Continuous Fluidized Bed Drying: Advanced Modeling and Experimental Investigations

Abstract

Fluidized bed drying is a technology which is widely applied in industry for the drying of particulate solids. One of the major advantages of fluidized bed system results from the fact that due to high heat, mass and momentum transfer, and intensive solids, mixing a good temperature control is possible, which allows an effective drying of heat-sensitive materials as, for example, food or pharmaceutical products, which are very often also porous and hygroscopic. A disadvantage of the nearly perfect solids mixing in the fluidized bed is the wide residence time distribution of the solids, that is, some particle will leave the dryer already a few seconds after they have been fed to it, while other particles stay for very long times inside the dryer, which may result in a wide moisture distribution of the solids at the outlet of the dryer.

Based on numerous works from the literature, a drying model for continuous fluidized bed drying has been developed and implemented as a module within the framework of the stationary flowsheet simulation program SolidSim, which allows the simulation of the drying process for many different solids, liquids, and gases.

In addition to the residence time distribution described by a population model, the influence of particle size distribution and the moisture distribution of the feed material was taken into account. The module computes the humidity and temperature of the gas versus the bed height and the moisture and temperature distribution of the solids by taking into account their distributed properties such as for the residence time distribution, particle size and initial moisture. Additionally, also the drying of mixtures of particles with different types of sorptive behavior and drying kinetics is possible while assuming that no particle segregation occurs. Furthermore, the model has been extended by a simple approach to simulate the drying in an elongated fluidized bed dryer.

For the validation of the model, the main operating parameters were varied and compared with experiments. The model can calculate the moisture distribution at the dryer outlet, but due to technical restriction, only the average moisture of the particles was measured and compared with the model prediction.

Appendix A

9.1.1 A.1 Mass and Heat Transfer Between Particles and Suspension Gas

Mass and heat transfer between particles and suspension gas after Gnielinski (1980) for fixed bed
$\operatorname{Re}=\frac{{\operatorname{Re}}_{\mathrm{mf}}}{\varepsilon_{\mathrm{mf}}}$	$\operatorname{Re}=\frac{{\operatorname{Re}}_{\mathrm{mf}}}{\varepsilon_{\mathrm{mf}}}$
$\mathrm{Sc}=\frac{\nu_{\mathrm{g}}}{\delta_{\mathrm{w},\mathrm{g}}}$	$\Pr =\frac{\nu_{\mathrm{g}}{c}_{\mathrm{g}}{\rho}_{\mathrm{g}}}{\lambda_{\mathrm{g}}}$
${\mathrm{Sh}}_{\mathrm{lam}}=0.664{\operatorname{Re}}^{\frac{1}{2}}{\mathrm{Sc}}^{\frac{1}{3}}$	${\mathrm{Nu}}_{\mathrm{lam}}=0.664{\operatorname{Re}}^{\frac{1}{2}}{\Pr}^{\frac{1}{3}}$
${\mathrm{Sh}}_{\mathrm{tur}}=\frac{0.037{\operatorname{Re}}^{0.8}\mathrm{Sc}}{1+2.443{\operatorname{Re}}^{-0.1}\left({\mathrm{Sc}}^{\frac{2}{3}}-1\right)}$	${\mathrm{Nu}}_{\mathrm{tur}}=\frac{0.037{\operatorname{Re}}^{0.8}\Pr }{1+2.443{\operatorname{Re}}^{-0.1}\left({\Pr}^{\frac{2}{3}}-1\right)}$
${\mathrm{Sh}}_{\mathrm{p}}=2+\sqrt{{\mathrm{Sh}}_{\mathrm{lam}}^2+{\mathrm{Sh}}_{\mathrm{tur}}^2}$	${\mathrm{Nu}}_{\mathrm{p}}=2+\sqrt{{\mathrm{Nu}}_{\mathrm{lam}}^2+{\mathrm{Nu}}_{\mathrm{tur}}^2}$
Shps = [1 + 1.5(1 − εmf)]Shp	Nups = [1 + 1.5(1 − εmf)]Nup
Back-mixing effect after Groenewold and Tsotsas (1999)
${\mathrm{Sh}}_{\mathrm{ps}}^{\prime }=\frac{{\operatorname{Re}}_0\mathrm{Sc}}{A/F}\ln \left(1+\frac{{\mathrm{Sh}}_{\mathrm{ps}}A/F}{{\operatorname{Re}}_0\mathrm{Sc}}\right)$	${\mathrm{Nu}}_{\mathrm{ps}}^{\prime }=\frac{{\operatorname{Re}}_0\Pr }{A/F}\ln \left(1+\frac{{\mathrm{Nu}}_{\mathrm{ps}}A/F}{{\operatorname{Re}}_0\Pr}\right)$
${\mathrm{Sh}}_{\mathrm{p}\mathrm{s}}^{\prime }=\frac{\beta_{\mathrm{p}\mathrm{s}}{d}_{\mathrm{p}}}{\delta }$	${\mathrm{Nu}}_{\mathrm{p}\mathrm{s}}^{\prime }=\frac{\alpha_{\mathrm{p}\mathrm{s}}{d}_{\mathrm{p}}}{\lambda_{\mathrm{g}}}$

where Re Reynolds number, Sc Schmidt number, ε_mf minimal fluidization velocity, and Pr Prandtl number.

9.1.2 A.2 Mass and Heat Transfer Between Suspension Gas and Bubble Phase

The Number of Transfer Unit (NTU) is given as

$$ {\mathrm{NTU}}_{\mathrm{sb}}=\frac{\rho_{\mathrm{g}}\cdot {\beta}_{\mathrm{sb}}{A}_{\mathrm{sb}}}{{\overset{.}{M}}_{\mathrm{g}}} $$

It is assumed that NTU increases linearly with the height; for a bed height of 5 cm, a value of 1 was set (Groenewold and Tsotsas 1999); therefore

$$ {\mathrm{NTU}}_{\mathrm{sb}}={\mathrm{NTU}}_{\mathrm{sb}}^0\cdot \frac{L_{\mathrm{bed}}}{50\; mm} $$

$$ \frac{\alpha_{\mathrm{sb}}{A}_{\mathrm{sb}}}{c_{\mathrm{g}}{\overset{.}{M}}_{\mathrm{g}}}=\frac{\rho_{\mathrm{g}}{\beta}_{\mathrm{sb}}{A}_{\mathrm{sb}}}{{\overset{.}{M}}_{\mathrm{g}}}{\mathrm{Le}}^{1-m} $$

$$ \mathrm{Le}=\frac{\lambda_{\mathrm{g}}}{c_{\mathrm{g}}{\rho}_{\mathrm{g}}{\delta}_{\mathrm{g}}} $$

$$ m=\frac{1}{3} $$

9.1.3 A.3 Heat Transfer Between the Particles and the Wall

The heat transfer coefficient between the particles and the wall is calculated after (Martin 1980).

$$ {\mathrm{Nu}}_{\mathrm{p}\mathrm{w}}=\frac{\alpha_{\mathrm{p}\mathrm{w}}{d}_{\mathrm{p}}}{\lambda_{\mathrm{g}}} $$

$$ {\mathrm{Nu}}_{\mathrm{pw}}=\left(1-\varepsilon \right)Z\left(1-{e}^{-N}\right) $$

With the coefficients

$$ Z=\frac{1}{6}\frac{\rho_{\mathrm{p}}{c}_{\mathrm{p},\mathrm{wet}}}{\lambda_{\mathrm{g}}}\sqrt{\frac{g{d}_{\mathrm{p}}^3\left(\varepsilon -{\varepsilon}_{\mathrm{mf}}\right)}{5\left(1-{\varepsilon}_{\mathrm{mf}}\right)\left(1-\varepsilon \right)}} $$

$$ N=\frac{{\mathrm{Nu}}_{\mathrm{pw}\left(\max \right)}}{C_{\mathrm{K}}Z} $$

$$ {C}_{\mathrm{K}}=2.6 $$

The maximal Nusselt number can be calculated from

$$ {\mathrm{Nu}}_{\mathrm{p}\mathrm{w}\left(\max \right)}=4\left\{\left(1+\frac{2l}{d_{\mathrm{p}}}\right)\ln \left(1+\frac{d_{\mathrm{p}}}{2l}\right)-1\right\} $$

with

$$ l=2\left(\frac{2}{\gamma }-1\right)\sqrt{\frac{2\pi \tilde{R}T}{{\tilde{M}}_{\mathrm{g}}}}\frac{\lambda_{\mathrm{g}}}{p\left(2{c}_{\mathrm{g}}-\tilde{R}/{\tilde{M}}_{\mathrm{g}}\right)} $$

$$ \lg \left(\frac{1}{\gamma }-1\right)=0.6-\frac{\frac{1000\;K}{T_{\mathrm{g}}}+1}{C_{\mathrm{A}}} $$

$$ {C}_{\mathrm{A}}=2.8 $$

where l is the modified free path of the gas molecules.