Phase equilibria supercritical vapor-liquid

Various modeling procedures have been proposed in the literature to predict the phase behavior of vapor-liquid systems at high pressures. (The designation vapor will be used synonomously with supercritical fluid in this chapter.) Regardless of the modeling procedure, the following thermodynamic relationships, or their equivalent relationships in terms of chemical potentials, must be satisfied for two phases to be in equilibrium. 

In these systems, the interface between two phases is located at the high-throughput membrane porous matrix level. Physicochemical, structural and geometrical properties of porous meso- and microporous membranes are exploited to facilitate mass transfer between two contacting immiscible phases, e.g., gas-liquid, vapor-liquid, liquid-liquid, liquid-supercritical fluid, etc., without dispersing one phase in the other (except for membrane emulsification, where two phases are contacted and then dispersed drop by drop one into another under precise controlled conditions). Separation depends primarily on phase equilibrium. Membrane-based absorbers and strippers, extractors and back extractors, supported gas membrane-based processes and osmotic distillation are examples of such processes that have already been in some cases commercialized. Membrane distillation, membrane... 

For gases, such as methane, which are supercritical at hydrate forming temperatures, there is one quadruple point, as indicated by point Q1 in Fig. 1. At this point, ice, liquid water, gas and hydrate are in equilibrium. For gases that are subcritical at hydrate forming temperatures, such as ethane, ° there are two quadruple points (Q1 and Q2 in Fig. 2). While Q1 lies at approximately the freezing point of water, Q2 is at approximately the intersection of the hydrate-water-gas three-phase equilibrium curve with the vapor pressure curve. At this latter point, liquid water, gas, hydrate, and liquid hydrate former are all in equilibrium. As seen in Fig. 2, the hydrate... 

In absorbers or strippers, components are transferred from the vapor phase to the liquid phase or vice versa. In liquid-liquid extraction, components are transferred from one liquid phase to the other. In supercritical extraction, components (the solute) are transferred from the liquid phase to the supercritical phase (the solvent) at equilibrium with the liquid. 

Consider first the schematic P-T and P-x diagrams for the naphthalene-ethylene system. Figure 3.18b depicts the solubility behavior of naphthalene in supercritical ethylene at a temperature greater than the UCEP temperature. Solid-gas equilibria exist at low pressures until the three-phase SLV line is intersected. The equilibrium vapor, liquid, and solid phases are depicted as points on the horizontal tie line at pressure Pj. As the pressure is further increased a vapor-liquid envelope is observed for overall mixture concentrations less than Xl- A mixture critical point is observed for this vapor-liquid envelope, as described earlier. If the overall mixture composition is greater than Xl, then solid-gas equilibria are observed as the pressure is increased above Pj. 

An equation of state, applicable to all fluid phases, is paitiodariy useful for phase-equilibrium calculations where a liquid phase and a vapor phase coexist at high pressures. At such conditions, conventional activity coefficients are not useful because, with rare exceptions, at least one of the mixture s components is supercritical that is, (he system temperature is above (hat component s critical temperature. In that event, one must employ special standard states for the activity coefficients of the supercritical components (see Section 1.5-2). That complication is avoided when ail fugacities are calculated front en equation of state. 

To date little or no thermodynamic modeling of the phase behavior of the ligand/C02 or metal chelate/C02 systems has been conducted. However, in order for supercritical fluid extraction to be considered as a possible replacement for organic solvent extraction, accurate models must be developed to predict the phase behavior of these systems to allow for both equipment and process design. Equation of state (EOS) modeling was chosen here to model the vapor-liquid equilibrium of the P-diketone/C02 systems studied. Cubic EOSs are the most widely used in modeling high pressure and supercritical fluid systems. This is... 

Since then. Dr. Woldfarth s main researeh has been related to polymer systems. Currently, his research topics are molecular thermodynamics, continuous thermodynamics, phase equilibria in polymer mixtures and solutions, polymers in supercritical fluids, PVT behavior and equations of state, and sorption properties of polymers, about which he has published approximately 100 original papers. He has written the following books Vapor-Liquid Equilibria of Binary Polymer Solutions, CRC Handbook of Thermodynamic Data of Copolymer Solutions, CRC Handbook of Thermodynamic Data of Aqueous Polymer Solutions, CRC Handbook of Thermodynamic Data of Polymer Solutions at Elevated Pressures, CRC Handbook of Enthalpy Data of Polymer-Solvent Systems, and CRC Handbook of Liquid-Liquid Equilibrium Data of Polymer Solutions. 

The red curve is the vapor-pressure curve of the liquid, representing equilibrium between the liquid and gas phases. The point on this curve where the vapor pressure is 1 atm is the normal boiling point of the substance. The vapor-pressure curve ends at the critical point (C), which corresponds to the critical temperature and critical pressure of the substance. Beyond the critical point, the liquid and gas phases are indistinguishable from each other, and the substance is a supercritical fluid. 

Both adsorption from a supercritical fluid to an adsorbent and desorption from an adsorbent find applications in supercritical fluid processing. The extrapolation of classical sorption theory to supercritical conditions has merits. The supercritical conditions are believed to necessitate monolayer coverage and density dependent isotherms. Considerable success has been observed by the authors in working with an equation of state based upon the Toth isoterm. It is also important to note that the retrograde behavior observed for vapor-liquid phase equilibrium is experimentally observed and predicted for sorptive systems. 

Lam, D.H., JangkamoUculchai, A. and Luks, K.D. (1990) Liquid-liquid-vapor phase equilibrium behavior of certain binary carbon dioxide + n-alkanol mixtures. Fluid Phase Equilibria, 60,131-141. Gurdial, G.S., Foster, N.R., Jimmy Yun, S.L. and Tilly, KJ3. (1993) Phase behavior of supercritical fluid-entrainer systems, in Siqtercritical Fluid Engineering Science, Fundamentals and Applications, E. Kiran and JJ. Brennecke (Eds.), ACS Symposium Series No. 514, pp. 34-45. 

Because of the close relationship between the MNM transition and the vapor-liquid transition, it is to be expected that immiscibility in the mercury-helium system reaches up to the critical point, or even into the supercritical region. This expectation is confirmed by measurements of the phase diagram at very low helium concentrations and at pressures close to the critical pressure of pure mercury. The experiments extend up to 1610 °C and to pressures up to 3325 bar (Marceca et al., 1996). The p — T — X phase equilibrium surface obtained is qualitatively like the one shown schematically in Fig. 6.4 for a binary fiuid-fluid system of the first kind. The critical line starts at the critical point of pure mercury (Tc(l) = 1478 °C, Pc(l) = 1673 bar) and runs to higher temperatures and pressures as the helium composition X2 increases. 

Isobaric-isothermal methods are often also called dynamic methods. One or more fluid streams are pumped continuoirsly into a thermostated equilibriirm cell. The pressure is kept constant during the experiment by controlling an effluent stream, irsually of the vapor phase. One can distinguish between continuorrs-flow methods and semi-flow methods. In continuous-flow methods, both phases flow throrrgh the eqrrihbrirrm cell. They can be used only for systems where the time needed to attain phase equilibrium is sufficiently short. Therefore, such equipment is usually not applied to polymer solutions. In semi-flow methods, only one phase is flowing while the other stays in the equilibrium phase. They are sometimes called gas-saturation methods or pure-gas circulation methods and can be used to measure gas solubilities in liquids and melts or solubilities of liquid or solid substances in supercritical fluids. 

Taking into account vapor-hquid equilibrium (VLE) data, liquid-liquid equilibrium (LLE) data, high-pressure phase equihhrium (HPPE) data of copolymer solutions in supercritical fluids, volumetric property (PVT) data of copolymer melts, enthalpy data, and second osmotic virial coefficients of copolymer solutions, the book covers all the necessary areas for researchers and engineers who work in... 

The Handbook is divided into seven chapters (1) Introduction, (2) Vapor-Liquid Equilibrium (VLB) Data of Binary Copolymer Solutions, (3) Liquid-Liquid Equilibrium (LLE) Data of Quasibinary or Quasitemary Copolymer Solutions, (4) High-Pressure Phase Equilibrium (HPPE) Data of Quasibinary or Quasitemary Copolymer Solutions in Supercritical Fluids, (5) Enthalpy Changes for Binary Copolymer Solutions, (6) PVT Data of Molten Copolymers, and (7) Second Virial Coefficients ( 2) of Copolymer Solutions. Finally, four appendices quickly route the user to the desired data sets. 

Critical Point This marks the end of the vapor-liquid equilibrium line. Above this temperature and pressure, the fluid will pass from properties that are liquid-like to properties that are gas-like without undergoing a phase change. A fluid above its critical point is said to be supercritical. 

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