Monolith models

In this paper, we first briefly describe both the single-channel 1-D model and the more comprehensive 3-D model, with particular emphasis on the comparison of the features included and their capabilities/limitations. We then discuss some examples of model applications to illustrate how the monolith models can be used to provide guidance in emission control system design and implementation. This will be followed by brief discussion of future research needs and directions in catalytic converter modeling, including the development of elementary reaction step-based kinetic models. 

Kuhn Jones (1982) examined various models for fluoride release and showed that release did not fit the membrane and homogenous monolith model. Instead, they concluded that the cement behaved as a porous granular monolith, as described by Kydonieus (1980). The release of fluoride appears to be an ion exchange phenomenon, as dental silicate cement takes up rather than releases fluoride from solution if it is present in sufficient concentration (Kuhn, Lesan Setchell, 1983). 

Pop III stars in classic monolithic models for ellipticals (closed-box) produce larger, although still acceptable, [< Mg/Fe > ] ratios. However, the predicted integrated colors are too red. As a consequence these models should be rejected. 

What happened to the gas expelled from the halo A traditional answer based on monolithic models of a Galaxy collapsing through successive stages of halo, thick disk and thin disk would be that the expelled gas formed the raw material of the disk. This hypothesis faces some severe difficulties. For one thing, the remaining mass in the halo should then be about 10 per cent of the mass of the disk, whereas it is probably a factor of 5 or so less than this (Carney, Latham Laird 1990). Another difficulty is the specific angular momentum, as is apparent qualitatively from Fig. 8.15 and is illustrated quantitatively in Fig. 8.21. 

Model separate views. Rather than build a single monolithic model, recognize when there are useful different external views of your component. Model each such view separately so that the model relates seamlessly to that part of the problem domain. 

The demand and procurement side is treated often as given and monolithic models do not analyze the integration of sales and procurement with production and distribution throughout the chain by volume and value... 

They focus on the ID simulation of an urea SCR system. The system includes a model for N02 production on a DOC, a model for urea injection, urea decomposition and hydrolysis catalyst, a model for a vanadium-type SCR catalyst and a model for NH3 decomposition on a clean-up catalyst. The catalyst models consist of a ID monolith model with global kinetic reactions on the washcoat surface, kinetic parameters have been taken from literature or adjusted to experimental data from literature. The complete model was implemented in AVL BOOST (2006). AVL BOOST is an engine cycle and gas exchange simulation software tool, which allows for the building of a model of the entire engine. 

The special case of linear kinetics with the axial Peclet number, Pe — 0 and flat velocity may be examined analytically. This case corresponds to the so-called short monolith model, which is given by... 

Modeling of monolith reactors from first principles presents a valuable tool in the design of such reactors and in the analysis of the underlying phenomena. The results presented show that the reactor behavior can be adequately described and understood by a combination of the reactor s transport characteristics and the intrinsic kinetics obtained with a laboratory reactor of another type. As such we can generalize monolith models to other reaction networks, e.g., extend the given description of the dynamic operation for combined CO oxidation and NO reduction in the automotive exhaust gas converter to include other reactions, like the oxidation of various hydrocarbons and of hydrogen. The availability, however, of a proper kinetic model is a definite prerequisite. 

Table 1 shows the optimum makespans computed with the monolithic model and the CPU times in seconds, including the time required to prove the optimality of the solution. The last two columns of the table list the makespans and the CPU times obtained with the decomposition approach. Out of the 28 instances, 17 could be solved to optimality, and the maximum relative optimality gap is less than 7 %. The results obtained for the larger instances indicate that our method scales quite well. The maximum CPU time is less than 3 seconds, versus more than two hours for the monolithic approach. In sum, the analysis shows that the decomposition approach is able to provide good feasible schedules at very modest computational expense. Hence, the method is well-suited... 

Figure 5 Ignition temperatures vs equivalence ratio during CH -oxidation on Pt foil experiments (symbols and dotted line) and monolith model (dashed line). (Please note that experimental temperatures are given in K. while model results are in °C.)...

Flytzani-Stephanopoulos et al. (MC), (S) Discrete model for the description of metallic monolith. Model was based on a cooling fin approach... 

Integration not only focuses on the spatial or temporal dimension of an SC but also on separated planning (sub-)problems. These (sub-)problems and their interdependencies are modeUed in a common framework. Basically, two options for integration can be distinguished The first option is to merge the sub-problems into a monolithic model (also called deep integration). The second option is to stay with the decomposition into... 

The decomposition of the monolithic model into suitable sub-problems and setting up a functional integration scheme. ... 

The development of tailored optimization techniques by exploiting specific properties of the monolithic model. 

A similar approach was used to validate the PGM kinetics data were collected over a PGM coated monolith and systematically compared with predictive model simulations. However, a different reactor model was used in this case. Indeed, simulation analysis of PGM coated monolith catalysts [20] pointed out that the extremely high reaction rates over this catalytic system result in full mass transfer control above 250 °C. For this reason, we assumed that in the case of washcoated monolith samples only the PGM washcoat surface was effectively active, thus we treated the PGM layer as a surface. The kinetics developed over the powdered PGM catalyst were thus referred to the catalyst surface and directly included in the PGM monolith model. 

The same approach for the PGM phase modeling was adopted in the development of the mathematical model of Dual-Layer ASC monolith catalysts [20]. Such a model, named LSM (Layer + Surface Model), was based on the mathematical model for SCR monolithic converters [12,25,26]. As detailed in the following, the PGM reactivity was directly included in the mentioned SCR converter model by simply modifying the inner boundary condition for the diffiision- -eaction equations within the SCR layer, i.e., the boundary condition at the interface with the PGM phase. It is worth emphasizing that the LSM model reduces to the PGM monolith model when the SCR layer thickness approaches zero. 

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