A statistical approach to determine Microbiologically Influenced Corrosion (MIC) Rates of underground gas pipelines.

Transcription

1 A statstcal approach to determne Mcrobologcally Influenced Corroson (MIC) Rates of underground gas ppelnes. by Lech A. Grzelak A thess submtted to the Delft Unversty of Technology n conformty wth the requrements for the degree of Master of Scence. Delft, The Netherlands Copyrght 006 by Lech A. Grzelak All rghts reserved

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3 Abstract A statstcal approach to determne Mcrobologcally Influenced Corroson (MIC) Rates of underground gas ppelnes. by Lech A. Grzelak Charperson of Graduate Commttee: Prof. dr Roger M. Cooke Department of Mathematcs Graduate Commttee: Prof. dr Roger M. Cooke Prof. Jolanta Msewcz Ir Paul M. Wesselus Dr Dorota Kurowcka Ir Danel Lewandowsk N.V. Nederlandse Gasune s the leadng Dutch gas transportaton company. Its man am to manage, mantan the gas transport system. The grd of gas ppelnes belongng to Gasune conssts of over km steel ppelnes (dameters from 4 to 48 nch) constructed n the 60s. Integrty management s based on the ablty of the ppelne operator to predct the growth of defects detected n nspecton programs. The predctons of the corroson and defect rates can be based on envronmental nput parameters. Accurate predctons allow nterventons/re-nspectons to be scheduled n order to elmnate defects whch pose a hgh potental rsk. Ths thess nvestgates three man ssues. Frstly, t shows an approprate tool for the corroson rate modelng when data from n-lne nspectons are avalable. A low number of nspectons contrbute to hgh uncertanty about the corroson rate estmaton. In many cases, a poor dataset combned wth hgh uncertanty about the measurements cause corroson estmates that are not agreeable wth realty; for example corroson s decreasng n tme. The outputs from the corroson rate model are ncorporated as nput to the second secton, where analyss s focused on nvestgatng parameters nfluencng Mcrobologcally Induced Corroson (MIC) rates. The last part of the thess presents the desgn and results of the defect rate. Keywords: Corroson, Corroson rate modelng, In-lne nspecton, MIC, factors nfluencng MIC, defect rate M.Sc. Thess Lech A. Grzelak

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5 v Acknowledgments The author wshes to express a grattude to Roger M. Cooke, Jolanta Msewcz and Dorota Kurowcka for the opportunty to spend unforgettable two years n the Rsk and Envronmental Modelng group. The author would also lke to acknowledge Thomas Mazzuch and Danel Lewandowsk for coordnaton whle dong the thess project; moreover; the author would lke to thank to the people at Gasune for a gven opportunty to work wthn ther organzaton, especally to Paul M. Wesselus, Karne Kutrowsk and Robert Kuk. Many people have nspred, guded and helped the author durng the two years at TUDelft, and the wrter would lke to thank them all for a great fun and experence. The author owes a huge debt of thankfulness to hs best frends: Poorwa, Msha and Gosa, for ther support, humor throughout not only the courses of M.Sc. program but all the way through entre tme. Last but not the least; the author would lke to express hs apprecaton to hs famly for the support and love they provded through author s entre lfe. M.Sc. Thess Lech A. Grzelak

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7 v Lst of contents Abstract... Acknowledgments...v Lst of contents...v Lst of tables...x Lst of fgures...x Introducton...xv The goals of the research...xv Outlne of the thess...xv Part I Corroson rate modelng... 1 Descrpton of the corroson data Introducton Magnetc Flux Leakage (MFL)-pg Matchng of the reported defects Number of matched defects Avalable data Reported defects Excavaton data Measurement data from matched defects...8 Descrpton of the corroson rate model Introducton Data calbraton Data calbraton procedures...11 Algorthm 1 (Calbraton data algorthm)...11 Algorthm (Measurement error dstrbuton algorthm) Data calbraton results General model for data calbraton General calbraton procedure: General corroson rate model Example Dealng wth mssng data Conclusons Implementaton (CoroGas 1.0v) Numercal results Introducton Approach M.Sc. Thess Lech A. Grzelak

8 v A statstcal approach to determne the MIC rate of underground gas ppelnes 3.3 Approach Approach Depth nfluence on the corroson rate Conclusons and recommendatons...4 Part II Parameters nfluencng mcrobologcally nduced corroson rate Potental analyss Introducton Measurements and smoothng method On-potental Grd constructon Correlaton between the corroson rate and average potentals recorded between frst and last nspecton Approach Approach Correlaton between the corroson rate and potentals standard devaton recorded between frst and last nspecton Conclusons Mcrobal Data analyss Introducton Mcrobologcally Influenced Corroson Dataset descrpton Independent varables Dependent varable Correlaton analyss Multple regresson analyss Analyss structure Mssng data Model wthout nteractons Model wth nteractons Stepwse regresson for ncluded varables Model wthout nteractons Model wth nteractons Senstvty analyss of the parameters nfluencng the corroson rate Conclusons and recommendatons...50 Part III Parameters nfluencng mcroblologcally nduced defect rate Ppelne characterstcs Defect dstrbuton Depth of cover Ppelne elevaton Sol data analyss Introducton Descrpton of avalable dataset Sol data collecton Sol type nfluence on defect rate...6 Delft Unversty of Technology

9 v Defect rate- Approach Defect rate- Approach Correlaton analyss Correlaton between sol exposures Correlaton between defect rates wrt sol types Correlaton between defect rates wrt sol types where bad coatng was assumed Conclusons and recommendatons Water table analyss Introducton Approach Approach Approach Conclusons and recommendatons Factors nfluencng defect rate Introducton Model wthout nteractons Model wth nteractons Conclusons and recommendatons Conclusons...86 Bblography...88 A: Analyss methods and nterpretaton...90 B: Tutoral fle for CoroGas M.Sc. Thess Lech A. Grzelak

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11 x Lst of tables Table 1: number of matched defects per combnaton of pgruns... 6 Table : szng accuracy of the pgs and number of reported defects... 7 Table 3: number of reference ponts per pgrun... 7 Table 4: calbraton results...11 Table 5: standard devatons of the measurement errors...1 Table 6: corroson rate and ntaton tme for approach...1 Table 7: corroson rate and ntaton tme for approach Table 8: correlaton between the corroson rate and average on-potental recorded between frst and last nspecton...34 Table 9: correlaton between the corroson rate and on-potental standard devaton recorded between frst and last nspecton...36 Table 10: groups of mcroorgansms...39 Table 11: factors and weghts for MCA score...41 Table 1 Mcrobal data descrpton...4 Table 13: corroson rate summary for 16 measurements ndcated by bo-analysts...4 Table 14 correlaton between corroson rate and the varables, cell wth red background ndcate that normalty assumpton doesn't hold, yellow rows ndcate varables for whch the null hypothess was rejected for sgnfcance level Table 15: parameters and assocated statstcs...46 Table 16: regresson model standard descrpton...46 Table 17: parameters and assocated statstcs...46 Table 18: regresson model standard descrpton...46 Table 19: parameters and assocated statstcs (model wthout nteractons)...47 Table 0: regresson model standard descrpton (model wthout nteractons)...48 Table 1: parameters and assocated statstcs (model wth nteractons)...48 Table : regresson model standard descrpton (model wth nteractons)...48 Table 3 senstvty analyss of the sgnfcant parameters...49 Table 4: general ppelnes descrpton...61 Table 5 Overall defect rate for the ppelnes...63 Table 6 defect rate for each specfc sol type...64 Table 7: descrpton of the potentally defectve and not defectve envronments...65 Table 8: comparson of potentally defectve and not defectve envronments...67 Table 9: defect rate for sectons where bad coatng was appled...69 Table 30: correlaton between sol compostons of the ppelnes...70 Table 31: correlaton between defect rates of the sol types for ppelnes...70 Table 3: correlaton between defect rates of the sol types for ppelnes, n the clusters where bad coatng was appled...70 Table 33: ground water step levels (legend)...7 Table 34: groundwater step level summary per each secton of.5 km...74 Table 35 defect rate summary- per each secton of.5 km...74 Table 36 correlaton between defect rate and water level for sectons of.5 km...75 Table 37: statstcs and confdence bounds for estmate (ppelne A1 and A)...75 Table 38: descrptve statstcs (ppelnes A1 and A)...75 Table 39: statstcs and confdence bounds for estmate (ppelnes A1, A and A3)...77 Table 40: descrptve statstcs (ppelnes A1, A and A3)...77 Table 41: defects and average groundwater level...78 Table 4 Stepwse regresson estmates (model wthout nteractons)...8 Table 43: standard model statstcs (model wthout nteractons)...8 Table 44 Stepwse regresson estmates (model wth nteractons)...83 Table 45: standard model statstcs (model wth nteractons)...84 Table 46: excavaton dataset [mm] Table 47: example of the measurements Table 48: The nomnal wall thckness M.Sc. Thess Lech A. Grzelak

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13 x Lst of fgures Fgure 0-1: deteroratng gas ppelnes... xv Fgure 0-: corroson modelng schema... xv Fgure 1-1: small and large dameter MFL-pg... 5 Fgure 1-: vsualzaton of matched defects... 5 Fgure 1-3: clock sprng nstallaton (left), gas ppelne excavaton (rght)... 8 Fgure 1-4: reported vs. measured defect depth... 8 Fgure 1-5: reported defect depth... 9 Fgure -1: error dstrbuton for pg A...1 Fgure -: example of defects clusterng...13 Fgure -3: corroson rate determnaton- general model...16 Fgure -4: corroson rate modelng- dealng wth mssng data...17 Fgure -5: calbraton data & optmzer wndow of CoroGas...17 Fgure 3-1: defect depth n tme...0 Fgure 3-: corroson rate dstrbuton...1 Fgure 3-3: dstrbuton of ntaton tme...1 Fgure 3-4: corroson rate dstrbuton... Fgure 3-5: dstrbuton of ntaton... Fgure 3-6: dstrbuton of corroson rates for shallow defect...4 Fgure 3-7: dstrbuton of corroson rates for deep defects...4 Fgure 4-1 cathodc protecton for a gas ppelne (left), voltage drops n a measurng crcut (rght)...9 Fgure 4-: Cu/CuSO 4 reference electrode...9 Fgure 4-3: Test posts dstrbuton over tme...30 Fgure 4-4: on-potentals measurements and results of appled smoothng method...30 Fgure 4-5: on-potentals before smoothng...31 Fgure 4-6: on-potentals after smoothng...31 Fgure 4-7: on-potental contour plot...3 Fgure 4-8: on-potental grd...33 Fgure 4-9: 5 dstngushed defects and estmated corroson rates...33 Fgure 4-10: concordance and dscordance...35 Fgure 5-1: mcrobologcally nfluenced corroson on gas ppelnes...39 Fgure 5-: mage of a sulphate-reducng bacteral culture wth a carbonate precptate, the bactera on the left are about 6-8 µm long and µm n dameter...40 Fgure 5-3 Corroson rate summary for 16 measurements ndcated by bo-analysts...4 Fgure 5-4 radar graph- Pearson product moment correlaton coeffcent...43 Fgure 5-5 correlatons and assocated p-values (orderng the varables)...43 Fgure 5-6 regresson modelng schema for the corroson rate...45 Fgure 6-1: Ppelne A1, profle, depth of cover, defect dstrbuton...55 Fgure 6-: ppelne A, profle, depth of cover, defect dstrbuton...55 Fgure 6-3: ppelne A3, profle, depth of cover, defect dstrbuton (PII)...56 Fgure 6-4: ppelne A1 defect dstrbuton wrt ppelne crcumference...57 Fgure 6-5: ppelne A defect dstrbuton wrt ppelne crcumference...57 Fgure 6-6 ppelne A3 defect dstrbuton wrt ppelne crcumference...57 Fgure 7-1: route map, geotechncal data...59 Fgure 7-: route map, geotechncal data- STEP Fgure 7-3: route map, geotechncal data- STEP...60 Fgure 7-4: Sol composton for the ppelne A Fgure 7-5: Sol composton for the ppelne A...61 Fgure 7-6: Sol composton for the ppelne A3...6 Fgure 7-7: Defect rate assocated for each possble sol composton...65 Fgure 7-8: ppelne A1, potentally defectve clusters, or clusters wth bad coatng...66 Fgure 7-9: ppelne A, potentally defectve clusters, or clusters wth bad coatng...66 Fgure 7-10: ppelne A3, potentally defectve clusters, or clusters wth bad coatng...66 Fgure 7-11: percentage dfference between sol composton vs. defect rate (ppelne A1)...68 Fgure 7-1: percentage dfference between sol composton vs. defect rate (ppelne A)...68 Fgure 7-13: percentage dfference between sol composton vs. defect rate (ppelne A3)...68 Fgure 7-14 defect rate for sectons where bad coatng was appled vs. sol types...69 Fgure 8-1: A1- no. of defects vs. water level per.5 km long sectons...73 Fgure 8- A- no. of defects vs. water level per.5 km long sectons...73 Fgure 8-3: A3- no. of defects vs. water level per.5 km long sectons...74 M.Sc. Thess Lech A. Grzelak

14 x A statstcal approach to determne the MIC rate of underground gas ppelnes Fgure 8-4: number of defects vs. coded groundwater level (ppelne A1)...76 Fgure 8-5: number of defects vs. coded groundwater level (ppelne A)...76 Fgure 8-6: number of defects vs. coded groundwater level (ppelne A3)...77 Delft Unversty of Technology

15 xv Introducton N.V. Nederlandse Gasune s the man gas-transportaton company n the Netherlands. Its gas ppelne network conssts of approxmately km of steel ppelnes (dameters from 4 to 48 nch) that was largely constructed n the perod of the md sxtes to early seventes. The network s splt nto a hgh pressure part (HTL) (5600 km, bar) and a medum pressure part (RTL) (600 km, 40 bar). The hgh pressure network s possble to nspect whereas the medum pressure part does not possess requred nspecton facltes. Untl 1999 Gasune had no ndcatons whatsoever that there was a corroson problem on one of ts ppelnes. Both regular Cathodc Protecton (CP) measurements as well as observatons durng excavatons or reroutngs ndcated that no sgnfcant corroson problem exsted. Nevertheless Gasune polcy was to verfy ppelne ntegrty perodcally by nspectng one of ts hgh pressure lnes on average once every 5 years snce The results of these nlne nspectons confrmed the exstng opnon that no corroson problem exsted. In-lne nspectons have been part of the verfcaton of ppelne ntegrty snce the late seventes n N.V. Nederlandse Gasune. The dscovery of external mcrobal corroson (MIC 1 ) n 1999 n one of the hgh pressure ppelnes changed the nspecton polcy from nspecton of a randomly selected ppelne once every 5 year to an nspecton program for the whole hgh pressure grd (approxmately km) to be completed n 10-1 years. Fgure 0-1: deteroratng gas ppelnes External Mcrobal Induced Corroson s a type of corroson where the corroson rate s nfluenced by the actvty of bactera, especally Sulfate Reducng Bactera (SRB). It can be found n many envronments. Wthn Gasune t s found as external corroson on gas ppelnes. The chemcal and mcrobal processes are complex and can therefore depend on many parameters. Based on experence, Gasune beleved that MIC s found n certan areas more than n others and that therefore the occurrence of MIC s related to sol type or other sol parameters. 1 Mcrobologcally Influenced Corroson M.Sc. Thess Lech A. Grzelak

16 xv A statstcal approach to determne the MIC rate of underground gas ppelnes MIC s ntated at locatons of dsbonded coatng (usually at feld appled coatng) when the bactera and also the ppelne surface are shelded from the cathodc protecton system. Even well mantaned cathodc protecton systems cannot protect aganst deterorated, dsbonded coatng. MIC s not only dangerous due to ncapacty of protectng, but also because of relatvely hgh corroson rate, whch s hgher than for galvanc corroson. TU Delft was commssoned by Gasune to make a statstcal analyss of the avalable data on three hgh pressure ppelnes where MIC was recognzed. Delft Unversty of Technology

17 xv The goals of the research The man ssue of the thess s the analyss of the MIC based on the data delvered by N.V. Nederlandse Gasune. One of the MIC nfluenced lnes was used to qualfy MFLpg (Magnetc Flux Leakage) from dfferent supplers. In the tme perod four dfferent MFL qualfcaton runs have taken place, resultng n 18 excavatons. After the fourth pgrun (5 years after the frst) Gasune decded to determne the corroson and defect rate and nvestgate nfluencng factors. The goal of ths thess s to dscuss to Mcrobologcally Induced Corroson and ts effects on the safety and mantenance ssues. The man objectves of Gasune are: Developng models descrbng the Mcrobal Induced Corroson and Defect rates Fndng a number of factors nfluencng both estmated rates. These models and results can be used for prortzatons of ppelnes for nspecton and determnaton of nspecton ntervals. The structure of corroson modelng s presented n the Fgure 0- below. Fgure 0-: corroson modelng schema Frst part of the schema ndcated by blue color refers to the frst secton of the thess where the corroson rate model s presented. The results from ths study are the nput for the part number two where the parameters nfluencng the mcrobologcally nduced corroson rate are nvestgated. The fnal secton shows the results of defect rate modelng of ppelne affected by MIC. Ths consttutes a detaled statstcal descrpton of a connecton between envronment measurements and the reported corroson events. The man research s drected to fnd factors (f there exst) that nfluence both: the corroson rate and the defect rate. The man assumptons n the analyss are: - Coatng condton s assumed unform and s not governng defect rate. - Pgrun feature type and statonng ndcatons are fully correct - Estmates of the corroson rate (prevous study) are certan - Nomnal wall thckness s assumed to be real Also called: Intellgent Pg, more detaled descrpton s presented n Chapter no. M.Sc. Thess Lech A. Grzelak

18 xv A statstcal approach to determne the MIC rate of underground gas ppelnes Outlne of the thess The thess conssts of three man parts. The frst secton ams to model the corroson rate. Frstly, Chapter 1 descrbes avalable corroson data and gves a small overvew on nspecton procedures and assocated nspecton tools. Later on, the data wll be used as an nput for corroson rate model. The model for corroson rate wll be ntroduced and dscussed n Chapter. Chapter 3 shows number of numercal approaches n order to get estmate of the corroson rate. The analyss s carred out startng from the smplest to more sophstcated models. The frst and the second approach are smply based on the unconstraned regresson analyss. The thrd model s based on the unbased measurements and pgs accuraces ntroduced prevously n Chapter. Second part of the thess begns wth Chapter 4 nvestgatng hstorcal data about the potental from the test-posts. Chapter no. 5 ncorporates the results from Part 1, onpotental analyss and bo-data n order to get number of parameters nfluencng the corroson rate. The last secton s dedcated to defect rate analyss. The secton starts wth ppelne characterstcs (Chapter 6) where general nformaton about gas ppelnes s presented. Chapter 7 shows procedures of collectng and analyzng the sol data from geotechncal surveys. The purpose of ths chapter s to assocate the defect rate of the ppelnes nduced by MIC wth sol compostons. The parameter whch s nvestgated n Chapter 8 s a groundwater step level data analyss. Chapter no. 9 combnes all the avalable sol data, ppelnes features and groundwater levels, and treats them as nputs for the regresson model descrbng the defect rate. Delft Unversty of Technology

19 Part I Corroson Rate Modelng M.Sc. Thess Lech A. Grzelak

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21 4 Chapter 1 1 Descrpton of the corroson data 1.1 Introducton In 1999 a 70 klometer long ppelne (36 nch) n the north of the Netherlands was nspected by MFL pg as part of the verfcaton program. The results of the pgrun ndcated, as an unpleasant surprse, 65 external corroson features but no nternal corroson. After a thorough defect assessment by the safety department of Gasune t was decded that 6 ndcatons had to be excavated and repared. The frst excavaton by the end of 1999 led to a second unpleasant surprse. At the excavaton the appearance of the corroson defect turned out to be totally dfferent from the few corroson defects that Gasune had experenced n the past. Analyss of the corroson products and the appearance of the defect led to the concluson that the corroson was nfluenced by sulphate reducng bactera (SRB s). Smlar experence was obtaned at three other excavatons. At the end the concluson was that at four out of the sx excavatons the corroson was Mcrobally Influenced Corroson (MIC). An addtonal excavaton n 000 showed also MIC. From the results Gasune concluded that t was no longer safe to assume that other lnes were free of ths corroson problem. Therefore the nspecton polcy was revsed. It was decded to start an n-lne nspecton program for all hgh pressure lnes to be completed n a tme frame of approxmately ten years. It was also decded that pg supplers had to qualfy before they could nspect Gasune ppelnes. Because of gas-transport reasons and because of the fact that some defects on the lne had been repared by clock sprng 3 or coatng repar and thus can be used as reference ponts for MFL pgs, the nspected lne was apponted as a qualfcaton lne. When startng up the nspecton program Gasune realzed that a relable corroson rate s paramount to determne a re-nspecton tme nterval for ts ppelnes. 3 Clock Sprng s a composte sleeve used to repar external defects n hgh-pressure ppelnes M.Sc. Thess Lech A. Grzelak

22 5 A statstcal approach to determne the MIC rate of underground gas ppelnes 1. Magnetc Flux Leakage (MFL)-pg In-lne nspectons are performed by so-called MFL-pgs also called ntellgent pgs that locate and characterze mechancal damage n ppelnes. It s a common approach to the management of external corroson n the ppelne ndustry. Inspectons followed by excavatons of extreme deep defects mnmze potental rsk. Fgure 1-1: small and large dameter MFL-pg 1.3 Matchng of the reported defects In order to compare reported defects from two pgruns the defects wll have to be matched. Ths can be done by usng the reported log-dstances from the pg, ppelne lengths, clock poston of the defect, and dstances to reference ponts lke welds, valves. Wthn Gasune ths process can be automatcally done wthn the PIMS 4 software. In ths software the matchng process vsualzaton of the defects on a ppelne segment s possble. Fgure 1- shows a typcal example of reported defects from two pgruns. Fgure 1-: vsualzaton of matched defects (defects 1 to 6 are from run 1 and 7 to 1 from run ) 4 Ppelne Integrty Management System Delft Unversty of Technology

23 6 As can be seen from Fgure 1- t s not always clear after the matchng of defects by the program, whch defects belong together (7 to 1 or 8 to 1?). In the program however the user has the possblty to defne certan areas around a defect. If a defect falls wthn such an area then the two defects are consdered to be the same defect. The advantage of the software s that when many defects are close together the user can optmze the area szes to get the best possble matchng of defects. Factors that complcate the matchng of defects are dfferences n termnology of supplers or dfferences n nterpretaton of defects: external corroson defect, nternal corroson defect, mll defect etc. Suppose that the software has matched a defect from run 1 to a defect from run. Suppler 1 calls the defect corroson whereas suppler dentfes t as mll defect. The queston s then f ths matched defect should be taken for the determnaton of the corroson rate. It was decded to work wth two scenaros to fnd out whether t was crtcal for the determnaton of the corroson rate f only the defects wth the same dentfcaton were used (only ndcated as External Corroson ) or also defects wth dfferent dentfcaton ( External Corroson and External metal loss, possble mll defect ). It turned out that the corroson rates that were calculated for both stuatons were almost the same. In order to keep the uncertantes n the process as small as possble t was decded to use only the matched defects wth the dentfcaton of External Corroson n all pgruns Number of matched defects In the matchng process dfferent categores of matchng defects orgnated: defects from run A that could not be matched or that could be matched only once (to B, C or D), twce (to B and C, C and D or B and D) or three tmes (to B, C and D). A smlar result was obtaned for the matchng of defects from the other runs. For the fnal data set used for the calculaton of corroson rate t was decded to use only the defects that had been detected by three or more pgs. Ths resulted n a data set of 5 matched defects wth a subdvson as ndcated below. A B C D A B C D Table 1: number of matched defects per combnaton of pgruns As can be seen from the table, the number of matchng defects wthn ths subset was smallest for the comparson of run A and B: only 30 defects matched there. Altogether a number of 9 defects were reported by all and only four supplers whereas 3 defects were reported by three supplers. 1.4 Avalable data For the analyss of the data two data sets are avalable: 1. reported defect dmensons from the pg suppler. defect dmensons as determned at the excavaton and repar of the defect M.Sc. Thess Lech A. Grzelak

24 7 A statstcal approach to determne the MIC rate of underground gas ppelnes Reported defects Although the clamed performance of the dfferent pgs s comparable (see Table ) the number of reported external corroson defects s dfferent per suppler as can be seen n the table below. Suppler Szng accuracy 5 Number of external corroson Date of nspecton A +/- 10% w.t. 65 October 1999 B +/- 10% w.t 7 Aprl 001 C +/- 10% w.t June 00 D +/- 10% w.t 441 March 004 Table : szng accuracy of the pgs and number of reported defects As t s generally known the process of defect recognton conssts of three steps: detecton of the defect, szng of the defect and dentfcaton of the defect. The experence of Gasune s that most of the dfferences between supplers arse from dfferences n dentfcaton. The dstncton between a mll defect and a corroson defect seems to be troublesome for the supplers n qute a number of stuatons. Ths accounts for part of the dfferences n the reported number of defects. Another explanaton for the dfference n numbers s tme related: n general the performance of pgs has mproved over the last 5 years and corroson defects that had a defect depth under the reportng threshold 5 years ago may have grown to a defect depth above the reportng threshold Excavaton data After the frst pgrun 7 excavatons have been performed, n whch 17 separate defects have been repared. All of the defects that have been repared were manually measured n the dtch by the usual gouges. The defects that have been repared by welded sleeves could not be used as reference ponts for the pgruns B, C and D whereas the defects that were repared by clock sprng or coatng could be used as reference ponts. Table 3 ndcates the number of reference ponts that have been detected by the dfferent supplers. Suppler Number of avalable reference ponts from excavaton A 17 B 9 C 11 D 10 Table 3: number of reference ponts per pgrun The fact that the number of reported reference defects vares between B, C and D s due to the fact that the appled POF- nteracton rules [1] lead to clusterng of defects. Dfferences n defect szes or dstances between defects wll nevtably lead to dfferent numbers of reported defects. 5 for defect depth of general corroson wth 80% confdence level (w.t. = wall thckness) 6 of whch 576 are below 10% of wall thckness Delft Unversty of Technology

25 8 Fgure 1-3: clock sprng nstallaton (left), gas ppelne excavaton (rght) Fgure 1-4 shows reported defect depths compared to the real metal loss measured at the excavaton (all pg measurements are oscllatng around a dashed lne- whch ndcates a lnear relatonshp between real metal loss, and pgs measurements). Fgure 1-4: reported vs. measured defect depth Because the excavatons were performed n a relatvely short tme perod after the pgrun, t s assumed that defect depth has not sgnfcantly changed between the tme of the pgrun and the tme of excavaton Measurement data from matched defects All the matched defects come from dfferent segments wth varyng wall thckness. In 10 cases the defects are from a segment wth a wall thckness of 11. [mm], whle the rest of the defects are from the ppe wth a wall thckness of 1.86 [mm] (These values are nomnal wall thcknesses). The measurement dataset of matched defects s presented n Fgure 1-5. M.Sc. Thess Lech A. Grzelak

26 9 A statstcal approach to determne the MIC rate of underground gas ppelnes Fgure 1-5: reported defect depth Snce the nspectons are chronologcally ordered (A, B, C and D), t s clear from the above fgure that some of the defects are mprovng n tme (corroson depth s decreasng), whch s physcally mpossble. Delft Unversty of Technology

27 10 Chapter Descrpton of the corroson rate model.1 Introducton Snce the corroson s reported by ntellgent pgs, t s very mportant to know what the accuracy of the pg s. Such nformaton can be obtaned from the calbraton data collected durng ppelne excavatons. Gven that all data gathered by pgs s not certan t s reasonable to combne the measurements wth error dstrbutons obtaned from the calbratng procedure. If the excavaton ndcates that for a certan pg the measurement error s sgnfcantly smaller than for the other pgs, then the model should also take ths nformaton nto account. Another demand whch model has to satsfy s to deal wth the mssng data f some of corroson spots haven t been regstered n all nspectons; so ths nformaton also needs to be taken nto account and to gve physcally unreadable estmates. Ths chapter shows ways of dealng wth uncertanty about measurements, estmatng reasonable corroson rate(s) (.e. non- decreasng n tme) and dealng wth the mssng corroson data.. Data calbraton The data measured at each pgrun can be calbrated by removng the bas. There can be dfferent reasons for ths bas n defect measurements. Two of the most mportant reasons are: a measurement error assocated wth the measurement technque of a MFL-pg, and an effect caused by the clusterng of defects. The result of clusterng of several ndvdual defects can be caused by that only the deepest ponts are compared they may not be related to the same ndvdual defect. The analyss starts wth the measurements calbraton for a possble bas. Ths s one of the most mportant actons because the calbraton nfluences all the collected measurements. M.Sc. Thess Lech A. Grzelak

28 11 A statstcal approach to determne the MIC rate of underground gas ppelnes Due to the small number of excavatons, t s dffcult to nvestgate how well a gven pg s calbrated for deeper or shallower defects. However, t s possble to check the pgs accuraces, assumng homogenety between defects for each pg. By comparng the calbraton results, a concluson on whch pg s the best, wth respect to a bas spread of the measurement errors can be obtaned. The calbraton algorthms are n the next paragraph...1 Data calbraton procedures Algorthm 1 (Calbraton data algorthm) In order to perform data calbraton we need to follow the procedure: take X as a vector of metal loss regstered by an ntellgent pg defne an actual metal loss vector Y defne the bas vector Z = X Y calculate the bas by takng the expectaton of Z ( EZ ) Ths procedure allows to measure (by means of the average value) how far s the regstered by a pg metal loss from actual the metal. The expectaton s equvalent to the measure of bas, and ndcates how pg measurements are consstent wth actual data. Algorthm (Measurement error dstrbuton algorthm) Ths algorthm presents the procedure for estmatng the dstrbuton of measurement error. Use the Calbraton algorthm and fnd EZ Defne the corrected (unbased) pg calbraton measurements as: X ' = X EZ Defne the resdual random varable ε = X ' Y Fnd the dstrbuton of ε (usng technques ntroduced n the background chapter- appendx A1) From Algorthm 1 and : EX ' = E( X EZ) = EX EZ = EX E( X Y ) = EX EX + EY = EY So, the expectaton of unbased pg equals the expected value of actual metal loss... Data calbraton results The calbraton procedure showed that all of the pgs have a bas. All the measurements requre removng the bas. The bas for all pgs dd not exceed a value of 0.6 [mm], and on average had a level of 0.1 [mm]. Two MFL-pgs led to underestmaton and two led to overestmaton of defect depth. Table 4 presents the results of the calbraton procedure appled to the excavaton dataset. nsp. no. of calbr. samp. bas [mm] concluson A overestmated B underestmated C underestmated D overestmated Table 4: calbraton results Delft Unversty of Technology

29 1 Removng the bas can be done by subtractng t from the measurements reported by the correspondng MFL pg. When all the measurements are unbased, the second stage of the pg calbraton can be ntated, namely- the measurement error analyss. Snce none of the MFL pgs reports measurements wthout error (see Fgure 1-4), all the pgs have ther own measurement error dstrbutons. The example of the measurement error hstogram for pg A wth the correspondng theoretcal curve s presented n Fgure -1. Fgure -1: error dstrbuton for pg A When the measurement error dstrbutons for all the pgs are known, the concluson about the pg s accuracy can be drawn. It depends on two factors. Frstly: on the level of the bas and secondly: on the standard devaton of the measurement error. The analyss showed that for all pgs, under the null hypothess, the measurement errors are normally dstrbuted cannot be rejected (a sgnfcance level s customarly chosen to be 0.05). The standard devatons of the measurement errors are tabulated and presented beneath n Table 5. nspecton dstrbuton 7 A N(0,0.93) B N(0,1.34) C N(0,0.77) D N(0,0.63) Table 5: standard devatons of the measurement errors The results from the table ndcate that pg D (the last nspecton) has the smallest spread of the measurement error. The worst one s pg B, whch has less than half the accuracy of D. Snce the uncertanty about the measurements reported by pgs s known, t s advsable to take ths nformaton nto account for corroson rate modelng. 7 N stands for a Normally dstrbuted random varable wth two parameters, mean and standard devaton M.Sc. Thess Lech A. Grzelak

30 13 A statstcal approach to determne the MIC rate of underground gas ppelnes..3 General model for data calbraton Let s assume that we have carred out n nspectons- done by n dfferent pgs. Each pg s based dependng on the regstered defects depth. Ths knd of stuaton requres specal treatment, whch s the man part of ths chapter. Proposed procedure shows ways to avod (reduce) the correlaton between reported defect depth and measurement error. Suppose, we take a certan pg for whch, measurements and actual metal loss can be presented as follows: Fgure -: example of defects clusterng Fgure - shows that for three dfferent defect populatons three dfferent bases can be specfed, and three assocated error devatons. Of course, the decson about combnng defects (clusterng 8 ) nto subpopulatons generally can be subjectve. However the choce of clusterng also can be done n mathematcal manner. Mathematcal tools that work wth ths problem are so called Clusterng algorthms. Lterature avalable on the topc of the clusterng s ntroduced n references [8], [9], [10] and [11]. Gven that th pg measurements are presented n Fgure - above, t s possble to recognze three dfferent defects groups: small defects (black dots) where the bas s negatve (pg gves lower values than actual loss) wth small standard devaton, second- where observatons oscllate around actual values but wth hgh spread, and thrd subpopulaton (blue dots) where the bas s postve. Ths observaton motvates to dstngush groups of shallow, mddle, and deep defects. Such groups should be calbrated separately. Presented stuaton, mght not the case of real measurement; but t s mportant to know that f such stuaton occurs then needs to be taken nto account n the modelng. Accordng to prevous notaton, we have n pgruns and each of them can be based for dfferent clusters of defects. Ths leads to more general procedure of data calbraton than the one ntroduced before. 8 The process of organzng objects nto groups whose members are smlar n some defned way Delft Unversty of Technology

31 14..4 General calbraton procedure: 1. Take calbraton data for pg where = 1, K, n. Check whether pg s measurements are homogenous, f not, then fnd number n of defects clusters (.e. subgroup of defects, where members are smlar n some way) a. For each j = 1, K,n apply the algorthm 1 and get the bas for group j. b. Remove the bas from all measurements obtaned by pg. c. Apply the algorthm and get the dstrbutons for ε, j where j = 1, K,n The effects of appled general procedure are: All measurements done by pgs can be calbrated accordng to pg accuracy for dfferent defects depth. n We have n dstrbutons functons of measurement error, = 1 whch wll be appled n order to estmate the corroson rate. In the prevous part t was checked that the measurement error dstrbutons for all pgruns are normally dstrbuted. In the general model, f both: the assumpton about the same populaton for all the errors and normal dstrbuton are satsfed then n order to estmate the corroson rate a lnear regresson can be appled. On the other hand the least squares errors approxmaton wthout mposed any constrans can produce best estmate whch for ex. ndcates decreasng corroson rate. Next paragraph presents the general corroson rate model and numercal results for descrbng corroson growth as a functonal dependence on tme (nspectons)..3 General corroson rate model Let s assume that accordng to dataset n dstngushable defects n tme were observed. Suppose that defect was observed n n nspectons. The task s to fnd the best functon of tme, whch descrbes the corroson growth for specfc defect. The frst dea s to apply lnear regresson to all observed values of defect. Ths s a reasonable guess, but has sgnfcant drawbacks: From the collected data t s clear that n many cases nspectons report the depths for whch the best lnear estmate s: o decreasng n tme- what s unacceptable o the slope of a functon s too hgh- t means that the corroson accordng to the functon grows too fast, and ndcates leakage- but such leakage n ppelne was not observed o corroson accordng to the best estmated functon starts before ppelne nstallaton or even ppelne producton The standard regresson estmaton can only be appled to the model f t s assumed that the errors are normal, come from the same dstrbuton and are uncorrelated. However, n the case when the calbraton procedure s appled, t s clear that the normalty mght not be the case; furthermore, t can happen that measurements error don t come from the same populaton (dstrbuton). M.Sc. Thess Lech A. Grzelak

32 15 A statstcal approach to determne the MIC rate of underground gas ppelnes The model that has none of ntroduced drawbacks and accordng to delvered data gves a functonal descrpton of the corroson rate s presented beneath. The dea behnd the model s to gve an estmate whch takes nto account nformaton about the measurement error dstrbuton for each specfc pg (f the case then also clusters for each pg). Frst, let s defne: 0 l + f : ( T j, α, K, α ) R - theoretcal model functon wth l+1 parameters, assocated wth th defect, T j - tme snce ppelne nstallaton at j th nspecton d -unbased depth of defect, measured at j th nspecton j w - nomnal wall thckness where th defect s observed m - total number of nspectons P, j - measurement error densty functon of defect at j th nspecton The functon f assocated wth th defect needs to satsfy followng optmzaton task: maxmze subject to : : L = m j= 1 P, j f 0 l ( f ( T j, α, K, α ) 0 l ( Tm, α, K, α ) w 1 0 l f ( 0, α, K, α ) f s d non decreasng The frst restrcton mposed on functon f says that a value of the functon at the last nspecton cannot be hgher than the ppelne wall thckness where defect was observed. The second condton rejects stuatons where corroson ntaton accordng to data s before ppelne nstallaton (f we want to fnd the corroson ntaton tme, we need to fnd 0 l a t, for such f ( t, α, K, α ) = 0.e. corroson level at ntaton tme s exactly equal to 1 0 l zero, hence t s equvalent wth f (0, α, K, α ) = t ). The thrd and last constrant says that the functon assocated wth defect s growth cannot be decreasng n tme..3.1 Example Suppose that: In three nspectons one defect was observed. Each tme, the measurements were done usng dfferent pgs. From calbraton procedure t s known that all three pgs have nonhomogenous measurement error.e. parameters (or dstrbuton) are dfferent for dfferent pgs. 0 Assumng lnearty of defect s growth, the model has to fnd such estmators of α and α for whch the Lkelhood functon L s maxmum. The functon: f = ˆ α ˆ + α t s a functon that descrbes the corroson growth n tme for specfc defect. The schema of ths procedure s presented below n Fgure -3., j 0 0 ) Delft Unversty of Technology

33 16 Fgure -3: corroson rate determnaton- general model It s clear that L gets the hgher value f the estmated lne s closer to real measurements. In the case when the lne goes through all observed measurements, then ths lne s the best, and the lkelhood s maxmal, hence ths approach agrees wth natural expectaton. Remark The optmzaton process can be performed by applyng technques ntroduced n a feld of optmzaton as multdmensonal constraned non- lnear programmng. The results presented n the report are obtaned by usng Matlab 9 optmzaton toolbox. Furthermore because of the computatonal complexty of ntroduced non-lnear task t s worth to transform the task by usng logarthm transformaton 10. The mplementaton of the formulated problem s presented n the appendces..3. Dealng wth mssng data Many of defects were observed only n three nspectons (whle total number of nspectons s four). The model assumes that f depth of certan defect was not reported durng nspecton, then the measurement error densty functon for ths defect s unform on the nterval bounded by the mnmum and maxmum observed defect s depth. Suppose that defect was not observed at thrd nspecton, then n optmzaton problem the measurement densty functon for unmeasured depth s P, 3 = 1[ mn depth of 'th defect,max depth of 'th defect]. Ths means that f a certan defect was not regstered, then the functon descrbng corroson growth s derved by usng only reported defects. The draft of such stuaton s presented on the Fgure Matlab (R14) 10 Any monotonc transformaton of a functon doesn t change ts extremes (ma1, mn). M.Sc. Thess Lech A. Grzelak

34 17 A statstcal approach to determne the MIC rate of underground gas ppelnes Fgure -4: corroson rate modelng- dealng wth mssng data.4 Conclusons The model presented n ths secton gves the corroson rate estmate when low number of the defect measurements s avalable. Very often standard regresson model doesn t gve relable and acceptable results; hence alternatve s requred. For many defects the regresson estmates are negatve or ndcate defect ntaton before ppelne nstallaton. The General corroson rate model solves all these drawbacks, and also takes nto account nformaton on pgs accuraces..5 Implementaton (CoroGas 1.0v) The theory ntroduced n ths chapter has been mplemented n CoroGas, software package developed by the author. Ths program analyzes the excavaton data, unbases the measurements, assesses the weghts for MFL-pgs and gves estmate of the corroson rate. The program has mplemented algorthms for predefnng the clusters for the calbraton. Fgure -5: calbraton data & optmzer wndow of CoroGas Appendx B descrbes CoroGas and all avalable functons. Delft Unversty of Technology

35 18 Chapter 3 3 Numercal results Ths chapter s mostly based on the artcle Determnaton of the corroson rate of MIC nfluenced ppelne usng 4 consecutve pgruns by Lech A. Grzelak & Gorgo G.J. Achterbosch publshed n Internatonal Ppelne Conference (IPC ) 3.1 Introducton Three dfferent approaches for corroson rate modelng wll be presented. The analyss s carred out startng from the smplest to more sophstcated models. The frst and the second approach are smply based on the unconstraned regresson analyss. The thrd and the last model, s based on the unbased measurements and pgs accuracy descrbed n the Chapter. 3. Approach 1 In the frst approach all the defects are pooled n 1 dataset and no corroson rate s calculated for ndvdual defects but only for the dataset as a whole. The frst approach starts wth verfcaton f the hypothess that the measurement errors for all MFL pgs are from the same populaton and are normally dstrbuted can be accepted. Ths was the case. Accordng to the maxmum lkelhood estmaton for the measurement error the parameters are 0 (mean) and 0.91 (for a standard devaton). If t s assumed that for all the errors, there s no correlaton between them, then the task of fndng a corroson rate assocated wth all the measurements s equvalent to a Gauss Markov regresson model. M.Sc. Thess Lech A. Grzelak

36 19 A statstcal approach to determne the MIC rate of underground gas ppelnes Let s defne necessary matrxes X and Y n followng way: ( T1 ) m1 1 X = 1 m 1 M ( T ) n m 1 n m Y = d ( T1 ) d( T ) L d( T ) d( T ) 1 1 where: [ ] T m 1 m 1 n 1 mn 1 n mn 1 1 m o d( T ) m d T d T d T m d T = m L 1 (,1) (,) (, 1) (, ) -a vector of m tmes unbased depths measured by pg at tme T, second ndex ndcates defect s number o n total number of nspectons o m - number of defects at th nspecton o m s total number of observed defects at n nspectons ( m = m + K+ mn o 1 1 L tmes m = m T T T 1 ) o ( T ) m x T T T T 1 = L where T s a tme of th nspecton m tmes If addtonally, t s assumed that the corroson rate s unform over tme (.e. corroson growth s lnear), then an applcaton of the Least Squares Error (LSE) method gves a lnear descrpton of the corroson growth n the followng form: y= ˆ α 0 + ˆ α1t and the 0 1 remanng ssue s to fnd the estmator [ ˆ ˆ ] T ˆ β = α α for the lnear functon. Standard calculatons gve that the estmators for unknown parameters are: ˆ α 0 =.4 and ˆ α 1 = Coeffcent ˆ α s equvalent to the measure of the corroson rate [mm/yr], so the LSE model estmated a corroson rate for the calbrated measurements of 0.1 [mm/yr] wth 95% confdence nterval [0.05, 0.0]. Delft Unversty of Technology

37 0 Fgure 3-1: defect depth n tme To check how well the model fts the data, a determnaton coeffcent s calculated. A goodness of ft measure resulted n R = Ths s poor because t ndcates low relatve predctve power of the model. Accordng to the model, the ntaton tme for corroson s 0 years [yrs snce ppelne nstallaton]. Even though the estmated parameters are n an acceptable range, ths approach has sgnfcant drawbacks: the model does not dstngush defects t does not take nto account that some of the defects are mprovng n tme (decreasng defect s depth whch s physcally mpossble), or for some the defects ntaton tme s before ppelne nstallaton the model assumes that all the defects have one corroson rate 3.3 Approach As was ponted out n the prevous secton, the frst approach has sgnfcant drawbacks. The second approach, proposes a way of dealng wth some of the enumerated dsadvantages. Lke before t s assumed that corroson growth s lnear n tme. The second model checks what the corroson rate s, f the defects are analyzed ndvdually.e. the model does not assume any more that there s only one corroson rate for all the defects but t calculates a corroson rate per defect. A smple regresson analyss appled to each unbased defect gves the followng graph. M.Sc. Thess Lech A. Grzelak

38 1 A statstcal approach to determne the MIC rate of underground gas ppelnes Fgure 3-: corroson rate dstrbuton Fgure 3-3: dstrbuton of ntaton tme From the hstogram presented n Fgure 3- t s clear that n many cases, smple regresson analyss appled to each defect results n negatve corroson rates. The mean corroson rate accordng to ths model s 0.16 [mm/yr] whch s close to the result obtaned before, however the 95% confdence nterval for the corroson rate s qute dfferent: [-0.31, 0.54]. The 95% confdence nterval comprses negatve values. The number of the defects ndcatng ether negatve corroson rate or corroson ntaton tme before the ppelne nstallaton s 16. One way of dealng wth a negatve corroson rate s to remove all the outlers from the dataset. However, such treatment s undesrable snce the dataset conssts of 30% bad defects. Further nvestgaton confrmed that the corroson rate follows a normal dstrbuton. The ntaton tme of the corroson s presented above, also n the form of a hstogram. The red bars n the pcture ndcate an ntaton tme outsde the nterval determned by the tme of ppelne nstallaton (t=0 [yr]) and the tme of the last nspecton (t=44.5 [yr]). A summary of the results obtaned from the second approach s presented n Table 6. results corroson rate nt. tme mean 0.16 [mm/yr] [yr] 95% conf. nt. Lower bound [mm/yr] [yr] Upper bound 0.54 [mm/yr] [yr] Table 6: corroson rate and ntaton tme for approach Stll the Least Squares Errors approach produces negatve corroson rates or ntaton tmes before ppelne nstallaton. Therefore an alternatve model for the presented models s presented: approach Approach 3 Ths approach s based on the General corroson rate model ntroduced n prevous chapter. The model takes nto account nformaton about the measurement error dstrbutons for each specfc pg and accordng to these dstrbutons assgns weghts to the measurements. The weghts are chosen n the followng way: a pg whch s accurate nfluences the fnal results stronger than a pg wth a lower level of accuracy. 11 Approach 3 s smplfed verson of General corroson rate model. Delft Unversty of Technology