FIGURE 9.26 Typical results obtained from mixing cell model (from Ranade, 1998).

increase with increase in gas flow rate, if CSC is equal or greater than 1% (within the range studied here). As expected, as airflow rate increases, emulsion temperature increases and the amount of coke on the regenerated catalyst decreases. The model parameters (kinetic and transport parameters) were calibrated by comparing model predictions with available plant data.

9.5.3. Bubble-Bubble Interaction Model

In a gas-solid fluidized bed, where gas velocity is equal to the minimum fluidization velocity, the solid particles are suspended and this suspension behaves as a fluid. When gas flows at a higher rate than required for minimum fluidization, it results in the formation of voids or bubbles (regions devoid of solids). Most of the gas supplied in excess of the minimum fluidization velocity flows through the bed in the form of bubbles. The gas velocity, orifice diameter and minimum fluidization velocity control bubble formation at the gas distributor. For a specific reactor configuration and gas-solid system, the latter two variables are well defined. If the gas distributor consists of multiple orifices, it will be necessary to estimate the non-uniform gas flow through these multiple orifices. The gas flow through each orifice is controlled by the pressure drop across the distributor (difference between pressure below the distributor orifice and the static head above that orifice). The static head at any point above the distributor plate is in turn controlled by the bubble voidage distribution within the whole dense bed. These phenomena were modeled in a second layer to estimate the bubble size distribution and effective bubble size within the dense bed of a regenerator.

A bubble-bubble interaction model based on potential flow over bluff bodies was developed and incorporated in a code called, BuDY (for Bubble DYnamics). The model is based on an assumption that the instantaneous velocity of an individual bubble in a fluidized bed can be obtained by adding to its rise velocity in isolation, the velocity which the emulsion phase would have had at the nose of the bubble, if the bubble was absent. The details of model development, model equations and solution procedures are described in Ranade (1997a). Appropriate representation of bubble formation, coalescence and exit of bubbles from the dense bed were included in the model. With the knowledge of initial bubble positions and bubble size, subsequent bubble positions can be tracked to predict instantaneous velocities and bubble positions within the dense bed.

The bubble-tracking model is capable of giving the number of bubbles present in the dense bed, their positions, diameter and velocity at any instant of time. Using these data, time variation of average bubble holdup as a function of time can be found. It can be used to examine the radial distribution of bubbles at various desired axial locations. A separate program was developed to calculate time-averaged voidage distribution (in a Eulerian framework) within the dense bed from the computed bubble trajectories. The model was also used to understand the role of bubble-bubble interactions and coalescence on the bubble dynamics of dense beds. Several numerical experiments were carried out to understand the influence of bubble diameter, orifice spacing etc. on bubble dynamics. The predicted bubble dynamics from the model reproduces the main dynamical characteristics observed in experiments. This model was used to simulate bubble distribution for the industrial gas distributor comprising 648 orifices. It was found that the number of bubbles decreased drastically as bubbles rise through the dense bed. The total number of bubbles and bubble volume fraction within the dense bed fluctuated quite significantly (the predicted fluctuations were found to be chaotic, Ranade, 1997a). The attractor reconstructed from the predicted voidage fluctuations showed remarkable similarity with that reconstructed from the experimental data. The model was used to obtain an effective bubble size within the dense bed of a FCC regenerator.

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