Upscaling multiphase viscous-to-capillary transitions in heterogeneous porous media

Abstract

Abstract

Two-phase gravity currents in layered porous media

“…There is a transition period at intermediate times where the behaviour does not obey a power law (as observed by Benham et al. (2021) in the absence of gravity). This can be explained by the fact that, as the gravity current spreads out radially, the capillary number reduces everywhere except near the origin (where ).…”

“…For example, a previous study (Benham et al. 2021) addressed the effects of heterogeneities on fluid displacement in a long-thin confined aquifer (also known as a Buckley–Leverett flow), for which gravity is negligible. However, it is not possible to make a direct analogy here, since the flow of the ambient phase is neglected in the present study (because the current is unconfined).…”

“…Following the same approach as Benham et al. (2021), we formulate composite functions for the upscaled properties of the flow, which capture both the viscous and capillary limit regimes, as well as the transition between these limits. The two upscaled quantities of interest are the integrated saturation and the flux .…”

“…For example, the power laws were already addressed by Benham et al. (2021) and the Brooks–Corey parameter was studied by Golding et al. (2013).…”

“…Many previous studies focus on each of these cases separately, though recently semi-analytical approaches have been derived by Benham et al. (2021) and Boon & Benson (2021) that capture the transition between the viscous and capillary regimes, demonstrating which regions of a confined aquifer are in each of these limits, and which regions are in between the limits. However, gravity was neglected in those studies, restricting the applicability to very thin aquifers.…”