A stochastic model for induced seismicity based on non-linear pressure diffusion and irreversible permeability enhancement

During deep reservoir engineering projects, in which permeability is enhanced by high-pressure fluid injection, seismicity is invariably induced, posing nuisance to the local population and a potential hazard for structures. Hazard and risk assessment tools that can operate in real-time during reservoir stimulation depend on the ability to efficiently model induced seismicity. We here propose a novel modelling approach based on a combination of physical considerations and stochastic elements. It can model a large number of synthetic event catalogues, and at the same time is constrained by observations of hydraulic behaviour in the injection well. We model fluid flow using non-linear pressure diffusion equations, in which permeability increases irreversibly above a prescribed pressure threshold. The transient pressure field is used to trigger events at so-called 'seed points' that are distributed randomly in space and represent potential earthquake hypocentres. We assign to each seed point a differential stress based on the mean estimates of the in situ stress field and add a normal distributed random value. Assuming a fault orientation with respect to the stress field and a Mohr-Coulomb failure criterion, we evaluate at each time step, if a seed point is triggered through a pressure increase. A negative proportional relationship between differential stress and b values is further assumed as observed from tectonic earthquakes and in laboratory experiments. As soon as an event is triggered, we draw a random magnitude from a power-law distribution with a b value corresponding to the differential stress at the triggered seed point. We thus obtain time-dependent catalogues of seismic events including magnitude. The strategy of modelling flow and seismicity in a decoupled manner ensures efficiency and flexibility of the model. The model parameters are calibrated using observations from the Basel deep geothermal experiment in 2006. We are able to reproduce the hydraulic behaviour, the space-time evolution of the seismicity and its frequency-magnitude distribution. A large number of simulations of the calibrated model are then used to capture the variability of the process, an important input to compute probabilistic seismic hazard. We also use the calibrated model to explore alternative injection scenarios by varying injection volume, pressure as well as depth, and show the possible effect of those parameters on seismic hazard.