A novel, particularly robust method for the calculation of critical curves of fluid mixtures is proposed that makes use of differential equations representing the critical conditions (isochoric thermodynamics formalism). These differential equations are integrated with adaptive numerical integration methods, thus avoiding the convergence problems that so often afflict methods using algebraic equations. The novel method can be used with all Helmholtz energy-explicit equations of state, including models that can return unphysical results when applied to thermodynamic states within a two-phase region, for example, the GERG equations of state. In combination with the “parametric marching” technique, the new approach is able to follow critical curves of arbitrary shape. The Supporting Information provides an implementation of this approach for the GERG-2008 and Peng–Robinson models in the Python language.

中文翻译：

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通过微分方程求解计算流体混合物的临界曲线

提出了一种新颖的，特别鲁棒的方法来计算流体混合物的临界曲线，该方法利用了代表临界条件的微分方程（等渗热力学形式主义）。这些微分方程与自适应数值积分方法集成在一起，从而避免了收敛问题，而这些收敛问题经常困扰使用代数方程的方法。该新方法可用于所有的亥姆霍兹能量-显式状态方程，包括当应用于两相区域内的热力学状态（例如GERG状态方程）时可以返回非物理结果的模型。结合“参数行进”技术，新方法能够遵循任意形状的关键曲线。