We present a model describing the seismicity rate of fluid injection-induced seismicity. We put the focus on seismicity induced after termination of fluid injections. Here, our primary objective is the identification of parameters controlling the decay rate of seismicity. The particular importance of a theoretical model for postinjection seismicity is underlined by observations after stimulations of geothermal reservoirs at different locations. For instance, the postinjection phase is relevant for a seismic risk, which up to now has been difficult to control, because processes leading to postinjection events are not well understood. Based on the assumption of pore pressure diffusion as the governing mechanism leading to the triggering of seismic events, we develop a method to calculate the seismicity rate during and after fluid injections. We find that the decay rate of seismicity after termination of injection is very similar to the Omori law, which describes the decay rate of aftershock activity after tectonically driven earthquakes. We propose a modified Omori law for fluid-induced seismicity to estimate the decay rate in dependence on parameters of injection, reservoir rock, and the strength of preexisting fractures in a reservoir. We analyze two models of fracture-strength distribution, which represent stable and unstable preexisting fracture systems. We find that the decay rate of induced seismicity depends on the fracture strength. We present a possible application of this dependency to reservoir characterization. Furthermore, we find that the existence of unstable fractures results in a critical temporal trend of seismicity, which can enhance the occurrence probability of events with large magnitudes shortly after injection has been terminated. We verify our model by finite-element modeling and application to real data collected in case studies performed at Fenton Hill in the United States and Soultz-sous-Forêts in France.

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