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.

This study is part of a larger effort to evaluate the use of microfluidics to represent foam generation and flow in geological porous media (Rossen, 2008). Specifically whether it is possible to have flow in a microfluidic device without fluctuating occupancy of pores and pore throats. Although there is no foam created during the study, three of the main foam generation mechanisms are discussed. The 2D network consists of a 32x32 square lattice of cylindrical pillars, where all the pillars are surrounded by at the top and bottom by a liquid film that constricts the gas flow. The pores and pore throats are filled with gas or water. The gas flow paths are gas filled pores connected with gas filled pore throats. The water flow paths are pillars connected with water filled pores or pore throats. Liquid/gas bridges are necessary for the two phases to flow simultaneously through the network. An equivalent conductance for the gas networks is obtained by Hadjisotiriou (2020). But for that value to have any relation with that of the water network, the gas and water flow should be simulated within shapes that fit into one another under the same conditions. Because the paths in the network could have countless different variations, these paths are broken up into the smallest repeated segments. Then the total resistance of a path is obtained from a combination of these segments. Two unique segments are identified for the gas paths and four for the water paths. The segments are created in COMSOL™. A conductance value is obtained for each segment. With these values it is possible to calculate the total conductance for both the gas and water networks. The result is a fraction of water flow relative to gas flow of around 0.015. This means that only a small amount of water flow can be sustained by the network without fluctuating the occupancy of pores and pore throats. This makes it hard to explore foam generation in a microfluid device. It also means that two-phase flow in a microfluidic device is not representative of that in 3D geological porous media, except for in some exceptional circumstances.