Optimizing the electrode position in sacrificial anode cathodic protection systems using boundary element method
Introduction
Cathodic protection (CP) is a technique to reduce the corrosion rate of a metal surface by making it the cathode of an electrochemical cell. This is accomplished by shifting the potential of the metal in the negative direction by the use of an external power source (referred to as impressed current CP) or by utilizing a sacrificial anode. In the case of an impressed current system, a current is applied on the structure by means of a power supply, referred to as a rectifier, and an anode buried in the medium. In the case of a sacrificial anode system, the galvanic relationship between a sacrificial anode material, such as zinc or magnesium, and the structure is used to supply the required CP current [1], [2].
An Evan’s diagram can provide the theoretical basis of CP. Such a diagram is shown schematically in Fig. 1, with the anodic metal dissolution reaction under activation control and the cathodic reaction diffusion limited at higher density. As the applied cathodic current density is stepped up, the potential of the metal falls, and the anodic dissolution rate is reduced accordingly [1].
Magnesium and zinc anodes are customarily used in sacrificial anode systems. The magnesium anodes are most popular because of their high current output while zinc anodes are frequently used for protection of submarine structures. Therefore many studies have been done on the usage of magnesium and zinc in applications of sacrificial anode systems [3], [4], [5], [6].
Surveys by Riemer and Orazem [7], Kranc and Sagüés [8], Adey and Niku [9], Allahar and Orazem [10], and Verbrugge [11] have illustrated that numerical methods are promising in study of galvanic corrosion and CP systems. Advancing computer technology made boundary element method (BEM) a prevalent method to study galvanic corrosion. Miyasaka et al. [12] evaluated the computational accuracy of BEM to estimate the galvanic corrosion and CP in an actual field. They analyzed the model by using single and multiple-region methods. It was indicated that both methods were consistent with each other when the element size was reduced. Study of Jia et al. [13] in evaluation of BEM showed that their calculated current density values were consistent with the theoretical expectations for the case of both linear and non-linear polarization curves as boundary conditions. They have also studied the credibility of BEM calculations in galvanic corrosion of magnesium coupled to steel in 5% NaCl solution, corrosive water and auto coolant, and showed that there was a good agreement between the BEM calculations and experimental measurements provided that adequate boundary conditions were used [14]. Varela et al. [15] used BEM to analyze the general and galvanic corrosion of carbon steel (SS400) and stainless steel (SUS304) in CO2 + NaCl aqueous solution at elevated temperatures. Zamani and Chuang [16] and Kishimoto et al. [17], [18] have applied BEM in impressed current systems to determine the optimum currents to electrodes, the locations of which are assumed to be fixed. Additionally, Aoki and Amaya [19] investigated not only the optimum currents but also the optimum locations of electrodes in impressed current systems.
In this study, the sacrificial anode CP of a carbon steel storage tank with rectangular cross section, full of 0.1 wt% NaCl solution, is simulated using BEM in 2D. The optimum location of zinc anode electrode is determined. In addition, the influence of anode length and paint defect (in the case of applying paint on structure) on corrosion current density (icorr) and potential distributions of this sacrificial anode CP system are investigated. The required boundary conditions to evaluate the system were obtained from experimental potentiodynamic polarization measurements.
Section snippets
Boundary element method
The mathematical formulation has been presented by Adey and Niku [9] for a uniform, isotropic electrolyte domain Ω as illustrated in Fig. 2. For a uniform, isotropic electrolyte system in steady state, the potential obeys the Laplace equation:
The Laplace equation is solved using the following boundary conditions:where Γ (≡Γ1 + Γ2 + Γ3a + Γ3c) is the entire surface of the electrolyte domain Ω, I is the current density across the boundary, and
Materials
The model considered in this work is shown in Fig. 4. The structure is a storage carbon steel tank, full of 0.1 wt% NaCl solution, with rectangular cross section of a × w (a = 20 cm and w = 10 cm) which is protected by a zinc sacrificial anode, located directly on the structure’s wall. The length of the electrode, L, is 0.5 cm, except where the influence of anode length is investigated. Although this is clearly a rough approximation, it is assumed that variations in ion concentration are negligible.
Optimizing the zinc electrode location
Fig. 10(a) shows iprot of zinc electrode as a function of anode location. It can be clearly seen that the zinc electrode produces the highest iprot for electrode center at s/a = 0.5 or 2. Considering the Evan’s diagram, since at these anode locations the protective current is maximum, both the potential and anodic dissolution rate (which is proportional with icorr) of the structure must be in their minimum values. BEM-calculated values of average and maximum potential over the potential
Conclusions
The following results can be obtained from the present simulation:
- (1)
The BEM-based program can reasonably predict the potential and icorr over the structure surface in sacrificial anode CP systems.
- (2)
The optimum anode location and minimum required anode length to reach the protection potential can be properly determined by BEM.
- (3)
Not only BEM is applicable for predicting the level of protection provided by CP system to bare structures, but also it can be used to simulate CP of painted structures.
- (4)
Given
Acknowledgements
The authors gratefully acknowledge Dr. M. Peikari, Mr. E. Poorqasemi, Mr. S.M. Hosseinieh, and Mr. A. Ostovari for their helpful suggestions and comments.
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