Time dependent dispersion in macro scale heterogeneous porous media

Abstract

Due to the difficulty of characterizing complex heterogeneities with mathematical equations, the analytical solution based on the convection-dispersion equation assumes dispersion that is independent of time and space. However, moreestablished results suggest that dispersion varies with space due to the complexity of a porous structure and the effect of large e heterogeneities in the field. This space dependence of dispersion has been considered as the primary reason for the "scale-up" problem, which is disparity between laboratory and field measured dispersion. In this work, the space dependence of dispersion is converted to time dependence by considering the fact that distance x = nt and K(x) = (nt) = nK(t) since average velocity flow is considered. Results from this work demonstrate that space or time independence of dispersion only occurs at relatively long duration of flow where the flow is generally stabilized and small values of fractal exponent. The concentration profile in a porous system assuming constant and time dependent dispersion is also evaluated