A stress model for nonlinear reservoir compaction and application to the post shut-in Groningen gas field

Seismic source models that use an elastic relation between pressure decrease, compaction and stress change have been shown to successfully reproduce induced seismicity in producing natural gas reservoirs undergoing differential compaction. However, this elastic relation is inconsistent with observations of nonlinear reservoir compaction in the Groningen field. We utilize critical state mechanics theory to derive a 3-D stress–strain framework that is able to house 1-D nonlinear stress–strain relations typically used for subsidence models, without the need for recalibration of the subsidence model parameters. This is used to adapt the elastic thin sheet stress model that is currently in use as the state-of-the-art for seismicity predictions as part of the hazard and risk assessment of the Groningen gas field. The new thin sheet model has one additional model parameter that modulates the impact of inelastic deformation on fault loading, whilst keeping the intended function of the model calibration from the original elastic thin sheet model intact. The resulting elastic-viscoplastic thin sheet stress model is consistent with previously reported nonlinear rate-dependent reservoir compaction in Groningen found from inverting subsidence data and from rock deformation experiments. Our elastic-viscoplastic thin sheet stress model is able to predict ongoing stress increase, and therefore ongoing seismicity, in areas where pressure does not decrease anymore due to shut in. A pseudo-prospective forecasting exercise indeed shows that the elastic-viscoplastic stress model performs better than the linear elastic stress model. This model addition ensures that the Groningen seismic source model is well suited for predicting seismicity in the post shut-in phase