Phase equilibrium of liquid mixtures: Experimental and modeled data using statistical associating fluid theory for potential of variable range approach

Fundamental Equation of State for Fluid Tetrahydrofuran

An empirical fundamental equation of state in terms of the Helmholtz energy for tetrahydrofuran is presented. In the validity range from the triple-point temperature up to 550 K and pressures up to 600 MPa, the equation of state enables the calculation of all thermodynamic properties in the liquid, vapor, and super-critical regions including saturation states. Based on an extensive literature review, experimental data are represented within their experimental uncertainty. In the homogeneous liquid phase at atmospheric pressure, the uncertainty in density is 0.015 %, speed of sound is represented with an uncertainty of 0.03 %, and isobaric heat capacity has an uncertainty of 0.4 %. Isobaric heat capacities in the homogeneous vapor phase are described with an uncertainty of 0.2 %. Higher uncertainties occur above atmospheric pressure for all homogeneous properties. Depending on the temperature range, vapor pressure can be calculated with an uncertainty from 0.02 % to 3 %. The extrapolation behavior is evaluated, showing reasonable extrapolation behavior towards extreme conditions.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10765-023-03258-3.

Understanding the Phase Behavior of Tetrahydrofuran + Carbon Dioxide, + Methane, and + Water Binary Mixtures from the SAFT-VR Approach

The high-pressure phase diagrams of the tetrahydrofuran(1) + carbon dioxide(2), + methane(2), and + water(2) mixtures are examined using the SAFT-VR approach. Carbon dioxide molecule is modeled as two spherical segments tangentially bonded, water is modeled as a spherical segment with four associating sites to represent the hydrogen bonding, methane is represented as an isolated sphere, and tetrahydrofuran is represented as a chain of m tangentially bonded spherical segments. Dispersive interactions are modeled using the square-well intermolecular potential. In addition, two different molecular model mixtures are developed to take into account the subtle balance between water-tetrahydrofuran hydrogen-bonding interactions. The polar and quadrupolar interactions present in water, tetrahydrofuran, and carbon dioxide are treated in an effective way via square-well potentials of variable range. The optimized intermolecular parameters are taken from the works of Giner et al. (Fluid Phase Equil. 2007, 255, 200), Galindo and Blas (J. Phys. Chem. B 2002, 106, 4503), Patel et al. (Ind. Eng. Chem. Res. 2003, 42, 3809), and Clark et al. (Mol. Phys. 2006, 104, 3561) for tetrahydrofuran, carbon dioxide, methane, and water, respectively. The phase diagrams of the binary mixtures exhibit different types of phase behavior according to the classification of van Konynenburg and Scott, ranging from types I, III, and VI phase behavior for the tetrahydrofuran(1) + carbon dioxide(2), + methane(2), and + water(2) binary mixtures, respectively. This last type is characterized by the presence of a Bancroft point, positive azeotropy, and the so-called closed-loop curves that represent regions of liquid-liquid immiscibility in the phase diagram. The system exhibits lower critical solution temperatures (LCSTs), which denote the lower limit of immiscibility together with upper critical solution temperatures (UCSTs). This behavior is explained in terms of competition between the incompatibility with the alkyl parts of the tetrahydrofuran ring chain and the hydrogen bonding between water and the ether group. A minimum number of unlike interaction parameters are fitted to give the optimal representation of the most representative features of the binary phase diagrams. In the particular case of tetrahydrofuran(1) + water(2), two sets of intermolecular potential model parameters are proposed to describe accurately either the hypercritical point associated with the closed-loop liquid-liquid immiscibility region or the location of the mixture lower- and upper-critical end-points. The theory is not only able to predict the type of phase behavior of each mixture, but also provides a reasonably good description of the global phase behavior whenever experimental data are available.