Analysis of Two Problems in Network Transport

Abstract

In this thesis two problems in network transport are analyzed.

The first problem concerns flow through static foam in artificial fractures. The objective is to determine whether the assumption of Li et al. (2021), that capillary pressure is uniform in the region of interest, with static foam in an artificial fracture, is justified. This would be the case if water can flow through Plateau borders at a rate that is quick enough for pressure differences to dissipate rapidly. Images of foam in the fractures are turned into networks of slits that are scaled down to flow through Plateau borders in foam. The results of this show that the capillary pressure can be assumed to be uniform.

The second problem concerns steady-state two-phase flow in microfluidic devices. The objective is to determine whether two phases can simultaneously flow at comparable fractional flows through a microfluidic device without alternating pore occupancy. This would be the case if the total mobility values of both phases are similar. To find the relative permeability values, a microfluidic device is simulated consisting of interface shapes based on the findings of Cox et al. (2022), arranged in a network according to bond percolation theory. The results show that it is unlikely that two phases with similar viscosity values can maintain steady-state flow at comparable fractional flows, and impossible if the viscosity ratio is that of gas and water. This implies that flow experiments done using microfluidic devices reflect the high-capillary-number flow regime where flow paths fluctuate in the pore network.