Seismic events induced by the depletion of hydrocarbon reservoirs can cause damage to housing and cause societal and economic unrest. However, the factors controlling the nucleation and size of production-induced seismic events are not well understood. Here we used geomechanical modeling of production-induced stresses and dynamic rupture modeling to assess the conditions controlling down-dip rupture size. A generic model of (offset) depleting reservoir compartments separated by a fault was modeled in 2-D using the Finite Element package DIANA FEA. Linear slip-weakening was used to control fault friction behavior. Fault reactivation was computed in a quasi-static analysis simulating stresses during reservoir depletion, followed by a fully dynamic analysis simulating seismic rupture. The sensitivity of reactivation and rupture size to in situ stress, dynamic friction, critical slip distance, and reservoir offset was evaluated. After reactivation, a critical fault length was required to slip before seismic instability could occur. In a subsequent fully dynamic analysis the propagation and arrest of dynamic rupture was simulated. Rupture remained mostly confined to the reservoir interval but could also propagate into the overburden and underburden or sometimes transition into a run-away rupture. Propagation outside the reservoir interval was promoted by a critical in situ stress, a large stress drop, a small fracture energy, and no or little reservoir offset. With increasing offset (up to the reservoir thickness), reactivation was promoted but dynamic rupture size decreased.Plain Language Summary Gas production can cause earthquakes, which can be felt at the Earth's surface. Even though these earthquakes are relatively small, they can sometimes cause damage to housing and infrastructure which may have large societal and economic impact. An example of this problem are the earthquakes in the Groningen gas field in the north of the Netherlands, where the damages due to induced earthquakes have led to a production cap and early phase-out of gas production. An important question is how the earthquakes are made, and how large the earthquakes may become. Here we modeled the production-induced earthquakes with geomechanical modeling, which calculates the effect of gas production (pressure changes) on the forces (stresses) in the subsurface. These altered stresses can exceed the strength of preexisting faults in the subsurface, causing the fault to break and generate an earthquake. The modeling results showed that earthquake size depended on many factors such as the initial stress in the reservoir and the fault behavior. The earthquakes often remained confined within the gas producing interval. The geometry of the gas reservoir and faults played a large role in generating the earthquake. Results are consistent with field observations and help to understand the timing, location, and size of seismic events.

Understanding the mechanisms and key parameters controlling depletion-induced seismicity is key for seismic hazard analyses and the design of mitigation measures. In this paper a methodology is presented to model in 2D the static stress development on faults offsetting depleting reservoir compartments, reactivation of the fault, nucleation of seismic instability, and the subsequent fully dynamic rupture including seismic fault rupture and near-field wave propagation. Slip-dependent reduction of the fault's strength (cohesion and friction) was used to model the development of the instability and seismic rupture. The inclusion of the dynamic calculation allows for a closer comparison to field observables such as borehole seismic data compared to traditional static geomechanical models. We applied this model procedure to a fault and stratigraphy typical for the Groningen field, and compared the results for an offset fault to a fault without offset. A non-zero offset on the fault strongly influenced the stress distribution along the fault due to stress concentrations in the near-fault area close to the top of the hanging wall and the base of the footwall. The heterogeneous stress distribution not only controlled where nucleation occurred within the reservoir interval, but also influenced the subsequent propagation of seismic rupture with low stresses inhibiting the propagation of slip. In a reservoir without offset the stress distribution was relatively uniform throughout the reservoir depth interval. Reactivation occurred at a much larger pressure decrease, but the subsequent seismic event was much larger due to the more uniform state of stress within the reservoir. In both cases the models predicted a unidirectional downward-propagating rupture, with the largest wave amplitudes being radiated downwards into the hanging wall. This study showed how a realistic seismic event could be successfully modelled, including the depletion-induced stressing, nucleation, dynamic propagation, and wave propagation. The influence of fault offset on the depletion-induced stress is significant; the heterogeneous stress development along offset faults not only strongly controls the timing and location of a seismic slip, but also influences the subsequent rupture size of the dynamic event.

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We implement a Coulomb rate-and-state approach to explore the nonlinear relation between stressing rate and seismicity rate in the Groningen gas field. Coulomb stress rates are calculated, taking into account the 3-D structural complexity of the field and including the poroelastic effect of the differential compaction due to fault offsets. The spatiotemporal evolution of the Groningen seismicity must be attributed to a combination of both (i) spatial variability in the induced stressing rate history and (ii) spatial heterogeneities in the rate-and-state model parameters. Focusing on two subareas of the Groningen field where the observed event rates are very contrasted even though the modeled seismicity rates are of similar magnitudes, we show that the rate-and-state model parameters are spatially heterogeneous. For these two subareas, the very low background seismicity rate of the Groningen gas field can explain the long delay in the seismicity response relative to the onset of reservoir depletion. The characteristic periods of stress perturbations, due to gas production fluctuations, are much shorter than the inferred intrinsic time delay of the earthquake nucleation process. In this regime the modeled seismicity rate is in phase with the stress changes. However, since the start of production and for two subareas of our analysis, the Groningen fault system is unsteady and it is gradually becoming more sensitive to the stressing rate.

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