Locus , three-phase systems

Figure 13.1 Changes in binary phase behaviour with size and energy as5mmetries labelled (phase type) classification of Bolz et u/. Cl and Ch are the critical points of the light and heavy compounds, respectively. The arrows qualitatively indicate the type of fluid phase behaviour that can be expected when the system components exhibit greater molecular interactions, size differences, or both.-----------------------, vapour liquid equilibria ., critical locus --------three phase region (LLV).

A constant interaction parameter was capable of representing the mole fraction of water in the vapor phase within experimental uncertainty over the temperature range from 100°F to 460°F. As with the methane - water system, the temperature - dependent interaction parameter is also a monotonically increasing function of temperature. However, at each specified temperature, the interaction parameter for this system is numerically greater than that for the methane - water system. Although it is possible for this binary to form a three-phase equilibrium locus, no experimental data on this effect have been reported. 

J. As with the alkane - water systems, the interaction parameters for the aqueous liquid phase were found to be temperature - dependent. However, the compositions for the benzene - rich phases could not be accurately represented using any single value for the constant interaction parameter. The calculated water mole fractions in the hydrocarbon - rich phases were always greater than the experimental values as reported by Rebert and Kay (35). The final value for the constant interaction parameter was chosen to fit the three phase locus of this system. Nevertheless, the calculated three-phase critical point was about 9°C lower than the experimental value. 

The normal freezing point of the liquid under pressure is given by Tp, and OS is the melting curve of the substance, i.e. the locus of the points defining the co-existence of solid and liquid. If we measure the freezing point of a liquid in a closed system, the Phase Rule tells us that since at that temperature all three phases will be in equilibrium, F=0, and we obtain the... 

The substitution of v, = xu-Kvu in the numerator of Equation 4.3a suggests that this equation applies at the bubble point, or the quadruple point (Lw-H-V-Lhc) that marks the lowest pressure of a three-phase (Lw-H-Lhc) region (point C in Figure 4.2c). The P-T locus of the three-phase (Lw-H-Lhc) line is almost vertical, so Equation 4.3a is an approximation of both the lowest pressure and the highest temperature for the three phases in equilibrium. Katz noted that Scauzillo (1956) had measured systems that did not appear to conform to the above equation. Later measurements by Verma (1974) and Holder (1976) confirmed Katz s analysis for hydrate formation from crude oil reservoirs. 

The emulsion polymerization system consists of three phases an aqueous phase (containing initiator, emulsifier, and some monomer), emulsified monomer droplets, the monomer-swollen micelles, and monomer-swollen particles. Water is the most important ingredient of the emulsion polymerization system. It is inert and acts as the locus of initiation (the formation of primary and oligomeric radicals) and the medium of transfer of monomer and emulsifier from monomer droplets or the monomer-swollen particle micelles to particles. An aqueous phase maintains a low viscosity and provides an efficient heat transfer. 

Type III behavior indicates the most extreme asymmetry between the components of a binary mixture. Nearly all H2 systems supply striking examples of type III behavior. CO2 mixtures with 2,5-hexanediol and 1-dodecanol are also classified as type III. The system CO2 -I- n-tridecane is peculiar because it was classified by van Konynenburg and Scott as type III, whereas Enick et al. have classified it as type IV, owing to experimental identification of a three-phase region. The system CO2 -I- n-tetradecane is a variation on type III, where the solute-rich locus terminates in a solid(wax)-liquid-liquid boundary. Several important systems fall into a similar category. For example, CO2 + naphthalene is commonly used as a model system for supercritical extraction. The naphthalene system differs from the n-tetradecane system in that the solute-rich locus terminates at a higher temperature... 

Figure 3.2 Plots of the salinity (5) versus the alkane carbon number (ACN). (a) Optimum formulation lines as the locus of the minimum interfacial tension, i.e. of the three-phase region centre, (b) Optimum formulation line as the locus in bidimensional S-ACN map for the same water-oil-alcohol systems containing different surfactants at constant temperature. CnOXS stands for alkylorthoxylene sulphonates, ABS for alkyl benzene sulphonate, PS for petroleum sulphonate (the number after PS indicates the average molecular weight).

Of the three binary systems SCF-OS, SCF-HC and OS-HC, the first is the most relevant to understanding the principle at the base of the process. In Figure 2.3-2(a) the vapour-liquid equilibrium curves for the system CO2-toluene is shown at T = 311 K. The liquid phase is represented by the boiling point locus, the vapor phase by the dew point locus experimental data are also reported in the figure. It is clear that ... 

Given the three phases present in an emulsion polymerization system, the locus of polymerization can conceivably be in the monomer droplets, in the aqueous phase within the micelles, or possibly at an interface. Some polymerization obviously takes place in the aqueous phase but with a limited contribution to the overall polymerization because of the low solubility of the monomer in water. The monomer droplets also do not provide the loci for polymerization because the negatively charged sulfate anions find the soap-stabilized monomer droplets virtually impossible to penetrate. Also, the primary sulfate radical anions are oil insoluble. The absence of polymerization in the monomer droplets has been verified... 

This prediction has now been subjected to several experimental tests. Lang and Widom have studied at saturation pressure the three-phase region of the quaternary system benzene + ethanol + water + ammonium sulphate. At each temperature the three-phase region consists of a stack of triangles lying between two critical end points, and the locus of the compositions of the three phases is defined by a single line in the isothermal composition tetrahedron. In the phenomenological theory there are three characteristic dimensions 1, 2,... 

Various mixtures first classified as belonging to type-V fluid phase behavior were found later to show type-IV instead. Rowlinson and Freeman [27] found some CO2 + hydrocarbon polymer mixtures to show type-V fluid phase behavior, i.e., they did not find any lower-temperature three-phase locus. However, using the van der Waals equation of state. Van Konynenburg and Scott [6] classified these systems as type-IV fluid phase behavior. Also the systems methane + pentane and methane + hexane, being members of the homologous series methane + alkane, were classified by Van Konynenburg and Scott [6] as a type-II and a type-IV system, respectively, although the UCEP s are situated below the solid phase boundary. Also Davenport and... 

According to the classification of Scott and Konynenburg (1970, the binary systems of Type I, have only one critical locus between both critical points of the pure components and do not have the inuniscibility phenomena. For this type binary aqueous solutions, the functions Tc(x),pc(x), and Pc(x) were represented as simple polynomial forms (see Equations (2.65)-(2.67) of x and (1 - x) (Kiselev and Rainwater, 1997, 1998 Kiselev et al, 1998). Water -I- toluene system corresponds to a Type 111 mixture (Scott and Konynenburg, 1970), in which there is a three-phase immis-cibility region L1-L2-V with two critical endpoints (Li = V-L2 and Li = L2-V) where the VLE critical locus, originated in the critical point of pme more-volatile component (toluene) and the LLE critical locus, started in the critical point of less-volatile component (water), are terminated. 

An emulsion polymerization system can comprise three phases (1) an aqueous phase, containing the water-soluble initiator, the micelle-forming surfactant, and a small amount of the sparingly soluble monomer (2) monomer droplets and (3) latex particles, consisting of the polymer and some monomer. The locus of polymerization is predominantly inside the latex particles. Usual free-radical water-soluble initiators are used, such as potassium persulfate for higher reaction... 

Figure 1.3 Phase behaviour of carbon dioxide/water system at temperatures between the critical hydrate temperature and the upper critical solution temperature, (a) Typical pressure/composi-tion diagram for carbon dioxide/water (a Class B2 system) at temperatures below the critical temperature of carbon dioxide but above the critical hydrate formation temperature. Data for arms B and C are shown in (b) and (c) respectively, (b) Solubility of liquid CO2 in water as a function of temperature and pressure (arm C in (a)), (c) Solubility of water in liquid CO2 as a function of temperature and pressure (arm B in (a)), (d) The three phase pressure curve compared with the vapour pressure curve of carbon dioxide showing the critical locus CsU (i.e. locus of points such as C on (e) where vapour properties merge with those of solvent-rich liquid). (Data reference [75].) (e) Detail of the isothermal pressure/composition diagram at 25°C (on left) and at temperature between Tc and Tu (on right). Subscripts 1 and 2 denote water-rich and C02-rich phase. Critical point C is shown as blocked-in circle. (Data reference for (b) and (c) is [81].)...

The vapour/liquid critical locus curve for Class B systems, instead of being continuous as in Figure 1.5, breaks into two parts as in Figure 1.9. The part originating at the solvent critical point (cs) terminates at the point U at which the composition of the solvent-rich liquid phase in the three phase mixture merges with that of the vapour. This part of the critical locus is marked branch I on Figure 1.9. It is very limited in extent for the CO2/H2O and C02/n-Ci6H32 systems shown, but is more extensive in some other systems. 

Factors affecting the inversion locus. The central A /A boundary depends on the position of the optimum formulation transition. However, it does not always correspond to a straight line crossing the three-phase region. In systems which exhibit wide three-phase regions (vertically) and a narrow A region (horizontally) there is no neat plateau. The position of the lateral branches of the inversion locus may depend on surfactant type and alcohol formulation and the oil viscosity may also alter and shift the locus.""... 

Nishiumi, H. Komatsu, M. Yokoyama, T. Kohmatsu, S. Two- and three-phase equilibria and eritical locus for the system of HCFC22-HFC134a. Fluid Phase Equilib. 1993, 83, 109-117. 

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