Robust Tracking for a 3D Diffusion Equation: Controlling Seismicity Rate in Geothermal Reservoirs

Deep Geothermal Energy has significant potential to meet the large-scale needs of the energy sector. However, the injection of fluids into the earth's crust, upon which it relies, can lead to the formation of new seismogenic faults or the reactivation of existing ones, thereby causing earthquakes. To date, no effective method exists for mitigating these human-induced earthquakes. In this study, we propose a novel approach based on control theory to address this issue. First, we model induced seismicity resulting from fluid injections in a geothermal reservoir using a diffusion equation in three dimensions. Then, we design a robust tracking control approach to force the seismicity rate to follow the desired references. In this way, the induced seismicity is minimized while ensuring fluid circulation for the needs of energy production. The designed control guarantees the stabilization of the error variable even in the presence of system uncertainties and unknown dynamics. Finally, we present simulations of a geothermal reservoir under different scenarios of intermittent energy demand to show the reliability and performance of the control approach, opening new perspectives for field experiments based on real-time regulators for the first time.