DEVELOPMENT OF TOOLS TO ESTIMATE ACTUAL CORROSION GROWTH RATES OF GAS PIPELINES

Transcription

1 DEVELOPMENT OF TOOLS TO ESTIMATE ACTUAL CORROSION GROWTH RATES OF GAS PIPELINES Fnal Report SwRI Projet.148 Contrat Number: DTPH 56-8-T- Prepared for U.S. Department of Transportaton Ppelne Hazardous Materals Safety Admnstraton 4 Seventh Street, SW, Room 1 Washngton, DC 59 Prepared by Frank Song Southwest Researh Insttute 6 Culebra Road San Antono, TX 788 Otober 11 S O U T H W E S T R E S E A R C H I N S T I T U T E SAN ANTONIO HOUSTON WASHINGTON, DC

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3 EXECUTIVE SUMMARY Both external and nternal orroson of gas ppelnes an pose threats to ppelne safety by thnnng the ppe wall, leadng to leaks or ruptures. To ensure the ppelne safety, t s mportant to know both ppelne nternal and external orroson rates. The orroson rates an be used to determne nspeton ntervals for nlne nspeton and pressure tests or the reassessment nterval for dret assessments. For external orroson, the orroson rate under a oatng dsbonded from a ppe surfae s of most onern beause t annot be measured n the feld. The default orroson rate (.4 mm/y n the NACE Standard SP 5-8) s generally too large for most ondtons. It has been argued that a athod proteton (CP) permeable oatng may sgnfantly mtgate ppelne external orroson even when the oatng dsbonds. However, t s also argued that under a so-alled CP-mpermeable (or sheldng) oatng, suh as hgh densty polyethylene oatng or a three-layer oatng, CP may stll provde proteton beause ts urrent penetrates the oatng-dsbonded regon through the holday (when present). It s unlear how effetve these oatngs are n protetng the ppelne external surfae when dsbonded. For nternal orroson, the hemstry and ondton at the ppe surfae ontrol the orroson rate, although they annot be dretly measured or known. The amount of lqud water nherently dfferent n the dry and wet gas ppelnes an sgnfantly affet the orroson rate, whle the same models have so far been used for predtng the dfferent orroson rates. In an earler Ppelne and Hazardous Materals Safety Admnstraton (PHMSA)-funded projet (DTRS56-4-T- ompleted n 6), models were developed to predt ppelne external and nternal orroson rates for natural gas ppelnes. However, the external model dd not onsder the effet of oatng permeablty and the effet of the geometry of the oatng dsbondment. The nternal orroson model was unable to dstngush the dfferent orrodng ondtons for wet and dry gas ppelnes. The objetve of ths work s to expand the earler modelng work and develop gudelnes for ppelne operators to predt orroson growth rates through Improvng the exstng external orroson rate model of Southwest Researh Insttute (SwRI ) to nlude the effet of oatng permeablty nludng arbon doxde (CO ) and the geometry of the oatng dsbondment, and valdatng the model wth laboratory and feld data, Developng a thn-flm nternal orroson model to predt the ppe orroson rates n dry gas ppelnes due to gas qualty upsets, and valdatng the model usng laboratory and feld orroson growth rate data, and Improvng the urrent SwRI nternal orroson rate model for wet gas ppelnes by nludng the effets of arbon doxde (CO ) hydrogen sulfde (H S), and oxygen (O ), and valdatng the model usng laboratory and feld orroson rate data. For both nternal and external orroson, omprehensve mehanst models were developed n ths work. These mehanst models form the foundaton of ths modelng work and were valdated wth laboratory data and feld data or feld observatons. Methods were then developed to smplfy the models, and the smplfed models were verfed. Fnally, pratal gudelnes were developed that may be used to gude feld orroson rate predtons.

4 For external orroson, the models enable predtng the hemstry and orroson rate n a oatng-dsbonded regon when the dsbondment gap vares wth loaton, for dfferent CP levels at the holday, and when the oatng s and s not permeable to CP urrent and oxygen or arbon doxde. The model-predted results are qualtatvely onsstent wth laboratory test results n terms of ph, hlorde onentraton, and potentals measured n smulated oatng-dsbonded regons. A few key model results are summarzed. Unlke onventonal reve orroson often assoated wth a large athode-to-anode area rato, the area rato for the ppelne orroson under a dsbonded oatng s rather small. Irrespetve of CP levels, the ph n the dsbonded regon falls n the neutral or alkalne range as long as the sol s not ad. Predted orroson rate s, n ths ase, not sgnfant. Pttng, mrobologally ndued orroson, and orroson due to alternatve urrent or dret urrent nterferenes are not part of ths study. When the ppe surfae at a holday s mantaned wth CP (e.g., -85 mv or -9 mv vs. opper/opper sulfate (CSE)), rrespetve of oatng permeablty to CP, the ph n the oatngdsbonded regon nreases over tme and the orroson rate dereases. Wth tme, the ph n the dsbonded regon may exeed that near the holday. In the absene of CP and n aerated sol, the overall ph n the dsbonded regon dereases over tme and an fall below that near the holday. CP sheldng s perhaps partally true for oatngs wth a holday. In the presene of CP, the nrease of ph over tme n oatng-dsbonded regons and the shft of potental n a more negatve dreton redues the loal orroson rate over tme. Corroson may happen when the sol s aerated and wet and the CP s ether lakng or nadequate. The varaton of gap wth loaton n a oatng-dsbonded regon (narrow-gapped regon s ¼ of the gap elsewhere) appears to have an nsgnfant effet on the soluton hemstry and orroson rate (relatve to a dsbondment of unform gap). The gap effet on the soluton hemstry, suh as sodum on (Na + ) onentraton f present, may be summarzed as follows. Wth CP, as the gap narrows (n the dreton away from the holday) Na + tends to aumulate and ts onentraton nreases. Conversely, as the gap expands, the Na + dffuson flux dereases and t tends to dsspate out, leadng to a redued onentraton. A permeable oatng behaves lke a membrane, whh, under athod polarzaton at the holday, tends to rase the aton (e.g., Na + ) onentraton and ph more rapdly (relatve to an mpermeable oatng). The Na + onentraton and the ph may exeed those at the holday, and subsequently, the mass transport aross the oatng starts to reverse to the opposte dreton. At a holday potental of -9 mv CSE, the athod urrent appears to be able to suffently suppress the orroson aused by ether O or CO (ombnaton not studed) f t penetrates nto the dsbonded regon both from the holday and aross the oatng. The pratal mplaton s that n the presene of suffent CP, a permeable oatng, when dsbonded, an stll be apable of protetng the substrate steel from orroson attak. The model an be saled wth respet to tme and geometry of the oatng-dsbonded regon (gap and length). For a dsbonded regon of unform gap, suh salng has been verfed

5 by model smulatons and s useful for redung model omputatons and salng experments when needed. The geometry salng fator s found to be L /δ (or L/ ), and the tme-salng fator s t/δ, where L s the dsbondment length, δ s gap, and t s tme. For ppelne nternal orroson, a omprehensve CO orroson model was developed and valdated wth laboratory and feld data for a wde range of ondtons. Ths model onsders both dffuson and mgraton of on spees n soluton. The general fundamentals of the model are the same for both wet and dry natural gas ppelnes. Nevertheless, the orrodng ondtons of these two systems are dfferent, and thus the predted orroson rates are dfferent. In dry gas ppelnes, ferrous ons as a orroson produt annot esape the soluton boundary layer at the ppe wall, and thus preptaton of FeCO, for example, wll our. The preptate redues mass transport and the exposed ppe surfae area avalable for orroson, and leads to an overall redued orroson rate ompared to a wet gas system. For wet gas systems where preptates an dssolve and travel out of the boundary layer nto the bulk soluton, preptaton may or may not our at the steel surfae dependng on the balane between the formaton rate and the dssoluton rate of a preptate. Ths model result suggests that when an nternal orroson rate n a dry gas system s predted, the fat that the rate n ths dry gas system s smaller than n a wet gas system should be onsdered. The model an be smplfed by negletng on mgraton aross the soluton boundary layer to yeld the same results. Ths smplfaton an greatly redue the hallenges n numeral soluton of the dfferental equatons, from nonlnear to lnear equatons. Predtng the effet of H S on CO orroson rate s stll a hallenge. In ths work, harts are provded to show ondtons where FeCO s domnant over FeS (and ve versa) and the CO orroson model s applable. O n a CO orroson system an nrease the orroson rate by dffuson. In the meantme, the generated hydroxyls from O reduton redue the orroson rate. Ths nteratve effet of O on CO orroson rate leads to a stuaton that oxygen dffuson s not entrely the ontrollng step n ontrbutng to CO orroson. In pratal predton of ppelne nternal orroson, t should be onsdered that the addtve total of CO orroson rate wthout O and O orroson rate (ontrolled by ts dffuson) overestmates the atual orroson rate. It s reommended that an ndustral survey and feld data analyss (a orrelaton of sol ondton, CP level, sample results of hemstry and orroson n oatng-dsbonded regons) be performed to understand the ondtons where CP both works and fals for a sheldng oatng. Ths helps the root auses of ppelne external orroson. The effet of sold preptaton on ppelne external orroson n a oatng-dsbonded regon needs to be studed. It s possble that alareous deposts formed at the holday blok the pathway of CP penetraton nto the dsbonded regon. The effets of H S and O on CO orroson need to be further explaned expermentally before a relable mehanst model an be developed for feld use.

6 ACKNOWLEDGMENTS Ths projet was performed under the DOT Contrat DTPH56-8-T-. James Merrtt (PHMSA/DOT) provded management oversght. The author wshes to thank the Department of Transportaton (DOT), Ppelne Researh Counl Internatonal (PRCI), and CenterPont Energy for ther support. Durng ths projet, PRCI members of the orroson ommttee provded projet revew and omments on the ntermedate results. Mark Pazza of PRCI and Rkey Payne of CenterPont Energy asssted n puttng ths projet together. The earler ontrbuton to ths projet by Dr. Fraser Kng of Integrty Corroson Consultng Ltd. and the assstane of Dr. Hu Yu of SwRI s greatly appreated. v

7 TABLE OF CONTENTS EXECUTIVE SUMMARY... ACKNOWLEDGMENTS... v 1. INTRODUCTION Bakground Objetves Tehnal Approah Report Outlne Referenes PIPELINE EXTERNAL CORROSION Bakground and Objetve Model Geometry General Equatons for the Model General Governng Equatons Intal and Boundary Condtons Seletve Model Results and Model Valdaton Key Model Results and Dsusson Aerated Dlute NaCl Soluton Wthout CO Creve Gap Varyng wth Dstane Creve Corroson Consderng Penetraton of Current and O va Coatng Dlute NaCl Soluton Contanng CO Summary of Model Results Model Smplfaton Bakground Salng Theory for Creve Corroson Key Model Results and Verfaton of Salng Theory Summary of the Model Salng Results Pratal Implatons of the Model Results Understandng the Term CP Sheldng and Corroson Under a Shelded Coatng The Sgnfane of a Permeable Coatng The Effet of Creve Geometry Parameters Referenes PIPELINE INTERNAL CORROSION Bakground Model Desrpton Volumetr Reaton Rates Eletrohemal Reaton Rates at the Metal Surfae Reaton Rates and Boundary Condtons for the System of Conern Volumetr Reaton Rates Intal and Boundary Condtons Movng Boundary Condton for a Dry Gas System Model Valdaton wth Lab and Feld Data Page v

8 TABLE OF CONTENTS (Contnued) Page.5 Results Model Smplfaton Effet of H S and O on CO Corroson Summary Pratal Implatons of the Model Results Understandng the Dfferenes n Corroson Rate Between Wet and Dry Gas Systems The Effet of H S and O on Ppelne Internal Corroson Rate Referenes CONCLUSIONS AND RECOMMENDATIONS Conlusons Ppelne External Corroson Ppelne Internal Corroson Reommendatons Ppelne External Corroson Ppelne Internal Corroson APPENDIX A Dervaton of Equaton (-1) as a Model Governng Equaton... A-1 APPENDIX B Reversble and Irreversble Homogeneous and Heterogeneous Reatons, Chemal Equlbrum Formula, and Knet Rates n the Creve Corroson System Wthout CO... B-1 APPENDIX C Creve Corroson Consderng the Effet of Flow Indued by Gap Varyng wth Metal Dssoluton... C-1 APPENDIX D Dervaton of Model Governng Equatons wth CO n Creve... D-1 APPENDIX E Results of Creve Corroson Consderng Passvty of Steel at ph 1.5 or Greater... E-1 MANUSCRIPTS MS #1 A mathematal model developed to predt the hemstry and orroson rate n a reve of varable gap... MS-1 MS # Predtng the hemstry, orroson potental, and rate n a reve formed between substrate steel and a dsbonded permeable oatng wth a mouth... MS-8 MS # Theoretal nvestgaton nto tme and dmenson salng for reve orroson... MS-4 MS #4 A Model Developed to Predt the Internal Corroson Rates of Wet and Dry Gas Ppelnes MS-61 v

9 LIST OF FIGURES Fgure Page 1-1 A shemat showng the external orroson rate-ontrollng ondton n a oatng dsbonded regon A shemat showng the ondton at the steel surfae for ppe nternal orroson A shemat showng the tehnal approah used n ths work to model ppelne nternal and external orroson Model reve geometry showng the oordnators and dmensons of the reve and transport At a fxed mouth potental of -.9 V CSE, evoluton of onentratons of (a) Na + and (b) Cl - over tme and dstane nto the dsbanded regon from the holday Varaton of [Cl - ] wth tme at varous dstanes from openng Smlar to Fgure -, but here the mouth potental s fxed at -.9V CSE ph hanges along stat smulated raks, for varous potentals appled at the rak mouth, for HY8 steel n seawater Varaton of [Cl - ] wth tme at varous dstanes from openng ph profles wthn the reve after 7 h of test Smlar to Fgure -, but here the mouth potental s fxed at -.9V CSE Potental profles wthn the reve at.5 hour and at 7 h of test Potental dstrbuton n a.1-mm-thk reve at varous tmes At a fxed mouth potental of V CSE, a omparson of Na + onentratons n two reves at dfferent tmes Smlar to Fgure -11, but here for a omparson of reve phs: (a) near the mouth and (b) away from the reve mouth Smlar to Fgure -11, but here for a omparson of reve potentals (a) near the mouth and (b) away from the reve mouth Smlar to Fgure -11, but here for omparson of reve orroson urrent denstes At a fxed mouth potental of -.9V CSE, a omparson of the model results for four ases studed at both the ntal and steady-state ondtons Smlar to Fgure -15, but for reve hemstry: (a) Na + onentraton, (b) Cl - onentraton, and () ph n the reve At a potental of -.88V CSE and a CO partal pressure of.5 atm at mouth, a omparson of model results obtaned when CO permeaton through the oatng s and s not onsdered Smlar to Fgure -17, but for reve hemstry: (a) Na + onentraton, (b) Cl - onentraton Smlar to Fgure -17, but for reve ph Smlar to Fgure -17, but for (a) reve potental and (b) orroson urrent densty At a fxed mouth potental of -.9V CSE, a salng plot for a omparson of Na + onentratons n the three reves at dfferent tmes Smlar to Fgure -1, but here the salng plot s for a omparson of reve ph Smlar to Fgure -1, but here the salng plot s for a omparson of (a) reve potental and (b) orroson urrent densty... - v

10 LIST OF FIGURES (Contnued) Fgure Page -1 Shemat dagram showng the hemal, eletrohemal, and mneral (preptaton) reatons that may our n a boundary layer Model-predted maxmum (or ntal) and steady-state orroson rates vs. expermental data Model-predted tme-dependent orroson rates vs. expermental data measured n a soluton Model-predted tme-dependent orroson rates vs. expermental data measured n a soluton Model-predted maxmum (or ntal) and at.1 th hour nstant orroson rates vs. expermental data Model-predted maxmum (or ntal) and steady-state orroson rates vs. expermental data measured n lab Model-predted maxmum (or ntal) and steady-state orroson rates vs. expermental data n lab Model-predted maxmum orroson rates for both wet and dry gas systems at 5 C Predted orroson rates and porosty for only the dry gas system at the same ondton of Fgure Model-predted orroson rates for both wet and dry gas systems at 5 C and P CO =1atm For the same ondtons of Fgure -1, the porosty varatons wth tme for both wet and dry gas systems Verfaton of model smplfaton by omparson of orroson rates obtaned from the model by onsderng and not onsderng the voltage drops n the boundary layer Regon of a domnant preptate: Sderte or Maknawte Sderte-Maknawte boundary determned based on Equaton (-6) for varyng temperatures and the rato of partal pressure The nteratve effet of CO and oxygen on steel orroson... - v

11 LIST OF TABLES Table Page -1 Intal and Boundary Condtons for Systems Wthout CO Intal and Boundary Condtons for Systems wth CO Senaros Modeled Wthout CO and Loatons of Results x

12 1. INTRODUCTION 1.1 Bakground Both external and nternal orroson of gas ppelnes an threaten ppelne safety by thnnng the ppe wall, leadng to leaks or ruptures. External orroson results manly from fators suh as orrosve sol envronment (gas, salts, or batera), oatng degradaton or damage (holday generaton), nadequate athod proteton (CP), and alternatng urrent or dret urrent nterferenes. Internal orroson ours due to the presene of lqud water and orrosve gas spees, nludng arbon doxde, hydrogen sulfde, oxygen, solds, ondensates, and batera. There s a sgnfant dfferene n nternal orroson for wet gas and dry gas ppelnes due to the sgnfant dfferenes n the amount of orrosve eletrolyte present nsde the ppelnes. In the ppelne ndustry, no sngle approah provdes all the neessary nformaton for a onfdent estmate of the orroson rate. For external orroson, the hallenge s to understand the ondtons at the ppe surfae under a oatng-dsbonded from the ppe. Suh ondtons, (e.g., soluton hemstry) annot be known or measured dretly n the feld, although they an ontrol the orroson proess. These ondtons under the dsbonded oatng are, however, lnked to the known ondtons n the sol, as shematally shown by Fgure 1-1(a). Ths lnk s governed by the fundamental prnples of mass onservaton, harge onservaton, and hemal reatons n the soluton and eletrohemal reatons at the metal surfae (Fgure 1-1(b)). These fundamental prnples are the bass of the external orroson model to be developed. For nternal orroson, the ondtons nludng orroson knets at the ppe surfae are unknown, but these ondtons are related to the eletrolyte hemstry at the ppe surfae, whh s further related to the man gas omposton (see Fgure 1-). The relatonshp between the ondtons at the ppe surfae and those of the lqud eletrolyte and the man gas omposton s governed by the fundamental prnples of mass onservaton, harge onservaton, and hemal reatons n the eletrolyte. The overall fundamental mehansms for modelng ppelne orroson, both nternal and external, are the same, although the proess and the steps needed for the modelng are dfferent. The author and oworkers have performed sgnfant researh to model the proesses of ppelne external orroson and nternal orroson. A work reently ompleted for PHMSA (DOT ontrat DTRS56-4-T-) nvolved the development of models for predtng external and nternal orroson rates for natural gas ppelnes. [1] 1. Objetves The goal of ths work s to expand the earler modelng work and develop gudelnes for ppelne operators to predt feld orroson growth rates through Improvng the exstng external orroson rate model of SwRI [1] to nlude the effet of CO permeaton from sol nto a oatng-dsbonded regon, and valdate the model wth laboratory and feld data, 1-1

13 Developng a thn-flm nternal orroson model to predt orroson rates n dry gas ppelnes due to gas qualty upsets (e.g. water ondensaton), and valdatng the model usng laboratory and feld orroson rate data, and Improvng the urrent exstng nternal orroson rate model of SwRI [1] for wet gas ppelnes by nludng the effets of CO, H S, and O, and valdatng the model usng laboratory and feld orroson rate data. 1. Tehnal Approah Mathematal models developed to smulate orroson proesses may be ategorzed as mehanst, empral, or sem-empral models. Mehanst models are n general omplex and not easy to mplement n feld applatons. By ontrast, empral models are easy to use but not suted for applaton n ondtons beyond the expermental data range used to develop the models. A smplfed mehanst model, on the other hand, an be potentally useful beause t allows for data extrapolaton and s also easy for feld mplementaton. An overall four-step modelng approah was proposed to develop a mehanst model and then, use t n the feld. Ths approah s shematally shown n Fgure 1- and explaned next. The frst step, labeled 1 on the left sde of the trangle hart, forms the foundaton of the modelng approah. In ths step, a omprehensve fundamental model s to be developed. Suh a model may onsst of omplex dfferental equatons, suh as the Laplae s equaton and/or the Nernst-Plank equaton. [1-6] The fundamental nature of ths model allows the model to be used n broad ranges of ondtons. The seond step s valdaton or albraton of the fundamental model wth feld or/and laboratory data. One valdated, the model an be used to predt the ondtons where ether expermental data are lakng or the development of suh data an be expensve or mpossble. For nstane, t would be extremely hallengng, even f possble, to dretly measure the feld orroson rates n a oatng-dsbonded regon on bured ppelnes. The thrd step s smplfaton of the fundamental model nto smpler models through mathematal manpulatons and senstvty analyses. Durng ths proess, the rate-ontrollng varables or groups of varables may be dentfed and only these varables or varable groups need to be used n the smpler models. These smpler models stll retan the nature of the fundamental models whle requrng only the values of the known ontrollng varables to evaluate the overall system performane. When neessary, verfaton and/or further valdaton of these smpler models may be needed. The end goal of the overall modelng approah s Step 4, development of gudelnes to gude feld applatons of the model(s). These gudelnes an be developed more readly from the smpler relatons and from the analyss of the omprehensve model results. When possble, these gudelnes ould be ntegrated nto ndustral standards, regulatory douments, or ndustral operatng manuals. The suess of ths step requres a ollaboratve effort of the researh nsttutons that develop the proedures, the ppelne operators who mplement them n feld operatons, and the regulators who ensure ther proper use. 1-

14 1.4 Report Outlne A sgnfant porton of ths report has already been presented n manusrpts for publatons n journals or onferene proeedngs. These manusrpts are appended at the end of ths report, and our am s not to repeat t n the man text. When needed, t wll be nstead ted or brefly desrbed. Ths report wll manly onsst of four hapters. Chapter wll desrbe the external orroson model, Chapter wll desrbe the nternal orroson model, and Chapter 4 wll summarze the fndngs and reommendatons for future work. 1.5 Referenes 1. F.M. Song, N. Srdhar, An Approah to Determnng Reassessment Intervals through Corroson, DOT Contrat No. DTRS56-4-T-, Fnal Report submtted n Otober 6.. F.M. Song, D.W. Krk, J.W. Graydon, D.E. Cormak, Corroson 58, 1 (): F.M. Song, D.A. Jones, D.W. Krk, Corroson 6, (5): F.M. Song, N. Srdhar, Corroson 6, 8 (6): F.M. Song, N. Srdhar, Corros. S. 5, 1 (8): F.M. Song, Eletrohma Ata 56 (11):

15 CP Potental & sol hemstry Mouth Measurable Dsbonded oatng Chemstry, potental not-measurable; rate ontrollng Known CP and sol hemstry Ppe steel (a) Unknown parameters n a dsbonded regon Fundamentals Mass transport, harge onservaton, hemal and eletrohemal reatons (b) Fgure 1-1. (a) A shemat showng that the external orroson rate-ontrollng ondton n a oatng-dsbonded regon, whh annot be dretly measured, s lnked to the measurable ondtons n sol. (b) The bass of the modelng that brdges the ondtons nsde and outsde the oatng-dsbonded regon omprses fundamental prnples onsstng of mass transport, harge onservaton, and hemal and eletrohemal reatons. These fundamental prnples are the bass of the model to be developed. 1-4

16 Gas/bulk known ondton Corr. rate H + Mass transport,, CO, H CO, H S Chemal reatons Steel Preptaton Corroson reatons Fgure 1-. A shemat showng that for ppe nternal orroson, the ondton at the steel surfae, whh annot be dretly measured, s lnked to the known or measured bulk ondtons followng fundamental prnples and s the bass of the model to be developed. The fundamental prnples here onsst of mass transport, harge onservaton, and hemal reatons. Valdaton Fgure 1-. A shemat showng the tehnal approah used n ths work to model ppelne nternal and external orroson. 1-5

17 . PIPELINE EXTERNAL CORROSION.1 Bakground and Objetve Sgnfant researh has been performed to understand the mehansms of external orroson of a steel ppe surfae wth ts oatng-dsbonded wth or wthout a holday. [1-5] In laboratory tests [4,17-4] or n mathematal modelng, [5-1] the dsbonded regon s smulated by a reve that s generally assumed to have a unform gap. In realty, ths gap rarely s unform. Even f the gap s ntally unform, t an beome nonunform as the metal dssolves and/or deposts suh as preptates form at dfferent rates along the oatng dsbondment. In addton, the effet of on urrent or oxygen or arbon doxde dffuson through a permeable dsbonded oatng on the ppe orroson has not been studed n expermental tests, although models were reported that onsder the effet of urrent or oxygen permeaton through the oatng. [7,1,6,7] A goal of ths work s to understand from a fundamental perspetve, by mathematal modelng, the effet of varable gap (wth loaton) and the permeablty of a oatng (to CP and/or oxygen or arbon doxde) on the ppe orroson rate. The model results wll be used as a gude for smplfyng the model and provde gudelnes for feld use.. Model Geometry The reve geometres to be used n ths modelng work, formed when a oatng on the steel ppe surfae dsbonds from the holday, are shown at the left edge of Fgure -1. For the reve geometry shown n Fgure -1a, the temporal and spatal varaton of the reve hemstry and orroson potental and rate were modeled extensvely n an earler work. [1] Corroson n a reve wth ts gap varyng wth dstane from the holday, as shown n Fgure -1b, has not been studed. Fgure -1b represents an extreme ase where the gap sharply hanges between ts sze at the holday and a quarter of the gap at 5, 6, 15, and 1, where x s dstane from the s x holday and s s the gap sze at the holday edge. It s expeted that suh a sharp varaton of gap would yeld the most sgnfant mpat on the reve orroson, relatve to a gap that vares gradually or s unform, as shown n Fgure -1a. The gap s desgned to have abrupt varatons at x/ s = 5 and 6 beause past studes [5-1] showed that the hange of varables would our most strongly wthn the frst 1 gaps from the mouth. Abrupt hanges of the gap are desgned to also our n ntermedate (x/ s = 15) and longer (x/ s =1) dstanes to understand how the gap hanges at these loatons would have an effet on the orroson proess.. General Equatons for the Model Equatons neessary for predtng the evoluton, over tme and dstane, of the soluton hemstry, orroson potental, and rate n a oatng-dsbonded regon are gven n MS #1 attahed at the end of ths report. Ths seton provdes more general fundamental equatons for the model. -1

18 ..1 General Governng Equatons For a dlute soluton ontanng multple spees n a one-dmensonal reve, mass onservaton for an arbtrary spees numbered by may be wrtten as s t v x s x x ( N s x ) N y R s R s (-1) The dervaton of Equaton (-1) s shown n Appendx A. In Equaton (-1), s onentraton of the th spees n the soluton; R s the total net volumetr produton rate (after onsumpton deduted) of the th spees; R s s the total surfae reaton rate of the th spees nludng orroson reatons; subsrpts x and y refer to x and y oordnators (e.g., see Fgure 1a); and s s gap at dstane x and vares wth x and tme t. Other terms n Equaton (-1) are defned n the followng dsusson. The varaton of s wth t an be the result of depleton of the metal by orroson as follows: s r t Fe (-) Wth Equaton (-), the average flow veloty aross the gap, varaton of s wth t, an be determned by v x, whh results from the v x L 1 r dx (-) s x Fe where r Fe s the orroson rate, L s the total length of the dsbondment, and β s a unt onverson fator from steel orroson rate r Fe n mol/m /s to m/s, or M M (-4) 1 M where M M and ρ M are molar weght and densty of the metal (steel), respetvely, n standard unts. In Equaton (-1), N s flux of the th spees n the soluton and an be expressed by N zf D ( ) (-5) RT where D and z are dffuson oeffent and harge of the th spees; F, R, respetvely and T are Faraday s onstant, unversal gas onstant, and temperature, respetvely and s eletrostat potental of the soluton. When the veloty n Equaton (-1) an be negleted due to neglgble varaton of the gap wth tme, Equaton (-1) beomes s t x ( N s x ) N y R s R s (-6) -

19 In Equaton (-1) or (-6), the total net produton rate of the th spees, R, an result from homogenous reatons n soluton, suh as CO hydraton f present, and mneral (preptaton) reatons, whle t s only the former reatons that are of onern n ths modelng work for external orroson. For a homogeneous reaton nvolvng the th spees, for suh a reaton numbered by h, n the form of _ r,h A A (-7) _ r _ p,h _ p where the subsrpts r and p represent reatant and produt, respetvely, the volumetr reaton rate may be wrtten as [8] _ r,h _ p,h r k k (-8) h h _ f h _ b where k h_f and k h_b are the forward and bakward reaton rate onstants, respetvely. The total net volumetr produton rate of the th spees for all suh reatons s R r (-9) h,h h At the steel surfae, only the eletrohemal reatons are of onern; the total rate for the th spees yelds R s. For suh a reaton numbered by e, n the form of _ r,e M z,r z,p _ r _ p,em _ p n ee (-1) where z represents harge arred by the spees M, the followng harge balane must be met,ez ne (-11) e where,e and n e are, respetvely, the stohometr oeffent of the th spees and the number of eletrons transferred durng the e th eletrohemal half-ell reaton. The total net produton rate of all the eletrohemal reatons nvolvng the th spees s,e,e n ef R r (-1) s,e e,e,e e where,e s anod or athod urrent densty nvolvng the th spees. -

20 The urrent densty of the e th eletrohemal reaton (Equaton (-1)) may be generally wrtten by the Butler-Volmer equaton as [9] _ r,e a _ e _ p,j _ e e e _ ref ( ( ) exp( e ) ( ) exp( e ) (-1) _ ref RT F or by the Tafel equatons when ether the anod or the athod porton of the eletrohemal reaton s rate ontrollng. e _ ref s exhange urrent densty of Equaton (-1) at a referene ondton orrespondng to the onentraton of the th spees _ref ; α a_e and α _e are transfer oeffents of the anod and athod half-ell reatons, respetvely; and η e s overpotental or the eletrode potental relatve to that at the referene ondton. For orroson of ppe steel n a oatng-dsbonded regon, the anod reaton s ron oxdaton _ ref RT F Fe Fe e (-14) The athod reatons are H e.5h (-15) H O e.5h OH (-16) 4H O 4e H O (-17) and, n the presene of CO, H CO e HCO.5H (-18) The total net surfae reaton rate of the th spees n Equaton (-1) or (-6) s R s R s,e (-19) e.. Intal and Boundary Condtons The ntal and boundary ondtons for solvng the model-governng equatons n ths work are gven for two senaros: (1) no CO n the orroson system (Table -1) and () CO present n the orroson system (Table -). Table -1 also shows the ntal and boundary ondtons n a model presented n an earler work [1] where the ntal and mouth ondtons are the same. For ether senaro, only onentratons of the prmary spees are provded wth the realzaton that the onentratons of the seondary spees are dependent on and an be determned from the onentratons of the prmary spees through the equlbrum relatons -4

21 between the prmary and the seondary spees. The equlbrum relatons nvolved for both senaros of ppelne external orroson are provded n Appendx B. For Senaro (1) wthout CO, the reve soluton used n the modelng of ths work s an aerated dlute sodum hlorde soluton smulatng sol water absent of CO. Shown n Table -1, the bulk hemstry s dfferent from that ntally present n the dsbonded regon wth the latter more dlute, and both solutons are assumed to be saturated by ferrous hydroxde, whh s only sparsely soluble n water. Negletng the effet of homogeneous ferrous on oxdaton on the reve orroson rate due to justfatons gven elsewhere, [7,] the followng spees n the soluton are of onern: (1) Na +, () Cl -, () Fe +, (4) H +, (5) OH -, (6) Fe(OH) +, (7) O, (8) H (aq), (9) Fe(OH), and (1) H O, where the underlned spees are defned as the prmary spees. Some of ther onentratons an be known, suh as spees (8)-(1), and the onentratons of the remanng prmary spees are gven n Table -1 together wth the potental at the holday. The onentratons of the seondary spees, or spees (), (5), and (6), an be omputed from the onentratons of the prmary spees based on the equlbrum equatons gven n Appendx A. For Senaro () wth CO, the soluton spees are (1) Na +, () Cl -, () Fe +, (4) H +, (5) OH -, (6) Fe(OH) +, (7) CO, (8) H CO, (9) HCO -, (1) CO -, (11) H (aq), (1) FeCO, and (1) H O. The onentratons of the prmary spees underlned are ether gven n Table - or known suh as spees (11)-(1). The soluton s assumed to be saturated by ferrous arbonate wth a very low solublty. The onentratons of the seondary spees an be determned from the onentratons of the prmary spees. As shown n Table -, the bulk hemstry s dfferent from that ntally present n the dsbonded regon wth the latter more dlute. The boundary ondton at the mouth for both senaros s a onstant onentraton and a fxed potental (see Tables -1 and -). The boundary ondton at the reve tp s zero flux for eah spees and zero urrent. The oatng at the reve tp s onsdered to be mpermeable to on and moleular spees..4 Seleted Model Results and Model Valdaton Model results obtaned from usng the reve geometry of Fgure -1(a) wth a unform gap are used to qualtatvely ompare wth laboratory data. Only model results obtaned from hemstry absent of CO for a mouth potental of -.9 V vs. saturated Cu/CuSO 4 eletrode (CSE) are used for ths omparson. In ths seton, the model results are also dsussed where needed. Suh a model valdaton wll also be made brefly n Seton.5. when the model results for a soluton ontanng CO are dsussed. Fgure - shows the Na + and Cl - onentratons obtaned n ths work and those obtaned n an earler work. [1] Shown n Table -1, the ntal and mouth onentratons are the same for earler work and they are dfferent for ths work. For both works, the mouth potental was -.9 V CSE, representng sgnfant CP. Fgure -(a) shows that Na + onentraton nreases over tme for both works. Ths nrease n Na + onentraton results from the synergst aton of Na + dffuson and mgraton -5

22 nto the reve. The dffuson results from a hgher onentraton of Na + at the mouth, and the mgraton results from a more negatve steel potental at the mouth mposed by CP (relatve to the potental nsde the reve) and the postve harge arred by Na +. The potental that s more negatve at the mouth than nsde the reve reates an eletrohemal drvng fore that pumps Na + nto the reve. The Na + onentraton obtaned n ths work s overall smaller than that n the prevous work beause a smaller ntal onentraton was gven wth ths work. However, the dfferene n Na + onentraton between these two works dereases over tme and dsappears at 1 7 s, when steady state s reahed. Over tme, the Na + onentraton n the reve beomes greater than that at the mouth and leads to the Na + dffuson reversed n dreton. Wth a greater onentraton nsde the reve, Na + now tends to dffuse from nsde the reve toward the mouth and ounters the drvng fore of mgraton, whh, drven by CP, stll pumps Na + nto the reve from the mouth. When the dffuson and mgraton rates n opposte dretons balane eah other, steady state s reahed. Fgure -(b) shows the evoluton of Cl - onentraton n the reve. For both works, the ntal Cl - onentraton s unform n the reve, although the magntude s dfferent. Carryng a negatve harge, Cl - s pumped out from the reve by CP. For the prevous work, wth the same onentraton at the mouth and ntally n the reve, the Cl - onentraton dereases over tme untl steady state s reahed at 1 7 s. Ths result s generally onsstent wth the expermental results shown n Fgure -. [1] where under athod polarzaton wth the mouth potental of - 1. V SCE, the Cl - onentraton measured at the three loatons: (4, 15,and 18 m nsde the reve from the mouth) dereases over tme, although wthn the tme of the test and wth the mouth Cl - onentraton not mantaned, the Cl - onentraton near the mouth nstead drops qukly and beomes smaller than nsde the reve. For the present modelng work, the Cl - onentraton at the mouth s set to be greater than ntally n the reve, and thus, Cl - tends to dffuse nto the reve, opposte to the dreton of Cl - mgraton drven by CP. The ounterng balane between Cl - mgraton and dffuson n opposte dretons s the net flux of Cl -. In Fgure -(b), the sharp nrease of Cl - onentraton near the mouth suggests that near the mouth, Cl - dffuson s domnant over mgraton. Wth tme, as the Cl - onentraton n the reve nreases and the Cl - onentraton gradent dereases near the mouth, ths dffuson domnane dereases. When the dffuson flux balanes the mgraton flux, steady state s establshed and the Cl - onentraton merges to the urve at 1 7 s, the same urve of the earler work. [1] In both ths work and the earler work, beause CP tends to draw out Cl - from nsde the reve, the Cl - onentraton n the reve annot surpass ts onentraton at the mouth.. Fgure -4 shows a omparson of reve phs obtaned n ths work and the earler work. The phs n both works nrease over tme (reasons were detaled elsewhere [1] ). The Na + onentraton n the reve beomes progressvely greater than Cl -, and ther net postve harge s manly balaned by OH - formed from athod reatons (e.g., water reduton) whh aumulates nsde the reve. In essene, the orgnal NaCl soluton s partally substtuted by NaOH soluton. Wth n-reve Na + and Cl - onentratons ntally smaller n ths work than n the earler work, the ph of ths work s smaller than that of the earler work and ther largest dfferene s shown at ntermedate tmes, suh as 1 4 s. At steady state or 1 7 s, the two urves merged nto one. The model-predted varaton, n tme and loaton, of the reve ph under -6

23 CP s n qualtatve agreement wth expermental data reported n earler papers [19-,5,] and wth feld observatons where alareous deposts and alkalne ph were found under a dsbonded hgh densty polyethylene (HDPE)-oatng, suggestng ngresson of CP through the holday and alkalnty of the soluton nsde the dsbondment. Landles et al. [] onduted expermental tests at room temperature to smulate a rak by usng a reve (.5 mm n thkness and 7 m n length) assembled between an HY8 steel plate (bottom) and an aryl plate (top). All the reve edges exept the mouth were sealed wth a gasket. The mouth dretly onneted to the bulk soluton wth the same hemstry as at the mouth (1N CO and 1N HCO soluton) and was mantaned onstant over tme. Referene eletrodes and ph eletrodes were plaed through holes n the aryl plate wth the tp fang downward nto the reve soluton. The holes were equally spaed along the reve longtudnal dreton from the mouth and epoxy sealed. These eletrodes were used to measure the loal steel potentals and phs n the reve. Fgure -5 shows the ph varaton vs. dstane along the reve for dfferent potentals appled at the reve mouth. In general, the reve ph shfts toward the ad dreton when the mouth potentals are more postve than the open rut potental (OCP) slghtly more negatve than -.7 V SCE. Conversely, the ph shfts toward the alkalne dreton when the potentals were more negatve than the OCP, relevant to the model results n Fgure -4. The qualtatve agreement between the model and expermental results s good. When the mouth s athodally polarzed and the ph at the mouth s not ontrolled, unlke n Fgure -5 other studes [,1,] show that the ph at the mouth nreases more rapdly than nsde the reve. Wthn the tme of test, Fgure -6 shows that exept at the two loatons (8 and 1 m from the mouth), the farther nto the reve the lower the ph. [1] Under all ondtons, the ph n the entre reve has a sgnfant shft toward the alkalne dreton. At 18 m from the mouth or at the farthest end of the reve, the ph nreased from 6.5 to above 8.5. [1] Ths general trend wth the reve ph shftng toward the alkalne dreton s onsstent wth the results predted from ths model. Correspondng to the hange of ph, the same study showed the orrespondng hange of Cl - onentraton over tme as shown n Fgure -. Fgure - shows that a hgher ph orresponds to a lower Cl - onentraton, beause CP draws Cl - out from nsde the reve. Ths expermental result s n general agreement wth the results of ths model. The model shows that CP tends to pump Na + n and draw Cl - out of the reve, and OH - balanes the dfferene n harge between Na + and Cl - and the soluton ph nreases. From a dfferent study, [] Fgure -7 shows that wth CP, the ph n the entre reve s elevated, and for two potentals appled at the mouth (-1. V SCE and -1. V SCE ), the ph n the reve s hgher than at the mouth. Fgure -8 shows a omparson of the reve potental and urrent densty at dfferent tmes obtaned n ths work and n the earler work. [1] A sgnfant dfferene s seen at tme zero, and the potental or the orroson urrent densty has a sharp hange at the mouth. At 1 7 s, the two urves are merged nto one rrespetve of the dfferent ntal ondtons. For both works, the potental n the entre reve shfts n the more negatve dreton exept at the mouth where the potental s mantaned unhanged. Farther nto the reve from the mouth, the -7

24 potental shft (relatve to open rut potental) s less sgnfant. Ths shft n potental agrees qualtatvely wth many expermental results. Fgure -9 shows reve steel potental at dfferent tmes, measured at (1).5 hour and () 7 hours from begnnng of the test. [] A omparson of the two fgures suggests that the presene of CP shfted the potental n the entre reve toward the more negatve dreton, and the loser the loaton n the reve to the mouth the more sgnfant the shft n potental. Smlar results [] are also shown n Fgure Key Model Results and Dsusson.5.1 Aerated Dlute NaCl Soluton Wthout CO Several senaros were modeled, and the results were prepared as three manusrpts (MS #1, #, and #) for publaton n journals and onferene proeedngs. These manusrpts are appended at the end of ths report, and only some key results are presented n ths seton. In addton to the manusrpts, Appendx C reports the results of the effet of onvetve flow, ndued by orroson tself due to metal depleton (or formaton of deposts) on the reve orroson. For the two ondtons presented n Appendx C (no CP and sgnfant CP), t s found that the flow veloty s extremely small and ts effet s nsgnfant. These results n Appendx C wll not be desrbed further n the man ontent of ths report. Presented here s a key porton of the model results where the effet of onvetve flow s not a fator Creve Gap Varyng Wth Dstane For the reve geometry shown n Fgure -1(b) where the gap vares along the reve longtudnal dreton, two ondtons have been explored to understand how varaton of reve gap may affet the hemstry and orroson nsde the reve. The frst ondton onerns no CP mposed at the reve mouth. The seond ondton assumes a fxed potental at the mouth (-.9 V CSE ), a ondton of sgnfant CP. For both ondtons, the mouth soluton s an aerated NaCl soluton. The model equatons and results are gven n MS #1 appended at the end of ths report. In ths seton, only a key porton of the model results for the no CP ondton s reported. At the mouth potental mantaned at V CSE, t was found that the CP urrent passng aross the reve mouth s neglgble. Wth oxygen present at the mouth and depleted nsde the reve by orroson reatons, a dfferental oxygen onentraton ell s set up and leads to a gradent of potental and varaton of reve soluton hemstry. The tme-dependent varaton of the reve potental and soluton hemstry s dsussed next. Fgure -11a shows a omparson of Na + onentratons near the mouth for the two reve geometres shown n Fgures 1a and 1b. The onentratons n the two reves are the same untl after 1 x s when the hange of gap at =5 s reahed. At 1 4 s and 1 7 s, a steeper s varaton of Na + onentraton ours n the reve of varable gap n the gap-narrowed regon -8

25 x wth =5-6. Compared to the reve of onstant gap, the Na + onentraton n the reve of s x x varable gap s greater around =5 but s smaller around =6. Ths effet may be explaned s s by treatng Na + dffuson n the reve smlar to flow. The total rate of Na + dffuson (analogous to flow rate) s approxmately the same aross an edge of the gap-narrowed regon. However, the dffuson flux of Na + (analogous to flow veloty) an have a sgnfant varaton mmedately before and after the edge, beause the flux s nversely proportonal to the rosssetonal area of the reve or the gap sze. For that reason, the dffuson flux, refleted by the slope on the Na + onentraton urve, s greater n the gap-narrowed regon. Around the left edge x ( =5), the Na + tends to volumetrally squeeze nto the gap-narrowed regon, whle, as the gap s x suddenly expands at =6, the Na + tends to dsspate out and the Na + dffuson flux dereases s (relatve to the reve of onstant gap). At 1 7 s when steady-state orroson s reahed, the net flux, onsstng of dffuson and mgraton, of Na + or Cl - s zero. That s, dffuson and mgraton fluxes are balaned out. Smlar varaton of Na + onentraton s also shown n Fgure -11b aross the seond x gap-narrowed regon wth =15-1. However, the hange of Na + onentraton n the range s x x of =5-6 s greater than n the range of =15-1 beause the Na + onentraton gradent s s s greater near the mouth and s more greatly affeted by the sharp hange of gap. Even wth a steeper hange of Na + onentraton due to the sharp hange of gap (relatve to a onstant reve gap), the Na + onentraton n the two reves are overall not sgnfantly dfferent. Fgures -1a and b show a omparson of the reve phs for the two reves shown n Fgures 1a and b. Although the sharp hange of the reve gap has resulted n a dfferent ph relatve to the reve of onstant gap, the overall dfferene n ph between the two reves s nsgnfant. Fgure -1 shows a omparson of the reve potentals n the two reves. The sharp hange of gap only has an effet on the reve potental n the regon of the gap hanges, and x x ths effet s greater near the mouth (e.g., =5) than deep n the reve (e.g., =1). The s s overall effet s not sgnfant. A smlar result s shown n Fgure -14 wth orroson urrent densty, whh s also not sgnfantly affeted by the gap hange Creve Corroson Consderng Penetraton of Current and O va Coatng Although an ntat oatng on bured ppes s generally not permeable to ons or CP urrent, t allows for permeaton of gases, suh as oxygen and arbon doxde. Some oatngs an beome permeable to ons when deterorated. The effet of oatng permeablty to CP on the reve orroson s not well known (e.g., how the CP penetraton through the oatng nterats wth CP from the mouth and how ths nteraton may affet the steel orroson rate n the oatng-dsbonded regon). In the presene of oxygen, t s unlear whether the CP penetraton through the oatng an suffently suppress the orroson resultng from the oxygen dffuson through the oatng. -9

26 Several ases were modeled and ompared: (1) nether urrent nor oxygen penetraton through the oatng, () only CP urrent penetraton, () only oxygen penetraton, and (4) penetraton of both oxygen and CP urrent. All organ oatngs used on bured steel ppelnes are permeable to O, whle some beome permeable to ons only after deteroraton. For that reason, the oatng porosty used for ons s assumed to be.1, whle t s assumed to be.11 when used for oxygen. Ths dfferene n porosty aounts for the fat that oxygen an permeate the oatng matrx. The model equatons and results are presented n MS # appended at the end of ths report. In ths seton, only Case 4 s reported. The results may have mplatons for understandng of the performane of exstng oatngs and the desgn of new oatngs. Fgure -15 shows a omparson of (1) steel potental and () orroson urrent densty for the four ases wth the penetraton of ether O or urrent, nether, or both. At tme zero, when no O dffuson through the oatng s onsdered, the ntal orroson potental and urrent densty s only affeted by CP penetraton through the oatng. Thus, the two dark urves wthout urrent penetraton through the oatng overlap, and smlarly, the two gray urves wth urrent penetraton overlap. At 1 8 s, the orroson proess reahes steady state. The effet of O dffuson through the oatng s learly demonstrated. Wth no urrent penetraton through the oatng, the steel potental wth O dffuson through the oatng s more postve and the orroson urrent densty s greater (dark dashed urve) than f no O dffuses through the oatng (dark sold urve). Ths same effet of O dffuson through the oatng also apples when CP urrent penetrates the oatng. From wthout to wth O penetraton through the oatng, the steel potental shfts n the more postve dreton, and the orroson urrent densty s greater. By omparng the two ondtons, (1) nether urrent nor O permeaton through the oatng (dark sold urve) and () both urrent and O permeaton through the oatng (gray dashed urve)), Fgure -15 shows that the orroson urrent densty nsde the reve s smaller for the latter. Ths result an have sgnfant mplatons for oatng desgn and for an understandng of the protetveness of a oatng one t dsbonds and beomes permeable. Even though a muh larger (1 tmes more) overall porosty of the oatng was used for O than for ons, the CP an stll adequately suppress the nreased orroson urrent densty by O dffuson through the oatng. Ths suggests that n the feld, a permeable oatng, when dsbonded, an stll allow adequate CP urrent to pass through and protet the steel ppe from orroson attak, despte O permeaton through the oatng. The CP penetraton through the oatng an stll be effetve, despte a muh greater permeablty of the oatng to O than to ons, beause the urrent penetraton an be drven by the potental gradent aross the oatng, whh does not our wth O. Fgure -16 shows a omparson of the reve hemstry for all four ases. The ntal ondtons are the same, and all urves for the four ases overlap at tme zero for eah fgure. At steady state (1 8 s), the effet of O or/and urrent penetraton through the oatng s learly exhbted. Irrespetve of urrent penetraton through the oatng, O dffusng through the oatng s eletrohemally redued at the steel surfae. Ths reduton of O generates hydroxyls, whh attrat atons suh as Na + and repel anons suh as Cl -. Ths effet, supermposed by addtonal generaton of hydroxyls from CP as well as by the potental-drven -1

27 on mgraton, leads to an nreased Na + onentraton n the reve, a dereased Cl - onentraton, and, orrespondngly, an nreased ph. Beause the mass transport of any on through the oatng s muh slower than through the soluton, the effet by CP through the oatng s less sgnfant than through the mouth. The hemstry hange n the reve s manly attrbuted to the on transport from the mouth. Although CP tends to pump Na + nto the reve aross the oatng (ontrolled by mgraton), wth a hgher onentraton nsde the reve Na + tends to dffuse out aross the oatng, and ths dffuson s more domnant than mgraton. Thus, a CP-permeable oatng funtons lke a membrane. The Na + onentraton n the reve s smaller than f the oatng s mpermeable to CP. Conversely, the Cl - onentraton n the reve wth a CP permeable oatng s greater than n the reve wth an mpermeable oatng to CP. Due to the derease n Na + onentraton, the soluton ph n the reve wth a CP-permeable oatng s smaller..5. Dlute NaCl Soluton Contanng CO The evoluton over tme of the reve hemstry, potental, and orroson rate was modeled when CO dffuson through the holday and the oatng s onsdered. The transport of ons through the oatng s not onsdered. The model governng equatons s gven n Appendx D. The soluton spees nlude (1) Na +, () Cl -, () Fe +, (4) H +, (5) OH -, (6) Fe(OH) +, (7) CO, (8) H CO, (9) HCO -, (1) CO -, (11) H (aq), (1) FeCO, and (1) H O, where the underlned spees are defned as the prmary spees. Ther onentratons an be ether gven suh as those lsted n Table - for the ntal and boundary ondtons, or known, suh as spees (11)-(1). The onentratons of the prmary spees an be used to determne the onentratons of the seondary spees based on the equlbrum relatons between the prmary and the seond spees. The CO partal pressure of.5 atm at the mouth and the oatng permeablty oeffent to CO at 1 tmes that of a new HDPE oatng are used for the modelng, whh represents a worst-ase senaro of the CO effet on ppelne reve orroson. The CO permeablty oeffent n a new oatng s mol/m.s.atm. The mouth potental of -.88 V CSE, a potental more negatve than reommended by the nternatonal CP standards, s used for the modelng. To ensure the steel orroson rate s more realst at the ntal ondton wth CO, values of some model parameters (relatve to those used for non-co ondtons) are modfed. The exhange urrent densty and Tafel slope of ron are hanged from 1-4 A/m and.4 V to 1 - A/m and.6 V, respetvely. The exhange urrent densty of water s hanged from 1 - A/m to 1-4 A/m. The model results are reported next. Fgure -17(a) shows a omparson of the n-reve CO partal pressures (whh an be onverted to onentraton by Henry s law) wth or wthout CO dffuson through the oatng. Clearly, CO dffuson through the oatng has led to a slghtly greater n-reve CO partal pressure. At steady state (reahed at 1 s or greater), the n-reve CO partal pressure s greater wth CO dffuson through the oatng than wthout. CO dffuses nto the reve from the mouth, dssolves n soluton, and dssoates nto other arbon spees. CO partal pressure -11

28 dereases from the mouth nto the reve due to the nrease of reve ph. Ths ph varaton wll be shown later. In ntermedate tmes suh as 1 4 s, a dp of the urve s shown, whh orresponds to the greatest ph. Fgure -17(b) shows that the arbonate onentraton n the reve s muh greater wth CO permeaton through the oatng than wthout, partularly at longer tmes suh as 1 4 s or greater. Fgure -18(a) shows the n-reve Na + onentraton. Irrespetve of CO dffuson through the oatng, the overall varaton of Na + onentraton s smlar, suggestng that the overall adty brought nto the reve by CO transport (through holday and oatng) s unable to balane out the alkalnty-generatng power from steel orroson and athod polarzaton by CP. Wth CO permeaton through the oatng, the Na + onentraton n the reve s smaller than f the oatng s mpermeable to CO. Ths result s more learly shown wth 1 4 s or greater. Overall, the Na + onentraton n the reve nreases over tme and eventually exeeds that at the mouth where the Na + onentraton s set to be onstant. The ontnuous njeton of CO nto the reve through the oatng redues the soluton alkalnty and the Na + onentraton. Contrary to the hange of Na + onentraton, Fgure -18(b) shows that the Cl - onentraton n the reve s greater wth CO permeaton through the oatng than wthout. Irrespetve of CO permeaton through the oatng, the Cl - onentraton n the reve nreases over tme, suggestng that dffuson of Cl - from sol through the holday and the oatng nto the reve s more domnant than the potental-drven mgraton. The potental-drven mgraton tends to draw out of Cl -. These two fores must, however, balane out at steady state. Beause the potental-drven mgraton of Cl - s opposte n dreton to ts dffuson, the Cl - onentraton n the reve annot exeed ts onentraton at the mouth. Fgure -19 shows the reve ph, whh nreases over tme. The formaton of hydroxyls nsde the reve overpowers the adty brought n by CO through the holday and the oatng. The shapes of the ph urves are onsstent wth those of CO partal pressure followng the dsusson gven earler wth Fgure -17(a); the peak ph orresponds to the dp of CO partal pressure. Fgure -(a) shows the steel potental and orroson urrent densty n the reve. The ntally sharp gradent of the potental near the mouth beomes nreasngly leveled off over tme, and overall, the reve potental shfts n the more negatve dreton, orrespondng wth the nrease of soluton ph. The orroson urrent densty dereases over tme as shown n Fgure -(b). Relatve to the ondton wth no CO dffuson through the oatng, CO dffuson through the oatng tends to slghtly nrease the orroson urrent densty (Fgure - (b)) and shfts the reve potental n the more postve dreton (Fgure -(a)). -1

29 .5. Summary of Model Results Due to the spef reve geometry (a small area of reve mouth), the overall temporal and spatal varaton of reve hemstry, potental, and orroson rate n a reve of varyng gap s not sgnfantly dfferent from the orrespondng hange n a reve of unform gap. Regardless of the varaton of reve gap, when a holday s proteted wth athod polarzaton, the ph n the reve nreases over tme and the orroson rate dereases. Gven a suffent tme and wth the athod polarzaton ontnuously mantaned at the mouth, ths ph nrease an go farther nto the dsbonded regon and beomes greater than at the mouth. These model-predted results are qualtatvely onsstent wth expermental data n the lterature. A permeable oatng behaves lke a membrane, whh, under a athod polarzaton at the reve mouth, tends to rase the n-reve sodum on onentraton and ph more rapdly relatve to an mpermeable oatng. Later, as the sodum on onentraton and ph n the reve beome greater than at the mouth, the permeable oatng tends to reverse the transport dreton for ons. At a mouth potental of -.9 V vs. saturated Cu/CuSO 4, the athod urrent s suffent to suppress all O penetratng the reve both from the mouth and through the oatng. The pratal mplaton s that n the presene of suffent athod polarzaton, a permeable oatng, when dsbonded, an stll be apable of protetng the substrate steel from orroson attak. Compared to the ondton wthout CO n the system, CO dffuson through the holday and the oatng tends to slghtly nrease the orroson urrent densty and shfts the reve potental n the more postve dreton..6 Model Smplfaton.6.1 Bakground The reve hemstry, potental, and orroson rate an vary wth tme and wth the reve geometral parameters, suh as reve gap and length. The effet of the geometral parameters may be ombned wth the model ndependent varables, suh as tme t and dstane x, to redue the number of model varables and potentally allevate model omputatons wth respet to the varous effets of the reve geometral parameters and tme. One hart plotted wth salng varables an over nformaton that otherwse must be obtaned by multple harts due to the varaton of the reve geometral parameters (e.g., length and gap) and tme. For ths projet, salng s used as a way to smplfy the model. Prevous work for salng reve orroson foused on reves of unform gap, and the orroson s n steady-state ondton. Salng for the unsteady-state ondton has not been performed, and the effet of varable reve gap on the salng has not been nvestgated. They are studed n ths work. The salng model and results are presented as a manusrpt MS # attahed at the end of the report. Only the key omponents of the model and results are presented n ths seton. -1

30 .6. Salng Theory for Creve Corroson Equaton (-1) may alternatvely be wrtten as (t / ) s N s x s s y s x x x R R N N (-) where Nx zdf 1 [ D ( )]( ) (-1) s x (x / s ) RT (x / s ) (x / s ) For a reve of unform gap shown n Fgure -1a (dδ s /dx= and s s ), applyng Equaton (-) for Na + yelds s s (t / ) N s x 1 1x s N 1y (-) where N 1y does not ontan δ s. Followng Equatons (-) and (-1), both tme salng and dmenson salng ( t and x ) are applable to Na +. Lkewse, the salng apples to Cl -. s s Wth no gap nvolved n the equaton of eletroneutralty ( z ), the salng also apples to that equaton as a governng equaton. The salng also apples to H + beause all reaton rates are not a dret funton of gap and tme..6. Key Model Results and Verfaton of Salng Theory Three reves of dfferent gaps are nvestgated to understand and verfy the dmensonand tme-salng method. Two of the reves have unform gaps as shown n Fgure -1(a): one gap s s and the other s s /4. The thrd reve has a varable gap as shown n Fgure -1(b), where the gap s = s exept at x=5-6 and 15-1, where s = s /4. When the ppe steel s exposed n an alkalne soluton, t an be passvated, and the effet of ths passvty on the model salng s presented n Appendx E. In ths seton and n MS # attahed at the end of ths report, the steel s assumed to be atve and the Tafel equaton for steel dssoluton knets s used. In salng, to mantan the same total salng length L for the two reves of unform s gaps wth a gap rato of four, the total length of the reve wth the larger gap, L L, s set to be twe the length of the smaller gap, L S (or L L =L S ). For the reve of varable gap, ts salngequvalent total length s L L δ relatve to the reves of unform gaps. δ 6 j1 j j -14

31 When L V = s, the equvalent length for the reve wth unform gap of δ s s L L =4 s (or L L =1.15L V ), and the equvalent length for the reve wth unform gap of δ s /4 s L S =11.5 s. For the reve of varable gap, to satsfy ts salng length, ts equvalent gap se s LV se ( L ) s s. L Followng tme-salng theory, to mantan a onstant salng tme t/δ, a smaller reve gap requres a smaller tme to retan the same reve ondton. The tme needed for the reve wth the smaller unform gap should be only one-quarter of the tme for the reve of a larger unform gap, or t S =.5t L. For the varable reve, the equvalent tme s t se t.6774t. These reve dmensons are used n the salng model omputatons. The ntal and boundary ondtons used for all three reves are the same as those shown n Table -1. For any gven reve, the Na + and Cl - onentratons at the mouth are equal and eah s 1 tmes ts value n the ntal ondton. The ph at the mouth s the same as ts ntal value. Although the model studed the ondton wth no CP and the ondton wth substantal CP, only the results wth substantal CP or an at mouth potental of -.9 V CSE are reported here. Fgure -1 s a salng plot showng Na + onentraton omputed for dfferent tmes for x the three reves. In ths fgure, the x oordnate s plotted as salng dstane, where δ se s t the equvalent gap applable to all three reves. Next to eah urve, the sale tme se s labeled. For the reve of unform and larger gap wth δ se =δ s =.5 mm, the tme sales at, 1 8, 1 9, 1 1, and 1 11 s/m orrespond wth atual tmes of, 1 5, 1 6, 1 7, and 1 8 s, respetvely. For the reve wth a unform but smaller gap at.5/4 mm, the atual tmes orrespond to a quarter of the atual tmes desrbed prevously. Lkewse, for the reve of varable gap, the same sale tme represents.6774 multpled by those atual tmes. For the two reves wth unform gaps, the Na + onentratons overlap for eah of the same sale tmes. They are, however, dfferent from the Na + onentraton n the reve of varable gap. Ths dfferene s greatest at the ntermedate tmes, suh as 1 1 s/m. At steady state (e.g., at the sale tme of 1 11 s/m), ths dfferene n Na + onentraton s smaller but stll obvous. These model results verfy that for the reves of unform gaps, both tme salng and dmenson salng are vald, whle for the reve of varable gap, the salng s not vald. Fgure -1 shows that startng from the same ntal onentraton, pror to or at the sale tme of 1 8 s/m, the Na + onentraton n the reve of varable gap nreases faster and s greater than n the reves of unform gaps. Ths result s attrbuted to the last term on the rght sde of Equaton (-), whh s analogous to a reaton soure term. Intally, both the onentraton-drven dffuson flux and the voltage-drven mgraton flux of Na + are greater than x zero. When the gap dereases at the sale dstane ( ) about.4 m.5, the rghtmost term of se Equaton (-) s greater than zero, lkely produng Na + and nreasng the loal Na + onentraton. The Na + x onentraton n the gap-narrowed regon ( =.4~1.5 m.5 ) s greater se than n the reves of unform gaps. v s L se L -15

32 As the Na + transport passes the loaton of the last gap hange (gap expanson) at =1.5 m.5, the gap expanson behaves as onsumng Na + and the Na + onentraton beomes smaller than n the reves of unform gaps. Wth nreasng tme, ths effet of gap expanson on Na + onentraton nreases. At the sale tme of 1 9 s/m, the Na + onentraton n nearly the entre reve of varable gap beomes smaller than n the reves of unform gaps, and ths dfferene s even greater at 1 1 s/m. Ths dfferene shrnks, however, as steady state s approahed, beause the value of the reaton soure term beomes smaller and eventually beomes zero at steady state. At steady state, Equaton (-) s smplfed so the Na + net flux s zero, whh has the same form as the Na + transport equaton for reves of unform gaps. Thus, lose results between reves of unform and varable gaps are expeted. At the sale tme 1 11 s/m (steady state for Na + transport), the Na + onentraton n the reve of varable gap s stll dfferent from that n the reves of unform gaps beause, for H +, ts flux at steady state s not zero aross the reve and affets the Na + onentraton dstrbuton n the reve. In the gap-narrowed regon, the Na + onentraton gradent s greater than n the regons wth a larger gap. An analogy to flow was used to desrbe ths effet [1]. The dffuson rate (analogous to flow rate) s the same aross the edges of the gap-narrowed regon, but the dffuson flux of Na + (analogous to flow veloty) vares sgnfantly, refleted by the slope of the urve n Fgure -1. Fgure - shows a omparson of the phs predted for the three reves. The urves for the two reves of unform gaps overlap for eah sale tme, whle they are dfferent from the orrespondng urves wth the reve of varable gap exept at tme zero. At tme zero, the same ntal ondtons were gven for all three reves set by the model. The varaton of soluton ph an be evaluated based on the varaton of Na + onentraton. As detaled elsewhere [9-1], n the presene of CP, a hgher Na + onentraton orresponds to a lower Cl - onentraton; ther dfferene n harge, whh s postve, has to be balaned by hydroxyls, and a hgher ph results. Fgure - shows (1) reve potentals and () orroson urrent denstes predted for the three reves. In general, the urves wth the two reves of unform gap approxmately overlap for eah sale tme exept very near the mouth. Ths dsrepany near the mouth s small and results from the presene of O n the reve. The O exsts only near the mouth, and ts mass transport equaton annot be saled n the same way as other dssolved spees. Ths dfferene n dmenson salng wth respet to O was examned n MS # appended at the end of ths report. The two urves for the reves of unform gaps are learly dfferent from those n the reve of varable gap, and ths dfferene nreases over tme. Agan, ths dsrepany n results between the reves of unform and varable gaps suggests that dmenson salng does not apply to the reve of varable gap. x se -16

33 .6.4 Summary of the Model Salng Results Modelng was performed for two reves of unform gaps and a reve of varable gap. The model results onfrm the valdty of tme salng and dmenson salng for reves of unform gap. The salng does not apply to the reve of varable gap. Dmenson salng and tme salng of reve orroson an be used to sale experments or redue model omputatons when broad ranges of the effets of reve geometral parameters and tme on reve orroson are studed..7 Pratal Implatons of the Model Results.7.1 Understandng the Term CP Sheldng and Corroson Under a Shelded Coatng It appears that the ppelne ndustry has an nadequate understandng of how CP may perform n a oatng-dsbonded regon. Despte of deades of laboratory and analytal studes on ths subjet, researhers do not appear to have ommunated adequately the broad laboratory results and feld observatons to ppelne prattoners. Ths seton summarzes some expermental and modelng results and ther mplatons n feld ondtons. CP sheldng s only partally true. In the presene of CP, the nrease of ph over tme n oatng-dsbonded regons and the shft of potental n a more negatve dreton redue the loal orroson rate over tme. The worst orroson may happen when the sol s aerated and wet and the CP s ether lakng or nadequate. Even then, the orroson may not be as bad as often beleved unless mrobologally nfluened orroson (MIC) and alternatng urrent (AC) and dret urrent (DC) nterferenes and ad sols are present. Unlke tradtonal reve orroson, whh when supported by a large area rato of athode to anode an lead to severe orroson, the orroson under a dsbonded oatng s onversely assoated wth a small athode (holday)-to-anode area rato. Modelng provdes a powerful tool to predt and nterpret omplex expermental results and omplex nterplays among multple parameters n a orroson proess. It also helps to further the understandng of the orroson proess wthout havng to ondut exhaustve expermental tests under numerous ondtons..7. The Sgnfane of a Permeable Coatng A permeable oatng behaves lke a membrane. Relatve to an mpermeable oatng, under CP a permeable oatng tends to rase the n-reve Na + onentraton and ph more rapdly. When the Na + onentraton n the reve beomes greater than at the holday, t tends to dffuse out through the oatng and reversely ounter ts mgraton, leadng to a smaller nreve Na + onentraton over tme (relatve to an mpermeable oatng). When a oatng s permeable to both oxygen and CP, even f the oatng permeablty to oxygen s tmes that of CP, the CP s found to be effetve due to the CP-drven mgraton of ons. -17

34 CO dffuson through the holday and the oatng only slghtly nreases the reve orroson rate and slghtly shfts the reve potental n the more postve dreton..7. The Effet of Creve Geometry Parameters The effet of the geometral parameters on orroson of steel ppes of a oatng dsbondment may be ombned wth model ndependent varables, suh as tme t and dstane x, to redue the number of model varables and potentally allevate model omputatons when the varous effets of the dsbondment geometral parameters and tme are onerned. One hart plotted wth salng varables an over nformaton that otherwse must be obtaned by multple harts. Geometry salng an also be used for salng experments (reve length and gap) and overomng hallenges of testng wth extremely small or large reve geometres. The geometry salng fator s found to be L /δ (or L/ ), and the tme-salng fator t/δ, where L s dsbondment length, δ s reve gap, and t s tme. These salng fators were verfed by modelng for two reves of unform gaps by fxng the value of L/. Ths verfaton was done wth the substrate steel under both atve and passve states..8 Referenes 1. H. Ledheser, W. Wang, L. Igetoft, Progress n Organ Coatngs 11 (198) C.G. Munger, Corroson Preventon by Protetve Coatngs (NACE, 1984) J.M. Leeds, Ppe Lne & Gas Industres, Marh (1995) M. Meyer, X. Campagnolle, F. Coeulle, M.E.R. Shanahan, Impat of Agng Proesses on Antorroson Propertes of Thk Polymer Coatngs for Steel Ppelnes, n Proeedngs of the Corroson/4 Researh Topal Symposum: Corroson Modelng for Assessng the Condton of Ol and Gas Ppelnes, F. Kng and J. Beavers (eds.) (NACE, 4) F.M. Song, Corroson 66(9) (1) F.M. Song, D.W. Krk, D.E. Cormak, D. Wong, Materals Performane 44(4) (5) F.M. Song, D.W. Krk, D.E. Cormak, D. Wong, Materals Performane 4(9) () F.M. Song, D.W. Krk, J.W. Graydon, D.E. Cormak, Corroson 58(1) () F.M. Song, D.W. Krk, J.W. Graydon, D.E. Cormak, Corroson 59(1) () F.M. Song, D.A. Jones, D.W. Krk, Corroson, 6() (5) F.M. Song, N. Srdhar, Corroson 6(8) (6) F.M. Song, N. Srdhar, Corroson 6(1) (6) F.M. Song, N. Srdhar, Corroson Sene 5(1) (8) N. Srdhar, D.S. Dunn, M. Seth, Corroson 57 (7) (1) N. Srdhar, Modelng the Condtons Under Dsbonded Coatng Creves A Revew, n Proeedngs of the Corroson/4 Researh Topal Symposum: Corroson Modelng for Assessng the Condton of Ol and Gas Ppelnes, F. Kng and J. Beavers (eds.) (NACE, 4)

35 16. M.E. Orazem, D.P. Remer, C. Qu, K. Allahar, Computer Smulatons for Cathod Proteton of Ppelnes, n Proeedngs of the Corroson/4 Researh Topal Symposum: Corroson Modelng for Assessng the Condton of Ol and Gas Ppelnes, F. Kng and J. Beavers (eds.) (NACE, 4) R.R. Fessler, A.J. Markworth, R.N. Parkns, Corroson 9(1) (198) T.R. Jak, G.V. Boven, M. Wlmott, R.L. Sutherby, R.G. Worthngham, Materals Performane (8) (1994) A. Turnbull, A.T. May, Materals Performane (198) 4.. J.J. Perdomo, I. Song, Corroson Sene 4 () M.H. Peterson, T.J. Lennox, Jr., Corroson 9 (197) 46.. A.C. Tonre, N. Ahmad, Materals Performane 19(6) (198) 9.. M.D. Orton, Materals Performane 4(6) (1985) F. Gan, Z.-W. Sun, G. Sabde, D.-T. Chn, Corroson 5(1) (1994) R. Brousseau, S. Qan, Corroson 5(1) (1994) F. Kng, T. Jak, M. Kolar, R. Worthngham, A Permeable Coatng Model for Predtng the Envronment at the Ppe Surfae under CP-Compatble Coatngs, (NACE, 4) paper no F.M. Song, Corroson Sene 5 (8) K. Kumaresan, Y. Mkhaylk, R.E. Whte, J. Eletrohem. So. 155 (8) A576-A J. Newman, K.E. Thomas-Alyea, Eletrohemal Systems, rd edton, John Wley and Sons, In. (4) F.M. Song, D.W. Krk, J.W. Graydon, D.E. Cormak, Corroson 58() () M.C. Yan, J.Q. Wang, E.H. Han, W. Ke, Corroson Engneerng Sene and Tehnology 4 (1) (7) K. Landles, J. Congleton, R.N. Parkns, Potental Measurements Along Atual and Smulated Craks, n Embrttlement by the Loalzed Crak Envronment, R.P. Gangloff (ed.) (AIME, 1984) 59.. X., Chen, X.G., L, C.W., Du, Y.F., Cheng, Corroson Sene 51 (9)

36 Table -1: Intal and Boundary Condtons for Systems Wthout CO 1 4 Condton (mol/m ) (mol/m ) (mol/m 7 ) (mol/m ) Intal * Mouth wth CP = Mouth wth no CP totx = Condton N 1x (mol/m s) N x (mol/m s) 6 N z 7x jn jx 1 (mol/m s) (mol/m s) totx (A/m ) Creve tal Prevous work [1] 1 (mol/m ) 4 (mol/m ) (V) (mol/m 7 ) (mol/m ) Intal and mouth * Ths value may also be determned from O dffuson va oatng at steady state (pror to holday formaton). or totx 6 z jfn jx 1 (V) (A/m ) Table -: Intal and Boundary Condtons for Systems wth CO Condton 1 4 p (mol/m ) (mol/m ) (mol/m CO 9 ) (atm) (mol/m or ) totx z jfn jx 1 (V) (A/m ) Intal Mouth wth CP = Condton N 1x (mol/m s) N x (mol/m s) 6 N z 7x jn jx 1 (mol/m s) N 9x (mol/m s) totx (A/m ) (mol/m s) Creve tal -

37 Table -: Senaros Modeled Wthout CO and Loatons of Results No. Condton Loaton Constant gap, no urrent & no O penetraton va oatng Appendx MS#1 Varable gap vs. x, no urrent & no O penetraton va oatng Appendx MS#1 Varable gap vs. x, no urrent but O penetraton va oatng Appendx MS# v Varable gap vs. x, urrent but no O penetraton va oatng Appendx MS# v Varable gap vs. x, urrent & O penetraton va oatng Appendx MS# v Varable gap vs. t, no urrent & no O penetraton va oatng Appendx C -1

38 CP, O y Dsbonded oatng CP, O, p O Depost (,) Creve soluton x Ppe steel y s (a) 1..8 s / s to x/ s (b) Fgure -1. Model reve geometry showng the oordnators and dmensons of the reve and transport of CP urrent and O nto the reve through the dsbonded oatng: (a) unform gap and (b) varable gap). (a) (b) Fgure -. At a fxed mouth potental of -.9 V CSE, evoluton of onentratons of (a) Na + and (b) Cl - over tme and dstane nto the dsbonded regon from the holday. The reve geometry used for smulaton s Fgure -1a. For ths work, the onentratons of Cl - and Na + are ntally the same n the reve but they are respetvely smaller than at the mouth. The results are ompared wth those n a prevous work where the Cl- and Na+ onentratons are the same at the mouth and ntally n the reve. -

39 Fgure -. Varaton of [Cl - ] wth tme at varous dstanes from openng after potental at openng was ontrolled at -1. V SCE n NS4 bulk soluton bubbled wth 5% CO +95% N : reve thkness.5 mm. [1] Fgure -4. Smlar to Fgure -, but here the mouth potental s fxed at -.9 V CSE. -

40 Fgure -5. ph hanges along stat smulated raks, for varous potentals appled at the rak mouth, for HY8 steel n seawater. [] Fgure -6. Varaton of ph wth tme at varous dstanes from openng after potental at openng was ontrolled at -1 mv SCE n NS4 bulk soluton bubbled wth 5%CO +95%N : reve thkness.5 mm. [1] -4

41 Fgure -7. ph profles wthn the reve after 7 h of test; potental n unt aganst SCE. [4] Fgure -8. Smlar to Fgure -, but here the mouth potental s fxed at -.9 V CSE. -5

42 Fgure -9. Potental profles wthn the reve at.5 hour and at 7 h of test. [4] Fgure -1. Potental dstrbuton n a.1-mm-thk reve at varous tmes after the holday potental was set at -.85 V SCE n a soluton of 1N-1N arbonate-barbonate soluton. [17] -6

43 Fgure -11. (a) (b) At a fxed mouth potental of V CSE, a omparson of Na + onentratons n two reves at dfferent tmes between a onstant gap shown by Fgure -1a (gray lnes) and varable gap vs. x shown by Fgure -1b (gray lnes): (a) near the mouth and (b) away from the reve mouth. (a) (b) Fgure -1. Smlar to Fgure -11, but here for a omparson of reve phs: (a) near the mouth and (b) away from the reve mouth. -7

44 (a) (b) Fgure -1. Smlar to Fgure -11, but here for a omparson of reve potentals: (a) near the mouth and (b) away from the reve mouth [note the redued sale of potental from (a)]. Fgure -14. (a) (b) Smlar to Fgure -11, but here for a omparson of reve orroson urrent denstes: (a) near the mouth and (b) away from the reve mouth [note the redued sale of orr from (a)]. -8

45 (a) Fgure -15. At a fxed mouth potental of -.9 V CSE, a omparson of the model results for four ases studed at both the ntal and steady-state ondtons: (a) reve potental and (b) orroson urrent densty. (b) (a) (b) () Fgure -16. Smlar to Fgure -15, but for reve hemstry: (a) Na + onentraton, (b) Cl - onentraton, and () ph n the reve. -9

46 (a) Fgure -17. At a potental of -.88 V CSE and a CO partal pressure of.5 atm at mouth, a omparson of model results obtaned when CO permeaton through the oatng s and s not onsdered: (a) n-reve CO partal pressure and (b) onentraton of arbonate. (b) (a) Fgure -18. Smlar to Fgure -17, but for reve hemstry: (a) Na + onentraton and (b) Cl - onentraton. (b) Fgure -19. Smlar to Fgure -17, but for reve ph. -

47 (a) Fgure -. Smlar to Fgure -17, but for (a) reve potental and (b) orroson urrent densty. (b) Fgure -1. At a fxed mouth potental of -.9 V CSE, a salng plot for a omparson of Na + onentratons n the three reves at dfferent tmes: onstant gap of s n Fgure -1a (blak sold lnes), varable gap vs. x of Fgure -1b or s (x) b (gray sold lnes), and onstant but redued to a quarter of the gap or s /4 (gray broken lnes). -1

48 Fgure -. Smlar to Fgure -1, but here the salng plot s for a omparson of reve ph. Fgure -. (a) (b) Smlar to Fgure -1, but here the salng plot s for a omparson of (a) reve potental and (b) orroson urrent densty. -

49 . PIPELINE INTERNAL CORROSION.1 Bakground A sgnfant dfferene n nternal orroson between dry and wet natural gas ppelnes s that for dry gas ppelnes, a thn stagnant soluton layer due to water ondensaton may form on the ppe surfae and an qukly go saturated. A preptate flm may then form and thken over tme, and the orroson rate dereases. In wet gas ppelnes, water may be onstantly present and the bulk soluton hemstry s relatvely stable. Due to ontnuous mass exhange between the soluton boundary layer and the bulk soluton, preptaton may or may not our. By ouplng mass transport, hemal and eletrohemal reatons, possble flm growth, and the dsplaement of the movng metal-soluton nterfae as the metal dssolves nto soluton, ths work developed a model based on fundamental prnples. Ths model allows for predtng the varaton of soluton hemstry over tme, the formaton and growth of a preptate flm when exstent, and the varaton of orroson rate over tme under a varety of operatng ondtons, nludng the hange of gas temperature, pressure, and omposton. Followng a bref desrpton of the model equatons and valdaton, key model results wll be presented and dsussed. A more detaled desrpton of the model equatons and results an be found n MS #4 appended at the end of ths report.. Model Desrpton For a porous medum wth a dlute soluton ontanng multple spees (see the orroson system shown n Fgure -1), mass transport for an arbtrary spees n the soluton numbered by may be expressed by ( ) t N R (-1) where s porosty or pore volume fraton of the aqueous system. s 1 when the soluton s homogeneous. R s the total net volumetr produton rate (after onsumpton deduted) of the th spees. The flux of the th spees n the dlute soluton, N, may be wrtten as N zf zf D ( ) D ( ) (-) RT RT where D and z are dffusvty and harge of the th spees, respetvely; τ s tortuosty, whh an be approxmated by.5 ; F, R and T are Faraday s onstant, unversal gas onstant, and temperature, respetvely; and s eletrostat potental of soluton. For eah soluton spees, eah onentraton orresponds to a mass transport equaton expressed by Equaton (-1). Two other unknowns n the system, potental and porosty, are yet to be solved from two addtonal equatons. These two addtonal equatons are the equaton of eletroneutralty for potental -1

50 z (-) and mass onservaton of solds for the preptate porosty (1) t m V r (-4) m m In Equaton (-4), V m s molar volume of the m th preptate, or M m / m, where M m and m are the molar weght and densty of a preptate, respetvely, and r m s the rate of preptaton soon to be desrbed. To solve these governng equatons, the volumetr reaton rates n Equaton (-1) and the boundary ondtons must be defned...1 Volumetr Reaton Rates The total net produton rate of the th spees n Equaton (-1), R, an result from two types of reatons: homogenous reatons and heterogeneous reatons. Homogenous Reatons: Suh a reaton nvolvng th spees and numbered by h may be expressed n the form of _ r,h A A (-5) _ r _ p,h _ p where the subsrpts r and p at the lower rght of the symbols sgnfy reatant and produt, respetvely. The ndvdual volumetr reaton rate n the soluton may be wrtten as r h _ r,h _ p,h (k k ) (-6) h _ f h _ b where k h_f and k h_b are the forward and bakward reaton rate onstants, respetvely. The net produton rate of the th spees for all reatons assoated wth t s R r (-7),h h,h h Pratally, when a reaton s reversble, the reaton rate an be anelled out when the governng equaton for the seondary spees s ombned nto that of the prmary spees. Ths has been detaled elsewhere [1-] and wll be used n ths work. By that onsderaton, only rreversble reatons need to be aounted for when Equaton (-7) s used. -

51 Mneral (Preptaton) Reatons: Suh a reaton nvolvng the th spees and numbered by m may be wrtten n the form of _ r,m A A (-8) _ r _s,m _s where subsrpt m at the lower rght of the symbols sgnfes mneral or preptate and the subsrpt s sgnfes a dssolved soluton spees. The ndvdual volumetr reaton rate onverted from the surfae reaton rate may be wrtten as _ r,m _ s,m m A m (k m _ f k m _ b ) r where A m s the nterfaal surfae area of the sold. (-9) The total net produton rate of all the mneral reatons nvolvng the th spees may be wrtten as R r (-1),m m,m m For the system of onern, only two preptates are possble FeCO and Fe(OH), whle preptaton of Fe(OH) s only possble when CO partal pressure s very small... Eletrohemal Reaton Rates at the Metal Surfae The reatons at the steel surfae are eletrohemal, ther rates are onneted wth boundary ondtons, and they are not a part of R n Equaton (-1). Suh a reaton numbered by e may be expressed n the form of _ r,e M z,r z,p _ r _ p,em _ p n ee (-11) where z at the upper rght of the symbols sgnfes the harge arred by the metall spees M. Charge balane for Equaton (-11) dtates that,ez ne (-1) e where,e and n e are stohometr oeffent of the th spees and the number of eletrons transferred durng the e th eletrohemal half-ell reaton, respetvely. -

52 s The total net produton rate of all the eletrohemal reatons nvolvng the th spees,e,e n ef R s r s (-1),e e e,e,e e e where s e s the nterfaal area of the eletrohemally atve surfae n the system. For the system of nterest here, the eletrohemal reatons our only at the steel surfae and the urrent densty of the e th eletrohemal reaton may be expressed by the Butler-Volmer equaton. [4] _ r,e a _ e _ p, j _ e e e _ ref ( ( ) exp( e ) ( ) exp( e ) (-14) _ ref RT F Equaton (-14) may be redued to Tafel equatons for all anod and athod reatons. _ ref In Equaton (-14), the overpotental, η e, s defned as [4-5] U E U (-15) e s e _ ref s e _ ref RT F where and s are, at the metal-soluton nterfae, the eletrostat potentals of the metal and the soluton, respetvely. U e_ref an be treated as the eletrode potental at a referene ondton orrespondng to the exhange urrent densty _ ref at the onentraton of the th spees _ref. U e_ref an also be treated as the equlbrum potental when and are measured at a gven ondton of the same system. E s = s s eletrode potental measured wth the referene eletrode plaed very near the metal surfae. The eletrode potental measured wth the referene eletrode plaed anywhere n soluton E s E (-16) E s s When there s no externally appled urrent to and from the metal surfae, the eletrode potental s the open rut potental (OCP), E orr, Es E orr (-17) and the OCP an be determned from,k,l (-18) a k l where a and are anod and athod urrent denstes, respetvely. -4

53 When an external urrent s appled, ether the potental n the bulk soluton E b or the external urrent densty appled must be provded for a omplete soluton of the system. When E b s gven, by settng the eletrostat potental n the bulk soluton as zero, E s n Equaton (-16) s E (-19a) s E b s Lkewse, f the eletrostat potental at the steel surfae s set as zero, the followng equaton s obtaned E (-19b) s E b b where b s the soluton potental at the nterfae between the boundary layer and bulk soluton. Ether Equaton (-19a) or (-19b) an be substtuted nto Equaton (-14) as a boundary ondton for potental at the steel surfae. Ths boundary ondton ontans only the varables to be solved for n the governng equatons. When an externally appled urrent densty net s gven, E s an be solved for from a,k,l net (-) k l By substtutng E s nto Equaton (-14), the boundary ondton for potental at the steel surfae s defned. Suh a boundary ondton ontans only the varables to be solved for n the governng equatons. For the system of onern, the anod reaton s ron oxdaton. The athod reatons are hydrogen on reduton, arbon ad reduton, and water reaton.. Reaton Rates and Boundary Condtons for the System of Conern For ppelne nternal orroson wth soluton ontanng dssolved CO, O, and NaCl, f the soluton prmary spees are hosen arbtrarly as the underlned: (1) Na +, () Cl -, () Fe +, (4) H +, (5) OH -, (6) FeOH +, (7) CO (aq), (8) O (aq), (9) CO -, (1) HCO +, (11) H CO, (1) FeHCO +, (1) H (aq), (14) H O, (15) Fe, (16) FeCO (s), (17) Fe(OH) (s). the onentratons of the seondary spees an be alulated from the onentratons of the prmary spees followng ther equlbrum relatons. The onentratons of the sold spees, suh as FeCO and Fe(OH), and the spees of H (aq) and H O are treated as onstants. -5

54 ..1 Volumetr Reaton Rates The only rreversble homogeneous reaton n the system of onern s arbon doxde hydraton CO (aq) H O H CO (-1) and the reaton rate an be expressed by [6-7] rco f 7 b 11 (k k ) (-) where k f and k b are the forward and bakward reaton rate onstants of CO hydraton, respetvely. The mneral reatons n the system of onern are preptatons of FeCO (s) and Fe(OH) (s) Fe CO FeCO (-) and Fe OH Fe(OH) (-4) whle Equaton (-4) ours only when CO partal pressure s very low and the ph s hgh. and The orrespondng reaton rates of Equatons (-) and (-4) are rp1 f 1 sp FeCO FeCO FeCO r k K (S 1) (-5) k K (S 1) (-6) p f sp Fe(OH) Fe(OH) Fe(OH) where r pj (j=1,) s the rate of preptaton; k and K sp are preptaton rate onstant and solublty produt, respetvely; S s the rato of relevant on onentraton produts to K sp and measures the level of saturaton or supersaturaton of the soluton; and 1 or s spef area (or the rato of surfae area over the volume of a preptate)... Intal and Boundary Condtons For ppelne nternal orroson n wet gas lnes, a boundary layer s assumed to be onstantly present on the ppe surfae and ts thkness depends on the flow veloty. The bulk onentraton of any spees may be onsdered to be onstant over tme. No boundary ondton s needed for Equaton (-4), beause ths equaton s dmenson ndependent. -6

55 Unlke wet gas ppelnes, n a dry gas ppelne, the soluton boundary layer formed by water ondensaton an be thn, and at the gas-soluton nterfae, the CO (or O gas f present) may be onsdered to be n equlbrum wth ts dssolved spees, CO (aq) (or O (aq)). The flux of all other dssolved spees, suh as H CO and ons, s zero at ths boundary. Irrespetve of wet and dry gas ppelnes, at the steel surfae only orroson reatons our. When the effetve reatve surfae area fraton s treated the same as porosty, the Tafel equaton for ron oxdaton may be expressed by orr E Eqref s E Fe bfea 1 (-7) Feref where ref shown as ether a subsrpt or supersrpt n Equaton (-7), as well as n Equatons (-8) through (-), s referred as a referene ondton whereby the orrespondng exhange urrent densty, bulk onentraton (=, 4, 5, 14), and equlbrum potental E Eq are known or gven. b s Tafel slope. For redutons of hydrogen on, water, and arbon ad, the Tafel equatons are H H H s 4 ref Eqref ( EsE H ) bh 4 Href 1 (-8) Eqref (EsE ) HO b H O H O Oref1 (-9) Eqref ( E s E ) H CO 11s 4s b H CO.5 CO H COref ( ) 1 11ref 4ref (-) where 4s and 11s are the onentratons of hydrogen on and arbon ad at the steel surfae respetvely... Movng Boundary Condton for a Dry Gas System For a dry gas system, when a boundary layer s mantaned at the steel surfae wth the rate of water ondensaton equal to the rate of evaporaton, the total mass of water of ths boundary layer does not vary over tme. The preptate flm and the boundary layer thkness, however, vary over tme beause the denstes and molar weghts of the steel and preptate dffer. The total mass of the dssolved Na + n the system s onserved x x S M dx (-1) 1 1 Dervaton of Equaton (-1) over tme t yelds -7

56 M 1M x t M x M ( 1 ) xs t dx S 1S t (-) x S The mddle term s zero beause there s no net loss or gan n mass of Na + at the two boundares. Wth ths onstrant, Equaton (-) may be rearranged as x t M xs s1s M1M x M t s1s t (-) The movng veloty of the steel surfae relatve to the soluton surfae as the referene s x t M x t S 1M orr ( 1 ) (-4) M s 1s where s a unt onverson fator, whh for steel s A s/m..4 Model Valdaton wth Lab and Feld Data Laboratory and feld data are avalable from tests smulatng ol and gas produton systems smlar to ondtons n a wet gas ppelne where abundant water s present. Beause the same fundamentals for orroson hold n both wet and dry gas ppelnes and n produton ppes, the model valdaton for a wet gas system an be onsdered applable to the model for a dry gas system. For the model valdaton usng data obtaned for produton systems, the varaton at the steel boundary due to metal dssoluton or formaton of deposts s not onsdered by assumng ths effet beng nsgnfant. The values of the model parameters used for modelng the orroson proess are detaled n MS #4 appended at the end of ths report. Fgure - shows a omparson of the predted orroson rates wth expermental data [8-9] ; the ntal soluton ontaned lttle or no ferrous on and the flow veloty n a ppe loop wth an 8-m nner dameter was m/s. The expermental data were aqured n stu by montorng the atvty derease resultng from the metal loss of neutron-atvated steel oupons wth Fe59 as the man radoatve sotope. Sntllaton ounters, plaed outsde the loop ppe, montored the atvty levels n 1-seond ntervals wth an auray of approxmately.%. The predted maxmum orroson rate n Fgure - (dashed urve) s the rate when orroson begns. The steel surfae s fresh, and the soluton ph at the steel surfae s low. Soon after orroson starts, the ph at the steel surfae rapdly elevates by the eletrohemal redutons of hydrogen ons and arbon ad and by the formaton of ferrous ons durng orroson. The boundary layer thkness at the ondton of the expermental test s determned to be 1 m based on the dameter of the test tubng and flow veloty. The predted results show that t takes tme for the orroson proess to reah steady state, and at steady state, no preptaton ours (the predted porosty at the steel surfae s 1). The predted steady-state orroson rates (sold urve) are ompared wth measured orroson rates. Exept for one pont, all expermental data fall slghtly below the predted orroson rates, suggestng that the predted steady-state orroson rates are slghtly more onservatve or greater than the measured rates. -8

57 Fgure - shows the measured orroson rates at 51 C n a soluton that was ntally saturated wth ferrous arbonate. [1] The orroson rates appeared to be measured by usng the lnear polarzaton resstane (LPR) method (not learly stated n the lterature). The predted orroson rate dereases over tme due to an nrease of soluton ph and formaton of sold preptate at the steel surfae. The formaton of sold preptate dereases the system porosty and the atve orrodng area at the steel surfae. Overall, the predted orroson rates are shown to be slghtly greater than the expermental data. Smlar to Fgure -, Fgure -4 shows the tme-dependent orroson rates measured n a lab at 5 C n a soluton ntally saturated by ferrous arbonate. [1] The expermental data were measured possbly by usng the LPR method and are shown to be slghtly less than and smlar to the predted rates. The formaton of preptate flm at the steel surfae and the dereasng porosty by sold preptates may be responsble for the orroson rate derease. Fgure -5 shows the model-predted maxmum (or ntal) orroson rates and those at the ffth hour n a soluton ntally saturated by ferrous arbonate. The temperature s 9 C. These predted results are ompared wth expermental data measured n a hgh pressure flow loop onneted to an autolave at 9 C. [1] The soluton was ntally saturated by ferrous arbonate. The CO partal pressure vares between 1.5 and 6 bars at a flow rate of m/s. Beause orroson rate vares wth tme as shown n Fgures - and -4, dependng on the tme of measurement the orroson rate an be dfferent. The tme and the methods of the orroson rate measurements are not learly stated n the lterature. [1]. The predted orroson rates at the ffth hour are slghtly greater than the measured rates. Fgure -6 shows data measured n lab testng wth the same faltes used for measurng the data shown n Fgures -1 through -4, and the data were possbly measured by the LPR method. [8,11] In the fgure, feld orroson rates reported elsewhere [1] are nluded. The temperature was 5 C. The lab and feld data are ompared wth the model-predted results. The flow veloty s shown to have a sgnfant effet on the orroson rate. Some orroson rates measured n lab testng are sgnfantly greater than the predted steady-state orroson rates and even greater than the predted maxmum orroson rates. It s possble that the orroson rates measured n the lab were affeted by the eroson proesses, whh the model does not over. It s also possble that the model parameters may not all be fully onsstent wth the test ondton. For ths model, the role of flow veloty s treated as redung the boundary layer thkness only. Beause the predted orroson rate s greater than the feld-estmated orroson rate, t appears that the predted orroson rates are more onservatve than the long-term orroson rate n feld ondtons. Smlar results are shown n Fgure -7 for the temperature range of 5-6 C. [8,11] The data ame from the same soures as, and were measured smlarly to, the data n Fgure -6. The dfferene s that none of the lab data exeed the predted maxmum orroson rates. The predted steady-state orroson rates are less than the lab rates but greater than the feld orroson rates. [1] -9

58 Note that not only an expermental data ontan errors, but also the model tself has ts lmtatons. The values of the model parameters ame from dfferent soures, and eah may be assoated wth errors. Thus, dsrepany between the model predtons and expermental or feld data an be expeted. A senstvty analyss of some model parameters s gven n MS #4 appended at the end of ths report..5 Results Fgure -8 shows the predted orroson rate, ph, and porosty at the steel surfae for a wet gas ppelne. A sgnfant drop of orroson rate over tme s shown shortly after the orroson proess begns. Ths derease n orroson rate s aompaned a ph nrease at the steel surfae. Beause the porosty at the steel surfae s unty onsstently, ths suggests that no sold preptaton s predted at the steel surfae. The orroson rate and the porosty at the steel surfae are shown for a dry gas system n Fgure -9. The ntal varaton of orroson rate wth tme s smlar to that n the wet gas system (Fgure -8) before the porosty at the steel surfae starts to derease. Ths derease n orroson rate s onsstent wth the nrease of ph at the steel surfae. Afterwards, as the orroson rate beomes steady for some tme, the onentraton of ferrous ons n the soluton nreases and the soluton beomes saturated wth ron arbonate. The formaton of sold FeCO n the dry gas system begns almost smultaneously n the entre boundary layer, revealed by the derease of porosty both at the steel surfae and at the gas-soluton nterfae. Ths derease n porosty at the steel surfae leads to a dereasng orroson rate beause of the total avalable steel surfae area for orroson (not overed by the preptate) s redued. The more sgnfant derease n porosty at the steel surfae than at the gas-soluton nterfae s the result of mass transport (of ferrous on n the boundary layer from the steel surfae) lmtaton. Fgure -1 shows the predted orroson rates n both wet and dry gas systems when the soluton layer s saturated at tme zero. The ntal orroson rates are muh smaller than those for the unsaturated ondton (shown n Fgures -8 and -9) beause of a hgher ntal ph elevated by the saturaton of FeCO n the soluton. The orroson rates for both wet and dry gas systems are smlar, although the rate n the wet gas system s slghtly greater than n the dry gas system. Ths smlarty n orroson rate s onsstent wth the porosty values for both systems, whh are smlar n magntude, as shown n Fgure -11. For the wet gas system, the porosty at the bulk boundary s mantaned at 1, whle at the steel t beomes smaller (a smaller average orroson rate results). The orroson rate n the wet gas system s greater overall beause ferrous ons formed from the orroson proess an transport aross the boundary layer nto the bulk soluton. Ths leads to a slower rate of preptaton and a slower hange of porosty ompared to a dry gas system where no ferrous on an esape the soluton boundary layer..6 Model Smplfaton The model results presented n Seton.4 an be smplfed by negletng the on mgraton term n the flux equaton or by negletng the effet of the voltage drop aross the -1

59 soluton boundary at the steel surfae. The valdty of ths model smplfaton has been dsussed qualtatvely n other works. [7, 1] A quanttatve valdaton of ths model smplfaton wll be presented later n ths work. Ths model smplfaton mples that Equaton (-), or the flux of the th spees n a dlute soluton, N, an be redued to N D (-5) Ths hange of model equatons an sgnfantly redue the dffultes n numeral modelng to solve the dfferental equatons. Ths hange has led to the nonlnear dfferental equatons beomng lnear. Fgure -1 shows a omparson of the model results obtaned when the voltage drop aross the boundary layer s and s not nluded, or Equatons (-) and (-5) are respetvely used for the model. Clearly, there s no dstnton n the model results regardless of whether Equaton (-) or (-5) s used, verfyng the valdty of Equaton (-5)..7 Effet of H S and O on CO Corroson The NACE report (n preparaton by a number of experts n modelng CO orroson wth and wthout H S n the system) [14] advses exersng are when usng exstng CO orroson models (a total of 17 models have been ompled n the report) for stuatons wth more than a few mbar H S, mplyng the exstng CO orroson models do not apply to orroson predtons n a CO orroson system ontanng H S. Even n the presene of a small amount of H S n a CO orroson system, the orroson produts tend to be ron sulfde rather than ron arbonate, beause ron sulfde s muh less soluble and preptates more rapdly than ron arbonate. Thus, exstng CO models developed based on the formaton of protetve ron arbonate flms annot be used for stuatons where ron sulfde flms are domnant. SwRI developed a formula that allows for predtng the type of domnant preptate at the steel surfae based on the molar rato of CO to H S n the gas phase. [1] p p HS CO H K K K CO spfes 11H CO H CO (-6) H H SK1H SK H SKspFeCO Fgure -1 developed by others [15] based on the same formula demonstrates the regons of preptates at two dfferent phs of the soluton. The effet of temperature on ths rato of partal pressures s shown n Fgure -14. The boundares an be used to determne the regons where the CO orroson model s applable. In the ase where the orroson produt s maknawte (FeS), the rate-ontrollng step s found to be dssoluton of maknawte. Maknawte forms under ondtons where the Fe + and H S onentratons n the bulk soluton are low enough that FeS s undersaturated and s stll soluble. A vsble tarnsh flm an exst when the FeS formaton reaton s fast and the -11

60 dssoluton step s slow. The reaton rate for the dssoluton of maknawte an be expressed as [14] Rate k 1 ph [FeS] (-7) where k = the reaton rate onstant (whh s a funton of temperature) and [FeS]= the molar onentraton of sold FeS (whh s defned as 1 for a sold spees). Tewar and Campbell [16] measured the ron on release rate from a dssolvng maknawte surfae n a seres of experments at varous flow rates and two temperatures. The data were extrapolated to nfnte flow rate to remove any onsderaton of ron on omplex dffuson. Ths allowed values for k to be determned at two temperatures as well as the atvaton energy and rate onstant for the reaton. Tewar s testng was lmted n that t ould not provde the type of data requred to model flud flow n a manner as has been studed for CO orroson. Corroson rate n an oxygen-ontanng envronment s often lmted by oxygen dffuson, and t ould be predted by an empral equaton developed by Psgan and Sngly [17] MPY = (TDS).5 (DO).8 (1 SI).876 (Day).7 (-8) where TDS s total dssolved solds n mg/l, DO s dssolved oxygen n mg/l, SI s the Langeler sale ndex, and Day s exposure perod n days. Oxygen n water obeys Henry's law followng p O = K O x O (-9) where p O s the partal pressure of oxygen n torr, x O s the mole fraton of oxygen n oxygensaturated water, K O s the Henry's law onstant for oxygen n water (about. 17 K/torr for oxygen at 98 K). [18] To determne saturated dssolved O onentraton (DO) n mg O /L water, the followng two empral equatons may be used C < t < C DO = (P-p).678/5 + t (-4a) C < t < 5 C DO = (P-p).87/49+t (-4b) These equatons apply to oxygen n dstlled water at a barometr pressure of P (n torr), at a temperature of t ( C), and wth a water vapor pressure of p (n torr). [19] The mehanst nature of oxygen effet on CO orroson rate was modeled by researhers at Unversty of Toronto, whh aounted for the dual effets of oxygen on the orroson rate. [] In an ad soluton ontanng dssolved CO, oxygen reduton at the steel surfae nreases the orroson rate by workng as a athod reaton. On the other hand, as t s beng redued, hydroxyls form and the soluton ph s elevated, thus, redung the orroson rate. Ths model s publly avalable, and Fgure -15 shows the model results. -1

61 .8 Summary A omprehensve CO orroson model onsderng both transport and mgraton of on spees n soluton was developed and valdated wth a sgnfant amount of data n a wde range of ondtons. Ths model was used to predt orroson rates n both wet and dry gas systems. The predton results show that n a dry gas system, ferrous ons annot esape the soluton boundary layer and preptaton wll our. The redued porosty at the steel surfae by the preptate leads to a redued orroson rate. For wet gas systems where preptates an dssolve and transport out of the boundary layer nto the bulk soluton, preptaton may or may not our at the steel surfae dependng on the balane between the rates of formaton and dssoluton of a sold preptate. Wth a smaller porosty of the preptate n dry gas orroson systems, the orroson rate n a dry gas system s less than n a wet gas system for the same ondtons. The model an be smplfed by negletng the voltage drop aross the soluton boundary layer (the on mgraton term n the flux equaton). By ths smplfaton, the hallenges n numeral soluton of the dfferental equatons an be greatly redued..9 Pratal Implatons of the Model Results.9.1 Understandng the Dfferene n Corroson Rate Between Wet and Dry Gas Systems The ppelne ndustry has been usng models developed for ol produton systems to predt nternal orroson rates of both wet and dry gas ppelnes. Suh model predton s reasonable for wet gas systems where abundant water s present; however, ths predton may sgnfantly overestmate the nternal orroson rate for dry gas systems. In a dry gas ppelne, lqud water may be present ondensaton, and suh a water layer an be thn and easly saturated. As a sold preptates, both mass transport and the metal surfae area avalable for orroson are redued, and thus a smaller orroson rate s possble. Ths effet of sold formaton on orroson rate s modeled. The predtons show that the nternal orroson rate n a dry gas system an be sgnfantly smaller than n wet gas systems. The model has been valdated by omparng the model results wth lab and feld data. The model has been smplfed to redue the hallenges n numerally solvng the dfferental equatons. By negletng the effet of the voltage drop n the boundary layer, the model dfferental equatons an be redued from nonlnear to lnear. The omplexty of the model an be sgnfantly redued. When an nternal orroson rate n dry gas systems s predted, the fat that the orroson rate s less than n a wet gas system should be taken nto aount. -1

62 .9. The Effet of H S and O on Ppelne Internal Corroson Rate The effet of H S on CO orroson rate has been studed for several deades, and t s stll hallengeng to predt ths effet. Charts are provded n ths work to show the ondtons where FeCO (vs. FeS) s domnant and the CO orroson model s applable. Ths provdes gudelnes for the use of the CO orroson model. The effet of O on CO orroson rate s twofold. The eletrohemal reduton of oxygen nreases orroson rate. In the meantme, ths reaton generates hydroxyls and dereases the orroson rate. Ths nteratve effet of O on CO orroson rate leads to a stuaton where oxygen dffuson does not entrely ontroloxygen orroson. In prate, the addtve total of CO orroson rate wthout O and the rate of oxygen orroson ontrolled by dffuson overestmates the atual orroson rate..1 Referenes [1] F.M. Song, N. Srdhar, Corroson Sene 5(1) (8) 7-8. [] F.M. Song, Eletrohma Ata 56 (11) [] F.M. Song, Corroson Sene 51 (9) [4] J. Newman, K.E. Thomas-Alyea, Eletrohemal Systems, rd edton, John Wley and Sons, In. (4) [5] K. Kumaresan, Y. Mkhaylk, R.E. Whte, J. Eletrohem. So. 155 (8) A576-A58. [6] F.M. Song, D.W. Krk, J.W. Graydon, D.E. Cormak, Corroson 6(8) (4) [7] F.M. Song, Eletrohma Ata 55 (1) [8] C. de Waard, D.E. Mllams, Corroson 1 (1975) 177. [9] K. Vdem, A. Dugstad, Materals Performane, Marh (1989) 6. [1] K. Vdem, A. Dugstad, Materals Performane, Aprl (1989) 46. [11] A. Dugstad, L. Lunde, K. Vdem, Parametr Study of CO Corroson of Carbon Steel, (NACE, 1994) Paper 14. [1] C. de Waard, U. Lotz, Predton of CO Corroson of Carbon Steel (NACE, 199) Paper 69. [1] F.M. Song, N. Srdhar, An Approah to Determnng Reassessment Intervals through Corroson, DOT Contrat No. DTRS56-4-T-, Fnal Report submtted n Otober 6. [1] NACE TG 76, Predton of Envronmental Agressveness n Olfeld Systems from System Condtons, draft report, 11. [15] R. Woollam, K. Tummala, J. Vera, S. Hernandez, Thermodynam Predton of FeCO, FeS Corroson Produt Flms, (NACE 11), Paper [16] P.H. Tewar, A.B. Campbell, Canadan J. Chemstry 57 (1979) [17] R.A. Psgan, J.E. Sngly, Materals Performane, Aprl [18] Z. Szklarska-Smalowska, Pttng Corroson of Metals (NACE,1986). [19] P.W. Atkns, Physal Chemstry, 6th ed., Oxford Unversty Press (1998) 174. [] F.M. Song, D.W. Krk, J.W. Graydon, D.E. Cormak, Journal of the Eletrohemal Soety, 149(11) () B479-B

63 Gas or lqud phase boundary y= s Chemal reatons n soluton Preptaton wth porosty Eletrohemal reatons at steel surfae y= Ppe steel Fgure -1. Shemat dagram showng the hemal, eletrohemal, and mneral (preptaton) reatons that may our n a boundary layer or at ppe steel surfae. 1 9 o C, Unsaturated Corroson rate (mm/y) 1 1 Model-unsaturated, max CR, 9 C Model-Unsaturated, steady CR, 9 C d&m V&D_X5_pure water_v= m/s V&D_X65_v= m/s Carbon doxde pressure (atm) Fgure -. Model-predted maxmum (or ntal) and steady-state orroson rates vs. expermental data measured n an unsaturated soluton at 9 C n a flowng system [8,9]. Corroson rate (mm/y) C Model 51 C Tme (mn) Fgure -. Model-predted tme-dependent orroson rates vs. expermental data measured n a soluton ntally saturated by ferrous arbonate at 51 C [1]. -15

64 5 C Model 5 C Corroson rate (mm/y) Tme (mn) Fgure -4. Model-predted tme-dependent orroson rates vs. expermental data measured n a soluton ntally saturated by ferrous arbonate at 5 C. [1] Corroson rate (mm/y) Model-Saturated, max CR, 9 C Model-Saturated, CR.1th hour, 9 C V&D_sat._v=- m/s 9 o C, saturated Carbon doxde pressure (atm) Fgure -5. Model-predted maxmum (or ntal) and at.1 th hour nstant orroson rates vs. expermental data measured n a saturated soluton at 9 C. [1] -16

65 Corroson rate (mm/y) Model-Unsaturated, max, 5 C Model-unsaturated, steady, 5 C D,L&V_ C_v=.1-1 m/s d&m Feld Estmate, -5 C Carbon doxde pressure (atm) Fgure -6. Model-predted maxmum (or ntal) and steady-state orroson rates vs. expermental data measured n lab [8,11] and estmated from feld [1] n an unsaturated soluton at 5 C wth flow. Corroson rate (mm/y) Model-unsaturated, max CR, 6 C Model-unsaturated, stready, 6 C Feld estmate, 5-6 C D,L&V_v=.1-1 m/s d&m Carbon doxde pressure (atm) Fgure -7. Model-predted maxmum (or ntal) and steady-state orroson rates vs. expermental data measured n lab [11] and estmated from feld [1] n an unsaturated soluton at 6 C wth flow. Fgure -8. Model-predted orroson rates for both wet and dry gas systems at 5 C and p CO =1 atm. The boundary layer thkness s 1 m and ntally ontans neglgble ferrous on. -17

66 Fgure -9. Predted orroson rates and porosty for only the dry gas system at the same ondton of Fgure -8. Fgure -1. Model-predted orroson rates for both wet and dry gas systems at 5 C and p CO =1 atm. The boundary layer thkness s 1 m, and t s ntally saturated wth ferrous arbonate. For wet gas, the bulk soluton s also saturated wth ferrous arbonate. -18

67 Fgure -11. For the same ondtons of Fgure -1, the porosty varatons wth tme for both wet and dry gas systems. Fgure -1. Verfaton of model smplfaton by omparson of orroson rates obtaned from the model by onsderng and not onsderng the voltage drops n the boundary layer. (a) (b) Fgure -1. Regon of a domnant preptate: Sderte (FeCO ) or Maknawte (FeS), determned based on Equaton (-6), when [Fe + ]=1-6 mol/lter and the soluton ph s (a) ph=6 and (b) ph=4. [15] -19

68 Sderte Maknawte Fgure -14. Sderte-Maknawte boundary determned based on Equaton (-6) for varyng temperatures and the rato of partal pressure. [15] Fgure -15. The nteratve effet of CO and oxygen on steel orroson. [] -