The fluidization gas acts as a heating media and promotes mass and heat transfer by inducing a movement on the solids particles as well as removing the volatile from the bed. The BFB can be divided into three phases: (1) the bubble phase (dilute phase—low solids fraction), (2) the emulsion phase (dense phase—high solids fraction) and (3) the cloud phase. The cloud phase is at the interface between the bubble and emulsion phases such that the local solids fraction is between dilute and dense [48]. Several gas-phase (1-phase, multiple-phase, multiple regions etc.) and solid-phase (counter-current back mixing etc.) hydrodynamic models are available

in the scientific literature [49]. These models can be coupled with pyrolysis kinetics (reviewed in Sect. 11.3) to estimate the yield of products. These models have been reviewed in detail in several publications [49].

When designing a BFB pyrolysis system, one could desire to minimize the flu­idization gas flow to facilitate post-pyrolysis separation of the products. However, the superficial gas velocity also affects the reaction rates since it influences the heat and mass transfer. When temperature is sufficiently high, the pyrolysis reaction char­acteristic time becomes shorter than the heating characteristic time, such that heat transfer is the limiting step. In this case, the particles reaction rate (and residence time) is determined by the convection heat transfer to the biomass particles in the fluidized bed; and the convection coefficient can be calculated from the following correlation [52]:

NUbed = = 0.033 Rep 133 for 0.1 < Rep < 100 (11.3)

kg

In Eq. (11.3), the overall fluidized bed Nusselt number (Nubed) is a function of the particle Reynolds number (Rep):

The convection coefficient from Eq. (11.3) is averaged over the bed of particles and it is shown to increase with increasing slip velocity (U-Up). As demonstrated by Avidan and Yerushalmi [53], the slip velocity (U-Up) for BFBs is equal to the superficial gas velocity. This is the case because the average particle velocity is zero: solids circulate within the bed (negligible or limited entrainment) and particles flow co-current or counter-current with the gas. Therefore, the fluidization gas velocity should be sufficiently high to maximize reaction rates and the yield in volatiles: there is therefore a trade-off associated with the selection of the fluidization velocity.

Note that Eq. (11.3) has been shown to yield a more accurate estimation of the convection coefficient than the typical correlations involving the Prandtl number [54]. Furthermore, Eqs. (11.3) and (11.4) should be used by considering the inert (sand) fluidization media, in which case the use of the inert material properties is generally sufficiently accurate (the biomass particles are highly diluted in the inert media). Basic heat transfer estimations with Eq. (11.3) and (11.4)[12] suggest that operating a fluidized bed in the bubbling regime widely promotes fast pyrolysis rather than conventional pyrolysis.

To model biomass pyrolysis in a BFB, less importance is generally given to the bubble characterization since the fluidization gas is inert. The modelling is therefore focused on the dense emulsion phase, which contains the solid biomass particles. If the fluidized bed temperature is uniform and the inert (sand) particles do not leave
the bed, the inert particles temperature can be assumed equal to the gas temperature. In this case, the heat balance strictly involves the biomass particles.