Real-gas (RG) thermodynamics is currently being employed in many fields of science and engineering ranging from energy production to planetary exploration to combustion and fluid mechanics. Particularly prediction of phase equilibrium, i.e. the condition at which two or more phases occur simultaneously in a multi-component mixture is of key importance because it represents a thermodynamic state that is more stable given that it occurs at a lower value of Gibbs free energy compared to the corresponding single phase state (i.e. only one phase exists). While the calculation of phase-equilibrium is a well-established tool, the determination of all the thermodynamic variables in the multi-phase mixture is relatively new and unexplored. In this work, we provide the complete analytical framework to compute multi-phase (we focus only on two phases for now), equilibrium properties in a generic multi-component system and demonstrate on mixtures with increasing level of complexity that approximate methods, sometimes used in the literature, provide inaccurate predictions, thus making the present model an important framework for all the simulation tools that employ RG thermodynamics with phase-equilibrium.

天然气（RG）热力学目前正在许多科学和工程领域中使用，范围从能源生产到行星勘探到燃烧和流体力学。特别重要的是预测相平衡，即在多组分混合物中同时出现两个或多个相的条件，这是至关重要的，因为与热平衡相比，吉布斯自由能值较低时，热力学状态更稳定到相应的单相状态（即仅存在一个阶段）。虽然相平衡的计算是一种行之有效的工具，但确定多相混合物中所有热力学变量的方法还是相对较新的且尚未探索。在这项工作中，我们提供了一个完整的分析框架来计算多相（目前我们仅关注两个相），通用多组分系统中的平衡性质，并论证复杂程度不断提高的混合物，这些方法有时会近似使用方法在文献中，提供了不准确的预测，从而使本模型成为所有采用RG热力学和相平衡的仿真工具的重要框架。