Event Detail

Event Type: 
Applied Mathematics and Computation Seminar
Date/Time: 
Monday, October 6, 2014 - 12:00 to 13:00
Location: 
Owen 106

Speaker Info

Institution: 
The University of Texas at Austin
Abstract: 

Textural equilibrium develops if the solid-liquid reaction kinetics is fast or time scales are long and is therefore common in partially molten materials. Similar behavior is observed in  development of connected water network in polycrystalline ice in polar ice sheets as well as formation of connected brine networks in rock salt. Rock salt and its permeability  is of specific interest in petroleum exploration: thick layers of salt cannot  be avoided in Gulf of Mexico fields. While salt is often considered impermeable and thus a seal for oil reservoirs, there is evidence that at high pressures and temperatures permeable pore network forms at very low porosity and its sealing properties reverse. 

In texturally equilibrated porous media the pore geometry evolves to minimize the energy of the liquid-solid interfaces, while maintaining the dihedral angle  at solid-solid-liquid contact lines. We present three-dimensional texturally equilibrated pore networks computed using a level-set method. Our results show that the grain boundaries with the smallest area can be fully wetted by the pore fluid even for θ>0. This was previously not thought to be possible at textural equilibrium and reconciles the theory with experimental observations. Even small anisotropy in the fabric of the porous medium allows the wetting of these faces at very low porosities, ϕ<3%. Percolation and orientation of the wetted faces relative to the anisotropy of the fabric are controlled by θ. The wetted grain boundaries are perpendicular to the direction of stretching for θ>60° and the pores do not percolate for any investigated ϕ. For θ<60°, in contrast, the grain boundaries parallel to the direction of stretching are wetted and a percolating pore network forms for all ϕ investigated. At low θ even small anisotropy in the fabric induces large anisotropy in the permeability, due to the concentration of liquid on the grain boundaries and faces.