Separation factor multicomponent

Relative volatility is the volatility separation factor in a vapor-liquid system, i.e., the volatility of one component divided by the volatility of the other. It is the tendency for one component in a liquid mixture to separate upon distillation from the other. The term is expressed as fhe ratio of vapor pressure of the more volatile to the less volatile in the liquid mixture, and therefore g is always equal to 1.0 or greater, g means the relationship of the more volatile or low boiler to the less volatile or high boiler at a constant specific temperature. The greater the value of a, the easier will be the desired separation. Relative volatility can be calculated between any two components in a mixture, binary or multicomponent. One of the substances is chosen as the reference to which the other component is compared. 

Displacement chromatography is suitable for the separation of multicomponent bulk mixtures. For dilute multicomponent mixtures it allows a simultaneous separation and concentration. Thus, it permits the separation of compounds with extremely low separation factors without the excessive dilution that would be obtained in elution techniques. 

For constant-separation factor systems, the /(-I rails formal ion of Helfferich and Klein (gen. refs.) or the method of Rhee et al. [AlChE J., 28, 423 (1982)] can be used [see also Helfferich, Chem. Eng. Sci., 46, 3320 (1991)]. The equations that follow are adapted from Frenz and Horvath [AlChE ]., 31, 400 (1985)] and are based on the h I ransiomialion. They refer to the separation of a mixture of M — 1 components with a displacer (component 1) that is more strongly adsorbed than any of the feed solutes. The multicomponent Langmuir isotherm [Eq. (16-39)] is assumed valid with equal monolayer capacities, and components are ranked numerically in order of decreasing affinity for the stationary phase (i.e., Ki > K2 > Km). 

Langmuir isotherm or model Simple mathematical representation of a favorable (type I) isotherm defined by Eq. (2) for a single component and Eq. (4) for a binary mixture. The separation factor for a Langmuir system is independent of concentration. This makes the expression particularly useful for modeling adsorption column dynamics in multicomponent systems. 

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. 

A frequently used indicator of how much two gases (say, gas m and gas n) in a multicomponent gaseous mixture are separated with respect to each other through a membrane is called separation factor. It is defined as... 

Generally, alcohols showed higher separation factors when present in model multicomponent solutions than in binary systems with water. On the other hand, aldehydes showed an opposite trend. The acmal tea aroma mixmre showed a rather different behavior from the model aroma mixmre, probably because of the presence of very large numbers of unknown compounds. Overall, the PDMS membrane with vinyl end groups used by Kanani et al. [20] showed higher separation factors and fluxes for most of the aroma compounds. Pervaporation was found to be an attractive technology. However, as mentioned above the varying selectivities for the different aroma compounds alter the sensory prohle and therefore application of PV for recovery of such mixmres needs careful consideration on a case-by-case basis. 

The number of theoretical stages is first determined by well-known shortcut methods and then by a multicomponent simulation of the separation process. Both parts can and will be used for analyzing the separation process with respect to the effect of separation factor, reflux ratio (the amount of top product reintroduced to the separation), degree of separation etc. on the number of theoretical stages. There, computational methods provide insight into the separation process without actually carrying out the separation. 

A better insight into composition of phases along the separation process is provided by multicomponent process simulation as it can be carried out with commercial process simulating programs, such as ASPEN-h. As usual, the process is separated into theoretical stages. Normally, ASPEN+ provides thermodynamic models and calculates thermodynamic properties such as the distribution coefficients and separation factors. As the accuracy of these results is not sufficient for a design analysis in many cases, distribution coefficients (and if necessary solubilities) can be provided by a user-defined module which uses empirical correlations for these values. 

Also from Figure 1.15 it can be seen that resolution is impossible without retention. Initially resolution increases rapidly with retention for k > 0. By the time the retention factor reaches a value of around 5, further increases in retention result in only small changes in resolution. The optimum resolution range for most separations occurs for k between 2 and 10. Higher values of k result in excessive separation time with little concomitant improvement in resolution. On the other hand, large values of k do not result in diminished resolution and may be required by necessity for the separation of multicomponent mixtures to accommodate all of the sample components in the separation. 

This justifies the use of Henry constants for prehminary screening of selective adsorbents, but in practice a significant loading dependence of the separation factor is generally observed as a result of deviations from the binary (or multicomponent) Langmuir model. 

Generally, alcohols showed higher separation factors when present in model multicomponent solutions than in... 

The theoretical treatment of multicomponent ion exchange is quite complex, especially if it involves species of different valency. The treatment of ion-exchange equilibria involving only ions of the same valence is quite straightforward since it can be assumed that the selectivity coefficient or separation factor is constant over the complete range of ionic concentration. 

Different regions of the variable space will often be associated with different critical peak-pairs. The resolution of a multicomponent mixture thus requires an analysis involving all components in the whole variable space. Inspection of the contour maps of global resolution will allow the evaluation of the robustness of the optimum. Figure 8.16 shows the contour maps for the separation of a set of fifteen phenols (the same cited previously in this chapter), with mobile phases of CTAB and 2-propanol, where an efficiency N = 2500 was considered for all solutes. For the positional criterion (separation factor), the optimum was found for a mobile phase of 0.12 M CTAB-10% 2-propanol (Fig. 8.16a, upper comer of the variable space), whereas for the valley-to-peak criterion it was 0.102 M CTAB-10% 2-propanol (Fig. 8.16b), and for the overlapped fi-actions, 0.107 M CTAB-10% 2-propanol (Fig. 8.16c). 

In most commercial process simulators, model parameters for pure component properties and binary parameters can be found for a large number of compounds and binary systems. However, the simulator providers repeatedly warn in their software documentations and user manuals that these default parameters should be applied only after careful examination by the company s thermodynamic experts prior to process simulation. For verification of the model parameters again, a large factual data bank like the DDE is the ideal tool. The DDE allows checking all the parameters used for the description of the pure component properties as a function of temperature and of the binary parameters of a multicomponent system by access to the experimental data stored. On the basis of the results for the different pure component properties and phase equilibria, excess enthalpies, activity coefficients at infinite dilution, separation factors, and so on, the experienced chemical engineer can decide whether all the data and parameters are sufficiently reliable for process simulation. 

In most cases not binary but multicomponent systems have to be separated. Sometimes an additional component is needed as an entrainer e.g. for the separation by extractive distillation. As an example selected separation factors of 12 for the system benzene (l)-cyclohexane (2)-NMP (3) calculated using modified UNIFAC and default UNIQUAC parameters from a simulator are shown in Figures 11.8 and 11.9, respectively. As benzene and cyclohexane form an azeotrope, the main task of the entrainer NMP is to shift the separation factor between benzene and cyclohexane as far from unity as possible this means au 1 or au 1- In practice, typical entrainer concentrations of 50-80 mol% are employed to achieve satisfying separation factors. A higher entrainer concentration usually improves the separation factor. 

In Chapter 8 the equilibrium factor for a single adsorbed species was defined by analogy with the relative volatility. This definition is easily extended to a binary or multicomponent system. For competitive sorption the binary separation factor is defined by... 

The equilibrium factor measures the affinity of the adsorbent for a particular component relative to the same component in the fluid phase whereas the binary separation factor measures the relative preference of the adsorbent for two different competing adsorbates. If the equilibrium obeys the multicomponent Langmuir model ... 

With the definition given above, the smaller the value of the more strongly held is component / relative to component j. Following Helfferich and Vermeulen it has become conventional to define the separation factor for a multicomponent system (a, ) as the reciprocal of Py. 

The equilibrium theory of binary and multicomponent isothermal adsorption systems appears to have been first developed by Glueckauf. More general and comprehensive treatments have been developed by Rhee, Aris, and Amundson and by Helfferich and Klein. The former treatment exploits the analogy between chromatographic theory and the theory of kinematic waves. The detailed quantitive theory has been developed only for ideal Langmuir systeiris without axial dispersion or mass transfer resistance and in which the initial and boundary conditions represent constant steady states. Subject to these constraints the treatment is sufficiently general to allow the dynamic behavior to be predicted for systems with any number of components, provided only that the separation factors are known. In the... 

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