Virtual catalyst model

The model was validated against heavy duty and passenger car diesel engine test bench experiments. A good correlation was obtained between ESC and ETC experiments and simulation with 0 and 0.5% NO2 NO ratios and a virtual oxidation catalyst. The virtual oxidation catalyst model was realized by placing an oxidation catalyst model in front of the SCR catalyst. 

In this chapter, the application of the virtual testbench as part of the development process is demonstrated. In this case, the virtual testbench represents the SCR system of the aftertreatment of Diesel exhaust, i.e., the SCR catalyst itself and the necessary algorithms for control of the AdBlue dosing into the exhaust stream, cf. Fig. 22.2. These algorithms are coupled with the catalyst model in the same manner as they are implemented in the control unit. However, the injection of AdBlue, its processing, and the generation of NH3 are not directly modeled. Ideal NH3-generation is assumed instead. 

As our first approach to the model, we considered the controlling step to be the mass transfer from gas to liquid, the mass transfer from liquid to catalyst, or the catalytic surface reaction step. The other steps were eliminated since convective transport with small catalyst particles and high local mixing should offer virtually no resistance to the overall reaction scheme. Mathematical models were constructed for each of these three steps. 

Similar analysis can be carried out for Samples II and III in Icenogle and Klingensmith s paper.(18) The results are tabulated in Table IV. It appears that Sample II (made with the same conventional catalyst as Sample I but without a selectivity control agent (18) also follows the three-site E/E/B model very well. Perhaps surprisingly the reaction probabilities for the two E-sites are virtually the same in Samples I and II (P l = 0.994, P 2 = 0.80). The B-site is indeed different. 

Because of the inadequacies of the aforementioned models, a number of papers in the 1950s and 1960s developed alternative mathematical descriptions of fluidized beds that explicitly divided the reactor contents into two phases, a bubble phase and an emulsion or dense phase. The bubble or lean phase is presumed to be essentially free of solids so that little, if any, reaction occurs in this portion of the bed. Reaction takes place within the dense phase, where virtually all of the solid catalyst particles are found. This phase may also be referred to as a particulate phase, an interstitial phase, or an emulsion phase by various authors. Figure 12.19 is a schematic representation of two phase models of fluidized beds. Some models also define a cloud phase as the region of space surrounding the bubble that acts as a source and a sink for gas exchange with the bubble. 

This model represents an effort to deal with ligand effects, but it is difficult to believe that the wide variety of catalysts studied can universally be as coordinatively unsaturated as this model requires. In fact, even pentacoordinate forms of tungsten (e.g., W(CO)5) are generally held to be much less stable than hexacoordinate species. Their scheme would also seem to predict the highly selective the formation of cis-butene from c/s-4-methyl-2-pentene, whereas the observed stereospecificity is virtually the same as that obtained with m-2-pentene (18). 

For porous catalyst pellets with practical loadings, this quantity is typically much larger than the pellet void fraction e, indicating that the dynamic behavior of supported catalysts il dominated by the relaxation of surface phenomena (e.g., 35, 36). This implies that a quasi-static approximation for Equation (1) (i.e., e = 0) can often be safely invoked in the transient modeling of porous catalyst pellets. The calculations showed that the quasi-static approximation is indeed valid in our case the model predicted virtually the same step responses, even when the value of tp was reduced by a factor of 10. 

Here we present an alternative concept for optimizing homogeneous catalysts. Using a virtual synthesis platform, we assemble large catalyst libraries (lO -lO candidates) in silica, and use statistical models, molecular descriptors, and... 

As the models presented in this chapter are relatively complex, they are not used for control purposes in their current status. They can however be used for the development of control models, either by linearization and simplification, or as virtual test bench . This way, a control model is pre-tuned on the catalyst or system model before parameterization on the real test bench, thus saving development time and costs. 

In this respect, Kuipers made an important point (as illustrated in Fig. 3.10c), namely that layers of thickness x which cover the support to a fraction 6, have the same dispersion as hemispheres of radius 2 x, or spheres with a diameter 3x. Even more interesting is the fact that these three particle shapes with the same surface-to-volume ratio give virtually the same fp/fs intensity ratio in XPS when they are randomly oriented in a supported catalyst The authors tentatively generalized the mathematically proven result to the following statement that we quote literally For truly random samples the XPS signal of a supported phase which is present as equally sized but arbitrarily shaped convex particles is determined by the surface/volume ratio. Thus, in Kuipers model the XPS intensity ratio fp/fs is a direct measure of the dispersion, independent of the particle shape. As the mathematics of the model is beyond the scope of this book, the interested reader... 

The region over which this balance is invoked is the heterogeneous porous catalyst pellet which, for the sake of simplicity, is described as a pscudohomoge-ncous substitute system with regular pore structure. This virtual replacement of the heterogeneous catalyst pellet by a fictitious continuous phase allows a convenient representation of the mass and enthalpy conservation laws in the form of differential equations. Moreover, the three-dimensional shape of the catalyst pellet is replaced by assuming a one-dimensional model... 

Employing 1-hexene isomerization on a Pt/y-ALOj reforming catalyst as a model reaction system, we showed that isomerization rates are maximized and deactivation rates are minimized when operating with near-critical reaction mixtures [2]. The isomerization was carried out at 281°C, which is about 1.1 times the critical temperature of 1-hexene. Since hexene isomers are the main reaction products, the critical temperature and pressure of the reaction mixture remain virtually unaffected by conversion. Thus, an optimum combination of gas-like transport properties and liquid-like densities can be achieved with relatively small changes in reactor pressure around the critical pressure (31.7 bars). Such an optimum combination of fluid properties was found to be better than either gas-phase or dense supercritical (i.e., liquid-like) reaction media for the in situ extraction of coke-forming compounds. 

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