Jan Dirk Jansen

The effects of stress perturbations on friction are crucial for understanding earthquake triggering. Previous experimental studies have primarily been conducted at room temperature, where fault gouge materials typically exhibit velocity‐strengthening and frictionally stable behaviour. In this study, we investigate how variations in effective normal stress () influence fault (in‐)stability by performing ‐perturbation experiments on simulated carbonate fault gouges under fluid‐drained, hydrothermal conditions. Our results indicate that in the velocity‐neutral or ‐weakening regime, perturbing can reinforce frictional instability, leading to accelerated slow slips or enhanced stick‐slip events. This effect is particularly pronounced when the excitation period () approaches or exceeds the characteristic recurrence period () associated with pre‐perturbation instabilities. Stress drops of the resulting events can have larger amplitudes than expected from quasi‐steady‐state. When cyclic perturbations are imposed, slip events tend to synchronize at specific phases when is close to — notably between 0.5π and 1π in radian, corresponding to maximum destressing rate and minimum , respectively. Additionally, short‐period () perturbations can induce significant shear stress reduction (or fault weakening), with magnitudes comparable to the stress drops from stick slips, yet they are surprisingly associated with acoustically quiet slow slip, suggesting a stabilizing effect. These findings underscore the critical role of perturbation period in controlling fault response. In the context of induced seismicity, our results imply that cyclic or monotonic fluid injections should be carefully designed, considering both perturbation amplitude and period. Properly turned cyclic injections could potentially mitigate seismic risk by promoting quiet, slow slip over seismic fault slip.

Effectively mitigating induced seismicity in subsurface engineering operations within highly permeable, porous geo‐energy reservoirs requires a clear understanding of how fluid injection parameters influence the seismic response. In this study, we performed injection‐driven fault reactivation experiments on highly permeable saw‐cut Red Felser sandstone to provide new insight into the effect of injection pattern and rate on fault slip behavior and seismicity evolution. Three different pressurization rates were applied: high, medium, and low rates of 2, 1, and 0.2 MPa/min, respectively. Three injection patterns were also used: cyclic recursive, monotonic, and stepwise injections. Our results reveal that a high pressurization rate leads to increased slip velocity, more microseismic events, higher total acoustic emission (AE) energy, and a lower b‐value compared to tests with low pressurization rates. We postulate that a high pressurization rate enhances the likelihood of a sudden reduction in effective normal stress, leading to fault opening and the disruption of asperity contacts. Furthermore, results from samples subjected to various injection patterns demonstrate that the cyclic recursive pattern exhibits a higher maximum slip velocity, more episodes of slow slip, and greater radiated AE energy than a monotonic pattern. In the case of the cyclic recursive pattern, increasing the number of cycles increases shear stress drop, shear slip, and maximum slip velocity. Our findings suggest that using a monotonic injection pattern and low pressurization rate may mitigate seismicity on pre‐existing faults in a highly permeable, porous reservoir.

Depletion‐induced fault slip and seismicity in the Groningen natural gas field are known to be caused by compaction of reservoir rock, most likely at locations in faults where reservoir rock juxtaposes non‐reservoir rock leading to severely‐peaked shear stresses at the reservoir‐fault corners. The resulting fault slip is probably initially aseismic until a critical nucleation length is reached. Under the assumption of slip‐weakening friction, the nucleation length can be approximated with a classic stability criterion developed by Uenishi and Rice (U&R) in 2003 for a single‐peaked stress distribution. Earlier work revealed that the validity of this criterion breaks down when the fault offset exceeds approximately 70% of the reservoir height because interaction effects between neighboring stress peaks can no longer be ignored. We therefore extended the U&R criterion to cope with such a double‐peaked shear stress. The key mathematical innovation involves a singular functional form of the slip gradient which allows for the formulation of slip‐patch end conditions that can be directly extended to multiple patches. We derived an exact double‐patch eigenvalue criterion and an approximate closed‐form “Extended Uenishi and Rice (EU&R) criterion” that is dependent on a parameter representing the scaled distance between the slip patches. For examples with parameter values roughly based on those of the Groningen field, we found a good agreement between our approximate EU&R criterion and an exact eigenvalue‐based approach. Our results can serve as a robust code‐independent termination criterion during numerical simulation of depletion‐induced onset of seismicity resulting from natural gas or geothermal energy production.

Pore pressure fluctuation in subsurface reservoirs and its resulting mechanical response can cause fault reactivation. Numerical simulation of such induced seismicity is important to develop reliable seismic hazard and risk assessments. However, modeling of fault reactivation is quite challenging, especially in the case of displaced faults, i.e., faults with non-zero offset. In this paper, we perform a systematic benchmarking study to validate two recently developed numerical methods for fault slip simulation. Reference solutions are based on a semi-analytical approach that makes use of inclusion theory and Cauchy-type singular integral equations. The two numerical methods both use finite volume discretizations, but they employ different approaches to represent faults. One of them uses a conformal discrete fault model (DFM) while the other employs an embedded (non-conformal) fault model. The semi-analytical test cases cover a vertical frictionless fault, and inclined displaced faults with constant friction and slip-weakening friction. It was found that both numerical methods accurately represent pre-slip stress fields caused by pore pressure changes. Moreover, they also successfully cope with a vertical frictionless fault. However, for the case with an inclined displaced fault with a constant friction coefficient, the embedded method can not converge for the post-slip phase, whereas the DFM successfully coped with both constant and slip-weakening friction coefficients. In its current implementation, the DFM is therefore the model of choice when accurate simulation of local faulted systems is required.

We critically review the derivation of closed‐form analytical expressions for elastic displacements, strains, and stresses inside a subsurface reservoir undergoing pore pressure changes using inclusion theory. Although developed decades ago, inclusion theory has been used recently by various authors to obtain fast estimates of depletion‐induced and injection‐induced fault stresses in relation to induced seismicity. We therefore briefly address the current geomechanical relevance of this method, and provide a numerical example to demonstrate its use to compute induced fault stresses. However, the main goal of our paper is to correct some erroneous assumptions that were made in earlier publications. While the final expressions for the poroelastic stresses in these publications were correct, their derivation contained conceptual mistakes due to the mathematical subtleties that arise because of singularities in the Green's functions. The aim of our paper is therefore to present the correct derivation of expressions for the strains and stresses inside an inclusion and to clarify some of the results of the aforementioned studies. Furthermore, we present two conditions that the strain field must satisfy, which can be used to verify the analytical expressions.

We consider steady-state single-phase confined flow through a subsurface porous layer containing a displaced, fully conductive fault causing a sudden jump in the flow path, and we employ (semi-)analytical techniques to compute the corresponding pressures and fault stresses. In particular, we obtain a new solution for the pressure field with the aid of conformal mapping and a Schwarz–Christoffel transformation. Moreover, we use an existing technique to compute the poro-elastic stress field with the aid of inclusion theory. The additional resistance to fluid flow provided by a displaced fault, relative to the resistance in a layer without a fault, is a function of dip angle, fault throw divided by reservoir height, and reservoir width divided by reservoir height. Fluid flow has a larger effect on fault stresses in case of injection than in case of depletion, where injection with up-dip flow results in increased zones of fault slip near the bottom of the reservoir. Opposedly, injection with down-dip flow results in increased slip near the top of the reservoir. An order-of-magnitude estimate of the effect of steady-state flow across displaced faults in the Groningen natural gas reservoir shows that the effect on fault stresses is probably negligible. A similar estimate of the effect in low-enthalpy geothermal doublets indicates that steady-state flow may possibly play a small role, in particular close to the injector, but site-specific assessments will be necessary to quantify the effect.

Quantification of the poromechanical response of subsurface formations due to human-induced pore pressure fluctuations is critical for the performance and stability assessment of many geo-energy systems. In particular, natural faults in the subsurface introduce the hazard of induced seismicity. Numerical modeling of fault reactivation is challenging, while the specific details of induced stresses and fault slip in reservoirs with displaced (i.e. non-zero offset) faults may cause additional challenges depending on the type of numerical formulation employed. To facilitate the systematic development and testing of numerical tools for the simulation of induced seismicity in faulted reservoirs we developed a set of semi-analytical test problems of increasing complexity, based on inclusion theory and Cauchy singular integral equations. With these we investigate the accuracy of two recently developed Finite Volume (FV) schemes with collocated and staggered arrangements of unknowns. One of them employs a conformal discrete fault model (DFM) which can guarantee sufficient accuracy at the cost of adaptive mesh refinement but may suffer from modelling and computational challenges when addressing large-scale realistic geological configurations. The second one employs an embedded (or non-conformal) discrete fault model (EDFM) which avoids the need for excessive mesh refinement, but of which the accuracy and the range of applicability are still to be investigated. We found that both numerical schemes accurately represent the pre-slip Coulomb stresses, but show different degrees of accuracy in representing the resulting depletion-induced fault slip. The semi-analytical benchmark data are available via DOI 10.4121/22240309. INTRODUCTION: The kernel of this paper is formed by a series of semi-analytical poro-mechanical test problems of increasing complexity with the aim to systematically compare the capacities of two poro-mechanical finite-volume-based simulation codes: one developed by Novikov et al. (2022b) which employs a discrete fault model (DFM). It forms part of a comprehensive porous media simulation package, the Delft Advanced Reservoir Terra Simulator (DARTS) and will be referred to with that acronym. The second code, developed by Shokrollahzadeh Behbahani et al. (2022), is based on a smoothed version of the embedded discrete fault model (sEFVM) and will be referred to with that last acronym. Both codes are being developed as part of the DeepNL Science4Steer project (NWO, 2017), and Appendices A and B give a brief overview of their characteristic features. The grids used in this study are presented in Appendix C.