Title: Transport phenomena in energy applications: Fluid-structure interactions and beyond

Abstract:

Unconventional fossil energy resources are revolutionizing the US energy
market. While the techniques developed over the last 50 years lead to
viable and profitable extraction of, e.g., trapped gas and hydrocarbons
from almost-impermeable rock formations via hydraulic fracturing, the
abysmal extraction rates (typically 15%) suggest the fluid mechanics of
these processes is not well understood. In this talk, I will describe three
basic theoretical fluid mechanics problems inspired by unconventional
fossil fuel extraction. The first problem is flow in a deformable
microchannel. Fluid-structure interaction couples the shape of the conduit
to the flow through it, drastically altering the flow rate--pressure drop
relation. Using perturbation methods, we show that the flow rate is a
quartic polynomial of pressure drop for shallow channels, in contrast to
the linear relation for rigid conduits. The second problem involves
two-phase (gas-liquid) displacement in a horizontal Hele-Shaw cell with an
elastic membrane as the top boundary. This problem arises at the pore-scale
in enhanced oil recovery for large injection pressures. Once again,
fluid-structure interaction alters the problem, leading to stabilization of
the Saffman--Taylor (viscous fingering) instability below a critical flow
rate. Using lubrication theory, we derive the stability threshold and show
that it agrees well with recent experiments. Finally, extensions to these
canonical problems will be discussed, specifically incorporating
miscibility (phase change) at the liquid-gas interface and the addition of
a dispersed particulate phase to the fluid.