Modeling of dynamic systems with a variable number of phases is still a challenge, especially for multiple liquid phases. A common approach from literature derives first‐order Karush–Kuhn–Tucker (KKT) conditions of the Gibbs free energy minimization and relaxes these if a phase does not exist. It aims at enabling dynamic simulation in all phase regimes of systems in vapor–liquid equilibrium by following a nonphysical continuous solution. In this work, we demonstrate that this continuous solution is not always possible in liquid–liquid equilibrium problems. The demonstration is done both theoretically and for illustrative examples. To overcome the demonstrated issues, we review the use of negative flash approach that allows negative molar amounts of nonexisting phases and propose a hybrid continuous formulation that explicitly assigns phase variables in the single‐phase regime and solves flash equations otherwise. Various dynamic case studies demonstrate the applicability and limitations of all three approaches. © 2018 American Institute of Chemical Engineers AIChE J, 65: 571–581, 2019

中文翻译：

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液-液平衡中具有可变相数的动态系统建模

具有可变数量的相的动态系统的建模仍然是一个挑战，特别是对于多个液相而言。从文献中得出的一种通用方法是得出吉布斯自由能最小化的一阶Karush-Kuhn-Tucker（KKT）条件，如果不存在相则将其放宽。它的目的是通过遵循非物理的连续解，在汽液相平衡的系统的所有相态下进行动态仿真。在这项工作中，我们证明了在液体-液体平衡问题中这种连续解决方案并非总是可行的。理论上和示例上都进行了演示。为了克服已证明的问题，我们回顾了负闪速方法的使用，该方法允许使用负摩尔量的不存在的相，并提出了一种混合连续公式，可在单相体系中明确分配相变量，并以其他方式求解闪速方程。各种动态案例研究证明了这三种方法的适用性和局限性。©2018美国化学工程师学会AIChE J，65：571–581，2019