colation implies a threshold between conduction and non-In many porous media the grains are packed in a disordered conduction depending on whether the fluid is totally conmanner, rather than in regular lattices. Theoretical treatments of nected in the pore space or broken into independent drops the properties of these media often assume that because there is or clusters. The practical importance of such thresholds is no regular lattice, the pore space between grains is completely evident in the long pedigree of percolation theory (1-8).
spatially disordered. Here we present an analysis of a real granular medium (a close packing of equal spheres) which shows that, Pore Space as a Graph contrary to the popular assumption, the pore space is spatially correlated. The origin of this pore space correlation is the strong
The conceptual picture underlying many theories of granspatial correlation of grain locations, which is a feature of all dense ular media is the graph. A graph is a set of connected points. granular media. Our analysis relies on physically representative Studies of transport dating back to Fatt (9) often refer to network models of the pore space constructed from knowledge graphs as networks, and we will use the terms interchangeof the grain locations. Simulated drainage experiments on these ably. To represent pore space we associate the points on the networks agree with mercury porosimetry experiments in simple graph, often called sites, with pore bodies. The connections sandstones, whereas simulations in uncorrelated but otherwise between the sites, known as bonds, represent pore throats.
identical networks do not. Thus the spatial correlation inherent in
The global structure of this graph corresponds to the comthe pore space of simple porous media significantly affects mercury plete interconnected pore space. Thus global properties of porosimetry. Deriving pore size distributions from mercury porosimetry without considering spatial correlation can give misthe graph can correspond to transport properties of the poleading results. The likelihood of error is compounded if such pore rous medium. For example, if bonds are assigned hydraulic size distributions are used to estimate transport coefficients such as conductances, then the overall conductivity of the graph corpermeability, diffusivity, and electrical conductivity. α§ 1996 Academic responds to permeability. Obtaining the graph that directly Press, Inc. corresponds to a real granular medium is a formidable task Key Words: porosimetry; pore size distribution; spatial correlararely attempted (10-14). Consequently it is customary to tion; network model; porous media. assume that the graph is a regular lattice (e.g., simple cubic) and that the properties of each bond and site are randomly distributed on it. Here we examine both of these assumptions a probe for pore size distribution. The data obtained in a