A mathematical model for the internal cathodic protection of cylindrical structures by wire anodes

The applicability of a two-dimensional mathematical model of the impressed current cathodic protection (CP) system of the interior wall of a cylindrical structure was investigated. The modelled system was an axisymmetric cylindrical column filled with electrolyte with a wire anode running along its entire length and displaced from the column axis. Model inputs included anode and cathode dimensions, the anode-to-cathode distance, the electrolyte conductivity and limiting current density of oxygen reduction. A semi-analytical solution to the Laplace equation was used to compute the distribution of electrical potential. From these results, the nonuniform current density distribution was obtained to a first approximation by entering the computed values of the position-dependent cathode polarization potential into the nonlinear experimentally obtained polarization expression. The experimental electrical potential distribution compared well with that predicted by the model. Results showed the possibility of overprotection occurring in the system. The mathematical analysis was also extended to the case of a system with two wire anodes.