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

摘要

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 σ~2 ∈ [0, 9], where σ~2 is the lognormal permeability variance. For purely advective transport, the asymptotic longitudinal dispersion coefficient depends linearly on σ~2 for σ~2 < 1 and quadratically on σ~2 for σ~2 > 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.