Arheotrope

Section 4.3 elucidates the role of vapor-liquid mass transfer resistances on the feasible products of nonreactive or reactive separation processes. The latter are considered under chemical equilibrium conditions (i.e., they are very fast reactions). The feasible products are denoted as arheotropes. 

The definition of, and the necessary conditions for, the existence of an arheotrope are based on the material balances of a batch distillation process in the presence of a stagnant or flowing sweep gas (Fig. 4.13). Let us first consider a nonreactive liquid mixture. In this case, the component and total mass balances are given by ... 

As a special case, if the relative flux equals the vapor phase bulk composition y being in equilibrium with the liquid bulk phase composition xu then we speak of a nonreactive azeotrope. Thus, the azeotropic case can be seen as a limiting case of the arheotropic case. 

Figure 4.15 shows the calculated residue curves according to Eq. (51) at various temperatures in the still, while the temperature at the condenser was kept constant by evaporation of water due to natural convection. The azeotropic concentration of this mixture (xi = 62 mol%) in practical terms does not vary much with pressure and temperature. The arheotropic iso-propanol content at 50 °C is as low as 38 % and will not decrease much further at even lower still temperatures. The minimum arheotro-... 

Figure 4.18 shows the function i(xi) - both predicted and measured - for the binary mixture of iso-propanol and water for various sweep gas inlet humidities, thus exhibiting various arheotropic compositions. For zero air humidity there is only one unstable arheotrope at 50 mol% of iso-propanol. For 7.2 g H2O kg-1 air, which corresponds to a typical winter climate (in Germany), we obtain two arheotropes -an unstable one at 58 mol% and a stable one at 90 mol%. 

For 16.1 g H2O kg-1 air, which corresponds to a typical summer climate, no arheotropes appear at all. Within those two regimes where %i > 1 (i.e., %2 < 0), evaporation of water reverses into condensation. Because of the low evaporation rate at 30 °C the liquid phase mass transfer resistance is negligibly small. 

Figure 4.21 shows the selectivity Si as a function of the iso-propanol concentration at various pore diameters dp. The gas phase-controlled arheotrope was chosen to be at 50 mol% iso-propanol. Surprisingly, on the left-hand side the arheotrope Si showed almost the same magnitude as the one for a free interface, provided that the pore diameters were not too small, while on the right-hand side the selectivity was absolutely zero, as to be expected. The reason for this unexpected phenomenon is as follows. 

This example considers distillation of a reacting ternary mixture in an open batch distillery with flowing sweep gas. From this example, one can see the determination of reactive azeotropes and reactive arheotropes . The considered hypothetical reaction is... 

Equation (81) can also be used to predict the existence of reactive arheotropes provided that the mixture is in permanent chemical equilibrium - that is, the Damkohler number is sufficiently large. The condition which must be fulfilled has been given by Frey and Stichlmair [30], who concluded that the slope of the nonreacting residue curve must coincide with the slope of the stoichiometric lines of the chemical reaction, given by the stoichiometric coefficients vu... 

Inserting Eq. (82) into Eq. (81) gives the qualifying Eq. (83) to predict the locus curve X],uz = l ),ky(xi,az) at which possible reactive arheotropes can be found (i.e., the potential singular point surface, PSPS). The second curve is given by the equation describing the chemical equilibrium x>az = Fchem(xi az)-... 

Figure 4.23 shows the curves according to Eq. (83) and Eq. (85) for various sweep gas flow rates G and vanishing liquid phase mass transfer resistance (i.e., Kiiq = 1). The points of intersection with the chemical equilibrium line mark the concentrations at which reactive arheotropes exist As can be seen, the reactive arheotrope... 

Figure 4.24 shows the reactive arheotrope trajectories according to Eq. (83) for various amounts of the liquid phase mass transfer resistance - that is, for various values of Kiiq and a low sweep gas flow rate G (at large NTt/ -values). As a result, the reactive arheotropic composition X, 02 is shifted to larger values as the liquid phase mass transfer resistance becomes more important - that is, as the value of Kuq decreases. Note that the interface liquid concentrations are in equilibrium with the vapor phase bulk concentrations. Therefore, gas phase mass transfer resistances cannot have any influence on the position of the reactive arheotrope compositions. On the other hand, liquid phase mass transfer resistances do have an effect, though the value of all binary hiq have been set equal. Again, this effect results from the competition between the diffusion fluxes and the Stefan flux in the liquid phase. 

This gives rise to a warning In feasibility studies for an open batch distillation process certain assumptions are made as to the heating policy (see e.g. Ref. [7]). Since the ratio of the evaporation velocity to the liquid phase mass transfer coefficient uiiq/knq also depends on the heating policy , one must ensure that this ratio is sufficiently low otherwise the composition of the reactive arheotrope will also depend on the heating policy. ... 

Figure 4.25 shows the reactive arheotrope trajectories according to Eq. (83) for various amounts of the liquid phase mass transfer resistance - that is, for various values of Kuq and larger sweep gas flow rates G = Vsweepgas/Aph. With increasing sweep gas flow rate the effect of the liquid phase mass transfer resistance vanishes, and at G = 0.4 m s-1 the reactive arheotropic composition X Mz is practically not affected at all. 

Fig. 4.25. Reactive arheotropes for the reaction A + B 2 C at various liquid phase mass transfer resistances Knq (large sweep gas flow rate C, Da -> , an = 5, 0 23 = 3, kl.gos = 0.5 cm s-, ...

The aim of this section is to show that in an open batch distillation process both gas-phase and liquid-phase mass transfer resistances have a remarkable effect on the compositions at which nonreactive arheotropes and reactive arheotropes appear. 

At kinetically controlled reactive conditions (Da = 1), Fig. 4.28(b) shows that the stable node moves into the composition triangle, as in reactive distillation (Fig. 4.27(b)). This point is termed the kinetic arheotrope because its location in the phase diagram depends on the membrane mass transfer resistances and also on the rate of chemical reaction. The kinetic arheotrope moves towards the B vertex with increasing C-selectivity of the membrane. At infinite Damkohler number, the system is chemical equilibrium-controlled (Fig. 4.28(c)), and therefore the arheotrope is located exactly on the chemical equilibrium curve. In this limiting case, it is called a reactive arheotrope . 

Nonreactive membrane separation Da = 0 and [k] is a non-scalar matrix. Then, the condition for a nonreactive arheotrope (Eq. (50)) is recovered ... 

Reactive membrane separation [k]-matrix is a non-scalar matrix. This case was intensively studied by Huang et al. [20] ( kinetic arheotrope ). 

For a more generalized analysis of the qualitative influence of membranes on the singular points, the reactive membrane separation process is now considered with a nondiagonal [/c]-matrix. The condition for a kinetic arheotropes is given by... 

A singular point of reactive membrane separation should be denoted as kinetic arheotrope because it is a process phenomenon rather than a thermodynamic phenomenon. The condition for arheotropy can be elegantly expressed in terms of new transformed variables, which are a generalized formulation of the transformed composition variables first introduced to analyze reactive azeotropes. 

In order to denote singular points, a clear terminology is needed. The well-known term a-zeo-trope should only be used for phase equilibrium-controlled singular points, whilst the newer term, a-rheo-trope, is proposed for mass transfer-controlled processes. Translated, the latter term means that the composition is not changing with flux . The different types of azeotropes and arheotropes, together with the names of those investigators who were the first to deal with these singular points, are summarized in Tab. 4.4. 

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