Scale-up of chaotic fluidized bed hydrodynamics

This paper focuses on scale-up of the dynamic behavior of gas-solids fluidized bubbling reactors. An empirical approach is followed that is based on the observation that the non-linear, hydrodynamic behavior of bubbling fluidized beds is of a chaotic nature. The degree of chaos is quantified by the Kolmogorov entropy, which is a measure of the rate of loss of information in the system (expressed in bits of information per second). The basic idea of the 'chaos scale-up methodology' proposed in this paper is that the rate of information loss should be kept similar when scaling up a bubbling bed from the small scale to the larger scale, in order to ensure dynamic (i.e. chaotic) similarity between the scaled beds. For a set of Geldart-B and -D particle systems, and for a range of bed diameters (from 0.1 m ID up to 0.8 m ID), an empirical correlation (Equation 4 in the paper) is derived that relates Kolmogorov entropy to main bubbling bed design parameters, viz. (i) fluidization conditions (superficial gas velocity, settled bed height), (ii) particle properties (minimum fluidization velocity), and (iii) bed size (diameter). It is illustrated by numerical examples how this correlation might be used in scaling up the chaotic dynamics of bubbling fluidized reactors. It is further shown that a similar type of correlation for Kolmogorov entropy can also be derived theoretically (Equations 1 and 5 in the paper).