Mathematical Models for Cathodic Protection of an Underground Pipeline with Coating Holidays: Part 1 — Theoretical Development

Mathematical models were developed to predict cathodic protection (CP) requirements for coated pipelines protected by parallel anodes. This work was motivated by the need to estimate current and potential distribution on a pipe when anodes are placed nearby or when discrete coating holidays expose bare steel. The mathematical model solves Laplace’s equation for potential with boundary conditions appropriate for the pipe being protected, the anode, and any region through which current does not pass. The current density on bare steel was assumed to be composed of contributions from corrosion, reduction of dissolved oxygen, and evolution of hydrogen. Kinetic parameters were obtained from independent experiments. The anode was assumed to have a constant potential, and current was allowed to flow through the coating under the assumption that the coating is a high-resistance ionic conductor. A boundary element technique coupled with Newton-Raphson iteration was used to solve the governing equations for two- (2-D) and three-dimensional (3-D) configurations. Results showed good agreement with experimental values and can be used to assess viability of CP designs.