結合 PC-SAFT 狀態方程式與 COSMO-SAC 模型於雙成份系統之汽液相平衡預測;Combining PC-SAFT Equation of State with COSMO-SAC Model foCombining PC-SAFT Equation of State with COSMO-SAC Model for Predicting Vapor Liquid Equilibrium in Binary Systemsr Predicting Vapor Liquid Equilibrium in Binary Systems

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Title:	結合 PC-SAFT 狀態方程式與 COSMO-SAC 模型於雙成份系統之汽液相平衡預測;Combining PC-SAFT Equation of State with COSMO-SAC Model foCombining PC-SAFT Equation of State with COSMO-SAC Model for Predicting Vapor Liquid Equilibrium in Binary Systemsr Predicting Vapor Liquid Equilibrium in Binary Systems
Authors:	陳宜汝;Chen, Yi-Ru
Contributors:	化學工程與材料工程學系
Keywords:	PC-SAFT狀態方程式;COSMO-SAC模型;雙成份氣液相平衡;二元交互作用參數;PC-SAFT equation of state;COSMO-SAC model;V LE in binary systems;binary interaction parameters
Date:	2024-07-25
Issue Date:	2024-10-09 15:24:40 (UTC+8)
Publisher:	國立中央大學
Abstract:	PC-SAFT狀態方程式被廣泛應用於純物質熱力學性質估算、藥物溶解度以及混合溶液相平衡的預測。在PC-SAFT狀態方程式中會根據物質的類型，需要不同數量的純物質參數來描述這些分子。對於非締合分子，需要三個參數來描述，即球體直徑(σ)、球體數量(m)以及長鏈分子之間的作用力參數(ϵ)。而對於締合分子，則需要增加兩個額外的參數來描述分子間的締合作用力，分別是締合體積(κAB)和締合作用力參數(ϵAB)，並且需要指定特定的締合模式來描述分子間的締合作用。在應用PC-SAFT狀態方程式於混合溶液相平衡的過程中，需透過二元交互作用參數k_ij來提高模型的準確度。這些k_ij參數通常是通過回歸混合溶液的相平衡實驗數據獲得的。在本研究中，我們嘗試應用COSMO-SAC模型來估算PC-SAFT狀態方程式所需的k_ij參數。具體而言，我們通過調整k_ij的數值，使得PC-SAFT狀態方程式在給定的系統條件下能夠提供與COSMO-SAC模型相匹配的excess Gibbs free energy (▁Gex)，從而求得所需的k_ij參數。我們期望通過這一方法，使得PC-SAFT狀態方程式在已知系統中物質的純物質參數與分子結構的前提下，能夠準確預測其流體相平衡行為，從而避免對混合流體實驗數據的依賴。本研究共探討了92種物質組成的273個雙成份混合流體系統的汽液相平衡，其中包括179個由非氫鍵締合分子構成的雙成份系統以及94個含有締合分子的雙成份系統。研究結果顯示，本研究所開發的方法在相平衡預測中表現出色，在非締合分子系統，壓力平均相對誤差(AARD-P: average absolute relative deviation in pressure)為4.13%，汽相組成平均絕對誤差(AAD-y: average absolute deviation in vapor phase mole fraction)為1.48%；而在含有締合分子的系統中，AARD-P和AAD-y分別為7.76%和3.44%。相比之下，PC-SAFT狀態方程式在不考慮k_ij參數的情況下進行相平衡預測時，在非締合分子系統的AARD-P為8.92%，AAD-y為3.27%；在含有締合分子的系統中，AARD-P為19.14%，AAD-y為5.03%。上述之結果顯示，在缺少實驗數據來迴歸求得PC-SAFT狀態方程式所需之k_ij參數時，本研究所提出的方法相對於PC-SAFT狀態方程式在沒有k_ij參數的條件下可以提供更準確和可靠的相平衡預測。本研究方法相較於純COSMO-SAC模型的優勢在於其能夠在高壓系統中進行準確預測，並且在混合系統中其中一個組成超過臨界點時，依然能提供相當精確的預測結果，而這正是COSMO-SAC模型的局限所在。另一方面是COSMO-SAC使用蒸氣壓實驗值去計算，但是本研究是透過純物質參數回歸的蒸氣壓去計算，這樣的優勢是能夠在缺乏蒸氣壓實驗數據的情況下，依然可以預測汽液相平衡的表現。此外，本方法能夠在高壓系統中的溫度範圍橫跨100 K的情況下，依然保持良好的預測精度，這在化學工程和工業應用中尤為重要，因為它能夠有效處理從低溫到高溫、從低壓到高壓的各種操作條件。為了驗證本研究方法所求得之k_ij參數的有效性，我們將本研究所得的k_ij參數與透過實驗數據優化的PC-SAFT模型之k_ij隨溫度變化的趨勢進行比較。 ;The PC-SAFT equation of state (EOS) is widely used for estimating the thermodynamic properties of pure substances, drug solubility, and predicting phase equilibrium in mixed solutions. In the PC-SAFT EOS, the number of pure substance parameters required to describe these molecules varies according to the type of substance. For non-associating molecules, three parameters are needed: the segment diameter (σ), the number of segments (m), and the interaction energy parameter between the chain molecules (ϵ). For associating molecules, two additional parameters are required to describe the intermolecular associating forces: the association volume (κAB) and the association energy parameter (ϵAB). Furthermore, a specific association scheme is necessary to describe the manner of molecular association. When applying the PC-SAFT EOS to phase equilibrium in mixed solutions, binary interaction parameters (k_ij) are used to enhance the model′s accuracy. These k_ij parameters are typically obtained by regressing phase equilibrium experimental data of mixed solutions. In this study, we attempt to estimate the k_ij parameters required for the PC-SAFT EOS using the COSMO-SAC model. Specifically, we adjust the k_ij values so that the PC-SAFT EOS can provide an excess Gibbs free energy (▁Gex) that matches the COSMO-SAC model under given system conditions, thereby obtaining the required k_ij parameters. We hope that this method will enable the PC-SAFT EOS to accurately predict fluid phase behavior in systems where the pure substance parameters and molecular structures are known, thereby avoiding reliance on experimental data for mixed fluids. In this study, we investigated the vapor-liquid equilibrium (VLE) of 273 binary mixture systems composed of 92 substances, including 179 systems consisting of non-associating molecules and 94 systems containing associating molecules. The results show that the method developed in this study performs excellently in VLE prediction. For non-associating molecule systems, the average absolute relative deviation in pressure (AARD-P) is 4.13%, and the average absolute deviation in vapor phase mole fraction (AAD-y) is 1.48%. For systems containing associating molecules, the AARD-P and AAD-y are 7.76% and 3.44%, respectively. In contrast, when the PC-SAFT EOS predicts phase equilibrium without considering k_ij parameters, the AARD-P and AAD-y are 8.92% and 3.27% for non-associating molecule systems and 19.14% and 5.03% for systems containing associating molecules, respectively. The above results indicate that in the absence of experimental data to regress and obtain the necessary k_ij parameters for the PC-SAFT EOS, the method proposed in this study can provide more accurate and reliable phase equilibrium predictions compared to the PC-SAFT EOS without k_ij parameters. The advantage of the proposed method compared to COSMO-SAC lies in its ability to accurately predict VLE under high-pressure conditions, especially when system conditions exceed the critical point of one component in the mixture. On the other hand, COSMO-SAC model requires experimental vapor pressure values for VLE calculations, whereas the PC-SAFT can estimate vapor pressures of pure substances with known pure substance parameters. This advantage allows for VLE prediction even in the absence of experimental vapor pressure data. Furthermore, the proposed method maintains high predictive accuracy across a temperature range of 100 K in high-pressure systems. This capability is particularly important in chemical engineering and industrial applications, as it effectively handles various operating conditions from low to high temperatures and pressures. To verify the effectiveness of the k_ij parameters obtained by the proposed method, we compared the k_ij parameters obtained from this work with those optimized through experimental VLE data to confirm the consistent temperature-dependence of k_ij parameters from these two methods.
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