Radial carbon profiles

Figure 5.37 Radial carbon profile in ring-shaped reformer catalyst [381].

Measured radial carbon profiles in the decoked particles are depicted in Figure 6.9.13. The experimental times to reach 50% burn-off are compared wiffi the numerically calculated data. [Coked catalyst particles were regenerated at different temperatures up to a burn-off degree of 50% (Kern, 2003).] The calculated and... 

The overall benefits of this high efficiency combustor over a conventional bubbling- or turbulent-bed regenerator are enhanced and controlled carbon-bum kinetics (carbon on regenerated catalyst at less than 0.05 wt %) ease of start-up and routiae operabiUty uniform radial carbon and temperature profiles limited afterbum ia the upper regenerator section and uniform cyclone temperatures and reduced catalyst iaventory and air-blower horsepower. By 1990, this design was well estabUshed. More than 30 units are ia commercial operation. 

Rachedi et al. [22] continued Zeaton et al. s work by examining the behavior of a real jet fuel (JP-10), and compared it to Zeaton et al. s carbon dioxide data. Their results showed that carbon dioxide could be used as a surrogate fluid for JP-10, since their behaviors were very similar. Both Rachedi et al. and Zeaton et al. found that the injected fluid radial concentration profile was well described by a Gaussian profile when the radius was normalized by the jethalf-radius. The jethalf-radius was defined as the radius where the concentration is half of the maximum (centerline) value. 

Figure 6. Measured and Calculated Axial and Radial Temperature Profiles. Topsoe Monotube Steam Reformer Pilot Data. Temperature approaches are shown for CH4-reforming (reaction (1)) and CH4-deposition (reaction (8)). If aT (1) > aT (8), there is not potential for carbon formation. This should be fulfilled at any position in the tube.

SL/RN Process. In the SL/RN process (Fig. 4), sized iron ore, coal, and dolomite are fed to the rotary kiln wherein the coal is gasified and the iron ore is reduced. The endothermic heat of reduction and the sensible energy that is required to heat the reactants is provided by combustion of volatiles and carbon monoxide leaving the bed with air introduced into the free space above the bed. The temperature profile in the kiln is controlled by radial air ports in the preheat zone and axial air ports in the reduction zone. Part of the coal is injected through the centerline of the kiln at the discharge end. The hot reduced iron and char is discharged into an indirect rotary dmm cooler. The cooled product is screened and magnetically separated to remove char and ash. 

The outside tubeskin temperature was taken to be identical to that generated in the previous simulation. The input data were also identical. Radial process temperature profiles are given in Figure 7. The ATg between the bed centerline and the wall amounts to 33°C, which is not excessive and permits the radially averaged temperature to be accurately simulated by means of the one dimensional model with "equivalent" heat transfer parameters, as discussed above. The methane conversion at the wall never differed more them 2% absolute from that in the centerline of the bed. The more detailed description which is possible by the two dimensional model would only be required if thermodynamic s predict possible carbon formation, and therefore catalyst deactivation, at locations different from those simulated by the one dimensional model. 

Owing to the rapid formation and dissolution of particle clusters which contribute to high slip velocities and solid backmixing but preserve a limited extent of gas backmixing, the fast fluidized bed regenerator exhibits unique axial and radial profiles for voidage, temperature and carbon concentration (see Figs. 9 and 11 and Table VIII). 

Consider now the mean oxygen density conditional on a specific alkyl configuration. Since that conditional mean oxygen density is less traditionally analyzed than the density profile shown in Fig. 1.9, we exploit another characterization tool, the proximal radial distribution (Ashbaugh and Paulaitis, 2001). Consider the volume that is the union of the volumes of spheres of radius r centered on each carbon atom see Fig. 1.10. The surface of that volume that is closer to atom i than to any other carbon atom has area fl, (r) with 0 < ff, (r) < 4tt. The proximal radial distribution function ( ) is defined as... 

The proximal radial distribution functions for carbon-oxygen and carbon-(water)hydrogen in the example are shown in Fig. 1.11. The proximal radial distribution function for carbon-oxygen is significantly more structured than the interfacial profile (Fig. 1.9), showing a maximum value of 2. This proximal radial distribution function agrees closely with the carbon-oxygen radial distribution function for methane in water, determined from simulation of a solitary methane molecule in water. While more structured than expected from the... 

We conclude that the proximal radial distribution function (Fig. 1.11) provides an effective deblurring of this interfacial profile (Fig. 1.9), and the deblurred structure is similar to that structure known from small molecule hydration results. The subtle differences of the ( ) for carbon-(water)hydrogen exhibited in Fig. 1.11 suggest how the thermodynamic properties of this interface, fully addressed, can differ from those obtained by simple analogy from a small molecular solute like methane such distinctions should be kept in mind together to form a correct physical understanding of these systems. 

Experiments in ultracentrifugation of binary solutions have been reported by Cullinan and Lenczyk (1969). In their experiments an equimolar mixture of hexane (1) and carbon tetrachloride (2) was placed in a sedimentation cell in an ultracentrifuge and rotated at 30,000 rpm. The temperature of the cell was held constant at 20°C. After sedimentation equilibrium had been obtained, samples were withdrawn from several radial positions and analyzed in a gas chromatograph with accuracy better than 1%. The composition profile at equilibrium is given in the following table. 

There is no physical overlap between the C and O atoms, yet in the projection of the ligand from the metal, the carbon atom eclipses oxygen. In the radial profile (Fig. 10), this overlap is eliminated. By using the solid-angle methodology, a quantitative measure of the amount of overlap can be attained (49). 

Figure 4.30 shows the effect of temperature on the structure and a pitch fiber, with an onion skin structure, is preferred to a radial type structure. Possible cross sectional microstmctures of mesophase carbon fibers are given in Figure 4.34 and modification of the flow profile during extrusion can produce a less flow-sensitive product and higher tensUe strength. The lines within each section depict carbon layers, which are at least preferentially parallel to the fiber axis. 

The two-dimensional reactor model developed by the authors is based on mass, energy and momentum balances. It allows axial and radial concentrations and temperature profiles to be evaluated under various effects, such as gas mixture residence time and pressure, and steam-to-carbon ratio. The model allows the plant performance to be evaluated in terms of hydrogen produced and separated and of electric power produced by the residual molten salt sensible heat. 

Snapshots of the final microstructure were analyzed in terms of density map profiles, radial distribution functions (RDFs), pore size distributions, and pore shapes. Figure 8.6 shows a snapshot of the carbon-Nafion-water-solvent (CNWS) blend. The interaction parameters of the carbon particles are selected to mimic the properties of Vulcan-type C/Pt particles. They are hydrophobic, with a repulsive interaction with water and Nafion sidechains, and semi-attractive interactions with other carbon particles as well as with Nafion backbones. 

Figure 6.9.11 Radial profiles of O2 content (relative to the gas phase) and carbon content (relative to the initial value) in a single cylindrical particle at different times [modeled results for Lc,o= 10 wt.%, yo = 2 vol.%, dp= 1.6 mm, p= 1 bar, and

The heat input through the reformer tube wall results in radial temperature and concentration gradients in addition to the axial gradients. Therefore, a two-dimensional model is required when a detailed knowledge of the conversion and temperature profile is necessary as is the case when the operation of the steam reformer is critical with respect to carbon formation (Rostrup-Nielsen, 1984a). 

One utility of such diagrams is in the prediction of the hardness traverse along the cross section of a specimen. For example. Figure 11.19a compares the radial hardness distributions for cylindrical plain carbon (1040) and alloy (4140) steel specimens both have a diameter of 50 mm (2 in.) and are water quenched. The difference in hardenabil-ity is evident from these two profiles. Specimen diameter also influences the hardness distribution, as demonstrated in Figure 11.19h, which plots the hardness profiles for oil-quenched 4140 cylinders 50 and 75 mm (2 and 3 in.) in diameter. Example Problem 11.1 illustrates how these hardness profiles are determined. 

Castaing micro-probe analysis was performed to determine the radial profile of Pd concentration along the diameter of the alumina beads. The preparation for the measurement includes an embedding in a metaciylate resin, pohshing with SiC paper and coating with carbon black. Measurements were performed with a JEOL 8100... 

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