熱力學模型的優勢在於能預測物質的行為，從而節省時間及經濟成本，並降低處理有毒或具爆炸性物質可能潛在的風險。PC-SAFT是以統計力學理論為基礎推導而出的狀態方程式，相較於立方型狀態方程，PC-SAFT在複雜流體與高分子系統之純物質計算與相平衡預測方面有更好的準確性。對於不具有分子間缔合作用之物質，其特徵可由三個參數描述：球體直徑(σ)、球體數量(m)以及分子間分散能量參數(ε)。而對於具有缔合作用之分子，則需多加引入兩項參數：缔合體積(κAB)與缔合能量(εAB)。 過去使用PC-SAFT預測溶液相平衡時，需藉由回歸實驗數據而得到二元交互作用參數kij來修正混合物分散能量參數εij，以提升模型的準確性。過去本研究團隊開發了一種結合PC-SAFT與COSMO-SAC的方法，透過調整PC-SAFT二元交互參數，在給定參考壓力下使PC-SAFT與COSMO-SAC所得之過量吉布斯自由能(Gex)相等，即可在無需實驗數據下求得kij。此方法預測流體相平衡雖然有不錯的結果，但參考壓力的選定，是經由我們從大量二元混合物系統的計算經驗，給出一個建議的參考壓力值，才能使此方法在預測多數二元相平衡系統能有較高的準確性。 近年來，有研究團隊開發全新的方法結合PC-SAFT與COSMO-SAC，其核心概念在於假定無窮壓力條件下堆積因子(packing fraction)為1，並在此條件下使PC-SAFT與COSMO-SAC之過量吉布斯自由能相等，從而預測εij。此方法相較於我們之前的研究方法，能在更具有理論基礎的公式下推導求得εij，然而其所呈現的預測系統數較少，且結果有非常大的改善空間，尤其是交叉缔合作用系統（cross-associating systems），我們認為問題在於無窮壓力條件下之堆積因子不該為1，亦即在無窮壓力下分子不會堆積得毫無空隙，因此本研究主題旨在探討無窮壓力下堆積因子對流體相平衡預測準確度之影響。此外，針對交叉缔合作用系統預測準確性不足的問題，亦提出改善方法。 本研究涵蓋更大量且更多樣之二元混合物汽液相平衡系統，使模型預測具有高度統計代表性，並能充分驗證其對於不同類型分子交互作用下之穩定性與預測能力。在不含氫鍵之系統，壓力平均相對誤差(AARD-P)為4.47%，汽相組成平均絕對誤差(AAD-y)為 1.64%；而在含有氫鍵分子的系統中，AARD-P和AAD-y分別為5.70%和2.32%。相較之下，PC-SAFT在不考慮kij參數的情況下預測相平衡時，在不含氫鍵分子系統的AARD-P為8.97%，AAD-y為3.27%；在含有氫鍵分子的系統中，AARD-P為12.45%，AAD-y為3.95%。從計算結果可知，在缺少實驗數據無法迴歸求得PC-SAFT所需之kij參數時，此次研究提出的方法，相較於PC-SAFT在沒有kij的條件下，能更準確的預測相平衡。而相較於純COSMO-SAC模型，此方法的優勢在於能在高壓系統中準確預測相平衡，而這正是活性係數模型的局限，此方法能夠在高壓系統中維持良好的預測準確性，對於化學工程與工業應用特別重要，因為這代表其能用於預測各種溫壓下的相平衡，即使在嚴苛的操作條件仍能適用。;Thermodynamic models offer the advantage of predicting the behavior of substances， thereby reducing the time and economic costs associated with experiments while minimizing the potential risks involved in handling toxic or explosive materials. PC-SAFT is an equation of state derived based on statistical mechanics. Compared with cubic equations of state， PC-SAFT generally provides better accuracy in pure-component property calculations and phase equilibrium predictions for complex fluids and polymer systems. For non-associating substances， their characteristics can be described by three parameters: segment diameter (σ)， segment number (m)， and dispersion energy parameter (ε). In contrast， for associating molecules， two additional parameters must be introduced: association volume (κAB) and association energy (εAB). In previous studies， the prediction of phase equilibria using PC-SAFT required the regression of experimental data to determine the binary interaction parameter， kij， which was used to correct the mixture dispersion energy parameter， εij， thereby improving the accuracy of the model. Previously， our research group developed a method combining PC-SAFT and COSMO-SAC， in which the binary interaction parameter in PC-SAFT was adjusted such that the excess Gibbs free energy (Gex) calculated by PC-SAFT was equal to that obtained from COSMO-SAC at a given reference pressure. Through this approach， kij could be determined without relying on experimental data. Although this method showed promising performance in predicting fluid phase equilibria， the selection of the reference pressure was based primarily on our computational experience from a large number of binary mixture systems. A recommended reference pressure was therefore proposed to achieve satisfactory accuracy for the prediction of most binary phase equilibrium systems. In recent years， a research group developed a novel approach combining PC-SAFT and COSMO-SAC. The core concept of this method is based on assuming that the packing fraction under infinite-pressure conditions is equal to unity. Under this assumption， the excess Gibbs free energies predicted by PC-SAFT and COSMO-SAC are constrained to be equal， allowing the prediction of εij. Compared with our previous approach， this method provides a more theoretically grounded formulation for deriving εij. However， the number of systems presented in their study was limited， and the predictive results were not entirely satisfactory， particularly for cross-associating systems. We consider that this issue arises from the assumption that the packing fraction under infinite-pressure conditions is equal to 1. In other words， molecules are unlikely to pack without any free volume even under infinite-pressure conditions. Therefore， the objective of this study is to investigate the influence of the packing fraction under infinite-pressure assumptions on the accuracy of fluid phase equilibrium predictions. This study covers a larger and more diverse set of binary VLE systems， providing greater statistical representativeness for model evaluation and enabling a comprehensive assessment of its robustness and predictive capability for different types of molecular interactions. For systems without hydrogen-bonding molecules， the average absolute relative deviation in pressure (AARD-P) and the average absolute deviation in vapor-phase composition (AAD-y) are 4.47% and 1.64%， respectively. For systems containing hydrogen-bonding molecules， the corresponding AARD-P and AAD-y values are 5.70% and 2.32%， respectively. In comparison， when PC-SAFT is used without the binary interaction parameter kij， the AARD-P and AAD-y values are 8.97% and 3.27%， respectively， for systems without hydrogen-bonding molecules， while the corresponding values for systems containing hydrogen-bonding molecules are 12.45% and 3.95%， respectively. These results demonstrate that， when experimental data are unavailable for regressing the kij parameters required by PC-SAFT， the proposed method provides more accurate VLE predictions than PC-SAFT without kij. Compared with the COSMO-SAC model， the advantage of the proposed method is its ability to maintain good predictive accuracy for VLE in high-pressure systems， where activity-coefficient-based models have inherent limitations. The proposed method therefore provides a more reliable framework for predicting phase equilibria over a wide range of temperature and pressure conditions. This capability is particularly important for chemical engineering and industrial applications， as it allows phase equilibrium behavior to be predicted under various operating conditions， including relatively severe conditions where conventional activity-coefficient models may have limited applicability.
