  The transport of single-phase fluid mixtures in porous media is described by
cross-diffusion equations for the mass densities. The equations are obtained in
a thermodynamic consistent way from mass balance, Darcy's law, and the van der
Waals equation of state for mixtures. The model consists of parabolic equations
with cross diffusion with a hypocoercive diffusion operator. The global-in-time
existence of weak solutions in a bounded domain with equilibrium boundary
conditions is proved, extending the boundedness-by-entropy method. Based on the
free energy inequality, the large-time convergence of the solution to the
constant equilibrium mass density is shown. For the two-species model and
specific diffusion matrices, an integral inequality is proved, which reveals a
minimum principle for the mass fractions. Without mass diffusion, the
two-dimensional pressure is shown to converge exponentially fast to a constant.
Numerical examples in one space dimension illustrate this convergence.
