Upscaled models of flow and transport in faulted sandstone: boundary condition effects and explicit fracture modelling

Abstract

Faults formed by shearing of joint zones in sandstone contain fine-scale features that cannot be represented explicitly in large-scale flow simulations. Upscaled models are, therefore, required for reservoir engineering computations. These models attempt to capture fine-scale effects through equivalent permeabilities that are computed from the underlying fine-scale characterization. In this paper the impact of several different local boundary conditions on the calculated equivalent permeability is assessed. Pressure–no-flow, periodic and mirror-periodic boundary specifications are considered. The resulting coarse-scale permeability tensors are shown to be highly dependent on the local boundary conditions used in the models. In cases with through-going high-permeability features, pressure–no-flow and mirror-periodic boundary conditions provide upscaled permeabilities that correctly capture global flow characteristics. Periodic boundary conditions, by contrast, are more suitable for systems lacking through-going high-permeability features. This sensitivity to boundary conditions calls into question the robustness of the equivalent permeability for the general case and suggests that dominant through-going features would best be modelled explicitly. In addition, due to the very small thickness and high permeability of some through-going structural features (e.g. slip surfaces), globally upscaled models are inadequate for the modelling of transport. To address these issues, a ‘partial upscaling’ method – removing the through-going high-permeability features from the fine model, upscaling to a coarse grid and then reintroducing the high-permeability features back into the coarsened model – is adopted. This procedure is shown to provide coarse models that give accurate predictions for both flow and transport.