Reactive residual curve

Figure A.4 Reactive residue curve maps for a ternary system containing inert, reaction A+B+/<- C+/.

Figure A.4 (left), the equilibrium curve from the previous case becomes a surface of conical shape limited by the inert-free equilibrium curve and the edges AI and BI. It is to be noted that all the reactive residue curves start at the reactive azeotrope but with different paths towards the vertex I.

Reactive residual curves can be used to estimate the potential products that can be obtained from a reactive distillation column. The main drawback of this concept... 

Mulopo, J.L., D. Hildebrandt, and D. Glasser, Reactive residue curve map topology Continuous distillation column with non reversible kinetics. Computers Chemical Engineering, 2008, 32(3) 622 629. 

The abbreviation RCM refers to the classical residue curve map discussed in Chapter 2. When a reaction is introduced, the equivalent map is known as a reactive residue curve map, abbreviated as R RCM, while the addition of mixing phenomena will result in a reactive residue curve map with mixing (R RCM M)... 

First simulation results on steady state multiplicity of etherification processes were obtained for the MTBE process by Jacobs and Krishna [45] and Nijhuis et al. [78]. These findings attracted considerable interest and triggered further research by others (e. g., [36, 80, 93]). In these papers, a column pressure of 11 bar has been considered, where the process is close to chemical equilibrium. Further, transport processes between vapor, liquid, and catalyst phase as well as transport processes inside the porous catalyst were neglected in a first step. Consequently, the multiplicity is caused by the special properties of the simultaneous phase and reaction equilibrium in such a system and can therefore be explained by means of reactive residue curve maps using oo/< -analysis [34, 35]. A similar type of multiplicity can occur in non-reactive azeotropic distillation [8]. 

When chemical reaction takes place all the reactive residue curves start at either pure iC4 corner or at the MeOH-nC4 azeotrope (MNAz) and end predominantly at the pure MeOH corner (figure 5.4). The remaining low-boiling azeotropes did not survive the... 

The transformed variables describe the system composition with or without reaction and sum to unity as do Xi and yi. The condition for azeotropy becomes X, = Y,. Barbosa and Doherty have shown that phase and distillation diagrams constructed using the transformed composition coordinates have the same properties as phase and distillation region diagrams for nonreactive systems and similarly can be used to assist in design feasibility and operability studies [Chem Eng Sci, 43, 529, 1523, and 2377 (1988a,b,c)]. A residue curve map in transformed coordinates for the reactive system methanol-acetic acid-methyl acetate-water is shown in Fig. 13-76. Note that the nonreactive azeotrope between water and methyl acetate has disappeared, while the methyl acetate-methanol azeotrope remains intact. Only... 

FIG. 13-76 Residue curve map for the reactive system methanol-acetic acid-methyl acetate-water in chemical eqiiihhriiim. 

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... 

Figure 4.27 shows residue curve maps for the reactive reboiler at three different Damkohler numbers. In the nonreactive case (Da = 0 Fig. 4.27(a)), the map topology is structured by one unstable node (pure B), one saddle point (pure C), and one stable node (pure A). Since pure A is the only stable node of nonreactive distillation, this is the feasible bottom product to be expected in a continuous distillation process. 

In analogous manner, residue curve maps of the reactive membrane separation process can be predicted. First, a diagonal [/e]-matrix is considered with xcc = 5 and xbb = 1 - that is, the undesired byproduct C permeates preferentially through the membrane, while A and B are assumed to have the same mass transfer coefficients. Figure 4.28(a) illustrates the effect of the membrane at nonreactive conditions. The trajectories move from pure C to pure A, while in nonreactive distillation (Fig. 4.27(a)) they move from pure B to pure A. Thus, by application of a C-selective membrane, the C vertex becomes an unstable node, while the B vertex becomes a saddle point This is due to the fact that the membrane changes the effective volatilities (i.e., the products xn a/a) of the reaction system such that xcc a. ca > xbbO-ba-... 

Fig. 4.28. Residue curve maps for reactive membrane separation ...

Residue curve maps of the THF system were predicted for reactive distillation at different reaction conditions (Fig. 4.29). The topology of the map at nonreactive conditions (Da = 0) is structured by a binary azeotrope (unstable node) between water and THF. Pure water and pure THF are saddle nodes, while the 1,4-BD vertex is a stable node. 

Fig. 4.30. Residue curve maps for reactive membrane separation 1,4-BD — THF + Water p= 5 atm Knudsen-membrane. (a) Da = 0 (b)...

As demonstrated by means of residue curve analysis, selective mass transfer through a membrane has a significant effect on the location of the singular points of a batch reactive separation process. The singular points are shifted, and thereby the topology of the residue curve maps can change dramatically. Depending on the structure of the matrix of effective membrane mass transfer coefficients, the attainable product compositions are shifted to a desired or to an undesired direction. 

The determination of feasible products is very important for conceptual process design and for the evaluation of competing process variants. In this chapter, methods have been discussed to identify feasible products as singular points of residue curve maps (RCM). RCM-analysis is a tool which is well established for nonreactive and reactive distillation processes. Here, it is shown how RCM can also be used for reactive membrane separation processes. 

Figu re 8.4 Residue curve map of the reactive mixture lauric acid/2-ethylhexanol/water/2-ethylhexyl dodecanoate a = initial estimation b = experimental data [2],... 

In the following, the strategy presented before will this time be applied for developing a process for the esterification of lauric acid with methanol. All the thermodynamic data for pure components and binary mixtures are available in Aspen Plus. A residue curve map of the reactive mixture at equilibrium can be computed as described in Appendix A. A useful representation can be done in reduced coordinates defined by Xx = water + add and X2 = add + ester. The diagram displayed... 

Appendix A Residue Curve Maps for Reactive Mixtures... 

Figure A.2 (right) emphasizes a particular position where phase equilibrium and stoichiometric lines are collinear. In other words the liquid composition remains unchanged because the resulting vapor, after condensation, is converted into the original composition. This point is a potential reactive azeotrope, but when the composition satisfies chemical equilibrium too it becomes a true reactive azeotrope. Some examples of residue curve maps are presented below. Ideal mixtures are used to illustrate the basic features, which may be applied to some important industrial applications.

Figure A.3 also illustrates graphically the formation of a reactive azeotrope as the point where a particular stoichiometric line becomes tangential to the nonreac-tive residue curve and intersects simultaneously the chemical equilibrium curve.

Another possibility is the representation in a two-dimensional diagram, as in Figure A.4 (right). The component C being chosen as the reference, the relation (A.3) gives the transformed co-ordinates XA = (xA + xc)/(l + xc) and X, = (xB + xc) / (1 + xc). The residue curves run from the reactive azeotrope to the vertex of component I. This situation is denoted by two degrees of freedom systems . 

Figure A.5 Residue curve map for an ideal reactive mixture with relative volatilities 4/6/2/1 and reversible reaction A + BhC+D with K = 5.

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. 

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