Study of degenerate parabolic system modeling the hydrogen displacement in a nuclear waste repository

TL;DR

This paper provides a rigorous mathematical analysis of a complex degenerate parabolic system modeling hydrogen displacement in nuclear waste repositories, establishing existence results without simplifying assumptions on gas density.

Contribution

The study introduces a new approach to analyze a nonlinear degenerate parabolic system modeling hydrogen flow, accounting for compressibility and dissolution without simplifying assumptions.

Findings

Established existence of solutions for the degenerate system.

Developed new energy estimates on pressures.

Handled the degeneracy due to vanishing terms.

Abstract

Our goal is the mathematical analysis of a two phase (liquid and gas) two components (water and hydrogen) system modeling the hydrogen displacement in a storage site for radioactive waste. We suppose that the water is only in the liquid phase and is incompressible. The hydrogen in the gas phase is supposed compressible and could be dissolved into the water with the Henry's law. The flow is described by the conservation of the mass of each components. The model is treated without simplified assumptions on the gas density. This model is degenerated due to vanishing terms. We establish an existence result for the nonlinear degenerate parabolic system based on new energy estimate on pressures.