Cornelius Langenbruch

Seismogenic index and magnitude probability of earthquakes induced during reservoir fluid stimulations

An important characteristic of seismicity is the distribution of magnitudes of earthquakes. Fluid injection in rocks, aimed to create enhanced geothermal systems (EGS), can sometimes produce significant seismic events (e.g., Majer et al., 2007). This is rarely the case in hydraulic fracturing of hydrocarbon reservoirs. However, in any case the behavior of the seismicity triggering in space and in time is controlled by the process of stress relaxation and pore-pressure perturbation that was initially created at the injection source. This relaxation process can be approximated by pressure diffusion (possibly a nonlinear one) in the pore fluid of rocks (e.g., Shapiro and Dinske, 2009). At some locations the tectonic stress in the Earths crust is close to a critical stress, causing brittle failure of rocks. Increasing fluid pressure in such a reservoir causes pressure in the connected pore and fracture space of rocks to increase. Such an increase in the pore pressure consequently causes a decrease of the eff...

How will induced seismicity in Oklahoma respond to decreased saltwater injection rates

Earthquake rates in Oklahoma should significantly decrease by the end of 2016 and approach historic levels within the next years. In response to the marked number of injection-induced earthquakes in north-central Oklahoma, regulators recently called for a 40% reduction in the volume of saltwater being injected in the seismically active areas. We present a calibrated statistical model that predicts that widely felt M ≥ 3 earthquakes in the affected areas, as well as the probability of potentially damaging larger events, should significantly decrease by the end of 2016 and approach historic levels within a few years. Aftershock sequences associated with relatively large magnitude earthquakes that occurred in the Fairview, Cherokee, and Pawnee areas in north-central Oklahoma in late 2015 and 2016 will delay the rate of seismicity decrease in those areas.

Decay rate of fluid-induced seismicity after termination of reservoir stimulations

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 t...

Acoustic emission induced by pore-pressure changes in sandstone samples

An understanding of microseismicity induced by pore-pressure changes in stressed rocks is important for applications in geothermal and hydrocarbon reservoirs as well as for CO 2 sequestrations. We have studied the triggering mechanisms of microseismicity (or acoustic emission in the laboratory) as a function of triaxial stress conditions and pore-pressure changes. In investigating the spatiotemporal distribution of acoustic emission activity in water-saturated triaxially stressed Flechtingen Sandstone samples subjected to changes in pore pressure, we assumed that acoustic events were triggered by pore-pressure increase. To estimate pore-pressure changes in the sample, we used an analytical solution of the 1D diffusion equation. A theoretical analysis of the spatiotemporal distribution suggested that for initially insignificantly stressed samples, acoustic events were triggered by the migration of a critical pore-pressure level through the sample. The critical level was controlled by the applied pore press...

Gutenberg‐Richter relation originates from Coulomb stress fluctuations caused by elastic rock heterogeneity

Based on measurements along boreholes, a characterization of the Earths crust elastic heterogeneity is presented. We investigate its impact on Coulomb stress distribution and earthquake magnitude scaling. The analysis of elastic modulus distribution at various borehole locations in different regions reveals universal fractal nature of elastic heterogeneity. By applying a homogeneous far-field stress to a representative model of elastic rock heterogeneity, we show that it causes strong Coulomb stress fluctuations. In situ fluctuations of Coulomb stress are mainly controlled by in situ elastic moduli. Fluctuations caused by surrounding heterogeneities are only of minor importance. Hence, the fractal nature of elastic heterogeneity results in Coulomb stress fluctuations with power law size distribution. As a consequence, fault sizes and magnitudes of earthquakes scale according to the Gutenberg-Richter relation. Due to the universal fractal nature of elastic heterogeneity, the b value should be universal. Deviation from its universal value of b ≈1 occurs due to characteristic scales of seismogenic processes, which cause limitations or changes of fractal scaling. Scale limitations are also the reason for observed stress dependency of the b value. Our analysis suggests that the Gutenberg-Richter relation originates from Coulomb stress fluctuations caused by elastic rock heterogeneity.

A statistical model for seismic hazard assessment of hydraulic-fracturing-induced seismicity

We analyze the interevent time distribution of hydraulic-fracturing-induced seismicity collected during 18 stages at four different regions. We identify a universal statistical process describing the distribution of hydraulic-fracturing-induced events in time. The distribution of waiting times between subsequently occurring events is given by the exponential probability density function of the homogeneous Poisson process. Our findings suggest that hydraulic-fracturing-induced seismicity is directly triggered by the relaxation of stress and pore pressure perturbation initially created by the injection. Therefore, compared to this relaxation, the stress transfer caused by the occurrence of preceding seismic events is mainly insignificant for the seismogenesis of subsequently occurring events. We develop a statistical model to compute the occurrence probability of hydraulic-fracturing-induced seismicity. This model can be used to assess the seismic hazard associated with hydraulic fracturing operations. No aftershock triggering has to be included in the statistical model.

Response to Comment on “How will induced seismicity in Oklahoma respond to decreased saltwater injection rates?”

Earthquake rates in Oklahoma confirm our forecasted response of induced seismicity to reduced saltwater injection rates. Goebel et al. question our forecasted response of induced seismicity to reduction of saltwater injection rates in north-central Oklahoma and raise the concern that “the probability of future damaging earthquakes may be underestimated.” We compare our prediction to earthquake data recorded in the 8 months after publication. Observed seismicity rates and magnitudes agree with the forecast of our model. Our use of a probabilistic model accounts for uncertainties and observed M ≥ 4.5 to date confirm the conservative nature of our prediction. The “realistic parameter range” suggested by Goebel et al. is based on a misunderstanding of our statistical model and disagrees with the long-term decay of seismicity in the region.

Elastic Rock Heterogeneity Controls Brittle Rock Failure during Hydraulic Reservoir Stimulation

It is still an open question, to what extend brittle rock failure and associated microseismicity during hydraulic reservoir stimulation is related to elastic heterogeneity of the rock being fractured. We compare occurrence of microseismicity to elastic rock heterogeneity, obtained from sonic logs. Our observations suggest that rock heterogeneity controls the occurrence probability of brittle failure. We observe that the density of events is increasing with the Brittleness Index (BI) of the rock, which is defined as a combination of Young’s modulus and Poisson’s ratio. Because the BI has been introduced without physical justification, we evaluate its physical meaning and present a model to characterize the influence of elastic rock heterogeneity on the occurrence probability of rock failure. Our analysis is based on the computation of stress fluctuations caused by elastic heterogeneity of rocks. In the case of elastically isotropic rocks, our model suggests that the probability of rock failure increases with the BI. However, evaluation of a transverse isotropic model confirms that there are limitations in the applicability of the BI as a sweet spot indicator for hydraulic fracturing placement. Interpretation of the BI has to be done with great care, because its physical meaning varies for different reservoir locations.

Induced Seismicity After Termination of Rock Stimulations: Possibilities For Reservoir Characterization

In this paper we analyze the temporal distribution of fluid induced microseismicity and show which information about reservoir and source can be extracted from the seismicity rate. We assume that microseismic events induced through fluid injections are triggered by a pure diffusive process of pore pressure relaxation. We improve an existing formulation for the seismicity rate of fluid induced microseismicity, which is developed based on this assumption. In this way we derive to a formulation, which describes the temporal distribution of microseismic activity in dependency on the parameters of source and reservoir. In the next step we show that the well known Omori law, which describes the frequency of aftershock occurrence, can be transferred to the case of fluid induced microseismicity to describe the temporal distribution of events induced after injection stop. Even in seismology the controlling parameters of the characteristic p-value of the Omori law are still under discussion. Here we identify the controlling parameters of the p-value for fluid induced seismicity and show, which parameters of source and reservoir can be reconstructed by a p-value analysis. Finally we apply the developed theory to synthetic data sets and to the Fenton Hill (1983) real data example.

Physics-based forecasting of man-made earthquake hazards in Oklahoma and Kansas

Reinjection of saltwater, co-produced with oil, triggered thousands of widely felt and several damaging earthquakes in Oklahoma and Kansas. The future seismic hazard remains uncertain. Here, we present a new methodology to forecast the probability of damaging induced earthquakes in space and time. In our hybrid physical–statistical model, seismicity is driven by the rate of injection-induced pressure increases at any given location and spatial variations in the number and stress state of preexisting basement faults affected by the pressure increase. If current injection practices continue, earthquake hazards are expected to decrease slowly. Approximately 190, 130 and 100 widely felt M ≥ 3 earthquakes are anticipated in 2018, 2019 and 2020, respectively, with corresponding probabilities of potentially damaging M ≥ 5 earthquakes of 32, 24 and 19%. We identify areas where produced-water injection is more likely to cause seismicity. Our methodology can be used to evaluate future injection scenarios intended to mitigate seismic hazards.Reinjection of saltwater, co-produced with oil, has the potential to trigger damaging earthquakes. Here, using Oklahoma and Kansas as an example, the authors present a new physics-based methodology to forecast future probabilities of potentially damaging induced-earthquakes in space and time.