MATHEMATICAL-MODELS FOR CATHODIC PROTECTION OF AN UNDERGROUND PIPELINE WITH COATING HOLIDAYS .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 distr ibution on a pipe when anodes are placed nearby or when discrete coati ng holidays expose bare steel. me mathematical model solves Laplace's equation for potential with boundary conditions appropriate for the pi pe being protected, the anode, and any region through which current do es not pass. The current density on bare steel was assumed to be compo sed of contributions from corrosion, reduction of dissolved oxygen, an d evolution of hydrogen Kinetic parameters were obtained from independ ent experiments. The anode was assumed to have a constant potential an d current was allowed to flow through the coating under the assumption that the coating is a high-resistance ionic conductor. A boundary ele ment technique coupled with Newton-Raphson iteration was used to solve the governing equations for two-(2-D) and three-dimensional (3-D) con figurations. Results showed good agreement with experimental values an d can be used to assess viability of CP designs.