Vertical random variability of the distribution coefficient in the soil and its effect on the migration of fallout radionuclides

In the field, the distribution coefficient, K-d, for the sorption of a radionuclide by the soil cannot be expected to be constant. Even in a well defined soil horizon, K-d will vary stochastically in horizontal as well as in vertical direction around a mean value. The horizontal random variability of K-d produce a pronounced tailing effect in the concentration depth profile of a fallout radionuclide, much less is known on the corresponding effect of the vertical random variability. To analyze this effect theoretically, the classical convection- dispersion model in combination with the random-walk particle method was applied. The concentration depth profile of a radionuclide was calculated one year after deposition assuming (1) constant values of the pore water velocity, the diffusion/ dispersion coefficient, and the distribution coefficient (K-d = 100 cm(3). g(-1)), and (2) exhibiting a vertical variability for K-d according to a log- normal distribution with a geometric mean of 100 cm(3). g(-1) and a coefficient of variation of CV = 0.53. The results show that these two concentration depth profiles are only slightly different, the location of the peak is shifted somewhat upwards, and the dispersion of the concentration depth profile is slightly larger. A substantial tailing effect of the concentration depth profile is not perceivable. Especially with respect to the location of the peak, a very good approximation of the concentration depth profile is obtained if the arithmetic mean of the K-d- values (K-d = 113 cm(3). g(-1)) and a slightly increased dispersion coefficient are used in the analytical solution of the classical convection- dispersion equation with constant K-d. The evaluation of the observed concentration depth profile with the analytical solution of the classical convection- dispersion equation with constant parameters will, within the usual experimental limits, hardly reveal the presence of a log- normal random distribution of K-d in the vertical direction in contrast to the horizontal direction.