Numerical Simulation Of Two-dimensionalUnderground Transport Processes With A SourceTerm Model (1970)

All the activities related to nuclear power generate radioactive waste. A great volume of them are high level waste (HLW). It is considered, as a definitive solution for the HLW, its storing in underground repositories built in extremely low permeability geologic media. A global study of a disposal requires the evaluation of the radioactive mass that could be released to the groundwater, and transported away through the geosphere. A modelling procedure for the migration of radionuclides in a two-dimensional domain of a porous media from an underground repository is presented in this paper. We take into account two models in our study: a source term model giving the radioactive substance rate dissolved into water and a transport model considering conservative and non-conservative physico-chemical mechanisms. The source term model is solved by a two step retrograde method with an automatic time step control and the numerical solution of the migration model is obtained bv means of a finite volume method. Transactions on Ecology and the Environment vol 16, © 1997 WIT Press, www.witpress.com, ISSN 1743-3541 542 Ecosystems and Sustainable Development 1. Source term model The source-term model considered in this paper is based upon Hartley [4]. The nuclear waste is to be stored in an underground repository within a matrix and with a backfill of bentonite, isolated from the geological medium by engineering barriers. The host medium will be chosen according to low permeability and geological stability requirements, so that the repository will be kept free from the groundwater action for very long. Therefore, salt, clays and granites are considered as the most suitable. However, the groundwater will manage to reach the repository after very long, causing the corrosion of the engineering barriers and radioactive release to groundwater so that the isotopes will be transported away. The aim of the present source-term model is the simulation of the processes taking place and the estimation of the amount released to the groundwater. First, the radioactive mass is supposed to mantein isolated from groundwater for approximately a thousand of years. Just radioactive decay reactions are taken into account, as other processes like spontaneous fissions and neutronic captures may be considered negligible. The O.D.E. set of equations governing this phase may be written as follows: = A,_i z,_i(f) A, z,(t) 1 = 1,..., NI zi(Q) = z® Initial condition / = 1, . . . , NI 0 < t <Tc NI = nTM of isotopes of each chain where is a decay constant of the isotope /, z\(i) is the quantity of the isotope /, zf the initial amount of the isotope /, NI the number of isotopes of each radioactive chain and TC is the time when starts the corrosion. Once the groundwater has reached the repository, it will dissolve as much as it can according to solubility constraints. It is supposed that a so called intermediate store containing the non-dissolved material will arise. The matrix dissolution is evaluated under the following restrictive hypothesis: It is assumed a spherical shape for the matrix with an homogeneous distribution of the isotopes, the contact with the water takes place homogeneously throughout its whole surface and the dissolution rate is a constant determined experimentally, see Hartley [4]. Therefore, the volume variation along the time is given by: — o -c at p being V(i) the volume, A(i) the surface exposed to groundwater action and p the density. LO is the lixiviation rate and TL is the end of life of the matrix. The previous considerations allow to settle the following O.D.E. Transactions on Ecology and the Environment vol 16, © 1997 WIT Press, www.witpress.com, ISSN 1743-3541 Ecosystems and Sustainable Development 543