Modeling of a diffusion-sorption experiment by linear and nonlinear sorption isotherms

In this paper the results of a diffusion-sorption experiment, using simulated groundwater spiked with a mixture of 125I, 85Sr, and 137Cs, are modeled by a one-dimensional porous-medium approach in which sorption is described by Freundlich isotherms. The governing equations are solved analytically for the special case of a linear isotherm and numerically using the RANCH-DIFF computer code for nonlinear isotherms. A set of time-dependent ordinary differential equations is obtained using the Lagrange interpolation technique and is integrated by Gear's variable-order predictor-corrector method. The analysis allows the diffusion coefficients and parameters of the Freundlich isotherms to be extracted from the experimental data. It is shown that the sorption behavior of 85Sr can be modeled successfully by a linear isotherm, using a sorption parameter consistent with batch-sorption tests. The behavior of 137 Cs may be modeled by a nonlinear isotherm, but the amount of 137Cs sorbed is less than that anticipate from batch-sorption tests. Iodine-125 is assumed to be nonsorbing and is used to determine the porosity of the rock