NUCLEAR MAGNETIC-RELAXATION IN POROUS-MEDIA - THE ROLE OF THE MEAN LIFETIME TAU(RHO,D)

We show that the mean lifetime tau(rho,D) provides a compact and convenient description of surface-enhanced nuclear magnetic relaxation in fluid-saturated porous media. Here rho 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 tau(rho,D) = a2/d(d + 2)D + a/d-rho. For more general pore shapes the relation between tau, D-1, and rho-1 is nonlinear, but is well represented by a Pade 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 tau(rho --> infinity, D). We show that a modified version of this bound can be expressed in terms of the directly measurable quantity tau(rho,D). The limitations of such bounds are illustrated by numerical simulations on simple three-dimensional pore geometries.