Figure 5. Pressure drop across the fluidized bed versus superficial gas velocity at (a) T = 20°C, (b) T = 200°C, (c) T = 400°C, and (d) T = 600°C.

4.3 Minimum fluidization velocity (\(\mathbf{U}_{\mathbf{\text{mf}}}\))

Under ambient conditions, silica particles used in our experiments are typically Geldart B particles. Therefore, the minimum bubbling velocity\(U_{\text{mb}}\) should be the same as the minimum fluidization velocity (\(U_{\text{mf}}\)). To determine \(U_{\text{mf}}\), we followed pressure drops across the fluidized bed versus superficial gas velocity as shown in Figure 5. It is normally accepted that the point, where the intersection of extrapolated line of pressure drop across the packed bed and that of the total pressure drop across the full fluidized bed, as can be seen in Figure 5, is regarded as the minimum fluidization point.41 Based on the pressure-drop versus superficial gas velocity curves, we could obtain \(U_{\text{mf}}\) = 3.60, 2.92, 2.48, and 2.40 cm/s for T= 20, 200, 400, and 600°C, respectively. Apparently, under the ambient condition (T= 20 °C), \(U_{\text{mf}}\)and \(U_{\text{mb}}\) are coincided.
\(U_{\text{mf}}\) is compared with the empirical correlations, showing that the dimensionless Ergun equation can be used to predict\(U_{\text{mf}}\) for Geldart B particles with reasonably good agreement even at high temperature41:
\(\frac{1.75}{\varnothing\varepsilon_{\text{mf}}^{3}}\text{Re}_{\text{mf}}^{2}+150\frac{1-\varepsilon_{\text{mf}}}{\varnothing^{2}\varepsilon_{\text{mf}}^{3}}\text{Re}_{\text{mf}}=Ar\)(13)
where the Reynolds number and Archimedes number are respectively defined as
\(\text{Re}_{\text{mf}}=\frac{d_{p}\rho_{g}U_{\text{mf}}}{\mu}\) (14)
\(Ar=\frac{d_{p}^{3}\rho_{g}\left(\rho_{p}-\rho_{g}\right)g}{\mu^{2}}\)(15)
Note that \(\varnothing\) is the sphericity of particles,\(\varepsilon_{\text{mf}}\ \)is the void fraction at minimum fluidization, \(\rho_{p}\) is the particle density, \(\rho_{g}\) is the gas density, \(d_{p}\) is the Sauter mean diameter of particles, \(\mu\)is the gas viscosity, and \(g\) is the gravitational constant.
Figure 6 compares the measured \(U_{\text{mf}}\) with the predicted\(U_{\text{mf}}\ \)via Eq. (13). As can be seen, at relatively low operating temperature (T= 20 and 200oC), the measured\(U_{\text{mf}}\) agrees well with the predicted \(U_{\text{mf}}\). At relatively high temperatures, however, the pronounced deviation between the measured and predicted \(U_{\text{mf}}\) can be observed. Note that in Eq. (13) the effects of gas density and viscosity are taken into account, which implicitly reflects the influence of high temperature via the change in gas properties. It can be argued that at relatively low temperature, the influence of temperature on fluidization of silica particles is mainly exerted via the change in gas properties. At even higher temperature (T = 400 and 600oC), other impact factors, such as enhanced cohesive inter-particle forces, may play an increasingly important role.