Macrodispersion in a radially diverging flow field with finite Peclet numbers 2. Homogenization theory approach

We study the transport behavior of a tracer in a radially diverging heterog eneous velocity field. Making use of homogenization theory, we derive effec tive transport equations. These effective transport equations are very simi lar to those defined on the local scale. However, the local transport param eters such as local dispersion coefficients are replaced by effective dispe rsion coefficients. For smoothly varying heterogeneous media, explicit resu lts for effective radial dispersion coefficients are derived. Starting with the purely advective transport behavior (infinite Peclet numbers), we exte nd our calculations to transport with finite Peclet numbers. We find that t he impact of molecular diffusion on the effective dispersivity differs from the impact of local dispersion: Including local dispersion leads to effect ive dispersivities which are constant and equivalent to the effective dispe rsivities found in uniform flow configurations. In contrast, effective disp ersivities including diffusion are not constant but depend on the radial di stance. We compare the results found by homogenization theory with those de rived by Neuweiler er al. [this issue] by standard method of moments.