Permeability relation for periodic structures.

Abstract

The permeability relation for periodic porous media is studied with respect to other petrophysical parameters such as formation factor, porosity, surface-to-volume ratio, and nuclear magnetic resonance (NMR) relaxation time. All these quantities were computed for periodic structures of simple, body-centered, and face-centered cubic arrays of touching and overlapping spheres. The formation factors were calculated by using a method which is based on a Fourier-space representation of an integral equation for the electric potential in a two-component composite. The nuclear magnetic resonance relaxation time for the case where surface-enchanced relaxation plays a dominant role is known to be V P/rho S (VP is the pore volume, S is the pore surface, is the surface relaxation strength) when rho is not too large. Previously calculated permeabilities for these structures from the literature were used for correlation studies with other petrophysical parameters. Various correlation schemes among these quantities, such as k = aTbFc, and k = aTb phi c, were investigated, where k is permeability, T is the NMR relaxation time, phi is the porosity, and F is the formation factor.