A tool concept using downhole electrical measurements for mapping electrically conductive proppant in hydraulic fractures is presented in this paper. The method relies on direct excitation of the casing, which overcomes the severe limitations of induction tools in cased wellbores. An array of insulating gaps is installed and cemented in place as a permanent part of the casing string. The electrical measurements are done by imposing a voltage across each insulating gap, one at a time, before and after hydraulic fracture operations. The voltages across other insulating gaps near the transmitter gap are recorded.
The proposed tool's response to the geometry of a single fracture was modeled by solving for the electrical potential using a finite volume method. Preliminary results have shown that the electrically conductive proppant alters the path of the electrical current in the formation and this is recorded as differential signals by the string of insulating gaps surrounding the source gap. The measured differential signals are highly sensitive to a fracture's location, size, and orientation, and less sensitive to the fracture shape. However, to enable the implementation of such a practical system, various aspects of the tool need to be further investigated. Following our previous work, this paper focuses on forward modeling of the tool's response to multiple fractures, which demonstrates the influence of these fractures to the signals and provides important guidance for inverse modeling. Parametric inversion of fractures from synthetic data, generated by exciting various insulating gaps, is solved by using Very Fast Simulated Annealing (VFSA).
Simulation results show that when multiple hydraulic fractures are present, the voltages measured at the receiver gaps are primarily determined by the geometry of the fracture, which is in direct contact with the excited section of casing. When two fractures touch the same casing section, they induce very similar voltages to those from a single fracture with equivalent conductance. Preliminary inversion results from synthetic data indicate that the proposed VFSA can solve for the multiple fractures' conductance and size at the same time, without requiring a large number of forward simulations. Even with noisy synthetic data, VFSA is able to make good estimates of the fractures' geometries. This indicates that the VFSA technique is a proper and robust inversion technique for the measured voltages at various receiver gaps.