利用第一原理計算預測純物質與混合物之熱力學性質與相平衡

First-Principles Predictions of Thermodynamic Properties and Phase Equilibria for Pure and Mixture Fluids

謝介銘(Chieh-Ming Hsieh)

指導教授 ： 林祥泰

國立臺灣大學/工學院/化學工程學研究所/博士(2010年)

https://doi.org/10.6342/NTU.2010.03308

摘要

本研究主要透過結合量子力學原理溶合自由能計算以及Peng-Robinson狀態方程式，預測純物質與混合流體之相行為。以往使用Peng-Robinson狀態方程式描述純流體性質時，必須先有該流體的臨界性質及離心因子，以計算分子間吸引力參數a(T)及分子體積b參數。對於混合流體，則還需要搭配混合律及使用適當的二元相互作用參數，才能得到較佳的相行為描述。對實驗數據的依賴大幅地限制了此類狀態方程式的應用範圍。在本研究中，我們透過統計力學理論的推導，建立溶合自由能計算中吸引力與狀態方程式中的能量參數a(T,x)間的關係，並以溶合計算中使用的分子體積與流體組成來估算狀態方程式中的體積參數b(x)。此方法結合Peng-Robinson狀態方程式與以溶合理論為基礎的COSMO-SAC模型(在本研究中稱為PR+COSMOSAC)，不需要任何與物質有關的參數或不同物質間的二元相互作用參數，即可用來預測純物質的蒸氣壓、液相密度與臨界性質，更能應用在預測混合流體的液-氣、液-液與氣-液-液相平衡。此方法應用在預測1296個純物質的臨界壓力、臨界溫度、臨界體積、蒸氣壓(常壓沸點下)、液體密度(常壓沸點下)的平均相對誤差分別為10%、4%、5%、49%與21%。此方法應用在預測混合流體的氣-液相平衡上，針對230個系統得到的系統總壓與氣相組成誤差分別為28%與5%。當系統中所有物質的實驗值(蒸氣壓或臨界性質與離心因子)可取得並用於溶合自由能計算中，此誤差可大幅減少至6%與2%。此方法應用在預測混合流體的液-液相平衡上，針對68個雙成分與39個三成分系統得到的液相組成的方均根誤差分別為0.0689 (80%) 與0.0775 (72%)。此方法對於混合流體之液-液與氣-液-液相行為的預測上，可與官能基貢獻法中最為廣泛應用的Modified UNIFAC得到相同的精確度。此方法應用於預測藥物在純溶劑與混合溶劑中的溶解度上，針對52種藥物於37種純溶劑與156種混合溶劑得到的方均根誤差分別為1.78 (495%) 與1.40 (304%)，此預測結果優於COSMO-SAC模型。當藥物在純溶劑中溶解度的實驗值可取得時，藥物於混合溶劑中溶解度的方均根誤差可大幅減少至0.65 (91%)。由於此方法沒有缺少官能基定義或是參數的問題，因此可應用於新製程的研發，特別是在缺少實驗值或二元相互作用參數的情況下，現有其他方法皆無法使用。

關鍵字

Peng-Robinson狀態方程式 ； COSMO-SAC模型 ； 溶合自由能 ； 相平衡預測 ； 第一原理計算

並列摘要

In this study, a novel approach combining quantum mechanical solvation free energy calculations and Peng-Robinson equations of state (PR EOS) is proposed for the prediction of phase equilibria of both pure and mixture fluids. For pure substances the critical properties and acentric factor must be used to determine the energy a(T) and volume b parameters. An appropriate mixing rule and often the binary interaction parameters are necessary in order to have a better description of the phase behavior for mixtures. The application of PR EOS is therefore limited by the need of input of experimental data. In this study, we found that the temperature and composition dependence of the energy parameter a(T,x) in the EOS can be derived from the attractive contribution of the solvation free energy. The volume parameter b(x) is estimated to be the mole-fraction weighted average of the molecular solvation cavity. Combined with first-principle solvation calculations, both parameters a(T,x) and b(x) can be obtained without the use of any experimental data (e.g., critical properties or acentric factor) and binary interaction parameters. The Peng-Robinson EOS combined with a solvation model based on COSMO-SAC calculation, denoted as PR+COSMOSAC, contains neither species dependent parameter nor binary interaction parameters, and can be used to predict vapor pressure, liquid density, and critical properties of pure substances, and vapor-liquid equilibrium (VLE), liquid-liquid equilibrium (LLE), and vapor-liquid-liquid equilibrium (VLLE) of mixtures. It is found that the overall relative average error from PR+COSMOSAC is 49% in vapor pressure, 21% in liquid density at normal boiling point, 10% in critical pressure, 4% in critical temperature, and 5% in critical volume for 1296 pure substances; and 28% in total pressure, and 5% in vapor phase composition for 230 binary mixtures in vapor-liquid equilibrium. The errors in binary VLE predictions can be reduced significantly down to 6% and 2% if experimental data (vapor pressures or critical properties and acentric factor) are used to correct for any error in the calculated charging free energy of pure species. The overall root-mean-square errors in the mutual solubility of 68 binary and 39 ternary mixtures predicted from PR+COSMOSAC are 0.0689 (80%) and 0.0775 (72%), respectively. This method provides the prediction of LLE and VLLE with accuracy similar to that from the widely used group contribution method, the modified UNIFAC model. The overall RMS errors of PR+COSMOSAC in drug solubility prediction of 52 drugs in 37 pure solvents and 156 mixture solvents are 1.78 (495%) and 1.40 (304%), respectively. This accuracy is better than that from COSMO-SAC model. The overall RMS of drug solubility prediction in mixture solvents can be greatly reduced to 0.65 (91%) when the experimental solubility of the drug in the relevant pure solvent is available. Since there is no issue of missing parameters or group definitions, this model is particular useful for the design of new processes involving chemicals whose interaction parameters are not available due to the lack of experimental data.

並列關鍵字

Peng-Robinson equation of state ； COSMO-SAC ； solvation free energy ； phase equilibrium ； prediction ； first-principles calculation

參考文獻

[146] Yaws, C.; Yang, H. C.; Xiang, P., Henry's law constants for organic 362 compounds in water. Chemical Engineering 1991, 98, (11), 179-185.

[107] Mullins, E.; Oldland, R.; Liu, Y. A.; Wang, S.; Sandler, S. I.; Chen, C. C.; Zwolak, M.; Seavey, K. C., Sigma-profile database for using COSMO-based thermodynamic methods. Industrial & Engineering Chemistry Research 2006, 45, (12), 4389-4415.

[81] Lin, S. T.; Hsieh, C. M.; Lee, M. T., Solvation and chemical engineering thermodynamics. Journal of the Chinese Institute of Chemical Engineers 2007, 38, (5-6), 467-476.

[142] Hait, M. J.; Liotta, C. L.; Eckert, C. A.; Bergmann, D. L.; Karachewski, A. M.; Dallas, A. J.; Eikens, D. I.; Li, J. J. J.; Carr, P. W.; Poe, R. B.; Rutan, S. C., Space predictor for infinite dilution activity-coefficients. Industrial & Engineering Chemistry Research 1993, 32, (11), 2905-2914.

[1] Cadoret, L.; Yu, C. C.; Huang, H. P.; Lee, M. J., Effects of physical properties estimation on process design: a case study using AspenPlus. Asia-Pacific Journal of Chemical Engineering 2009, 4, (5), 729-734.