Fractional brownian motion modelling of pressure fluctuations in multiphase flow systems

Multiphase flow systems lend themselves to a stochastic description due to their random behaviour. Fluidized beds and bubble columns are notable examples of such systems wherein random generation and coalescence of bubbles lead to pressure and density fluctuations. Analyses of these systems utilizing short‐memory models based on Markovian assumptions have been widely reported. Nevertheless, a review of the available data and the results of preliminary experiments have indicated that the time series of pressure fluctuation signals from various multiphase flow systems exhibit a a long‐term correlation. These signals appear to be better described by a long‐memory model, specifically “fractional Brownian motion” (FBM) comprising fractional Gaussian noise (FGN). In the present work, pressure fluctuations in a gas‐solid fluidized bed and a bubble column have been analysed and modelled by resorting to the relatively new concept of FBM. The stochastic model developed visualizes the bubble motion in a multiphase flow system to be composed of a random movement, generating irregular signals, and a linear movement, generating wave‐like signals. Autocorrelation and spectral density functions have been derived from the model. Comparison between the model‐based and experimentally determined autocorrelation functions has indicated that FBM is indeed a viable model for pressure fluctuations in multiphase flow systems.