Prediction of the Capillary Pressure-Saturation curve from a Pore-Network Model that is Grid-Free and Based on Duality

Most methods for extracting pore networks from 3D gray-scale images of porous media first segment the images such that a voxel is occupied entirely either by the solid phase or pore space. This discretization represents smooth pore spaces by stairwell-type objects and may further result in inaccurate estimation of local pore size. To overcome this limitation, we developed an approach for deriving pore networks from polyhedral pore spaces, whose pore boundaries are not constrained by an underlying numerical grid. Such a smooth pore boundary can, for example, be obtained through image-analytical algorithms that are routinely used to display 3D gray-scale images of multiphase systems. Our approach is based on mathematical duality between the Delaunay and Voronoi complex with respect to points sampled on the pore boundary of a porous medium. By employing rules for simplifying the Delaunay and Voronoi complex in a way that (1) maintains the topology of the pore space, (2) maintains mathematical duality, and (3) is free of fit parameters, we are able to decompose a polyhedral pore space into polyhedral pore bodies separated by polygonal pore throats and to construct a polygonal pore network that is homotopy equivalent to the pore space. Using the network, we simulated drainage in a glass bead packing. The simulated capillary pressure-saturation curve agrees well with the measured one.