開發全域重整化群理論以預測混合物在臨界區域之熱力學性質與相行為

Abstract

在液-液分離的臨界點附近，準確預測相行為一直是熱力學中的一大挑戰。特別是化學工程常用的局部組成模型，普遍無法正確描述混合物在臨界區域的相平衡行為，限制了這些模型在液-液萃取程序設計中的應用。為了提升模型在臨界區域的預測準確度，本研究將全域重整化群理論（Global Renormalization Group Theory, GRGT）結合至局部組成模型中，並提出一種新方法來決定原需依賴臨界區域之實驗數據的參數，使此理論具備預測能力。此外，本研究進一步強化 GRGT 的理論基礎，納入不對稱組成波動的影響，提升對臨界現象的描述能力。 本研究分為三個部分。首先，開發一套名為 GRGT2 的參數決定方法，並將其應用於 Margules、NRTL、Wilson 與 COSMO-SAC 等四種局部組成模型，在立方晶格系統上評估其預測能力。結果顯示，GRGT2 有效提升臨界溫度的預測準確性，其中 COSMO-SAC 模型的誤差降低約 20%，其餘模型約降低 6–10%；同時，該方法亦可不依賴實驗或模擬數據，即可重現正確的臨界指數。第二部分將 GRGT2 應用於 21 組真實的二元混合物資料。結果顯示，NRTL+GRGT2 方法在不使用臨界區資料進行參數擬合的情況下，可將上臨界溶解溫度（UCST）預測誤差降低 48%，但下臨界溶解溫度（LCST）預測誤差則略為增加約 20%。 最後，本研究提出一套進階版本的 GRGT，稱為 GRGT-SAF（Symmetric and Asymmetric Fluctuations），能同時考慮對稱與不對稱的組成波動。在立方晶格模型的測試中，GRGT-SAF 對 COSMO-SAC 模型的臨界溫度預測誤差降低約 40%，並更準確地重現比熱與組成波動在臨界點附近的發散行為。此外，GRGT-SAF 可滿足如 Rushbrooke 恆等式等關鍵熱力學一致性關係，確保模型對臨界指數間的相依性具備熱力學合理性。 綜合而言，本研究建立了一套具預測能力且具有物理一致性的理論架構，適用於晶格模型與真實混合物的臨界現象模擬。此方法亦為未來推廣至更複雜、多組分系統的 GRGT 模型提供了基礎，具有應用於化工與程序設計的潛力。

Classical local composition models widely used in chemical engineering often fail to describe phase equilibrium near criticality, which limits their applicability in designing liquid-liquid extraction processes. To improve predictive accuracy in this region, this study combines Global Renormalization Group Theory (GRGT) with local composition models and proposes a new method to determine the two GRGT parameters that previously relied on experimental data near the critical point. This enhancement enables a predictive, data-independent approach. Furthermore, the theoretical framework of GRGT is extended to account for asymmetric composition fluctuations, increasing the model’s capability to capture critical phenomena. This dissertation is structured in three parts. First, a parameter estimation method called GRGT2 is developed and applied to four classical local composition models: Margules, NRTL, Wilson, and COSMO-SAC on a cubic lattice system. Results show that GRGT2 significantly improves critical temperature predictions, reducing the error by approximately 20% for COSMO-SAC and by 6–10% for the other models. In addition, GRGT2 accurately reproduces critical exponents without requiring empirical fitting. In the second part, GRGT2 is applied to 21 real binary mixtures. The NRTL+GRGT2 model, without using near-critical experimental data, reduces the prediction error of the upper critical solution temperature (UCST) by 48%, although the error for the lower critical solution temperature (LCST) increases by approximately 20%. Finally, this work introduces an extended GRGT framework called GRGT-SAF (Symmetric and Asymmetric Fluctuations), which incorporates both symmetric and asymmetric composition fluctuations. In cubic lattice tests, GRGT-SAF reduces critical temperature prediction error by about 40% for the COSMO-SAC model and more accurately captures the divergence of heat capacity and composition fluctuations near the critical point. Notably, GRGT-SAF satisfies important thermodynamic consistency relations, such as the Rushbrooke’s identity, ensuring that the interdependence between critical exponents adheres to the principles of equilibrium thermodynamics. In summary, this dissertation establishes a predictive and thermodynamically consistent modeling framework for simulating critical phenomena in both model systems and real liquid mixtures. The proposed methods lay a foundation for future extensions of GRGT to more complex and multicomponent systems, offering potential applications in chemical and process engineering.