Critical point fluids

There is also a temperature above which a substance cannot be liquefied regardless of the pressure applied. This temperature is called the critical temperature. The pressure required to produce liquefaction while the substance is at the critical temperature is called the critical pressure. Together, the critical temperature and critical pressure define the critical point. Fluid beyond the critical point has characteristics of both gas and liquid, and is called supercritical fluid. 

Physical properties. Gas-oil ratios for the Pre-Cretaceous fluids vary from fairly low values of 1224 and 1691 scf/bbl for wells 30/7a-6 and 30/ 7a-3 to a maximum of 6287 scf/bbl in 30/7a-l Iz (Table 1). Most of the petroleums are near-critical point fluids, being either single-phase... 

The initial condition for the dry gas is outside the two-phase envelope, and is to the right of the critical point, confirming that the fluid initially exists as a single phase gas. As the reservoir is produced, the pressure drops under isothermal conditions, as indicated by the vertical line. Since the initial temperature is higher than the maximum temperature of the two-phase envelope (the cricondotherm - typically less than 0°C for a dry gas) the reservoir conditions of temperature and pressure never fall inside the two phase region, indicating that the composition and phase of the fluid in the reservoir remains constant. 

For both volatile oil and blaok oil the initial reservoir temperature is below the critical point, and the fluid is therefore a liquid in the reservoir. As the pressure drops the bubble point is eventually reached, and the first bubble of gas is released from the liquid. The composition of this gas will be made up of the more volatile components of the mixture. Both volatile oils and black oils will liberate gas in the separators, whose conditions of pressure and temperature are well inside the two-phase envelope. 

There has been extensive activity in the study of lipid monolayers as discussed above in Section IV-4E. Coexisting fluid phases have been observed via fluorescence microscopy of mixtures of phospholipid and cholesterol where a critical point occurs near 30 mol% cholesterol [257]. 

Statistical mechanical theory and computer simulations provide a link between the equation of state and the interatomic potential energy functions. A fluid-solid transition at high density has been inferred from computer simulations of hard spheres. A vapour-liquid phase transition also appears when an attractive component is present hr the interatomic potential (e.g. atoms interacting tlirough a Leimard-Jones potential) provided the temperature lies below T, the critical temperature for this transition. This is illustrated in figure A2.3.2 where the critical point is a point of inflexion of tire critical isothemr in the P - Vplane. 

Ebeling W and Grigoro M 1980 Analytical calculation of the equation of state and the critical point in a dense classical fluid of charged hard spheres Phys. (Leipzig) 37 21... 

Stell G, Wu K C and Larsen B 1976 Critical point in a fluid of charged hard spheres Phys. Rev. Lett. 211 369... 

Unlike the pressure where p = 0 has physical meaning, the zero of free energy is arbitrary, so, instead of the ideal gas volume, we can use as a reference the molar volume of the real fluid at its critical point. A reduced Helmlioltz free energy in tenns of the reduced variables and F can be obtained by replacing a and b by their values m tenns of the critical constants... 

Figure A2.5.10. Phase diagram for the van der Waals fluid, shown as reduced temperature versus reduced density p. . The region under the smooth coexistence curve is a two-phase liquid-gas region as indicated by the horizontal tie-lines. The critical point at the top of the curve has the coordinates (1,1). The dashed line is the diameter, and the dotted curve is the spinodal curve.

Figure A2.5.11. Typical pressure-temperature phase diagrams for a two-component fluid system. The fiill curves are vapour pressure lines for the pure fluids, ending at critical points. The dotted curves are critical lines, while the dashed curves are tliree-phase lines. The dashed horizontal lines are not part of the phase diagram, but indicate constant-pressure paths for the T, x) diagrams in figure A2.5.12. All but the type VI diagrams are predicted by the van der Waals equation for binary mixtures. Adapted from figures in [3].

This vanishes at the critical-solution point as does (d p/d k) at the one-component fluid critical point. Thus... 

A third exponent y, usually called the susceptibility exponent from its application to the magnetic susceptibility x in magnetic systems, governs what m pure-fluid systems is the isothennal compressibility k, and what in mixtures is the osmotic compressibility, and detennines how fast these quantities diverge as the critical point is approached (i.e. as > 1). 

However, the discovery in 1962 by Voronel and coworkers [H] that the constant-volume heat capacity of argon showed a weak divergence at the critical point, had a major impact on uniting fluid criticality widi that of other systems. They thought the divergence was logaritlnnic, but it is not quite that weak, satisfying equation (A2.5.21) with an exponent a now known to be about 0.11. The equation applies both above and... 

The field-density concept is especially usefiil in recognizing the parallelism of path in different physical situations. The criterion is the number of densities held constant the number of fields is irrelevant. A path to the critical point that holds only fields constant produces a strong divergence a path with one density held constant yields a weak divergence a path with two or more densities held constant is nondivergent. Thus the compressibility Kj,oi a one-component fluid shows a strong divergence, while Cj in the one-component fluid is comparable to (constant pressure and composition) in the two-component fluid and shows a weak... 

However, for more complex fluids such as high-polymer solutions and concentrated ionic solutions, where the range of intemiolecular forces is much longer than that for simple fluids and Nq is much smaller, mean-field behaviour is observed much closer to the critical point. Thus the crossover is sharper, and it can also be nonmonotonic. 

Surface waves at an interface between two innniscible fluids involve effects due to gravity (g) and surface tension (a) forces. (In this section, o denotes surface tension and a denotes the stress tensor. The two should not be coiifiised with one another.) In a hydrodynamic approach, the interface is treated as a sharp boundary and the two bulk phases as incompressible. The Navier-Stokes equations for the two bulk phases (balance of macroscopic forces is the mgredient) along with the boundary condition at the interface (surface tension o enters here) are solved for possible hamionic oscillations of the interface of the fomi, exp [-(iu + s)t + i V-.r], where m is the frequency, is the damping coefficient, s tlie 2-d wavevector of the periodic oscillation and. ra 2-d vector parallel to the surface. For a liquid-vapour interface which we consider, away from the critical point, the vapour density is negligible compared to the liquid density and one obtains the hydrodynamic dispersion relation for surface waves + s>tf. The temi gq in the dispersion relation arises from... 

Critical Point Properties for Selected Supercritical Fluids... 

Hydrothermal crystallisation processes occur widely in nature and are responsible for the formation of many crystalline minerals. The most widely used commercial appHcation of hydrothermal crystallization is for the production of synthetic quartz (see Silica, synthetic quartz crystals). Piezoelectric quartz crystals weighing up to several pounds can be produced for use in electronic equipment. Hydrothermal crystallization takes place in near- or supercritical water solutions (see Supercritical fluids). Near and above the critical point of water, the viscosity (300-1400 mPa s(=cP) at 374°C) decreases significantly, allowing for relatively rapid diffusion and growth processes to occur. 

Supercritical Fluid Extraction. Supercritical fluid (SCF) extraction is a process in which elevated pressure and temperature conditions are used to make a substance exceed a critical point. Once above this critical point, the gas (CO2 is commonly used) exhibits unique solvating properties. The advantages of SCF extraction in foods are that there is no solvent residue in the extracted products, the process can be performed at low temperature, oxygen is excluded, and there is minimal protein degradation (49). One area in which SCF extraction of Hpids from meats maybe appHed is in the production of low fat dried meat ingredients for further processed items. Its apphcation in fresh meat is less successful because the fresh meat contains relatively high levels of moisture (50). 

Va.por Pressure. Vapor pressure is one of the most fundamental properties of steam. Eigure 1 shows the vapor pressure as a function of temperature for temperatures between the melting point of water and the critical point. This line is called the saturation line. Liquid at the saturation line is called saturated Hquid Hquid below the saturation line is called subcooled. Similarly, steam at the saturation line is saturated steam steam at higher temperature is superheated. Properties of the Hquid and vapor converge at the critical point, such that at temperatures above the critical point, there is only one fluid. Along the saturation line, the fraction of the fluid that is vapor is defined by its quaHty, which ranges from 0 to 100% steam. 

Eig. 1. Schematic pressure—temperature diagram for a pure material showing the supercritical fluid region, where is the pure component critical point... 

Solvent Strength of Pure Fluids. The density of a pure fluid is extremely sensitive to pressure and temperature near the critical point, where the reduced pressure, P, equals the reduced temperature, =1. This is shown for pure carbon dioxide in Figure 2. Consider the simple case of the solubihty of a soHd in this fluid. At ambient conditions, the density of the fluid is 0.002 g/cm. Thus the solubiUty of a soHd in the gas is low and is given by the vapor pressure over the total pressure. The solubiUties of Hquids are similar. At the critical point, the density of CO2 is 0.47 g/cm. This value is nearly comparable to that of organic Hquids. The solubiHty of a soHd can be 3—10 orders of magnitude higher in this more Hquid-like CO2. 

Although modeling of supercritical phase behavior can sometimes be done using relatively simple thermodynamics, this is not the norm. Especially in the region of the critical point, extreme nonideahties occur and high compressibilities must be addressed. Several review papers and books discuss modeling of systems comprised of supercritical fluids and soHd orHquid solutes (rl,i4—r7,r9,i49,r50). 

This equation is useful for gases above the critical point. Only reduced pressure, P, and reduced temperature, T, are needed. In the form represented by equation 53, iteration quickly gives accurate values for the compressibiUty factor, Z. However, this two-parameter equation only gives accurate values for simple and nonpolar fluids. Unless the Redhch-Kwong equation (eq. 53) is expHcifly solved for pressure in nonreduced variables, it does not give accurate hquid volumes. 

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