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Rabiot, D.; Dalard, F.; Rameau, J.J.; Caire, Jean-Pierre; Boyer, Sébastien

doi:10.1023/a:1003408122084

Cited by 15 publications

(14 citation statements)

References 15 publications

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“…As the conductivity of the computational domain is constant, BEM is to be preferred over other discretization methods as finite element (FEM), finite volume (FVM), and finite difference methods (FDM) to solve the simplified charge conservation Equation (9). When the BEM is applied, only the boundaries of the domain are to be discretized.…”

Section: Numerical Solution Methodsmentioning

confidence: 99%

“…For example, Reaction (2) will show a diffusion limitation due to the restricted amount of oxygen being present in the soil. As a consequence, for CP simulations, the steel electrode polarization is often encompassed in a single, measured electrode polarization curve, 6,9 relative to a mixed corrosion potential (E corr ) for which the combined current density from Reactions (1), (2), and (3) is zero:…”

Section: Bare and Coated Steel Surfacesmentioning

confidence: 99%

See 1 more Smart Citation

Numerical 3-D Simulation of a Cathodic Protection System for a Buried Pipe Segment Surrounded by a Load Relieving U-Shaped Vault

Purcar¹,

Bossche²,

Bortels³

et al. 2003

CORROSION

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A three-dimensional, multi-domain boundary element method approach was used to determine the performances of a cathodic protection system applied to a buried pipeline of limited longitudinal dimension, surrounded by a U-shaped vault of infinite resistivity (insulator). A Laplace model describing the potential problem was solved in combination with nonlinear boundary conditions that hold for the polarization behavior of the coated pipeline and coating holidays. The efficiency of this cathodic protection system was examined as a function of the soil conductivity, the position of the defects, and the presence of the U-shaped vault. The objective of these simulations was the quantitative determination of the reducing effect of this structure on the protection level of the outer pipe surface, as a result of its spatial obstruction for the protective currents that originate from the far-field anode beds.

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Section: Numerical Solution Methodsmentioning

confidence: 99%

Section: Bare and Coated Steel Surfacesmentioning

confidence: 99%

Numerical 3-D Simulation of a Cathodic Protection System for a Buried Pipe Segment Surrounded by a Load Relieving U-Shaped Vault

Purcar¹,

Bossche²,

Bortels³

et al. 2003

CORROSION

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“…In order to find the corrosion rate at any point on a cathodically protected metallic structure submerged in an electrolyte (most frequently ground or seawater), a corrosion engineer needs to know the potential distribution over the electrolyte/structure interface. Today, the calculation of current and potential distribution is considered an indispensable means for study of cathodic protection (CP) systems and improvement of their reliability 1–25. Traditional CP design methods are mostly based on simple empirical formulas that require the use of large safety factors and rely, to a great extent, on the engineer's experience.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of the uniform current density assumption in cathodic protection systems with close anode‐to‐cathode arrangement

Martinez

2010

Materials & Corrosion

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Cathodic protection modelling often involves making assumptions about geometric features and material characteristics that directly impact accuracy of solutions. In the present paper, predictive power of the model using approximate uniform current boundary condition on the cathode is validated against the model using nonlinear cathode polarization curves representative of low-carbon steel structure of common geometry, buried in soil or immersed in seawater. In order to explore the worst case scenario, the present example deals with a large diameter pipeline (Ø 1.2 m) and a wire anode (Ø 0.05 m), separated by a distance d, both embedded in an infinite space of conductivity k. The calculation is performed for the two sets of parameters -k and limiting current density of oxygen reduction, i l . For simulation of CP systems in seawater k ¼ 4.79 S/m and i l ¼ À86 mA/cm 2 and for CP system in soil, k ¼ 10 À3 S/m and i l ¼ À1.1 mA/cm 2 . The other physical parameters were identical for both systems (Tafel slopes b a ¼ 60 mV/dec, b c ¼ 120 mV/dec and equilibrium potentials f a e ¼ À700 mV, f a c ¼ À800 mV). The results were visualized to best exemplify the general trends in potential and current distributions that appear upon switch between uniform and nonlinear cathodic boundary conditions.

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“…Applications that deal with current density distributions for more complex 3D geometries can be found in the field of cathodic protection. [16][17][18][19][20][21] Most simulations presented in these papers are based on a BEM approach.The terminal effect of thin resistive electrodes is modeled in a few papers ͑for 2D reactor cross-sections͒, for example by Marshall and Wolf, 22 for ͑linearized͒ secondary distributions, using semianalytical techniques. Matlosz et al 23 also simulated terminal electrode effects coupled with the Laplace model for the electrolyte resistivity.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Three-Dimensional Current Density Distribution Simulations for a Resistive Patterned Wafer

Purcar

Bossche

Bortels

et al. 2004

J. Electrochem. Soc.

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A combined boundary element method ͑BEM͒-finite element method ͑FEM͒ numerical approach is used for the simulation of current density and layer thickness distributions in a wafer plating reactor. The current and potential distribution effects due to the electrolyte resistivity are modeled with BEM, while the transient internal resistive 'terminal' effect of the wafer is modeled using FEM. A nonlinear Butler-Volmer type overpotential relation is considered to describe cathode kinetics. The declining internal wafer resistivity that is due to the growth of the initial copper seed layer, is modeled over a number of discrete time steps. Different contacting methods ͑4 or 8 contact points, ring contact͒ are investigated, and their terminal effect time is compared. The wafer consists of a ring-shaped current thief, with adjacent photoresist area's and a central electroactive patterned zone.Modeling current density distributions in electrochemical reactors has become common practice over the last few decades. A first general class of models is based on a complete description of the multi-ion transport ͑migration, convection, and diffusion͒ and electrode reactions ͑MITRe͒. 1 These MITRe models have been solved for two-dimensional ͑2D͒ reactor cross-sections with various numerical techniques, and for different process types. In most cases however, simulations are based on models with important simplifications. Even now, papers dealing with unsimplified MITRe models are scarce. For example, Georgiadou and Alkire presented results for an etching process, based on the finite difference method ͑FDM͒, in combination with an upwind scheme for the convection. 2 Bortels et al. used finite volumes ͑with a convection upwind scheme͒ for a copper deposition process. 3 More recently, Leah et al. modeled a chlor-alkali reactor with an FDM approach. 4 A second class of ͑simplified͒ models is based on the description of ohmic drop effects in the electrolyte ͑Laplace model, primary current density distributions͒, in most cases combined with linear or nonlinear electrode polarization/current density relations ͑secondary current density distributions͒. 5 The validity and accuracy of these 'potential' models depends on the rate of stirring or electrolyte refreshment in the reactor ͑compared to the range of applied current densities͒, enabling to neglect convective diffusion mass transfer problems. Papers presenting potential model results for 2D or axisymmetrical ͑AX͒ reactor cross-sections are widespread. For example Matlosz et al. 6 studied primary and secondary current density distributions in a Hull cell. Simulated results using the boundary element method ͑BEM͒ and the finite element method ͑FEM͒ agreed well. Mehdizadeh et al. 7 used BEM to examine the influence of a coplanar auxiliary electrode ͑current thief͒ on the uniformity of the current density on a flat electrode. More recently, Subramanian and White presented a semi-analytical method for solving potential models with nonlinear electrode polarization. 8 The practical relevance of...

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Untitled

Cited by 15 publications

References 15 publications

Numerical 3-D Simulation of a Cathodic Protection System for a Buried Pipe Segment Surrounded by a Load Relieving U-Shaped Vault

Numerical 3-D Simulation of a Cathodic Protection System for a Buried Pipe Segment Surrounded by a Load Relieving U-Shaped Vault

Evaluation of the uniform current density assumption in cathodic protection systems with close anode‐to‐cathode arrangement

Three-Dimensional Current Density Distribution Simulations for a Resistive Patterned Wafer

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