Pressure phase equilibria

Vapor-phase fugacity coefficients are needed not only in high-pressure phase equilibria, but are also of interest in high-pressure chemical equilibria (D6, K7, S4). The equilibrium yield of a chemical reaction can sometimes be strongly influenced by vapor-phase nonideality, especially if reactants and products have small concentrations due to the presence in excess of a suitably chosen nonreactive gaseous solvent (S4). 

Chueh s method for calculating partial molar volumes is readily generalized to liquid mixtures containing more than two components. Required parameters are and flb (see Table II), the acentric factor, the critical temperature and critical pressure for each component, and a characteristic binary constant ktj (see Table I) for each possible unlike pair in the mixture. At present, this method is restricted to saturated liquid solutions for very precise work in high-pressure thermodynamics, it is also necessary to know how partial molar volumes vary with pressure at constant temperature and composition. An extension of Chueh s treatment may eventually provide estimates of partial compressibilities, but in view of the many uncertainties in our present knowledge of high-pressure phase equilibria, such an extension is not likely to be of major importance for some time. 

With a suitable equation of state, all the fugacities in each phase can be found from Eq. (6), and the equation of state itself is substituted into the equilibrium relations Eq. (67) and (68). For an A-component system, it is then necessary to solve simultaneously N + 2 equations of equilibrium. While this is a formidable calculation even for small values of N, modern computers have made such calculations a realistic possibility. The major difficulty of this procedure lies not in computational problems, but in our inability to write for mixtures a single equation of state which remains accurate over a density range that includes the liquid phase. As a result, phase-equilibrium calculations based exclusively on equations of state do not appear promising for high-pressure phase equilibria, except perhaps for certain restricted mixtures consisting of chemically similar components. 

The purpose of phase equilibria calculations is to predict the thermodynamic properties of mixtures, avoiding direct experimental determinations, or to extrapolate the existing data to different temperatures and pressures. The basic requirements for performing any thermodynamic calculation are the choice of the appropriate thermodynamic model and knowledge of the parameters required by the model. In the case of high pressure phase equilibria, the thermodynamic model used is generally an equation of state which is able to describe the properties of both phases. 

M.L. Japas and E.U. Franck, High Pressure Phase Equilibria and PVT-Data of the Water-oxygen System including Water-air to 673 K. and 25.0 MPa, Ber. Bunsenves. Phys. Chem., 89, (1985), 1268. 

Daneshvar M, Kim S, Gulari E (1990) High-pressure phase equilibria of polyethylene glycol-carbon dioxide systems. J Phys Chem 94(5) 2124—2128... 

Gourgouillon D, Nunes da Ponte M (1999) High pressure phase equilibria for poly(ethylene glycol) s + C02 experimental results and modelling. Phys Chem Chem Phys l(23) 5369-5375... 

Wiesmet V, Weidner E, Behme S et al (2000) Measurement and modelling of high-pressure phase equilibria in the systems polyethylene glycol (PEG)-propane, PEG-nitrogen and PEG-carbon dioxide. J Supercrit Fluids 17(1) 1-12... 

High-Pressure Phase Equilibria in Ternary Fluid Mixtures with a Supercritical Component... 

Experimental results are presented for high pressure phase equilibria in the binary systems carbon dioxide - acetone and carbon dioxide - ethanol and the ternary system carbon dioxide - acetone - water at 313 and 333 K and pressures between 20 and 150 bar. A high pressure optical cell with external recirculation and sampling of all phases was used for the experimental measurements. The ternary system exhibits an extensive three-phase equilibrium region with an upper and lower critical solution pressure at both temperatures. A modified cubic equation of a state with a non-quadratic mixing rule was successfully used to model the experimental data. The phase equilibrium behavior of the system is favorable for extraction of acetone from dilute aqueous solutions using supercritical carbon dioxide. 

PANAGIOTOPOULOS AND REID High-Pressure Phase Equilibria... 

Clark S.P.Jr. (1966) High-pressure phase equilibria. In Handbook of Physical Constants (ed. S.P. Clark, Jr.), pp. 345-370. Geol. Soc. America Memoir 97. 

The present paper gives an overview of results on high-pressure phase equilibria in the ternary system carbon dioxide-water-1-propanol, which has been investigated at temperatures between 288 and 333 K and pressures up to 16 MPa. Furthermore, pressure-temperature data on critical lines, which bound the region where multiphase equilibria are oberserved were taken. This study continues the series of previous investigations on ternary systems with the polar solvents acetone [2], isopropanol [3] and propionic add [4], A classification of the different types of phase behaviour and thermodynamic methods to model the complex phase behaviour with cubic equations of state are discussed. 

Shibata, S.K. and Sandler, S I. Critical Evaluation of Equation of State Mixing Rules for the Prediction of High-Pressure Phase Equilibria, Ind. Eng. Chem. Res. Vol 28, 1989, pp. 1893-1898. 

There are many alternatives for modeling high pressure phase equilibria. Therefore, it is required a discrimination procedure capable to screen these models satisfactorily. In this work we have compared two discrimination methods in order to select the next experimental point. The first one is the Hunter-Reiner methodology that considers only the predicted response of each model according to the following equations ... 

Predictive Quasilattice Equation of State for Unified High Pressure Phase Equilibria of Pure Fluids and Mixtures... 

High-Pressure Phase Equilibria Data of Systems Containing Limonene, Linalool and Supercritical Carbon Dioxide... 

Calculation of High-Pressure Phase Equilibria Involving Light Gases... 

Figure 3. High-pressure phase equilibria of the (H2 + CO) system.

D Souza, R., J.R. Patrick, and A.S. Teja. 1988. High pressure phase equilibria in the carbon dioxide - n-hexadecane and carbon dioxide - water systems. Can. J. Chem. Eng. 66 319-323. 

Elthon D. and Scarfe C. M. (1984) High-pressure phase equilibria of a high-magnesia basalt and the genesis of primary oceanic basalts. Am. Mineral. 69, 1-15. 

Ohtaka O, Yaman a T, Kume S, Ito E, Navrotsky A (1991) Stability of monoclinic and orthorhombic zirconia studies by high-pressure phase equilibria and calorimetry. J Am Ceram Soc 74 505-509... 

Shibata, S. K., and Sandler, S. L, 1989. Critical evaluation of equation of state mixing rules for the prediction of high pressure phase equilibria. Ind. Eng. Chem. Res., 28 1893-1898. 

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