Predicting the fate of CO2 injected underground for carbon storage or enhanced oil recovery requires understanding physical processes associated with the underground rearrangement of a buoyant material. This raises new questions regarding multiphase flows in porous media, which the Stone group is investigating with a combination of bench-scale laboratory experiments and theory.


Inhibiting viscous fingering

In 2012, Howard Stone and colleagues completed an important study of viscous fingering in the presence of gradients of permeability in the direction of flow. The results were published in Nature Physics and also highlighted in Physics Today.

Using a modified Hele-Shaw cell, an experimental apparatus composed of two plates that are conventionally parallel, the team led by Talal Al-Housseiny simulated the displacement of a more viscous fluid by a less viscous fluid (analogous to water displacing oil) in a tapered channel. The researchers demonstrated that, though such an interface between these fluids is always unstable between parallel plates, a contracting geometry can stabilize the interface and allow the less-viscous fluid to “sweep” the more-viscous fluid more efficiently. Their results have implications for sweeping contaminants from sensors and cleaning of measuring devices used in applications, and also for enhanced oil recovery. The study suggests that to increase oil recovery in oil-wet reservoirs, injection and production wells might be positioned such that the sweep flow is driven in the direction of decreasing permeability or decreasing grain size to minimize viscous fingering and fluid breakthrough.

Figure 18. Schematic illustrating the injection of gas below a deformable boundary initially separated by a thin liquid film from a solid impermeable substrate. The injected gas pushes the liquid forward in the form of a plug while simultaneously deforming the upper surface.


Two-phase injection in deformable systems

Recent experimental work in the physics community has shown that the presence of an elastic boundary can also facilitate the suppression of viscous fingering. Since real materials in nature can deform when stressed, as in the case of two-phase injection processes, the Stone group has examined this phenomenon by studying fluid displacement underneath a flexible membrane. The researchers analyzed this two-phase flow and demonstrated how the deflection of the membrane and surface tension at the gas-liquid interface provide the mechanism of suppression (Figure 18), and also determined the corresponding critical conditions.

Figure 19: Top: a) Sketch of a gravity current draining from the edge of a model porous medium. (b) Comparison of the experimental results and the theoretical predictions for drainage from uniform Hele-Shaw cells. Experimental results: rescaled liquid mass remaining in a Hele-Shaw cell versus time. The solid line is the prediction (2.5) from the theoretical study, with no fitting parameters. The typical value of gap thickness b in the experiments is 5 mm.

Bottom: Images of a gravity current draining from a uniform Hele-Shaw cell, with comparisons between the experimental results and theoretical predictions (solid curve) for the shape, at various times: (a) t D 0 s; (b) t D 250 s; (c) t D 350 s; (d) t D 500 s; (e) t D 2000 s. In the late period, the self-similar solutions are seen to agree well with the experimental data. The liquid is pure glycerol, which is leaking from the right-hand edge of the cell after removal of a barrier. The grid has markings 1 cm apart.


Fluid escape from a reservoir

Studies of underground CO2 storage require some understanding of possible failure modes, and the temporal and spatial rearrangements of the buoyant material in such cases. In order to describe fluid drainage behavior from porous media, Stone and colleagues have examined the fundamental problem of drainage from an edge, the extreme case when the vertical leakage pathway becomes infinitely permeable. Previous studies have only been theoretical, but this study used both theory and laboratory experiments in uniform Hele-Shaw cells and V-shaped cells to model gravity currents in both homogeneous reservoirs and those with varying permeability and porosity. In each case, a self-similar solution for the shape of these gravity currents was found and the mass remaining in the system is governed by power-law behavior. Measured profile shapes and the mass remaining in the cells agree well with model predictions (Figure 19). The study provides new insights into drainage processes that may occur in a variety of natural and industrial activities, including the geological storage of carbon dioxide.