Kinetic azeotrope

Section 4.2 is focused on phase equilibrium-controlled vapor-liquid systems with kinetically or equihbrium-controlled chemical reactions. The feasible products are kinetic azeotropes or reactive azeotropes, respectively. 

For example 2, Figs. 4.4(a) and (b) show the bifurcations of all singular points with respect to the Damkohler numbers of the reactive condenser and the reactive reboiler, respectively. As can be seen from the feasibility diagram in Fig. 4.4(c), at Damkohler numbers Dac > 0.830, two possible condenser products - that is, the top products of a fully reactive distillation column, are predicted. The kinetic azeotrope in the reactive reboiler is always the possible bottom product of a column. 

Fig. 4.8(b)). At Damkohler numbers Dac> 0.085 and Dar> 0.166, pure isobutene and pure MeOH are feasible top and bottom products, respectively. At Dar< 0.166, both pure MeOH and a kinetic azeotrope (i.e., the mixture on the branch from MTBE to the pinch point) are possible bottom products, while another kinetic azeotrope (i.e., the mixture on the branch between isobutene and the nonreactive azeotrope isobutene-MeOH) is the possible top product. 

At Da = 0.4 (Fig. 4.29(b)), the two saddle points from the pure vertices move into the composition triangle. The stable node from the 1,4-BD vertex moves to the kinetic azeotrope at x = (0.0328, 0.6935). Pure water and pure THF now become stable nodes. The unstable node between water and THF remains unmoved, and forms two separatrices with the two saddle points. Thereby, the whole composition space is divided into three subspaces which have each a stable node, namely pure water, pure THF and the kinetic azeotrope. 

Reactive distillation Da 0 and [k] is a scalar matrix. This case was intensively studied by Qi et al. [14], who analyzed the existence and location of reactive and kinetic azeotropes. 

The first quantitative model, which appeared in 1971, also accounted for possible charge-transfer complex formation (45). Deviation from the terminal model for bulk polymerization was shown to be due to antepenultimate effects (46). Mote recent work with numerical computation and C-nmr spectroscopy data on SAN sequence distributions indicates that the penultimate model is the most appropriate for bulk SAN copolymerization (47,48). A kinetic model for azeotropic SAN copolymerization in toluene has been developed that successfully predicts conversion, rate, and average molecular weight for conversions up to 50% (49). 

Note It is essential to carefully examine the analytical data for the presence of cyclic compounds as a result of side reactions involved. The cyclization occurs as dendrimer amidation versus bridging amidation are kinetically similar. To prevent the intradendrimeric cyclization a large excess (50-fold) of 1,2-ethylenediamine is required. The excesses are removed to an undetectable level by azeotropic techniques. 

Figure 4.33 illustrates the PSPS and bifurcation behavior of a simple batch reactive distillation process. Qualitatively, the surface of potential singular points is shaped in the form of a hyperbola due to the boiling sequence of the involved components. Along the left-hand part of the PSPS, the stable node branch and the saddle point branch 1 coming from the water vertex, meet each other at the kinetic tangent pinch point x = (0.0246, 0.7462) at the critical Damkohler number Da = 0.414. The right-hand part of the PSPS is the saddle point branch 2, which runs from pure THF to the binary azeotrope between THF and water. 

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. 

The number of plates (defining the column configuration), feed, feed composition, column holdup, etc. for the problem are given in Table 4.9 (Chapter 4). The vapour-liquid equilibrium data and the kinetic data are taken from Simandl and Svrcek (1991) and Bogacki et al. (1989) respectively and are shown in Table 4.10 (Chapter 4). The vapour and liquid enthalpies are calculated using the data from Reid et al. (1977). As mentioned in Chapter 4, these data do not account for detailed VLE calculations and for any azeotropes formed. 

The kinetics of a reaction rate has a substantial influence on residue curve maps. Distillation boundaries and physical azeotropes can vanish, while other singular points due to kinetic effects might appear. The influence of the kinetics on RCM can be studied by integrating Eq. (A. 10) for finite Da numbers. In addition, the singular points satisfy the relation ... 

Summing up, the influence of the kinetics of a chemical reaction on the vapor-liquid equilibrium is very complex. Physical distillation boundaries may disappear, while new kinetic stable and unstable nodes may appear. As result, the residue curve map with chemical reaction could look very different from the physical plots. As a consequence, evaluating the kinetic effects on residue curve maps is of great importance for conceptual design of reactive distillation systems. However, if the reaction rate is high enough such that the chemical equilibrium is reached quickly, the RCM simplifies considerably. But even in this case the analysis may be complicated by the occurrence of reactive azeotropes. 

The accuracy of the thermodynamic data has a significant effect on RCM computation. In the case of slow reactions both kinetics and phase equilibrium should be modelled accurately. If the reaction is fast enough the chemical reaction prevails. In many cases chemical equilibrium may be taken as the reference. Consequently, accurate knowledge of the chemical equilibrium constant is needed. When reactive azeotropes and/or phase splitting might occur accurate modelling of phase equilibrium is also needed. 

Hence, within the framework of the traditional kinetic model (2.8) there is a mathematically rigorous solution of the problem of the calculations of the azeotropic composition x under the copolymerization of any number of monomer types knowing their reactivity ratios, i.e. the elements of matrix ay. However, since the values of au can be estimated from the experiment with certain errors Say, the calculated location of azeotrope x is also determined with an accuracy, the degree of which is characterized by vector 8x with components 8xj (k = 1,2,..., m) and modulus 8X ... 

The calculations of the statistical characteristics of such polymers within the framework of the kinetic models different from the terminal one do not present any difficulties at all. So in the case of the penultimate model, Harwood [193-194] worked out a special computer program for calculating the dependencies of the sequences probabilities on conversion. Within the framework of this model, Eq. (5.2) can be integrated in terms of the elementary functions as it was done earlier [177] in order to calculate copolymer composition distribution in the case of the simplified (r 2 = Fj) penultimate model. In the framework of the latter the possibility of the existence of systems with two azeotropes was proved for the first time and the regions of the reactivity ratios of such systems [6] were determined. In a general version of the penultimate model (2.3-24) the azeotropic compositions x = 1/(1 + 0 ) are determined [6] by the positive roots 0 =0 of the following... 

The results of the above analysis are not restricted within the framework of the simplest kinetic scheme (2.8) and allow one to consider similarly the copolymerization described by the more complex models. In particular, in the case of the penultimate model (2.3), systems which have the stable inner azeotrope are possible. Hence when the initial compositions x° are located inside its basin, one should know for certain whether this azeotrope is regular or not. If the regularity condition Re Ax > — 1 in the following form [14, 18] ... 

The situation becomes more complicated when the reaction is kinetically controlled and does not come to complete-chemical equilibrium under the conditions of temperature, liquid holdup, and rate of vaporization in the column reactor. Venimadhavan et al. [AIChE J., 40, 1814 (1994)] and Rev [Ind. Eng. Chem. Res., 33, 2174 (1994)] show that the existence and location of reactive azeotropes is a function of approach to equilibrium as well as the evaporation rate. 

Xylose is not a by-product of furfural but its precursor. On account of this, its production is governed by the very kinetics of furfural formation, but with the aim of avoiding the latter as best as possible. However, the technically most important difference between xylose production and furfural production is the fact that furfural, because of its low-boiling azeotrope with water, is readily recovered as a vapor, whereas xylose, being nonvolatile, ends up dissolved in the liquid reaction medium, together with many other unwanted by-products, from where a recovery in a sufficiently pure form is not as easy as in the case of separating a product from a vapor mixture. Consequently, xylose plants are far more complicated, and therefore more costly, than furfural plants. 

---