CHARACTERIZATION OF REGIMES AND REGIME TRANSITIONS IN BUBBLE-COLUMNS BY CHAOS ANALYSIS OF PRESSURE SIGNALS

In this study it is shown that the transition from the homogeneous to the heterogeneous flow regime in bubble columns can be quantitatively found with high accuracy by analysing the chaotic characteristics of t he pressure fluctuation signal (PFS). In previous work (van den Bleek and Schouten, 1993; Schouten et al., 1996), the authors have already a pplied this technique to time series from gas-solid fluid beds. Also, it was shown (Krishna et nl., 1993, Ellenberger and Krishna, 1994) tha t hydrodynamics of bubble columns and fluid beds can be described in a n analogous manner. Therefore in this work, the method of chaos analys is is applied to bubble columns. A distinctive feature of the pressure signal from bubble columns is that it is composed of two different pa rts: a low frequency part resulting from the motion of the large bubbl es and a high frequency part resulting from all other processes (coale scence, collapse, breakup) that take place in the column. From the pha se of-the cross spectrum of two pressure probes, placed at different a xial positions, it was possible to identify the bands in the spectrum of the PFS that show a significant time delay. This time delay is of t he order of the passage time of bubbles between the measurement locati ons. This I,and in the spectrum of the PFS was used to estimate the Ko lmogorov entropy to quantify-the chaotic dynamics in the bubble column . The Kolmogorov entropy as a function of gas velocity indicates a sha rp transition from the homogeneous to the churn-turbulent flow regime. From other methods considered (e.g. holdup and other properties of th e signal such as variance), this transition was less clear. Therefore chaos analysis of PFSs is believed to be a powerful technique for on-l ine identification of flow regimes. (C) 1997 Elsevier Science Ltd.