Fast electrical imaging of injected fluid in hydraulic fracturing using a practical interactive parameter estimation method

Highly conductive steel cased wells have been proposed to be used as long electrodes in the electrical survey for hydraulic fracturing monitoring. Recent advancements have enabled accurate 3D numerical modeling of complex well casings, but few have investigated the feasibility of imaging the fracturing fluid using the electrical method. In this work, we develop an interactive inversion scheme powered by a fast forward modeling algorithm using an equivalent resistor network (RESnet). Our inversion fits anomalies in time-lapse differential data, so biases caused by inaccuracy in the background model can be cancelled out. The fluid model is parameterized as a polygon of full saturation on the fracture plane and a thickness-integrated conductivity of the fluid sheet. Surface electrical field data are mapped to the HSV (hue, saturation, value) color space to aid visual inspection and model adjustment by hand. In our blind test with the presence of three horizontal wells, the computing time of one trial model was about 8 s and the geometry and conductivity of an asymmetric fluid slab was imaged after 30 trials; the entire inversion is completed within 20 minutes including both human and computer time on a desktop PC. Our results show the feasibility of electrical method in high-resolution fracturing fluid monitoring, as well as the practicality of interactive inversion in real-time imaging.