Modeling Frictional Processes in the Presence of Fluids: From Earthquakes in the Laboratory to Induced Seismicity in Geothermal Reservoirs

Citation

Kim, Taeho (2025) Modeling Frictional Processes in the Presence of Fluids: From Earthquakes in the Laboratory to Induced Seismicity in Geothermal Reservoirs. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/pp3a-2609. https://resolver.caltech.edu/CaltechTHESIS:08132024-035518437

Abstract

Induced seismicity - earthquakes driven by injections of fluids into the subsurface - is of growing societal importance in its impact on clean energy technology. Advancements central to the world’s transition to a greener economy such as geothermal energy and long-term geologic storage of CO2 are hampered by a lack of understanding and control of the associated seismic hazards. In its mechanics, frictional processes in the presence of fluids is a difficult problem to model given the challenges of studying frictionally unstable material in a controlled environment. Unstable gouge material is commonly found along faults in nature, due to pulverization of brittle rock in to granular layers called `gouge.' This thesis approaches the challenge at two different scales: 1. at the scale of the localized shear layer along the interface between two faults where we model laboratory earthquakes in the presence of pressurized fluids, and 2. at the scale of a reservoir where we model the rate of earthquakes given the injection/extraction schedule.

In order to infer the frictional properties of unstable gouge material from laboratory experiments, we develop a probabilistic model based on a spring-slider representation of the experiment along with the rate-and-state friction law. Inversions indicate that the presence of pressurized pore fluids stabilizes the gouge - by an increase in the strength of the contacts and a lesser decrease in the grain size with slip - even under the same effective normal stress. Assuming purely slip-dependent healing of friction leads to an evolution of parameters with slip that is consistent with previously established interpretations of rate-and-state parameters. The best fitting spring-slider model still shows significant discrepancies to the experiment in the evolution of creep and in the dependence on loading rate. A quasi-static finite-element model with the same rate-and-state properties suggests that the gouge in the sample likely slides in a spatially uniform manner. Thus, the discrepancies between the spring-slider model and the experiment can likely be attributed to flaws in the rate-and-state formalism and the slip law rather than the idealization of a finite geometry to a single-degree-of-freedom system. The results prove that quantitative analysis of frictional processes of gouge in the unstable regime is possible, and that future development of constitutive relationships for friction should aim to reproduce key features of stick-slip in detail.

To model seismicity induced by a geothermal well stimulation, we develop physical and statistical models of the seismicity rate. The physical models are based on rate-and-state friction and stress changes due to pore-pressure diffusion. The statistical model performs a convolution of a kernel function inspired by Omori law decay with the injection rate. Both models successfully reproduce the seismicity observed during the 2018 enhanced geothermal system (EGS) simulation in Otaniemi, Finland. We find that the effect of time-dependent nucleation from rate-and-state friction is crucial in reproducing the temporal and spatial patterns of the observed seismicity. We also find that the effect of finite nucleation cannot be approximated well by introducing a stress threshold in the standard Coulomb friction model, at least in the context of rapid variations of injection rates common in EGS operations.

We highlight the major assumptions of the Dieterich seismicity rate model and examine how they may bias interpretations of induced seismicity observed in real reservoirs by comparing it directly to a Discrete Fault Network (DFN) model. The spatio-temporal pattern of seismicity in the finite setting is not only dependent on fluid transport properties and its combination with nucleation characteristics but also the distribution of initial conditions of the fault network. The back-propagation front, in particular, occurs co-injection if the time to instability for the minimum slip rate is shorter than the injection duration. The relocated catalogue of the 1993 GPK1 stimulation in Soultz-Sous-Forets shows such a back-front which can be fit qualitatively using the time to instability measure. A simple model for the rate of magnitudes that accounts for the evolution of frictional stability reproduces the apparent increase in the source radius of induced events in Soultz-Sous-Forets. The rate of larger events is overestimated by the model, possibly due to an overestimation of maximum magnitudes by the volume of stimulation. The comparisons reveal that parameters of the Dieterich model lack clear physical meaning in the finite analogue and highlight the importance of using realistic physics, especially in models at large scales where uncertainty due to assumptions at smaller scales may be amplified.

We end the thesis with the application of rate-and-state friction to dynamic rupture modeling of seismic data from distributed acoustic sensing (DAS). The modeling of the high-frequency DAS recordings of a Magnitude 6.0 earthquake suggests a highly heterogeneous underlying fault with several prominent asperities and barriers that may control rupture dynamics. The model demonstrates how the high-stress patches both inhibit and promote the overall rupture, while also contributing to a significant amount of the energy release themselves. The successful interpretations of modern seismological data encourage future development efficient models that can be used for dynamic inversions.

Thesis Files