Projecting seismicity induced by complex alterations of underground stresses with applications to geothermal systems

Seismicity associated with subsurface operations is a major societal concern. It is therefore critical to improve predictions of the induced seismic hazard. Current statistical approaches account for the physics of pore pressure increase only. Here, we present a novel mathematical model that generalises adopted statistics for use in arbitrary injection/production protocols and applies to arbitrary physical processes. In our model, seismicity is driven by a normalised integral over the spatial reservoir volume of induced variations in frictional Coulomb stress, which—combined with the seismogenic index—provides a dimensionless proxy of the induced seismic hazard. Our model incorporates the classical pressure diffusion based and poroelastic seismogenic index models as special cases. Applying our approach to modeling geothermal systems, we find that seismicity rates are sensitive to imposed fluid-pressure rates, temperature variations, and tectonic conditions. We further demonstrate that a controlled injection protocol can decrease the induced seismic risk and that thermo-poroelastic stress transfer results in a larger spatial seismic footprint and in higher-magnitude events than does direct pore pressure impact for the same amount of injected volume and hydraulic energy. Our results, validated against field observations, showcase the relevance of the novel approach to forecast seismic hazards induced by subsurface activities

Production-induced seismicity indicates a low risk of strong earthquakes in the Groningen gas field

The maximum possible earthquake related to gas production in Western Europe’s largest gas field, Groningen, Netherlands, is an urgent practical question. Here we show how to distinguish between induced and triggered tectonic earthquakes. We estimate the maximum possible induced magnitude in the Groningen gas field to be around Mw = 4. We extend the concept of the seismogenic index to gas-production, and calculate the worst-case probability of triggering a larger-magnitude tectonic earthquake in a continuum. The probability of a Mw5.5 earthquake at Groningen is significantly higher than at Pohang Geothermal System (South Korea), where a Mw5.5 earthquake was actually triggered. Due to a long history of production in Groningen, our model estimates that strong earthquakes (Mw ≥ 4) must have occurred there several times, in disagreement with the observations. This indicates that the Groningen gas field is inherently stable and the physical conditions to trigger large tectonic earthquakes likely do not exist

The surge of earthquakes in Central Oklahoma has features of reservoir-induced seismicity

The recent surge of seismicity in Oklahoma and Kansas is related to fluid disposal. Evidences suggest that critical parameters are the injection volume as well as injection depth but dominant physical processes and a corresponding model to describe the physics are still not clear. We analyse the spatio-temporal distribution of induced earthquakes in the basement and find visible signatures of pore pressure diffusion and poroelastic coupling, features which strongly resemble seismicity induced by the filling of artificial lakes, so-called reservoir-induced seismicity. We developed a first-principle model of underground reservoir-induced seismicity. The physics of the model are based upon the combined mechanisms of fluid mass added to the pore-space of the injection layer and acting as a normal stress on the basement surface, pore-fluid pressure diffusion in the basement as well as poroelastic coupling contributing to the pore-fluid pressure and stress. Furthermore, we demonstrate that underground reservoir-induced seismicity occurs preferably in normal faulting and strike-slip settings, the latter being prevalent in Oklahoma. Our model explains observed injection volume and depth dependence of the seismicity and should be considered as a basis for future hazard prediction and prevention as well as for planning possible disposal sites

Are maximum magnitudes of induced earthquakes controlled by pressure diffusion?

There is an ongoing discussion about how to forecast the maximum magnitudes of induced earthquakes based on operational parameters, subsurface conditions and physical process understanding. Although the occurrence of damage caused by induced earthquakes is rare, some cases have caused significant economic loss, injuries and even loss of life. We analysed a global compilation of earthquakes induced by hydraulic fracturing, geothermal reservoir stimulation, water disposal, gas storage and reservoir impoundment. Our analysis showed that maximum magnitudes scale with the characteristic length of pressure diffusion in the brittle Earth’s crust. We observed an increase in the nucleation potential of larger-magnitude earthquakes with time and explained it by diffusion-controlled growth of the pressure-perturbed part of faults. Numerical and analytical fault size modelling supported our findings. Finally, we derived magnitude scaling laws to manage induced seismic hazard of upcoming energy projects prior to operation. This article is part of the theme issue ‘Induced seismicity in coupled subsurface systems’

Temperature-dependent poroelastic and viscoelastic effects on microscale—modelling of seismic reflections in heavy oil reservoirs

We develop a new model for elastic properties of rocks saturated with heavy oil. The heavy oil is represented by a viscoelastic material, which at low frequencies and/or high temperatures behaves as a Newtonian fluid, and at high frequencies and/or low temperatures as a nearly elastic solid. The bulk and shear moduli of a porous rock saturated with such viscoelastic material are then computed using approximate extended Gassmann equations of Ciz and Shapiro by replacing the elastic moduli of the pore filling material with complex and frequency-dependent moduli of the viscoelastic pore fill. We test the proposed model by comparing its predictions with numerical simulations based on a direct finite-difference solution of equations of dynamic viscoelasticity. The simulations are performed for the reflection coefficient from an interface between a homogeneous fluid and a porous medium. The numerical tests are performed both for an idealized porous medium consisting of alternating solid and viscoelastic layers, and for a more realistic 3-D geometry of the pore space. Both sets of numerical tests show a good agreement between the predictions of the proposed viscoelastic workflow and numerical simulations for relatively high viscosities where viscoelastic effects are important. The results confirm that application of extended Gassmann equations in conjunction with the complex and frequency-dependent moduli of viscoelastic pore filling material, such as heavy oil, provides a good approximation for the elastic moduli of rocks saturated with such material. By construction, this approximation is exactly consistent with the classical Gassmann's equation for sufficiently low frequencies or high temperature when heavy oil behaves like a fluid. For higher frequencies and/or lower temperatures, the predictions are in good agreement with the direct numerical solution of equations of dynamic viscoelasticity on the microscale. This demonstrates that the proposed methodology provides realistic estimates of elastic properties of heavy oil rock

Scaling Microseismic Cloud Shape During Hydraulic Stimulation Using In Situ Stress and Permeability

Forecasting microseismic cloud shape as a proxy of stimulated rock volume may improve the design of an energy extraction system. The microseismic cloud created during hydraulic stimulation of geothermal reservoirs is known empirically to extend in the general direction of the maximum principal stress. However, this empirical relationship is often inconsistent with reported results, and the cloud growth process remains poorly understood. This study investigates microseismic cloud growth using data obtained from a hydraulic stimulation project in Basel, Switzerland, and explores its correlation with measured in situ stress. We applied principal component analysis to a time series of microseismicity for macroscopic characterization of microseismic cloud growth in two- and three-dimensional space. The microseismic cloud, in addition to extending in the general direction of maximum principal stress, expanded in the direction of intermediate principal stress. The orientation of the least microseismic cloud growth was stable and almost identical to the minimum principal stress direction. Further, microseismic cloud shape ratios showed good agreement when compared with in situ stress magnitude ratios. The permeability tensor estimated from microseismicity also provided a good correlation in terms of direction and magnitude with the microseismic cloud growth. We show that in situ stress plays a dominant role by controlling the permeability of each existing fracture in the reservoir fracture system. Consequently, microseismic cloud growth can be scaled by in situ stress as a first-order approximation if there is sufficient variation in the orientation of existing faults

Post-Einsteinian tests of gravitation

Einstein gravitation theory can be extended by preserving its geometrical nature but changing the relation between curvature and energy-momentum tensors. This change accounts for radiative corrections, replacing the Newton gravitation constant by two running couplings which depend on scale and differ in the two sectors of traceless and traced tensors. The metric and curvature tensors in the field of the Sun, which were obtained in previous papers within a linearized approximation, are then calculated without this restriction. Modifications of gravitational effects on geodesics are then studied, allowing one to explore phenomenological consequences of extensions lying in the vicinity of general relativity. Some of these extended theories are able to account for the Pioneer anomaly while remaining compatible with tests involving the motion of planets. The PPN Ansatz corresponds to peculiar extensions of general relativity which do not have the ability to meet this compatibility challenge.Comment: 19 pages Corrected typo

Post-Einsteinian tests of linearized gravitation

The general relativistic treatment of gravitation can be extended by preserving the geometrical nature of the theory but modifying the form of the coupling between curvature and stress tensors. The gravitation constant is thus replaced by two running coupling constants which depend on scale and differ in the sectors of traceless and traced tensors. When calculated in the solar system in a linearized approximation, the metric is described by two gravitation potentials. This extends the parametrized post-Newtonian (PPN) phenomenological framework while allowing one to preserve compatibility with gravity tests performed in the solar system. Consequences of this extension are drawn here for phenomena correctly treated in the linear approximation. We obtain a Pioneer-like anomaly for probes with an eccentric motion as well as a range dependence of Eddington parameter $\gamma$ to be seen in light deflection experiments.Comment: 15 pages. Accepted version, to appear in Classical and Quantum Gravit

Exchange Rate Regime, Real Exchange Rate, Trade Flows and Foreign Direct Investments: The case of Morocco

We study the behavior of the Real Effective Exchange Rate (REER) of the dirham against the European currencies (Europe of the 15), over the period 1960-2000 (annual data). We measure the volatility using standard deviation, and the misalignments as the difference between the actual REER and the equilibrium REER (NATREX model). We show that a rise of the volatility of the dirham reduces the trade flows (exports and imports). The misalignments affect also the trade flows: an overvaluation leads to a reduction in Morocco exports from, to a raise of Morocco imports, and globally to a deterioration of the trade balance with the European Union. On the other hand, neither the volatility nor the misalignments have an effect on the direct investments (FDI) in favor of Morocco