Asymptotic dispersion in 2D heterogeneous porous media determined by parallel numerical simulations

1] We determine the asymptotic dispersion coefficients in 2D exponentially correlated lognormally distributed permeability fields by using parallel computing. Fluid flow is computed by solving the flow equation discretized on a regular grid and transport triggered by advection and diffusion is simulated by a particle tracker. To obtain a well-defined asymptotic regime under ergodic conditions ( initial plume size much larger than the correlation length of the permeability field), the characteristic dimension of the simulated computational domains was of the order of 10 3 correlation lengths with a resolution of ten cells by correlation length. We determine numerically the asymptotic effective longitudinal and transverse dispersion coefficients over 100 simulations for a broad range of heterogeneities sigma(2) epsilon [ 0, 9], where sigma(2) is the lognormal permeability variance. For purely advective transport, the asymptotic longitudinal dispersion coefficient depends linearly on s2 for s2 < 1 and quadratically on s2 for s2 > 1 and the asymptotic transverse dispersion coefficient is zero. Addition of homogeneous isotropic diffusion induces an increase of transverse dispersion and a decrease of longitudinal dispersion.