以配位數模型建構新的流體狀態方程式

Abstract

化工程序中相平衡研究是相當重要的一環，對於各種化工單元操作程序設計都有舉足輕重的影響。一般說來，相平衡的計算著重在逸壓(fugacity)的計算，呈現相平衡的系統在每個相的逸壓都應該相等。常用的熱力學模型用以計算出逸壓的值，如氣體方程式(equation of state)或過量吉布式能液體模型(Gex model)。 現在常用的熱力學模型各有優缺點，如氣體方程式在各種條件下皆能有不錯的準確度，但是當進入混合系統的時候，常常因為不準確的混合律(mixing rule)加入而使的準確度大幅下降；同時常用的液體模型針對設計的系統有不錯的準確度，但卻沒有一種液體模型能夠在各種條件下都適用，如Walas研究指出NRTL model針對液相有機水溶液的準確度才比較好，而Wilson model則比較針對醇類、酚類等。這些缺點導致以上的各種模型在相平衡「預測」上，較不具有優勢，而趨向於需要實驗數據的幫助。 我們的研究從統計熱力學理論出發，透過對配位數(Coordination number)的研究來了解現有熱力學模型的差異，進而推導出理論上較正確的模型已達到「預測」熱力學平衡的目的。在本研究中，我們推導出了常用的氣體方程式和液體模型的配位數模型並且歸納出這些模型應該具有的特性。一個正確的熱力學模型，其配位數應滿足(1) 在無限壓力下總配位數為一常數(2)分子對守恆，從一對分子對中任何一種分子透過配位數計算所得的分子對總數應該總是相等。一般液體模型通常不能滿足第二個條件。我們進而根據這些特性發展出一套推導理論上較「正確」的熱力學模型的方法。

In this work we study the local composition models in existing thermodynamic models and then propose a general way for developing liquid activity coefficient models or equation of state. We found that to develop an activity coefficient model, there are at least two physical concepts needed to be satisfied: (1) the total number of molecules near one certain molecule has to be a constant at any temperature or mixture composition, and (2) the number of molecular pairs should be conserved, that is, the total number of molecule A -B pairs calculated from the local composition of A around B should be the same as that from B around A. We have derived local compositions of most commonly used liquid activity coefficient models, which is only satisfied the concept (1) but concept (2). Therefore, we propose a new local composition model to make sure the concept (2) satisfied and then we solve the temperature and composition dependency from the concept (1), resulting in a new class of excess Gibbs free energy models. Models developed based on this approach are theoretically correct and can be validated using simulation results. Furthermore, the lattice gas theory is applied in this model to develop a new kind of equation of state by adding an imaginary material which represents void sites to the system.