Reduced model methanation

Figure 28 shows comparisons of the transient gas and solid axial temperature profiles for a step-input change with the full model and the reduced models. The figure shows negligible differences between the profiles at times as short as 10 sec. Concentration results (not shown) show even smaller discrepancies between the profiles. Additional simulations are not shown since all showed minimal differences between the solutions using the different linear models. Thus for the methanation system, Marshall s model reduction provides an accurate 2Nth-order reduced state-space representation of the original 5/Vth-order linear model. 

Jiang et al. [225] fitted a five-step global mechanism to a detailed methane oxidation mechanism. They identified the dominant reactions in the detailed mechanism and determined the rate expressions for the steps of the global mechanisms on the basis of the rate of the corresponding reaction rates of the detailed model. The reduced model was also tested in reactive shock calculations. 

Fig. 14. Fraction of the grid points used by various models during a 1-d Adaptive Chemistry simulation of a premixed stoichiometric methane-air flame. The full chemistry model is GRI-Mech 3.0. Reduced models were accurate at about 80% of the grid points.

An example The temperature field computed for a partially-premixed radi-ally-symmetric methane/air flame is shown in Fig. 15. This is the same 4> — 2.464 laminar flame simulated by Bennett et al. (2000). We used the same 217 reaction full chemistry model used by Bennett et al. (2000) to compute the temperature field shown on the left-hand side of Fig. 15. On the left-hand side is shown the temperature field computed using the full chemistry model everywhere. On the right-hand side is shown the temperature field computed by the Adaptive Chemistry method using 13 different reduced models ranging in size from zero reactions to 156 reactions. As guaranteed by the error control... 

The reader might question what has been gained in this QSSA example. After all, the full model solution requires the simultaneous solution of eight ODEs and the reduced model requires solving five ODEs. If one had experimental data, such as effluent ethane, ethylene, hydrogen and methane concentrations for different residence times (Vr I Qf). one would need to fit these data to find the five rate constants for either the... 

III. A complete model allowing all Internal degrees of freedom of R to acquire energy. For substituted methanes, it was useful to employ a reduced model III, named III-R, in which large molecules were treated as a six-body system, CH X, with X a structureless atom of appropriate mass. 

Reduced models based on low-dimensional manifolds can usually be simulated faster than full systems of differential equations because the resulting dynamical system contains fewer variables and is usually not stiff (see Sect. 6.7). However, the search and retrieval algorithms required to access the look-up tables can consume significant amounts of computer time. As an example, the simulation of methane combustion based on the ILDM method was eight times faster than that using a detailed mechanism (Riedel et al. 1994). Special algorithms have been developed to speed up the search and retrieval process (Androulakis 2004). In situ tabulation methods have also been developed as discussed in Sect. 7.12 below. 

Fig. 7.15 An example of a predicted feasible region of a reduced model based on the GRI-3.0 starting mechanism for methane oxidation. Adapted from Banerjee and lerapetritou (2006) with permission from Elsevier...

Methane can be oxidatively coupled to ethylene with very high yield using the novel gas recycle electrocatalytic or catalytic reactor separator. The ethylene yield is up to 85% for batch operation and up to 50% for continuous flow operation. These promising results, which stem from the novel reactor design and from the adsorptive properties of the molecular sieve material, can be rationalized in terms of a simple macroscopic kinetic model. Such simplified models may be useful for scale up purposes. For practical applications it would be desirable to reduce the recycle ratio p to lower values (e.g. 5-8). This requires a single-pass C2 yield of the order of 15-20%. The Sr-doped La203... 

The results so far available, and the models derived from them, indicate the following a reducing atmosphere is more favourable for amino acid synthesis. If, however, the partial pressure of methane on the primeval Earth was either zero or very low, a relatively high H2/CO or H2/CO2 ratio still allowed good rates of amino acid synthesis. It is, however, still an open question as to whether these concepts are realistic, because of the possibility that hydrogen could have escaped into space. It is arguable that in certain areas on the young Earth (and under unknown conditions),... 

This was the first example in which models for presumed Fischer-Tropsch intermediates have been isolated and their sequential reduction demonstrated. Neither methane nor methanol was observed from further reduction of the methyl and the hydroxymethyl complexes. The use of THF/H20 as solvent was crucial in this sytem in THF alone CpRe(C0)(N0)CH3 was the only species observed, probably because the initial formyl complex was further reduced by BH3.— When multihydridic reagents are reacted with metal carbonyl complexes, formyl species are usually not observed. The rapid hydrolysis of BH3 by aqueous THF allowed NaBH to act as a... 

Co2(CO)g has been used to obtain encapsulated cobalt clusters in Y-faujasite, which have been used as model catalysts for methane homologation [152]. The gas phase adsorption of Co2(CO)8 under N2 rendered predominately encaged Co4(CO)i2 species whereas Co,s(CO)iis was obtained when the impregnation of Co2(CO)8 was carried out under a CO/H2 atmosphere [152, 155], Samples were oxidized at 80°C, subsequently reduced at 400 °C and then structurally characterized by EXAFS. Clusters of two and three cobalt atoms were formed from encaged Co4(CO)i2 and COis(CO)iis, respectively. Higher methane conversion and selectivity to C2+ products in the CH4 homologation reaction have been obtained for the two atoms-size cluster sample the results were discussed using a DFT model [152]. 

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