Temporal behavior of a solute cloud in a heterogeneous porous medium 3. Numerical simulations

M.Dentz, H. Kinzelbach, S. Attinger, W. Kinzelbach,Chemical Physics Letters, 451, 1-3, 136-140


The article presents systematic numerical simulations of the temporal behavior of a
passive solute in a saturated three-dimensional heterogeneous medium. The
groundwater flow is derived from the linearized solution of the Darcy equation with
Gauss-distributed log hydraulic conductivity. The transport of a passive solute is
studied by a random-walk method, which allows for a systematic study of the temporal
behavior of the effective and ensemble dispersion coefficients. The numerical results
are compared to the second-order perturbation theory expressions given in two
companion papers [Dentz et al., 2000a, 2000b] and to nonperturbative results which
follow from Corrsin’s conjecture. The low-order perturbation theory is intrinsically
based on the assumption of small heterogeneity, while Corrsin’s conjecture does not
take into account certain contributions due to higher-order terms of the perturbation
series. The simulations yield, for the first time, systematic quantitative information on
the validity and the limitations of these analytic approximations. For increasing
heterogeneities, considerable deviations from the theoretically predicted transport
behavior are observed.