Investigating Compaction by Intergranular Pressure Solution Using the Discrete Element Method

Abstract

Intergranular pressure solution creep is an important deformation mechanism in the Earth's crust. The phenomenon has been frequently studied and several analytical models have been proposed that describe its constitutive behavior. These models require assumptions regarding the geometry of the aggregate and the grain size distribution in order to solve for the contact stresses and often neglect shear tractions. Furthermore, analytical models tend to overestimate experimental compaction rates at low porosities, an observation for which the underlying mechanisms remain to be elucidated. Here we present a conceptually simple, 3‐D discrete element method (DEM) approach for simulating intergranular pressure solution creep that explicitly models individual grains, relaxing many of the assumptions that are required by analytical models. The DEM model is validated against experiments by direct comparison of macroscopic sample compaction rates. Furthermore, the sensitivity of the overall DEM compaction rate to the grain size and applied stress is tested. The effects of the interparticle friction and of a distributed grain size on macroscopic strain rates are subsequently investigated. Overall, we find that the DEM model is capable of reproducing realistic compaction behavior, and that the strain rates produced by the model are in good agreement with uniaxial compaction experiments. Characteristic features, such as the dependence of the strain rate on grain size and applied stress, as predicted by analytical models, are also observed in the simulations. DEM results show that interparticle friction and a distributed grain size affect the compaction rates by less than half an order of magnitude.

Microphysics of Inelastic Deformation in Reservoir Sandstones from the Seismogenic Center of the Groningen Gas Field

“…This series of simplified models represents a first exploratory attempt to test whether the microphysical mechanisms described by Pijnenburg et al (2019b) can (semi-)quantitatively account for the inelastic behavior of the Slochteren sandstone seen at the sample scale in our triaxial deformation experiments. Our hope is that, if so, the underlying physical processes will be explored in further detail in the future, using more rigorous approaches for linking grainscale to aggregate-scale behavior, i.e., by specialists in homogenization treatments (Bardet and Vardoulakis 2001;Fortin et al 2003), granular mechanics modeling (Einav 2007a, b;Tengattini et al 2014) and the discrete element method (Kawamoto et al 2016;Van den Ende et al 2018). Alternatively, if the processes explored here cannot account for the experimentally observed deformation behavior, then they should be rejected in playing a dominant role in the compaction behavior seen in experiments, and likely in the Groningen and perhaps other, similar reservoir rocks.…”

Time‐Dependent Compaction as a Mechanism for Regular Stick‐Slips

“…As a result, local concentrations of contact stress diminish and cease to exist. This has been demonstrated quantitatively by Van den Ende, Marketos, et al () for uniaxially compacting aggregates. Overall, pressure solution negatively impacts the formation of isolated force chains, so that force chain collapse is unlikely to constitute the observed stick‐slip behavior.…”

“…To investigate the effect of pressure solution creep on stick‐slip behavior, we simulate laboratory biaxial shear tests numerically using the DEM (Cundall & Strack, ). We employ the open‐source 3‐D DEM software package granular LAMMPS (Landry et al, ; Plimpton, ), which was modified by Marketos () and by Van den Ende, Marketos, et al (). The DEM approach is summarized in supporting information S1 (Guo & Morgan, ; Hanley et al, ; Jiang et al, ; Mair & Abe, ; Scholtès & Donzé, ).…”

“…The DEM approach is summarized in supporting information S1 (Guo & Morgan, ; Hanley et al, ; Jiang et al, ; Mair & Abe, ; Scholtès & Donzé, ). For a detailed description of the numerical method and the implementation of intergranular pressure solution in DEM, the reader is referred to Van den Ende, Marketos, et al (). All simulation parameters reported below and in Table S2 are presented in their physical dimensions for easy comparison with laboratory values (see Van den Ende, Marketos, et al, , for details of the adopted scaling procedure).…”

“…Following Niemeijer and Spiers () and Chen and Spiers (), we consider the interplay between dilatant granular flow and compaction by intergranular pressure solution, which has been proposed by these authors as a mechanism for velocity‐weakening behavior, a requirement for stick‐slip behavior (Gu et al, ; Ruina, ). By employing the implementation of pressure solution in DEM by Van den Ende, Marketos, et al (), we simulate unstable frictional sliding of fault gouges while systematically varying the kinetics of pressure solution, and we investigate the effect of these fluid‐rock interactions on the frictional behavior of the gouge. Simulations with appreciable pressure solution kinetics display stick‐slips with regular recurrence time and stress drop, demonstrating that the interplay between dilatant granular flow and time‐dependent compaction leads to periodic unstable sliding.…”