Topology, geometry, and physical properties of porous rocks

Abstract

By use of the concepts of skeletization and deformation retract, we characterize the geometry and topology of a porous sedimentary rock in particularly simple ways. We briefly introduce the underlying topological concepts and present a skeletization procedure which leads to clear definitions of such concepts as grain, contact, pore chamber, channel, and throat. We apply this procedure in developing novel formulations of the problems of nuclear magnetic relaxation within the pore space; of steady flow through the pore space, and of the frame moduli. We show how the ambiguity between pore chambers and channels can be exploited for the NMR and flow problems. In particular, we find that a flow problem can be reduced to a resistance network problem, but the network is not a deformation retract of the pore space. The frame moduli problem can be mapped into the long wavelength the limit of a random “lattice” - vibration problem.