The paper considers thermodynamics as a measurement of extensive variables, such as energy, volume and mass. In this sense, thermodynamic states are Legendrian or Lagrangian surfaces in the corresponding contact or symplectic space. The Beattie–Bridgeman model was chosen to describe phase transitions and their features for the equation of state of a real gas. This model describes the state of a substance in two phases: liquid and vapor. Real gas can be either single gase or a mixture. Formulas for calculating model constants for any mixture of gases are obtained. The caloric equation of state and various potentials are derived. The phase transition for a mixture of alkanes from oil production is constructed. Three critical phenomena for the phase transition of such a mixture are found. The Lagrangian manifold is constructed.