Abstract We study the theoretical response of electromagnetically energized steel casing in the presence of subsurface variations of electrical resistivity. Casing is energized with a finite-size solenoid antenna located along the axis of the borehole. Measurements consist of the azimuthal component of the electric field acquired either on the surface or in a separate well in the same hydrocarbon field. We assume two-dimensional (2D) axisymmetric variations of subsurface electrical resistivity and casing excitation. Simulations of electromagnetic (EM) fields excited by energized steel casing are performed with a goal-oriented hp-adaptive finite-element method that automatically generates a sequence of optimal grids delivering exponential convergence rates in terms of the EM fields at the receiver antennas against CPU time. This advanced finite-element method enables accu-rate modeling of problems with high conductivity contrasts inlarge computational domains. Numerical simulations quantify the measurement sensitivity to variations of frequency, distance from casing to receivers, resistivity of the target oil-bearing layer, and pistonlike radial invasion of water within a target layer initially saturated with oil. When receivers are placed in a nearby well, numerical results indicate that measurements exhibit the largest sensitivity to the target (oil-saturated) layer when the transmitter or receiver antenna is located just above the target layer, and another antenna is located below the target layer. A frequency range from 5–30Hz provides optimal results for the detection of oil-bearing layers and estimation of radial extent of water invasion. Large horizontal distances (up to 1500m) between transmitter and receivers and a background material with resistivity above 50Ωm also enhance the measurement sensitivity to radial variations of water invasion. This sensitivity can be as large as 15%–20% of the measured electric field.