Nuclear-magnetic-resonance diffusion simulations in two phases in porous media

International audienceTime-dependent diffusion simulations which can be measured by nuclear magnetic resonance (NMR) were numerically performed in consolidated reconstructed porous media saturated by two immobile fluids. The phase distributions were obtained by an immiscible lattice Boltzmann technique which incorporates interfacial tension and wetting. The apparent diffusion coefficient in each fluid was determined by a random walk algorithm. Permeability and conductivity tensors were calculated by finite-difference schemes. The major properties valid for a single phase could be generalized to two phases. First, the characteristic length Λ introduced by Johnson [Phys. Rev. Lett. 57, 2564 (1986)] is of the order of twice the phase volume to surface ratio. Second, the apparent diffusion coefficients for all porosities, saturations, and phases can be represented by a single dimensionless curve

Nuclear magnetic resonance diffusion with surface relaxation in porous media

International audienceNuclear magnetic resonance (NMR) diffusion simulations with surface relaxation were performed numerically in unconsolidated and consolidated porous media by a random walk technique. Two uniform and nonuniform models of surface relaxation were proposed and compared. The apparent diffusion coefficient and extinction function were determined and studied in the fast, slow and intermediate diffusion regimes of relaxation. According to theoretical predictions, it was observed that the extinction function does not depend on surface relaxivity parameter ρ2 in the slow diffusion regime. The apparent diffusion coefficients are independent of ρ2 in the fast diffusion regime and tend to be superposed onto a single curve in the slow one. The evolution of the apparent diffusion coefficients is gathered by a reduced representation in the fast diffusion regime