PVP STATISTICAL APPROACH OF STRESS CONCENTRATION FACTOR (SCF) WITHIN PIPELINE GIRTH WELDS ECA

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1 Proceedings of the ASME 2014 Pressure Vessels & Piping Conference PVP2014 July 20-24, 2014, Anaheim, California, USA PVP STATISTICAL APPROACH OF STRESS CONCENTRATION FACTOR (SCF) WITHIN PIPELINE GIRTH WELDS Pierre-Louis Auvret Antonio Carlucci SAIPEM SPA San Donato Milanese, Italy Jun Li Kamel MCirdi ABSTRACT Engineering design must take care of local peaks within stress field, in order to provide relevant forecast of material behavior. Within pipeline girth welds, pipe misalignment is an ordinary cause of significant stress concentrations. The matching of pipe ends depends of the quality of alignment procedure but it is also much influenced by pipe fabrication tolerances. In general, misalignment is estimated considering the maximal and minimal values of each pipe size according to pipe fabrication tolerances. But, in practice, the probability to get a such case is very low. This paper describes how to improve the calculation of stress concentration factor (SCF) through a statistical analysis of pipe dimensions. The use of actual pipe measurements is not necessary even if it provides better SCF estimation. Indeed the distribution of pipe size can be estimated through the fabrication tolerances which require acceptable capacities of the manufacturing system. INTRODUCTION Internal or external Hi/Lo (or High/Low) is the gap between respectively internal or external surfaces of two pipe ends to be welded together. This is a very common characteristic of pipe matching for welding. The maximal allowable value of internal Hi/Lo is often imposed by contract specifications while maximal external Hi/Lo is deduced from pipe fabrication tolerances and the assumed maximal internal Hi/Lo. This notion of Hi/Lo has an important impact on Engineering Critical Assessment (ECA) as it allows to calculate the stress concentration factor (SCF). Stress concentrations have been studied by many researchers, equations have been developed and improved for many weld configurations (Ref [7], [8], and [9]). The variations of material properties and geometry have also been already studied in Ref [6] which presents a reliability based assessment of pipe wall thickness. The variation of wall thickness due to pipe ovality has been particularly investigated in the Pipe Property Variation Characteristics section. This paper proposes a method to calculate the external Hi/Lo assumed in SCF calculations. This method is based on a statistical analysis of the pipe wall thickness (WT). A variation of the statistical approach is also explained which do not require pipe measurements. An example for each method is presented in order to compare the obtained results with the common practice. NOMENCLATURE Lower limit of intervals used in the χ² test ECA FQ Upper limit of intervals used in the χ² test Engineering Critical Assessment Empirical number of occurrence of each interval used in the χ² test Theoretical number of occurrence which corresponds to in the χ² test Fabrication quality factor Hi/Lo at the outer surfaces Hi/Lo at the inner surfaces N ; Normal distribution with mean and standard deviation 1 Copyright 2014 by ASME

2 OD SD WT Nominal outer diameter Confidence criteria Standard deviation Degree of freedom of chi square law Pipe Wall thickness Maximal wall thickness as per fabrication tolerances Minimal wall thickness as per fabrication tolerances The highest value of WT actual measures The lowest value of WT actual measures Mean of a given variable Cumulative distribution function (CDF) Quantile function (inverse of CDF) Standard deviation of a given variable PIPE ALIGNMENT Figure 1 illustrates schematically the alignment of two pipes before welding. A clamp is introduced by one free end of a pipe. Each part of the clamp extends independently to become centralized with the internal dialmeter of each pipe end. So the internal surfaces of both pipe ends become approximately coaxial. COMMON PRACTICE As per Ref [1], Appendix A, Subsection D205, the calculus of SCF requires the maximal values of and. The measurement of is commonly required and the maximal value of can be derived from the fabrication tolerances of pipes. Equation (2) illustratres this common practice: (2) WT METHOD FOR HI/LO CALCULUS The aim of the WT Method is a statistical analysis of wall thickness measures in order to forecast the maximal value that can be encountered for. To do so, the calculus will be based on Equation (1). and are two independent random variables. So if WT has a normal distribution N ; with as mean and as standard deviation, the Central limit theorem states that : is a random variable with a normal distribution N 0; with: 2 (3) Hence it is possible to calculate for the probability that is inside ; : (4) And 1 (5) Hence Hence (6) (7) Therefore 2 (8) Figure 1 : Pipe Alignment with an internal clamp Figure 1 above shows the relation between internal Hi/Lo, external Hi/Lo and wall thicknesses of both pipes as expressed by Equation (1): (1) The value estimated through this method depends on the probability that the actual is lower than the statistically predicted. Whatever the value of, the value of calculated from this method cannot be higher the one predicted by the classical method mentioned in the Common Practice section. The main difficulty of the WT Method is getting WT measures and making sure that they are normally distributed. Various normality tests are available. Here, the ² test will be used as per Ref [5]. The measurement of pipes must satisfy the international standards (API 5L [4], Section 7 for instance). The WT Method requires the measures of the wall thickness of pipe 2 Copyright 2014 by ASME

3 ends, i.e. the parts of pipe located in the 150 mm length from each pipe end. Indeed, the values of WT measured in the pipe body is not appropriate for the calculation of Hi/Lo. No distinction in WT values is set whatever the angular position of the measure. However it can be relevant to do such distinction if particular requirements exist for the alignment of weld-made pipes, but this is not taken to account in this paper. For example, Figure 2 below shows the distribution of WT measures from an 8 inch pipes used for offshore facilities. The mean value is 23.4 and the standard deviation The distribution of WT has been compared to the normal distribution N ;.The values on the vertical axis represent the theoretical and empirical number of measures which are included in the interval indicated in each rectangles. The first and the last interval are different from the others since the width is infinite and not limited to 0.1 mm. The empirical data seem to fit well with the theoretical normal distribution. In Figure 2 below, the empirical WT distribution have been plotted with the normal WT distribution N μ; σ where μ and σ are respectively the mean and the SD of the set of WT measures. Figure 2 : Actual WT distribution versus normal distribution The ² test [5] can be used in order to check if the sampling distribution well fit with a specific distribution law. Consider the null hypothesis 0: WT is having a normal distribution N ;. The common practice is setting the error risk to 5%, which is the risk of rejecting H0 when it is true. The WT values are distributed between 10 classes of interval ;. The classes must be determined in accordance with the WT distribution. For instance, it is recommended that for each class the theoretical and empirical number of occurrences must be higher than 5. The classes are presented in Table 1. The ² test compares the empirical number of occurrences with the theoretical number of occurrences as per the normal distribution N ; H0 is accepted if the following expression follows a χ² law with degree of freedom. ² (9) The degree of freedom must be defined by equation (10) : 1 (10) is accepted if ;% Table 1 : Classes for X² Test The conclusion is that 0 is accepted. Therefore the WT measures are assumed to be normally distributed. Note that the sampling may have a bias due to the fact that extreme values have been removed by the quality checks of the pipe factory. The bias is likely more significant if the reject rate are high because of the WT. However, if the WT distribution does not fit with normal distribution, the random variable X may still fit with normality criteria. A huge amount of values X can be generated by picking randomly two different WT measures and subtract one to the other. For one sampling value, the two measures must be from different measurements but however having the same numerical value. If the generated X values are normally distributed N ; then a maximal value of can be easily calculated from the assumed maximal as detailed in the WT Method for Hi/Lo calculus section. FQ METHOD FOR HI/LO CALCULUS The maximal HiLo can be preliminary estimated even without the actual measures of wall thickness. This is the FQ Method. Indeed, an expected value of the WT standard deviation can be calculated from the fabrication tolerances. The below ratio FQ, defined as per equation (11), characterizes the ability of the manufacturing process to achieve the WT tolerances. 3 Copyright 2014 by ASME

4 (11) When WT measures are not available, can be estimated from an acceptable value of FQ, and then a preliminary calculation of HiLo can be performed as described in the WT Method for Hi/Lo calculus section. Table 2 below provides the appraisal and quantitative interpretations of common FQ values. The choice of FQ depends on the manufacturing process and previous experiences with pipe makers. 3 is generally a realistic assumption which usually provides higher SD than the actual one from WT measures. Table 2 _ Fabrication Quality Ratio FQ Value Appraisal Quantitative definition 2.5 Low Less than 1.24% of reject* 3.0 Medium Less than 0.17% of reject* 3.5 High Less than 0.05% of reject* 4.0 Very High Less than 0.01% of reject * *Note: because of wrong WT on pipe ends, total reject rate is of course higher. EXAMPLE OF SCF CALCULUS This section presents an application of the statistical method in order to calculate the SCF. As example the SCF equation given in Subsection D205, Appendix A of Ref [1] has been selected: 1 where (12) (13) (14) (15) When the actual measures of pipe geometry are available, as for the WT Method, the minimum and maximal WT values used in SCF equations will be the highest and lowest WT actual measures ( and ). For other methods, the extreme WT values will be assumed according to the WT fabrication tolerances. Table 3 below summarizes the input data for the SCF calculation. Note that the following data have been conservatively selected assuming the worst value. Therefore the results issued from these data are more conservative than a detailed calculus as part of an actual pipeline project for which more detailed information are given. The actual WT measures used in this calculus are the ones presented in Figure 2 above. Table 3 _ Input data for the SCF calculus Nominal wall thickness WT [mm] 23.2 Max WT as per tolerances [mm] Min WT as per tolerances [mm] Highest measured WT [mm] Lowest measured WT [mm] Outside Diameter OD [mm] Weld Cap width L [mm] 18.0 Internal Hi/Lo [mm] 1.5 Fabrication Quality Factor FQ [ - ] 3.0 Confidence Criteria p [%] 99.9% According to the common practice, Equation (2) implies: Using the FQ Method and as per Equation (11), the WT standard deviation is expected to be: While the actual standard deviation of the WT measures is: 0.25 Hence Equation (8) implies, - for the FQ Method : for the WT Method : For each method, the values of SCF have been calculated, based on Equation (12) to (15) and using the different values of calculated above. Note that for the WT Method, the Equations (12) to (15) have been applied with and in order to be more consistent with the WT measures, since actual measures are always available when this method is used. The result is then even more realistic. 4 Copyright 2014 by ASME

5 Table 4 presents the results of Hi/Lo and SCF calculi. Table 4 _ SCF and Hi/Lo results for the different methods SCF Calculus Method [mm] [ - ] skewed T-joint plate connections, International Journal of Fatigue, Volume 22, Issue 7, Pages [9] M.M.K. Lee, October, 1999, Estimation of stress concentrations in single-sided welds in offshore tubular joints, International Journal of Fatigue, Volume 21, Issue 9, Pages Common Practice FQ Method WT Method Comparing to the common practice, the two statistical methods provide lower maximal external Hi/Lo with acceptable probability, even without available WT measures. The FQ Method does not require pipe measurements to be performed, it uses the notion of Fabrication quality factor FQ. The WT Method which uses WT measurements is more accurate and provides less pessimistic predictions. Thus this method prevails over the other methods. Hence this method could be applied when WT measurements are available which is usual in offshore projects. CONCLUSIONS The described method reduces the conservatism of SCF calculation by estimating realistic Hi/Lo values. The calculated values of SCF can be used for structural calculations such as ECA in order to provide more relevant safe results. This method could be included later in a general statistical approach of ECA which is allowed by the use of the confidence criteria. It could allow to make safer calculations, optimizing the risk management according to international codes. REFERENCES [1] August 2012, DNV-OS-F101 Submarine Pipeline Systems. [2] April 2010, DNV-RP-C203 Fatigue design of offshore steel structures. [3] 2005, BS 7910:2005 Guide to methods for assessing the acceptability of flaws in metallic structures, British Standard [4] March 2004, API 5L Specification for Line Pipe. [5] P. E. Greenwood et M. S. Nikulin, 1996, A Guide to Chi- Squared Testing Wiley, New York. [6] G. Brown, B. Howard, T. Tkaczyk, October 2004, Reliability based assessment of minimum reelable wall thickness for reeling, IPC [7] Inge Lotsberg, 2009, Stress concentrations due to misalignment at butt welds in plated structures and at girth welds in tubulars, International Journal of Fatigue, Volume 31, issues 8-9, Pages [8] F.P. Breman, P. Peleties, A.K. Hellier, August 2000, Predicted weld toe stress concentrations factor for T and 5 Copyright 2014 by ASME