International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP) (12th : 2015)

Reliability-based maintenance optimization of pipelines considering space-variant corrosion rate Sahraoui, Yacine; Chateauneuf, Alaa; Khelif, Rabia 2015-07

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  1Reliability-Based Maintenance Optimization Of Pipelines Considering Space-Variant Corrosion Rate Yacine Sahraoui Professor Assistant, LR3MI, Badji Mokhtar University, BP 12, Annaba 23000, Algeria. Alaa Chateauneuf Professor, Pascal Institute, University Clermont-Ferrand II, Clermont Ferrand, France. Rabia, Khelif Professor, LR3MI, Badji Mokhtar University, BP 12, Annaba 23000, Algeria. ABSTRACT: The present work aims at developing a procedure for inspection optimization of pipelines subject to corrosion, including predictive degradation modelling, space-variant corrosion rate, time-dependent reliability assessment and inspection uncertainties. The space-variant corrosion is considered by the mean of Karhunen-Loève expansion in order to take account of soil aggressiveness regarding the variability of corrosion rate along the pipe length. The failure probability is evaluated by a series system combination, using Monte Carlo simulations. Then, the maintenance model is developed according to the inspection decision tree, where imperfect inspections are taken into account. Finally, the developed model is applied to gas pipeline under various corrosion rates, in order to show the effects of the main parameters of the system.   1. INTRODUCTION Due to degradation, the pipelines undergo various maintenance operations, such as: regular inspections to assess degradation, repair actions to recover existing damage, overall repair to bring the structure close to its initial state, and finally complete replacement when the structure becomes technically inappropriate for operation. From the safety point of view, the optimal maintenance program should be defined on the basis of the minimum acceptable level of failure probability. From the cost-benefit point of view, the optimal maintenance planning should be defined on the basis of minimum expected cost (Laggoune et al., 2009). As the real degradation state can only be known at the inspection time, the optimization of the intervals between inspections becomes a fundamental problem for maintenance quality and safe operation of pipelines. In practice, the inspection of existing pipelines cannot be perfect and their performance should be defined in terms of probability of good assessment and probability of wrong assessment (Straub and Faber, 2003; Rouhan and Schoefs, 2003). The application of Risk Based Inspection methods (RBI), on the basis of structural reliability analysis, failure consequence assessment and probabilistic modelling of inspection results, allows us to establish and to optimize the maintenance policies of aging installations by satisfying safety and availability requirements.  The present work aims at developing a procedure for inspection optimization of pipelines subject to corrosion, including predictive degradation modelling, space-variant corrosion rate, time-dependent reliability assessment, inspection uncertainties and expected cost minimization. The originality of this work lies in coupling space variability with inspection uncertainties, in order to allow for practical and accurate applications in the field of pipe engineering. First, the degradation model of pipelines under corrosion is described. The  space-variaKarhunen-Laccount thepipe lenaggressivenevaluated bMonte Carmodel is dtree, whereaccount. Fito gas pipethe effectsprobabilisti  2. DEGRA2.1. PipelinThe corrostochasticathe materigeometry icorrosion corrosion pare a coConsequenlocation x sum of thes dwhere (xdClocation x uniform colocalized clongitudinain the walland Melchpipe wall tcorrosion, and LCl  isaccording t12th Internt corrosiooève expa variabilitygth, depess. The fy a series lo simulatioeveloped  imperfect nally, the dline under v of the c model areDATION Me corrosionsion distrilly describeal space. s usually dor localizroblems enmbination tly, the totand time Te two types),( dTx UC ),T  is the and time Trrosion andorrosion dlly-oriented of a pressuers, 1997).hickness, dLCd  is the d the lengtho the longitnational Confn is consnsion in or of corrosioending oailure probsystem comns. Then, taccording tinspectionseveloped marious corrmain para analyzed. ODEL  bution in d by randAlthough escribed byed corroscountered iof theseal corrosio can be de of corrosio()( dT LCC total corros, )(TdUC  i ),( Txd LCefect. Figu surface crized pipe In this FUC  is the deepth of loca of the cudinal axis.erence on Apidered throder to take n rate alongn the ability is bination, uhe mainteno the deci are taken odel is apposion rates,meters of pipes canom fieldsthe corro either unifion, mostn the real w two fon depth at scribed byn:  ),Tx  ion depth as the depth is the deptre 1 showorrosion deline (Ahamigure, d  ispth of uniflized corroorroded re plications of S2ugh into  the soil then sing ance sion into lied  and the  be over sion orm  of orld rms. any  the (1)   t the  of h of s a fect med  the orm sion gion 2.1A unthe(KMcowhlayanevdaChcoresUan2.1In beto enof susenuin enunshreltatistics and Figure.1. Uniforpractical iform corro loss of waucera and elchers, 19rrosion powere (TdUCer, T is thed UC  and aluated by ta (Kuceraateauneuf anditions, thpectively, C , and 0.53d Mattsson.2. Localithe past den performderive vironmentaIn order localized rface, the pgments in mber of locFigure 2. Avironmentderground ould be coiability.   Probability inVancouv 1. Idealized m corrosioengineeringsion is to ull thicknessMattsson, 97). The er law is wUC Td )()  is the thi elapsed timn are the cofitting Eq and Mand Chaouie mean and0.066 and  and 0.14 , 1987). zed corrosiecades, exed on localempirical l conditionsto account corrosion ipeline is coseries. Eaalized corrs corrosion(i.e. sopipes), tnsidered t Civil Engineer, Canada, J corrosion dn   way to se a power  with the e1987; Ahgeneral fritten as: nUC T  ckness of e (i.e. agerrosion con. (2) to fiettsson, 19, 2006). For standard d0.037 for tfor the powon  tensive reseized corrosmodels f.  for randomdefects ovnsidered ach segmenosion defec is inducedil comphe spatialo computeering, ICASP1uly 12-15, 201efect. account folaw to modxposure timammed anorm of th(2the corrode of the pipstants, to bld corrosio87; Amira atmosphereviation arhe multiplier n (Kucearches havion, in ordor differen distributioer the pips a system ot presents ts, as show by externosition fo correlatio the system2 5  r el e d e ) d e) e n t, ic e, erra e er t n e f a n al r n   Figure 2. P The emcorrosion literature (eNiffeneggeinclude theLC xd (LC xl ,(where d LCthe localizedefines thaggressivencoordinate,ratio betwlocalized co 3. PIPELIN3.1. StochaAn appropcorrosion fKarhunen-LSpanos, 19field is givindependen,( xk12th Interipeline segmppirical equusually .g. Ahar and Li, 20 space-variaxkT ,(), xkT ,() ),( Tx and d corrosione corrosioness, x  is   is the seen the lrrosion. E RELIABstic corrosiriate represield can be oève ex91). In thisen by the t standard g)()Mixk national Confents and locrofile. ations for considermmed, 11) are extnt field as fnT)  nT)  ),( TxlLC  a depth and  rate, acc the lontochastic seength and ILITY on field entation ofperformed pansion ( expansionsum of a fiaussian var)(1 ii xerence on Apalized corrostime-depened in 1998; Qended hereiollowing:((re respectilength, (xkording to gitudinal t, and   isthe depth the stochby the meaGhanem , the stochnite numbeiables i :)(i   plications of S3 ion dent the ian, n to 3.a)            3.b)            vely ),  soil pipe  the  of astic n of and astic r of (4) arethevafunfunto stostothe3.2Themdeas codeet remfurtheof givcogiv19PrwhstrgivfacMformares(AChtatistics and              In this ex defined b covarianclues andctions. Inction is asconsiderchastic fichastic fiel same type. Failure pe failure ofpirical motermine thea function rrosion developed in al. (1972) aain the mthermore u B31G (ASthe approaen by AhamBy consirrosion, theen cross-se98):  (2),( fTxere D  is ess, )(Tden by (Tdtor, as givelchers (199The limi reliabilityrgin, givenistance Prmirat, Chatateauneuf aProbability inVancouvpression, ty introducie kernel, wi  are  our cassumed to eHermite oreld expand is conside of soil.  robability pipes is idedel based o pressure aof the size fect. Thisthe early send Kiefeneost widelysed in sevME-B31Gch and difmed and Mdering un expressionction can b )95.68 dythe pipe dis the wal() dd UCen in the w6). t state fun analysis i by the diff),( Tx  and eauneuf annd Chaoui, Civil Engineer, Canada, Jhe space-vng the eighere i  aappropriate e, the auxponential,thogonal fsion. Mored as statintified by un fracture mt which theand the geo approachventies ( et al. (197 applied aperal standa, 1991, 199ferent modielchers (1iform an of the pipee written as11)(MddDTLLiameter, yfl thickness)T , and Mork of Ahction ( ixGs defined berence betwthe appliedd Chaoui, 2 2007),  ering, ICASP1uly 12-15, 201ariant effecen modes ore the eigeorthogontocorrelatio allowing uunctions foreover, thonary withsing a semechanics t vessel faimetry of th has bee. see Maxe3)), and stiproach. It rds, such a5). A reviefications a996).  d localize capacity at (Ahamme )(),()(),(TdTxTdTxCC (5is the yie at time T is the Foliaammed an)  considerey the safeteen the pip pressure P006; Kheli2 5 ts f n al n s r e in i-o ls e n y ll is s w re d  a d, ) ld , s d d y e a  f,  For aassociated  TxG ,The failureevaluated simulationssystem reliof the limitix  along thcan be exprf TP )(4. COST MThe optimithe minimwhich is geach brancha given timStraub and Eminwhere [CEthe total occurrencecost of the ][ TCE  is d  TCEwhere CE RCE  is ththe expectethese expec- Expected   FF CCE12th Interny cross-selimit state fu  r TxP , probabilitby pe (Ditlevsenability can  state evene pipe. Theessed as:  ixxGP (ODEL zation of inization of iven by the of the dece span (GFaber, 2002TC  min][]T  is the mcost TC ,  of the i-th i-th scenarecomposed  INCE IN  is the e expectedd failure cted costs cafailure cost1 1()(F TPnational Confction at lnction xGaP     y of the prforming  and Madsbe evaluatets at variou system faiTx 0),    spection pthe expec expected ision tree inoyet et al.). iiPC   athematicaliP  is the scenario andio. The expas followin  R CECE expected i repair cosost. Referrin be easily: 611))(jF TPerence on Apocation x, T,  is: ipeline canMonte-Cen, 1996). d as the us cross-sectlure probablan is basedted total ccosts relate Figure 3, , 1994; Go expectatioprobability iC  is the ected total g:  F      nspection ct, and  FCEng to Figur calculated..1. (ActFjF PPCplications of S4the (6)  be arlo The nion ions ility (7)    on ost, d to over yet, (8) n of  of total cost (9) ost,  is e 3,  )jS  - EE- EE  whinstheanaft 5.Thgrandepralltatistics and xpected rep 1(CC RR xpected ins  1(IN PCere FC  andpection co failure prod ActFjP .1.  ier inspectio FigurAPPLICATe above moade X52, wd subjectedsigned for obabilistic d variables a Probability inVancouvair costs: ))( 1 PTPFpection cos 1))( iF CT iC  are ressts, RC  is tbability at s the updan at time T e 3. InspectiION TO Cdel is nowith diamete to internala service ata are prore lognorm Civil Engineer, Canada, J()( 43 SPS ts: 611(ji PCpectively thhe repair cthe inspectted failure1  for the j-thon decision ORRODED applied to r D and wal pressure plife of 50vided in Taally distribu ering, ICASP1uly 12-15, 201)  .1. () jActFj SPe failure anost, )( 1TPFion  time T probabilit scenario.tree.  PIPE steel pipe ol thickness . This pipe  years. Thble 1, wherted.  2 5 )d  is 1 , y  f t, is e e 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  5Table 1. Statistical moments of random variables.  Variable  Mean St. Dev. Diameter D  (mm) 600 18 Wall thickness d  (mm) 10 0.5 Yield stress yf  (MPa) 423 28.3 Internal pressure aP  (MPa) 5 0.5 Length-to-depth ratio of localized corrosion  10 2 Uniform corrosion  rate UC  0.02 0.005 Average Localized corrosion  rateLC  0.164 0.028 Corrosion parameter n  0.780 - 5.1. Pipeline reliability In the numerical application, we consider a length of 200 km for the underground pipeline. Figure 4 compares the time-variant failure probability considering space variability (i.e. stochastic field with correlation length lc = 20m) with the case without space variability (i.e. lc = ∞). It can be seen that considering the stochastic field reduces the dispersion of the lifetime distribution, leading to a reliability increase in the first part of the lifetime (i.e. before 35 years herein) and a reliability decrease in the second part of the lifetime. It can be concluded that neglecting the spatial variability leads to pessimistic estimation of the lifetime, and consequently to lowering the operating conditions or to early replacement of the pipeline.      Figure 4. Effect of spatial variability on the pipe failure probability.  5.2. Optimal inspection interval To determine the maintenance policy, it is necessary to specify the costs related to failure, inspection and repair, as well as the minimum detectable defect mind  and the defect size at conventional failure crd ; these parameters are given in Table 2. The critical defect size crdcorresponds to the failure probability of 10-2.   Table 2. Cost data and maintenance thresholds.  Item  Value Failure cost FC  230 000 €Inspection cost iC  3 500 €Repair cost RC  10 400 €Detection threshold mind  1.5 mmSize of critical defect crd  2.8 mm 5.3. Optimal time between inspections Figure 5 depicts various expected costs (failure][ FCE , inspection ][ INCE  and repair ][ RCE ) in terms of time interval between inspections. Naturally, by increasing the time between inspections, the inspection and repair costs decrease, while the failure cost increase. The optimal time interval between inspections is obtained at 34 years.                                                                Figure 5. Expected costs in terms of inspection time. 1,00E‐051,00E‐041,00E‐031,00E‐021,00E‐011,00E+0025 30 35 40 45 50probability of failureTime  (years)with spatial variabilitywithout spatial variability0,00E+005,00E+021,00E+031,50E+032,00E+032,50E+033,00E+035 15 25 35 45Expected total cost (€/year)Time (years)E[CF] E[CR]E[CIN] E[CT]12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  65.4. Inspection quality In order to allow for clear understanding of the contribution of cost components, Figure 7 plots the cost evolutions with time, for the case of perfect inspections. As can be observed, the variation of the expected total cost increases rapidly around the optimum value of 30 years, due to high increase of failure cost.     Figure 6. Expected costs as a function of perfect inspection time.  The inspection quality is now considered in terms of cost and detection level. Four detection precisions are considered: low mmd 0.2min  , medium mmd 5.1min  , high mmd 0.1min  , perfect mmd 0.0min  . For a given inspection cost, a better precision leads to a reduction of the time interval between inspections. For three inspection costs (i.e. initial, ten times less and ten times more), Figure 7 shows that the expected total cost increases with the detection quality. It can be observed that the curves resulting from low qualities are more scattered. This can be explained by the lack of precision leading to high overall uncertainties.       Figure 7. Influence of the quality of detection of the expected total cos. 0,00E+005,00E+021,00E+031,50E+032,00E+032,50E+033,00E+035 15 25 35 45Expected total cost (€/year) Time (years)E[CF]E[CR]E[CIN]E[CT]02000400060005 15 25 35 45Expected total cost (€/year) Time (years)0.1CiLow precisionMedium precisionHigh precisionPerfect inspection02000400060005 15 25 35 45Expected total cost (€/year) Time (years)CiLow precisionMedium precisionHigh precisionPerfect inspection0,00E+002,00E+034,00E+036,00E+038,00E+031,00E+041,20E+041,40E+041,60E+041,80E+042,00E+045 15 25 35 45Expected total cost (€/year) Time (years)10CiLow precisionMedium precisionHigh precisionPerfect inspection12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  75.5. Influence of corrosion rates In order to analyze the influence of corrosion rate on the optimal interval between inspections, three corrosion rates are considered: low, moderate and high, according to the parameters indicated in table 3.  Table 3. Uniform and localized Corrosion rates.  Uniform corrosion rate UC Mean St. Dev. Low 0.14 0.014 Moderate 0.37 0.037 High 0.62 0.062 Localized corrosion rate LC Mean St. Dev. Low 0.14 0.028 Moderate 0.37 0.074 High 0.62 0.124    The expected total cost is depicted in Figure 8 for the three corrosion rates. As expected, the optimal inspection time is strongly dependent on the corrosion rate, as it highly decreases with the environment aggressiveness. In case of high corrosion rate, the optimal interval is about 10 years and 34 years in the case of a moderately aggressive (Table 4). The optimal time is beyond the service life when the corrosion rate is low, and no inspection should be scheduled during the design lifetime.   Fig. 8. Expected total costs for various corrosion rates  Table 4. Inspection times and total cost for different corrosion rates.  Corrosion rate Optimal inspection interval        Minimum expected cost Low  - - Moderate  34 yr 822.6 €/yr High 10 yr 2445 €/yr 6. CONCLUSION This work presents a complete approach for inspection-repair planning of corroded pipelines allowing the consideration of space variability and inspection uncertainties. The proposed procedure allows us to compare various strategies, by comparing the effectiveness of inspection techniques. The formulation of the expected cost in different situations provides a decision-making tool for optimal scheduling of inspections according to corrosion rates. The numerical application shows the coherence of the proposed model as well as its capacity to take account for practical inspection planning. 7. REFERENCES M. Ahammed, R.E. 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