Trapping and hysteresis in two-phase flow in porous media: A pore-network study

Several models for two-phase flow in porous media identify trapping and connectivity of fluids as an important contribution to macroscale hysteresis. This is especially true for hysteresis in relative permeabilities. The trapping models propose trajectories from the initial saturation to the end saturation in various ways and are often based on experiments or pore-network model results for the endpoints. However, experimental data or pore-scale model results are often not available for the trajectories, that is, the fate of the connectivity of the fluids while saturation changes. Here, using a quasi static pore-network model, supported by a set of pore-scale laboratory experiments, we study how the topology of the fluids changes during drainage and imbibition including first, main and scanning curves. We find a strong hysteretic behavior in the relationship between disconnected nonwetting fluid saturation and the wetting fluid saturation in a water-wet medium. The coalescence of the invading nonwetting phase with the existing disconnected nonwetting phase depends critically on the presence (or lack thereof) of connected nonwetting phase at the beginning of the drainage process as well as on the pore geometry. This dependence involves a mechanism we refer to as "reversible corner filling." This mechanism can also be seen in laboratory experiments in volcanic tuff. The impact of these pore-network model results on existing macroscopic models is discussed.