Technical Report NTB 90-11

The results of a diffusion-sorption experiment on a sample of Darley Dale sandstone, using simulated groundwater spiked with a mixture of ¹²⁵I, ⁸⁵Sr and ¹³⁷Cs, are modelled 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 computer code RANCHDIFF for non-linear isotherms. A set of time-dependent, ordinary differential equations is obtained using the Lagrange interpolation technique and integrated by Gear's variable order predictor-corrector method.

It is shown that the sorption behaviour of ⁸⁵Sr can be modelled successfully by a linear isotherm, using a sorption parameter consistent with batch-sorption tests. The behaviour of ¹³⁷Cs may be modelled by a non-linear isotherm, but the amount of ¹³⁷Cs sorbed is less than that anticipated from batch-sorption tests. ¹²⁵I is assumed to be non-sorbing and is used to determine the porosity of the sandstone.