# Colloquium: I.C.Christov (LANL)

### Event Description:

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.