Jan Spiekhout
N.V. Nederlandse Gasunie
Groningen, The Netherlands
Fracture mechanics models have been developed that predict the leak area that originates from failure in a gas-transmission pipeline.
Results of these calculations will improve pipeline and safety control-system design requirements and the evaluation of safety risks of existing pipelines.
FAILURE MECHANISMS
A leak or a break in a pipeline is a result of failure of a defect in the pipewall. Failure of an existing defect may occur as a result of change in load level, dynamic events, defect growth (for example, fatigue, corrosion), or diminishing material toughness (for example, temperature drop, aging).
Defects in pipelines can derive from any of the following causes:
- Accidental damage during digging, tapping water (by water company), during drilling operations (e.g., for cable), hot-tapping.
- Corrosion
This may manifest itself as general and pitting corrosion caused by ineffective paint maintenance of aboveground pipelines, for example, by a malfunction in the cathodic protection system, or by disbonding.
Or, corrosion may be hydrogen-induced cracking in specific metallurgical microstructures, sulfide stress-corrosion cracking and blistering, or carbonate-bicarbonate and CO2 acid solution stress corrosion (external).
- Manufacturing defects, such as rolling defects or defects in longitudinal or spiral welds
- Defects originating from construction or transportation and defects in girth welds
- Buckling due to bending caused by soil movements, for example.
Two main defect types have been distinguished:
- Pressure-controlled defects, such as axial notches, dents, and most corrosion defects, which may lead to bursting (leak or break)
- Such defects as circumferential notches and defects in girth welds. Outside forces determine how the latter behaves.
In case of failure of a pressure-controlled defect, two failure mechanisms are possible.
The defect becomes a through-wall defect and leads to leakage only (Fig. la).
Or, if the defect exceeds critical dimensions and becomes through-wall, unstable fracture will occur (Fig. lb). Unstable fracture of a pressure-controlled defect results in fracture propagation.
The propagation may arrest after a certain distance in a girth weld or in a pipe made of a more ductile material (Fig. 1c).
If propagation in an axial direction arrests in a girth weld, the entire girth weld can be fractured and, at the open end where the gas escapes, pipe whip may occur (Fig. 1d). It is also possible that a part of the fractured pipe may blow out of the crater.
In case of failure of a defect controlled by outside forces, mostly only leakage will occur (Fig. 1e). In some cases, when the defect is not purely displacement controlled, pipe whip can occur (Fig. 1f).
Such can be the case, for example, in settling situations where the elastic energy is stored in the connecting parts and where the loads and reaction forces cannot simply be calculated from equilibrium, or in landslide or free span situations.
INITIATION, PROPAGATION
An unstable fracture can occur if the defect exceeds a certain "critical" length. For pipelines with a longitudinal gouge, the critical length can be calculated in an iterative way from Equations 1-3 found in the accompanying box.1 2
For materials with a high Kc value, the so called "flowstress"-dependant materials, Equation 1 simplifies into Equation 4.
EXAMPLE 1
Pipe 36 in. x 15 mm (0.591 in.) W.T. X60 grade with an internal pressure 80 bar (1,160 psi) and a Charpy V-value at minimum service temperature of 40 Joules (1/1 Charpy V-notch specimen); flow stress (sflow) = 482 Newtons/sq mm (N/sq mm).
From the Charpy V-value, a conservative estimate of the fracture toughness (Kc) can be derived from Equation 5.3 4
With sy = 415 N/sq mm and Cv = 40 Joules, Kc = 3,103 N/mm1 5.
By trial and error the critical length (1) for unstable fracture can be evaluated. One finds I = 75 mm (for I = 75 mm, MT = 1.12).
Flow-stress dependency will occur for Kc values which exceed 17,000 N/mm1-5.
Hence plastic collapse will occur and Equation 4 can be applied. One then finds I = 255 mm (for I = 255 mm, MT = 1.99).
For gouged dents, the defect sizes at which unstable fracture occurs are less well defined because research has mainly been focused on fracture initiation of the defect breaking through the wall.5-7
For pit corrosion, evidence suggests that the risk of fracture propagation is less than for an axial gouge with equivalent length.8 9
For gouged-dents, pit corrosion, and other types of defects, however, if the critical dimensions are exceeded and results in fracture propagation, the effect will be the same as in the case of a longitudinal gouge.
A propagating crack which runs in a pipe will arrest in that pipe if the toughness of the pipe material is sufficient.
Several empirical or semiempirical relations, such as those shown in Equations 612, evaluate the minimum required fracture toughness for fracture arrest.10-13
All the relations predict the minimum required Charpy V-impact energy (two thirds of the specimen) for fracture arrest in 1 pipe (95% probability) for land gas-transmission pipelines (no rich gas) with normal backfill and burial depth.
The results of the relations may show some variation. For normal pipeline steels and normal design pressures, however, the difference between the calculated Charpy V values is generally minimal.
EXAMPLE 2
Calculate the minimum required toughness for fracture arrest for the pipeline from Example 1 (36-in. OD X 0.591-in. W.T., s = 240 N/sq mm). The required toughnesses, varied according to calculations of Equations 612, are shown in Table 1.
[For very high pressures and very high-strength steels (greater than X70), these relations have not been sufficiently substantiated by tests; further research is being conducted.
Also, research is being conducted on the effect of different backfills, burial depths, and offshore pipelines.
Further research will better substantiate the fracture-propagation behavior from a theoretical point of view. 14 Much of this work is sponsored by the European Pipeline Research Group (EPRG) and American Gas Association (AGA) under the Pipeline Research Committee's (PRC) Line Pipe Research Supervisory Committee.]
If a propagating crack starts to initiate in a pipe that meets the toughness requirement for fracture arrest, the total length the fracture propagated in the pipe (on each side of the origin) depends on the ratio of toughness of the pipe to toughness required for fracture arrest ( 1).
The higher the ratio the quicker the arrest.
Fig. 2 indicates that the arrest will not occur before about 4.50 m either side of the origin.1
This results in a fracture length of 9 m in addition to the length of the defect from which the unstable fracture initiated. Current research would seem to indicate that the length for fracture arrest depends more on diameter. Available test results, however, are too few to be indicative.
For a fracture that propagates through one or more pipes of lower toughness and enters a higher toughness pipe which meets the toughness requirement for fracture arrest, the arrest will be sooner (Fig. 3).
This phenomenon can be explained by the decompression behavior during the fracture-propagation process.
A propagating crack can also be arrested in a girth weld. The arrest mechanism can develop if the girth weld behaves in a low toughness or brittle manner for dynamic loads because a ductile fracture has an intense plastic longitudinal strain field well ahead of the crack tip, which can cause the girth weld to fracture prior to the arrival of the fracture.15
A pipeline generally consists of segments which meet the toughness requirements for fracture arrest (so called "arrest" pipes) and those that fail to meet the toughness requirement for fracture arrest ("fail" pipes).
For a pipeline, the statistical distribution of arrest and fail pipes is known. For new pipelines, this is determined by requirements and test procedures;16 for existing pipelines, the toughness values are available from the pipe certificates.
The number of fractured segments (which equals the fracture length) can be estimated by a probability calculation assuming a random distribution of fail and arrest pipes along the pipeline. This assumption is acceptable because pipe segments are mixed during production, transportation, storage, and construction, and the number of segments in a pipeline is generally high (1,00010,000).
Equation 13 presents calculations for determining the total probability of a specific number (n) of fractured pipes, exclusive of the arrest pipes.
The probability that a pipe is an arrest pipe equals 1-p, where p = the fraction of fail pipes.
Table 2 presents the probabilities of the number of fractured pipes, exclusive of the arrest pipes, for three different values of p.
EXAMPLE 3
Given p = 0.5, what is the probability of three fractured pipes?
The probability of three fractured pipes (five, including the arrest pipes) is 0.094. The probability of no fractured pipes (one pipe including the arrest pipe) is 0.5.
The probability of three or more fractured pipes (in addition to two arrest pipes) is 0.25.
For most West European countries, the concept of at least 50% arrest pipes (p 0-5) will be valid for pipelines of recent construction.10 11 17 18
This means that the fracture length equals five pipe lengths plus twice the length necessary to arrest the propagating crack in the arrest pipe (accepting a probability of 0.05 that the fracture lengths exceed this length).
From Fig. 3, the maximum length to arrest the propagating crack in the arrest pipe is about 9 m. Usually such a crack will arrest within 3 m.
Pipe-whip phenomena may be expected. For example pipe-whip phenomena have been observed in the first full-scale test of EPRG on the 36-in. pipeline at Otterburn (U.K.) and the EPRG test on a 48-in. x 0.670-in. W.T. pipe in 1984 at Perdasdefogu (Sardinia).
So far no pipe-whip phenomena concerning the open ends where the gas escapes have been observed.
However, this may be expected in the case of weak backfill or insufficient burial depth.
STABLE, SUBCRITICAL CRACKS
Under the assumption of a parabolic shape of a through-wall crack, the crack opening area can theoretically be derived.
For the different geometries and material behavior, the area (A) is calculated according to Equations 14-21 .19 20
EXAMPLE 4
The leak areas for the pipe in Example 1 are calculated (v = 0.3; E = 2.1 - 105 N/sq mm) as follows:
- Toughness-dependant material with I = 75 mm, Equation 21: lambda = 0.83; and Equation 18: a = 1.19; Equation 14: Ael = 12 sq mm results in (Equation 17) Apipe = 14 sq mm.
- Flow-stress-dependant material with I = 255 mm, Equation 21: lambda = 2.82; and Equation 18: (a = 2.56; Equation 14: Ael = 140 sq mm; Equation 15: Apl = 175 sq mm; Equation 17: Apipe 448 sq mm.
EXAMPLE 5
In the same way as in Examples 1 and 4, leak areas are calculated for three wall thicknesses (Table 3) with p = 70 bar, OD = 36-in., Grade X60, flow-stress-dependant material.
For nuclear plants, tests and finite-element computer calculations have verified the outcome of these theoretical calculations in order to evaluate:
- The minimum values for the design of leak-detection systems to ensure that the leak will be detected before there is a risk of unstable fracture (leak-before-break concept); and,
- The maximum values for controlling jet and reaction forces.
The real leak area in general will vary between 1.0 and 2.5 times the theoretically calculated value.20 At most the leak area can conservatively be estimated at three times the calculated value.
It should be noted that two of the four experimental leak-area values20 result from unstable cracks, cracks that propagated over a certain distance and arrested (experiment Nos. BVZ 012 and BVS 010).
In a pipeline this distance would have been larger.
Other experiments (Nos. BVZ 020 and BVZ 022), however, support a leak area of 2.5 times the calculated value at most.21
Further, Bartholome, et al.,20 conclude that the ratio of leakage area to pipe cross section is at maximum on the order of 10%. Sturm, et al.,21 conclude that this ratio is about 20%.
Both ratios are influenced by leak areas evaluated from unstable cracks.
If only stable cracks are considered, the ratio for axial cracks is 5% at maximum. For circumferential cracks, the ratio is less than 1%.
Recently published work more reliably predicts the leak area of circumferential cracks.22
If the gas contains some dust, the leak area may increase by erosion.
The outflow of gas through the leak area causes a cooling down of the adjacent material. A local decrease in toughness can occur which will result in crack extension or unstable fracture if the critical crack length is exceeded.
For longitudinal defects, failure as a break is unlikely at hoop-stress levels of less than 0.3sy.8 Hence, cracks beyond the critical length are still stable, and a leak can be as large as or larger than the pipeline diameter.
This is the case for small-diameter, gas-transmission pipelines because the OD/W.T. ratio is relatively small.
Wall thicknesses for small diameter pipes are determined by manufacturing requirements (seamless pipe) and the minimum wall thickness required for welding.
If pit corrosion breaks through the wall, the leak may develop in the shape of the pit. The result, for example, will be a leak of about circular shape with a diameter of 50 mm.
When a group of pits is present, usually one of the pits will start to leak without interference with the surrounding pits in first instance.
The critical dimensions for a gouged dent are less than those for an axial crack. The leak area will resemble that for an axial crack.6
EVALUATING LEAK AREAS
Two main fracture cases are relevant in the evaluation of possible leak areas in gas-transmission pipelines: leak (stable fracture) and break (rupture, unstable fracture).
In case of a leak, the maximum dimensions of the leak area are determined by the critical dimensions of the defect for unstable fracture. If, for pressure-controlled defects, these dimensions are exceeded, such a defect will result in a propagating crack in the case of failure.
This propagation will not arrest before about 4.5 m of the origin. Hence, the crack length at minimum equals twice 4.5 plus the critical length of the defect.
The maximum possible fracture length in the case of propagation depends on the portion of segments in the pipeline (1 - p) that have sufficient fracture toughness for fracture arrest.
Pipelines of recent construction will at least contain a fraction of 0.5 "arrest" pipes. The probability that the fracture propagation is limited to the arrest pipe is 50%.
The probability that more then five pipes with insufficient toughness plus two arrest pipes are involved is 5%. The maximum fracture length in that case will be 5 pipe lengths plus 2 x 9 m.
If the fracture-arrest pipes are fewer or more, the number of pipes involved in the propagation with the set probability can be calculated according to Equation 13.
For a pipeline with a hoop stress of less than 0.3 x sy, no fracture propagation will occur.
Pipe-whip effects can occur at the fracturing part of the pipe, and parts of the fractured pipe can be blown out of the crater.
These effects at the open ends where the gas escapes will be less likely under "normal" conditions. In the case of weak backfill or insufficient burial depth, pipe whip is possible.
If such phenomenon occurs, it will increase the area influenced by the fracture propagation. And the dispersion of natural gas which escapes through the open end can differ.
The same considerations for possible pipe whip also apply for circumferential defects (like defects in girth welds) which fail in an unstable manner.
For stable cracks, the maximum leak area depends on the type of defect.
A gouge in the longitudinal direction when it fails will break through the wall and result in a crack. The same applies for other types of crack-like defects in the longitudinal direction; stress corrosion, for example.
If the toughness of the pipeline material is known, the critical length and the leak area can be calculated, The real leak area ranges between 1 and 2.5 times the theoretically calculated leak area, and the leak area has a parabolic shape,
The critical dimensions of a gouged dent cannot exactly be determined. If such a defect remains stable, however, when breaking through the wall, the dent will have rerounded and bulged outwards, and the crack will be much like a crack that results from a notch only.
When pit corrosion breaks through the wall, normally only one pit will break through, in the first instance. The shape of this area will be about circular, with a radius of about 50 mm at maximum.
A crack in the circumferential direction is mainly governed by outside forces. But if the crack remains stable, the leak area will be less than for a longitudinal crack.
The possible fracture areas are summarized in Table 4.
ACKNOWLEDGMENTS
Thanks are due to numerous Gasunie colleagues and to Dr. Re, SNAM, Milan.
REFERENCES
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