Insights on electromagnetic field distribution due to a vertical electric dipole source inside an infinite steel casing

Abstract

Energized vertical steel casings have been developed to excite and monitor changes in the electrical properties of resistivity anomalies associated with hydrocarbon production and [Formula: see text] injection, among other applications. Accordingly, the spatial distribution of the fields expected in the medium surrounding a casing source has received considerable attention. However, investigations of the in-borehole distribution of the fields, currents, and charges have been lacking. Such an analysis is the objective of this work. Inside the borehole, the electric field is dominantly vertical, owing to the azimuthal symmetry of the charge density induced at the inner and outer casing boundaries. At the inner surface, charges accumulate dominantly in the vicinity of the source. At the outer surface, charges distribute along the extent of the casing, driven by the vertical channeling and radial leakage of the current flow. Inductive effects arise as the source oscillates in time, effectively resulting in a vanishing flux of azimuthal magnetic field and switching of the sign of the charge density along the vertical extent of the pipe. The alternating charge distribution yields fields propagating inward and outward within the metallic medium, describing inhomogeneous Zenneck surface waves that can interfere as they propagate and superimpose up and down the borehole. In the surrounding medium, the azimuthal magnetic field is driven by the current flowing vertically along the borehole, whereas a dominantly radial electric field is driven by the charge distributed on the outer casing surface.