We show that the mean lifetime τ(ρ,D) provides a compact and convenient description of surface-enhanced nuclear magnetic relaxation in fluid-saturated porous media. Here ρ is a parameter that measures the relaxation rate at the pore-grain interface and D is the bulk diffusion constant for the fluid in the pore space. In the case of simple pore shapes with uniform magnetization at the interface, e.g., slabs (d=1), cylinders (d=2), or spheres (d=3) of radius a, we derive the equation τ(ρ,D)=${\mathit{a}}^2$/d(d+2)D +a/dρ. For more general pore shapes the relation between τ, ${\mathit{D}}^{\mathrm{-}1}$, and ${\mathrm{\rho }}^{\mathrm{-}1}$ is nonlinear, but is well represented by a Padé approximant based on four parameters that are characteristic of the pore geometry. The utility of this representation is illustrated by numerical calculations on a series of two-dimensional pore geometries. The average lifetime is also of interest because a recently established bound on the permeability of porous media can be recast in terms of τ(ρ→∞,D). We show that a modified version of this bound can be expressed in terms of the directly measurable quantity τ(ρ,D). The limitations of such bounds are illustrated by numerical simulations on simple three-dimensional pore geometries.

• Received 22 February 1991

DOI:https://doi.org/10.1103/PhysRevB.44.4960