Robust in situ power harvesting underlies the realization of embedded wireless sensors for monitoring the physicochemical state of subsurface engineered structures and environments. The use of electromagnetic (EM) contrast agents in hydraulically fractured reservoirs, in coordination with completion design of wells, offers a way to transmit energy to remotely charge distributed sensors and interrogate fracture width, extent, and fracture-stage cross-communication. The quantification of available power in fracture networks due to energized steel-cased wells is crucial for such sensor designs; however, this has not been clarified via numerical modeling in the limit of Direct Current (DC). This paper presents a numerical modeling study to determine the EM characteristics of a subsurface system that is based on a highly instrumented field observatory. We use those realistic field scenarios incorporating geometry and material properties of contrast agents, the wellbore, and the surrounding geologic environment to estimate volumetric power density near the wellbore and within hydraulic fractures. The numerical modeling results indicate that the highest power densities are mainly focused around the wellbore excited by a point current source and the fracture boundary. Using DC excitation, the highest power density in the fracture is at the fracture tip. The relatively high-power density on the order of tens of mW/m3 at the vicinity of the wellbore and at fracture tips suggests that remote charging of sensor devices may be readily possible. Simulation results also show that the region of the highest power density can be significantly increased when the EM source is located inside a conductive fracture, which may lead to a promising deployment strategy for embedded micro-sensors in geologic formations.

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