The seminal work of Gurson (J Eng Mater Technol 99:2–5, 1977) on a simplified pore structure, a single spherical pore, first provided a theoretical relationship between the yield stress and the porosity. This contribution extends the approach to determine the macroscopic yield of a porous material by taking explicitly into account its internal structure. As the yielding of a porous material is controlled by the geometry of its internal structure, we postulate that it is nearly independent of the constitutive plastic behaviour of the material. Here, we show that the influence of that internal structure on the yield could be retrieved from a finite element computation with just an elastoplastic ideal (J2) material equivalent of the skeleton’s. With some basic knowledge about the skeleton’s mechanical properties, this process allows the determination of the yield stress without requiring the experimental compression of the material. We showcase the predictive power of the method against experimental testing, initially for a unit cell following Gurson, i.e., unique cylindrical void in a 3D printed cylinder sample. Eventually, the applicability of the method is demonstrated on a complex 3D printed rock microstructure, reconstructed from a sandpack’s CT-scan.

Modelling anisotropic flow in rocks requires their full permeability tensor. While theories derived from the upscaling of Stokes flow to Darcy's law may justify the tensor symmetry, homogenisations from micro-scale rock samples often return a non-zero level of asymmetry. Since most studies dismiss these controversial observations as numerical errors, this contribution looks more closely at the physical possibility of such behaviour. Asymmetry of the permeability tensor, which induces a rotatory flow, is manifested at the micro-scale by tortuous streamlines. Conversely, when considering a larger scale – above the Representative Elementary Volume for permeability – these tortuous paths do not statistically affect the flow direction any longer. At this point, the homogenisation of Stokes flow to Darcy's law reaches its domain of validity. We show that the asymmetry in the permeability tensor vanishes for this scale separation, regardless of the choice of boundary conditions unlike previously thought, if the boundary layer effect is disregarded.

Faulted and fractured systems form a critical component of fluid flow, especially within low-permeable reservoirs. Therefore, developing suitable methodologies for acquiring structural data and simulating flow through fractured media is vital to improve efficiency and reduce uncertainties in modelling the subsurface. Outcrop analogues provide excellent areas for the analysis and characterization of fractures within the reservoir rocks where subsurface data are limited. Variation in fracture arrangement, distribution and connectivity can be obtained from 2D fractured cliff sections and pavements. These sections can then be used for efficient discretization and homogenization techniques to obtain reliable predictions on permeability distributions in the geothermal reservoirs. Fracture network anisotropy in the Malm reservoir unit is assessed using detailed structural analysis and numerical homogenization of outcrop analogues from an open pit quarry within the Franconian Basin, Germany. Several events are recorded in the fracture networks from the Late Jurassic the Alpine Orogeny and are observed to be influenced by the Kulmbach Fault nearby with a reverse throw of 800Â m. The fractured outcrops are digitized for fluid flow simulations and homogenization to determine the permeability tensors of the networks. The tensors show differences in fluid transport direction where fracture permeability is controlled by orientation compared to a constant value. As a result, it is observed that the orientation of the tensor is influenced by the Kulmbach Fault, and therefore faults within the reservoirs at depth should be considered as important controls on the fracture flow of the geothermal system.

The design of any manufactured material requires the knowledge of its limit of elasticity, called yield strength. Whilst laboratory experiments are currently necessary to do so, this study is part of initiatives which aim at deriving the strength value from simple and fast numerical simulations. The seminal work of Gurson (1977) on a simplified pore structure, a single spherical pore, provided the first theoretical relationship between a material's strength and its porosity, showing that the presence of pore space is responsible for lowering the yield strength. The complexity of new structures requires however to take explicitly into account the internal geometry, usually using direct numerical simulations. This can be particularly challenging since the yield strength of a structure is actually reached after some of its parts have already entered the plastic regime. Therefore, the mere computation of the structure's yield strength currently necessitates the modelling of the exact plastic behaviour of the skeleton's material. In this contribution, we propose to simplify the numerical modelling necessary to predict the yield strength of a porous material, by postulating that yielding is mostly controlled by the geometry of the internal structure. We show that the influence of that internal geometry on the yield can effectively be retrieved from a finite element computation implementing a simple elasto-plastic model to represent the solid phase of the porous material. We showcase the predictive power of this new method against an experimental testing, initially benchmarked for 3D-printed samples with either a unique spherical void or a grid infill, before demonstrating its applicability on a complex 3D-printed real rock microstructure, reconstructed from segmented micro-Computerised Tomography scans.

In experiments designed to understand deep shear zones, we show that periodic porous sheets emerge spontaneously during viscous creep and that they facilitate mass transfer. These findings challenge conventional expectations of how viscosity in solid rocks operates and provide quantitative data in favour of an alternative paradigm, that of the dynamic granular fluid pump model. On this basis, we argue that our results warrant a reappraisal of the community's perception of how viscous deformation in rocks proceeds with time and suggest that the general model for deep shear zones should be updated to include creep cavitation. Through our discussion we highlight how the integration of creep cavitation, and its Generalised Thermodynamic paradigm, would be consequential for a range of important solid Earth topics that involve viscosity in Earth materials like, for example, slow earthquakes.

Creep cavities are increasingly recognized as an important syn-kinematic feature of shear zones, but much about this porosity needs investigation. Largely, observations of creep cavities are restricted to very fine grained mature ultramylonites, and it is unclear when they developed during deformation. Specifically, a question that needs testing is should grain size reduction during deformation produce creep cavities? To this end, we have reanalyzed the microstructure of a large shear strain laboratory experiment that captures grain size change by dynamic recrystallization during mylonitization. We find that the experiment does contain creep cavities. Using a combination of scanning electron microscopy and spatial point statistics, we show that creep cavities emerge with, and because of, subgrain rotation recrystallization during ultramylonite formation. As dynamic recrystallization is ubiquitous in natural shear zones, this observation has important implications for the interpretation of concepts such as the Goetze criterion, paleopiezometery, and phase mixing.

Fluid injection or production in petroleum reservoirs affects the reservoir stresses such that it can even sometime reactivate dormant faults in the vicinity. In the particular case of deep carbonate reservoirs, faults can also be chemically active and chemical dissolution of the fault core can transform an otherwise impermeable barrier to a flow channel. Due to the scale separation between the fault and the reservoir, the implementation of highly non-linear multiphysics processes for the fault, needed for such phenomenon, is not compatible with simpler poromechanics controlling the reservoir behaviour. This contribution presents a three-scale finite element framework using the REDBACK simulator to account for those multiphysics couplings in faults during fluid production. This approach links the reservoir (km) scale – implementing poromechanics both for the fault interface and its surrounding reservoir – with the fault at the meso-scale (m) – implementing a THMC reactivation model – and the micro-scale (μm) – implementing a hydro-chemical model on meshed μCT-scan images. This model can explain the permeability increase during fault reactivation and successfully replicate fault activation, slip evolution and deactivation features, predicted by common fault reactivation models, yet with continuous transitions between the sequences. The multiscale coupling allows to resolve the heterogeneous propagation of the fault slip which can be uncorrelated from the initial highest slip tendency location. We also demonstrate the advantage of dynamically upscaled laws compared to empirical ones as we show that a hydraulically imperceptible alteration of the microstructure's geometry can lead to different durations of the reactivation event at the macro-scale.

Permeability is a critical parameter for geological resources characterization. Its evolution with respect to porosity is particularly interesting and many research initiatives focus on deriving such relationships, to understand some hydraulic impacts of microstructure alteration. Permeability evolution from chemical reactions, for instance, can become complex as flow channels may open during rock dissolution. In this contribution, we show that this phenomenon can lead to irregular porosity-permeability curves and permeability hysteresis after reprecipitation. Current approaches describing permeability as a simple function of porosity can therefore not capture this behavior, and we advocate instead the use of dynamic modeling for such scenarios. We demonstrate our approach by modeling a dissolution/precipitation cycle for a unit cell pore channel and quantify the process at larger scale on three different rock samples, whose microstructures are reconstructed from segmented micro-Computerised Tomography scans.

Flow simulators have become increasingly popular to compute permeability on digital porous rocks reconstructed from Computerised Tomography (CT) scan data as part of Digital Rock Physics workflows. Various schemes are being used that focus mainly on numerical efficiency but do not necessarily provide the flexibility to account for more complex couplings between other physical models than the flow itself, like irreversible mechanical deformation for instance. To overcome this limitation, we present a finite element implementation of an Eulerian flow solver that is coupled to a Lagrangian solid mechanics solver, both in a sequential or tight manner. The flow simulator is successfully benchmarked for permeability computation on a digital rock that has been previously used for other code validations. The need for a tightly coupled hydro-mechanical simulator is then highlighted by comparing the loose and tight coupling approaches, revealing that the tight approach is more accurate and more efficient computationally. Finally, the use of the simulator in real cases is illustrated by running a hydro-mechanical simulation on a digital rock sample, where plastic deformation and fluid flow in the porous space are resolved simultaneously.