Multicomponent mixtures, alternate

An alternative method, particularly useful for the separation of multicomponent mixtures of hydrocarbons, is to use the simple relation yA = KxA. K values have been measured for a wide range of hydrocarbons at various pressures, and some values are shown in Figure 11.39. 

Binary systems of course can be handled by the computer programs devised for multicomponent mixtures that are mentioned later. Constant molal overflow cases are handled by binary computer programs such as the one used in Example 13.4 for the enriching section which employ repeated alternate application of material balance and equilibrium stage-by-stage. Methods also are available that employ closed form equations that can give desired results quickly for the special case of constant or suitable average relative volatility. 

There can be several alternative STNs for multicomponent mixtures depending on the number of main-cuts and off-cuts to be produced. The two basic modules of Figures 3.2 and 3.3 can be combined as many times as required to describe the entire operation. A few alternative STNs for ternary batch distillation are given in Figures 3.5-3.7 as the combination of these two basic modules. 

Mujtaba (1989) suggested an alternative strategy to collect and store the off-cuts separately and recycle each of them to the reboiler in sequential order (Figure 3.31). Quintero-Marmol and Luyben (1990) discussed a similar recycling strategy. They also considered other alternative off-cuts handling strategies for multicomponent mixtures. 

In sections 6.2 to 6.4, the formulation and solution method proposed by Mujtaba and Macchietto (1993) will be presented in detail. Several example problems (involving binary and multicomponent mixtures) from Mujtaba and Macchietto are also presented to demonstrate the idea. Operational alternatives involving separations of binary and multicomponent mixtures are presented in detail in Chapter 3. 

Another class of separation problem attacked has been that of designing the most effective thermally coupled distillation column arrangement to separate a multicomponent mixture. Sargent and Gaxninibandara (1975) present a general column superstructure which they optimize. Imbedded in the superstructure are all the alternative thermally coupled and ordinary column sequences to be considered. The optimization eliminates those portions of the superstructure which are not economic leaving, hopefully, the optimal substructure. 

In principle, mixtures containing a very large number of components behave in a way described by the same general laws that regulate the behavior of mixtures containing only a comparatively small number of components. In practice, however, the procedures for the description of the thermodynamic and kinetic behavior of mixtures that are usually adopted for mixtures of a few components rapidly become cumbersome in the extreme as the number of components grows. As a result, alternate procedures have been developed for multicomponent mixtures. Particularly in the field of kinetics, and to a lesser extent in the field of phase equilibria thermodynamics, there has been a flurry of activity in the last several years, which has resulted in a variety of new results. This article attempts to give a reasoned review of the whole area, with particular emphasis on recent developments. 

It is possible to use alternative formulations considering mole fractions rather than mass fractions. For most cases, mass fraction formulations will be adequate. An estimation of the diffusion coefficient (of component k) in a multicomponent mixture Dkm) however, is not straightforward. For mixtures of ideal gases, the diffusion coefficient in a mixture can be estimated as (Hines and Maddox, 1985)... 

This program can be used to create a new input file for a multicomponent liquid mixture and then to calculate the isothermal bubble point pressure and the composition of the coexisting vapor phase for this mixture. In this mode the information needed is the number of components (up to a maximum of ten), the liquid mole fractions, the temperatures at which calculations are to be done (for the number of sets of calculations, as the the user wishes, up to a maximum of fifty), critical temperatures, pressures (bar), acentric factors, the constants of the PRSV equation for each compound in the mixture, and, if available, the experimental bubble point pressure and vapor phase compositions (these last entries are optional, and are used for a comparison between the experimental and calculated results). In addition, the user is requested to supply model parameters for each pair of components in the multicomponent mixture. These model parameters can be obtained using the program WS (see Appendix D.5) if experimental data are available for each of the binary pairs. Alternatively, the user can select an already existing file (for tliese files we use the extensions WSN, WSW, and WSU, respectively, for the W,S-NRTL, WS-WILSON, and WS-UNIQUAC options, and some examples are provided on the accompanying disk) and calculate the multicomponent VLE for the mixture of that input file. 

An alternative to the complete Maxwell-Stefan model is the Wilke approximate formulation [103]. In this model the diffusion of species s in a multicomponent mixture is written in the form of Tick s law with an effective diffusion coefficient instead of the conventional binary molecular diffusion coefficient. Following the ideas of Wilke [103] we postulate that an equation for the combined mass flux of species s in a multicomponent mixture can be written as ... 

Due to the tremendous costs associated to distillative separations, many alternate schemes to the simple column shown above have been proposed over the past several years both to improve on some of its inherent costs. Traditionally, when purifying a multicomponent mixture, an entire series of distillation columns are used in series, and the way in which these columns are sequenced may make a tremendous difference in the eventual process costs. However, due to the large energy requirements of even the most optimal sequence, more complex column arrangements have been proposed and subsequently utilized. These arrangements include thermally coupled columns such as side rectifiers and strippers, the fully thermally coupled columns (often referred to as the Petlyuk and Kaibel columns). 

Here Ax, = X - x° and the derivative is constant with composition because it represents the slope of the ideal-solution straight line. For binary mixtures, this derivative is well defined but for multicomponent mixtures, it is not, because many ways exist to vary one mole fraction while constraining others. The resolution of this ambiguity provides alternative standard states for multicomponent mixtures, as we shall see. 

Phase Equilibria. From recent research (Schneider and Peters) it became apparent that in the near-critical region of certain ternary carbon dioxide mixtures, due to co-solvency effects of the two solutes relative to each other, the fluid multiphase behavior can be quite complex. Phenomena like immiscibility windows and holes are not unusual, which have their consequences for separations in near-critical processing. Peters stressed that for many applications in supercritical technology carbon dioxide is not an appropriate choice since for many solutes it is a poor solvent that would require the use of a cosolvents. If safety and environmental constraints permit, it is certainly worthwhile to consider alternatives for carbon dioxide. Gulari, Schneider and Peters emphasized the importance of studying representative model systems in order to obtain insight into the systematic variations of the complex phase behavior that may occur in near-critical multicomponent mixtures. Debenedetti stressed the importance of focusing on complex fluids like emulsions. 

Not all mixtures are amenable to this approach, or are perhaps amenable in principle but would require an impracticably complicated scheme of analysis. But with the right strategy, and preferably with some crosschecking by using alternative routes or a mass balance, a high proportion of multicomponent mixtures can be analysed by the techniques described in the preceding chapters. 

The synthesis of partially thermally coupled column configurations for a multicomponent distillation has b n studied in the context of the thermodynamic equivalent structures. There has been formulated a conqtlete space of the possible thermodynamic equivalent alternatives of the partially coupled (PC) configurations for multicomponent mixtures. A formula is presented to calculate the number of all the partially coupled schemes for any n-conqx)nent mixture. The formulated alternatives of all the possible arrangements of PC configurations provide a complete subspace for optimal design of multicomponent distillation systems not only for the economics, but also for column equipment designs. 

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