Pore-fluid Pressure Diffusion Research Articles

Hydro-mechanical earthquake cycles in a poro-visco-elasto-plastic fluid-bearing fault structure

A major goal in earthquake physics is to derive a constitutive framework for fault slip that captures the dependence of shear strength on fault rheology, sliding velocity, and pore-fluid pressure. In this study, we present H-MEC (Hydro-Mechanical Earthquake Cycles), a newly-developed two-phase flow numerical framework — which couples solid rock deformation and pervasive fluid flow — to simulate how crustal stress and fluid pressure evolve during the earthquake cycle. This unified, continuum-based model, incorporates a staggered finite difference–marker-in-cell method and accounts for inertial wave-mediated dynamics and fluid flow in poro-visco-elasto-plastic compressible medium. Global Picard-iterations and an adaptive time stepping allow the correct resolution of both long- and short-time scales, ranging from years to milliseconds. We present a comprehensive in-plane strike-slip setup in which we test analytical poroelastic benchmarks of pore-fluid pressure diffusion from an injection point along a finite fault width. We then investigate how pore-fluid pressure evolution and solid–fluid compressibility control sequences of seismic and aseismic fault slip. While the weakening phase is controlled by localized compaction of pores and dynamic self-pressurization of fluids inside the undrained fault zone, the subsequent propagation of dynamic ruptures is driven by pore-pressure waves. Furthermore, pore-fluid pressure conditions on the fault and shear strength weakening associated with rapid self-pressurization of fluids control the characteristic slip-weakening distance, the final size of seismic events, and the scaling between slip and fracture energy observed for large earthquakes. Our modeling results demonstrate that fault failure can occur due to poroelastic coupling on a finite-width shear zone, thus highlighting the importance of considering the realistic hydro-mechanical structure of faults to investigate fluid-driven seismic and aseismic slip, either as a natural process or induced by human activities.

Investigation of the Thiva 2020–2021 Earthquake Sequence Using Seismological Data and Space Techniques

We investigate an earthquake sequence involving an Mw = 4.6 mainshock on 2 December 2020, followed by a seismic swarm in July–October 2021 near Thiva, Central Greece, to identify the activated structures and understand its triggering mechanisms. For this purpose, we employ double-difference relocation to construct a high-resolution earthquake catalogue and examine in detail the distribution of hypocenters and the spatiotemporal evolution of the sequence. Furthermore, we apply instrumental and imaging geodesy to map the local deformation and identify long-term trends or anomalies that could have contributed to stress loading. The 2021 seismic swarm was hosted on a system of conjugate normal faults, including the eastward extension of the Yliki fault, with the main activated structures trending WNW–ESE and dipping south. No pre- or coseismic deformation could be associated with the 2021 swarm, while Coulomb stress transfer due to the Mw = 4.6 mainshock of December 2020 was found to be insufficient to trigger its nucleation. However, the evolution of the swarm is related to stress triggering by its major events and facilitated by pore-fluid pressure diffusion. The re-evaluated seismic history of the area reveals its potential to generate destructive Mw = 6.0 earthquakes; therefore, the continued monitoring of its microseismicity is considered important.

Scaling properties and anomalous diffusion of the Florina micro-seismic activity: Fluid driven?

Episodic earthquake activity associated with pore-fluid pressure diffusion in the crust can frequently be observed in intraplate regions, particularly related with past volcanism. Increased micro-seismicity has been observed during 2012–2014 in such an area, near the CO2-rich Florina basin (North Greece). Using a high-resolution relocated catalog for the area, we use concepts of statistical physics to study the spatiotemporal and diffusion properties of micro-seismicity and investigate the possible involvement of fluids in the triggering mechanism. The spatial distribution of events shows that seismicity mainly occurred in two clusters, one dipping to the north (cluster A) and the other on an almost vertical fault plane (cluster B). We focus on cluster B, which was mainly activated after the installation of a local seismic network, able to detect and record the increased micro-seismicity in the area. Cluster B was activated during two main periods (periods B1–B2), with an almost vertical alignment of events with depth. During the second period of activation (period B2), events are migrating towards the surface with time indicating a diffusive process. Furthermore, the estimation of the mean square displacement of seismicity with time during the two main periods of activation shows very weak earthquake diffusion during period B1, but more pronounce earthquake diffusion during period B2, with a diffusion exponent that corresponds to a sub-diffusive process. In addition, we use non-extensive statistical mechanics to study the spatiotemporal scaling properties of seismicity, with results that indicate correlated behavior and organization patterns during both periods of activation. Observations and analysis indicate the possible involvement of fluids in the triggering mechanism of micro-seismicity. However, continued monitoring of seismicity and CO2 discharging would be required to better constrain the relation between seismicity and CO2 emissions in the CO2-rich Florina basin and to better quantify the associated earthquake and environmental hazards.

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.

Scaling of seismicity induced by nonlinear fluid‐rock interaction after an injection stop

AbstractFluid injections into unconventional reservoirs, performed for fluid‐mobility enhancement, are accompanied by microseismic activity also after the injection. Previous studies revealed that the triggering of seismic events can be effectively described by nonlinear diffusion of pore fluid pressure perturbations where the hydraulic diffusivity becomes pressure dependent. The spatiotemporal distribution of postinjection‐induced microseismicity has two important features: the triggering front, corresponding to early and distant events, and the back front, representing the time‐dependent spatial envelope of the growing seismic quiescence zone. Here for the first time, we describe analytically the temporal behavior of these two fronts after the injection stop in the case of nonlinear pore fluid pressure diffusion. We propose a scaling law for the fronts and show that they are sensitive to the degree of nonlinearity and to the Euclidean dimension of the dominant growth of seismicity clouds. To validate the theoretical finding, we numerically model nonlinear pore fluid pressure diffusion and generate synthetic catalogs of seismicity. Additionally, we apply the new scaling relation to several case studies of injection‐induced seismicity. The derived scaling laws describe well synthetic and real data.

Groundwater recharge as the trigger of naturally occurring intraplate earthquakes

Abstract I explore the hypothesis that most intraplate earthquakes and their aftershock sequences are triggered by pore-fluid pressure increases. As proposed in this paper, data from the magnitude 5.7 Virginia earthquake of 23 August 2011 show that this is a two-step process. (1) First, from areas where there is greater than normal meteoric recharge, pore-fluid pressure diffusion by means of Biot slow waves transfers more pore-fluid pressure towards a future hypocentre. Here the cumulation of Biot slow waves produces a steady increase in pore-fluid overpressure until a main shock is triggered. (2) Then, aftershocks occur in the zone reaching from the depth of the main shock to a depth of a few kilometres below the land surface, preferring to localize in a weaker, pervasive anisotropic crustal fabric, in response to locally increased permeability and pore-fluid pressure transients caused by the main shock. The primary corrosive agent responsible for reducing the strength of silicate minerals in this upper crustal zone is water, so that quartz-rich crust tends to have lower values of Poisson's ratio. I show here that increases in pore-fluid overpressure from normal groundwater recharge can start crack dilation leading to fracturing and the creation of new permeability. Previous chemical analyses across the Central Virginia Piedmont that hosted the 2011 Virginia shock show high upper crustal quartz content. This proposed two-step model for a main shock-aftershock sequence explains why intraplate earthquakes are rarely correlated with recognizable brittle faults at the Earth's surface. Supplementary material: A biography of John Costain is available at https://dx.doi.org/10.6084/m9.figshare.c.2854324.v3

Breakdown of a Pressurized Fingerlike Crack in a Permeable Solid

This paper is concerned with the analysis of a low-viscosity fluid injection into a pre-existing, fingerlike crack within a linear elastic, permeable rock, and of the conditions leading to the onset of the fracture propagation (i.e., the breakdown). The problem is of interest in reservoir waterflooding, supercritical CO2 injection for geological storage, and other subsurface fluid injection applications. Fluid injection into a stationary crack leads to its elastic dilation and pressurization, buffered by the fluid leak-off into the surrounding rock. The solution of the problem, therefore, requires coupling of the crack deformation and the full-space pore-fluid pressure diffusion in the permeable rock. Contrary to the case of propagating hydraulic fractures, when significant part of the energy input is dissipated in the viscous fluid flow in the fracture, we find that the viscous fluid pressure drop inside a stationary fracture can be often neglected (we establish the conditions when one can do so). This, in turn, allows for a semi-analytical solution of the problem using the Green's function method, and, furthermore, for the full analytical treatment of the small/large injection time asymptotics. We apply the transient pressurization solution to predict the onset of the propagation based on the criteria derived from the energy considerations for a fingerlike crack.

Back front of seismicity induced by non-linear pore pressure diffusion

Borehole fluid injections are accompanied by microseismic activity not only during but also after termination of the fluid injection. Previously, this phenomenon has been analysed, assuming that the main triggering mechanism is governed by a linear pressure diffusion in a hydraulically isotropic medium. In this context the so-called back front of seismicity has been introduced, which allows to characterize the hydraulic transport from the spatiotemporal distribution of post-injection induced events. However, rocks are generally anisotropic, and in addition, fluid injections can strongly enhance permeability. In this case, permeability becomes a function of pressure. For such situations, we carry out a comprehensive study about the behaviour and parametrization of the back front. Based on a model of a factorized anisotropic pressure dependence of permeability, we present an approach to reconstruct the principal components of the diffusivity tensor. We apply this approach to real microseismic data and show that the back front characterizes the least hydraulic transport. To investigate the back front of non-linear pore-fluid pressure diffusion, we numerically consider a power-law and an exponential-dependent diffusivity. To account for a post-injection enhanced hydraulic state of the rock, we introduce a model of a frozen (i.e., nearly unchanged after the stimulation) medium diffusivity and generate synthetic seismicity. We find that, for a weak non-linearity and 3D exponential diffusion, the linear diffusion back front is still applicable. This finding is in agreement with microseismic data from Ogachi and Fenton Hill. However, for a strong non-linear fluid–rock interaction such as hydraulic fracturing, the back front can significantly deviate from a time dependence of a linear diffusion back front. This is demonstrated for a data set from the Horn River Basin. Hence, the behaviour of the back front is a strong indicator of a non-linear fluid–rock interaction.

Evidence of Low-Magnitude Continued Reservoir-Induced Seismicity Associated with the Pertusillo Artificial Lake (Southern Italy)

The most common observations of reservoir‐induced seismicity (RIS) by filling artificial lakes are generally associated with the initial impoundment of the lake or the lake level increase above a previous maximum. Rarely, RIS persists for many years without a decrease in frequency or magnitude; if this occurs, it is called “protracted” or “continued” seismicity. Pertusillo artificial lake in high Agri Valley (southern Italy) is a small reservoir with a water column that fluctuates yearly by about 10–15 m (on average), corresponding to a pressure perturbation at the bottom of the lake of 0.10–0.15 MPa. Although the reservoir was filled in 1963, the microearthquake activity still occurring around the lake allows the categorization of such RIS as continued seismicity. We collected all microearthquakes ( M L≤2.7) recorded near the reservoir by two different seismic networks from January 2005 to June 2012 and analyzed their frequency–magnitude distribution, which showed a b value ( b =1.40) much higher than that expected for the investigated area. Even though the spatial seismicity pattern shows two distinct clusters to the northeast and southwest of the lake, we found that only the southwest seismicity is significantly correlated with the water level. The findings suggest that the physical driving mechanism is the 1D pore fluid pressure diffusion along the northeast–southwest fault zones, connecting the reservoir to the southern termination of the Monti della Maddalena fault system, with an average hydraulic diffusivity of ∼7.8 m2/s. Online Material: Figures of magnitude comparisons between catalogs, temporal occurrence of events, rainfall versus number of earthquakes, and number of events versus water level, and animated 3D views of seismicity and reservoir.

Control of pore fluid pressure diffusion on fault failure mode: Insights from the 2009 L'Aquila seismic sequence

The MW 6.13 L'Aquila earthquake ruptured the Paganica fault on 2009/04/06 at 01:32 UTC, and started a strong sequence of aftershocks. For the first four days, the region north of the hypocenter of the main quake was shaken by three large events (MW ∼ 5.0) that ruptured different patches of the Monti della Laga fault (hereafter “Campotosto”). In our hypothesis, these aftershocks were induced by a dramatic reduction in the fault's shear strength due to a pulse of pore fluid pressure released after the L'Aquila main earthquake. Here we model the time evolution of the pore fluid pressure northward from the main hypocenter. We show that, during the sequence, the Campotosto fault failed in multiple episodes, when the specific patches/asperities underwent fluid pressure‐related strength reductions of 7–10 MPa. Although such drops in strength are very large in amplitude, the contribution of other weakening mechanisms (perturbations of the Coulomb shear stress, and/or dynamic stresses induced by passing seismic waves) cannot be ruled out by our observations. However, the Coulomb shear stress variations either had negative amplitudes down to −0.2 MPa (i.e., tended to inhibit further seismic activity), or had very small positive amplitudes (<0.05 MPa). Paleoseismological evidence supports the hypothesis that larger events (MW 6.5–7) have occurred on the Paganica fault [EMERGEO Working Group, 2009], whereas Lucente et al. [2010] concluded that an important migration of pore fluids characterized the preparatory phase of the L'Aquila main shock. Consequently, the MW 6.13 L'Aquila earthquake may be analogous, at a larger scale, to one of the three Campotosto largest aftershocks. The complex behavior observed for the L'Aquila‐Campotosto fault system seems to be common to other seismogenic structures in the Central Apennines (e.g., the Umbria‐Marche fault system), and need to be taken into consideration for the assessment of seismic hazard.

Microseismic estimates of hydraulic diffusivity in case of non-linear fluid-rock interaction

SUMMARY As a rule, rock stimulation by fluid injection induces microearthquakes. Assuming that pore-fluid pressure diffusion is responsible for this phenomenon, one can use seismicity to estimate the hydraulic properties of rocks. Previously, for the estimation of hydraulic transport properties from the triggering front, it has been assumed that they are independent of time and pressure. However, fluid injections can strongly change permeability of rocks (e.g. hydraulic fracturing). In this paper, we investigate what kind of diffusivity estimates are provided by the triggering front in cases where hydraulic transport properties are functions of pore-fluid pressure (i.e. they are changing during the injection). In this case, the pressure relaxation results in a non-linear pore-fluid pressure diffusion associated with heterogeneously and time-dependent distributed permeability. We consider numerically two models of pressure-dependent hydraulic diffusivity, a power law and an exponential law. We generate synthetic microseismicity by solving corresponding 1-, 2- and 3-D non-linear diffusion equations. Our results show that the triggering front provides reasonable estimates of the effective diffusivity approximately corresponding to the hydraulic diffusivity resulting from the stimulation (including hydraulic fracturing) of rocks and thus constitute a significant conceptual update of the seismicity-based reservoir characterization approach.

Anisotropic P-SV-wave dispersion and attenuation due to inter-layer flow in thinly layered porous rocks

Elastic upscaling of thinly layered rocks typically is performed using the established Backus averaging technique. Its poroelastic extension applies to thinly layered fluid-saturated porous rocks and enables the use of anisotropic effective medium models that are valid in the low- and high-frequency limits for relaxed and unrelaxed pore-fluid pressures, respectively. At intermediate frequencies, wave-induced interlayer flow causes attenuation and dispersion beyond that described by Biot’s global flow and microscopic squirt flow. Several models quantify frequency-dependent, normal-incidence P-wave propagation in layered poroelastic media but yield no prediction for arbitrary angles of incidence, or for S-wave-induced interlayer flow. It is shown that generalized models for P-SV-wave attenuation and dispersion as a result of interlayer flow can be constructed by unifying the anisotropic Backus limits with existing P-wave frequency-dependent interlayer flow models. The construction principle is exact and is based on the symmetry properties of the effective elastic relaxation tensor governing the pore-fluid pressure diffusion. These new theories quantify anisotropic P- and SV-wave attenuation and velocity dispersion. The maximum SV-wave attenuation is of the same order of magnitude as the maximum P-wave attenuation and occurs prominently around an angle of incidence of [Formula: see text]. For the particular case of a periodically layered medium, the theoretical predictions are confirmed through numerical simulations.

Fluid-induced microseismicity in pre-stressed rock masses

We model microseismicity triggered by fluid injection on the basis of the theory of poroelasticity accounting for the external stress field. Consideration of the fully coupled poroelastic field equations enables us to apply a Coulomb failure criterion using pore fluid pressure and stress tensor as well as the coefficient of friction. The poroelastic fields are calculated with the finite-element method simulating fluid injection with constant injection rate into a 2-D domain. The influence of diffusivity, injection rate and stress field on the occurrence of microseismicity is analysed and compared to simulations based on pore fluid pressure diffusion only. We show that an anisotropic initial stress field causes elongated microseismic clouds. These clouds are indistinguishable from those generated in poroelastic solids under isotropic stress but exhibiting anisotropic hydraulic diffusivity. This similarity shows that microseismicity distributions dependent on both, the hydraulic properties and the coupling of pore fluid pressure to the stress field. In particular, neglecting the influence of the external stress field may lead to overestimation of the anisotropy of diffusivity tensor components. Furthermore, the results of our numerical simulations are strongly sensitive to changes of fluid injection rate.

Microseismic signatures of non-linear pore-fluid pressure diffusion

SUMMARY Most fractured porous rocks show a strong dependence of their fluid transport properties on the effective pressure and thus on the pore-fluid pressure. We investigate the case where the hydraulic transport properties are exponentially dependent on pore-fluid pressure. As a consequence, the process of pore-fluid pressure diffusion is governed by a non-linear diffusion equation. Solutions of this equation that describe fluid injection experiments are analysed and the associated microseismic signatures are explored. In particular, it is shown that this process of non-linear pore-fluid pressure diffusion allows us to define two signatures. One which is the triggering front corresponding to the triggering of microseismic events without changing the fluid transport properties significantly. The other signature is the so-called fracturing domain. It triggers the majority of microseismic events and alters the fluid transport properties significantly. Evidence for the microseismic signature of a fracturing domain at the Fenton Hill hydrofrac experiment is given.

Numerical simulation of seismicity due to fluid injection in a brittle poroelastic medium

It has recently been shown that rather small perturbations in effective stress due to fluid injection or withdrawal may trigger microseismi c events. Such events, typically in the magnitude range below magnitude 4 ML, have similar characteristics to normal tectonic earthquakes, with double-couple focal mechanisms implying a dominant shear motion at the source. In this paper we examine the nature of this mechanical fluid—rock interaction for the case of fluid injection in a hydrocarbon reservoir. Our model is based on the combination of a model of seismicity in dry rocks and a model of pore fluid pressure diffusion. The former involves a finite difference approximation of the equation of motion, and the latter follows a lattice Boltzmann approach. They are coupled via the concept of effective stress, applied both to the Mohr—Coulomb rupture criterion and to the volumetric elastic deformations, which in turn perturb the pore pressure. The simplifying assumptions are that the fluid and solid phases have the same bulk moduli and that strain compatibility conditions are not included. 2-D plane-strain simulations of fluid injections in an anisotropically pre-stressed elastic brittle medium illustrate the capabilities of the model: spontaneous inception and growth of shear fractures, in both the near and far fields, and explicit calculation of their seismic radiation, which feeds back into pore pressure perturbations. They also show that, as expected, the amount and rate of stress drop during the brittle rupture control the size and spatial density of the resulting fractures. Our model should prove to be relevant at least in two cases: as a simulation tool in the investigation of correlations between injection and producer wells which are thought to be of geomechanical origin in certain oil fields, and as a forward model in the inversion of focal mechanisms of pore-pressure-induced shear events.