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

Abstract

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.

Application of the coupled BEM/FEM method for calculation of cathodic protection system parameters

“…where q is the observation point, p is the field source point, c(q) is the constant, j s (q) is the potential at the observation point q in soil, j s (p) is the potential at the field source point p in soil, n is the normal unit vector, G(p,q) is the Green's function, Γ is the boundary of the domain and ∇ is Nabla operator. Additional term j¢ given on the right side of the eqn (1) is the constant potential on the infinite boundary [6,7,11]. To calculate this potential, additional integral equation must be added [5][6][7]:…”

“…Equations (11) and (12) are valid for matrix elements of one finite element. To form global matrix eqn (10), it is necessary to take into account contributions of all finite elements that share the same node.…”

Numerical Model for Simulation of the Cathodic Protection System with Dynamic Nonlinear Polarization Characteristics

“…By including matrix equations (9) and (10) in the equation 8, following equation can be written [11,12]:…”

“…For modeling of the cathodic protection systems, boundary element method is mostly used [6][7][8]. The main advantage of this method, in comparison to the other numerical methods, is that it requires discretization only of boundaries of considered domain and there is no need for discretization of infinite boundaries [9]. Additionally, iterative techniques for solution of nonlinear equations (such as Newton -Raphson technique) must be included because nonlinear boundary conditions (nonlinear polarization characteristics) are given on electrode surfaces of cathodic protection system.…”

Comparative analyses of modeling techniques for cathodic protection

“…One of the most effective methods for taking care of issues in the field of use of cathodic protection frameworks is the boundary element technique. The fundamental merit of this technique is that discretization is needed distinctly at the boundary of the domain of intrigue and there is no requirement for discretization of infinite boundaries [15][16][17][18].…”