Two-dimensional nuclear magnetic resonance measurements and numerical simulations of fluid transport in porous rocks

Pulsed magnetic field gradient nuclear magnetic resonance (PFG-NMR) measure ments have been performed for water flowing through porous Fontainebleau sa ndstones and are compared with flow through a packed bed of monodisperse gl ass beads. Pulsed gradients were applied both parallel (Z) and perpendicula r (X) to the main flow axis simultaneously to obtain the two-dimensional di splacement joint probability density P-Delta(X,Z) of the moving spins. The evolution of P-Delta(X,Z) as a function of encoding time Delta and flow rat e Q is investigated. Good agreement is found between experimental P-Delta(X ,Z) and those obtained by numerical simulations of flow through computer-ge nerated structures of equivalent statistical properties to those studied. T he simulations are employed to compare a wider range of flow parameters tha n those accessible by experiment. In addition to averaged quantities, such as dispersion coefficients and moments of displacement distributions, the c orrelations between displacements in both directions are presented. The ave rage transverse dispersion, < X-2>, for a subset of particles possessing a given axial displacement, Z, at any encoding time Delta is found to scale w ith Z; for flow rates and times discussed in this study, a power law relati on < X-2> proportional to Z(gamma) is observed with the spreading exponent gamma being characteristic of the connectivity and statistical geometric fe atures of the pore space. The correlation coefficient rho(X2,Z) is found to be positive in all cases and strongly influenced by the ratio of convectiv e to diffusive contributions to the total particle displacements, expressed by the Peclet number. A maximum in the correlation coefficient occurs at a time scale dependent on the Peclet number and in the structures studied he re, this corresponds to a characteristic lengthscale of the systems, approx imated by their average pore size. (C) 2000 American Institute of Physics. [S1070-6631(00)01803-1].