Two-phase, partially miscible flow and transport modeling in porous media; application to gas migration in a nuclear waste repository

Abstract

We derive a compositional compressible two-phase, liquid and gas, flow model for numerical simulations of hydrogen migration in deep geological repository for radioactive waste. This model includes capillary effects and the gas high diffusivity. Moreover, it is written in variables (total hydrogen mass density and liquid pressure) chosen in order to be consistent with gas appearance or disappearance. We discuss the well possedness of this model and give some computational evidences of its adequacy to simulate gas generation in a water-saturated repository.

Henry’ Law and Gas Phase Disappearance

“…There are clearly alternative ways to solve this problem without using such a solver. See for recent examples [2], [1]. However nonlinear problems with complementary constraints occur in many circumstances as for example in a black oil model [3] or in problems with dissolution-precipitation.…”

“…Recently two other papers [2], [1] adressed the formulation of this problem. In this paper, for the sake of the simplicity of exposition, we will assume that only hydrogen is in the gas phase (water does not vaporize).…”

“…The resulting formulation is a set of partial differential equations with complementarity constraints. A similar formulation is also presented in [2] and it also can be viewed as a variation of the formulation of the black oil model presented in [3].…”

Isothermal water flows in low porosity porous media in presence of vapor–liquid phase change

“…For details we refer to [1] and [35]. A similar approach, but extending different unknowns, was presented by Bourgeat et al in [9].…”

Two-Component Two-Compressible Flow in a Porous Medium

“…Under non-degeneracy and slow oscillation assumptions on the diagonal coefficients and with small data for the hydrogen, the author establishes the existence of a weak solution. A similar physical model was studied in [13]. The authors derive a compositional model of compressible multiphase flow in porous media.…”