  Steady adiabatic filtration of real gases is studied. Thermodynamical states
of real gases are presented by Legendrian surfaces in 5-dimensional
thermodynamical contact space. The relation between phase transitions and
singularities of projection of the Legendrian surfaces on the plane of
intensive variables is shown. The constructive method of finding solutions of
the Dirichlet filtration problem together with analysis of critical phenomena
is presented. Cases of van der Waals and Peng-Robinson gases are discussed in
details.
