Isothermal compressibility supercritical fluids

A gaseous pure component can be defined as supercritical when its state is determined by values of temperature T and pressure P that are above its critical parameters (Tc and Pc). In the proximity of its critical point, a pure supercritical fluid (or a dense gas as it is alternatively known) has a very high isothermal compressibility, and this makes possible to change significantly the density of the fluid with relatively limited modifications of T and P. On the other hand, it has been shown that the thermodynamic and transport properties of supercritical fluids can be tuned simply by changing the density of the medium. This is particularly interesting for... 

Fluids are highly compressible along near-critical isotherms (L01-1.2 Tc) and display properties ranging from gas-like to Liquid-Like with relatively small pressure variations around the critical pressure. The liquid-like densities and better-than-liquid transport properties of supercritical fluids (SCFs) have been exploited for the in situ extraction of coke-forming compounds from porous catalysts [1-6], For i-hexene reaction on a low activity, macroporous a catalyst, Tiltschcr el al. [1] demonstrated that reactor operation at supercritical... 

The terms "gas and vapor are often used interchangeably, but there is a technical difference between them that you are now in a position to understand. A vapor is a gaseous species below its critical temperature, and a gas is a species above its critical temperature at a pressure low enough tor the species to be more like a vapor than a liquid (i.e., a density closer to 1 g/L than 1000 g/L). You can condense a vapor by compressing it isothermally, but while you can make a gas denser and denser by compressing it isothermally you will never achieve a separation into two phases. Substances at temperatures above Tc and pressures above Pc are referred to as supercritical fluids. 

The critical temperature Tc of a species is the highest temperature at which isothermal compression of the species vapor results in the formation of a separate liquid phase, and the critical pressure is the pressure at which that phase forms. Isothermal compression of a species above its critical temperature—a gas (as opposed to vapor) or supercritical fluid—results in a fluid of increasing density but not a separate liquid phase. 

Supercritical fluid extraction Supercritical fluid extraction (SFE) uses compressed gas as the extraction medium and circumvents some of the problems associated with the use of classical separation techniques involving organic solvents. This technique combines features of distillation (i.e., separation because of differences in component volatiles) and liquid extraction (i.e., separation of components that exhibit little difference in their relative volatilities or that are thermally labile). A number of gases, when compressed isothermally at a temperature greater than their critical temperature and to pressures greater than their critical pressure, exhibit an enhanced solvating power (136), which has been known since the nineteenth century (137, 138), but its actual applications did not come to practice until the late twentieth century. 

No amount of compression can liquefy the supercritical fluid. In fact pressure can be used to continuously change the density from gas-like conditions to liquidlike conditions. Near the critical region, small changes in the pressure can give rise to large changes in the density. Fig. 1 shows how density of carbon dioxide is varied by pressure at different isotherms. 

A supercritical fluid (SCF) is any compound above its critical point, which is the maximum in both temperature and pressure at which a gas and liquid can coexist. Above the critical point, isothermic compression yields a continuous increase in density without condensation to a liquid state. All substances theoretically have a critical point, but many experience thermal degradation well before reaching it. 

Abildskov, J., M. D. Ellegaard, and J. P. O Connell. 2010a. Densities and isothermal compressibilities of ionic liquids-modeling and application. Fluid Phase Equilibria. 295, 215. Abildskov, J., M. D. Ellegaard, and J. P. O Connell. 2010b. Phase behavior of mixtures of ionic liquids and organic solvents. Journal of Supercritical Fluids. 55, 833. 

In summary a fluid is critical when the difference between coexisting liquid and vapor phases disappears. At this point the isothermal compressibility of the one-phase fluid becomes infinite. In the supercritical region, a state of liquid-like density can transform into one of vapor-like density by tuning the pressure or the temperature, without the appearance of an interface. The further from the critical point, the easier it is to gently manipulate the density by tuning pressure or temperature. In the supercritical fluid, a range of intermediate-density states can be reached which are not available at subcritical temperatures and pressures. 

A fluid in the supercritical region can have a density comparable to that of tbe liquid, and can be more compressible than the liquid. Under supercritical conditions, a substance is often an excellent solvent for solids and liquids. By varying the pressure or temperature, the solvating power can be changed by reducing the pressure isothermally, the substance can be easily removed as a gas from dissolved solutes. These properties make supercritical fluids useful for chromatography and solvent extraction. 

If, however, we increase p at constant T, the supercritical fluid will change to a solid. In the phase diagram of H2O, the coexistence curve for ice VII and liquid shown in Fig. 8.4 extends to a higher temperature than the critical temperature of 647 K. Thus, supercritical water can be converted to ice VII by isothermal compression. Refs. [162] and [9]. 

The isotherm above the critical point is representative of a supercritical fluid. This isotherm continuously decreases in pressure as the volume increases. A supercritical fluid has partly hquidlike characteristics (e.g., high density) and partly vaporlike characteristics (compressibflity, high-diffusivity). Not surprisingly, there are many interesting engineering appUcations for substances in this state. There can be confusion between the terms gas and vapor. We refer to a gas as any form of matter that fills the container it can be either subcritical or supercritical. When we speak of vapor, it is gas that if iso-thermaUy compressed will condense into a liquid and is, therefore, always subcritical. 

Other workers [112, 113] have shown that a chemical equilibrium model of hydrocarbons based on an exponential-6 fluid model using Ross s soft-sphere perturbation theory is successful in reproducing the behavior of shocked hydrocarbons. Our model of the supercritical phase includes the species H2, CH4, C2H6, and C2H4. We have chosen model parameters to match both static compression isotherms and shock measurements wherever possible. The ability to match multiple types of experiments well increases confidence in the general applicability of our high-pressure equation of state model. 

Properties near the critical point are quite different compared to states at lower temperatures and pressures. As the difference between vapor and liquid becomes less clear near the critical point, the liquid becomes substantially more compressible than typical liquids. This is indicated on the PVgraph by the gentle slope of the isotherm as it approaches the critical point. Isotherms below but near the critical temperature (not shown in Figure 2-2) show similar behavior. The usual approximation that treats liquids as incompressible is acceptable only at temperatures well below the critical. In the supercritical region, the behavior of a fluid is somewhere between that of a liquid and a gas. The gentle slope of the isotherms indicates that the fluid is quite compressible, even at high, liquid-like densities Qow molar volumes). 

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