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AN EXACT SOLUTION FOR THE ASSESSMENT OF NONEQUILIBRIUM SORPTION OF RADIONUCLIDES IN THE VADOSE ZONE
Citation:
Drake, R. L., J. S. Chen, AND D G. Jewett*. AN EXACT SOLUTION FOR THE ASSESSMENT OF NONEQUILIBRIUM SORPTION OF RADIONUCLIDES IN THE VADOSE ZONE. Waste Management 2002 Symposium, Tucson, AZ, 02/24-28/2002.
Description:
In a report on model evaluation, the authors ran the HYDRUS Code, among other transport codes, to evaluate the impacts of nonequilibrium sorption sites on the time-evolution of 99Tc and 90Sr through the vadose zone. Since our evaluation was based on a rather low, annual recharge rate, many of the numerical results derived from HYDRUS indicated that the nonequilibrium sorption sites, in essence, acted as equilibrium sorption sites. To help explain these results, we considered a "stripped-down" version of the HYDRUS system. This "stripped-down" version possesses two dependent variables, one for the radionuclides in solution and the other for the radionuclides adsorbed to the nonequilibrium sites; and it possesses constant physical parameters. The resultant governing equation for the radionuclides in solution is a linear, advection-dispersion-reaction (i.e., radioactive decay) partial differential equation containing a history integral term accounting for the nonequilibrium sorption sites. It is this "stripped-down" version, which is the subject of this paper. We found an exact solution to this new version of the model. The exact solution is given in terms of a single definite integral of terms involving elementary functions of the independent variables and the system parameters. This integral possesses adequate convergence properties and is easy to evaluate, both in a quantitative matter and in a qualitative manner. The parameters that are considered in the system are as follows: the radionuclide's equilibrium partition coefficient between water and soil, the bulk density of the soil, the fractions of equilibrium/nonequilibrium sorption sites, the volumetric water content, the first order equilibrium adsorption rate constant, the first order radioactive decay rate constant, the liquid water soil tortuosity factor, the molecular diffusion coefficient in water, the longitudinal dispersivity factor, and the Darcian fluid flux density. In addition, the system possesses a stepwise, variable source of radionuclides at the ground surface and a variable flux of pollutants from the vadose zone at the water table. Although this new system is a "stripped down" version of the HYDRUS Code, it is a valuable system in its own right for the assessment of nonequilibrium sorption of radionuclides in the vadose zone.