Application of the truncated perturbed chain-polar statistical associating fluid theory (tPC-PSAFT) to alcohol/alkane mixtures at high pressures.

Abstract

Constitutive equations, such as equations of state (EoS) characterize mathematical relationships between state functions under set physical conditions and are imperative for the accurate design of chemical processes (Devilliers, 2011; Al-Malah, 2015). Most models, however, fail to accurately predict thermophysical properties of complex mixtures such as those exhibiting molecular association and hydrogen bonding. The Statistical Associating Fluid Theory (SAFT), based on thermodynamic perturbation theory, explicitly accounts for molecular association, hence, providing a more suitable prediction of thermophysical properties (Devilliers, 2011). This work investigates the performance of the truncated Perturbed Chain-Polar Statistical Associating Fluid Theory (tPC-PSAFT) model in accurately accounting for the effect of molecular association on compressed liquid density in liquid alkane-alcohol mixtures at elevated pressures. This was achieved by comparing the density predictions calculated by the tPC-PSAFT model to novel experimental density data. Isothermal measurements were conducted utilizing an Anton Paar DMA HP densimeter with a upplier stated uncertainty ranging between 0.1 and 1 kg.m-3. Measurements were conducted in the temperature and pressure ranges of 313.15 to 353.15 K and 0.1 to 20 MPa, respectively, over the entire composition range. Furthermore, a test system consisting of ethanol (1) + n-heptane (2) was used to confirm the reliability of the experimental setup and procedure. The density data obtained for the test system was compared to literature and demonstrate excellent correlation of the data, with a maximum relative difference of 0.0005, confirming the reliability of the procedure utilized in this study. The density data of six novel binary systems namely, butan-1-ol/butan-2-ol/2-methylpropan-1-ol (1) + n-octane/n-decane (2) are presented in this work. The maximum expanded combined uncertainties for pressure, temperature, composition and density were 0.032 MPa, 0.02 K, 0.0002 mole fraction, and between 1.10 to 1.12 kg.m-3, respectively. Density data obtained experimentally for all six binary systems comply with the general trend regarding temperature and pressure in that the density of the liquid mixtures decreased with an increase in temperature and increase with an increase in pressure. Furthermore, derived thermodynamic properties namely, the excess molar volume, thermal expansivity and isothermal compressibility were computed for each of the binary systems. Large positive deviations from ideality were noted for the excess volumes for all systems. This is attributed to the different shapes and sizes of the molecules as well as the attractive mixture interactions when compared to those of the individual pure components. In addition, the thermal expansivity and isothermal compressibility demonstrate highly non-linear behaviour which is indicative of systems comprising complex mixtures. The experimental data were compared to correlations/predictions resulting from five models namely, the Modified Toscani-Szwarc (MTS) equation of state (EoS), the Benedict-Webb-Rubin-Starling (BWRS) EoS, Peng-Robinson (PR) EoS, Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT) model and the truncated Perturbed Chain-Polar Statistical Associating Fluid Theory (tPC-PSAFT) model. Both the MTS and BWRS EoS demonstrated excellent correlation of the data for all six of the binary systems attributed to the empirical nature of the model and the significant number of fitting parameters employed. The maximum root mean square deviation (RMSD) was found in the butan-2-ol (1) + n-octane (2) binary system at RMSD = 4.72 x 10-4. In addition, improvements in model performance were noted for the BWRS EoS at higher temperatures and pressures. The PR EoS demonstrated poor correlation of the density data of the mixtures (exceeding RMSD = 0.024), attributed to the poor prediction of the pure component data by the model and the use of a single binary interaction fitting parameter in the cases of the mixtures. Density predictions from the PC-SAFT model demonstrated significant deviation from experimental data (exceeding RMSD = 0.011) in that the PC-SAFT model underpredicts densities for the binary systems. Furthermore, a progressive deterioration in the model’s performance was noted as the respective alcohol concentration increases. Accurate prediction of the density was however noted for the 2-methylpropan-1-ol binary systems in the alcohol dilute region. In addition, some improvement in model performance was observed at higher pressures and temperatures for the butan-2-ol and 2-methylpropan-1-ol binary systems. The tPC-PSAFT model demonstrated improvement in accurately predicting the density data, for all six systems, when compared to those obtained via the PC-SAFT model, with an improvement in excess of 72% in some cases. In addition, the model performs well in the alcohol dilute region and at high pressures and temperatures. However, a progressive deterioration in the model’s performance is noted as the concentration of the alcohol in solution is increased. This was unexpected as both the PC-SAFT and tPC-PSAFT models explicitly account for molecular association and were theorized to perform well in predicting the alcohol mixture behaviour. The model’s poor performance can be attributed to the lack of high precision pure component parameters currently available in the literature that do not effectively characterize the density of the systems under high pressure. All five models exhibit similar trends to that of the experimental data despite their individual merits and shortcomings.