Stable drainage in a gravity field

During drainage, as a voxel of porous material is being actively invaded prior to percolation, the invading nonwetting fluid cannot be transmitted to the neighboring downstream voxel until a critical nonwetting saturation (Snc) is reached. This occurs when the invading fluid forms a percolating path across the voxel. We present novel laboratory observations of gravitationally stable, air/water drainage in thin bead packs, with 2D saturation fields monitored at high spatial and temporal resolution using transmitted light. We also present Invasion Percolation simulations. Both show that Snc has a strong dependence on capillary number (Ca), Bond number (Bo), and voxel size (Lz). We propose a percolation model that describes the functional form of Snc(Bo,Ca,Lz). We also produce a new theoretical model for the macroscopic capillary pressure function Pc(Sw,Bo,Ca,Lz), where Sw is the saturation of wetting fluid in the voxel