A boundary element model of cathodic well casing protection

Abstract An efficient boundary element method was developed to study cathodic protection of a well casing in a formation with layered conductivities. Even though the electrical potential in soil is governed by the linear Laplace equation, electrochemical reactions at the well casing introduce complex, nonlinear boundary conditions. Furthermore, the complexity of boundary geometries makes the numerical computation nontrivial. Use of Green's function allows a general solution of the Laplace equation to be expressed in the form of a Fredholm integral equation of the second kind. The present formula employs a fundamental solution that eliminates the discretization of the top ground surface. Because the potential distribution within the well casing metal greatly affects the current distribution, the model includes the potential change along the axial direction of the well casing. A Newton-Raphson method was employed to estimate iteratively the current distribution at the well casing, and then the integral equations of the boundary element method were numerically solved by a collocation technique. This boundary element model was used to investigate the effects of soil conductivities, well casing geometry, well casing resistivity, and the location of a current source on the current and potential distribution at the well casing.