Abstract The polynomial PM, integrated quadratic-linear IQLM and factorial analytic FAM solvation models are studied with the aim of estimating and optimizing the quaternary liquid-liquid equilibria. The reliability of existing models is analyzed with respect to three extraction factors by examining three literature quaternary systems, and the general ranking approximates the order PM > FAM > IQLM. A robust hybrid gradient method HGM is proposed for tackling the optimization problem on the basis of the first and second derivative conditions in combination with the interval gradient analysis of the modeled property. Given the nonsmooth nature of the optimization problem, we resort to a derivative solution scheme aimed at simplifying the convergent analysis of finding a global extremum with no a need for the evaluation of any objective function. The model sensitivity to mimic the global optimum of the extraction factors keeps to the order FAM ≥ IQLM > PM. This paper is completed by the numerical results of three test problems, manifesting the fact that there are significant benefits to be gained from the combination of gradient and interval analysis tools, particularly as the distribution of the solutes is a primary concern to be accounted for optimizing the quaternary equilibria.

中文翻译：

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使用多项式和二次可微模型通过混合梯度法 (HGM) 优化四元液-液系统的相平衡

摘要 以估计和优化四元液-液平衡为目的，研究了多项式PM、二次线性积分IQLM和阶乘解析FAM溶剂化模型。通过考察三个文献四元体系，从三个提取因素分析现有模型的可靠性，总体排序近似为 PM > FAM > IQLM。提出了一种基于一阶和二阶导数条件并结合建模属性的区间梯度分析来解决优化问题的鲁棒混合梯度方法HGM。鉴于优化问题的非光滑性，我们采用了一种导数解决方案，旨在简化寻找全局极值的收敛分析，而无需评估任何目标函数。模拟提取因子全局最优的模型敏感性保持顺序 FAM ≥ IQLM > PM。本文由三个测试问题的数值结果完成，表明梯度和区间分析工具的结合可以获得显着的好处，特别是溶质的分布是要考虑的主要问题进行优化四元均衡。