Model for long-term assessment of radioactive waste repositories
(Modèle d'Evaluation à LOng terme des Déchets Irradiants Enterrés)
IRSN has created the MELODIE computer code, numerical software for simulating the flow and the transport of species in solution, and continues to develop it with a view to making available a tool for evaluating the long term safety of a radioactive waste disposal facility. The understanding of the phenomena that will come into play in a radioactive waste disposal facility over long periods (which can extend from several hundred years to several million years) requires in particular numerical simulation support. This software makes it possible to simulate, in 2 and 3 dimensions, underground flow and the transport of solutes in porous media, saturated or non-saturated with water.
The evaluation of the safety of a radioactive waste disposal facility necessitates understanding and modelling, firstly, the hydrogeological system that governs underground flow (free and/or captive aquifers) and, secondly, the transfer of radionuclides through built structures and geological formations up to the outlets of the hydrogeological system in question.
The MELODIE computer code is provided with procedures enabling the modelling of flows in captive aquifers as well as in free surface aquifers that include non-saturated zones.
MELODIE represents the migration of radionuclides in the geosphere, while taking into account phenomena of convection, dispersion, diffusion, the solubility of radionuclides, retention by natural or man-made materials as well as decay and radioactive relationships.
The equations are discretised by a method that combines both the finite volumes method and the finite elements method (VFEF). This method consists in using a Galerkin development for the temporal and diffusive terms, as well as a finite volumes method via Godunov’s scheme for the convective term. The VFEF discretisation method enables the partial differential equation to be transformed into a discretised problem in order to numerically approach the solution, which comes down to resolving a finite number of equations corresponding to the number of nodes of the mesh used for the discretisation of the domain. It also makes it possible to ensure the stability of the numerical scheme in order to calculate a solution that is coherent with the physical properties studied.
Furthermore, a domain breakdown method has been incorporated in Melodie in order to offset the difficulties of contrast of spatial scales and to optimise calculation times. This method makes it possible to break down a numerical model into sub-models spread out over several processors while conserving the continuity of flows and the transport of radionuclides (uniquely for saturated media). The exchange of information between sub-models is then carried out by PVM (Parallel Virtual Machine) libraries.
The MELODIE computer code is made up of several different tools, including the Melomail utility programme, the MeloView graphic representation tool and the Melo code. The Melomail utility programme has been developed in order to construct the meshing and parameterise the numerical model containing the data required for calculations. MeloView is a pre- and post-processing tool for calculations, which allows the user to construct in an interactive manner the numerical model and to have at his or her disposal a wide choice of graphic representations for analysing and presenting results. The Melo code resolves flow equations in permanent or transitory regime and equations of transport of radionuclides in saturated and non-saturated porous media.
Compatibility with external software
The meshing constructed with external software (Gmsh, Mefisto, etc.) can be integrated in MELODIE and simulation results can be adapted in order to be visualised with free-access graphic tools such as Paraview.Some examples of modelling performed with MELODIE Release and migration of radionuclides
Simulations have been performed by IRSN to support its evaluation of the safety of a potential geological disposal of radioactive waste in a clay formation. The example opposite illustrates the release and the migration of radionuclides in a geological medium constituted of an alternation of semi-permeable layers and aquifers. The activity plume progressively evolves from the release zone through diffusion and convection to a zone constituting a surface outlet.
IRSN note on the feasibility of geological disposal of radioactive waste in clay formation (35 Mo - in French)
Within the framework of the NF-Pro project (FP6 project) concerning the understanding and the modelling of physical/chemical parameters in a geological waste disposal facility, transport calculations of different radioactive elements have been carried out on a model constituted of different inter-coupled meshes. These make it possible to simulate the behaviour of a storage facility, from the near field - with the characterisation of man-made barriers and the degradation kinetics of disposal packages - up to the far field - with the characteristics of the host rock. The method employed uses the PVM software package to transfer the conditions to the limits between the different meshes. The results presented simulate in 3D the release and the migration of activity outside of the disposal cells towards the access drifts and the geological formation (for 6 control disposal cells).
The example opposite is taken from the Couplex international exercise (code qualification exercise proposed by Andra in partnership with GdR Momas). This exercise made it possible to compare the discretisation methods available in Melodie with the simulation of the transfer of solutes through very heterogeneous media (by alternating transport regions with prevailing diffusive and convective character). Recommendations for using Melodie for models having parameters that can vary by more than 6 orders of magnitude have been deduced from this test; by way of example, for the VFEF method, constraints at the level of the meshing and the temporal discretisation need to be respected in order to guarantee that the calculated solution indeed possesses the physical properties of the variable modelled (principle of the maximum and numerical stability of this scheme).
The example below is taken from the Mamern 2011 congress. It illustrates the application of an a posteriori error indicator to the generation of adaptive meshing with the aim of managing as best as possible the numerical instabilities of applications having anisotropy of the dispersion tensor.