Stochastic analysis of a three‐phase fluidized bed: Fractal approach

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Abstract
Three‐phase fluidized beds have played important roles in various areas of chemical and biochemical processing. The characteristics of such beds are highly stochastic due to the influence of a variety of phenomena, including the jetting and bubbling of the fluidizing medium and the motion of the fluidized particles. A novel approach, based on the concept of fractals, has been adopted to analyze these complicated and stochastic characteristics. Specifically, pressure fluctuations in a gas‐liquid‐solid fluidized bed under different batch operating conditions have been analyzed in terms of Hurst's rescaled range (R/S) analysis, thus yielding the estimates for the so‐called Hurst exponent, H. The time series of the pressure fluctuations has a local fractal dimension of dFL = 2 − H. An H value of ½ signifies that the time series follows Brownian motion; otherwise, it follows fractional Brownian motion (FBM), which has been found to be the case for the three‐phase fluidized bed investigated.