Binary phase behavior

THE IMPACT OF SOLIDIFICATION ON OBSERVED PHASE BEHAVIORS (BINARY MIXTURES)... 

P11.3 Calculate the separation factor for the system acetone (l)-water (2) for an acetone concentration of Xi = 0.95 at 50 C and at 1 atm with the help of the NRTL equation assuming ideal vapor phase behavior. Binary NRTL parameters can be found in Table 5.9. All other properties are given in Appendix A. 

To illustrate, predictions were first made for a ternary system of type II, using binary data only. Figure 14 compares calculated and experimental phase behavior for the system 2,2,4-trimethylpentane-furfural-cyclohexane. UNIQUAC parameters are given in Table 4. As expected for a type II system, agreement is good. 

Ternary Blends. Discussion of polymer blends is typically limited to those containing only two different components. Of course, inclusion of additional components may be useful in formulating commercial products. The recent Hterature describes the theoretical treatment and experimental studies of the phase behavior of ternary blends (10,21). The most commonly studied ternary mixtures are those where two of the binary pairs are miscible, but the third pair is not. There are limited regions where such ternary mixtures exhibit one phase. A few cases have been examined where all three binary pairs are miscible however, theoretically this does not always ensure homogeneous ternary mixtures (10,21). 

Fig. 6. Qualitative piessuie—tempeiatuie diagiams depicting ctitical curves for the six types of phase behaviors for binary systems, where C or Cp corresponds to pure component critical point G, vapor 1, Hquid U, upper critical end point and U, lower critical end point. Dashed curves are critical lines or phase boundaries (5). (a) Class I, the Ar—Kr system (b) Class 11, the CO2—CgH g system (c) Class 111, where the dashed lines A, B, C, and D correspond to the H2—CO, CH —H2S, He—H2, and He—CH system, respectively (d) Class IV, the CH —C H system (e) Class V, the C2H -C2H OH...

B.H. Sage, Phase Behavior in Binary and Multi-component Systems at Elevated Pressures n-Pentane and Methane-m-Pentane , NSRDS-NBS 32 (1970) 20)A.S. Mal tseva et al,... 

The dilated van Laar model is readily generalized to the multicomponent case, as discussed in detail elsewhere (C3, C4). The important technical advantage of the generalization is that it permits good estimates to be made of multicomponent phase behavior using only experimental data obtained for binary systems. For example, Fig. 14 presents a comparison of calculated and observed -factors for the methane-propane-n-pentane system at conditions close to the critical.7... 

For helium, a = 2.56 A and e/k = 10.22°K, where k is Boltzmann s constant. For xenon, e/k = 221 °K and a = 4.10. Because of symmetry, the subscript 1 may refer to either helium or xenon from the assumption of corresponding-states behavior, v°2 should be independent of the component chosen for subscript 1. Equation (108) is an equation of state for the binary mixture, and from it the phase behavior can be calculated without further assumptions. 

Effect of Binary Margules Constants on Phase Behavior... 

A brief discussion of sohd-liquid phase equihbrium is presented prior to discussing specific crystalhzation methods. Figures 20-1 and 20-2 illustrate the phase diagrams for binary sohd-solution and eutectic systems, respectively. In the case of binary solid-solution systems, illustrated in Fig. 20-1, the liquid and solid phases contain equilibrium quantities of both components in a manner similar to vapor-hquid phase behavior. This type of behavior causes separation difficulties since multiple stages are required. In principle, however, high purity... 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binary and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predictive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilibria that is useful for estimating nonideal binary or multicomponent solid-liquid phase behavior has been reported by Muir (Pap. 71f, 73d ann. meet., AIChE, Chicago, 1980). 

Based on the above, we can develop an "adaptive" Gauss-Newton method for parameter estimation with equality constraints whereby the set of active constraints (which are all equalities) is updated at each iteration. An example is provided in Chapter 14 where we examine the estimation of binary interactions parameters in cubic equations of state subject to predicting the correct phase behavior (i.e., avoiding erroneous two-phase split predictions under certain conditions). 

It is well known that cubic equations of state have inherent limitations in describing accurately the fluid phase behavior. Thus our objective is often restricted to the determination of a set of interaction parameters that will yield an "acceptable fit" of the binary VLE data. The following implicit least squares objective function is suitable for this purpose... 

Blanco et al. have also correlated the results with the van Laar, Wilson, NRTL and UNIQUAC activity coefficient models and found all of them able to describe the observed phase behavior. The value of the parameter ai2 in the NRTL model was set equal to 0.3. The estimated parameters were reported in Table 10 of the above reference. Using the data of Table 15.7 estimate the binary parameters in the Wislon, NRTL and UNIQUAC models. The objective function to be minimized is given by Equation 15.11. 

Wilding, N. B. Schmid, F. Nielaba, P., Liquid-vapor phase behavior of a symmetrical binary fluid mixture, Phys. Rev. E 1998, 58, 2201-2212... 

The interaction parameters for binary systems containing water with methane, ethane, propane, n-butane, n-pentane, n-hexane, n-octane, and benzene have been determined using data from the literature. The phase behavior of the paraffin - water systems can be represented very well using the modified procedure. However, the aromatic - water system can not be correlated satisfactorily. Possibly a differetn type of mixing rule will be required for the aromatic - water systems, although this has not as yet been explored. 

Propane - Water System. The interaction parameters for the propane - water system were obtained over a temperature range from 42°F to 310°F using exclusively the data of Kobayashi and Katz (24). This is because among the available literature on the phase behavior of this binary system, their data appear to give the most extensive information. A constant interaction parameter was obtained for the propane-rich phases at all temperatures. The magnitude of the temperature - dependent interaction parameter for this binary was less than that for the ethane - water binary at the same temperature. Azarnoosh and McKetta (25) also presented experimental data for the solubility of propane in water over about the same temperature range as that of Kobayashi and Katz but at pressures up to 500 psia only. However, a different set of temperature - dependent parameters... 

Two-constant equation of state phase behavior calculations for aqueous mixtures often require the use of temperature dependent binary interaction parameters. The methods used for evaluating these parameters for some of the typical aqueous binary pairs found in coal gasification and related process streams are described. Experimental and predicted phase compositions based on these methods are illustrated for aqueous pairs containing CO2. H2S, NH3, and other gases. 

Schwahn, D. Willner, L. Phase Behavior and Flory-Huggins Interaction Parameter of Binary Polybutadiene Copolymer Mixtures with Different Vinyl Content and Molar Volume. Macromolecules 2002,35, 239-247. 

Shariati, A. and Peters, C. J., High-pressure phase behavior of systems with ionic liquids Measurements and modeling of the binary system fluoroform + l-ethyl-3-methylimidazolium hexafluorophosphate, /. Supercrit. Fluids, 25, 109, 2003. 

Much of what we need to know abont the thermodynamics of composites has been described in the previous sections. For example, if the composite matrix is composed of a metal, ceramic, or polymer, its phase stability behavior will be dictated by the free energy considerations of the preceding sections. Unary, binary, ternary, and even higher-order phase diagrams can be employed as appropriate to describe the phase behavior of both the reinforcement or matrix component of the composite system. At this level of discussion on composites, there is really only one topic that needs some further elaboration a thermodynamic description of the interphase. As we did back in Chapter 1, we will reserve the term interphase for a phase consisting of three-dimensional structure (e.g., with a characteristic thickness) and will use the term interface for a two-dimensional surface. Once this topic has been addressed, we will briefly describe how composite phase diagrams differ from those of the metal, ceramic, and polymer constituents that we have studied so far. 

For given binary pair, two-phase behavior likely when infinite dilution activity coefficient of either component in other component is >7.5. 

---