Blast residence time distribution

The notion of an effectiveness factor introduced by Thiele, Amundson s exploitation of the phase plane (34), Gavalas use of the index theorem (41), the Steiner symmetrization principle used by Amundson and Luss (42) and the latter s exploitation of the formula for Gaussian quadrature (43)—perhaps the prettiest connection ever made in the chemical engineering literature—are theoretical counterparts, large and small, of the careful craft of the experimentalist. So perhaps also the very important insight that Danckwerts contributed in his formulation of the residence time distribution is a happy foil to his heroic ambition to trace a blast furnace (44). 

One final reaction engineering aspect of a blast furnace that should be discussed here is the residence time distribution. The hydrodynamics and the configuration of the different phases consisting of the upflowing reduction, gas and coke, and iron ore that slowly go downwards are complicated, as shown schematically by the sectional view of the interior in Figure 6.5.21. 

Nevertheless, the blast furnace is an instructive example to examine the question of to what extent this reactor can be regarded as an ideal plug reactor. As deduced in Section 4.10.5.1, we need the residence time distribution, which was measured in 1969 by a pulse experiment with the injection of Kr into the blast air (Standish and Polthier, 1975, see also Levenspiel, 1999). Figures 6.5.22 and 6.5.23 give the dimensions of the blast furnace and the experimental results. 

Tanks-in-Series Model Figure 6.5.23 shows the residence time distribution of the investigated blast furnace in comparison to a cascade of stirred tanks with 20, 30, and 50 tanks. The best fit is obtained for a number N of 30. For conversion of a gaseous reactant i in a blast furnace, we therefore have according to Eq. (4.10.32) with N=30 ... 

Figure 6.5.22 Measurement of residence time distribution in a blast furnace. Standish and Polthier (1975) adapted from Levenspiel (1999).

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