Macrodispersion in a radially diverging flow field with finite Peclet numbers 1. Perturbation theory approach

In this paper large-scale dispersion coefficients for tracer transport in a radially diverging flow field with cylindrical geometry in an unbounded do main are investigated. The effect of small-scale dispersion as well as smal l-scale diffusion on the large-scale dispersion is analyzed. Macrodispersio n coefficients are derived analytically from ensemble-averaged second radia l cumulants of the tracer concentration distribution. The cumulants are cal culated to second order in the fluctuations of permeability of the heteroge neous porous medium. A macrodispersion coefficient is found, which is propo rtional to the mean velocity field. It is shown that the macrodispersivity is modified because of the impact of the small-scale diffusion and small-sc ale dispersion. The vertical small-scale mixing leads to a decrease of the macrodispersivity. Small-scale diffusion makes this decrease time-dependent . Horizontal diffusion, however, leads to an increase of the macrodispersiv ity.