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PAGE 1 1 CATHODIC PROTECTION FOR ON AND OFF SHORE STRUCTURE S By CHAO LIU 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 UNIV ERSITY OF FLORIDA 2012 PAGE 2 2 2012 C hao L iu PAGE 3 3 To m y parents and my grandparents PAGE 4 4 ACKNOWLEDGMENTS Here I would like to thank my advisor, Professor Mark E. Orazem, for his teaching and guidance. I thank Professor Jennifer Sinclair Curtis for her sup port as well I also want to thank every colleague in my group: Alok Shankar, Rui Kong, Ya Chiao Chang, Chris topher Cleveland, Salim Erol, Yan Yu, Yu min Chen, Darshit Shah and Pei han Chiu. PAGE 5 5 TABLE OF CONTENTS page ACKNO WLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIA TIONS ................................ ................................ ........................... 1 2 ABSTRACT ................................ ................................ ................................ ................... 13 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 15 2 LITERATURE REVI EW ................................ ................................ .......................... 17 Cathodic Protection and Stray Current Effects ................................ ....................... 17 Electrochemical Kinetics ................................ ................................ ......................... 18 Bare Steel Pipeline ................................ ................................ ................................ 21 Pipeline with Coatings ................................ ................................ ............................. 22 Cathodic Protection Methods ................................ ................................ .................. 23 Galvanic Anodes (Sacrificial Anodes) ................................ .............................. 23 Impressed Current Anodes ................................ ................................ ............... 24 3 MATHEMATICAL MODEL OF C ATHODIC PPOTECTION ................................ .... 29 Domains for the Flow of Current ................................ ................................ ............. 29 Soil Domain ................................ ................................ ................................ ...... 29 Internal Domain ................................ ................................ ................................ 30 ................................ ................ 31 Boundary Element Method ................................ ................................ ............... 32 Finite Element Method ................................ ................................ ..................... 33 Coupling FEM/BEM ................................ ................................ .......................... 33 4 RESULTS AND ANALYSIS ................................ ................................ .................... 34 Dimensional Analysis for Primary Current Distribution ................................ ............ 34 Stray Current Modeling ................................ ................................ ........................... 38 Stray Current Effects Due to a Single Anode ................................ ................... 38 Stray Current Effects Due to an Anode Bed ................................ ..................... 39 Rectifier War Modeling ................................ ................................ ............................ 40 Rectifier Wars in Soil Environment ................................ ................................ ... 40 Rectifier Wars in Seawater Environment ................................ .......................... 41 PAGE 6 6 Anode Distribution ................................ ................................ ................................ .. 42 Anode Distribution in Soil Environment ................................ ............................ 42 Anode Distribution in Seawater Environment ................................ ................... 44 5 CONCLUSIONS AND FUTURE WORK ................................ ................................ 73 LIST OF REFERENCES ................................ ................................ ............................... 75 BIOGRAPHICAL SKET CH ................................ ................................ ............................ 77 PAGE 7 7 LIST OF TABLES Table page 2 1 Parameters for some typical galvanic anodes ................................ .................... 26 4 1 List of variables affecting current distribution along a pipe ................................ 46 4 2 Physical and chemical properties of four different types of coatings .................. 46 4 3 Configuration of two pipes in stray current effect system due to a single anode ................................ ................................ ................................ ................. 47 4 4 Configuration of two pipes in stray current effect system due to an anode bed .. 47 4 5 Configuration of condition 1 for rectifier war in soil environment ......................... 47 4 6 nitial configuration of two pipes for rectifier war i n seawater environment .......... 47 4 7 ............. 47 4 8 Comparison between CP3D an ..... 48 PAGE 8 8 LIST OF FIGURES Figure page 1 1 Annual cost of corrosion of gas and liquid transmission pipelines ...................... 16 2 1 Cathodic protection system of buried steel pipeline. The shorter vertical rod represents anode, the longer horizontal rod represents pipeline. ....................... 27 2 2 Stray current resulting from cathodic protection ................................ ................. 27 2 3 Prevention of stray current corrosion by proper design ................................ ...... 28 4 1 Normalized resistance as a function of normalized anode distance ................... 49 4 2 Normalized resistance as a function of normalized depth of anode .................... 49 4 3 Normalized resistance as a function of normalized diameter of anode ............... 50 4 4 Normalized resistance as a function of normalized length of anode ................... 50 4 5 Scaled resistance as a function of normalized anode distance .......................... 51 4 6 Scaled resistance as a function of normalized depth of anode ........................... 51 4 7 Scaled resistance as a function of normalized diameter of anode ...................... 52 4 8 Scaled resistance as a function of normalized length of anode in different anode diameter conditions. ................................ ................................ ................ 52 4 9 Normalized resistance as a function of normalized anode distance with normalized depth of anode as a parameter ................................ ........................ 53 4 10 Scaled resistance as a function of normalized anode distance with scaled depth of anode as a parameter ................................ ................................ ........... 53 4 11 Normalized resistance as a function of nor malized anode distance with normalized diameter of anode as a parameter ................................ ................... 53 4 12 Scaled resistance as a function of normalized anode distance with normalized diameter of anode as a parameter ................................ ................... 54 4 13 Normalized resistance as a function of normalized anode distance with normalized length of anode as a parameter ................................ ....................... 54 4 14 Sc aled resistance as a function of normalized anode distance with normalized length of anode as a parameter ................................ ....................... 54 PAGE 9 9 4 15 Normalized resistance as a function of normalized depth of anode with normaliz ed anode distance as a parameter. The black line: d=10m; blue line d=70m, red line: d=200m. ................................ ................................ ................... 55 4 16 Scaled resistance as a function of normalized depth of anode with normalized anode distance as a parameter. The black line d=10m; blue line: d=70m, red line: d=200m. ................................ ................................ ................... 55 4 17 Normalized resistance as a function of normalized depth of anode with normalized diameter of anode as a parame ter ................................ ................... 55 4 18 Scaled resistance as a function of normalized depth of anode with normalized diameter of anode as a parameter ................................ ................... 56 4 1 9 Normalized resistance as a function of normalized depth of anode with normalized length of anode as a parameter ................................ ....................... 56 4 20 Scaled resistance as a function of normalized depth of anode with norm alized length of anode as a parameter ................................ ....................... 56 4 21 Normalized resistance as a function of normalized diameter of anode with normalized anode distance as a parameter Black line: d=10m; blue line: d =70m, red line: d=200m ................................ ................................ .................... 57 4 22 Scaled resistance as a function of normalized diameter of anode with normalized anode distance as a parameter ................................ ........................ 57 4 23 Normalized resistance as a function of normalized diameter of anode with normalized depth of anode as a parameter Black line: H a =1m; blue line: H a =2m, red line: H a =3m ................................ ................................ ..................... 57 4 24 Scaled resistance as a function of normalized diameter of anode with normalized depth of anode as a parameter ................................ ........................ 58 4 25 Normalized resistance as a function of normalized diameter of anod e with normalized length of anode as a parameter ................................ ....................... 58 4 26 Scaled resistance as a function of normalized diameter of anode with normalized length of anode as a parameter ................................ ....................... 58 4 27 Normalized resistance as a function of normalized length of anode with normalized anode distance as a parameter Black line: d=10m; blue line: d=70m; red line: d=200m ................................ ................................ .................... 59 4 28 Scaled resistance as a function of normalized length of anode with normalized anode distance as a parameter ................................ ........................ 59 PAGE 10 10 4 29 Normalized resistance as a function of normal ized length of anode with normalized depth of anode as a parameter Black line: H a =1m, blue H a =2m, red H a =3m ................................ ................................ ................................ .......... 59 4 30 Scaled resistance as a function of normalized length of anode with normaliz ed depth of anode as a parameter ................................ ........................ 60 4 31 Normalized resistance as a function of normalized length of anode with normalized diameter of anode as a parameter Black line: D a =0.1m; blue line: D a = 0.125m; red line: D a =0.15m. ................................ ................................ ......... 60 4 32 Scaled resistance as a function of normalized length of anode with normalized diameter of anode as a parameter ................................ ................... 60 4 33 Configuration of stray current effect system due to a single anode .................... 61 4 34 Potential distribution along the unprotected pipe in a stray current effect system due to a single anode ................................ ................................ ............. 61 4 35 Current density distribution along the unprotected pipe in a stray current effect system due to a single anode ................................ ................................ ... 62 4 36 A close up of current density distribution along the interested section of the unprotected pipe in a stray current effect system due to a single anode ............ 62 4 37 Configuration of st ray current effect system due to an anode bed ..................... 63 4 38 Potential distribution along the unprotected pipe in a stray current effect system due to an anode bed ................................ ................................ .............. 63 4 39 Current density distribution along the unprotected pipe in a stray current effect system due to an anode bed ................................ ................................ ..... 64 4 40 A close up of current density distribu tion along the interested section of the unprotected pipe in a stray current effect system due to an anode bed ............. 64 4 41 Configuration of condition 1 for rectifier war modeling in soil environme nt ......... 65 4 42 Comparison of potential distributions along pipe 1 before and after introducing pipe 2. Black solid line: before introducing pipe 2; Rose red dash line: after introducing pipe 2 ................................ ................................ ............... 65 4 43 Comparison of current density distributions along pipe 1 before and after introducing pipe 2. Black solid line: before introducing pipe 2; blue dash line: after introducing pipe 2 ................................ ................................ ....................... 66 4 44 Comparison of potential distributions along pipe 1 and pipe 2 respectively in condition 1. Black solid line: pipe 1; red dash line: pipe 2 ................................ ... 66 PAGE 11 11 4 45 Comparison of current density distributions along pipe 1 and pipe 2 respectively in condition 1. Black solid line: pipe 1; red dash line: pipe 2 ........... 67 4 46 Comparison of poten tial distributions along pipe 1 and pipe 2 respectively in condition 2. Black solid line: pipe 1; red dash line: pipe 2 ................................ ... 67 4 47 Comparison of current density distributions along pipe 1 and pip e 2 respectively in condition 1. Black solid line: pipe 1; red dash line: pipe 2 ........... 68 4 48 Potential distributions of pipe 2 in condition1and 2 respectively. Black solid line: pipe 2 in conditio n 1; blue dash line: pipe 2 in condition 2 .......................... 68 4 49 Visual configurations of condition 1, 2 and 3 for rectifier war modeling in seawater environment ................................ ................................ ........................ 69 4 50 Current density distributions of pipe 1 in condition 1, 2 and 3. Black solid line: pipe 1 in condition 1; blue long dash line: pipe 1 in condition 2; red short dash line: pipe 1 in condition 3. ................................ ................................ ................... 69 4 51 Potential distributions of pipe 1 in condition 1, 2 and 3. Black solid line: pipe 1 in condition 1; blue long dash line: pipe 1 in condition 2; red short dash line: pipe 1 in condition 3. ................................ ................................ ........................... 70 4 52 A close up of potential distributions along pipe 1 in condition 2 and 3. Blue long dash line: pipe 1 in condition 2; red short dash line: pipe 1 in condition 3 .. 70 4 53 Potential distribution along the pipe of 18,300m with two anodes connected. .... 71 4 54 Comparison of minimum number of anodes by using CP3D and Dwight Formula in soil environmen t respectively. Black solid line: CP3D; red dash line: Dwight formula. ................................ ................................ ........................... 71 4 55 Comparison of minimum number of anodes by using CP3D and Dwight Formula in seawater environment respectively. Bla ck solid line: CP3D; red dash line: Dwight formula. ................................ ................................ .................. 72 PAGE 12 12 LIST OF ABBREVIATION S BEM Boundary Element Method CP Cathodic protection CP3D Three dimensional cathodic protection simulation system CSE Copper Sulfate Electrode FEM Finite Element Method ICCP Impressed c urrent c athodic p rotection PAGE 13 13 Ab stract 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 CATHODIC PR OTECTION FOR ON AND OFF SHORE STRUCTURES By Chao Liu May 2012 Chair: Mark E. Orazem Major: Chemical Engineering Natural gas and liquid petroleum products have been transported by a n extensive network of steel pipelines all over the world Steel pipelin es are usually buried in soil or aquatic environment wh ere electrolyte contains oxygen, and then they are subject to corrosion. Corrosion even can happen under cathodic protection. One type of this corrosion i s caused by stray current effect Stray curren t s from the anodic part of the cathodic protection system are picked by a foreign pipe and result in localized corrosion at the site where stray current leaves from the foreign pipe. Thus, it is very important to optimize the design of cathodic protection system and design the methods to prevent the pipelines from corrosion caused by stray current s In the thesis, a CP3D numerical simulation model was used to simulate the stray current effects that happened in a cathodic protection system, understand the i nteraction behavior between the protected pipe and the unprotected pi pe in the system, and predict the position on the unprotected pipe where localized corrosion occurred M ethods of modeling stray current effects were then applied to simulate rectifier wa r in soil and seawater environment respectively. The mechanism that underlies rectifier PAGE 14 14 war s, in which interference of cathodic protection systems results in under protection, was clearly illustrated. In addition, simulations were used to calculate the min imum number of anodes needed to provide adequate cathodic protection in both soil and seawater environment s PAGE 15 15 CHAPTER 1 INTRODUCTION With the development of modern industries from the beginning of the twentieth century, increasing amount s of petroleum prod ucts and natural gas have been tran sported b y long steel pipelines The steel pipelines are usually buried in soil environment s (on shore environment) or aquatic environment (off shore environment) As these environments contain oxygen the steel pipelines and their surroundings constitute an electrochemical system where corrosion happens. Corrosion is one of main cause s of pipeline failures. It was estimated that the average annual cost of corrosion of infrastructure is $22.6 billion from 1997 to 1999 in U .S [1]. T he annual cost of gas and liquid transmission pipelines co rrosion is nearly $ 7.0 billion, as is shown in Figure 1 1. It is therefore essential to apply cathodic protection t o the buried pipelines and prevent them from corrosion. However, even if c athodic protection is applied, se vere pipeline accidents may happen due to inadequate cathodic protection. For example, in 1996, a pipeline transporting fuel oil ruptured where the ruptured section of the pipeline crossed a river in South Carolina [2] 957 ,600 gallons of fuel oil came ou t of the ruptured pipeline and flowed into the river. This accident killed nearly 35,000 fish and resulted in an economic loss more than $20.5 million The subsequent investigation after the accident indicated that the corro sion problem had already happened before the accident, and that the river current had washed away the coating of the ruptured section. This accident was attributed to the negligence and inadequate cathodic protection PAGE 16 16 Figure 1 1 A nnual cost of corrosion of gas and liquid transmission pipelines PAGE 17 17 CH APTER 2 LITERATURE REVIEW Cathodic P rotection and Stray Current Effects It is essential to understand the corrosion behavior in a cathodic protection system and to tak e corresponding meas ures to prev ent corrosion of the pipelines The first step is to know what cathodic protection is. Cathodic protection is a method in which the corrosion of a metal surface is controlled by letting it be the cathode of an electrochemical cell A n anode tha t is connected to the pipeline is applied to provide external current as is shown in Figure 2 1 There are mainly two ways to apply cathodic protection to a steel pipeline [ 3 ]: 1) by applying an external power supply (Impressed current cathodic protection: ICCP), or 2) by placing it in contact with a more electrochemically active metal to form a galvanic couple In the first method, a rectifier is usually used to provide power supply. I n the second method, the anode is called a sacrificial anode or galvanic anode since it is consumed during the cathodic prot ection The second step is to understand a typical corrosion behavior in cathodic protection system s associated with s tray current effects. Stray currents may accompany with impressed current cathodic pr otection system s in the manner shown in Figure 2 2 In Figure 2 2 a foreign steel pipe is introduced close to the cathodic protection system S tray currents from the anode of the cathodic protection system can flow into a foreign pipe. Th e site of the for eign pipe where stray currents leave will experience localized corrosion The solution to prevent stray current effects is to use electrical bonding to connect the pipe and the tank as is shown in Figure 2 3 PAGE 18 18 Electrochemical Kinetics In order to develop a mathematical model describing cathodic protection of the steel pipelines, it is essential to know the boundary conditions at the pipe steel and anode surface where electrochemical reactions are involved. Here the Butler Volmer equation is applied, which i s one of the most fundamental relationships in electrochemical kinetics. It demonstrates how the electrode current dep ends on the electrode potential [ 4]. Bockris and other researchers indicated that the rate of dissolution and deposition of Iron depends o n p H value [5] There are several mechanisms discussed by Bockris [ 5 ]. Since b uried structures under cathodic protection are in soil form alkaline environments [ 6 ], the mechanism for the dissolution of iron in this case can be written as (2 1) Here R.D.S. means rate determining step. This reaction is followed by (2 2) By c ombining equation ( 2 1 ) and ( 2 2 ) the net equation ( 2 3 ) can be obtained as (2 3) The deposition of iron from ferrous hydroxide can be represented as (2 4) or, after introduction of equation (2 3), as (2 5) Bockris and other researchers also described the anodic current density in terms of hydroxi de ion activity and electrochemical potential as [5] PAGE 19 19 (2 6) w here is the kinetic rate constant, is the activity of ions, is the transfer coefficient, is potential difference between metal and solution ( ), is is the Gas Constant and is the temperature of the electrochemical system. Here, the activity of ions and pH are in a linear relationship. The expression of cathodic current can be written as (2 7) w here is t he activity of Fe 2+ ions. The net current density can be expressed as [ 4 ] (2 8) The e quilibrium potential V 0 can be obtained by setting equation ( 2 8 ) equal to zero and solving for (2 9) The exchange current density can be obtained by putting equation ( 2 9 ) into equation ( 2 6 ) and solving for (2 10) Putting equation ( 2 9) into equation ( 2 10 ) yields (2 11) E quation ( 2 8 ) can be rewritten in terms of the exchange current density as PAGE 20 20 ( 2 12) w here a and c are Tafel slopes (2 13) (2 14) and and are standard potentia l s for anodic and cathodic reaction s respectively. In a practical corrosion system, such as corrosion of steel pipelines, the anodic reaction is (2 15) Th is is often accompanied by two cathodic reactions: one is called the oxygen reduction reaction (2 16) The other possible cathodic protection is called the hydrogen evolution reaction (2 17) The potential required for oxygen reduction reaction is more positive than that for hydro gen evolution reaction. T here are many papers which illustrate the mechanism of the hydrogen evolution reaction (HER) [ 7 1 1 ] T he hydrogen evolution cur rent density can be written as (2 18) PAGE 21 21 Thus, the total current can be expressed as the sum of net current density with respect to dissolution of metal, oxygen reduction reaction and hydrogen which is shown in equation ( 2 19 ) (2 19) The corrosion potential is the potential difference between a freely corroding surface and a reference electrode. We can obtain the corrosion potential by setting equa tion ( 2 19 ) equal to zero It should be noticed that is different from equilibrium potential which is shown in equation ( 2 9 ) since there is more than one reaction which occurs in a freely corroding system [1 2 ]. Bare Steel P ipel ine If a numerical method is used to build a corrosion model, equation ( 2 19 ) can be applied to describe the kinetics at the boundary. In order to simplify equation ( 2 19 ) some terms which are out of potential range of interest can be cancelled out. If a mass transfer limitation factor is considered, the total current density will be written as (2 20) w here is the mass transfer limited current density for oxygen reduction, is the potential difference between metal and solution. Nisoncioglu was the first to consider mass transfer limitation into this expression of total current density [1 3 1 5 ]. Yan and other researchers also used this total current density expression in a nu merical PAGE 22 22 simulation to determin e potential and current density distribution along a cathodically protected pipeline in artificial seawater numerically [16] Equation (2 20) was also applied to describe corrosion of bare steel in steady state soil condition [17] It is noticed that there is no mass transfer limitation term for hydrogen evolution reaction in equation ( 2 20 ) because it was assumed that adequate water exit in the vicinity of steel pipe to maintain hy drogen evolution reaction [1 2 ]. Pipeline with C oatings C oatings are needed to be applied to the metal surface. There are t hree common types of coatings : organic barrier coatings, chemically active coatings and sacrificial metallic coatings [18] Of these three types of coatings, organic barrier coati ngs, especially polymers are usually used. A coating is considered to be barrier of ions and oxygen transportation. If diffusion barrier effect of the coatings is considered, the equation ( 2 20 ) will be modified as: (2 21) w h ere is the effective surface area available for reactions, is the potential at the underside of the coating just above the steel and block is the reduction to the transport of oxygen through the barrier [1 2 ]. This form was published by Riemer and Orazem [1 9 20 ]. Orazem and Kenelley expressed the potential drop through the coating as (2 22) PAGE 23 23 w here is the potential in the electrolyte next to the coating, the resistivity of the coating and is the thickness of the coating. S ubstitute equation ( 2 22 ) into equation ( 2 21 ) (2 23) can be obtained by applying the Newton Ralphson method. If is calculated, the current density can be obtained by using equation ( 2 22 ) Cathodic Protection Methods Anodes experience the similar electrochemical process as t he steel pipelines do. In cathodic protection, both galvanic anodes and impressed current anodes can be applied. Galvanic Anodes (Sacrificial Anodes) Galvanic anode s are more electrochemically active than the metal pipeline. The electrical driving force va ries with materials of the anodes, so it is very important to choose the proper anode in different en vironments. In soil environment, in which larger driving force is required, zinc and magnesium ar e used. In seawater environment, in which smaller driving force is needed, aluminum is used [ 18 ]. Riemer [1 2 ] introduced a model for curr ent density in a galvanic anode (2 24) w here is the mass transfer limited current density with respect to reduction of oxygen. is the potential in the electrolyte next to the anode surface, is the equilibrium PAGE 24 24 corrosion potential, and is the Tafel slope for the anodic reaction. Table 2 1 give s some parameters for different types of galvanic anodes. Impressed Current Anodes Impressed current systems depend on an external power source to provide current. A direct current (DC) rectifier is usually used. The negative terminal of the rectifier is c onnected to the steel pipeline and the positive terminal of the rectifier is connected to a dimensionally stable anode [1 2 ]. T he rectifier provides a larger potential difference (electrical driving force) than provided by sacrificial anodes Thus, impress ed current cathodic protection system s use fewer anodes than galvanic cathodic protection system s when protecting the same section of the pipe. Since dimensionally stable anode s are applied in impressed current cathodic protection system s the anodic react ion cannot be dissolution of metal, the most possible anodic reactions will be (2 25) a nd (2 26) In impressed current anode system, the potential that supplied by the rectifier is considered, so eq uation ( 2 24 ) is modified to be (2 27) w here is the voltage added by the rectifier, is the potential of the anode, is the potential in the ele ctrolyte just next to the surface of the anode, is the equilibrium potential for evolution of oxygen, and is the Tafel slope for the oxygen evolution PAGE 25 25 reaction. If the system is in a chloride ion domina n t environment, equation ( 2 27 ) will be written as (2 28) w here is the equilibrium poten tial for evolution of chloride and is the Tafel slope for the chloride evolution rea ction. PAGE 26 26 Table 2 1 P arameters for some typical galvanic anodes Anode type E eql (mV CSE ) i O2 2 ) Al 1.0 60 1.0 Zn 1.1 60 1.0 Mg(Standard) 1.5 60 1.0 Mg(High p otential) 1.75 60 1.0 PAGE 27 27 Figure 2 1 Cathodic protection system of buried steel pipeline. The shorter vertical rod represents anode, the longer horizontal rod represents pipeline. Figure 2 2 Stray current resulting from cathodic protection PAGE 28 28 Figure 2 3 Prevention of stray current corrosion by proper design PAGE 29 29 CHA PTER 3 MATHEMATICAL MODEL OF CATHODIC PPOTECTI ON Domains for the Flow of Current In practical cathodic protection for pipelines, the potential and current density var y along the metal structures and the electrolyte adjacent to their surface. T he current de nsity and potential distribution s in the soil and along the pipe influence cathodic protection. Hence, there are two different domains for flow of current: the soil domain and the internal domain [1 2 ]. Soil Domain The boundary of the soil domain is along w ith the surfaces of the steel pipeline and anodes. As is discussed in Chapter 2 expressions for current density depend on the pipe surface property and on the materials of anodes, in other words, the boundary conditions for the soil domain vary with the k inetics involved The the soil domain. Newman gives a detailed [21] The flux density of each dissolved species in a dilute electrolytic solution is written as (3 1) w here is the flux density of species is the charge number of species is the mobility of species is the Faraday Constant, is the concentration of species is the electric field, is the diffusion c oefficient of species is the concentration gradient of species and is the fluid velocity. Here and are vectors. Equation ( 3 1 ) applies for dilute electrolytes. PAGE 30 30 The current density can be expressed in terms of flux as (3 2) Substitut ion of equation ( 3 2 ) in to equation ( 3 1 ) yields (3 3) The last term can be cancelled out in the equation because of electroneutrality. The assumption that there are no concentration variations in the solution is made, so the second term of equation ( 3 3 ) is equal to zero. Finally, equation ( 3 3 ) reduces to (3 4) w here (3 5) Equation ( 3 4 ) applies when there are no graduate concentration gradients in electrolyt es. The expression of conservation of charge gives (3 6) Substitut ion of equation (3 4 ) into equation ( 3 6 ) yields (3 7) which is know n Internal Domain The i nternal domain con tains the internal pipe metal, the anode metal and the connecting wire between anodes and pipelines [1 2 ]. The current flow in the internal domain is governed by the three dimensional Laplace equation [1 2 ] i.e., PAGE 31 31 (3 8) w here is the potential difference between the potential of the metal and reference value and is the material conductivity. The conductivity is not always a constant. In some situat ions, the potential drop in internal domain can be expressed as [1 2 ] i.e. (3 9) w here is the wire resistance, is the electrical resistivity, is the length of wire, and is the cross sectional area. Two numerical methods were element method and finite element method. The b oundary element method is used to solve for soil domain with nonlinear boundary condition. Brebbia was the first to use weighted residual techniques to solve for potential with the boundary element method. [22]. Aoki simplified the corrosion behavior in the simple nonlinear boundary conditions and solved it by using the boundary element method [23]. Aoki also estimated the optimum impressed current anode locations and optimum current output from the anode by applying the boundary element method [24] The f in ite element method is used in internal domain. This idea was first brought by Brichau and other researchers [25]. They linked the finite element method with the developed boundary element method solution in soil environment s to illustrate cathodic protecti on numerically. FEM/BEM coupling approach is applied at the interface between soil domain and internal domain [1 2 ]. PAGE 32 32 Boundary Element Method A symmetric Galerkin Boundary Element Method [26] is applied to the constant boundary condition since the direct Bo undary Element Method will create non symmetric matrices, and fast iterative method s cannot be employed to solve the resulting linear PDE equation The boundary element formulations in this method [12] can be written as (3 10) a nd (3 11) w here and represent the and source element respectively, is the boundary of the domain, is the shape function, is a constant, is the outward normal vector to the surface of the domain, is the potential of electrolyte, is the boundary of the domain, and is the Green function However, the symmetric Galerkin Boundary Element Method does not work for nonlinear boundary conditions, so the dir ect Boundary Element Method is applied to a surface that can be divided into individual finite elements. The form of this method can be written as (3 12) More detail is provided by Riemer [12]. PAGE 33 33 Finite Element Method The formul a used in this type of Finite Element Method [12] is (3 13) w here is the element, is the thickness of the steel, i s the domain of parent elements, is the shape function, is a constant, is the Jacobian. is the shell element, is the weighing function, is the outward normal vector to the surface of the domain, and is the potential of metal. Coupling FEM/BEM The formula applicable at the interface between the soil domain and inte rnal domain [12] is written as (3 14) w here these parameters are described in the above two sections. More detail is provided by Riemer [12]. PAGE 34 34 CHAPTER 4 RESULTS AND ANALYSIS Dimensional Analysis for P rimary C urrent D istributi on The Buckingham method was used in dimensional analysis [27] It is a method of obtaining the important dimensionless numbers constructed by the original variables. This method states that if a certain number, of physical var iables are involved in an equation, and the units of these physical variables are given in terms of fundamental unit s, then the equation can be expressed in terms of ( ) independent dimensionless variab les. It is essential to understand the variables which a ffect the current density distribution along a single pipe. There are nine variables involved in the current distribution which are shown in the T able 4 1. By applying the Buckingham method, the relat ionship between these nine variables can be written as (4 1) w here is the normalized resistance, is the normalized anode distance, is the norma lized diameter of the pipe, is the normalized depth of the pipe, is the normalized diameter of the anode, is the normalized length of the anode, and is the normalized depth of the anode. The n ormalized resistance is a function of the other six normalized numbers. PAGE 35 35 For a primar y current distribution, the kinetic resistance is neglected since the ohm ic resistance dominates. Thus the resistance can be e xpressed in terms of as (4 2) Equation ( 4 1 ) may then be modified as (4 3) Among these variables, and do not have a significant impact on the resistance ; whereas, and are dominant variables. and can be proved to be in significant by running the CP3D simulation. By altering the value of or and keeping the rest of the variables fixed, it can be observed that the current does not change significantly. In order to get the relationship between the normalized resistance and the dimensionless number related to the anode properties, the first step was to specify and which were specified to be 0.1m and 1m respectively, so the normalized resistance was controlled by the other four dimensionless variables. The length of pipe was chosen to be 6000m and the soil resistivity was chosen to be 10,000 ohm cm. The second step was to scale the normalized resistance. A proper method was to divide it by another normalized resistance which is obtained by Dwig formula was used to calculate the resistance of a vertical rod. It is written as (4 4) PAGE 36 36 w here is the soil resistivity, is the length of an anode, and is the diameter of the anode. Under the condition specified above, the resistance calcula formula is (4 5) The corresponding normalized resistance can be written as (4 6) Thus, a scaled resistance R scale can be defined as (4 7) F rom the p revious analysis, and are dominant variables and their effect s on the current density distribution along the single pipe can be obtained from the relationships between normalized resistance and the four normalized dominant variables respectively. The simulation used the base condition of =6000m, =0.3m, =10m, = 0.1m, = 1m = 1m, the pipe with equal potential of 1V T he potential difference between pipe and anode is always equal to 1V The process of modeling was : 1) Increase keeping and fixed (Figure 4 1) 2) Increase keeping and fixed (Figure 4 2) 3) Increase keeping and fixed (Figure 4 3) 4) I ncrease keeping and fixed (Figure 4 4) From these four PAGE 37 37 rela tionships, it was concluded that: 1) normalized resistance increase s with the anode distance initially and then remains stable. The probable explana tion is that more ohm ic resistance is added between anode the pipe if the anode distance increases. 2) Normalized resistance deceases sharply as the depth of anode goes u p and then remains stable. If the depth of anode is increased, more current will come out of the top of the anode and go to the pipe, and the corresponding normalized resistance will decrease. 3) The normalized resistance deceases when normalized diameter of anode increases. The reason is that the dimension of the anode will expand with inc reasing diameter of the anode. 4) The normalized resistance decreases as normalized length of anode increases. The explanation is the same with observation 3). In addition to obtain ing the relationship between normalized resistance and anode variables, th e relationship between scaled resistance (normalized resistance divided by Dwight fo rmula) and the anode variables was also needed since it is essential to compare the simulation results with analytical solution. The four relationships are shown from Figur e 4 5 to Figure 4 8. The corresponding conclusion s can be obtained: 1) The calculate r esistance is closer to that provided by the Dwight formula at a larger anode distance s 2) The calculated r esistance is closer to that provided by the Dwight Fo rm ula at s maller depth of anode. 3) The calculated r esistance is closer to the that provided by the Dwight Formula at smaller and larger diameters of anode respectively. 4) The calculate r esistance is closer that provided by the Dwight Formula at a larger length s of anode. Particularly, the scaled resistance increases with normalized length of anode under the condition of 0m < <0.8m while it decre ases initially and then increases under the condition of PAGE 38 38 T he base condition was changed to different sets of new conditions such that the relationships between resistance and one anode variable were obtained under different sets of another anode variable, keeping the r emaining two anode variable s fixed (Figure 4 9 to Figure 4 32 ). From the se figures, it is obvious that and a ffect the resistances more than and do. Particularly, for the relationship betwee n the scaled resistance and the normalized diameter of anode for different lengths of anode, the three curves intersect at the section of larger diameter of anode because the scaled resistance decreases at the section of smaller length of a node when normal ized diameter of anode is large. Stray C urrent M odeling As is discussed in Cha pter 2, corrosion caused by stray cur rent effects may be observed in cathodic protection systems. The corrosion level on the pipes depends on the coating properties of the pipes. In CP3D software, four typical coating properties are involved which are shown in Table 4 2 especially, for the pipes with coating A (aged bare steel pipe) and coating B ( fresh bare steel pipe), there are actually no coating films present on the surface of the pipes Two kinds of stray current effects were modeled: 1) stray current effects due to a single anode; and 2) stray curr ent effects due to an anode bed. Stray C urrent E ffects D ue to a S ingle A node Table 4 3 shows the config uration of the pipes in a stray cur rent effect system due to a single anode. The anode which was c onnected to the protected pipe ha d dimensions : =0.5m, =0.2m, =1m, =10m, an d was considered to be impressed current anode with an applied voltage of 8V. The visual con figuration is PAGE 39 39 shown in Figure 4 33 T he blue pipe represents the protected pipe; whereas, the red pipe represents the unprotected pipe. From Figure 4 33 it is clea rly seen that stray current s which c a me from the anode w ere picked by the unprotected pipe (foreign pipe). The potential and current density distribution along the unprotected pipe are shown in Figure s 4 34 and 4 35 respectively. The valleys both in the tw o figures are related to the site at the foreign pipe whe re stray currents from the anode entered A peak in Figure 4 35 can be clearly seen at the site of unprotected pipe which is associated with the cross over section of two pipes. A close up profile is shown in Figure 4 3 6 T he peak represe nts section where stray currents exited the unprotected pipe. Thus, this section tends to be more cor rosive than the other sections along the unprotected pipe. Stray C urrent Effects D ue to an A node B ed The configurati on of this stray current effect system due to an anode bed is shown in Table 4 4 Each anode in the anode bed ha d the dimensions : =0.5m, =0.2m, =1m, d 1,2,3 =0.012m, 0.016m, 0.0 2m, and was considered to be impressed current anode with impressed voltage of 4V. A visual configuration is shown in Figure 4 3 7 w here the blue pipe represents the protected pipe and the red on e represents the unprotected pipe. The potential and current density distributions along the unprotected pipe are shown in Figure s 4 3 8 and 4 3 9 respectively. Just like the analysis for stray current effects due to a single anode, the valleys both in the two figures are related to the site at the unprotected pipe wh ere stray currents from the anode bed c a me in and the peak in Figure 4 40 represent s the site where stray currents exited the unprotected pipe. This section is also more cor rosive than the other sections along the unprotected pipe. PAGE 40 40 Rectifier War Modeling The method of modeling stray current effect s was extended to a more complex situation: rectifier war s The rectifier war is a term of describing corrosion happened between two cathodic protection systems. It is caused by the potential difference of the cat hodic protection o f two pipes. Here, the criteri on that 850mV CSE 1200mV CSE for adequate cathodic protection was a pplied Rectifier Wars in Soil E nvironment For the purpose of the present calculations, the r ectifier war modeling in a soil environm ent start ed with condition 1. The c onfiguration of condition 1 is shown in Table 4 5 The two pipes in condition 1 had the same properties and experienced the same cathodic protection. The corresponding visual configuration is shown in Figure 4 41 The pot ential and current density distribution s along pipe 1 and pipe 2 in condition 1 were obtained by CP3D calculations For pipe 1, a comparison of the potential and current density distribution s before and after introducing pipe 2 is shown in Figure s 4 4 2 and 4 4 3 respectively The valleys that appear in both figures were associated t o the site of pipe where anodes were connected. T he peaks indicate the interference between two pipe s but the interference was not very strong because the potential difference of the peak is small in Figure 4 4 2 A comparison of potential and current distributions between pipe 1 and pipe 2 are shown in Figure s 4 4 4 and 4 4 5 respectively. These two figures indicate that pipe 1 and pipe 2 nearly experience the same cathodic protect ion. Then, condition 1 was changed to condition 2, where the impressed voltage of cathodic protection on pipe 1 was increased t o 5.8V and cathodic protection on pipe 2 was fixed The new potential and current density distribution s in condition 2 are show n in Figure s 4 4 6 and 4 4 7 respectively These two figures indicate that pipe 1 PAGE 41 41 experience d more cathodic protection than did pipe 2 since the potential and current density distributions along pipe 1 were more negative than that along pipe 2. In conditio n 2 corrosion b egan to occur on the site of pipe 2 which is associ ated with the cross over section. This point can be clearly illustrated by Figure 4 4 8 which provides a comparison of potential distributions of pipe 2 in two conditions. The peak, which w as above 850mV CSE in condition 2 plot indicates that the cathodic protection difference between the two pipes may result in the localized corrosion on the pipe which has less cathodic protection at the cross over section. Rectifier War s in Seawater Env ironment For the purpose of the present calculations, the r ectifier war modeling in seawater environment started with condition 1. The c onfiguration of condition 1 is shown in Table 4 6 In condition 1, only pipe 1 was installed in the system, and two anod es with impressed voltage s of 7.3V provided cathodic protection to pipe 1 For condition 2, pipe 2 was introduced to the system which also was connected to two anodes with impressed voltage s of 7.3V Finally condition 2 was changed to co ndition 3. In cond ition 3, the potentials of the anodes connected to pipe 2 was increased to 10V, while the potentials of the anodes connected to pipe 1 remained at 7.3V The process of this modeling is shown in Figure 4 49. Here only the current density and potential distr ibutions of pipe 1 (Figure s 4 50 and 4 51 ) were taken into account since they show ed directly the localized corrosion due to the rectifier war In Figure 4 51 the potential peaks in condition 2 and 3 were both above the level of 850mV CSE, which indicate localized corrosion. Also the current densities in condition s 2 and 3 were more positive than in condition 1 at peak area in Figure 4 51 These two figures indicate that: 1) introducing pipe 2 will result in localized corrosion on the pipe 1 at the cross over PAGE 42 42 sections and the corrosion is caused by interference between two pipes 2) I ncreasing cathodic protection on pipe 2 will intensify localized corrosion that has already occuring on the pipe 1. This point can be further illustrated by Figure 4 52 An o de Distribution It is important to understand the anode distribution for a certain length of pipe. The most important factor in the determination of anode distribution is the number of anodes. Inadequate numbers of anodes will result in corrosion of the pi pe; whereas, s uperfluous anodes, especially impressed current anodes will result in unnecessary energy loss. Thus, it is essential to determine the minimum number of anodes required to prov ide sufficient cathodic protection. Anode Distribution in S oil E nvi ronment Th e first step to establish an anode distribution model was to specify the base condition s The dimensional analysis indicated that the current density distribution is affected by the soil resistivity and anode properties. Thus, i n this model, the base conditions were : = 10,000 ohm cm, = 1m, = 0.1m, = 1m and = 40m. Th e anode used in this model was a high performance M agnesium anode. The pipe dimensions were: = 0.3m and = 1m T h e coating property of the pipe was Coating C The second step was to calculate the current output from the single anode, which can be obtain e d by (4 8) The potential range for a system under adequate cathodic pro tection is 850 mV CSE to 1200mV CSE This means that the critical value of the off potential is 850 mV CSE i n PAGE 43 43 order to get mini mum number of anodes. The corresponding driving potential for activation of the cathodic protection was (4 9) Thus, the current output from a single anode is (4 10) The third step was to calculate the total current required to protect the pipe. The equation for calculation of total current was written as (4 11) whe re is the total area of pipe, is the current densi ty and is the length of the pipe. Finally, the minimum number of anodes required was written as (4 12) The current density, can be obtained b y implementing CP3D simulati on. For a pipe with a length of 18,300m at least two anodes were needed to obtain potential range which was close to a critical value of 850mV CSE The o ff potential distribution along the pipe is shown in Figure 4 53 T he corresponding minimum current d ensity for Poor 20mil FBE pipe was (4 13) In order to verify accuracy of the value o f the minimum current density, the results obtained by implementing CP3D software w ere compared with those obtained by ap la, shown in Table 4 7 Figure 4 54 gives a vivid comparison PAGE 44 44 between the CP3D simulation and the It is observed that the plots of these two methods almost overlap. In conclusion, the minimum current density required to protect Poor 20mil FBE pipe is under the initial conditions specified. Anode Distribution in S eawater E nvironment The base condition for anode distribution determination model in seawater environment was different from that in soil environment: = 20 ohm cm, =1m, =0.1m, = 1m and = 40m. The anode used in this model was an i mpressed current anode with impressed potentia l of 4V. So for the pipe, = 0.3m, = 1m, and the coating property of the pipe was Coating A Here the limiting current density for oxygen reduction of Coating A was changed to 9 in seawater environment. The second step was to calculate the current output from the single anode using the Dwight formula (4 14) An i mpressed voltage of 4V was provided by a rectifier in the cathodic protection system, bu t the effective potential added between the anode and the protected pipe was less than 4V. This result can be explained by using CP3D. For the same configuration of cathodic protection system, when impressed voltage decreased to 0, the potential difference between the anode and the pipe was e qual to ( 0.85 0.382) V, and the anode became the cathode in the electrochemical system. This result shows that, if 4V was applied, the actual driving potential between the anode and the pipe was : (4 0.85 0.382 ) V 0.85V= 1.918V Thus, the current output from a single anode was PAGE 45 45 (3 10) This result is used to estimate the minimum numbers of anodes. The third step was to calculate the minimum current density needed. Using the same strategy in anode distribution in soil environment, the minimum current density in this situation was In order to verify the accuracy of the value of this minimum current density, the result obtained by implementing CP3D software was co mpared with those by applying the as is shown in Table 4 8 Figure 4 55 la in seawater condition It is evident that the plots of these two methods overlap. In conclusion, t he minimum current density required to protect aged bare steel pipe is under the base condition specified. PAGE 46 46 Table 4 1. List of variables affecting current distribution along a pipe Parameter Definition L L ength of the single pi pe D L D iameter of the single pipe H L D epth of the single pipe L A L ength of the anode D A D iameter of the anode H A D epth of the anode D D istance between the single pipe and the anode R R esistance of the anode and single pipe system Soil resistivity Table 4 2 Physical and chemical properties of four different types of coatings Coating property Coating A Coating B Coating C Coating D Coating Resistivity *10 8 (ohm cm) 2 5 0 Coating Thickness (mm) 0.508 0.508 Oxygen Blocking (%) 99 9 9.9 Corrosion Potential (mV CSE ) 520.7 457.4 635.7 654.3 E Fe (mV CSE ) 522 522 522 522 Fe (mV/ decade) 59 62.6 62.6 62.6 I O2 2 ) 1.0 5 10.76 1.0 5 1.0 5 E O2 (mV CSE ) 172 172 172 172 O2 (mV/ decade) 61 66.5 66.5 66.5 E H2 (mV CSE ) 942 942 942 942 H2 (mV/ decade) 132.1 132.1 132.1 132.1 PAGE 47 47 Table 4 3 Configuration of two pipes in stray current effect system due to a single anode L D L H L C oating property Protected pipe 100m 0.3m 1m Coating C Unprotected pipe 1,000m 0.3m 1m Coating A Table 4 4. Configuration of two pipes in stray current effect system due to an anode bed L D L H L C oating property Protected pipe 200m 0.3m 1m Coating C Unprotected pipe 1,000m 0.3m 1m Coating A Table 4 5 C onfiguration of condition 1 for rectifier war in soil environment L Coating property Initial anode type Soil resistivity Pipe 1 1,000m Coating C Iccp 1.35V 10,000ohm cm Pipe 2 1,000m Coating C Iccp 1.35V Table 4 6 Initial configuration of two pipes for rectifier war in seawater environment L Coating property Initial anode type Seawater resistivity Pipe 1 1,000m Coating A 2 Iccp 7.3 V 10,000ohm cm Pipe 2 1,000m Coating A 2 Iccp 7.3 V Table 4 7 C Length of the pipe N min,anode (CP3D) N min,anode (Dwight) 1 9km 1 0.98 2 18km 2 1.96 3 27km 3 2.95 4 36km 4 3.93 5 45km 5 4.91 6 54km 6 5.89 7 63km 7 6.84 8 72km 8 7.86 9 81km 9 8.84 10 90km 10 9.82 PAGE 48 48 Table 4 8 C f ormula in seawater environment Length of the pipe N min,anode (CP3D) N min,anode (Dwight) 1 212m 1 0 .997 2 425m 2 1.998 3 638m 3 2.999 4 850m 4 3.996 5 1 063m 5 4.997 6 1 276m 6 5.999 7 1 488m 7 6.995 8 1 701m 8 7.997 9 1 914m 9 8.998 10 2 127m 10 10.000 PAGE 49 49 Figure 4 1 Normalized resistance as a function of normalized anode distance Figure 4 2 Normalized resistance as a function of normalized depth of anode PAGE 50 50 Figure 4 3 Normalized resistance as a function of normalized diameter of anode Figure 4 4 Normalized resistance as a function of normalized length of anode PAGE 51 51 Figure 4 5 Sc aled resistance as a function of normalized anode distance Figure 4 6 Scaled resistance as a function of normalized depth of anode PAGE 52 52 Figure 4 7 Scaled resistance as a function of normalized diameter of anode Figure 4 8 S caled resistance as a function of normalized length of anode in different anode diameter conditions. PAGE 53 53 Figure 4 9 N ormalized resistance as a function of normalized anode distance with normalized depth of anode as a parameter Figure 4 10 Scaled resistance as a function o f normalized anode distance with scaled depth of anode as a parameter Figure 4 11 Normalized resistance as a function of normalized anode distance with normalized diameter of anode as a parameter PAGE 54 54 Figure 4 12 Scaled resistance as a function of norma lized anode distance with normalized diameter of anode as a parameter Figure 4 13 Normalized resistance as a function of normalized anode distance with normalized length of anode as a parameter Figure 4 14 Scaled resistance as a function of normali zed anode distance with normalized length of anode as a parameter PAGE 55 55 Figure 4 15 Normalized resistance as a function of normalized depth of anode with normalized anode distance as a parameter. The black line: d=10m; blue line d=70m, red line: d=200m. F igure 4 16 S caled resistance as a function of normalized depth of anode with normalized anode distance as a parameter The black line d=10m; blue line: d=70m, red line: d=200m Figure 4 17 N ormalized resistance as a function of normalized depth of an ode with normalized diameter of anode as a parameter PAGE 56 56 Figure 4 18 Scaled resistance as a function of normalized depth of anode with normalized diam eter of anode as a parameter Figure 4 19 Normalized resistance as a function of normalized depth of an ode with normalized length of anode as a parameter Figure 4 20 Scaled resistance as a function of normalized depth of anode with normalized length of anode as a parameter PAGE 57 57 Figure 4 21 N ormalized resistance as a function of normalized diameter of ano de with normalized anode distanc e as a parameter Black line : d=10m; blue line: d=70m, red line: d=200m Figure 4 22 Scaled resistance as a function of normalized diameter of anode with normalized anode distance as a parameter Figure 4 23 Normalized resistance a s a function of normalized diameter of anode with normalized depth of anode as a parameter B lack line: H a =1m ; blue line: H a =2m, red line: H a =3m PAGE 58 58 Figure 4 24 Scaled resistance a s a function of normalized diameter of anode with normalized depth of anode as a parameter Figure 4 25 Normalized resistance as a function of normalized diameter of anode with normalized length of anode as a parameter Figure 4 2 6 Scaled resistance a s a function of normalized diameter of anode with normalized length of anode as a parameter PAGE 59 59 Figure 4 27 Normalized resistance as a function of normalized length of anode with normalized anode distance as a parameter Black line : d=10m; blue line: d=70m ; red line: d=200m Figure 4 28 Scaled resistance a s a fu nction of normalized length of anode with normalized anode distance as a parameter Figure 4 29 Normalized resistance as a function of normalized length of anode with normalized depth of anode as a parameter B lack line: H a =1m, blue H a =2m, red H a =3m PAGE 60 60 Figure 4 30 Scaled resistance a s a function of normalized length of anode with normalized depth of anode as a parameter Figure 4 31 Normalized resistance as a function of normalized length of anode with normalized diameter of anode as a parameter B lack line: D a =0.1m ; blue line: D a =0.125m ; red line: D a =0.15m. Figure 4 3 2 Scaled resistance a s a function of normalized length of anode with normalized diameter of anode as a parameter PAGE 61 61 Figure 4 33 Configuration of s tray current effect system due t o a single anode Figure 4 34 Potential distribution along the unprotected pipe in a stray current effect system due to a single anode PAGE 62 62 Figure 4 3 5 Current density distribution along the unprotected pipe in a stray curren t effect system due to a single anode Figure 4 3 6 A close up of c urrent density distribution along the interested section of the unprotected pipe in a stray current effect system due to a single anode PAGE 63 63 Figure 4 3 7 Configuration of s tray current ef fect system due to an anode bed Figure 4 3 8 Potential distribution along the unprotected pipe i n a stray current effect system due to an anode bed PAGE 64 64 Figure 4 39 Current density distribution along the unprotected pipe in a stray current effect system due to an anode bed Figure 4 4 0 A close up of current density distribution along the interested section of the unprotected pipe in a stray current effect system due to an anode bed PAGE 65 65 Figure 4 4 1 Configuration of condition 1 for rectifier war modelin g in soil environment Figure 4 4 2. Comparison of potential distribution s along pipe 1 before and after introducing pipe 2. B lack solid line: before introducing pipe 2 ; Rose r ed dash line: after introducing pipe 2 PAGE 66 66 Figure 4 4 3. Comparison of current d ensity distribution s along pipe 1 before and after introducing pipe 2. Black solid line: before introducing pipe 2; blue dash line: after introducing pipe 2 Figure 4 4 4. Comparison of p otential distribution s along pipe 1 and pipe 2 respectively in condi tion 1 Black solid line: pipe 1; red dash line: pipe 2 PAGE 67 67 Figure 4 4 5. Comparison of current density distribution s along pipe 1 and pipe 2 respectively in condition 1. Black solid line: pipe 1; red dash line: pipe 2 Figure 4 4 6. Comparison of potenti al distribution s along pipe 1 and pipe 2 respectively in condition 2. Black solid line: pipe 1; red dash line: pipe 2 PAGE 68 68 Figure 4 4 7. Comparison of current density distribution s along pipe 1 and pipe 2 respectively in condition 1. Black solid line: pipe 1; red dash line: pipe 2 Figure 4 4 8. Potential distributions of pipe 2 in condition 1and 2 respectively Black solid line: pipe 2 in condition 1; blue dash line: pipe 2 in condition 2 PAGE 69 69 Figure 4 4 9 Visual configurations of condition 1, 2 and 3 for rect ifier war modeling in seawater environment Figure 4 50 Current density distributions of pipe 1 in condition 1, 2 and 3 Black solid line: pipe 1 in condition 1; blue long dash line: pipe 1 in condition 2; red short dash line: pipe 1 in condition 3. PAGE 70 70 F igure 4 51. Po tential distributions of pipe 1 in condition 1, 2 and 3 Black solid line: pipe 1 in condition 1; blue long dash line: pipe 1 in condition 2; red short dash line: pipe 1 in condition 3. Figure 4 52. A close up of p otential distributions along pipe 1 in condition 2 and 3 B lue long dash line: pipe 1 in condition 2; red short dash line: pipe 1 in condition 3 PAGE 71 71 Figure 4 5 3. Potential distribution along the pipe of 18,300m with two anodes connected. Figure 4 5 4. Comparison of minimum num ber of anodes by using CP3D and Dwight Formula in soil environment respectively. Black solid line: CP3D; red dash line: Dwight formula. PAGE 72 72 Figure 4 5 5. Comparison of minimum number of anodes by using CP3D and Dwight Formula in seawater environment respecti vely. Black solid line: CP 3D; red dash line: Dwight formula. PAGE 73 73 CHAPTER 5 CONCLUSION S AND FUTURE WORK Motivated by the Buckingham method, a systematic study of anode parameters was obtained. There are mainly four anode parameters affecting the current densit y distribution along a single pipe: and Of these, and have larger effect than do and This study provides a guideline of choosing proper value of anode parameter s to achieve adequate cathodic protection or simulate corrosion behavior in the cathodic protection system. By choosing pro per value of anode variables for the base conditions, stray current effects due to a single anode and due to an anode bed were simulated by applying CP3D From these simulations, the locations are predicted for sites where localized corrosion is experience d on the unprotected pipes. In addition, stray current modeling method s were applied to rectifier wars From rectifier war simulations, it is vividly illustrated that a potential difference between cathodic protection systems for two pipes will result in l ocalized corrosion on the pipe with lesser cathodic protection. Hence corresponding measures can be obtained t o prevent localized corrosion. Determination of the minimum number of anodes is a key part of cathodic protection From this work, two types of m inimum current density were obtained in two specific situations: soil environment ( off shore environment ) and seawater environment (on shore environment ). The m inimum current density needed to protect the pipe with Coating C under the base condition specif ied is and minimum current density to protect with Coating A under th e base condition specified is This PAGE 74 74 work provide s a guideline to determine the minimum number of anodes needed to achieve adequate c athodic protection. For the future work, the first suggestion is to develop a similar dimensional analysis in secondary current distribution condition in which kinetics resistance is considered. The secon d suggestion is to determine the length of the sect ion along the unprotected pipe which experiences localized corrosion quantitative ly. The last suggestion is to simulate alternating stray current corrosion and develop an effective mathematical model to predict the potential and current distribution in thi s situation. PAGE 75 75 LIST OF REFERENCES [1] G. H. Koch, M.P. H Brongers, N.G. Thompson, Y.P. Virm ani, J. H. Payer, Corrosion c osts and p reventive s trategies in the Unites States, NACE International, Houston, T exas 2001 [2] NTSB, Pipeline Accident Report: Pipelin e Rupture and Release of Fuel Oil into the Reedy River, Fork Shoals, South Carolina June 26 1996, Technical report, National Transportation Safety Board, Washington, D.C. 1998. [3] M. G. Fon t a n a, Corrosion Engineering, 3rd ed McGraw Hill, Singapore, 198 6 [4] A.J. Bard, L. R. Faulkner, Electrochemical M ethods: Fundamentals and Applications, Wiley, New York, 1980 [5] J.O. Bockris, D. Drazic, A.R. Despic, The Electrode k inetics of the d epo sition and d issolution of i ron, Electrochimica Acta 4 (1961) 325 361 [6] J. Wagner, Cath odic Protection Design I, NACE International, Houston, T exas, 1994. [ 7] G. Jerkiewicz, Hydrogen s orption a t/In e lectrode, Progress in Surface Science 57 (1998) 137 186. [8] M. de Chialvo, A. Chialvo, The Tafel Heyrovsky route in the kine tic mechanism of the hydrogen evolution reaction, E lectrochemistry Communications 1 (1999) 379 382 [9] M. de Chialvo, A. Chialvo, Existence of two sets of kinetic parameters in the correlation of t he hydrogen electrode reaction, Journal of the Electrochem ical Society 147 (2000) 1619 1622 [10] A. Lasia, D. Gregoire, General m odel of e lectrochemical h ydrogen a bsorption i nto m etals, Journal of the Electrochemical Society 142 (1995) 3393 3399. [11] L.J. Bai, Behavior of a h ydride p hase f ormed in the h ydrogen e volution r eaction at a r otating Pt e lectrode a nalysis of p otential r elaxation t ransients from a k inetic a pproach, Journal of Electroanalytical Chemistry 355 (1993) 37 55. [12] D.P. Riemer, Modeling c athodic p rotection for p ipeline n etworks, Ph D dissert ation, the University of Florida, Gainesville, Florida, 2000 [13] K. 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Orazem, Current and p otential d istribution on a c oated p ipeline with h oliday s Part I m odel and e xperimental verification. Corrosion 49 (1993) 199 210. [18] J. Morgan, Cathodic Prot ection, 2nd ed. NACE International, Houston, Texas 1993. [19] D. Riemer, M. Orazem, Development of m athematical m odels for c athodic p rotection of m u ltiple p ipelines in a r ight of w ay, Proceedings of the 1998 International Gas Research Conference 117 (1998) 19. [20] D. Riemer, M. Orazem, Cathodic p rotection of m ultiple p ipelines with c oating h olidays, Procedings of the NA CE 19 99 Topical Research Symposi um ( 1999) 65 81. [21] J. S. Newman, Electrochemical Engineering, 2nd ed Prentice Hall, Englewood Cliffs, New Jersey:, 1991. [22] C.A. Brebbia, J. Dominguez, Boundary e lement m ethods for p otential problems, A pplied Mathematical Modeling 1 (1977) 371 378. [ 23] S. Aoki, K. Kishimoto, M. Sakata, Boundary e lement a nalysis of galvanic c orrosion, Boundary Elements VII 1 ( 1985) 73 83. [24 ] S. Aoki, K. Amaya, Optimization of c athodic p rotection s ystem by BEM, Engineering Analysis with Boundary Elements 19 (1997) 14 7 156. [25] F. Brichau, J. Deconinck, Numerical model for cathodic protection of buried pipes, Corrosion 50 (1994) 39 49. [26] F. Hartmann, C. Katz, B. Protopsaltis, Boundary e lements a nd symmetry, INGENIEUR ARCHIV 55 (1985) 440 449 [27] C .J Geankoplis, T ransport P rocesses and U nit Operations, 3 rd ed .,Prentice Hall, Englewood Cliff New Jersey, 1993. PAGE 77 77 BIOGRAPHICAL SKETCH Chao Liu grad uated from Nanchang University in China, with a Bachelor of Scien ce degree in applied chemistry in July 2010. He enrolled in the Master of Engineering program in chemical engineering at the U niversity of Florida in August 2010 Then he transferred to the Master of Science program and joined Professor Mark working on the project of CP3D simulation on buried pipeline corrosion. He received his Master of Science degree from the University of Florida in May 2012. 