Publications

2024

1. 

   Fluid-driven slow slip and earthquake nucleation on a slip-weakening circular fault

   Alexis Sáez ,  and  Brice Lecampion

   Journal of the Mechanics and Physics of Solids, 2024

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   We investigate the propagation of fluid-driven fault slip on a slip-weakening frictional interface separating two identical half-spaces of a three-dimensional elastic solid. Our focus is on axisymmetric circular shear ruptures as they capture the most essential aspects of the dynamics of unbounded ruptures in three dimensions. In our model, fluid-driven aseismic slip occurs in two modes: as an interfacial rupture that is unconditionally stable, or as the quasi-static nucleation phase of an otherwise dynamic rupture. Unconditionally stable ruptures progress through four stages. Initially, ruptures are diffusively self-similar and the interface behaves as if it were governed by a constant friction coefficient equal to the static friction value. Slip then accelerates due to frictional weakening while the cohesive zone develops. Once the latter gets properly localized, a finite amount of fracture energy emerges along the interface. The rupture dynamics is then governed by an energy balance of the Griffith’s type. In this stage, fault slip transitions from a large-toughness to a small-toughness regime due to the diminishing effect of the fracture energy in the near-front energy balance. Ultimately, self-similarity is recovered and the fault behaves again as having a constant friction coefficient, but this time equal to the dynamic friction value. This condition is equivalent to a fault interface operating to leading order with zero fracture energy. When slow slip is the result of a frustrated dynamic instability, slip also initiates self-similarly at a constant peak friction coefficient. The maximum size that aseismic ruptures can reach before becoming unstable can be as small as a critical nucleation radius (shear modulus divided by the slip-weakening rate) and as large as infinity when faults are close to a well-defined limit that separates the two modes of aseismic sliding. In the former case, earthquake nucleation occurs unaffected by the dynamic friction coefficient. In contrast, the latter case exhibits fracture-mechanics behavior, characterized by a finite influx of elastic strain energy being supplied to and dissipated at the rupture front. We provide analytical and numerical solutions for the problem solved over its full dimensionless parameter space, including expressions for relevant length and time scales characterizing the transition between different stages and regimes. Due to its three-dimensional nature, the model enables quantitative comparisons with field observations as well as preliminary engineering design of hydraulic stimulation operations. Existing laboratory and in-situ experiments of fluid injection into simulated and natural faults are briefly discussed in light of our results.

2023

1. 

   Three-dimensional fluid-driven frictional ruptures: theory and applications

   Alexis Sáez

   2023

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   Fluid-driven frictional ruptures are important in a broad range of subsurface engineering technologies and natural earthquake-related phenomena. Some examples of subsurface operations where borehole fluid injections can induce frictional slip are deep geothermal energy, CO2 and hydrogen geological storage, and wastewater disposal from oil and gas production, among many others. On the other hand, natural phenomena such as seismic swarms, aftershock sequences, and slow earthquakes, are often associated with transients of pore-fluid pressure and fault slip. Motivated by the aforementioned applications and phenomena, this doctoral thesis aims to mechanistically understand how pre-existing geological structural discontinuities such as fractures and faults slide due to the pressurization of pore fluids, in a three-dimensional configuration that can be used for quantitative comparisons with field observations and preliminary engineering designs. We first develop a numerical solver for frictional slip and fault opening along pre-existing networks of discontinuities in 3D elastic media. We then examine a model with Coulomb’s friction to reproduce the initiation, propagation, and arrest of fluid-driven stable frictional ruptures. We show that a dimensionless number containing information about the initial stress state of the fault and the intensity of the injection governs the dynamics and shape of the ruptures in all its stages. Next, we extend the model to account for a friction coefficient that weakens with slip. This results in a broader range of fault slip behaviors, from unconditionally stable slip to dynamic instabilities. We quantify the conditions controlling both the propagation of stable slip and the nucleation of earthquakes. It is shown that the Coulomb’s friction model is both an early-time and late-time asymptotic solution of the more general slip-weakening model. After, we generalize some important fault rupture regimes to account for fairly arbitrary fluid injections. In particular, the connection between the expansion rate of the slipping surface and the history of injection volume rate is established. Using field observations, we then apply and explore the implications of our modeling results to injection-induced seismicity –a critical concern in the geo-energy industry. We show how the history of injection rate may control the migration patterns of micro-seismicity, and how these patterns may contain important information about in-situ conditions such as the fault stress state. Further, we elaborate on how post-injection pulses of stable slip can continue triggering seismicity due to stress-transfer effects, long after fluid injections stop. Finally, we propose a theoretical scaling relation for the maximum magnitude of injection-induced slow slip events, which sheds light on how aseismic motions release potential energy during injection operations. This doctoral research offers for the first time a quantitative and conceptual framework for understanding various subsurface and earthquake-science problems associated with frictional ruptures induced by fluid injections. While some implications of our findings are already explored in detail here, this work opens the possibility of understanding a much broader range of field observations. Moreover, our research paves the way for designing laboratory experiments, which is the next step to ground the theory we develop.

2. 

   Post-injection aseismic slip as a mechanism for the delayed triggering of seismicity

   Alexis Sáez ,  and  Brice Lecampion

   Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2023

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   Injection-induced aseismic slip plays an important role in a broad range of human-made and natural systems, from the exploitation of geo-resources to the understanding of earthquakes. Recent studies have shed light on how aseismic slip propagates in response to continuous fluid injections. Yet much less is known about the response of faults after the injection of fluids has stopped. In this work, we investigate via a hydro-mechanical model the propagation and ultimate arrest of aseismic slip during the so-called post-injection stage. We show that after shut-in, fault slip propagates in pulse-like mode. The conditions that control the propagation as a pulse and notably when and where the ruptures arrest are fully established. In particular, critically stressed faults can host rupture pulses that propagate for several orders of magnitude the injection duration and reach up to nearly double the size of the ruptures at the moment of shut-in. We consequently argue that the persistent stressing of increasingly larger rock volumes caused by post-injection aseismic slip is a plausible mechanism for the triggering of post-injection seismicity—a critical issue in the geo-energy industry. Our physical model shows quantitative agreement with field observations of documented cases of post-injection induced seismicity.

3. Shearing and opening of a pre-existing discontinuity in response to fluid injection

   B. Lecampion ,  A. Sáez ,  and  A. Gupta

   Jun 2023

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   We investigate the fluid-driven growth ofa shear crack along a frictional discontinuity and its transition to hydraulic fracturing (sometimes referred to as hydraulic jacking) under plane-strain conditions. We focus on the case of a constant friction coefficient and account for the permeability changes associated with the fracture opening. By combining the scaling analysis and numerical simulations, we examine the evolution of both the shear and opening fronts as a function of the hydro-mechanical properties of the pre-existing discontinuity, in-situ stress state, and the fluid injection conditions. Further, we derive an approximate analytical solution for the relation between the positions of the slip and opening fronts at large times. We notably show that the ratio between the slip and opening fronts converges to a constant value at late times which only depends on the ratio between the shear stress and shear strength acting initially along the discontinuity. We compare this approximate solution against numerical simulations and demonstrate its usage to serve as a benchmark solution in the development of coupled hydro-mechanical numerical solvers for frictional fluid-driven fractures.Hydraulic stimulation of pre-existing fractures is used in the geothermal development in order to increase reservoir permeability and achieve economical flow rates - with mixed success (Jung, 2013; McClure and Horne, 2014). Although the primary idea is to shear dilate these pre-existing discontinuities via injection, in a number of field tests (Guglielmi et al., 2020), a large increase of permeability is only observed when fracture opening has been reached (sometimes denoted as hydraulic jacking). Shearing of pre-existing discontinuities can also occur during more traditional hydraulic fracturing operations in oil and gas reservoirs, either by direct fluid pressurization or via stress transfer from the main fractures. In this contribution, we investigate the fluid-driven growth of a shear crack along a frictional discontinuity and its transition to hydraulic fracturing. We focus on the case of a constant friction coefficient and account for permeability changes associated with fracture opening. We use a fully coupled implicit numerical scheme for the solution of this non-linear hydro-mechanical problem. Notably, the frictional interface behavior is modeled using an elastoplastic constitutive relation with a non-associated flow rule.

2022

1. 

   Three-dimensional fluid-driven stable frictional ruptures

   Alexis Sáez ,  Brice Lecampion ,  Pathikrit Bhattacharya , and 1 more author

   Journal of the Mechanics and Physics of Solids, Jun 2022

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   We investigate the quasi-static growth of a fluid-driven frictional shear crack that propagates in mixed mode (II+III) on a planar fault interface that separates two identical half-spaces of a three-dimensional solid. The fault interface is characterized by a shear strength equal to the product of a constant friction coefficient and the local effective normal stress. Fluid is injected into the fault interface and two different injection scenarios are considered: injection at constant volume rate and injection at constant pressure. We derive analytical solutions for circular ruptures which occur in the limit of a Poisson’s ratio ν=0 and solve numerically for the more general case in which the rupture shape is unknown (ν≠0). For an injection at constant volume rate, the fault slip growth is self-similar. The rupture radius (ν=0) expands as R(t)=λL(t), where L(t) is the nominal position of the fluid pressure front and λ is an amplification factor that is a known function of a unique dimensionless parameter T. The latter is defined as the ratio between the distance to failure under ambient conditions and the strength of the injection. Whenever λ>1, the rupture front outpaces the fluid pressure front. For ν≠0, the rupture shape is quasi-elliptical. The aspect ratio is upper and lower bounded by 1/(1−ν) and (3−ν)/(3−2ν), for the limiting cases of critically stressed faults (λ≫1, T≪1) and marginally pressurized faults (λ≪1, T≫1), respectively. Moreover, the evolution of the rupture area is independent of the Poisson’s ratio and grows simply as Ar(t)=4παλ2t, where α is the fault hydraulic diffusivity. For injection at constant pressure, the fault slip growth is not self-similar: the rupture front evolves at large times as ∝(αt)(1−T)/2 with T between 0 and 1. The frictional rupture moves at most diffusively (∝αt) when the fault is critically stressed, but in general propagates slower than the fluid pressure front. Yet in some conditions, the rupture front outpaces the fluid pressure front. The latter will eventually catch the former if injection is sustained for sufficient time. Our findings provide a basic understanding on how stable (aseismic) ruptures propagate in response to fluid injection in 3-D. Notably, since aseismic ruptures driven by injection at constant rate expand proportionally to the squared root of time, seismicity clouds that are commonly interpreted to be controlled by the direct effect of fluid pressure increase might be controlled by the stress transfer of a propagating aseismic rupture instead. We also demonstrate that the aseismic moment M0 scales to the injected fluid volume V as M0∝V3/2.