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Quantifying grain-contact and grain-volume stress-strain fields in simulated sandstone: a high-resolution FEM approach

Fluid extraction from subsurface reservoir sandstones frequently results in surface subsidence and induced seismicity, such as observed in the Groningen Gas field (the Netherlands). The cause lies in reservoir compaction driven by the increase in effective overburden stress. Deformation mechanisms in sandstone include instantaneous elastic deformation, inelastic, time-independent processes, such as critical grain breakage and/or compaction of intergranular clay rims, and/or creep due to stress corrosion and pressure solution. However, no physics-based models exist to predict inelastic reservoir compaction under in-situ conditions, limiting the ability to evaluate the impact of reservoir exploitation. Deformation is driven by stresses transmitted across grain-to-grain contacts. Therefore, it is key to relate the grain-scale deformation mechanisms to grain-scale stress distribution, grain strength and deformation rate. These stress-strain relationships cannot be obtained experimentally. As a first step to obtaining such relationships, we performed 2D high-resolution (i.e. sub-micron) linear elastic Finite Element Method simulations on aggregates consisting of quartz, feldspar and/or intergranular clay, with porosities in the range 12-26%. We systematically investigated the effect of porosity and mineralogy, as well as aggregate texture (i.e. grain contact roughness, pre-existing flaws, large pores (i.e. voids) and grain packing), under boundary conditions relevant for the Groningen gas field (i.e. macroscopic vertical strain up to 0.2%, no lateral displacement). Our fixed-displacement simulations (200 µm diameter grains, flattened contacts, cubic packing), showed compressive stress concentrations (σ1 and σ3) at contact edges, which increased in magnitude with increasing porosity, as opposed to the tensile stress concentrations expected for point contacts following Hertzian contact theory. Locally replacing quartz grains by feldspar showed no significant change in grain-contact or -volume stress. By contrast, the presence of intergranular clay rims, with a thickness of up to 10 µm, reduced the compressive stress concentrations at contact edges between quartz grains by a factor of three, while also reducing Bulk Modulus by up to 20%. In addition, our simulations particularly illustrated the effect of aggregate texture on local stress. As expected, grain contact roughness substantially increased the normal stress acting on contact asperities, while tensile stresses up to 60 MPa developed at the grain-contact ‘channels’. These stresses increased with increasing asperity amplitude and/or contact area. Locally enhanced tensile stresses were also observed at surface flaw tips and around larger voids in the aggregate. However, compared to a cubic-packed aggregate, the largest effect was observed for a hexagonal-packed aggregate, with tensile stress concentrations at inclined contact edges, which intensify with increasing porosity, and/or other textural changes. Our results suggest that rock microstructure and texture play an important role in controlling the grain-contact and -volume stress-strain behaviour, which could lead to over/underestimation of the magnitude of local stress, hence the driving force for grain-scale deformation, if not adequately accounted for.


Takahiro Shinohara, Cedric A.P. Thieulot and Suzanne J.T. Hangx
Department of Earth Sciences, Faculty of Geosciences, Utrecht University, Utrecht, The Netherlands
GeoUtrecht 2020
The Netherlands