Condensation and the Gas-Liquid Critical Point

Comparing term-by-term with (2.30), we obtain the desired Van der Waals virial coefficients in the form 

The approach to the critical point, from above or below, is accompanied by spectacular changes in optical, thermal, and mechanical properties. These include critical opalescence (a bright milky shimmering flash, as incident light refracts through intense density fluctuations) and infinite values of heat capacity, thermal expansion coefficient aP, isothermal compressibility /3r, and other properties. Truly, such a confused state of matter finds itself at a critical juncture as it transforms spontaneously from a uniform and isotropic form to a symmetry-broken (nonuniform and anisotropically separated) pair of distinct phases as (Tc, Pc) is approached from above. Similarly, as (Tc, Pc) is approached from below along the L + G coexistence line, the densities and other phase properties are forced to become identical, erasing what appears to be a fundamental physical distinction between liquid and gas at all lower temperatures and pressures. 

TABLE 2.4 Critical Constants 7C, Pc, VC9 and Compressibility Factor Zc = PCVC/RTC for Selected Gases 

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Supercritical fluids represent a different type of alternative solvent to the others discussed in this book since they are not in the liquid state. A SCF is defined as a substance above its critical temperature (Tc) and pressure (Pc)1, but below the pressure required for condensation to a solid, see Figure 6.1 [1], The last requirement is often omitted since the pressure needed for condensation to occur is usually unpractically high. The critical point represents the highest temperature and pressure at which the substance can exist as a vapour and liquid in equilibrium. Hence, in a closed system, as the boiling point curve is ascended, increasing both temperature and pressure, the liquid becomes less dense due to thermal expansion and the gas becomes denser as the pressure rises. The densities of both phases thus converge until they become identical at the critical point. At this point, the two phases become indistinguishable and a SCF is obtained. 

The phase diagram of a retrograde gas has a critical temperature less than reservoir temperature and a cricondentherm greater than reservoir temperature. See Figure 5-3. Initially, the retrograde gas is totally gas in the reservoir, point 1. As reservoir pressure decreases, the retrograde gas exhibits a dew point, point 2. As pressure is reduced, liquid condenses from the gas to form a free liquid in the reservoir. This liquid will normally not flow and cannot be produced. 

Gas flow processes through microporous materials are important to many industrial applications involving membrane gas separations. Permeability measurements through mesoporous media have been published exhibiting a maximum at some relative pressure, a fact that has been attributed to the occurrence of capillary condensation and the menisci formed at the gas-liquid interface [1,2]. Although, similar results, implying a transition in the adsorbed phase, have been reported for microporous media [3] and several theoretical studies [4-6] have been carried out, a comprehensive explanation of the static and dynamic behavior of fluids in micropores is yet to be given, especially when supercritical conditions are considered. Supercritical fluids attract, nowadays, both industrial and scientific interest, due to their unique thermodynamic properties at the vicinity of the critical point. For example supercritical CO2 is widely used in industry as an extraction solvent as well as for chemical... 

In ordinary drying, the liquid in a specimen evaporates, and the resulting surface (interfacial) tension can distort the structure. In critical point drying [425], heating a specimen in a fluid above the critical temperature to above the critical pressure permits the specimen to pass through the critical point (that temperature and pressure where the densities of the liquid and vapor phases are the same and they coexist and thus there is no surface tension). By definition, a gas cannot condense to a liquid at any pressure above the critical temperature. The critical pressure is the minimum pressure required to condense a liquid from the gas phase at just... 

The initial temperature of a gas condensate lies between the critical temperature and the cricondotherm. The fluid therefore exists at initial conditions in the reservoir as a gas, but on pressure depletion the dew point line is reached, at which point liquids condense in the reservoir. As can be seen from Figure 5.22, the volume percentage of liquids is low, typically insufficient for the saturation of the liquid in the pore space to reach the critical saturation beyond which the liquid phase becomes mobile. These... 

D line represents the variation in the melting point with pressure. The A to B line represents the variation of the vapor pressure of a liquid with pressure. This B point shown on this phase diagram is the critical point of the substance, the point beyond which the gas and liquid phases are indistinguishable from each other. At or beyond this critical point, no matter how much pressure is applied, it is not possible to condense the gas into a liquid. Point A is the triple point of the substance, the combination of temperature and pressure at which all three states of matter can exist. 

The critical point on a phase diagram is that point beyond which the gaseous and liquid states merge. No matter how much pressure is applied or how much the gas is cooled, the substance cannot be condensed into a liquid. 

Temperature at the critical point (end of the vapor pressure curve in phase diagram) is termed critical temperature. At temperatures above critical temperature, a substance cannot be liquefied, no matter how great the pressure. Pressure at the critical point is called critical pressure. It is the minimum pressure required to condense gas to liquid at the critical temperature. A substance is still a fluid above the critical point, neither a gas nor a liquid, and is referred to as a supercritical fluid. The critical temperature and pressure are expressed in this text in -C and atm, respectively. 

Figure 2.8 Representative supercritical (T = 31 OK) and subcritical (T = 280K) Van der Waals isotherms for C02, showing the liquid-gas (L + G) condensation plateau (P = 52 atm) for T = 280K, and outlining the 2-phase liquid-gas coexistence dome (dotted line) topped by the critical point (x) at Tc = 304K, Pc = 73 atm.

Since in the critical point the bubble point curve (l+g—tf) and the dew-point curve (l+g-+g) merge at temperatures between 7C and 7 , an isotherm will intersect the dew-point curve twice. If we lower the pressure on this isotherm we will pass the first dew-point and with decreasing pressure the amount of liquid will increase. Then the amount of liquid will reach a maximum and upon a further decrease of the pressure the amount of liquid will decrease until is becomes zero at the second dew-point. The phenomenon is called retrograde condensation and is of importance for natural gas pipe lines. In supercritical extraction use is made of the opposite effect. With increasing pressure a non-volatile liquid will dissolve in a dense supercritical gas phase at the first dew point. 

We will first consider phase diagrams. Then we will define the critical point for a two-component mixture. This will be the correct definition for multicomponent mixtures. Also, we will look at an important concept called retrograde condensation. Then the pressure-volume diagram will be discussed, and differences between pure substances and two-component mixtures in the two-phase region will be illustrated. Finally, the effects of temperature and pressure on the compositions of the coexisting liquid and gas will be illustrated. 

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