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- Permanent Link:
- https://ufdc.ufl.edu/UFE0043868/00001
## Material Information- Title:
- Influence of CO2 on Corrosion of Steel in Saline Electrolytes
- Creator:
- Chen, Yu-Min
- Place of Publication:
- [Gainesville, Fla.]
- Publisher:
- University of Florida
- Publication Date:
- 2011
- Language:
- english
- Physical Description:
- 1 online resource (71 p.)
## Thesis/Dissertation Information- Degree:
- Master's ( M.S.)
- Degree Grantor:
- University of Florida
- Degree Disciplines:
- Chemical Engineering
- Committee Chair:
- Orazem, Mark E
- Committee Members:
- Chauhan, Anuj
- Graduation Date:
- 12/17/2011
## Subjects- Subjects / Keywords:
- Confidence interval ( jstor )
Corrosion ( jstor ) Current density ( jstor ) Electrodes ( jstor ) Error rates ( jstor ) Hydrodynamics ( jstor ) Jet impingement ( jstor ) Mass transfer ( jstor ) Stagnation point ( jstor ) Steels ( jstor ) Chemical Engineering -- Dissertations, Academic -- UF co2 -- corrosion -- impedance - Genre:
- Electronic Thesis or Dissertation
born-digital ( sobekcm ) Chemical Engineering thesis, M.S.
## Notes- Abstract:
- The electrochemical behavior of 5LX52 and 5LX65 steels, widely used for pipelines transporting petroleum products, was studied under a submerged impinging jet of 3 wt% NaCl electrolyte. Formation of a red colloidal gel was observed for both 5LX52 and 5LX65 grade steels with an air-saturated electrolyte. On the other hand, a gray film was produced for both 5LX52 and 5LX65 steels in the presence of a deaerated CO2-saturated electrolyte. The impedance response showed that, for both steels, the corrosion reaction was controlled by the steel in both air-saturated and deaerated CO2-saturated electrolyte. The impedance data could be fit by models employing a constant phase element (CPE). An analysis based on the assumption that the CPE response could be attributed to a power-law distribution of resistivity was used to determine the thickness of the films forming on the electrode surface. The thickness of the corrosion product on 5LX65 steel was found to depend on jet velocity. The films on 5LX52 steel were thicker than those formed on 5LX65 steel in both aerated and deaerated CO2-saturated electrolytes. The impedance response revealed that 5LX65 steel had greater resistance to corrosion as compared to 5LX52 steel. ( en )
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- In the series University of Florida Digital Collections.
- General Note:
- Includes vita.
- Bibliography:
- Includes bibliographical references.
- Source of Description:
- Description based on online resource; title from PDF title page.
- Source of Description:
- This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
- Thesis:
- Thesis (M.S.)--University of Florida, 2011.
- Local:
- Adviser: Orazem, Mark E.
- Statement of Responsibility:
- by Yu-Min Chen.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- Copyright Chen, Yu-Min. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
- Resource Identifier:
- 814306369 ( OCLC )
- Classification:
- LD1780 2011 ( lcc )
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PAGE 1 1 INFLUENCE OF CO 2 ON CORROSION OF STEE L IN SALINE ELECTROL YTES By Y U M IN C HEN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2011 PAGE 2 2 2011 Yu Min Chen PAGE 3 3 To my girlfriend, parents and friends PAGE 4 4 ACKNOWLEDGMENTS First of all, I would like to thank Prof Mark Orazem for his technical guidance support and insightful suggestions throughout my graduate research with his knowledge and experiences in electrochemical engineering field He always has been positive and patient to me. Second, I thank to my research group members who helped and support ed me whenever I need. Last but not least, I would like to express of thanks to my family members for the financial support and encouragement PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .............. 4 LIST OF TABLES ................................ ................................ ................................ ......................... 7 LIST OF FIGURE S ................................ ................................ ................................ ....................... 8 LIST OF ABBREVIATIONS ................................ ................................ ................................ ...... 10 ABSTRACT ................................ ................................ ................................ ................................ 15 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ ................. 16 2 CONVECTIVE IMPEDANCE UNDER IMPINGING JET ................................ .............. 19 2.1 Introduction of Impinging Jet ................................ ................................ ...................... 19 2.2 Fluid Flow Model and Mass Transfer Impedance of Impinging Jet ...................... 20 2.3 Determination of Hydrodynamic Constant ................................ ................................ 21 2.4 Convective Diffusion Mass Transfer of Impinging Jet ................................ ............ 23 3 ELECROCHEMICAL IMPEDANCE SPECTROSCOPY ................................ ............... 27 3.1 Introduction of Electrochemical Impedance Spectroscopy ................................ .... 27 3.2 Electrochemical Impedance Spectroscopy of Electrochemical Reaction ........... 28 3.3 Electrochemical Impedance Spectroscopy Model of System ............................... 28 3.3 Overall Cell Impedance Model ................................ ................................ ................... 34 4 CONSTANT PHASE ELEMENT ................................ ................................ ....................... 36 4.1 Introduction of Constant Phase Element ................................ ................................ .. 36 4.2 Constant Phase Element Impedance Expression ................................ ................... 37 5 EXPERIMENTAL METHOD ................................ ................................ .............................. 40 5.1 Experiment Setup ................................ ................................ ................................ ......... 40 5.2 Instruments and M easurement Method ................................ ................................ .... 40 6 RESULTS AND DISCUSSIONS OF EXPERIMENTS ................................ .................. 44 6.1 Hydrodynamic Constant Determination ................................ ................................ .... 44 6.2 Impedance Responds at Different Circumstance ................................ .................... 44 6.3 Determination of Dominated Impedance ................................ ................................ .. 45 6.4 Impedance Response with Different Jets Velocity ................................ .................. 46 PAGE 6 6 6.5 Error Structure Analysis ................................ ................................ .............................. 47 6.6 Complex Nonlinear Regression ................................ ................................ ................. 48 6.7 The Levenberg Marquardt Method ................................ ................................ ............ 50 6.8 Measurement Model ................................ ................................ ................................ .... 50 6.9 The Kramers Kronig Relations ................................ ................................ ................... 51 6. 10 Error Structure of 5LX52 and 5LX65 Pipe Grade Steel ................................ ....... 52 6.1 1 Monte Carlo Simulation ................................ ................................ ............................. 52 6.12 Film Thickness Determination ................................ ................................ .................. 54 7 CONCLUSION ................................ ................................ ................................ ..................... 67 LIST OF REFERENCES ................................ ................................ ................................ ........... 68 BIOLOGICAL SKETCH ................................ ................................ ................................ ............. 71 PAGE 7 7 LIST OF TABLES Table page 5 1 Nominal chemical composition of the 5LX52 steel used in this study ................... 41 5 2 Nominal chemical composition of the 5LX65 steel used in this study ................... 41 6 1 Limiting current and hydrodynamic constant of different flow rates ....................... 66 6 2 Error Structure Coefficient of 5LX52 and 5LX65 Steel ................................ ............. 66 PAGE 8 8 LIST OF FIGURES Figure page 2 1 Four distinct f low regions under impinging jet ................................ .......................... 26 2 2 Values for dimensionless contributions Z (0) Z (1) and Z (2) to the diffusion impedance as a function of Sc 1/3 /a : a) r eal part; and b) imaginary part ............ 26 3 1 A equivalent circuit of electrochemical impedance spectroscopy .......................... 35 3 2 Perturbation of an electrochemical system with a small si nusoidal signal at steady state ................................ ................................ ................................ ..................... 35 5 1 Schematic diagram of the impinging jet syste m ................................ ........................ 42 5 2 Schematic illustration of reaction cell champer and important cell components ................................ ................................ ................................ ..................... 43 6 1 Equivalent Circuit of electrochemical system. ................................ ........................... 54 6 2 Impedance response s of 5LX52 steel with air saturated at a=140s 1 ................... 55 6 3 Impedance responses of 5LX52 steel with CO 2 saturated a=140s 1 .................... 55 6 4 Impedance responses of 5LX65 steel with air saturated at a=140s 1 .................. 56 6 5 Impedance responses of 5LX65 steel with CO 2 saturated at a=140s 1 ............... 56 6 6 Impedance responses of 5LX52 steel at +0.05V and 0.05V vs. open circuit potential with CO 2 saturated at a=140s 1 ................................ ................................ .. 57 6 7 Impedance responses of 5LX52 steel at +0.05V and 0.05V vs. open circuit potential with air saturated at a=140s 1 ................................ ................................ ..... 57 6 8 Impedance responses of 5LX65 steel at +0.1V and 0.1V vs. open circuit potential with CO 2 saturated at a=140s 1 ................................ ................................ .. 58 6 9 Impedance responses of 5LX65 steel at +0.1V and 0.1V vs. open circuit potential with air saturated at a=140s 1 ................................ ................................ ..... 58 6 10 Impedance responses of 5LX52 steel a=140, 252 and 381s 1 with CO 2 saturated and a=140s 1 with air saturated. ................................ ................................ 59 6 11 Impedance responses of 5LX65 steel a=140, 252 and 381s 1 with CO 2 saturated and a=140s 1 with air saturated. ................................ ................................ 59 PAGE 9 9 6 12 Impedance data, error structure and confidence interval of 5LX52 pipe grade steel with CO 2 saturated at a=140s 1 ................................ ................................ .......... 60 6 13 Impedance data, error structure and confidence interval of 5LX52 pipegrade steel with CO 2 saturated at a=252s 1 ................................ ................................ .......... 60 6 14 Impedance data, error structure and confidence interval of 5LX52 pipe grade steel with CO 2 saturated at a=381s 1 ................................ ................................ .......... 61 6 15 Impedance data, error structure and confidence interval of 5LX52 pipe grade steel with air saturated at a=140s 1 ................................ ................................ ............. 61 6 16 Impedance data, error structure and confidence interval of 5LX65 pipe grade steel with CO 2 saturated at a=140s 1 ................................ ................................ .......... 62 6 17 Impedance data, error structure and confidence interval of 5LX65 pipe grade steel with CO 2 saturated at a=254s 1 ................................ ................................ .......... 62 6 18 Impedance data, error structure and confidence interval of 5LX65 pipe grade steel with CO 2 saturated at a=381s 1 ................................ ................................ .......... 63 6 19 Impedance data, error structure and confidence interval of 5LX65 pipe grade steel with air saturated at a=140s 1 ................................ ................................ ............. 63 6 20 Film thickness of 5LX52 pipe grade steel with CO 2 saturated at a=140,252, and 381 s 1 and with air saturated at a=140 s 1 ................................ ......................... 64 6 21 Film thickness of 5LX65 pipe grade steel with CO 2 saturated at a=140,252, and 381 s 1 and with air saturated at a=140 s 1 ................................ ......................... 64 6 22 C eff of 5LX52 pipe grade steel with CO 2 saturated at a=140,252, and 381 s 1 and with air saturated at a=140 s 1 ................................ ................................ .............. 65 6 23 C eff of 5LX65 pipe grade steel with CO 2 saturated at a=140,252, and 381 s 1 and with air saturated at a=140 s 1 ................................ ................................ .............. 65 PAGE 10 10 LIST OF ABBREVIATION S Romans a H ydrodynamic constant for the impinging jet, s 1 C i C oncentration of species i, mol/cm 3 C i,0 C oncentration of species i on the electrode surface, mol /cm3 C i B ulk concentration of species i, mol/cm 3 Oscillating of surface concentration of bulk species C k Local capacitance C dl D ouble layer capacitance, F/cm 2 D i D iffusion coefficient of species i, cm 2 /s F constant, 96 487 C/equiv i f Faradic current density, A/cm 2 i 0 E xchange current density, A/cm 2 I lim Limiting current density, A/cm 2 j I maginary number, k i R eaction rate constant for species i K i D imensionless frequency n N umber of electrons transferred for a given electrochemical reaction n i N umber of electrons transferred for a given electrochemical reaction for species i Number of Voigt element P i ,P j Parameter vector of complex fitting model R U nive rsal gas constant, 8.3143 J/mol K R e E lectrolyte resistance, cm 2 PAGE 11 11 R eff E ffective lumped kinetic resistance, Eq. (40), cm 2 R k Adjustable parameter of Voigt element R m Resistance of the current measurement circuit Parameters for Monte Carlo simulation R t, i K inetic r esistance for species i cm 2 r R adial coordinate, cm r 0 R adius of disk, cm Sc Schmidt number, Sc=/D i dimensionless T T emperature, K t T ime, s U C ell potential, V V P otential of the metal referenced t o the potential of the solution V Actual applied potential, V V i ,0 E quilibrium potential of specie i V V 0 P otent ial in the electrolyte adjacent to the electrode V V m P otential of working electrode, V V r R adial velocity component, cm/s V z A xial velocity component, cm/s Z a Anodic Faradaic reaction impedance, cm 2 Z c Cathodic Faradaic reaction impedance, cm 2 Z i I mpedance for species i cm 2 Z D, i Warburg impedance for species I cm 2 N et diffusion impedance of both film and convective diffusion cm 2 Z d,i F inite length di ffusion impedance cm 2 PAGE 12 12 Z d,o S tagnant or a convective region impedance cm 2 Imaginary part impedance cm 2 Z k k th T erm for the expansion of the Warburg impedance, cm 2 Impedance of fitting model cm 2 Experiment observed impedance cm 2 Real part impedance cm 2 z A xial distance from disk, cm Greeks Constant phase element coefficient Apparent transfer coefficient of specie i for anodic reaction Apparent transfer coefficient of specie i for cathodic reaction Parameters of c omplex n onlinear r egression Parameter for Levenberg Marquardt method Error structure coefficient Parameters of c omplex n onlinear r egression Error structure coefficient S urface c overage of adsorbed species k Oscillating of surface coverage of adsorbed species k Vacuum permittivity Local dielectric constant Systematic experimental bias error other than model inadequacies Systematic error structure PAGE 13 13 S tochastic error Characteristi c length for mass transfer m T hickness of P orous layer m Thickness of stagnant or a convec tive region m Dimensionless axial position scaled to the characteristic length for fluid flow Dimensionless position variable Overpotenital V Error structure coefficient Constant for method of steepest descent Adjustable parameter of Voigt element Parameters for Monte Carlo simulation Dimensionless concentration variable, Dimensionless steady concentration variable Dimensionless oscillating concentration variable Dimensionless oscillating concentration variable following the series expansion Viscosity g cm/s Kinematic viscosity, cm 2 /s Dimensionless axial position scaled to the characteristic length for mass transfer Density, g/cm3 L ocal resistivity PAGE 14 14 R esistivity of electrolyte, R esistivity of film, Standard deviation Standard deviation of real impedance Standard deviation of imaginary impedance S h ear stress, N/cm 2 P arameter defined as stream function F requency of perturbation, s 1 Resistivity, ohm O thers Parameters for Monte Carlo simulation PAGE 15 15 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science INFLUENCE OF CO 2 ON CORROSION OF STEE L IN SALINE ELECTROL YTES By Yu Min Chen December 2011 Chair : Mark E. Orazem Major : Chemical Engineering The electrochemical behavior of 5LX52 and 5LX65 steel s widely used for pipelines transporting petroleum pro duct s was studied under a submerged impinging jet of 3 wt% NaCl electrolyte Formation of a red colloidal gel was observed f or both 5LX52 and 5LX65 grade steel s with an air saturated electrolyte On the other hand a gray film was produced for both 5LX52 and 5LX65 steels in the presence of a deaerated CO 2 saturated electrolyte The i mpedance response showed that, for both steels, the corrosion react ion was controlled by the steel in both air saturated and deaerated CO 2 saturated electrolyte The impedance data could be fit by models employing a constant phase element (CPE) An analysis based on the assumption that the CPE response could be attributed to a power law distribution of resistivity was used to determine the thickness of the films forming on the electrode surface The thickness of the corrosion product on 5LX65 steel was found to depend on jet velocity The film s on 5LX52 steel were thicker than those formed on 5LX65 steel in both aerated and deaerated CO 2 saturated electrolytes T he impedance response revealed that 5LX65 steel had greater resistance to corrosion as compared to 5LX52 ste el. PAGE 16 16 CHAPTER 1 INTRODUCTION Steel is an alloy that c onsists mostly of iron and has carbon content between 0.2 and 2.1 weight percent depending on the grade. Carbon is the most common alloying material for iron, but various other alloying elements are used, such as manganese, chromiu m, vanadium, and tungsten Since e very variety of s teel has man y unique properties such as mechanical strength, chemical resistance, and hardne ss, it make s a great material for many industrial applications Generally, the c orrosion of metals may take on many forms: uniform corrosion, galvanic corrosion, erosion corrosion, pitting, intergranular corrosion, selective reaching, stress corrosion, and hydrogen damage 1 For erosion corrosion e xperiment al systems such as the rotating disk electrode(RDE) 2 and stationary impinging jet disk electrode 3,4 are attractive because the convective diffusion solution is available and current is uniformly distributed at the mass transfer limited situations. T he prese nt work studies 5LX65 and 5LX 52 pipe grade steel under submerged impinging jets, which produce s CO 2 erosion corrosion on steel surface. T he carbon dioxide pre sence in solution leads to the formation of carbonic acid The first step is : ( 1 1) Then t he carbonic acid H 2 CO 3 is assumed to follow the cathodic reaction : ( 1 2) will follow the cathodic reaction : ( 1 3) F or the hydrogen ion : PAGE 17 17 ( 1 4) T he iron underg oes anodic corrosion: ( 1 5 ) With the corrosion reactions above a chemical environment which promotes the f ormation of iron carbonate ( FeCO 3 ) formed FeCO 3 can form from a couple of reaction s 5 as following. ( 1 6) also can react with as follows: ( 1 7 ) But d ue to the instability of it will follow equation (1 8) ( 1 8 ) This precipitate has the potential to form passive film on the surface of 5LX65 and 5LX 52 pipe grade steel In the case without CO 2 the main cathodic reaction is (1 9) The Fe 2+ from equation (1 5 ) further oxidize s to form Fe 3+ then combine with oxygen to form ferric oxide The ferric oxide is then hydrated with varying amounts of water The overall equation may be written as (1 10) is a red colloidal fluid. PAGE 18 18 In sum mation the CO 2 corrosion behavior is significantly affect ed by the reaction environments. The films formed on the steel in brine under a CO 2 saturated impinging jet have complex structure s 2 These structures dep end on the fluid velocity and the physicochemical and electrochemical properties of different developed corrosions layers, which can be modified as function of time 5 Using the developed impinging jet flow system in C hapter 2 and the convecti ve diffusion impedance model in C hapter 3 the impedance behavior models of the corrosion and film formation o n the electrode surface are developed The constant phase element model is introduced in C hapter 4. In C hapter 5 the experiments are set up and the composition s of 5LX52 and 5LX65 pipe grade steel are presented as well the impedance measurement protocol In C hapter 6 the results of the 5LX52 and 5LX65 pipe grade steel s under CO 2 saturated or air saturated jets, with flow rates of 1. 1 2.0, and 3 .0 GPM are presented. In order to verify the confidence of the data, error structure and Kramer Kronig relations are developed. PAGE 19 19 CHAPTER 2 CONVECTIVE IMPEDANCE UNDER IMPINGING JET 2 .1 Introduction of Impinging Jet The impinging je t electrode is commonly used for erosion corrosio n research since it allows an analytical solution of the fluid flow W ithin the stagnation region the axial velocity is independent of radial position and the convective diffusion to the disk is uniform 4,6 9 Generally speaking, w hen a submerg ed jet collides perpendicularly with a flat plate in a stat ionary electrolyte, four distinct flow regi on s are formed as illustrated in Fig. 2 1 Region I is called the potential core region in which the velocity prof ile of the jet changes from pipe flow to a free jet flow. When the flow leaves the submerged nozzle, the elect rolyte starts to mix with the surrounding fluid. The mixing zone grows in width along the downstream direction of the jet. Typically, t his core le ngth varies from 4.7 to 7.7 nozzle diameters 10 Region II is the estab lished flow region in which the velocity profile is well develop ed. In this region, the centerline velocity of the jet starts to decrease; its magnitude is inverse ly proportional to the distance f rom the nozzle exit and becomes zero near the stagnation point. This region covers a distance from the apex of the potential core to a height of 1.6 2.2 nozzle diameters from the surface of the flat plate 11 Region III is the stagnation re gion. This is a layer of fluid, about 1.6 2.2 nozzle diameters thick and 0.6 1.4 nozzle diameters in radius, on the flat plate in which the jet is deflected from the axial direction to a radial flow. The flow in this region is an axisymmetric inviscid irrotational type T he thickness of the boundary layer is relatively ind ependent of the radial position near the stagnation point 11,12 PAGE 20 20 Region IV is called the wall jet region. This is a region adjacent to the flat plate at some distance from the stagnation point where the radial velocity starts to decay and the thickness of the boundary layer increases with radial position The flow in this region can be divided into two sublayers. They are the inner layer w here the flow is influenced by the wall and the outer layer where the flow i s influenced by the surrounding fluid 13 2 .2 Fluid Flow Model and Mass Transfer Impedance of Impinging Jet In order to maintain the uniformly distributed current on the electrode surface, the electrode should be inside the uniform accessible region which is R/d < 0.5 for a laminar jet and < 1.0 for a turbulent jet 4 9 The axial velocity profile of this region, given by (2 1) is independent of radial position, and the radial velocity is given by (2 2) w here is the hydrodynamic constant that is only a function of geometry and fluid velocity ; r and y are the radial and axial positions, r espectively ; is the kinematic viscosity; and is the stream function as shown in equation (2 3) ( 2 3 ) th is is given in terms of dimensionless axial position 9 (2 4) The shear stress w ithin the stagnation region can be expressed as the function of radius r and the hydrodynamic constant a PAGE 21 21 ( 2 5 ) S ince a is a function of flow rates, the shear stress on the electrode s surface will increase as flow rates increases 2.3 Determination of Hydrodynamic Constant A m athematical model considering the mass transfer of electroactive species from a laminar impinging electrolyte jet to the electrode under steady state conditions is adopted in this research for the determination of the hydrodynamic constant With the cylindrical coordinates, the equations of convective diffusion can be reduce d to (2 6) w here C i and D i are the concentration and diffusivity of the reaction species I respectively The boundary conditions on the electrode and in the bulk system are A s (2 7) A t for (2 8) At for (2 9) W here is the bulk concentration and is the diameter of the electrode The following assumptions were made in solving the governing equation: 1. T he size of the ring electrode is confined within the stagnant region such that mass transfer i s uniform. 2. The boundary layer flow is not affected by the cell walls 3. T he physical properties of the solution are constant and uniform 4. M igrating effects are negligible in the presence of a supporting electrolyte PAGE 22 22 5. T he effects of external forces such as gravity are negligible A fter making Equation (2.6) and the boundary conditions of Equation (2.7) to (2.9) dimensionless Hickey introduced the Lighthill variable transformation 7 which reduced the partial differential equation to an analogous fo rm of the Leveque equation. Radial diffusion had been neglected over radial convection The solution of the concentration profile as a function of radial and axial position is given: (2 10) w here is the dimensionless concentration is the species concentration at the electrode surface and z is the normal distance. The Lighthill variable is (2 11) and (2 12) where r is radial position T he limiting current density can be expressed as (2 13 ) where =0. The total current can be expressed as a function of the hydrodynamic constant and the electrolyte solution properties. Therefore, the hydrodynamic constant (2 1 4 ) PAGE 23 23 W here s i is the stoichiometric coefficient of species i in the electrochemical reaction. Equation (2 11) is used under the assumption of large Schmidt numbers and a high concentration supporting electrolyte. This implies that velocity profile is not influenced by the mass transfer to and from the electrode surface and that migration effects are negligible. 2 4 Convectiv e D iffusion Mass Transfer of Impinging Jet For an impinging jet within a uniformly accessible region at the interface axial velocity is independent of the radial coordinate T he boundary condition at y = 0 is also independent of the radial coordinate Thus, the concentration is only a function of y Therefore, the convective diffusion equation can be expressed as : (2 15 ) W ith the boundary and initial conditions given by: for (2 16 ) at (2 17 ) at (2 18 ) is composed of a steady state term and an oscillating term. ( 2 19 ) Then, e quation (2 12) become s ( 2 20 ) F or steady state conditions, equation (2 20) is simplified to: PAGE 24 24 (2 21 ) Using boundary conditions ( 2 13) and (2 14 ) t he solution is given by: ( 2 22 ) U pon cancellation of the steady state te rms and division by the term equation (2 20) is further simplified as: (2 23 ) Using from equation ( 2 1) and defining dimensionless concentration as dimensionless position is given by where (2 24 ) and dimensionless frequency is given by: 14 (2 25 ) e quation ( 2 20 ) become s ( 2 26 ) w ith boundary conditions as (2 27 ) PAGE 25 25 as (2 28 ) Fol lowing Tribollet and Newman 14 the solution of dimensionless concentration c an be expressed as a function of the Schmidt number : ( 2 29 ) w here represents the solution to (2 30 ) ( 2 31 ) (2 32 ) t he convective diffusion impedance can be derived as function of Schmidt number (2 33 ) a nd values of and can be found from Figure 2 .2 PAGE 26 26 Figure 2 1 F our distinct flow regi on s under impinging jet (Refer to Figure 2 2 Values for dimensionless contributions Z (0) Z (1) and Z (2) t o the diffusion impe dance as a function of Sc 1/3 /a : a) real part; and b) imaginary par t. [ Referred to Mark E. Orazem 2006. Electrochemical Impedance Spectroscopy (Page 2 08 Figure 11 11 ). John Wiley & Sons, Inc ] PAGE 27 27 CHAPTER 3 ELECROCHEMICAL IMPED ANCE SPECTROSCOPY 3 .1 Introduction of E lectrochemical I mpedance S pectroscopy Electrochemical impedance spectroscopy is a useful method for analyzing and characterizing electrochemical systems The first step in developing an equivalent electrical circuit for an electrochemical system is to analyze the nature of the overall current and potential An electrochemical system, as shown in Fig ure 3 1, can be view e d as an equivalent circuit which consists of resistances and capacitances. Here C dl is double layer capacitance R e is resistance of solution and Z f is Faradaic impedance Faradaic impedance can be referred to charge transfer resistance mass transfer resistance reactions involving adsorbed species, and reactions on non uniform surfaces. The basic idea of impedance is the complex ratio of osci llating potential, and current. 15 ( 3 1 ) w here is impedance, is a complex number equal to is the phase difference between the potential and current, and and are the real and imaginary components of the impedance, respectively. Based on the equation ( 3 1 ) the electrochemical system should be perturbed by oscillating potential or curr ent wi th a significantly small value which is indicated in Figure 3 2. 16 PAGE 28 28 3 .2 E lectrochemical Impedance S pectroscopy of Electroc hemical R eaction For the current density of a Faradaic reaction of specie i can be expressed as a function of an interfacial potential V the surface concentration of bulk species C i,0 and surface c overage of adsorbed species k, as 15 (3 2 ) w here interfacial potential V is defined as ( 3 3 ) V m : potential of working electrode V 0 : potent ial in the electrolyte adjacent to the electrode The current density can be expressed in terms of a steady, time independent term and an oscillating term : (3 4 ) A Taylor series expansion about the oscillating term can be written as (3 5 ) w here is oscillating of interfacial potential is oscillating of surface concentration of bulk species and is oscillating of surface coverage. 3 3 E lectrochemical Impedance S pectroscopy M odel of System The current density of a single reversible reaction can be expressed from Butler Volmer equation : ( 3 6) PAGE 29 29 is widely adopted to describe the relationship between overpotential and current density. Where is n is number of electrons involved within reac tion, F is faraday constant, is rea ction rate constant of specie I is overpotential, defined as the difference between actual applied potential and equilibrium potential of specie i ,V i ,0 and is apparent transfer coefficient of specie I for cathodic and anodic reaction At very positive potentials, the cathodic term is n egligible, and the current den sity can be expressed by ( 3 7 ) Similarly, at very negative potentials, t he an odic term is n egligible, and the current den sity can be expressed by ( 3 8 ) With the equation above, the impedance model of Iron Dissolution can be developed. For equation ( 1 5 ) t he steady state current density is given by (3 9) f rom Equation ( 3 5 ), the oscillating curr ent density can be expressed as (3 10) a nd the faradaic impedance of Fe can be expressed as ( 3 1 1 ) f or equation ( 1 2), the steady state current density can be expressed as PAGE 30 30 (3 1 2 ) and For equation (1 3), the steady state current density can be expressed as (3 1 3 ) f or equation (1 4), the steady state current density can be expressed as (3 1 4 ) f or equation (1 2 ) assumed to be affected by mass transfer the oscillating current density is (3 1 5 ) and for equation (1 3 ) assumed to be affected by mass transfer the oscillating current density is (3 1 6 ) and for equation (1 4 ) assumed to be affected by mass transfer the oscillating current density is (3 1 7 ) f or reaction on working electrode the steady state current can be expressed as ( 3 1 8 ) and the oscillating current can be expressed as (3 19 ) PAGE 31 31 a nd the impedance response can be expressed as ( 3 2 0 ) a lso, if t he oxygen present in the system were assumed to react according to (3 2 1 ) t he corresponding steady state current density is given by (3 2 2 ) f rom Equation ( 3 5 ) the oscillating current density can be expressed as (3 2 3 ) For the reaction above depends on variation of concentration, to solve the relationships between oscillating component of the current density and the oscillati ng component of the interfacial potential second equation is needed T o derive the second equation the current density on the electrode surface can be used. For example, the current density of on surface electrode (3 2 4 ) c an also be expressed as oscillating concentration (3 2 6 ) w ith equation (3 15) and (3 2 6 ) can be eliminated and derived PAGE 32 32 (3 2 7 ) w here (3 28 ) a nd (3 29 ) F r om the same manner impedance of can be derived as (3 3 0 ) and for H + (3 3 1 ) and for O 2 ( 3 32 ) w here (3 33 ) and (3 34 ) PAGE 33 33 f or (3 35 ) and (3 36 ) For (3 37 ) and (3 38 ) wi th the oscillating current density on electrode surface, all the faradaic impedance responses can be derived. Finally, the net diffusion impedance of both film and convective diffusion can be derived from 171 (3 39 ) w here the inner term Z d,i i s the finite length di ffusion impedance corresponding to a porous layer of thickness and the outer term Z d,o may correspond to either a thickness of stagnant or a convective region of finite thickness In this case, the PAGE 34 34 effective diffusion impedance Z D ,net is a function of the time constant = / the ratio and the Schmidt number Sc. 3 3 Overall Cell Impedance Model From F igure 3 1, current density is the sum of Faradaic and charging current densities (3 40 ) Then oscillating terms of current density are (3 41 ) t he cell potential ca n be expressed as the sum of an ohmic contribution to the electrode potential and interfacial potential (3 42 ) t he oscillating cell potential is expressed as (3 43 ) A s the results, the effective impedance of cell is given by sum of charge transfer impedance, double layer capacitance and resistance of solution (3 4 4 ) f rom equation (3 44 ), the effective impedance response is sensitive to mass transfer, mainly caused by jets velocity. PAGE 35 35 Figure 3 1 A equivalent circuit of electrochemical impedance spectroscopy [ Referred to Mark E. Orazem 2006. Electrochemical Impedance Spectroscopy (Page 156 Figure 9 1 ). John Wiley & Sons, Inc ] Figure 3 2 Perturbation of an electrochemical system with a small sinusoidal signal at steady state, where and represent the potential and current oscillating at the same frequency and the phase difference between potential and current is PAGE 36 36 CHAPTER 4 CONSTANT PHASE ELEMENT 4.1 Introduction of Constant Phase Element Due to the complex of electrochemical reaction on electrode, t he impedance response rarely show the ideal response except ed for single electrochemical reactions. The time constant dispersion is caused by the variation of reactivity, current or potential. Time constant dispersion can be attributed to the surface heterogeneities such as grand boundary or the conductivity of oxide layers changed 30 32 Therefore, a constant phase element for a blocking electrode can be expressed as 18 (4 1) = 1 the system is described by a single time constant and the parame ter Q has units of capacitance; otherwise, Q has units of s / cm 2 The regression method in this thesis was presented by measurement model, discussed in C hapter 6.7 For measurement model, where C k is local capacitance can be expressed as (4 2) w here i s the permittivity of vacuum is local dielectric constant and is the thickness associated with element k The local resis tance can be expressed in terms of a local resistivity as (4 3) f rom equation (4 2) and (4 3) PAGE 37 37 (4 4) a nd local resistivity can be expressed as (4 5) A resistivity distribution model can be inferred from the regressed value of and C k. 4.2 Constant Phase Element Impedance Expression Assuming the dielectric constant is uniform, the impedance of the film can be written as 19 (4 6 ) w ith dimensionless position where is the thickness of film, equation (4 6 ) can be expressed as (4 7 ) i ntroduced e quation (4 8 ) (4 8 ) i n to equation (4 6) yields, (4 9 ) w here (4 10 ) (4 1 1 ) PAGE 38 38 U nder the condition that a general expression can be proposed as (4 1 2 ) w here (4 1 3 ) c ould be obtained in the range of Due to t he electrochemical impedance of an oxide layer re veals a n apparent CPE behavior in the high frequency range for equation (4 11) can be expressed as (4 1 4 ) t herefore, from inspection (4 1 5 ) t hus, (4 1 6 ) a nd (4 1 7) a lso, the effective capacitance of film can be expressed as (4 1 8 ) f rom equation (4 16), equation (4 17) yields PAGE 39 39 (4 1 9 ) t he typical value of for Fe 2 O 3 oxide is 2 and for Al 2 O 3 oxide is 0.5 PAGE 40 40 CHAPTER 5 EXPERIMENTAL METHOD 5 .1 Experiment S etup A schematic diagram of the impinging jet system is shown in Figure 5 1. A centrifugal pump with a variable speed motor drew the solution from tank and then jets it through a flowmeter into reaction cell chamber. T he electrochemical impedance instrument was Multichannel Electrochemistry Systems from Gamry Instruments. The instrument was controlled by PC 5.2 Instruments and M easurement M ethod The experiment cell chamber, displayed in Figure 5 2 consisted of a working electrode, a platinum counter electrode, a saturated calomel reference electrode, a submerged impinging jet, an exit port and a thermometer A tubing (3/8 was used as a jet nozzle to the electrode cell chamber. The working electrode was a 0 .188" diameter 1.25" long for 5LX52 pipe grade steel and 0 24 diameter 1.25" long for 5LX65 pipe grade steel with two ends flat embed ded in an insulating epoxy surface, fixed onto in the center of bottom plate of cell chamber. The surface of working electrode was polished by 800 grit SiC paper and rinsed with deionized water. The nominal chemical co mposition of the steel is given in Table 5 1 and Table 5 2 The 3 wt % brine was prepared using deionized water and biological certified grade sodium chloride The electrolyte was deareated by purging with 99.9 9 % N 2 and CO2 were purged for 1 hour before measurement and both were continuously purged during whole experiment process Temperature was maintained at 25 o C by Fisher Scientific Isotemp Refrigerated Circulator model 910 A saturated calomel reference electrode PAGE 41 41 was also located in the cell chamber. The oxygen c ontent of the solution was measured with a Cole Parmer oxygen meter model 5946 50. Impedance measurement was made in the frequency range 5KHz 0.05Hz and sinusoidal signal amplitude of 0.005V under Hybrid Electrochemical impedance spectroscopy measurement a t open circuit potential to ensure that the net system current equal to zero. Table 5 1 Nominal chemical composition of the 5LX52 steel used in this study Elements Al C Fe Mn P S Si V W t% 0.04 0.09 98.487 1.070 0.007 0.009 0.25 0.047 Table 5 2. Nominal chemical composition of the 5LX65 steel used in this study Elements Cr C Fe Mn P S Ni V Nb Ti Si W t% 0.4 0.09 97.1 2 1.6 0.01 5 0.00 5 0.25 0.05 0.05 5 0.02 0.4 PAGE 42 42 F igure 5 1. Schematic diagram of the impinging jet system. ( A ) C entrifugal pump( B ) T ank (C) Fl owmeter (D) R eaction cell chamber (E) Exit port [ Photo (s) courtesy of Yu Min Chen ] PAGE 43 43 F igure 5 2. Schematic illustration of reaction cell champer and important cell components ( A ) Saturated calomel electrode ( B ) Working electrode (C) Viewing port (D) Platinum counter electrode (E) Jets pipe [ Photo (s) courtesy of Yu Min Chen ] A B C D E PAGE 44 44 CHAPTER 6 RESULTS AND DISCUSSI ON S OF EXPERIMENTS The series of experiments consisted of measuring the open circuit potential for 15 minutes and then the impedance at open circuit potential for 10 minutes. This cycle was repeated until the total reaction time reach ed 450mins All experiments were run in the presence of brine with either an air saturated or CO 2 saturated impinging jet at different jet rates Also, the impedance change with different potential s versus the open circuit potential was me asured to determine whether the anodic or the catho d ic reaction was significant 6.1 Hydrodynamic Constant Determination The hydrodynamic constant, a s 1 can be derived from the limiting current of O 2 reduction on a nickel electrode. The limiting current s at different flow rates and parameters needed for equation (2 14) are in Table 6 1. From (2 14 ), th e hydrodynamic constant for the jet flow rates of 1 .1GPM, 2.0 GPM and 3.0 GPM are 140, 252 and 381 s 1 respectively. 6 2 Impedance Responds at Different Circumstance The i mpedance response s as a function of time of different reaction circumstances of 5LX52 pipe grade steel with the hydrodynamic constant 140 s 1 are presented in Figure 6 2 and Figure 6 3 T he impedance response s as a function of time of different reaction circumstances of 5LX65 pipe grade steel with the hydrodynamic constant 140 s 1 are presented in Figure 6 4 and Figure 6 5 At the very beginning of the reactions the impedance of the 5LX52 pipe grade steel in CO 2 saturated brine wa s smaller than with air saturated brine However, the impedance of 5LX52 pipe grade steel in CO 2 saturated brine increas ed with time In ot her words, the formation of FeCO 3 created a PAGE 45 45 diffusion barrier that inhibited the mass transfer of Fe 2+ and On the other hand the impedance of the 5LX52 steel with an air saturated impinging jet did not have obvious changed For 5LX65 pipe grade steel t he impedance response in air saturated brine decreased around 150 minutes ; after 150 minutes the impedance response increased with time. A s time pass ed, the reddish brown colloidal layer on the electrode was observed to full y cover the 5LX65 pipe grade steel. As f or the response of 5LX65 pipe grade steel with CO 2 saturated brine the impedance of 5LX 65 pipe grade steel continually increased with time T he surface of electrode was observed to change color from silver to gray. The formation of FeCO 3 also created a diffusion barrier on the 5LX65 pipe grade steel, which inhibited the mass transfer of Fe 2+ and 6 3 Determination of Dominated Impedance The effective impedance of Figure 6 1 can be expressed as ( 6 1) The dominated impe dance was determined by deviating from the open circuit potential for 5LX52 pipe grade steel and for 5LX65 pipe grade steel This experiment was done with either CO 2 saturated or a ir saturated brine both with a hydrodynamic constant 140 s 1 F rom Figure 6 6 and Figure 6 7 it is shown that the impedance of the cathodic Faradaic reaction is small er than that of the anodic Faradaic reaction for 5LX52 pipe grade steel In ot her words, the mass transfer of and and the chemical reac tion on the electrode surface are less significant than PAGE 46 46 the anodic reaction of the dissolving of Fe. Note that the impedance gradually increase d after the potential was changed, w hich means the FeCO 3 films increase d at both +0.05V and 0.05V. F rom Figure 6 8 and Figure 6 9 the impedance of the cathodic Faradaic reaction is smaller than that of the anodic Faradaic reaction for 5LX65 pipe grade steel as well From the discussion above, the corrosion reaction primarily depends on the steel not on the reaction environments. 6 4 Impedance Response with Different Jets Velocity From equation (2 1), the impinging jet V z component is a function of the hydrodynamic constant, a. The mass transfer to the electrode surface increase s with the jet s velocity, and f rom eq uation (2 5) the shear stress on the electrode surface is proportional to The impedance response s of 5LX52 and 5LX65 pipe grade ste el at 450 minutes under a CO 2 saturated jet with hydrodynamic constant s 140, 252, and 381 s 1 and under an air saturated jet with hydrodynamic constant 140 s 1 are presented in Figure 6 10 and Figure 6 11 The impedance responses at high frequency primarily depend on the surface phenomena and at low frequency primarily depend on mass transfer. For 5LX52 pipe grade steel case, presents in Figure s 6 10 show s that the velocity effect is not obvious. F or 5LX65 pipe grade steel case, presents in Figures 6 11, low freq uency impedance response s gradually decrease as the jet velocities increase The surface changes as function of time due to the change in the jet s velocity will be discuss ed in section 6 11. Also the characteristic length for transport from equation (2 22) is smaller for low jet velocity than for hi g h jet velocity. PAGE 47 47 6. 5 Error S tructure Analysis The error structure of an impedance measu rement can expressed as the difference between the observed value and a model value : 20 (6 2) where is the systematic error from the inadequacies of the model, is the s tochastic error from the expectation and represents the systematic experimental bias error that is not considered in the model inadequacies. The error comes from an integrat ion of time domain signals that contain noise from thermal fluctuations of resistivity thermal fluctuations of concentration and rates of electrochemical reactions, instrument sources, and the events of bubble formation in the electrolyte and pitting on the electrode surface. Bias errors are systematic errors for which a mean value is zero, which cannot be attributed to an inadequate descriptive model of the system. Generally, bias error comes from instrument artifacts and non stationary behavior of the system. For example, the impedance response of the low frequency pa rt may include the finite impedance behavior of wires and connectors. The reference electrode can also contribute to high frequency artifacts. Non stationary behavior of the system comes from the growth of surface films and changes in concentrations of r eactants or products in the electrolyte 15 A general model of the error structure 21 can be expressed as (6 3) PAGE 48 48 where and are the standard deviations of the real and imaginary impedances and R m is the resistance of the current measurement circuit. Also, and are constants determined for a specific potentiostat, set of measurement parameters, and an electrochemical sys tem. 6. 6 Complex Nonlinear Regression The object of complex nonlinear regression 22,23 is to fit complex data Z with a complex function with minimization of the sum of squares S(P) (6 4) where and represents the complex impedance measure at frequencies and and are the complex model s of the real and imaginary part s as a function of a parameter P. and are the square of error structure s from equation (6 3). To achieve the least square root regression, consider a general nonlinear function that h as nonlinear behavior with respect to parameters P k If the assumption that is twice continuously differentiable, a Taylor series ex pansion about a parameter set P 0 yields : (6 5) The optim um for P is found when f(P) has a minimum value. At the minimum, derivatives with respect to the parameter increments should be equal to zero; thus, PAGE 49 49 (6 6) equation (6 6) can be rearrange d to (6 7) where (6 8) and (6 8) From the equation above, the sum of square s for the real part is given by: (6 9) (6 10) and (6 11 ) Since the second term is le ss important than the first term, (6 12) equation (6 12) is used for the nonlinear regression. PAGE 50 50 6. 7 The Levenberg Marquardt Method The Levenberg Marquardt Method 22 24 is a compromise between the Gauss Newton and the Steepest Descent methods. F rom the Levenberg Marquardt m ethod Equation (6 6) can be arranged as (6 13) where l i s the intera c tion counter, is evaluated from equation (6 8), a nd is from equation (6 9). For Levenberg Marquardt Method is replace d by for j=k (6 14) for j k (6 15) where is a constant chosen to be sufficiently small to avoid overrunning the minimum. From the statements above, equation (6 14) can be expressed as (6 16) Equation (6 16) is the regression method used in this thesis. 6. 8 Measurement Model The Measurement model 25 for fitting function of equation (5 4) can be expressed as (6 17) W here R 0 is the resistance of solution, and are adjustable parameters of the Voigt element. The advantages of this measurement model are: 1. Freely adjustable parameters R k and k PAGE 51 51 2. Measurement model will satisfy Kramer Kronig relations. 3. With a sufficient number of parameters, the Voigt model is able to provide a statistically significant fit to a broad variety of impedance spectra 6. 9 The Kramers Kronig Relations The Kramers Kronig relations are integral equatio ns which constrain the real and imaginary components of complex quantities for systems that satisfy conditions of cau sality, linearity, and stability 26 29 I mpedance response as function of frequency can be expressed as (6 18) The application of Kramers Kronig Relations of impedance response is f or a complex function Z Z r jZ j analytic in the upper half plane which vanishes faster than as T he Kramers Kronig relations are given by (6 19) and (6 20) In principle, the Kramers Kronig relations can b e used to determine whether the impedance responses of a given system have been in fluenced by bias errors caused, for example, by instrumental artifacts or time dependent phenomena PAGE 52 52 6 10 Error Struc ture of 5LX52 and 5LX65 Pipe Grade Steel The error structure measurement was derived from the impedance response of 4 hours to 6 hours measurement with hydrodynamic constant 140, 252, and 381 with CO 2 saturated and hydrodynamic const ant 140 with air saturated of both 5LX52 and 5LX65 Pipe Grade Steel The error structure parameters: and are presented in Table 6 .1. The confidence intervals are from Monte Carlo simulation for 5000 times. To verify the Kramer Kronig relations the impedance measurements at 1 5mins are applied. From Figure 6 13 to Figure 6 21all the data are within the confidence interval. In other words, those data are satisfied Kramer Kronig relations excep t last five data of 5LX65 pipe grade steel in CO 2 saturated brine at a =140s 1 and last two data of 5LX52 pipe grade steel in air saturated brine with a=140s 1 Therefore, the impedance data did not satisfy Kramer Kronig relations, should be delete d 6.1 1 Monte Carlo Simulation Monte Carlo simulations are used to explore the manner in which the uncertainty in parameter esti mates is propagated through the model. T he 95.4% confidence interval for a model prediction was used to p rovide a quantitative criterion for rejection of experimental data corru pted by bias er rors. For a value for the impedance at certain frequency, Monte Carlo simulation 20 is expressed as: ( 6 2 1 ) W here is number of Voigt element in the measurement model. The parameters and stand for ( 6 2 2) PAGE 53 53 ( 6 2 3 ) ( 6 2 4 ) w here 2 +1unique with zero mean and a standard deviation of one were calcula ted for each evaluation of In this thesis, Monte Carlo calculation at each frequency was repeated for 5000 times. The mean and standard deviation above were calculated b y ( 6 2 5 ) a nd ( 6 2 6 ) Finally, the 95.4% confidence upper interval can be expressed as ( 6 2 7 ) and the lower interval can be expressed as ( 6 2 8 ) If the impedance data at all frequencies are within the 95.4% confidence interval, all data are satisfied Kramer Kronig relations. Otherwise, the data should be deleted. PAGE 54 54 6.1 2 Film Thickness Determination From equation (4 16) film thickness can be derived as (6 29 ) W here =12 for steel in air saturated brine and =24 for steel in CO 2 saturated brine F/cm, =450 cm. The film thickness as function of time for 5LX52 and 5LX65 pipe grade steel with hydrodynamic constant s 140, 252, and 381 s 1 with CO 2 saturated and hydrodynamic constant 140 s 1 with air saturated are presented in Figure 6 20 and 6 21. The C eff of the film of 5LX5 2 and 5LX65 pipe grade steel from equation (4 18) as function of time are presented in Figure 6 22 and 6 23 .Film thickness es in the air saturated cases are always thicker than in the CO 2 saturated case but the impedance responses are smaller for both 5LX5 2 and 5LX65 pipe grade steel. The films on 5LX52 pipe grade steel are always thi ck er than on 5LX65 steel in all case s but the impedance response s for 5LX52 pipe grade are always smaller than those of 5 LX65 pipe grade steel in all cases. The summary we can draw here is that 5LX65 pipe grade steel has better anti corrosion properties than 5LX52 pipe grade. Figure 6 1. Equivalent Circuit of electrochemical system. PAGE 55 55 Figure 6 2 Impedance response s of 5LX52 steel with air saturated at a=1 40 s 1 Figure 6 3 Impedance response s of 5LX52 steel with CO 2 saturated a=1 40 s 1 PAGE 56 56 Figure 6 4 Impedance response s of 5LX65 steel with air saturated at a=1 40 s 1 Figure 6 5 Impedance response s of 5LX65 steel with CO 2 saturated at a=1 40 s 1 PAGE 57 57 Figure 6 6 Impedan ce respon se s of 5LX52 steel at +0.05V and 0.05V vs. open ci rcuit potential with CO 2 saturated at a=1 40 s 1 Figure 6 7 Impedance response s of 5LX 52 steel at +0.05V and 0.05V vs. open circuit potential with air saturated at a=1 40 s 1 PAGE 58 58 Figure 6 8 Impedance responses of 5LX65 steel at + 0.1V and 0.1V vs. open circui t potential with CO 2 saturated at a=1 40 s 1 Figure 6 9 Impedance responses of 5LX65 steel at +0. 1 V and 0. 1 V vs. open circuit potential with air saturat ed at a=1 40 s 1 PAGE 59 59 Figure 6 10 Impedance response s of 5LX52 steel a=1 40 252 and 381s 1 with CO 2 saturated and a=1 40 s 1 with air saturated Figure 6 11 Impedance response s of 5LX65 steel a=1 40 252 and 381s 1 with CO 2 saturated and a=1 40 s 1 with air saturated PAGE 60 60 F igure 6 1 2 Impedance data, error structure and confidence interval of 5LX52 pipe grade steel with CO 2 saturated at a=1 40 s 1 F igure 6 1 3 Impedance data, error structure and confidence interval of 5LX52 pipegrade steel with CO 2 saturated at a=252s 1 PAGE 61 61 F igure 6 1 4 Impedance data, error structure and confidence interval of 5LX52 pipe grade steel with CO 2 saturated at a=381s 1 F igure 6 1 5 Impedance data, error structure and confidence interval of 5LX52 pipe grade steel with air saturated at a=1 40 s 1 PAGE 62 62 F igure 6 1 6 Impedance data, error structure and confidence interval of 5LX65 pipe grade steel with CO 2 saturated at a=1 40 s 1 F igure 6 1 7. Impedance data, error structure and confidence interval of 5LX 65 pipe grade steel with CO 2 saturated at a=254s 1 PAGE 63 63 F igure 6 1 8. Impedance data, error structure and confidence interval of 5LX65 pipe grade steel with CO 2 saturated at a=381s 1 F igure 6 19. Impedance data, error structure and confidence interval of 5LX65 pipe grade steel with air saturated at a=1 40 s 1 PAGE 64 64 F igure 6 2 0 Film thickness of 5LX52 pipe grade steel with CO 2 saturated at a=140, 252, and 381 s 1 and with air saturated at a=140 s 1 F igure 6 2 1 Film thickness of 5LX65 pipe grade steel with CO 2 saturated at a=140, 252, and 381 s 1 and with air saturated at a=140 s 1 PAGE 65 65 F igure 6 22 C eff of 5LX52 pipe grade steel with CO 2 saturated at a=140,252, and 381 s 1 and with air saturated at a=140 s 1 F igure 6 23 C eff of 5LX65 pipe grade steel with CO 2 saturated at a=140,252, and 381 s 1 and with air saturated at a=140 s 1 PAGE 66 66 Table 6 1 Limiting current and hydrodynamic constant of different flow rates Flow rates (GPM) 1.1 2.0 3.0 Limiting current (mA) 1 8. 21 24.47 30.0 5 H ydrodynamic constant (s 1 ) 140 252 381 Table 6 2 Error Structure Coefficient of 5LX52 and 5LX65 Steel Error structure coefficient 0 9 0 PAGE 67 67 CHAPTER 7 CONCLUSION From the impedance responses of 5LX52 and 5LX65 pipe grade steel, the corrosion reactio n rates of 5LX65 steel are slower than those of 5LX52 steel in all circumstance s The corrosion reaction pri marily depends on the steel not the environments and th e dissolved reaction of steel is more significant than the mass transfer of other species The jet s velo city effect s are compl ex. For both 5LX52 and 5LX65 pipe grade steel with an air saturated jet, red colloidal fluid was produced on the electrode. On the other hand for 5LX52 and 5LX65 pipe grade with a CO 2 jet, gray film was produced. B oth the mass transfer rate and shear stress influence the film thickness and impedance responses. F rom Kramer Kronig relations, the stability of impedance responses are reliable exce pt for the low frequency impedance response s of 5LX65 pipe grade steel with a CO 2 saturated jet at a=140 s 1 and 5LX52 pipe grade s teel with an air saturated jet at a=140 s 1 PAGE 68 68 LIST OF REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] PAGE 69 69 [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] PAGE 70 70 [29] [30] [31] [32] PAGE 71 71 BIOLOGICAL SKETCH Yu Min Chen re ceived his Bachelor of Science d egree in c hemical e ngi neering from National Taiwan University in June, 200 9 He came to U.S. in August 2010, and started his m aster s program in the fall 2010. He has been in the electrochemical impedance research group under the direction of Mark E. Orazem. He graduated in the f all semester 2011 after sp ending one and a half years being educated in chemical engineering |