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.

Digital Rock Physics has reached a level of maturity on the characterisation of primary properties that depend on the microstructure - such as porosity, permeability or elastic moduli - by numerically solving field equations on μCT scan images of rock. After small deformations or at depth though, most rocks eventually reach their limit of elasticity and the complementary plastic properties are needed to describe the full mechanical behaviour. Currently, determination of a rock's yield surface from its microstructure is often restricted to semi-analytical criteria derived by limit analysis or numerical simulations performed on idealised geometries. Such simplification lacks representativeness, particularly for processes that affect directly the pore-grain interface such as the cementation phenomenon, happening during diagenesis. Eventually, only direct numerical simulation of elasto-plasticity performed on digitalised microstructures can be used to assess the strength of different cemented materials and its evolution with the alteration of the microstructure. In this study, we provide a comprehensive parametric study on the impact of cementation on rock strength for real microstructures of cemented granular materials. Compared to most previous studies, the whole yield surface is determined numerically (using Finite Element Method) in order to assess the influence of cementation for different stress-paths. The previously known tendency of rock to strengthen with increasing cementation volume is verified. New results on the influence of cement property namely Young's modulus, friction and cohesion on the rock's yield surface are explored. The envelopes obtained are compared to the ones obtained by experimental data and existing models. The framework presented in this study showcases the wider possibility of determining any rock's or porous material's yield surface from its microstructure.

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.

We propose a Lagrangian solid mechanics framework for the simulation of salt tectonics and other large-deformation geomechanics problems at the basin scale. Our approach relies on general elastic-viscoplastic constitutive models to characterize the deformation of geologic strata, in contrast with the majority of published works on the subject, which utilize nonlinear Stokes flow models. By means of multiscale asymptotics, we also show that the inertia term in the momentum balance equation can be safely neglected, if the goal is to track the Earth's crust deformation over long periods of time. Our time integration strategy is a blended transient/quasistatic approach, in that it consists of a constitutive stress update, subject to the constraint that the stresses must satisfy static equilibrium. In addition, we use stabilized finite element methods specifically built for triangular and tetrahedral grids, which can also perform well under incompressibility constraints. Our approach offers computational geologists the following advantages: (1) improved flexibility in the choice of subsurface constitutive models with respect to the nonlinear Stokes flow; (2) improved efficiency over transient dynamics algorithms used in this context in the past, which are forced to resolve seismic events over geologic time scales; and (3) improved robustness in large strain computations over quadrilateral/hexahedral finite elements. We demonstrate the performance of the proposed approach with simulations of passive diapirism.

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.

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.

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.