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. In addition, geological transport processes require understanding the flows of granular materials. These themes raise new questions regarding multiphase flows in porous media, which the Stone group is investigating with a combination of bench-scale laboratory experiments and theory.


Impact of heterogeneity on viscous gravity currents

The gravitationally driven spreading of viscous fluids, also known as viscous gravity currents, is a process common to a large number of industrial and geological phenomena, including carbon sequestration. It is always helpful to supplement common numerical simulations with analytical results, which can highlight spreading rates as a function of relevant input variables, and laboratory experiments, which can test and characterize assumptions made in the modeling efforts. In the Stone group, new experimental, theoretical and numerical results have been reported for the effects of horizontal heterogeneities on the propagation of viscous gravity currents.

In the analytical work, two types of self-similar solutions – so-called first- and second-kind similarity – were explored to predict the time-dependence of invasion processes. These theoretical predictions were compared to experimental results and numerical solutions of the governing partial differential equations and all three results were found to be in good agreement.

Figure 4: Different configurations where a viscous gravity current propagates in a porous medium or confined system where there are gradients of permeability.


Shear dispersion of granular materials

Modeling transport of particulate materials is important in geophysical flows such as snow avalanches, mud and landslides. For example, in a polydisperse avalanche, segregation among different particle types drives the large particles to the front. The resulting distribution of debris upon the cessation of flow can dictate the ecological impact of the event, hence it is important to know how the various constituent materials are dispersed during the landslide. Similar questions arise in the industrial handling of granular materials.

It is well known that rapidly flowing dense granular materials can behave similarly to fluids and can be approximated as a continuum, hence the dispersion can be studied using methods familiar from the similar problem of a chemical dispersing in a pressure-driven pipe flow. The Stone group has formulated and solved a model problem of dispersion of dense granular materials in rapid shear flow down an incline. The findings can be applied to transport of all manners of granular materials, such as coal, sand, and powders, and also to natural processes such as landslides.

Figure 5: Schematic of the flow of a granular material down an incline, which is a common geological flow situation. The Stone group has given one of the first analytical descriptions of dispersion during such a flow of a granular material.