A New Homogeneous Non-Equilibrium Model to Compute Vapor-Liquid Two-Phase Critical Pressure Ratios of Multicomponent Hydrocarbon Mixtures

The critical pressure ratio (η_c) is an essential parameter for computing the vapor-liquid two-phase critical pressure and mass flow rate of multicomponent hydrocarbon mixtures flowing through valves and leakage orifices. The Homogeneous Non-Equilibrium Diener-Schmidt (HNE-DS) model widely used to calculate η_c assumes that the fluid's volume linearly changes with the pressure (using the Clausius-Clapeyron equation), which is not suitable for multicomponent gas mixtures. In this paper, a new Homogeneous Non-Equilibrium (new-HNE) model is proposed to calculate η_c of gas mixtures. Firstly, a new critical flow compressibility factor (ω_c) is developed from its thermodynamic definition and the Peng-Robinson equation of state (EOS), overcoming the inherent limitations of the Clausius-Clapeyron equation. Then, η_c is correlated to the newly derived ω_c by fitting experimental data at various pressures and gas mass fractions of both single-component and multicomponent gas mixtures, yielding the new HNE-DS model. Results show that, for the water-steam and air-water two-phase flow, the average relative deviations (ARD) between the calculated critical pressure ratios and experimental values are equal to 2.8% and 4.93%, respectively, which represents a significant improvement in comparison with the original HNE-DS model. Moreover, this new model is extended to the applications of Liquefied natural gas (LNG)/liquefied petroleum gas (LPG) fluids, and will further contribute to the calculation of the leakage mass flow rate of fluid flowing through the orifices/valves.