INFLUENCE OF FIELD GRADIENT STRENGTH IN NMR-STUDIES OF DIFFUSION IN POROUS-MEDIA

Pulsed Field Gradient Spin Echo (PGSE) NMR experiments have been carried out to investigate the diffusion of water and light hydrocarbons in model porous media and reservoir core samples. The measurements have shown that if the experiment is carried out as a function of the diffusion time (DELTA), it is possible to observe the transition in the character of the diffusion from unrestricted (at small-DELTA) to hindered, averaged diffusion through the porous structure. From these experiments, a measure of the effective rate of diffusion of the fluid through the medium (D(eff)) can be obtained. Further observations have demonstrated that if the experiments are performed with different values of the field gradient strength (g), the value obtained for D(eff) (assuming Gaussian spin-echo decay) is dependent on g. The reason for this curious effect lies in the fact that the PGSE experiment yields the Fourier Transform of the autocorrelation function of spin displacements in the sample. In this sense, the gradient (of duration-delta) plays the role of a wavevector (q = gamma-delta-g) which can give rise to interference phenomena whenever its magnitude is of the order of the inverse of typical pore length scales. Numerical simulations for diffusion in a model porous network substantiate our observations. The effect is analogous to X-ray diffraction phenomena, and demonstrates that a correct measure of D(eff) is only obtained with small values of q.