed to be the largest sizes that could barely survive at the hydrostatic test pressure. The final defects (or cracks) are assumed to be those that would fail at the maximum operating pressure (MOP).

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The hydrostatic test pressure level, the pipe geometry (diameter and wall thickness), and the material properties, flow stress, and fracture toughness, are important parameters in this assessment. They determine the initial crack sizes that could survive the hydrostatic test and the final crack sizes that will fail at the MOP.

Since the number of defects of all possible sizes (length-and-depth combinations) that could survive the hydrostatic test is infinite, the analysis utilizes nine defect depths ranging from 10-90% through-the-wall thickness (in 10% increments).

The corresponding length for each of these nine defects is determined based on its depth, the hydrostatic test pressure, and the Charpy V-notch impact energy and flow stress. A mathematical model is used to calculate these sizes.³

The pressure-cycle data are used as the mechanism for fatigue-crack growth. The actual pressure data are rainflow-cycle counted.⁴ This procedure appropriately matches pressure pairs (peaks and valleys) for the pressure-cycle spectrum.

The pressure-cycle data (DPs) are applied to each of the nine defects defined above until the defect reaches the final size (calculated as explained above) that will fail in service. A linear-elastic model is used to calculate the applied stress-intensity-factor ranges (Ds) that cause the cracks to grow in response to the pressure cycles (DPs).⁵

This approach is suitable because the cracks grow in microscopic steps in an essentially elastic-strain regime in response to the cycles of pressure. The length of time (in years) to failure is then determined based on the representative time period of the pressure-cycle data.

For example, if the pressure-cycle data represent 1 month of operations and the analysis applies these same pressure data 18 times before the defect reaches a critical size, the fatigue life of the defect is 1.5 years (18 months).

The rate of crack growth induced by the pressure-cycle spectrum is modeled using the Paris Law equation:⁶

da over dN = C (DK)nwhere:a = Crack depthN = Number of pressure cyclesda over dN = Amount of crack growth per cycleK = Stress-intensity factor for a given pressure cycle.The constant (C) and the exponent (n) characterize the rate of fatigue-crack growth applicable to the particular material and environment of interest.PropertiesThe material properties (C and n) appropriate for the analysis are typically established on the basis of an actual fatigue-related leak in a pipeline. The constants are determined based on the apparent dimensions of the initial defect that has been observed to grow to failure after a certain number of years in service.The yield strength (YS) of the pipe material is used in the analysis to define a flow stress (FS) of the pipe material: YS + 10,000 psi.The fracture toughness of the material is approximated by an equivalent full-size Charpy V-notch impact energy. This value of toughness is based on the defect size and failure pressure level determined during the examination of the leak and on the apparent size of the flaw that caused the failure.Operating cyclesFor the typical pipeline to be analyzed, pressure data can be supplied in digital format for relevant pump stations. These pressure data can be acquired simultaneously at 15-min intervals for representative operating periods.To calculate pressures at intermediate points between each of the stations, we typically use a gradient factor of k = the specific gravity of the product times 0.433 to represent head loss. An average of the specific gravities of all products can be used.Accordingly, the pressure (P_X) at any point between stations under flowing conditions is shown in the accompanying equation box. This method is used to determine the pressure cycles for all of the chosen locations between pump stations.Results

Click here to enlarge imageTable 1 shows typical partial results of RETEST-1 analyses. The table presents years to failure for six locations on a particular pipeline.Each line in Table 1 represents one analysis case. Numerous cases may have to be run for a given pipeline because of changes in features, hydrostatic test pressures, and operating circumstances along a pipeline.In Table 1, several cases are shown for illustrative purposes, but, to simplify the table, only four of the nine initial flaw depths are shown. Only growth in depth, not growth in length is considered because experience shows that flaw length changes very little with pressure cycles, an amount that can be ignored for analysis purposes.This is not to say that length is unimportant. It is important because it significantly affects the failure pressure and the crack-driving force.While one would suspect that the most fatigue-prone regions of a pipeline would be the regions immediately downstream from the pump stations, this is not always the case.For example, one critical case in Table 1 is Case 6. It has about the same time to failure as Case 1. While its location is 30 miles from the pump station, thus making it subject to a smaller range of pressure per cycle, it happens to be a point where the wall thickness changed.As a result, the stress cycles based on the pressure cycles are nearly as large as those at the pump station where the wall thickness is greater. The point is that several areas have to be checked to determine which one governs the retest interval.The choices of cases for analyses are driven by changes along the pipelines, as mentioned previously. Case 1, for example, was chosen because it was just downstream of the first pump station where one would expect the largest ranges of pressure cycles.Cases 2 and 5 were chosen because of the relatively low test-pressure-to-operating-pressure ratios at those locations. Cases 4 and 6 were chosen because, even though both are quite a ways downstream from the first pump station, they represent changes in wall thickness. The pressure cycles are smaller, but the stress cycles are actually fairly large.There are other ways to display the data obtained from RETEST analyses. These include plots of initial defect depth vs. years to failure and plots of defect depth vs. time (the inverse of the previous plots). The latter type of plot is useful as discussed below for illustrating the effects of test-pressure-to-operating-pressure ratio and for comparing the effectiveness of testing to in-line inspection.It may already be clear to the reader that this type of analysis could be used to predict times to failure after an appropriate in-line inspection. Certainly that is the case.A reliable in-line tool for locating and characterizing longitudinally oriented cracks typically will have a threshold detection size. Below that threshold size, detection and sizing will be less than highly certain. Above that threshold, detection and sizing is expected to be reliable to a high degree of certainty.Using that threshold size (length and depth), one can conduct a remaining-life assessment for the flaw that is at the detection threshold size limits. The reinspecting interval can then be based on that predicted time to failure.Safety factorGiven the relatively recent application of remaining-life assessment to pressure-cycle fatigue in the pipeline industry, no standard exists for setting a safety factor. Traditionally, we have recommended a safety factor of two.That is, we believe that it is prudent to retest or re-inspect a pipeline in which fatigue-crack growth is suspected after one-half of the predicted time to failure has elapsed.This choice is based on our standard practice of making all other assumptions on a worst-case basis. For example, we assume that the largest possible undetected flaw is present. We also use worst-case crack-growth rates unless a less aggressive crack-growth rate has been demonstrated. And, we use the most aggressive pressure-cycle spectrum when the spectra change from time to time.We believe that the factor of two adequately covers the uncertainties regarding changes in operations and unknown factors in the environment that might accelerate crack growth.Other circumstancesIn the foregoing, we have described only the mechanics of the analysis process and the standards for its use. In this final section, it is important to point out factors that should be taken into account if and when a pipeline operator chooses to conduct periodic hydrostatic testing or in-line inspections to deal with a known or suspected fatigue-crack problem.The following discussion leads to the conclusion that if an operator is going to the trouble and expense to conduct retesting, the highest possible test-pressure-to-operating-pressure ratios should be used.This discussion also shows that because in-line inspection will locate smaller flaws than a hydrostatic test, it can be done with less frequency than a hydrostatic test.

Click here to enlarge imageFig. 4 presents an actual crack-depth-vs.-cycles relationship similar to one type of plot that can be obtained from a RETEST analysis. Fig. 4, however, is based on an actual experiment with a particular type of pipe into which a flaw was machined.Once the flaw began to grow by the application of uniform pressure cycles, continuous monitoring of the crack using the DC electric-potential technique generated the "a" -versus- "N" relationship shown in Fig. 4. Notice that the relationship is highly nonlinear. This is because the crack-driving force, DK, is a function not only of DP (the change in pressure that was constant throughout the test), but also a function of "a" that is growing larger with each cycle. The crack-growth rate da/dN is proportional to DK; hence, it increases steadily.Shown on Fig. 4 are three potential levels of hydrostatic tests, each of which is considerably above the maximum pressure in the service-simulating pressure cycles (0 to 1,000 psig).The levels represent the crack depth (for a fixed crack length) that will just barely survive the test to the level shown. In other words, a crack that is 0.10-in. deep will just survive the 1,300-psig test, a crack that is 0.12-in. deep will just survive the 1,250-psig test, and a crack that is 0.13-in. deep will just survive the 1,200-psig test.The "a"-vs.-"N" curve shows that the crack was initially slightly more than 0.09-in. deep at the start of pressure cycling, and that it grew to failure in about 8,000 cycles. None of the three tests would have revealed the initial crack with its depth of only 0.09 in.If a hydrostatic test to 1,300 psig had been conducted at any point during the 8,000-cycle life, one of two things would have happened:If the test had been conducted before the 2,000th cycle, the defect would have survived and failed 6,000 cycles later.If the test had been conducted after the 2,000th cycle but before the 8,000th cycle, the defect would have failed in the test and, thus, would not have failed in service.The important thing to remember is that the test ensures a life of at least 6,000 cycles.In a similar manner, one can assess the possible outcomes of testing to levels of 1,250 or 1,200 psig. In the case of the 1,250-psig test, the important conclusion is that the test ensures a life of only 3,500 cycles because it will find the defect only after 4,500 cycles have elapsed.In the case of the 1,200-psig test by similar reasoning, one finds only a 2,200-cycle life is ensured because the test would only find the defect after 5,800 cycles had elapsed.The critical finding here is that relatively small increases in test pressure buy considerably greater assurance of serviceability. The life ensured by the 1,300-psig test is 6,000/2,200 or 2.7 times that ensured by the 1,200-psig test.The effect of using an in-line tool with a threshold depth detection size of 25% WT (0.0625 in. in this case) is even more dramatic. The flaw would have been revealed even before the cycling started in that case.

Click here to enlarge imageFig. 5 illustrates the effect of being able to find ever-smaller flaws by means either of higher test pressure or of in-line tools with small-flaw-detection thresholds.First, let us compare the relative effective intervals required for the 1,200-psig hydrostatic test vs. the 1,300-psig hydrostatic test. A 1,200-psig test would have necessitated five tests within the period required for 10,000 cycles to accumulate, if one assumes that the first test is carried out before the first cycle.The second test is made at 2,500 cycles and nothing happens because the flaw is only 0.10-in. deep. It would have to be 0.13-in. deep to fail at 1,200 psig.Similarly, the third test is made at 5,000 cycles and still nothing happens.Finally, on the fourth test of 7,500 cycles, the flaw fails because it has grown to 0.16 in. (more than the 0.13-in. depth required for failure at 1,200 psig).Now consider the 1,300-psig test.Only three tests in the 10,000-cycle time period would have been sufficient. The second test at 5,000 cycles causes the flaw to fail. Note the three tests (at 0, 5,000, and 10,000 cycles) would not have been sufficient at a test pressure level of 1,200 psig.The 1,200-psig test at 5,000 cycles would not have revealed the flaw, but the flaw would have failed in service before the third test was conducted.It should be clear on extrapolation of the "ILI" (in-line inspection) threshold size level in Fig. 5 to the left that an interval between in-line inspections much longer than the 1,300-psig retest interval would be sufficient.The rationales derived from the discussions of Figs. 4 and 5 show that great benefits are to be derived from small increases in test pressure levels or the use of in-line inspection in lieu of hydrostatic testing when it becomes necessary to address periodic revalidation of pipeline integrity.The rationale for using in-line inspection is even stronger when one considers the benefits of reduced service disruption and the fact that hydrostatic testing can be less than 100% effective, as we described in Part 1 of this series (OGJ, July 31, 2000, p. 54).ReferencesKiefner, J.F., Kiefner, B.A., and Vieth, P.H., "Analysis of DOT Reportable Incidents for Hazardous Liquid Pipelines, 1986 Through 1996," Final Report to the U.S. Department of Transportation, Office of Pipeline Safety, and the American Petroleum Institute, Publication 1158, Kiefner and Associates Inc. (Jan. 7, 1999).Maxey, W.A., Vieth, P.H., and Kiefner, J.F., "An Enhancement Model for Predicting Pipeline Retest Intervals to Control Cyclic-Pressure-Induced Crack Growth," Proceedings of the 12th International Conference on Offshore Mechanics and Arctic (OAME) 1993, Vol. V (Pipeline Technology), 1993.Kiefner, J.F., Maxey, W.A., Eiber, R.J., and Duffy, A.R., "Failure Stress Levels of Flaws in Pressurized Cylinders," Progress in Flaw Growth and Toughness Testing, ASTM STP 536, ASTM, pp. 461-481; 1973.Rice, R.C., Fatigue Design Handbook, 2nd Edition Society of Automotive Engineers Inc., pp. 133-136; 1988.Raju, I.S., and Newman, J.C. Jr., "Stress-Intensity Factors for Internal and External Surface Cracks in Cylindrical Vessels," ASME Journal of Pressure Vessel Technology, pp. 293-298; November 1982.Paris, P.C., and Erdogan, F., "A Critical Analysis of Crack Propagation Laws," Transactions of the ASME, Journal of Basic Engineering, Series D, Vol. 85, No. 5, pp. 405-09.