Upscaling and dispersion for transport in heterogeneous media

This paper focuses on upscaling of the transport equation for heterogeneous porous media with random flow. We consider the local flow field being a stationary random field and develop an upscaling by the recently developed coarse graining method which is based on filtering procedures in Fourier space. The coarse graining method is used to obtain an upscaled dispersion tensor which depends on the given length scale of the upscaling. We give explicit results for the scale-dependent dispersion coefficient in lowest-order perturbation theory. For finite length scales the upscaled dispersion models the effect of the unresolved subscale flow fluctuations, and for a global upscaling the upscaled value agrees with the well-known macrodispersion coefficient, which is, however, nearly approached for length scales larger than tenfold of the correlation length