How long have they got? ... predicting the remaining lifetime of in-service pipelines

TWI Bulletin, March/April 2001

Charles Schneider graduated in Mathematics from Oxford in the eighties. He joined TWI in 1997 as a Principal Project Leader having worked with CEGB/Nuclear Electric and Magnox Electric. He has 14 years experience in developing theoretical models for non-destructive testing.

Ruth Sanderson is a Project Leader in TWI's Finite Element Section. She joined Abington shortly after graduating in mathematics from Warwick University in 1998. Her FEA experience includes long range UT modelling for development of rail line inspection.

Amin Muhammed has worked in TWI's structural integrity technology group since 1996, when he joined TWI following research work at UMIST, for which he was awarded a PhD in 1995. Amin is involved in the development and industrial application of probabilistic and reliability-based methods to the integrity assessment of structures including pipelines, pressure vessels and offshore jacket structures.

The integrity of a pipeline system on a North Sea oil platform has recently been assessed, using an ultrasonic corrosion mapping technique. However, part of the system is inaccessible for inspection. As Charles Schneider, Ruth Sanderson and Amin Muhammed report, in this region, therefore, it was necessary to estimate the condition of the pipe based on sample inspections in the accessible area.

The analysis shows that, for the majority of the line, the risk of leakage within its planned lifetime is negligible. However, the work highlighted the need for a better understanding of the rate of corrosion in two particular regions. As a result, a small number of ultrasonic transducers have now been permanently attached to these two sections of pipe. These transducers will yield more detailed information on the rate of corrosion over the remaining lifetime of the line.

Introduction

Before inspection, the overall condition of the pipeline system was unknown, and corrosion attack was suspected. Inspection of the whole line was not possible, so it was decided that statistical extrapolation would be used to assess those parts of the system that were not inspected. The sample inspection was carried out using ultrasonics. Figure 1 shows the overall pipeline system. The part of the line that passes through the storage cells is at a higher temperature than the rest of the line, so it may have corroded more than the accessible pipes. We incorporated this 'temperature effect' into our assessment by applying a scaling factor F to the assumed rate of corrosion.

Objectives

• Analyse results from the inspection of a portion of the line and thereby make an assessment of the whole pipeline system.
• Calculate future probabilities of leakage for the system.

Key assumptions

• The loss of wall thickness in each uninspected region of the system follows the same distribution (after scaling by the 'temperature factor' F where appropriate) as some region that has been inspected.
• At start of life, the mean wall thickness was midway between the manufacturing tolerances. In all cases, this value was a little larger than the nominal thickness, and was judged to be reasonably conservative.
• The numerical predictions of leakage probabilities (see Summary of predictions) further assume that the thicknesses at start of life were normally distributed. ^[1] The standard deviation of this distribution was estimated from the inspection data for the least corroded pipe.
• The ultrasonic measurement errors are negligible. If the systematic (mean) measurement error is zero, any random measurement errors will again introduce a small degree of conservatism into estimates of leakage probability (see Fig.2).
• The corrosion rate does not change with time.
• In extrapolating the leakage predictions to the storage cells, the corrosion rate is increased by a 'temperature factor' F. The base assumption is that F = 2, but the sensitivity of the predictions to the assumed value of F was also investigated (see Fig.3).
• Leakage does not occur until the minimum thickness reaches zero.

Statistical methods

TWI identified three potential methods for the analysis:

• Identify a fit to the underlying distribution of the raw data (Method A).
• Partition the pipe surface into rectangular 'blocks', and fit an extreme value distribution to the minimum thicknesses of these blocks (Method B).
• Fit a generalised Pareto distribution to the K smallest block minima (called exceedances). Reiss and Thomas ^[2] give detailed guidance on the choice of K (which effectively becomes the sample size) (Method C).

In practice, it was found that different thickness distributions applied to different regions of the line. For example, greater corrosion had occurred at the bottom of low-lying horizontal pipes. Field welds were also treated separately from workshop welds. Three distinct regions in the tie-in and nine such regions in the main pipe were identified.

Choice of method

The most suitable method depends on the data. For the data used here, Method A was quickly ruled out, because the raw inspection data did not fit any common distribution. If a satisfactory fit to the underlying distribution cannot be identified using Method A, then it is usually possible instead to fit an extreme value distribution directly to the minimum wall thicknesses X measured over rectangular 'blocks' of a certain fixed size. Because Method A was found not to be feasible for the data, Method B was the next to be attempted. Method B was suitable for most of the inspection data, although Method C was used in just one region of the line. For brevity, Method B only is described, but the methodology for Method C is mostly analogous. ^[2]

Choice of block size

Most of the statistical theory of extreme values is based on the assumption (sometimes implicit) that individual thickness measurements are statistically independent or, at least, that any correlation between the data is negligible. Stronger correlation between (for example) adjacent data points is described by Reiss and Thomas ^[2] as 'clustering'.

Methods B and C mitigate this clustering effect, to a certain extent, by reducing the sample to that of the block minima. Thus each dimension x _i of the block was chosen such that pairs of data points separated by a distance x _i (in the appropriate direction) are weakly correlated. The strength of the correlation can be gauged from the two-dimensional auto-correlation function ^[3] (2D ACF). The 2D ACF was calculated by successively applying a pair of fast Fourier transforms (invoking the auto-correlation theorem for two-dimensional transforms ^[4] ).

Note that there is always a trade-off between the 'declustering' effect of larger block sizes (together with a better fit to the appropriate distribution), on the one hand, and the resulting increase in sampling errors, on the other hand. For analyses using Method B, it was generally found that a block area of 0.03m ² resulted in a satisfactory fit to an extreme value distribution.

Fitting an extreme value distribution to the block minima (Method B)

Probability plot

We can judge how well a Type I ^[5] extreme value distribution fits the data by examining whether the block minima show a linear trend when plotted on an extreme value probability plot. ^[6] Figure 2 is an extreme value probability plot of block minima from the most corroded region of the tie-in pipe. The fitted line indicates, for instance, that there is a 5% probability of the minimum thickness over a 0.03m ² patch being less than 11mm. The plotted 95% confidence limits (shown dashed in Fig.2) can also be used as an aid to judgement. In this case, the data show a good fit to an extreme value distribution. Statistical software ^[7] can then be used to estimate the location and scale parameters ( µ and σ) of the distribution, using the maximum likelihood method.

Extrapolation over area

µ _A = µ - σlog _eM (1)

When extrapolating to a pipe having a reduced initial thickness T _hk (relative to that inspected), µ _A is further reduced by the difference in the (mean) initial thicknesses.

The parameters of the distribution were then input to the structural reliability package STRUREL to predict the leakage probabilities of Summary of predictions.

Analytic checks

Summary of predictions

Tie-in

Even after another ten years service, the predicted probability of leakage elsewhere in the tie-in is reassuringly small (~0.04%).

Main pipe

Assuming that the temperature factor F = 2, the predicted probability of leakage after another ten years service is about 8%. This represents the largest probability of leakage in the entire system. Therefore it is recommended that continuous monitoring be applied as close as possible to the accessible field welds at this level.

Figure 3 also shows the sensitivity of the predictions to the temperature factor F. The curve labelled ' F = 2 then 1', is based on F = 2 for the first 20 years service, but F = 1 for the next 10 years. These predictions would apply if the operating regime in the storage cells were changed now to reduce their temperature to that in the inspected regions of the main pipe. Figure 3 shows that this would reduce the predicted probability of leakage at year 30 to about 1%. This information helps the operator to make informed decisions on the future operation of the plant.

The predicted leakage probability elsewhere in the main pipe was about 1% at year 30.

Conclusions

References