On persistent primary variables for numerical modeling of gas migration in a nuclear waste repository

Abstract

Numerical simulation of gas migration driven by compressible two-phase partially miscible flow in porous media is of major importance for safety assessment of deep geological repositories for long-lived high-level nuclear waste. We present modeling of compositional liquid and gas flow for numerical simulations of hydrogen migration in deep geological radioactive waste repository based on persistent primary variables. Two-phase flow is considered, with incompressible liquid and compressible gas, which includes capillary effects, gas dissolution, and diffusivity. After discussing briefly the existing approaches to deal with phase appearance and disappearance problem, including a persistent set of variables already considered in a previous paper (Bourgeat et al., Comput Geosci 13(1):29–42, 2009), we focus on a new variant of the primary variables: dissolved hydrogen mass concentration and liquid pressure. This choice leads to a unique and consistent formulation in liquid saturated and unsaturated regions, which is well adapted to heterogeneous media. We use this new set of variable for numerical simulations and show computational evidences of its adequacy to simulate gas phase appearance and disappearance in different but typical situations for gas migration in an underground radioactive waste repository.