Numerical simulation of compaction bands in high-porosity sedimentary rock

Abstract

Geologists have recently discerned naturally occurring discrete localized planar zones of deformation, associated with compaction of initially high-porosity rock. Such compaction bands may influence fluid transport, and stress/strain distribution in sedimentary formations. In order to gain insight into the formation mechanisms of compaction bands under a variety of boundary conditions, we developed a discrete model, in which the material is represented as a hexagonal lattice of springs that can transfer only normal forces (Central Force Spring model). The model easily allows for a discrete statistical distribution of material properties at a physically relevant scale. The occurrence of grain crushing and porosity reduction is represented by a change in the equilibrium length and elastic properties of each element that exceeds a certain stress threshold. Parametric analysis is conducted to explore and predict the conditions under which compaction bands form and develop. Our results also duplicate the different types of compaction propagation, observed in laboratory tri-axial compression experiments. The most important result of the simulations is the evaluation of the role of disorder. In our analysis, the differences in the patterns due to the extent of disorder in material's properties are systematically studied. Patterns resulting from different elastic mismatches at the boundaries are examined as well. Both of these parameters modulate the compaction nucleation sites. As a result, different patterns of compaction are generated in a competition between the elastic mismatch and the disorder. The case with no disorder allows compaction to be dominated by the large values of elastic mismatch and promotes a discrete mode of propagation starting from the specimen's boundaries. Larger values of disorder shift the nucleation sites into the interior of the specimen and promote the homogeneous front advance. Still larger disorder resulted in diffuse compaction inside the specimen. The origin of the distinct macroscopic differential stress vs. axial strain curves observed in laboratory experiments can be understood from our parametric analysis. If a material is sufficiently homogeneous, large stress drops, originating due to the elastic mismatch, will characterize its stress–strain graph. For a non-homogeneous material, the stress drops, originating mainly due to the large disorder, will be small and quite frequent. These important features have not yet been explained in the literature, although they were observed in the experiments.