Time-series analysis of pressure fluctuations in gas–solid fluidized beds – A review

Abstract

This work reviews methods for time-series analysis for characterization of the dynamics of gas–solid fluidized beds from in-bed pressure measurements for different fluidization regimes. The paper covers analysis in time domain, frequency domain, and in state space. It is a follow-up and an update of a similar review paper written a decade ago. We use the same pressure time-series as used by Johnsson et al. (2000). The paper updates the previous review and includes additional methods for time-series analysis, which have been proposed to investigate dynamics of gas–solid fluidized beds. Results and underlying assumptions of the methods are discussed. Analysis in the time domain is often the simplest approach. The standard deviation of pressure fluctuations is widely used to identify regimes in fluidized beds, but its disadvantage is that it is an indirect measure of the dynamics of the flow. The so-called average cycle time provides information about the relevant time scales of the system, making it an easy-to-calculate alternative to frequency analysis. Autoregressive methods can be used to show an analogy between a fluidized bed and a single or a set of simple mechanical systems acting in parallel. The most common frequency domain method is the power spectrum. We show that – as an alternative to the often used non-parametric methods to estimate the power spectrum – parametric methods can be useful. To capture transient effects on a longer time scale (>1 s), either the transient power spectral density or wavelet analysis can be applied. For the state space analysis, the information given by the Kolmogorov entropy is equivalent to that of the average frequency, obtained in the frequency domain. However, an advantage of certain state space methods, such as attractor comparison, is that they are more sensitive to small changes than frequency domain methods; this feature can be used for, e.g., on-line monitoring. In general, we conclude that, over the past decade, progress has been made in understanding fluidized-bed dynamics by extracting the relevant information from pressure fluctuation data, but the picture is still incomplete.