以狀態方程式結合COSMO-SAC模型預測混合物之液氣相平衡

Abstract

本研究的主要透過結合Peng-Robinson狀態方程式以及COSMO-SAC液體模型，預測混合物的液氣相平衡。基於量子力學的計算，COSMO-SAC模型本身已能準確的預測任何物質在遠離臨界點處，混合物的液氣相平衡。我們發現，將COSMO-SAC模型與Peng-Robinson狀態方程式，透過諸如Wong-Sandler （WS）或是一次修正Huron-Vidal (modified 1st order Huron-Vidal, MHV1）這些以過量吉布氏自由能為基準的混合律結合，可以大幅增加預測混合物液氣相平衡的能力。我們已測試包含烷類、醇類、酮類、水，甚至芳香烴等物質間所構成的兩成份系統，預測的範圍廣佈自壓力一大氣壓以下到將近兩百大氣壓，溫度從攝氏約零下一百度到攝氏五百五十度。 雖然相較於MHV1，WS混合律遵守統計力學中要求第二維禮係數與組成的二次關係，但是PR+WS+COSMOSAC的表現（壓力誤差6.79%，氣相成份誤差2.20%）卻不如PR+MHV1+COSMOSAC（壓力誤差4.00%，氣相成份誤差1.51%），而此非預期的缺失已由研究結果發現是源自WS混合律的假設。我們發現PR+WS+COSMOSAC的準確性可以經由兩種管道大幅的提升：其一，省略在COSMO-SAC模型中的Stavermann-Guggenheim combinatorial項，而此種模型註記為PR+WS+COSMOSACres，透過此種改良可將壓力誤差下降25%；其二，重新設定WS混合律中的參數值，此種模型則註記為PR+WS*+COSMOSAC，透過此種改良更可將壓力誤差下降33%。 總而言之，由本研究結果顯示，PR+MHV1+COSMOSAC、PR+WS+COSMOSACres，以及PR+WS*+COSMOSAC皆為可信賴的液氣相平衡之預測模型。

In this work we examined the prediction of vapor-liquid equilibria (VLE) of mixtures from the combined use of the Peng-Robinson equation of state (PR EOS) and the COSMO-SAC liquid activity coefficient model (LM). Based on the results of quantum mechanical calculations, it has been shown that the COSMO-SAC model is capable of predicting VLE of mixtures away from the critical point of any constituent component. With excess Gibbs free energy based mixing rules, such as the Wong-Sandler (WS) mixing rule and the modified Huron-Vidal (MHV1) mixing rule, we found that the combined model is capable of prediction the VLE of binary mixtures, including alkane and alkane, alkane and alcohol, alkane and ketone, alcohol and water, and other highly nonideal systems including aromatic compounds over a wide range of temperature (183.15K~623.15K) and pressure (0.1MPa~19MPa). Although the WS mixing rule ensures a correct quadratic composition dependence in the second virial coefficient, the performance of PR+WS+COSMOSAC [6.79% error in P and 2.20% error in y] is found to be inferior to that of PR+MHV1+COSMOSAC [4.00% error in P and 1.51% error in y]. The unexpected low accuracy with PR+WS+COSMOSAC model is found to be a result of the liquid model used and the assumptions made in the WS mixing rule. We found that the accuracy can be greatly improved either by neglecting Stavermann-Guggenheim combinatorial term in the COSMO-SAC model or by reparameterize the global parameters in WS mixing rule. The average error in the pressure from the latter approaches, denoted as PR+WS+COSMOSACres and PR+WS*+COSMOSAC, is lowered by more than 25% and 33% compared to that from the PR+WS+COSMOSAC. Our results show that all the above three methods: PR+WS+COSMOSACres, PR+WS*+COSMOSAC and PR+MHV1+COSMOSAC are all promising approaches for mixture VLE predictions over a large range of conditions.