Modelisation et simulation des dispositifs de ventilation dans les stockages de dechets radioactifs

摘要

the objective of this thesis is to develop models and algorithms to simulate efficiently the mass exchanges occuring at the interface between the nuclear waste deep geological repositories and the ventilation excavated galleries. To model such physical processes, one needs to account in the porous medium for the flow of the liquid and gas phases including the vaporization of the water component in the gas phase and the dissolution of the gaseous components in the liquid phase. In the free flow region, a single phase gas free flow is considered assuming that the liquid phase is instantaneously vaporized at the interface. This gas free flow has to be compositional to account for the change of the relative humidity in the free flow region which has a strong feedback on the liquid flow rate at the interface. In chapter 1, three formulations of the gas liquid compositional Darcy flow are studied. Their equivalence from the point of phase transitions is shown and they are compared numerically on 1D and 3D test cases including gas appearance and liquid disappearance. The 3D discretization is based on the Vertex Approximate Gradient (VAG) scheme and takes into account discontinuous capillary pressures. In chapter 2, a reduced model coupling a 3D gas liquid compositional Darcy flow in a fractured porous medium, and a 1D compositional free gas flow is introduced. The VAG discretization is extended to such models taking into account the coupling between the 3D matrix, the 2D network of fractures and the 1D gallery. Its convergence is studied both for the linear single phase stationary model and for a non linear model coupling the Richards equation to a single phase 1D flow or a 1D tracer equation in the gallery. Different test cases with Andra data sets are presented.In Chapter 3, a splitting algorithm to solve the coupling between the gas liquid compositional Darcy flow in the porous medium and the gas compositional free flow in thegallery is developed. The idea is to solve, in a first step, the porous medium equations coupled to the convection diffusion equations for the gas molar fractions in the gallery at fixed velocity and pressure in the gallery. Then, the total molar normal flux at the interface is computed and used in the second step of the algorithm to compute the velocity and pressure in the gallery solving the Navier Stokes equations. This algorithm is tested on several 2D test cases and the solutions obtained are compared with the ones obtained by the previous reduced model. To that end, the gas molar fraction boundary layer thickness used as a parameter in the reduced model is computed based on a low frequency diagonal approximation of a Steklov Poincar´e type operator for the stationary convection diffusion equation at fixed velocity.