Discrete bubble model

An advantage of this approach to model large-scale fluidized bed reactors is that the behavior of bubbles in fluidized beds can be readily incorporated in the force balance of the bubbles. In this respect, one can think of the rise velocity, and the tendency of rising bubbles to be drawn towards the center of the bed, from the mutual interaction of bubbles and from wall effects (Kobayashi et al., 2000). In Fig. 34, two preliminary calculations are shown for an industrial-scale gas-phase polymerization reactor, using the discrete bubble model. The geometry of the fluidized bed was 1.0 x 3.0 x 1.0 m (w x h x d). The emulsion phase has a density of 400kg/m3, and the apparent viscosity was set to 1.0 Pa s. The density of the bubble phase was 25 g/m3. The bubbles were injected via 49 nozzles positioned equally distributed in a square in the middle of the column. 

For the discrete bubble model described in Section V.C, future work will be focused on implementation of closure equations in the force balance, like empirical relations for bubble-rise velocities and the interaction between bubbles. Clearly, a more refined model for the bubble-bubble interaction, including coalescence and breakup, is required along with a more realistic description of the rheology of fluidized suspensions. Finally, the adapted model should be augmented with a thermal energy balance, and associated closures for the thermophysical properties, to study heat transport in large-scale fluidized beds, such as FCC-regenerators and PE and PP gas-phase polymerization reactors. 

Bokkers, G. A., Laverman, J. A., Van Sint Annaland, M., and Kuipers, J. A. M., Modelling of large-scale dense gas-solid bubbling fluidised beds using a novel discrete bubble model, Chem. Eng. Sci. 61, 5590-5602 (2006). 

Delnoij E, Lammers FS, Kuipers JAM, van Swaaij WPM. Dynamic simulation of dispersed gas-liquid two-phase flow using a discrete bubble model. Chem Eng Sci 1997 52 1429-1458. 

Discrete bubble model (DBM) In order to study the hydrodynamics in large-scale fluidized beds, the DBM approach is used. In the DBM, the emulsion phase is modeled as a continuum, and the bubbles are regarded as discrete elements (Bokkers et al., 2006). The bubble trajectories are computed by integrating the equations of motion (Newton s second law), accounting for bubble coalescence when two bubbles collide, using closures for the forces acting on the individual bubbles. More detailed and fundamental models could be used in addition to experiments to derive the required closures for the bubble behavior and the emulsion... 

Darmana D, Henket RLB, Deen NG, Kuipers JAM (2007) Detailed modelling of hydrodynamics, mass transfer and chemical reactions in a bubble column using a discrete bubble model Chemisorption of CO2 into NaOH solution, numerical and experimental study. Chem Eng Sci 62 2556-2575... 

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