Finite element modelling of transient electromagnetic fields near steel-cased wells

Wells and boreholes are routinely steel-cased in oil and gas fields and geological storage sites. There have been a number of studies on the effects of a steel-cased well on various electrical and electromagnetic (EM) geophysical methods. In this paper, we examine the use of a steel-cased well as a virtual vertical electric source for sensing deep localized resistive (e.g. CO2, oil and gas) and conductive (e.g. conductive-proppant-filled fractures) targets when concentric electric sources are grounded around the collar of the well. To simulate the casing effects, we present a 3-D finite-element time-domain (FETD) algorithm with tetrahedral elements. The FETD algorithm is designed to reduce memory usage in adaptive time stepping by utilizing parallel direct and iterative solvers appropriately together. To avoid a larger number of tiny elements required for discretizing a thin wall of the casing, the hollow casing is approximated with a rectangular prism. By not discretizing the thin wall of and the curvature of the round casing, the approximation not only reduces the number of unknowns by an order of magnitude but also improves overall mesh qualities. We show that surface EM responses over the hollow casing and the prism are practically the same. Through FETD modelling of a rectangular prism as an approximation of a steel casing, we demonstrate that a steel casing can serve as a conduit through which a high concentration of electrical currents can flow downward from the surface, interact with deep localized reservoirs/fractures and produce a measurable perturbation in the surface EM fields. Concentric electric sources can further improve both the sensitivity to the deep targets and the overall magnitude of surface EM fields.