Monte Carlo simulation of the bubble size distribution in a fluidized bed with intrusive probes

► We create a model to randomly simulate bubbles in a cross-section of a fluidized bed. ► We investigate how the bubble size is measured by an intrusive probe. ► The mean chord length of pierced bubbles is an approximation of the mean bubble size. ► Intrusive probes are best positioned at a 1/3 of the column diameter. ► Statistical backward transforms do not outperform the chord length approximation. Intrusive probes such as optical probes are commonly used to measure the bubble size distribution in a fluidized bed. However, usually only a chord length distribution is measured which is typically smaller than the actual centerline bubble size distribution of the pierced bubbles. Moreover, since small bubbles are less likely hit by the probe than large bubbles, the effective bubble size distribution in the entire bed is generally hidden to an intrusive probe. In order to elucidate the bubble size distribution in a fluidized bed measured by an intrusive probe, a Monte Carlo (MC) model is established. MC simulations are conducted with varying sample distributions (gamma and Rayleigh), varying probe positions, and varying spatial distributions of bubbles in the cross-section. Provided the bubble shape is ellipsoidal, it is shown that for all of these variations, the mean chord length can be taken as a representative measure of the mean bubble size in the bed. Furthermore, the applicability of statistical backward transforms (analytical, non-parametrical, and maximum entropy approach) to convert the chord length distribution to the overall bubble size distribution in the bed is assessed. None of these backward transforms outperforms the simple and straightforward approach to just take the mean chord length as the representative mean bubble size in the bed.