A Combined Equation of State for Methane, Based on Bender’s Regular Equation with a Scaling Part in Explicit Form up to 50 MPa

A combined equation of state of methane in real variables (pressure p, temperature T, density ρ) is proposed that allows calculations of heat capacities \({{C}_{{v}}}\) , C_p, and speed of sound W in explicit form in single-phase states, including the critical region. The equation contains a regular part in the form of Bender’s equation for p(ρ,T) with 19 coefficients, a scaling part with 6 coefficients, and a crossover function in explicit form (2 coefficients). The coefficients are determined from a CH₄ p, ρ,T data array up to 30 MPa. Data on \({{C}_{{v}}}\) , C_p, and W are not involved, except for the \({{C}_{{v}}}\) (T) dependence in the ideal gas state and value \({{C}_{{v}}}\) at 100 K on the liquid branch of the boundary curve. In the regular region, the calculated values of \({{C}_{{v}}}\) , C_p, and W are close to the experimental and tabulated values. Discrepancies with the tabular values are no more than 5% in the critical region. The RMS error for p is σ_p = 0.8%, and error for \({{C}_{{v}}}\) is no more than 5%. Results from calculations are compared to crossover equations of state for CH₄. It is concluded that the proposed model of the combined equation of state is preferable for calculating the thermophysical properties of methane.