A Combined Analytical Model for Performance Assessment of the Waste Package/Geologic Medium Systems
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ASIT K. RAYt, SHYAM NAIRt, AND H. ERIC NUTTALL-t tDepartment of Chemical Engineering, University of Kentucky, Lexington, Kentucky, 40506-0046, USA; tiDepartment of Chemical Engineering, University of New Mexico, Albuquerque, New Mexico, 87131, USA
INTRODUCTION Geologic waste isolation systems currently under consideration for long term containment of high-level radioactive waste is based on a set of sequential barriers to release of radionuclides.
Recently,
Klingsberg and Duguid
and Pigford2 have reviewed in detail the multiple-barrier disposal concept. These barriers are the waste form, canister, geologic media.
buffer, overpack, backfill and
Each of these barriers acts to retard ground water penetra-
tion to the repository as well as migration of radionuclides to the biosphere. The possibility of water contamination is one of the major concerns from these wastes.
Once a repository is filled with radioactive waste and sealed,
the contamination can take place by the following sequence of events: Groundwater intrusion into the repository Canister failure and initiation of leaching Transport of radionuclides from the repository to groundwater Transport of radionuclides to biosphere For an overall performance assessment of the geologic isolation systems, one needs to take the above sequence of events and interdependent functions of Several numerical codes are currently the barriers into consideration. available for performance assessment, but analytical solutions are needed to check accuracy of these codes.
Analytical solutions for radionuclide
transport in porous media have been developed by Lester et al. 3 and Burkholder et al. 4 In this study we have developed a three dimensional model which incorporates the sequence of events preceding migration of nuclides to biosphere. The model (i) (ii)
is based on the following assumptions:
Canister failure occurs before groundwater invades the repository. Leaching of radionuclides begins when the repository is saturated by groundwater.
(iii)
Leaching is solubility controlled.
Thus, at the canister/backfill
interface the concentration of radionuclides in water is equal to equilibrium concentration.
612 (iv)
All the engineered barriers are treated as a single homogeneous medium, having same physical properties, and the migration of radionuclides through the barriers is diffusion controlled.
(v)
Radionuclides migrating out of the waste package are transported through groundwater by diffusion as well as by convection, geomedium surrounding the waste package is
and the
assumed to be infinite in
expanse in all directions.
THEORETICAL ANALYSIS (a) Ground Water Intrusion Time.
A simple but crude estimate of the time,
ti, needed for groundwater to saturate the repository may be obtained from Darcy's Law K
v0
-
-Vp, 1~1
(1)
where K is the permeability of engineered barriers, p is the viscosity, Vp is the pressure gradient, and v0 is the superficial velocity of water. The intrusion time, ti, can be calculated from a material balance across the barriers,
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