Locus , three-phase

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. 

Nevertheless, a calculated locus is included for completeness and to indicate the possible region of three-phase equilibrium. 

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 work of Loh et al. (1983) was done using the same principles as those used to generate Figure 4.7. That is, from the initial temperature and pressure, an isenthalpic cooling curve, and its intersection with the hydrate three-phase locus, was determined. However, the isenthalpic line was determined via the Soave-Redlich-Kwong equation-of-state rather than the Mollier charts of... 

The three-phase (Lw-V-Lhc) pressure-temperature line is approximated by the vapor pressure (Vhc-Lhc) locus for the pure component due to two effects, both of which are caused by the hydrogen-bond phenomenon described in Chapter 2. First, hydrogen bonds cause almost complete immiscibility between the hydrocarbon liquid and the aqueous liquid, so that the total pressure may be closely approximated by the sum of the vapor pressures of the hydrocarbon phase and that of water. Second, hydrogen bonds cause such a self-attraction of the water molecules that the water vapor pressure is very low, composing only a small fraction of the total vapor pressure at any temperature. Because each immiscible liquid phase essentially exerts its own vapor pressure, and because the water vapor pressure is very small, the hydrocarbon vapor pressure is a very good approximation of the three-phase (Lw-V-Lhc) locus. 

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. 

However, the condensed three-phase P-T locus is not exactly vertical. Ng and Robinson (1977) measured the Lw-H-Lhc equilibrium for a number of structure II hydrate mixtures and suggested that a better estimation of the slope dP/dT might be obtained through the Clapeyron equation ... 

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).

We discussed the determination of the univariant (in this case three-phase) equilibrium curve in Chapter 8 in terms of finding the locus of P and T for G = 0. This is always... 

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... 

A three-phase line will terminate when two of the three phases become identical such states mark the intersection of the three-phase line with a critical line. Consider the three-phase vapor-hquid-hquid situation. If the two liquid phases become identical, then the VLLE line has intersected a locus of liquid-liquid critical points. Similarly, if the vapor phase becomes identical to one of the liquid phases, then the VLLE line has intersected a gas-hquid critical line. These intersections are called upper critical end points (UCEP) if they occur at a maximum temperature on the VLLE locus they are called lower critical end points (LCEP) if they occur at a minimum temperature. The number and kinds of critical end points help distinguish the classes in the Scott-van Konynenburg scheme. 

Class B. These binaries have continuous gas-liquid critical lines and undergo liquid-liquid phase splits at low temperatures. The LLE curves have only UCSTs and the three-phase VLLE line terminates at a UCEP by intersecting the locus of UCSTs (see Figure 9.22). From the UCEP the UCST locus extends to higher pressures, but it does not intersect the gas-liquid critical line. The slope of the UCST locus may be positive or negative. 

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,... 

If, on the other hand, the gap between the two three-phase loci widens, the temperature range of the higher-temperature three-phase locus will decrease. When this higher-temperature three-phase line just vanishes, two CEP s of different nature (the LCEP f= f+g and the UCEP t=g ) merge, see Figure Id. The resulting point is called a tricritical point (TCP), since at this point three phases become identical simultaneously (g=t= ). This state can be seen as a transition state between type-IV and type-II fluid phase behavior. 

Type-II fluid phase behavior is represented schematically in Figure le. The observed three-phase locus g is terminated by a UCEP from where a critical... 

Towards higher N, the region of type-IV fluid phase behavior ends with the occurrence of a DCEP, and type-III fluid phase behavior can be found. With the appearance of the DCEP (transition point between type-III and type-IV fluid phase behavior), the gap between the higher- and the lower-temperature three-phase loci has vanished. For constant N > Ndcep one continuous three-phase locus has formed, which is terminated towards higher temperature by an UCEP i.e., type-III fluid phase... 

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