In order to characterise a rock formation prior to subsurface operations, it is required to find a microscale rock volume for which the homogenised property does not fluctuate when the size of the sample is increased; the Representative Elementary Volume (REV). Its determination usually comes at the cost of a large number of simulations, making it overall a computationally expensive process. Therefore, many scientific studies have been dedicated to optimising the process of finding REV. Using statistical numerical methods, it is shown that the fluctuation of the effective property corresponds overall to a cone-like shape convergence. We suggest determining the generic evolution law of the cone of convergence, which can be used to predict the size of the REV and the effective physical property. This study is based on simulations of Stokes flow through idealised microstructures from which the permeability is upscaled. By tracing and plotting the convergence of permeability for multiple samples, the full cone of convergence appears. The cone shows exponential growth and decay, converging towards the effective permeability of the microstructure. By fitting a log-normal distribution on the collected data points, we show that the generic evolution law of the cone of convergence can always be described with two parameters, independently of the porosity. We show that the determined law of the cone also applies to real microstructures, despite the presence of natural heterogeneities. The new method allows us to reduce the computational costs of finding all characteristics related to REV by simulating several subsamples rather than the full-sized sample, unlocking thereby high-resolution samples which are often too computationally expensive. The use of a statistical model provides quantification of the precision level we can obtain on the REV determination.

Underground Hydrogen Storage (UHS) is a feasible option for large-scale energy storage considering the advancements of the large-scale production of green hydrogen. One of the main engineering objective is to ensure the continuous safety of the storage, such that subsurface operations can be carried under safe stress regimes. Despite obvious similarities to Carbon Capture and Storage, a few differences make the task a new research challenge. The first one relates to the cyclic nature of UHS, which is expected to be carried at variable frequency and injection/production loads. Current models are not adequate for the lower frequency range considered in this application. In that case, the visco-plastic nature of rocks becomes non-negligible and needs to be taken into account. As a second observation, UHS revolves around a new gas, much lighter than CH4 and super critical CO2. Hydrogen’s atoms are so small they can diffuse even inside rock and this absorption causes rock matrix mechanical properties to weaken. This process is know as Hydrogen Embrittlement. When unaccounted for, such physical phenomenon could lead to catastrophic failure of the caprock, which is supposed to maintain stability to ensure safe storage. The caprock being responsible for the confinement of the hydrogen in the reservoir, development of cracks would enhance greatly permeability of an otherwise impermeable medium, resulting in an environmental disaster as the hydrogen suddenly leaks towards the subsurface and through groundwater aquifers. No empirical model is able to capture those two behaviours at the macro-scale since they are both phenomena principally related to grain-scale physics. As such, this contribution presents a Digital Rock Physics framework to upscale rock mechanical properties from the grain-scale. Rocks of interest are microCT-scanned to extract the digitized microstructure. Direct numerical simulations of elasto-plasticity are performed for different stress paths in order to compute the full yield surface instead of just the Uniaxial Compressive Strength. While most studies use Discrete Element Modelling to consider grain contacts explicitly, our simulator uses Finite Element Modelling which allows more flexibility in the approach to model multiphysics processes present during UHS. The contacts are modelled instead as an upscaled plastic law. Details of the numerical algorithms are presented in references. As a first case study for this framework, we present a comprehensive parametric study on the impact of cementation on rock strength for real microstructures of granular materials. The framework is then coupled with a numerical erosion algorithm that simulates homogeneous precipitation of mineral matter to represent cementation. New results on the influence of cement property namely Young’s modulus, friction and cohesion on the rock’s yield surface are explored. This study contributes to preliminary results on Hydrogen Embrittlement which directly influences those same mechanical properties. However more work is needed to model realistically the Hydrogen Embrittlement, which is the aim of our new PhD project OCEAN. The process will be observed experimentally at the micro-scale in order to calibrate the simulator. MicroCT-scan images will determine the spatial distribution of the phenomenon. Visco-plasticity will be implemented to go one step further and determine the effect of Hydrogen Embrittlement during cyclic injection/production of hydrogen.

The foundation of homogenisation methods rests on the postulate of Hill–Mandel, describing energy consistency throughout the transition of scales. The consideration of this principle is therefore crucial in the discipline of Digital Rock Physics which focuses on the upscaling of rock properties. For this reason, numerous studies have developed numerical schemes for porous media to enforce the Hill–Mandel condition to be respected. The most common method is to impose specific boundary conditions, such as periodic ones. However, these boundary conditions influence both the effective property and the size of the REV. The recent study of Thovert and Mourzenko (2020) has shown that most boundary conditions still result in the same intrinsic effective physical property if the averaging is applied outside the range of the boundary layer. From this discovery, it becomes logical to question the status of Hill–Mandel postulate in porous media when homogenising away from the boundary. In this contribution, we simulate Stokes flow through random packings of spheres and a range of rock microstructures. For each, we plot the evolution of the ratio micro- vs macro-scale of the energy of the fluid transport outside the boundary layer, for a growing subsample size of porous media. Here, we prove that we naturally find energy consistency across scales when reaching the size of the Representative Elementary Volume (REV), which is a known condition for rigorous upscaling. Furthermore, we show that this index for the energy consistency is a more accurate indicator of REV convergence since the mean value is already known to be unitary.