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

Jean-Raynald de Dreuzy, Anthony Beaudoin, Jocelyne Erhel
2007 Water Resources Research  
9 We determine the asymptotic dispersion coefficients in 2D exponentially-correlated 10 lognormally-distributed permeability fields by using parallel computing. Fluid flow is 11 computed by solving the flow equation discretized on a regular grid and transport triggered by 12 advection and diffusion is simulated by a particle tracker. To obtain a well-defined asymptotic 13 regime under ergodic conditions (initial plume size much larger than the correlation length of 14 the permeability field),
more » ... e characteristic dimension of the simulated computational domains 15 was of the order of 10 3 correlation lengths with a resolution of ten cells by correlation length. 16 We determine numerically the asymptotic effective longitudinal and transverse dispersion 17 coefficients over 100 simulations for a broad range of heterogeneities [ ] 9 , 0 2 ∈ σ , where σ 2 is 18 the lognormal permeability variance. For purely advective transport, the asymptotic 19 longitudinal dispersion coefficient depends linearly on σ 2 for σ 2 <1 and quadratically on σ 2 for 20 σ 2 >1 and the asymptotic transverse dispersion coefficient is zero. Addition of homogeneous 2D asymptotic dispersion 2 isotropic diffusion induces an increase of transverse dispersion and a decrease of longitudinal 22 dispersion. 23
doi:10.1029/2006wr005394 fatcat:uhycqk2qqvbehckihjjegnuwbm