Flow regimes during immiscible displacement

Fractional flow of immiscible phases occurs at the pore-scale where grain surfaces and phases interfaces obstruct phase mobility. However, the larger scale behavior is described by a saturation dependent phenomenological relationship called relative permeability. As a consequence, pore scale parameters such as phase topology and/or geometry and details of the flow regime cannot be directly related to Darcy scale flow parameters. It is well understood that relative permeability is not a unique relationship of wetting phase saturation and rather depends on the experimental conditions at which it is measured. Herein we use fast X-ray microcomputed tomography to image pore scale phase arrangements during fractional flow and then forward simulate the flow regimes using the lattice Boltzmann method to better understand the underlying pore scale flow regimes and their influence on Darcy scale parameters. We find that relative permeability is highly dependent on capillary number and that the Corey model fits the observed trends. At the pore scale, while phase topologies are continuously changing on the scale of individual pores, the Euler characteristic of the non-wetting phase (NWP) averaged over a sufficiently large field of view can describe the bulk topological characteristics; the Euler characteristic decreases with increasing capillary number resulting in an increase in relative permeability. Lastly, we quantify the fraction of NWP that flows through disconnected ganglion dynamics and demonstrate that this can be a significant fraction of the NWP flux for intermediate wetting phase saturation. Rate dependencies occur in our homogenous sample (without capillary-end effect) and the underlying cause is attributed to ganglion flow that can significantly influence phase topology during the fractional flow of immiscible phases.