Method of Constructing the Fundamental Equation of State for Methane Taking into Account the Features of a Wide Vicinity of the Critical Point

A unified fundamental equation of state for methane has been developed, conveying experimental data on density, isochoric and isobaric heat capacity, and the speed of sound within the experimental uncertainty of these data in the range of parameters of state for pressure up to 500 MPa, density up to 450 kg/m³, at temperatures from 90.641 to 620 K. A unified fundamental equation of state has been developed using the large-scale theory of critical phenomena. In accordance with the power laws of scale theory, this equation conveys the behavior of isothermal compressibility, isochoric and isobaric heat capacity, and the speed of sound in the asymptotic vicinity of the critical point. The expression for the Helmholtz free energy, which underlies the unified fundamental equation of state, consists of three terms: the ideal gas component, the regular component, and the singular component. The structure of the singular component includes a crossover function in the form of an exponential dependence on density, which in the region of low densities and pressures ensures the transition of the unified fundamental equation of state to a virial equation of state. The singular component of the unified fundamental equation of state is calculated based on a new representation of the scaling hypothesis, which is based on the linear Scofield–Litster–Ho model and Benedek hypothesis. The similarity relation is also used to calculate the parameters of the singular component of the unified fundamental equation of state, based on which a relationship is established between the parameters of the singular component of the unified fundamental equation of state and parameters of the Pokrovsky model for a real liquid. It is shown that the use of the similarity relation made it possible to reduce the number of individual parameters of the unified fundamental equation of state and exclude data on the isochoric heat capacity \({{C}_{v}}\) related to the asymptotic vicinity of the critical point from the calculation scheme when determining its coefficients. The agreement between results obtained and calculations performed, first, using crossover models for a wide vicinity of the critical region, and second, using Setzmann and Wagner’s fundamental equation of state (1991) and Bezverkhy and Dutova’s combined equation (2023) is discussed.