A method of moments approach to model the electromagnetic response of multiple steel casings in a layered earth

In oil and gas production environments, controlled-source electromagnetics can be used to aid brownfield exploration, development, and reservoir monitoring efforts. However, such environments typically have many highly conductive steel-cased wells in the area of interest. We have developed a modeling algorithm using a method of moments (MoM) approach to calculate the electromagnetic response of multiple 3D steel-cased wells of arbitrary geometry in a layered earth conductivity model. This approach involves dividing each casing into a collection of segments, each carrying a uniform current density. A matrix is computed that describes how the casing segments interact with each other electromagnetically. Then, we solve a linear system for the current within each casing segment, given a transmitter of arbitrary frequency and location. From these currents we are able to solve for the secondary electromagnetic fields produced solely by the casings at any point in our layered model, and we add these to the primary fields produced by the transmitter. To validate the algorithm, we compared results with a pseudoanalytic MoM algorithm for a single vertical casing in a half-space. We also compare results with a finite-element solution using Comsol Multiphysics for vertical and single tilted wells buried in various layered earth models. Our results indicate a good match between these different approaches, with tilted casings in a layered model requiring further study. Finally, we applied our algorithm to a realistic synthetic model with three casings (one vertical and two deviated) extending into a layered earth model containing the classic thin resistive layer. This example illustrates how the algorithm can be used to compute the electromagnetic response of multiple steel casings. The example also illustrates how the electromagnetic field changes due to the presence of the casings and how the casings may be used to inject the signal at depth