Gas filtration governed by the Darcy law at constant thermodynamic potential in threedimensional porous media is onsidered. We study the real gas described by the Landau–Lifshitz state equations and consider filtration with constant specific entropy, specific enthalpy and specific Gibbs free energy. Filtration equation can be written in one variable only due to constant potential. The initial and the first terms of long-time asymptotics of filtration equations are taken into consideration. The equations for the initial and the first terms are the Laplace and the Poisson ones, respectively. In addition, we consider phase transitions of methane, which is described by the Landau–Lifshitz equations of state. It is shown that phase transitions do not occur at constant specific entropy and specific enthalpy in the case of methane.