Response function of the convection-dispersion equations describing radionuclide migration in a finite medium

Analytical expressions are derived for the response functions for the set of n coupled convection-dispersion equations in 1-D with constant coefficients. The equations are solved for a finite medium, and for an n-member radioactive decay chain with radionuclide-specific retardation factors. An exponential transformation and the Laplace transformation are applied to this set of partial differential equations to obtain a general set of transformed solutions. These are then inverted by two procedures to produce complementary forms of the response functions. One form converges quickly for small values of dimensionless time while the other converges quickly for large values. These response functions are used to model radionuclide transport in an underground nuclear waste disposal vault.