Composition paths

The compositional paths of liquids for melting processes in closed systems of initial composition Cl or C2 are exactly the opposite of those observed in crystallization events. 

Properties of Coherent Systems Affinity Cuts, Composition Paths, and Composition Velocities... 

A model depicting composition paths in the simplex tetrahedron of a four-component system is shown in Figure 3. For systems with more than four components, one runs out of dimensions for graphical or spatial... 

Figure 2. Composition-path grid in mobile-phase composition simplex of three-component system with separation factors au — % and < i i = 4...

A simple example may serve to illustrate the development of a noncoherent profile, the use of the composition-path concept in predicting the behavior even of noncoherent systems, and the physical factors re-... 

Figure 3. Model showing sets of composition paths in mobile-phase composition simplex of four-component system with separation factors a12 = 2, aim = 4, and au = 8...

The -transformation is designed to orthogonalize the composition-path grid. Thus, since any path is normal to all coordinates but one, only one H-function root can vary along any path. The coherence requirement can therefore be simply expressed as... 

Determination of Phase Diagrams and Composition Paths The dynamics of the membrane formation process is predicted by combining the kinetics and thermody-... 

FIGURE 3.8 Schematic representation of the composition path of the cast film immediately after immersion in the coagulation bath for (a) instantaneous and (b) delayed demixing systems, and the scanning electron microscope (SEM) picture of the resulting membranes (c) and (d). 

When the system follows Langmuir competitive equilibrium behavior, the coherence condition defines a grid of coherent composition paths to which the system is restricted once the coherence condition is satisfied. Knowing the feed history, i.e., the boxmdary condition, one can use this grid, find the composition routes for the column and predict the column effluent history. 

Although for the sake of clarity the previous discussion was limited to the case of a binary mixture, these results are easily generalized to the study of an n-component mixture. Because of the coupling between the mobile phase components, the velocity eigenvalues are related to the slopes of the tangents to the n-dimensional isotherm surface, in the n composition path directions. These slopes can be calculated when the isotherm surface is known. Conversely, systematic measurement of the retention times of very small vacancy pulses for various compositions of the mobile phase may permit the determination of competitive equilibrium isotherms, but only if a proper isotherm model is available. Least-squares fitting of the set of slope data to the isotherm equations allows the calculation of the isotherm parameters. If an isotherm model, i.e., a set of competitive isotherm equations, is not available, the experimental data cannot be used to derive an empirical isotherm (see Chapter 4). 

Fig. 1 Compositional path in vaporizing multi-contact miscible flood. (View this art in color at www.dekker.com.)...

Fig. 2 Examples of the composition path on a triangular diagram. P = polymer, S = solvent, N = nonsolvent composition paths A, B, and C depend on the ratio of solvent/ nonsolvent flux rate during the solvent exchange, a, composition at the beginning of solvent exchange P, composition at the point of crossing the phase boundary y, composition at the point of gelation c5, composition at the end of solvent exchange. (From Ref l)...

Fortunately, however, the curvature of vapor and liquid composition profiles follow each other quite closely [1], and in general we can assume that there is a continuous liquid composition path between bottoms and distillate products, then the design is considered feasible. This approximation may be slightly off in the approximation of minimum reflux since one may And, for a liquid feed, that the liquid profiles just intersect each other but the vapor profiles miss each other (or vice versa). Nonetheless, liquid profile intersection still gives an excellent approximation and the design parameters found using this approach are very closely aligned with... 

Some composite path could take advantage of different helpful features, as in case where the initial emulsification is carried out at some distance ... 

In two of the precipitation tests, the asphalts were first precipitated by addition of n-butane and n-pentane to the tank oil. After separation of asphalts from the crude, the deasphalted crude was analyzed by gas-liquid chromatography. Table 2 shows that the original oil composition is considerably altered by asphalt precipitation. The amount of heavier ends in the deasphalted crude is less than in the original crude. Also, n-butane removed greater amount of heavier fraction iC y + ) than n-pentane. The deasphalted crude has lower density than original crude. This Indicates that in a miscible process, asphaltene precipitation can alter the composition of crude oil which needs to be accounted for in prediction of solvent-oil phase behavior, compositional path and miscibility conditions for solvent-oil systems. 

Asphaltene precipitation results in removal of heavier fractions of the crude leaving behind lighter deasphalted crude. This indicates that in a miscible process, the alteration of crude composition needs to be accounted for in prediction of phase behavior, compositional path and miscibility conditions for solvent-oil systems. 

FIGURE 9.5. Equilibrium diagram for ternary Langmuir system showing possible coherent composition paths. 

The chemical flooding systems discussed in this section are without alcohol present as cosnrfactant. As pointed ont by Sanz and Pope [J 7], a major difficulty was to preclude gels, liquid crystals, macroemulsions, and precipitates along the compositional path during a chemical flood if cosurfactants/alcohols are not part of the chemical formnlation. Phase trapping and blockage of the porous medium must be avoided. 

Two types of demixing process will now be distinguished leading to different types of membrane structure. These two different types of demixing process may be characterised by the instant when liquid-liquid demixing sets in. Figure III - 39 shows the composition path of a polymer film schematically at the very moment of immersion in a nonsolvent bath (at t < 1 second). The composition path gives the concentration at any point in the film at a particular moment. For any other time another compositional path will exist. 

Figure III 39. Schematic composition path of the cast film immediately after immersion t is the top of the film and b is the boRom. The left-hand figure shows instantaneous liquid-liquid demixing whereas the right-hand figure shows the mechanism for the delayed onset of liquid-liquid demixing.

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