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

Time-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 Lambda 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.