Example Problems using Multicomponent Mixtures

Mujtaba (1989) and Mujtaba and Macchietto (1992) considered a ternary separation using Butane-Pentane-Hexane mixture. Only the optimal operation for the first main-cut and the first off-cut was considered. Table 8.7 lists a variety of separation specification (on CUT 1) and column configurations in each case. A fresh feed of 6 kmol at a composition of 0.15, 0.35, 0.50 (mole fraction) is used in all cases. Also in each case a constant condenser vapour load of 3 kmol/hr is used. For convenience Type IV-CMH model was used with ideal phase equilibrium. 

The column compositions are initialised to the composition of the mixed reboiler charge and a total of 2% of the fresh feed is used as column holdup. Half of the column holdup is assumed to be in the condenser and the rest is distributed equally over the plates. Piecewise constant reflux ratio was used, with 3 time intervals for the main-cut separation and 1 interval for the off-cut. 

As in binary cases, recycling of off-cuts offers a possibility of significant reduction in batch time. In some cases it is found to be more than 45%. The results also show that the measure q can be used to predict qualitatively whether recycle is beneficial or not. As the value of q increases the benefit of recycle increases and so do the amount of and composition of the lighter component in the cut. 

An interesting part of the results mentioned so far is that in all cases, an initial total reflux operation was found to be necessary. This was to eliminate the third component from the overheads. The length of that period again depends on the ease of separation. For no recycle cases, the times at total reflux are slightly larger than those for recycle cases. This is due to the fact that the recycle of off-cut eases the separation of the main-cut. After the total reflux period of operation an increasing reflux ratio profile was obtained for the main-cut in all cases. The off-cut was always obtained at low reflux ratio as were the case with binary mixtures (Rose, 

the operation with off-cut recycling requires lower energy consumption due to shorter batch time. 

---

In some multicomponent mixture problems, it may be desirable to hold one component at some constant level and vary the others. In this case, we ignore the constant component and use the Simplex designs in the other components, assuming the constant total of these as 100% of the mixture. In the case of an oil additive, for example, we may wish to specify a mixture of additives which add up to 10% of the total composition. A possible design for a study of this type is given below ... 

For binary and multicomponent mixtures, the thermal conductivity depends on the concentrations as well as on temperature, and the formulas of the accurate kinetic theory are quite complicated [5]. Empirical expressions for X are therefore more useful for both binary [9] and ternary [6], [26] mixtures, although few data exist for ternary mixtures. Tabulations of available experimental and theoretical results for thermal conductivities may be found in [5], [6], [13], and [18]-[21], for example. The thermal diffusivity, defined as 2p/Cp, often arises in combustion problems its pressure and temperature dependences in gases are XjpCp T7p ( < a < 2), and its typical values in combustion lie between 10 cm /s and 1 cm s at atmospheric pressure. 

Nevertheless, analytical problems can be found where such disadvantages can be outweighed by the convenient final resolution of the problem based on LTP data. On other occasions, both fluorescence and phosphorescence data can easily be obtained from a given sample, providing complementary information. One example is the use of phosphorescence measurements at low temperature to examine mixtures of aromatic compounds dissolved in -alkanes (Shpol skii spectrometry). The narrow-band fluorescence and phosphorescence spectra complement one another and have proved most useful in the analysis of complex samples such as multicomponent mixtures of polycyclic aromatic hydrocarbons (PAHs) in fuel materials. 

SOLUTION This problem corresponds to quadrant I in the grid of Figure 8.1. We illustrate the solution method using the van der Waals equation of state, since we learned how to solve for the fugacity coefficients in Chapter 7. There are other, more accurate equations of state to use however, the basis of the solution method remains the same. Additionally, it is straightforward to extend the solution to mixtures with more than two components. For example, the text software uses the Peng-Robinson equation for dew-point calculations of multicomponent mixtures. 

For a pure supercritical fluid, the relationships between pressure, temperature and density are easily estimated (except very near the critical point) with reasonable precision from equations of state and conform quite closely to that given in Figure 1. The phase behavior of binary fluid systems is highly varied and much more complex than in single-component systems and has been well-described for selected binary systems (see, for example, reference 13 and references therein). A detailed discussion of the different types of binary fluid mixtures and the phase behavior of these systems can be found elsewhere (X2). Cubic ecjuations of state have been used successfully to describe the properties and phase behavior of multicomponent systems, particularly fot hydrocarbon mixtures (14.) The use of conventional ecjuations of state to describe properties of surfactant-supercritical fluid mixtures is not appropriate since they do not account for the formation of aggregates (the micellar pseudophase) or their solubilization in a supercritical fluid phase. A complete thermodynamic description of micelle and microemulsion formation in liquids remains a challenging problem, and no attempts have been made to extend these models to supercritical fluid phases. 

Widespread use of natural CyDs as hosts for drugs is restricted by their low aqueous solubility, particularly that of [3-CyD. Methylation or hydroxyalkylation of the hydroxyl groups of 3-CyD has been used to obviate this problem. For example, hydroxyalkylated CyDs are amorphous mixtures of chemically related components with different degrees of substitution. This multicomponent character prevents crystallization, and thus the hydroxyalkylated CyDs have higher solubility (>50%) in both water and ethanol. The solubility of natural [3-CyD in water increases with increase in temperature. On the other hand, 2,6-dimethyl-(3-CyD (DM-p-CyD) shows exothermic dissolution in water, so that the solubility decreases with increase in temperature, because of... 

In principle, the broad range of functional monomers eurrently available makes it possible to design an MIP specific for any type of stable ehemical compound. Currently the selection of the best monomers for polymer preparation is one of the most crucial issues in molecular imprinting. Thermodynamic calculations and combinatorial screening approaches olfer possible solutions, and have already been used successfully for predicting polymer properties and for the optimization of polymer compositions (see Ref. 9,57,58, and Chapter 8), however, in practical terms, application of these methods is not trivial. The problem lies in the technical difiiculty of performing detailed thermodynamic calculations on multicomponent systems and the amount of time and resources required for the combinatorial screening of polymers. To check a simple two-component combination of 100 monomers, for example, one has to synthesize and test more than 5000 polymers, a very difiicult task. This task will be further complicated by the possibility that these monomers could be used in monomer mixtures in dilferent ratios. 

Modeling of the behavior of multicomponent systems can be done using several methods and looking at the problem at different spatial scales. Eringen and co-workers [38,39] have developed the micromorphic theory of mixture of several constituents in anticipation of the possible application, for example, to crystal lattices in which the lattice sites are regularly occupied by two or more different ions or molecules, to granular or polycrystalline mixture, to composite materials, or to fluid suspensions. 

---