Faculty Bibliography

Under ideal conditions, in an isotropic homogeneous system, pulsed field gradient spin-echo (PFGSE) experiments measure the probability P(R,t), that a diffusing water molecule will travel a root mean square distance, R, in a time interval of length t. We will show that random walk simulations on model porous media provide valuable insight to the sensitivity of this measurement to (1) complex pore geometries and (2) enhanced relaxation at the pore-grain interface

The NMR pulsed field gradient spin-echo (PFGSE) amplitude M(k,t) is a direct measure of the diffusion propagator of the molecules of a fluid diffusing in the pores of a porous medium. For small values of k = gamma g delta, where g is the gradient strength, delta is the duration of the gradient pulse, and gamma the gyromagnetic ratio, the PFGSE amplitude gives the diffusion coefficient D(t). The exact short-time diffusion coefficient, D(t)/D0 = 1-(4 square root of D0tS)/(9 Vp square root of pi)-D0tHS/(12Vp) + rho tS/6Vp, provides an important method for determining the surface to pore-volume ratio S/Vp. Here the mean surface curvature H = <1/R1 + 1/R2>. Combining early D(t) with the magnetization decay one obtains the surface relaxivity rho. The long-time effective diffusion constant derived from PFGSE gives information on the tortuosity of the connected space. The diffusion coefficient measured by PFGSE equals that derived from electrical conductivity only when rho = 0. Exact solutions with partially absorbing boundary conditions for a periodic structure are used to illustrate the influence of rho on the diffusion coefficient. M(k,t) can be well represented by a convolution of the structure factor of the connected pore space with an appropriate Gaussian propagator. This ansatz provides a model-independent way of obtaining the structure factor