Van de Vusse kinetics

A technique developed by Professors Glasser and Hildebrandt allows one to find the optimum reaction system for certain types of rate laws. The WWW uses modified van de Vusse kinetics, that is,... 

Figure 6.7 illustrates the attainable region for van de Vusse kinetics (van de Vusse, 1964), based on the reactions ... 

For the case of van de Vusse kinetics with a feed of 1 kmol/m of A, Figure 6.7 indicates that the AR boundary is composed of an arc representing a CSTR with bypass (curve C), a... 

A systematic method for the construction of the attainable region using CSTRs and ITRs, with or without mixing and bypass, for a system of chemical reactions, as presented by Hildebrandt and Biegler (1995), is demonstrated for van de Vusse kinetics ... 

TABLE 5.1 Rate Constants for Van de Vusse Kinetics in the Equal Rate Case... 

Figure 5.7 Species eoncentrations profiles achieved in a CSTR for Van de Vusse kinetics, with a, = 20 and aj = 2.

Figure 6.6 shows an illustrative example of the AR boundary for three-dimensional Van de Vusse kinetics. The boundary structures have been exaggerated slightly to help emphasize certain characteristics for the discussions below." Elements of the AR boundary are composed of surfaces that are initiated from either mixing or reaction surfaces. Reaction surfaces themselves must produce extreme points (specifically protrusions) that result from PFR solution trajectories alone. Determination of the AR boundary structures is simplified greatly as a result we know that the final approach to any exposed point on the true AR boundary... 

EXAMPLE 12 Critical a policy for three-dimensional Van de Vusse kinetics... 

In the next chapter, we shall plot critical DSR trajectories for three-dimensional Van de Vusse kinetics. The calculations carried out here will prove useful later on. The reactions are given by ... 

Three-dimensional Van de Vusse kinetics has been used extensively in AR research papers in the past. Since the system is well understood, AR practitioners often use the system as an acid test for many AR construction algorithms and hypotheses. Understanding this system therefore assists in understanding many research investigations that employ the system, and future research in the field of AR theory is easier to undertake if we are able to understand past work. 

Figure 7.5 (a) Unfilled candidate region for the three-dimensional Van de Vusse kinetics inclnding a critical DSR trajectory from the feed point and (b) the full AR for the three-dimensional Van de Vnsse system in c -Cg-Cp space. Mixing fines have been removed from the plot to make interpretation of the AR boundary structures easier to identify. (See color plate section for the color representation of this figure.)... 

This concludes the AR construction for the three-dimensional Van de Vusse kinetics. Note that the inclusion of critical CSTRs and DSRs complicates construction, but these structures are required in order to generate the true AR. 

For the full three-dimensional BTX system, we find that the AR construction procedure is similar to that for Van de Vusse kinetics. Hence, we can summarize the key steps as follows ... 

Critical CSTRs Let us now investigate the existence of any critical CSTR points in the BTX system. The determination of critical CSTR points follows the proeedure given in Section 7.2.1.4 for Van de Vusse kinetics. We shall use the CSTR locus from the feed point in this analysis. 

Example Three-Dimensional Van de Vusse Kinetics Revisited... 

Figure 8.17(a) and (b) shows construction results obtained by the iso-state method for three-dimensional Van de Vusse kinetics. These results are those obtained using 25 two-dimensional planes for each component... 

Figure 8.20 Results for three-dimensional Van de Vusse kinetics, taken at snapshots during construction. Ming (2014). Reproduced with...

For problems that are bound by the vertex enumeration step, eonstmction times may be improved via rotations. This approach allows for either faster computation times for the same level of accuracy, or more detail to be added for the same computation time. In Figure 8.25, a comparison of con-stmction results for the two-dimensional Van de Vusse kinetics is shown. 

Figure 8.33 Two-dimensional AR for Van de Vusse kinetics, constructed using the IDEAS framework, as a function of grid size. Burri et al. (2002). Reproduced with permission of Elsevier.

The absence of a sufficiency condition— which will signify when the true AR has been determined—presents a large theoretical challenge for both AR theorists and practitioners who employ AR theory to solve reactor synthesis problems. Without a sufficiency condition, there is no certainty that the regions produced are the true AR. This is true even if the region computed has been generated from an automated AR construction method, such as those described in Chapter 8. Only for systems of a simplified or unique nature (i.e., when a rate field contains completely convex PFR trajectories), or for systems that have been well studied (i.e.. Van de Vusse kinetics), is one confident that the true AR has been foimd. 

Figure 8.10 DSR trajectories for constant a values using the feed point as the DSR sidestream composition. The CSTR locus from the feed point is also shown for comparison. It is clear that the equilibrium points for the DSR trajectories coincide with the CSTR locus points. Van de Vusse kinetics is used here.

Figure 9.8 (a) Full AR for the Van de Vusse system in mass fraction space, (b) AR for the Van de Vusse kinetics, converted to concentration... 

We have discussed reaction mechanism and kinetics of sulfonation of benzene (B) with SO3 (A) in aprotic media [3] and have concluded that the reaction proceeds according to Van de Vusse kinetics (1-3), with kj (25°C) >9.4 m /kmol s and z = >4. Pyrosulfonic acid (I) and Ar S3O9H d ) are both unstable and react with benzene to give the desired product benzenesulfonic acid (P) and the unwanted product diphenyl sulfone (X), respectively... 

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