Gas-liquid-solid fluidized beds are used extensively in the refining, petrochemical, pharmaceutical, biotechnology, food, and environmental industries. An extensive review of gasliquid-solid fluidization has been published by Fan (1989).
The performance of multiphase reactors is affected by the flow regime and the quality of the gas distribution. The liquid and gas velocities at which flow regime transitions occur depend on liquid and solid properties which often evolve unpredictably in industrial reactors (Nacef et al., 1991;Wild et al., 1984). There is at present no reliable method to identify the flow regime in industrial gas-liquid-solid fluidized beds. Even well-designed reactors encounter gas distribution problems as the distributor becomes plugged or particles agglomerate and form defluidized zones.
Simple, robust and effective ways of determining the flow regime and the gas distribution in industrial units would make it possible to maintain optimal operating conditions through on-line control of liquid or gas velocity. The various measurement systems may be classified according to the scale of their measuring volume. First, probes such as bubble probes have a measurement volume smaller than the size of most bubbles and particles (Saxena et al., 1988). Second, "local probes" have a measurement volume smaller than the reactor crosssection. Third, cross-sectional probes measure cross-sectional averages. Fourth, bed average probes measure at the scale of the bed volume. All these probes measure properties such as capacitance, conductivity, density, light, or ?-ray absorption (Deckwer, 1992;Fan, 1989; Hetsroni, 1982). Their application to on-line control of industrial units is impaired by their sensitivity to fouling, misalignment, and variations in particle or liquid properties.
Although nonlinear chaos analysis of a probe signal can provide useful information, it is time-consuming and requires an expert for the selection of parameters such as delay time (Hay et al., 1996). This makes it unsuitable for on-line process-control.
Hurst's rescaled range analysis of a probe signal is not significantly affected by moderate changes in probe calibration constants (Hurst, 1951). Hurst's analysis of probe signals could eliminate problems associated with changes in probe, liquid,