  The modeling of migration of hydrogen produced by the corrosion of the
nuclear waste packages in an underground storage including the dissolution of
hydrogen involves a set of nonlinear partial differential equations with
nonlinear complementarity constraints. This article shows how to apply a modern
and efficient solution strategy, the Newton-min method, to this geoscience
problem and investigates its applicability and efficiency. In particular,
numerical experiments show that the Newton-min method is quadratically
convergent for this problem.
