Infinite separation factor

The effect of reactant loss on membrane reactor performance was explained nicely in a study by Harold et al [5.25], who compared conversion during the cyclohexane dehydrogenation reaction in a PBMR equipped with different types of membranes. The results are shown in Fig. 5.4, which shows the cyclohexane conversion in the reactor as a function of the ratio of permeation to reaction rates (proportional to the ratio of a characteristic time for reaction in the packed bed to a characteristic time for transport through the membrane). Curves 1 and 2 correspond to mesoporous membranes with a Knudsen (H2/cyclohexane) separation factor. Curves 3 and 4 are for microporous membranes with a separation factor of 100, and curves 5 and 6 correspond to dense metal membranes with an infinite separation factor. The odd numbered curves correspond to using an inert sweep gas flow rate equal to the cyclohexane flow, whereas for the even numbered curves the sweep to cyclohexane flow ratio is 10. 

The most common method for screening potential extractive solvents is to use gas—hquid chromatography (qv) to determine the infinite-dilution selectivity of the components to be separated in the presence of the various solvent candidates (71,72). The selectivity or separation factor is the relative volatihty of the components to be separated (see eq. 3) in the presence of a solvent divided by the relative volatihty of the same components at the same composition without the solvent present. A potential solvent can be examined in as htfle as 1—2 hours using this method. The tested solvents are then ranked in order of infinite-dilution selectivities, the larger values signify the better solvents. Eavorable solvents selected by this method may in fact form azeotropes that render the desired separation infeasible. 

FIG. 16-14 Constant separation factor batch adsorption curves for external mass-transfer control with an infinite fluid volume and n j = 0. 

Both liquid and vapor phases are totally miscible. Conventional vapor/liqiiid eqiiilihriiim. Neither phase is pure. Separation factors are moderate and decrease as purity increases. Ultrahigh purity is difficult to achieve. No theoretical limit on recovery. Liquid phases are totally miscible solid phases are not. Eutectic system. Sohd phase is pure, except at eutectic point. Partition coefficients are very high (theoretically, they can be infinite). Ultrahigh purity is easy to achieve. Recovery is hmited by eutectic composition. 

The condition (9) expresses the fact that the s particles, whose phases are xx,. . . , xs at the instant t, were, in the far distant past t= — oo), infinitely separated from each other. There existed at this moment no correlation among these particles and, in these conditions, /, can be factorized into a product of fv... 

The thermodynamic connection between IE s on gas solubility, infinite dilution Henry s law constants, and transfer free energy IE s, implies that gas-liquid chromatography should be a convenient way to study solvent effect IE s. That in fact is the case, and many authors have reported on chromatographic isotope separations and on the interpretation of the separation factors in terms of the transfer free energy IE s (Section 8.5). 

In Equation 21, T is the absolute temperature, h is Planck s constant, is Boltzmann constant, and AG is the free energy barrier height relative to infinitely-separated reactants. The temperature-dependent factor r(7) represents quantum mechanical tunneling and the Wigner approximation to tunneling through an inverted parabolic barrier ... 

Activity coefficients at infinite dilution, of organic solutes in ILs have been reported in the literature during the last years very often [1,2,12,45,64, 65,106,123,144,174-189]. In most cases, a special technique based on the gas chromatographic determination of the solute retention time in a packed column filled with the IL as a stationary phase has been used [45,123,174-176,179,181-187]. An alternative method is the "dilutor technique" [64,65,106, 178,180]. A lot of y 3 (where 1 refers to the solute, i.e., the organic solvent, and 3 to the solvent, i.e., the IL) provide a useful tool for solvent selection in extractive distillation or solvent extraction processes. It is sufficient to know the separation factor of the components to be separated at infinite dilution to determine the applicability of a compound (a new IL) as a selective solvent. 

The obtained values of FX2 for these samples are plotted against time from solvent injection to establish the maximum value for the separation factor, F12 (max). Further details about the experimental technique are in the original paper (35). The larger the value of FX2 (max), the better the solvent can separate the mixture, indicating a better extractive distillation solvent. This was verified by comparing values for FX2 (max) and infinite dilution relative volatilities (a°i2) for the system n-hexane-benzene with six different solvents. The results presented in... 

Infinite Dilution Relative Volatilities through GLC. If the solvent amount injected in the column is high enough so that infinite dilution conditions for the injected solute prevail, it is readily shown (38) that the separation factor becomes equal to the infinite dilution relative volatility ... 

Doring (39) has shown that infinite dilution relative volatilities can be evaluated through GLC. He prepared a special column for each solvent under consideration, a tedious project. A year later Sheets and Marchello (38) showed that separation factors increase with increased amounts of injected solvent. Later Tassios (35) found out the same to... 

Table V. Separation Factors and Infinite Dilution Relative Volatilities for the System ft-Hexane (l)-Benzene (2) at 67°C (35)...

Figure 7. Relationship between maximum separation factors and infinite dilution relative volatilities for the system n-hexane-benzene with various solvents at 67°C (35)...

The definition of the separation factor, Equation 7, when combined with infinite reflux condition. Equation 11, gives... 

The evaluation of the separation factor enables characterization of the initial slopes of the adsorption isotherm for the product and neighboring impurities under various conditions. The term linear conditions means, under analytical conditions or under conditions where the injection size is small and the injection concentration is in the linear region of the ad.sorption i.sotherm. Retention experiments enable evaluation of the thermodynamics under infinite dilution. 

We consider methanol first. For a quick estimate of the separation factors that water can produce, we consider the limiting selectivity that would be obtained if the methanol and pentane were infinitely dilute in both the extract phase (water-rich) and the raffinate (pentane-rich) phases if we were to use liquid/ liquid extraction ... 

For absorption processes, the partition coefficients and the separation factors at infinite dilution can be calculated directly using Henry coefficients. 

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