Having established a basic failure probability, the COD can be evaluated independently of this probability. Once this is established, the leakage area of the defect follows, and given this leak area, the flow rate can be evaluated using the information from Figure G.1. A mean power law was then used to calculate the mean flow rate given a leakage area. The table below gives the elastic COD values evaluated for this case and the resultant flow rate.

Interpolating between the results in Table G.4, it can be seen that a defect approximately 160 mm (6.2 inches) long, which is approximately 15 percent of the pipe circumference, results in the first leakage category of 380 lpm (100 gpm).

Clearly it is the behaviour of the defect beyond the elastic range that is of interest for the larger leak categories. If it were to be assumed that at the critical defect size the pipe would simply tear, in an unstable manner, to result in a Double Ended Guillotine Break (DEGB) failure, then the leak rate would simply jump from a Category 1 failure to the gpm associated with the DEGB. In this case that would be 250,000 lpm (65,000 gpm) or a Category 4 leak. The probability of a Category 2 leak rate would then be the same as a Category 3, which would be the same as the Category 4!

Such an assumption could be considered valid. However, in this work, it was assumed that the defect would continue opening in a stable, but plastic manner. Whilst models do exist to evaluate the plastic deformation of defective pipes, no such model was used in this analysis. Instead expert judgement was used to assess how the COD would develop beyond this elastic point, and at what defect size the pipe would finally tear into a DEGB failure. The results of this judgement are shown in Figure G.2. The area of leakage can then be calculated, and the leak rate, given a defect length also follows. The resulting gallon per minute flow rate, for this example, is shown in Figure G.3.

The failure probability gives the basic probability of a breach of the pressure boundary. Figure G.3 shows the leak rate in gallons per minute, given a defect of a given length. In order to obtain the probability of a leak rate greater than ‘X’ gallons per minute, it only remains to provide a distribution of the defect size at the moment of failure.

G. 4.4 Defect Distribution and Leak Rate at Failure — No Leak Detection

First consider the case with no leak detection. For this case the instantaneous size of the defect, and its associated COD, at the moment of snap through to a breach of containment is required. As an example, if the aspect ratio were of the order of 8/1 at snap through, then given a pipe wall thickness of about 36 mm (1.4 inches), the defect length would be approximately ten or eleven inches long. If it were then pessimistically assumed that this was the full through wall defect length, then the instantaneous leak rate would be just above (actually about twice) our ‘Category 1’ failure criteria of 380 lpm (100 gpm). Thus, the probability of a leak rate greater than Category 1 becomes the basic probability of failure times the probability that the defect at snap through was greater than 250 mm (10 inches), i. e., the defect had an aspect ratio at snap through of about 8/1 or greater. It then follows, from Figure G.3, that in order to exceed the Category 2 leak rate, the instantaneous defect size at snap through would have to be greater than 380 or 405 mm (15 or 16 inches), i. e., the defect had an aspect ration of about 11/1. Furthermore, the defect snapped straight open to the fully plastic COD.

As stated earlier, RR-PRODIGAL has the capability of simulating the crack growth both around and through the pipe wall. However, this is not generally used as the solutions require a detailed knowledge of the stress distribution around the pipe, including any weld residual stress, and generally such knowledge is not well enough defined. Thus, expert judgement was again used. The expert
judgement required is to generate a defect distribution at the moment the defect snaps to the COD of Figure G.3, assuming no leak detection.

This base case is for the surge line elbow and it has been assumed that most of the deformation and high stress will result from large bending moments at the elbow. It was felt that this would initiate a defect preferential on the hogging side of the elbow, and promote a crack to grow through the wall thickness on this side of the elbow. This would then imply that the crack growth around the pipe diameter would be restricted. Figure G.4 represents the distribution decided upon for this analysis. This distribution shows the most likely defect length to be up to about 250 mm (10 inches), which is about a quarter of the way around the pipe circumference. The probability of the defect being over halfway around the pipe is seen as a rare event, being about 0.025 or a 1 in 40 chance. If the loading were not dominated by bending, then this distribution would probably be judged to be flatter, with perhaps a 1 in 10 chance of being greater than halfway round the pipe circumference.

Combining Figures G.3 and G.4 gives the conditional probability of a leak greater than a given leak rate. This final plot is given in Figure G.5 and is combined with the basic failure probability to derive the values given in Table D. 1 in Section D of the main body of this report.