Tight dual models of pore spaces

The pore throats in a porous medium control permeability, drainage, and straining through their pore scale geometry and through the way they are connected via pore bodies on the macroscale. Likewise, imbibition is controlled through the geometry of the pore bodies (pore scale) and through the way the pore bodies are connected via pore throats on the macroscale. In an effort to account for both scales at the same time we recently introduced an image-based model for pore spaces that consists of two parts related by duality: (1) a decomposition of a polyhedral pore space into polyhedral pore bodies separated by polygonal pore throats and (2) a polygonal pore network that is homotopy equivalent to the pore space. In this paper we stick to the dual concept while amending the definition of the pore throats and, as a consequence, the other elements of the dual model. Formerly, the pore throats consisted of single two-dimensional Delaunay cells, while they now usually consist of more than one two-dimensional Delaunay cell and extend all the way into the narrowing ends of the pore channel cross sections. This is the first reason for naming the amended dual model "tight". The second reason is that the formation of the pore throats is now guided by an objective function that always attains its global optimum (tight optimization). At the end of the paper we report on simulations of drainage performed on tight dual models derived from simulated sphere packings and 3D gray-level images. The C-code for the generation of the tight dual model and the simulation of drainage is publicly available at https://jshare.johnshopkins.edu/mhilper1/public_html/tdm.html.