Homogeneous Model for

The porous titanosilicates have made a tremendous impact industrially as oxidation catalysts, however the mechanisms of their reactions are not fully understood. Nearly every solid-state analytical method has been applied to the problem. One reason for this is that the active titanium centres are only present in very low concentrations. Consequently, whilst there is a continuing search for new heterogeneous titanosilicates for selective oxidation, there has also been an interest in the preparation of homogeneous models for such materials, in an... 

Severn JR, Duchateau R, van Santen RA, EUis DD, Spek AL (2002) Homogeneous models for chemically tethered sihca-supported olefin polymerization catalysts. OrganometaUics 21 4... 

Prins-Jansen, J.A. Fehribach, J.D. Hemmes, K. de Wit, J.H.W. A three-phase homogeneous model for porous electrodes in molten carbonate fuel cells. J. Electrochem. Soc. 1996, 143 (5), 1617-1628. 

Consider the time-homogeneous model for a disease as exemplified in Figure 26.1, where the transition probabilities are constant over time. Probabilities for the transitions are contained in the transition probability matrix P t). The probability matrix could simply be written as... 

Organic sources of Cr(VI) have also been investigated as the chromium source. Baker and Carrick [148] first investigated bis(triphenylsilyl) chromate as a homogeneous model for the surface chromate structures postulated to exist on the Phillips catalyst. This chromate ester is quite stable, but like Cr(VI) /silica, it can also be reduced by olefins under polymerization conditions to give the corresponding aldehyde and Cr(II) or Cr(III). Thus, it mimics the behavior of Cr(VI)/silica in many respects [149]. Bis(triphenylsilyl) chromate does catalyze ethylene polymerization,... 

From the profiles of r], it is clear that the performance of some reactions under bulk conditions is fundamentally different from that at the catalyst surface conditions, especially for reactions 4, 5, and 7 which show very high values of tj. Pseudo-homogeneous models for such reactions will give predictions very far from the actual performance. 

Several studies have been carried out to optimize the operation of fixed bed reactors experiencing catalyst decay using pseudo-homogeneous models for the reactor. 

The behaviour of the pseudo-homogeneous model for this case is similar in principle to that for run 8 except that the temperature profile does not show a maximum before the end of the catalyst bed. 

This syndiotactic model resembles the isotactic one in that it also is based on an octahedral complex that has an alkyl ligand as the growth site, and a vacant octahedral position through which propylene is complexed. In this homogeneous model for polymerization, methyl-methyl interactions force the propylene to be complexed in opposite configuration at each consecutive growth step. Copolymerization studies (85) with soluble syndiotactic-specific catalysts support this view. 

Remember that the rate equation must be consistent with the measure of the extent of reaction employed if conversion is used, (—r) must be expressed in terms of x if concentration is used, (—r) is in terms of C. If Fis mass flow rate, (—r) and C must be in mass units, and so on. Also, equation (4-45) is often used as a pseudo-homogeneous model for two-phase PER catalytic reactors. In such cases the rate constant contained in (—r) is usually expressed in terms per volume or weight of catalyst. In the former case, V would refer to catalyst volume and a value for bed porosity would be required to obtain reactor volume. In the latter case, catalyst weight would be... 

Note that we have used a pseudo-homogeneous model for the diffusion/reaetion process in the catalyst particle. 

Calculate the heat transfer parameters of the two-dimensional pseudo homogeneous models for the design of the reactor for hydrocarbonoxidation of Ex. 11.7.c, using the correlations given in Sec. 11.7.a. Compare the value of calculated from the expressions... 

Androver, Lopez, Borio, and Pedemera (2009) used a one-dimensional pseudo-homogeneous model for the WGS reaction in an MR with the scope of simulating the steady-state operation by neglecting dispersion effects. Different variables such as temperarnre, the heat transfer coefficient, and the countercurrent mode of sweep... 

KENO IV. However, there appears to be no decided advantage to doing so, as a homogenized model agrees much more closely with mqieriment. Using a homogenized model for the experiment system, an l% conservative bias in terms of keff is calculated. 

Figure 3.5 Relative error (S %) associated with the calculation of conversion from a pseudo-homogeneous model for a first-order isothermal reaction as a function of tj Da = rcA/ R,obs, with e = TjvrrAoi =0.1 or 0.5.

The solid phase energy balance is also required to continue the calculation (a pseudo-homogeneous model for mass transfer is also considered) ... 

The mathematical model which allows for differences in concentrations and temperature between the bulk gas stream and the particles is called a heterogeneous reactor model by Froment l. This is contrary to a socalled pseudo-homogeneous model for a catalytic reactor, where the concentrations and temperature in the bulk gas phase and in the particles are considered identical. 

For each region a mean value of the void fraction was calculated and a hydraulic radius was defined which was used in a pressure drop correlation. Martin [20] divided the bed into two regions a wall and a bulk region. He calculated for both different flow rates and a different rate of heat transfer. Carbonell [2] also used a two zone model for his analysis of the dispersion phenomena. In more recent work Vortmeyer et al. [5>6] tried to use the complete radial void fraction profile, and so did Chang [3]. They followed the same itinerary outlined by Lerou and Froment [l] and Marivoet et al. [2l]. Starting from the void fraction profile the radial velocity profile is calculated. With both profiles the effective thermal conductivity is established and the temperature and concentration profiles can be calculated by means of a two dimensional pseudo homogeneous model for the reactor. 

MacAdams LA, Buffone GP, Incarvito CD, Rheingold AL, Theopold KH. A chromium catalyst for the polymerization of ethylene as a homogeneous model for the phiUips catalyst. J Am Chem Soc 2005 127 1082-1083. 

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