Normalized radial concentration distribution

Figure 6. Normalized radial concentration distribution for NE. Solid line theoretical for central injection with Oh - 0.188 mm. Circles experimental. The dashed lines are the estimated position of the column walls. (Reproduced from ref. 13. Copyright 1988 American Chemical Society.)...

Pattemators may comprise an array of tubes or concentric circular vessels to coUect Hquid droplets at specified axial and radial distances. Depending on the pattemator, various uniformity indexes can be defined using the accumulated relative values between the normalized flow rate over a certain sector or circular region and a reference value that represents a perfectly uniform distribution. For example, using an eight-sector pie-shaped coUector, the reference value for a perfectly uniform spray would be 12.5%. The uniformity index (28) could then be expressed as foUows, where is the normalized volume or mass flow rate percentage in each 45-degree sector. 

The base metal-noble metal monolithic NO catalyst (15 wt % wash-coat) was subjected to the equivalent of 40,000 miles of engine dynamometer testing normal operating temperature of the catalyst was 677°-732°C. At the conclusion of the test, the catalyst was cored and sectioned into quarters (see Figure 7) for analysis of the axial and radial distributions of the various contaminants. Contaminant concentrations were determined by x-ray fluorescence, and they are reported as a percentage of the total catalyst weight. Almost all (>90% ) of the poisons (Ca, Zn, Pb, P) present on contaminated catalysts were confined, for... 

While lumped parameter models are normally used to describe processes, many important process units are inherently distributed parameter, that is, the output variables are functions of both time and position. Hence, their process models contain one or more partial differential equations. Pertinent examples include shell-and-tube heat exchangers, packed-bed reactors, packed columns, and long pipelines carrying compressible gases. In each of these cases, the output variables are a function of distance down the tube (pipe), height in the bed (column), or some other measure of location. In some cases, two or even three spatial variables may be considered for example, concentration and temperature in a tubular reactor may depend on both axial and radial positions, as well as time. 

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