Modeling of a Diffusion-Sorption Experiment by Linear and Nonlinear Sorption Isotherms

The results of a diffusion-sorption experiment, using simulated groundwater spiked with a mixture of ^I25I, 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 ¹³⁷Cs may be modeled by a nonlinear isotherm, but the amount of ¹³⁷Cs sorbed is less than that anticipated from batch-sorption tests. Iodine-125 is assumed to be nonsorbing and is used to determine the porosity of the rock.