Simple analytic expressions are presented for radionuclide transport from a KBS 3-type repository, where spent nuclear fuel is placed in copper canisters surrounded by bentonite clay and deposited at a depth of 500 m in fractured granitic rock.
Dissolution of readily accessible and fuel matrix embedded nuclides, chain decay, and nuclide precipitation is treated within the canister. Transport in the canister void and buffer is modeled with a dual stirred tank analogy, where transport resistances represent an assumed small initial damage in the canister and transport features of the buffer-geosphere interface. Initial, transient diffusion in the buffer is treated with a simple correction term. Chain decay is not included in the buffer.
Geosphere transport expressions handle advection, longitudinal dispersion, matrix diffusion, sorption, and radioactive decay, but not chain decay. The treatment is based on earlier results for an instantaneous inlet and for a constant inlet to the geosphere in the nondispersive case. A correction is added so that longitudinal dispersion is taken approximately into account. The correction utilizes analytical expressions for the temporal moments of the geosphere release curve in the dispersive case.
The near-field/geosphere integration is treated in a simplified manner avoiding numerical convolutions. The instantaneous inlet expression for the geosphere release is used when the near-field release decreases rapidly in comparison to a typical response time in the geosphere; the constant inlet expression is used in the opposite case.
Twenty-seven calculation cases from a safety assessment of a KBS 3 repository using borehole data from three different field investigation sites were repeated with the analytic expressions. The agreement in both near-field and geosphere releases is in general well within an order of magnitude for the variety of long- and short-lived, sorbing, nonsorbing, solubility limited, immediately accessible, and fuel matrix embedded single and ingrowing species dominating the releases and doses in the safety assessment calculations. Also, probabilistic dose calculation results are in good agreement, making the analytic model a versatile complement to the various tools used in long-term safety evaluations of a KBS 3 type of repository in saturated fractured rock.
