Permeability relation for periodic structures

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 Vp/ρS (Vp is the pore volume, S is the pore surface, is the surface relaxation strength) when ρ 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 = aTbφc, were investigated, where k is permeability, T is the NMR relaxation time, φ is the porosity, and F is the formation factor.