Characterization of porous media by NMR imaging and flow-diffraction

The echo attenuation function EΔ(q) and the displacement probability P(Z, Δ) for water flowing through a bed of 0.3 mm glass beads has been measured by means of Pulsed Gradient Spin Echo (PGSE NMR). The encoding time Δ and the flow rates used in the experiments were chosen such that the average displacement was at least one bead diameter. The EΔ(q) shows, as expected, a diffraction peak at about the inverse of the bead diameter. For longer times EΔ(q) shows another peak at about the inverse of twice the bead diameter. In analogy with PGSE NMR in presence of diffusion in a closed system, these data suggest that the pore space correlation function or features closely related to it, can be accessed through the PGSE experiment with flow. The conditions, which lead to this possibility, are discussed and supported with the results of network modelling of fluid flow in a periodic structure. The true pore space correlation function has been determined using the Patterson function approach applied to a NMR image data set. This has been compared with the one obtained by PGSE NMR with flow. The displacement distributions P(Z, Δ) for fluid flow/diffusion in this system also show structural information and, it is suggested, can be regarded as a product of the pore space correlation function with an evolving smooth distribution which starts as an exponential and tends to a Gaussian in the longer time limit.