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.@en

Induced seismicity refers to seismic events (earthquakes) triggered by human activities. Such events, even when characterized by relatively modest magnitudes, have the potential to jeopardize the safety of individuals, the surrounding environment, and infrastructure.

Production from hydrocarbon reservoirs can alter the in-situ stress state, leading to induced seismicity. This is reported in the Groningen field, where substantial gas production caused fault reactivation and subsequent earthquakes. Understanding events in the deep subsurface is crucial to proactively mitigate future seismic occurrences. To understand the causes of induced seismicity, the underlying physics are examined and defined in terms of relevant governing equations and models. This reveals the interconnected nature of fluid depletion, rock deformation, and fault slip. The goal of this study is to develop simulation techniques to solve these equations.

Towards this end, firstly, a finite volume embedded-numerical simulation method, called the Smoothed Enhanced Finite Volume method (sEFVM), is developed. This method is revealed to be computationally efficient for reservoir-scale modeling of heavily faulted systems and performed well in comparison to known solutions and other simulators.

However, in settings where analytical solutions indicated noncontinuous shear stress profiles, sEFVM accuracy suffers. Recognizing this limitation, a semi-analytical approach is developed, extending analytical expressions to be solved over the sEFVM mesh. This extension allows for more accurate solutions, accommodating complex reservoir and fault geometries. The semi-analytical method is successfully used to estimate the onset of fault nucleation and the magnitude of the seismic moment resulting from depletion.

The semi-analytical approach is limited to simulating fault slip up to the point of nucleation. To overcome this constraint, a hybrid method is developed. With appropriate assumptions regarding the post-nucleation state and the use of sEFVM to numerically calculate post-nucleation stresses, the hybrid method can effectively model multi-fault systems in the seismic stage assuming quasi-static behavior.

In summary, this research contributes by presenting novel computational frameworks for studying fault reactivation in faulted poroelastic media, offering insights into the complex interactions of the physics at play. The proposed embedded-numerical, semi analytical, and hybrid methods pave the way for further advancements in the field.
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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.

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A smoothed embedded finite-volume modeling (sEFVM) method is presented for faulted and fractured heterogeneous poroelastic media. The method casts a fully coupled strategy to treat the coupling between fault slip mechanics, deformation mechanics, and fluid flow equations. This ensures the stability and consistency of the simulation results, especially, as the fault slip is implicitly found through an iterative prediction-correction procedure. The computational grid is generated independently for embedded faults and rock matrix. The efficiency is further enhanced by extending the finite-volume discrete space by introducing only one degree of freedom per fault element. The embedded approach can lead to an oscillatory stress field at the fault, which damages the robustness of the implicit slip detection strategy. To resolve this challenge, a smoothed embedded strategy is devised, in which the stress and slip profiles are post processed within the iterative loops by fitting the best curve based on a least-square error criterion. The sEFVM provides locally conservative mass flux and stress fields, on staggered grid. Its performance is further investigated for several proof-of-the-concept test cases, including a multiple fault system in a heterogeneous domain. Results indicate that the method develops a promising approach for field-scale relevant simulation of induced seismicity.

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