A versatile thermodynamic consistency test for incomplete phase equilibrium data of high-pressure gas–liquid mixtures

Application of a Thermodynamic Consistency Test to Binary Mixtures Containing an Ionic Liquid

“…Once the model parameters are determined and the calculated solubilities are within acceptable limits of deviations, the Gibbs-Duhem equation is applied. The equations defining the consistency criteria for binary mixtures have been presented by Valderrama and Álvarez [13]. The development for binary mixtures containing ionic liquids has not been yet presented in the literature, and is summarized as follows.…”

“…The inclusion of vapor concentrations in the objective function allows low deviations in pressure and predicts true physical concentrations in the vapor phase [13]. Then the consistency of VLE data set is tested by the objective function, OF, (23) where N is the number of data points, P is the pressure, y fluid is the vapor mole fraction of the supercritical fluid for data point i, the superscripts "exp" and "cal" refers to the experimental and calculated values respectively, and A , P and y are the standard deviations of the measured quantities.…”

“…These intervals defined for consistency criteria are based on information presented in the literature related to the accuracy of experimental data for this type of mixtures (ionic liquids, solids and heavy alkanes dissolved in a high pressure gas) and on the criteria used by Valderrama and Álvarez [13]. In order to analyze the limits for consistency criteria, calculations of error propagation on the measured experimental data have been performed by using the general equation of error propagation [26], with the liquid phase mole fraction, the temperature and the interaction parameters as the independent measured variables.…”

“…Bertucco et al [12] proposed a consistency test applicable to isothermal, binary VLE data at moderate and high pressures, also for the entire concentration range in both phases. Valderrama and Álvarez [13] presented a new method to test the thermodynamic consistency of incomplete binary VLE data; that is, where PTxy data are not fully available for the entire concentration range, and for low liquid solute concentrations in the vapor phase (mole fractions < 10 -3 ). For these cases, the classic derivative or integral methods are not applicable.…”

“…In this work, an extension of the consistency test of Valderrama and Álvarez [13] is applied to four systems supercritical fluid + ionic liquid; this test is useful when the data do not cover the entire concentration range in liquid or gas phase, that is, where PTxy data are not fully available for the entire concentration range, and for low solute liquids concentrations in the vapor phase. So far, few attempts have been done to treat binary mixtures as presented in this work.…”