Multicomponent mixtures reversibility

When multicomponent mixtures are to be separated into three or more products, sequences of simple distillation columns of the type shown in Fig. 13-1 are commonly used. For example, if aternaiy mixture is to be separated into three relatively pure products, either of the two sequences in Fig. 13-4 can be used. In the direct sequence, shown in Fig. 13-4, all products but the heaviest are removed one by one as distillates. The reverse is true for the indirect sequence, shown in Fig. 13-4 7. The number of possible sequences of simple distillation columns increases rapidly with the number of products. Thus, although only the 2 sequences shown in Fig. 13-4 are possible for a mixture separated into 3 products, 14 different sequences, one of which is shown in Fig. 13-5, can be synthesized when 5 products are to be obtained. 

In practice, RSPs rarely operate at thermodynamic equilibrium. Therefore, some correlation parameters, such as tray efficiencies or HETS values, have been introduced to adjust the equilibrium-based theoretical description to reality. For multicomponent mixtures, however, this concept often fails, since diffusion interactions of several components result in unusual phenomena such as osmotic or reverse... 

Extractive distillation is commercially used for separating mixtures of butanes, butenes, butadienes, and various acetylenes with four carbon atoms (13). Separating these multicomponent mixtures by fractional distillation is very difficult because the natural volatilities pf the various components, paraffinic as well as olefinic, overlap considerably. For instance, n-butane is less volatile than 1-butene but more volatile than cis-and trans-2-butenes. Thus, separation of butanes from butenes is more difficult by fractional distillation than by extractive distillation where the solvent increases the volatilities of all the butanes to make them greater than the butene volatilities. For 1,3-butadiene recovery extractive distillation is also more attractive than ordinary distillation because the large polarizability of the conjugated double bonds interacts strongly with the polar solvent. Also, in C4 hydrocarbon separations the solvent often only enhances and does not reverse the natural relative volatility for many of the components however, even for those components for which the rela-... 

In mass transfer apparatus one of two processes can take place. Multicomponent mixtures can either be separated into their individual substances or in reverse can be produced from these individual components. This happens in mass transfer apparatus by bringing the components into contact with each other and using the different solubilities of the individual components in the phases to separate or bind them together. An example, which we have already discussed, was the transfer of a component from a liquid mixture into a gas by evaporation. In the following section we will limit ourselves to mass transfer devices in which physical processes take place. Apparatus where a chemical reaction also influences the mass transfer will be discussed in section 2.5. Mass will be transferred between two phases which are in direct contact with each other and are not separated by a membrane which is only permeable for certain components. The individual phases will mostly flow countercurrent to each other, in order to get the best mass transfer. The separation processes most frequently implemented are absorption, extraction and rectification. 

The differential form of the energy balance for a multicomponent mixture can be written In a variety of forms.1 6 It would contain terms reprenenting heat conduction and radiation, body forces, viscous dissipation, reversible work, kinetic energy, and the substantial derivative of the enthalpy of die mixture. Its formulation is beyond the scope of this chapter. Certain simplifled forms will be used in later chapters in problems such as simultaneous heal and mass transfer in air-water operations or thermal effects in gas absorbent. 

The RCMC method allows for Monte Carlo moves in the reaction coordinates of a multicomponent mixture that enhances the convergence to the equilibrium composition. Reactions are sampled directly, avoiding the problem of traversing high energy states to reach the lower energy states. In this section we derive the microscopically reversible acceptance probability for RCMC. 

As shown above, reaction kinetics have a significant influence on RD process performance in binary mixtures and the same is true for multicomponent mixtures. In the following, the attainable products of kinetically controlled RD processes are analyzed, first for ideal ternary mixtures, then for non-ideal ternary mixtures occurring in industrially important fuel ether synthesis, and finally for an extremely non-ideal system with potential liquid-phase splitting. In all cases, reversible reactions of type A + B o C are considered. 

Consider a container filled with a one-phase multicomponent mixture of composition x the container is immersed in a reservoir that imposes its temperature T and pressure P on the mixture. The container is fitted with a single inlet by which more material can be reversibly injected, as shown schematically in Figure 3.9. The process considered here is addition to the container of a small amount of pure component 1. The reversible work associated with this process is given by (3.7.14) for an isobaric injection of material through one inlet with no outlets, (3.7.14) reduces to... 

Low Temperature Electrical Resistance of Fifteen Commercial Conductors (1 156 REVERSIBLE PROCESSES The Reversible Separation of Multicomponent Mixtures (2) 27 The Reversible Separation of Multicomponent Mixtures (3) 47 Hydrogen Separation—A Compromise with Reversibility (4) 319 SEPARATION [see also DISTILLATION]... 

The Effect of Some Variables in Low Temperature Processes (1) 342 The Reversible Separation of Multicomponent Mixtures (2) 27 Gas Chromatography as Applied to the Industrial Separation of Neon from Nitrogen and Helium (2) 197... 

The Reversible Separation of Multicomponent Mixtures (3) 47 Hydrogen Separation—A Compromise with Reversibility (4) 319... 

As far as only one component can be exhausted in each section of the reversible distillation column (i.e., this component is absent in the product of this section), the system of columns shown in Fig. 4.4 (for n = 3) or in Fig. 4.5 (for n = 4) will be required to perform the complete separation of a multicomponent mixture into pure components. 

The following main peculiarities of the columns of reversible distillation for separation of multicomponent mixtures into pure components arise from the aforesaid ... 

The location of trajectory bundles and possible product composition segments at reversible distillation of three-component mixtures determines the location of trajectory bundles, and of possible product composition regions of multicomponent mixtures and the locations of trajectory bundles of real adiabatic columns. 

Trajectories Bundles of Reversible Distillation for Multicomponent Mixtures 93... 

Grunberg, J. (1960). Reversible Separation of Multicomponent Mixtures. In Advances in Cryogenic Engineering Proceedings of the 1956 Cryogenic Engineering Conference, Vol. 2, New York, pp. 27-38. 

To understand the structure of section trajectory bundles for multicomponent mixtures and their evolution with the increase of reflux number, let s examine first three-component mixtures, basing on the regularities of distillation trajectory tear-off at finite reflux and the regularities of location of reversible distillation trajectories. 

Later, these columns were independently rediscovered (Petlyuk, Platonov, Slavinskii, 1965 Platonov, Petlyuk, Zhvanetskiy, 1970) on the basis of theoretical analysis of thermodynamically reversible distillation because this distillation complex by its configuration coincides with the sequence of thermodynamically reversible distillation of three-component mixture (see Chapter 4), but in contrast to this sequence it contains regular adiabatic columns. The peculiarities of Petlyuk columns for multicomponent mixtures are (1) total number of sections is n(n - 1) instead of 2(n - 1) in regular separation sequences (2) it is sufficient to have one reboiler and one condenser (3) the lightest and the heaviest components are the key components in each two-section constituent of the complex and (4) n components of a set purity are products. 

Traditional equilibrium stage models and efficiency approaches are often inadequate for reactive separation processes. In multicomponent mixtures, diffusion interactions can lead to unusual phenomena, and it is even possible to observe mass transport of the component in the direction opposite to its own driving force - the so-called reverse diffusion (Talyor and Krishna, 1993). For multicomponent systems, the stage efficiencies are different for different components and may range from -< to + >. To avoid possible qualitative errors in the parameter estimation, it is necessary to model... 

Ideal Adsorbed Solution Theory. Perhaps the most successful approach to the prediction of multicomponent equiUbria from single-component isotherm data is ideal adsorbed solution theory (14). In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equiUbrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equihbrium pressure for the pure component at the same spreadingpressure. The theoretical basis for this assumption and the details of the calculations required to predict the mixture isotherm are given in standard texts on adsorption (7) as well as in the original paper (14). Whereas the theory has been shown to work well for several systems, notably for mixtures of hydrocarbons on carbon adsorbents, there are a number of systems which do not obey this model. Azeotrope formation and selectivity reversal, which are observed quite commonly in real systems, ate not consistent with an ideal adsorbed... 

Zhou and Pietrzyk [41] found that increasing the mobile-phase ionic strength not only increases the retention of AS and AES on a reversed stationary phase, but also improves the resolution since the peak widths are significantly reduced. The authors achieved baseline separation of a multicomponent alkane sulfonate and alkyl sulfate mixture from C2 to Cis using a mobile-phase gradient whereby acetonitrile concentration increases and LiOH concentration decreases. 

Colistin (COL) is a multicomponent antibiotic (polymyxins E) that is produced by strains of inverse Bacillus polymyxa. It consists of a mixture of several closely related decapeptides with a general structure composed of a cyclic heptapeptide moiety and a side chain acetylated at the N-terminus by a fatty acid. Up to 13 different components have been identified. The two main components of colistin are polymyxins El and E2 they include the same amino acids but a different fatty acid (216). A selective and sensitive HPLC method was developed for the determination of COL residues in milk and four bovine tissues (muscle, liver, kidney, and fat). The sample pretreatment consists of protein precipitation with trichloracetic acid (TCA), solid-phase purification on Cl 8 SPE cartridges, and precolumn derivatization of colistin with o-phthalaldehyde and 2-mercaptoethanol in borate buffer (pH 10.5). The last step was performed automatically, and the resulting reaction mixture was injected into a switching HPLC system including a precolumn and the reversed-phase analytical column. Fluorescence detection was used. The structural study of El and E2 derivatives was carried out by HPLC coupled with an electrospray MS. Recoveries from the preseparation procedure were higher than 60%. 

Although the multicomponent Langmuir equations account qualitatively for competitive adsorption of the mixture components, few real systems conform quantitatively to this simple model. For example, in real systems the separation factor is generally concentration dependent, and azeotrope formation (a = 1.0) and selectivity reversal (a varying from less than 1.0 to more than 1.0 over the composition range) are relatively common. Such behavior may limit the product purity attainable in a particular adsorption separation. It is sometimes possible to avoid such problems by introducing an additional component into the system which will modify the equilibrium behavior and eliminate the selectivity reversal. 

In a binary mixture, diffusion coefficients are equal to each other for dissimilar molecules, and Fick s law can determine the molecular mass flows in an isotropic medium at isothermal and isobaric conditions. In a multicomponent diffusion, however, various interactions among the molecules may arise. Some of these interactions are (i) diffusion flows may vanish despite the nonvanishing driving force, which is known as the mass transfer barrier, (ii) diffusion of a component in a direction opposite to that indicated by its driving force leads to a phenomenon called the reverse mass flow, and (iii) diffusion of a component in the absence of its driving force, which is called the osmotic mass flow. 

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