A closed-form multi-parameter fluid equation of state (EoS) is proposed and tested with empirical pressure isotherms of water and hydrogen. The EoS is non-algebraic but elementary, applicable in the full temperature range above the melting point, and remains accurate at high pressure. The critical-point conditions (vanishing density-derivatives of pressure) are exactly implemented in the exponential attractive term of the EoS. The singular repulsive term is structured similar to the Carnahan-Starling EoS and depends on five substance-specific parameters, which can be regressed from the critical isotherm. The temperature evolution of the EoS above the critical temperature is regressed from supercritical isotherms. In the subcritical regime above the melting point, the temperature-dependent scale factors of the EoS are inferred from the empirical coexistence curve, which is fully implemented in the EoS. The pressure singularity occurs at a limit density that is noticeably higher than predicted by universal cubic EoSs such as the Peng-Robinson EoS. The parameters of the analytic and non-perturbative EoSs of water and hydrogen are derived from high-pressure data sets.

提出了一种封闭形式的多参数流体状态方程 (EoS)，并使用水和氢的经验压力等温线进行了测试。EoS 是非代数但基本的，适用于熔点以上的整个温度范围，并在高压下保持准确。临界点条件（压力的消失密度导数）在 EoS 的指数吸引项中完全实现。奇异排斥项的结构类似于 Carnahan-Starling EoS，取决于五个特定于物质的参数，这些参数可以从临界等温线回归。EoS 在临界温度以上的温度演变是从超临界等温线回归的。在高于熔点的亚临界状态下，EoS 的温度相关比例因子是从经验共存曲线中推断出来的，这在 EoS 中完全实现。压力奇点的极限密度明显高于通用立方 EoS（如 Peng-Robinson EoS）预测的密度。水和氢的分析和非微扰 EoS 的参数来自高压数据集。