**4.**

*Theoretical calculation results of minimum fluidization velocity for refined salt particles from equations and empirical correlation formulas of published authors, which compareexperimental results of the physical model of author.*

 *to the*

**2.4 The materials of refined salt particles**

analysis (**Table 3**) [14].

*Current Drying Processes*

**3. Results and discussions**

**refined salt particles**

The material of refined salt particles was supplied by a combined hydraulic separating-washing-grinding machine in the saturated saltwater condition and which was dried by a continuous centrifugal machines. Samples of refined salt were

The above section presented nine methods to calculate minimum fluidization velocity based on the physical parameters of particles and physical thermal parameters of gas stream. These parameters were obtained from experiments in combi-

In order to have the basis of comparison and accuracy evaluation of each calculating method in comparison with the empirical method, the theoretical calculation was carried out for refined salt particles with diameters of 1.5 mm, 1.2 mm, 0.9 mm, 0.6 mm and 0.3 mm. On the other hand, to achieve empirical result, samples of dried refined salt particles (of which mean-diameter was determined) were taken randomly from a combined hydraulic-separating-washing-crushing machine, presenting various particle sizes of the raw material that was put in the dryer.

**3.1 Results of theoretical and empirical calculations for determining Vmf of**

*3.1.1 Some primary conditions for determining the Vmf by theoretical calculations*

a. Calculation based on Ergun equations and correlations of pressure

**Table 4**). Specific notes for each calculating method are as follows:

particles with the fixed bed height (H

degree value of refined salt particle is 0.71 (

recommended that Remf had no limit [13

from the empirical results according to **Table 5**

particle layer at minimum fluidization state (

**96**

c. Determination of the (Vmf) value according to Wen and Yu

When calculating the pressure drop across a refined salt particle layer, we relied on the empirical results of physical parameters of particles and air (summarized in

Applying to calculate the minimum fluidization velocity (Vmf) for refined salt

using Eqs. (35) and (36) to find out the minimum fluidization state including Hmf = 1.1 H0 = 33 mm; bed voidage εmf = 1.1 ε<sup>0</sup> = 0.56. Using the spherical

were taken from the **Table 5** which described in Bui (2009). Then we use the

b. Calculation based on the correlation between (Remf), (Ar) and Kozeny-Carman

In these two calculation methods, the parameters in the calculations are taken

According to Wen and Yu methods, the bed voidage of the refined salt

–15].

.

Ergun equations to calculate the minimum fluidization velocity. It is

0) is 30 mm, the bed voidage (

ϕ = 0.71) and other parameters

εmf) was unknown, but we had

ε 0) is 0.5

randomly taken at different sizes at Vinh Hao salt company in Binh Thuan Province, Bac Lieu salt company and Sea salt Research Center of Vietnam for

nation with the correlation calculation or empirical formulas.


#### **Table 5.**

*Physical parameters of refined salt grains and physical air.*

the value of spherical degree particle from experiments (see **Table 5**)*.* We put the value of spherical degree into Eq. (5) or Eq. (16) and found out the value of bed voidage (εmf) from which the velocity value of gas passing through the minimum fluidization particle layer (Vmf) was calculated.

particles in experiment. The dryer model was designed with its capacity of 48 kg/ hour, the height of salt particle layer at the static bed was 30 mm (H0 ≥ 30 mm). In the experiments, the authors determined the minimum fluidization velocity (Vmf) for refined salt particles with diameter 1.65, 1.35, 1.05, 0.9, 0.65, 0.4 and 0.3 mm. The experimental results of determination of the minimum fluidization velocity of the particle layers with the different particle sizes are shown in **Table 4**. Besides, these experimental minimum fluidization velocity values were also compared with results of theoretical models that were published by authors presented in the

*The model of continuous fluidized bed dryer used in experiments. 1. Air fan; 2. heating chamber; 3. air supplier; 4. air duct; 5. product outlet; 6. drying chamber; 7. dust separation chamber; 8. inlet feeder; 9. cyclone*

*Determination on Fluidization Velocity Types of the Continuous Refined Salt Fluidized Bed Drying*

• The obtained values of minimum fluidization velocity (Vmf) calculated by the Ergun equation and the correlation between Remf number and Ar number for

*Comparison of the minimum fluidization air velocity between calculated values of published authors and*

methodology part above (**Figure 5**).

*DOI: http://dx.doi.org/10.5772/intechopen.92077*

**3.2 Discussions**

**Figure 5.**

**99**

*experimental values of the model [14].*

**Figure 4.**

*dust collector.*

d. Determination of Vmf according to Groshko-Todes

In this method, we also used the results of physical parameters of refined salt particles and air supplied to the dryer from **Table 5** to calculate Ar number. The Remf is determined by using Eq. 2 and the obtained result was multiplied by the error coefficient k = 1.2 and it was considered as the result of calculation of Remf for non-spherical salt particles (described by Lebedev, [21]). In addition, in Todes method there was another calculation by using Eq.(29) based on the available results of the minimum fluidization velocity (εmf = 0.4). We put this value into Eq. (15) and we found out the spherical degree of salt particles according to correlation given byWen and Yu. Then we put this value into Eq. (12) to determine Ar number. By replacing Eq. (29) with the value of Ar number, we found out Remf,from which we could calculate Vmf value by using Eq. (10).

e. Determination of Vmf by the formula of Beayens-Geldart, Goroshko, Leva, and Kunii-Levenspiel

The minimum fluidization bed velocity (Vmf) was determined by using theoretical calculation of formulas of Beayens-Geldart, Goroshko, Leva, and Kunii-Levenspiel with the available physical parameters of refined salt particles and gas given in **Table 5** [18, 19, 22, 25, 26]. **Table 4** shows the calculated results from the formulas of authors published last time.

#### *3.1.2 Primary conditions for determining Vmf by experimental method*

A model in **Figure 3** and the other of fluidized bed dryer in **Figure 4** was designed by authors to define the minimum fluidization velocity of refined salt *Determination on Fluidization Velocity Types of the Continuous Refined Salt Fluidized Bed Drying DOI: http://dx.doi.org/10.5772/intechopen.92077*

#### **Figure 4.**

the value of spherical degree particle from experiments (see **Table 5**)*.* We put the value of spherical degree into Eq. (5) or Eq. (16) and found out the value of bed voidage (εmf) from which the velocity value of gas passing through the

**Technical parameter Symbol Unit Value Ref.**

1.05; 0.75; 0.45; 0.225 [13, 14] [15]

Refined salt particle diameter dp mm 1.65; 1.35;

Average diameter of particle dm mm 0.953 Static bed voidage ε<sup>0</sup> 0.51 Bed voidage in minimum fluidization velocity εmf 0.56 Particle density ρ<sup>p</sup> kg/m3 2138 Bulk density ρ<sup>b</sup> kg/m3 982 Spherical degree of particle ϕ 0.71 Gas density (at 160°C) ρ<sup>f</sup> kg/m3 0.815 Dynamic viscosity (at 160°C) <sup>μ</sup><sup>f</sup> kg/m.s 2.45 <sup>10</sup><sup>5</sup> Fixed refined salt particle bed height H0 m 30

In this method, we also used the results of physical parameters of refined salt particles and air supplied to the dryer from **Table 5** to calculate Ar number. The Remf is determined by using Eq. 2 and the obtained result was multiplied by the error coefficient k = 1.2 and it was considered as the result of calculation of Remf for non-spherical salt particles (described by Lebedev, [21]). In addition, in Todes method there was another calculation by using Eq.(29) based on the available results of the minimum fluidization velocity (εmf = 0.4). We put this value into Eq. (15) and we found out the spherical degree of salt particles according to correlation given byWen and Yu. Then we put this value into Eq. (12) to determine Ar number. By replacing Eq. (29) with the value of Ar number, we found out Remf,from which we could calculate Vmf value by using Eq. (10).

e. Determination of Vmf by the formula of Beayens-Geldart, Goroshko, Leva,

The minimum fluidization bed velocity (Vmf) was determined by using theoretical calculation of formulas of Beayens-Geldart, Goroshko, Leva, and Kunii-Levenspiel with the available physical parameters of refined salt particles and gas given in **Table 5** [18, 19, 22, 25, 26]. **Table 4** shows the calculated

A model in **Figure 3** and the other of fluidized bed dryer in **Figure 4** was designed by authors to define the minimum fluidization velocity of refined salt

results from the formulas of authors published last time.

*3.1.2 Primary conditions for determining Vmf by experimental method*

minimum fluidization particle layer (Vmf) was calculated.

d. Determination of Vmf according to Groshko-Todes

*Note: The particle diameter d = 0.953 is the average diameter of the salt particles.*

*Physical parameters of refined salt grains and physical air.*

and Kunii-Levenspiel

**Table 5.**

*Current Drying Processes*

**98**

*The model of continuous fluidized bed dryer used in experiments. 1. Air fan; 2. heating chamber; 3. air supplier; 4. air duct; 5. product outlet; 6. drying chamber; 7. dust separation chamber; 8. inlet feeder; 9. cyclone dust collector.*

particles in experiment. The dryer model was designed with its capacity of 48 kg/ hour, the height of salt particle layer at the static bed was 30 mm (H0 ≥ 30 mm). In the experiments, the authors determined the minimum fluidization velocity (Vmf) for refined salt particles with diameter 1.65, 1.35, 1.05, 0.9, 0.65, 0.4 and 0.3 mm. The experimental results of determination of the minimum fluidization velocity of the particle layers with the different particle sizes are shown in **Table 4**. Besides, these experimental minimum fluidization velocity values were also compared with results of theoretical models that were published by authors presented in the methodology part above (**Figure 5**).

#### **3.2 Discussions**

• The obtained values of minimum fluidization velocity (Vmf) calculated by the Ergun equation and the correlation between Remf number and Ar number for

#### **Figure 5.**

*Comparison of the minimum fluidization air velocity between calculated values of published authors and experimental values of the model [14].*

all particle sizes agreed well with the experimental values. The value of Remf number varies from 0.3 to 51.7. Particles with sizes dp = 0.225; 0.45 and 0.75 had the tendency for laminar flow.

Vmf < Vhf < Vcf (38)

<sup>0</sup>*:*<sup>815</sup> � <sup>0</sup>*:*<sup>956</sup> � <sup>10</sup>�<sup>3</sup> <sup>¼</sup> <sup>1</sup>*:*6*m=<sup>s</sup>* (41)

Re hf1 <sup>¼</sup> ð Þ� <sup>0</sup>*:*22÷0*:*<sup>33</sup> Ar<sup>0</sup>*:*<sup>52</sup> (42)

� �<sup>3</sup>

� 0*:*815 � ð Þ 2138 � 0*:*815 <sup>2</sup>*:*<sup>45</sup> � <sup>10</sup>�<sup>5</sup> � �<sup>2</sup> <sup>¼</sup> <sup>8818</sup>*:*<sup>4</sup>

<sup>0</sup>*:*<sup>815</sup> � <sup>0</sup>*:*<sup>956</sup> � <sup>10</sup>�<sup>3</sup> <sup>¼</sup> <sup>0</sup>*:*99 m*=*s (43)

¼ 32 (39)

The air superficial velocity value from A to C (**Figure 2**) was determined by the

*Determination on Fluidization Velocity Types of the Continuous Refined Salt Fluidized Bed Drying*

*:* <sup>4</sup> � <sup>9</sup>*:*8 2138 ð Þ � <sup>0</sup>*:*<sup>815</sup> <sup>0</sup>*:*<sup>815</sup> <sup>3</sup>*:* <sup>2</sup>*:*<sup>45</sup> � <sup>10</sup>�<sup>5</sup> � �<sup>2</sup>

Re hf2 <sup>¼</sup> ð Þ <sup>0</sup>*:*19÷0*:*<sup>285</sup> Fe<sup>1</sup>*:*<sup>56</sup> � <sup>&</sup>gt; Re hf2 <sup>¼</sup> <sup>0</sup>*:*<sup>237</sup> � <sup>32</sup><sup>1</sup>*:*<sup>56</sup> <sup>¼</sup> 53 (40)

<sup>¼</sup> <sup>2</sup>*:*<sup>45</sup> � <sup>10</sup>�<sup>5</sup> � <sup>53</sup>

According to Ginzburg (1973), Rehf2 was calculated by Eq. (40) [20, 27].

The homogeneous fluidization velocity (Vhf1) was calculated by Eq. (41).

Reynolds value at homogeneous fluidization velocity (Vhf1) was measured

*ρ <sup>f</sup> ρ<sup>p</sup>* � *ρ <sup>f</sup>*

Substituting parameters of air and refined salt particles into the Eq. (12),

The homogeneous fluidization velocity (Vhf1) was calculated by Eq. (43).

Re-calculating the homogeneous fluidization velocity (Vhf1) by using the

<sup>¼</sup> <sup>2</sup>*:*<sup>45</sup> � <sup>10</sup>�<sup>5</sup> � <sup>31</sup>*:*<sup>53</sup>

� �*<sup>g</sup> <sup>ϕ</sup>dp*

*μ*2 *f*

!1*=*<sup>3</sup>

The air velocity through the solid particle layer at the optimum fluidization regime (Vof) was calculated according to Fedorov standard (Fe) by Eq. (39) (as cited in Lebedev [21]), with refined salt particles and drying air parameters taken

two standard equations as follows:

*DOI: http://dx.doi.org/10.5772/intechopen.92077*

from **Table 5** (tf = 160°C) [13, 15].

0 @

4*g ρ<sup>p</sup>* � *ρ <sup>f</sup>* � �*<sup>ρ</sup> <sup>f</sup>* 3*μ*<sup>2</sup> *f*

*Vhf* <sup>2</sup> <sup>¼</sup> *<sup>μ</sup> <sup>f</sup> :* Re *hf ρ <sup>f</sup> :dp*

according to Archimedes standard by Eq. (42) [20].

*Ar* ¼

Therefore, Rehf1 = 0.275 � (8818.4)0.52 = 66.917 = 31.53.

where Ar was calculated by Eq. (12):

*Ar* <sup>¼</sup> <sup>9</sup>*:*<sup>81</sup> � <sup>0</sup>*:*71 956 � <sup>10</sup>�<sup>6</sup> � � � � <sup>3</sup>

*Vhf* <sup>1</sup> <sup>¼</sup> *<sup>μ</sup> <sup>f</sup> :* Re *hf ρ <sup>f</sup>ϕdp*

experimental equation Eq. (44) [27].

**101**

The Ar value is 8818.4

<sup>¼</sup> <sup>0</sup>*:*<sup>71</sup> � <sup>0</sup>*:*<sup>956</sup> � <sup>10</sup>�<sup>3</sup>

1 A

1*=*3

*Fe* ¼ *ϕdp*


#### **3.3 Determination of air velocity through the particle layer at the optimum fluidization regime (Vof)**

The optimal fluidization velocity Vof was in the region from A to C (**Figure 2**). It meets the conditions:

*Determination on Fluidization Velocity Types of the Continuous Refined Salt Fluidized Bed Drying DOI: http://dx.doi.org/10.5772/intechopen.92077*

$$\mathbf{V\_{mf}} < \mathbf{V\_{hf}} < \mathbf{V\_{cf}} \tag{38}$$

The air superficial velocity value from A to C (**Figure 2**) was determined by the two standard equations as follows:

The air velocity through the solid particle layer at the optimum fluidization regime (Vof) was calculated according to Fedorov standard (Fe) by Eq. (39) (as cited in Lebedev [21]), with refined salt particles and drying air parameters taken from **Table 5** (tf = 160°C) [13, 15].

$$\begin{split}Fe &= \phi d\_p \left(\frac{4\mathbf{g}\left(\rho\_p - \rho\_f\right)\rho\_f}{3\mu\_f^2}\right)^{1/3} \\ &= 0.71 \times 0.956 \times 10^{-3} \cdot \left(\frac{4 \times 9.8 (2138 - 0.815) \text{0.815}}{3.{\left(2.45 \times 10^{-5}\right)}^2}\right)^{1/3} = 32 \end{split} \tag{39}$$

According to Ginzburg (1973), Rehf2 was calculated by Eq. (40) [20, 27].

$$\mathrm{Re}\_{\mathrm{hf2}} = (0.19 \div 0.285) \,\mathrm{Fe}^{1.56} - > \mathrm{Re}\_{\mathrm{hf2}} = 0.237 \times 32^{1.56} = 53\tag{40}$$

The homogeneous fluidization velocity (Vhf1) was calculated by Eq. (41).

$$\mathbf{V}\_{hf2} = \frac{\mu\_f \cdot \mathbf{Re}\_{hf}}{\rho\_f \cdot d\_p} = \frac{2.45 \times 10^{-5} \times 53}{0.815 \times 0.956 \times 10^{-3}} = 1.6 m/s \tag{41}$$

Reynolds value at homogeneous fluidization velocity (Vhf1) was measured according to Archimedes standard by Eq. (42) [20].

$$\mathbf{Re}\_{\mathrm{hf1}} = (\mathbf{0.22} \div \mathbf{0.33}) \times \mathbf{Ar}^{0.52} \tag{42}$$

where Ar was calculated by Eq. (12):

$$Ar = \frac{\rho\_f \left(\rho\_p - \rho\_f\right) \text{g}\left(\phi d\_p\right)^3}{\mu\_f^2}$$

Substituting parameters of air and refined salt particles into the Eq. (12),

$$Ar = \frac{9.81 \times \left(0.71 (956 \times 10^{-6})\right)^3 \times 0.815 \times (2138 - 0.815)}{\left(2.45 \times 10^{-5}\right)^2} = 8818.4$$

The Ar value is 8818.4

Therefore, Rehf1 = 0.275 � (8818.4)0.52 = 66.917 = 31.53. The homogeneous fluidization velocity (Vhf1) was calculated by Eq. (43).

$$V\_{hf1} = \frac{\mu\_f \cdot \text{Re}\_{hf}}{\rho\_f \phi d\_p} = \frac{2.45 \times 10^{-5} \times 31.53}{0.815 \times 0.956 \times 10^{-3}} = 0.99 \text{ m/s} \tag{43}$$

Re-calculating the homogeneous fluidization velocity (Vhf1) by using the experimental equation Eq. (44) [27].

all particle sizes agreed well with the experimental values. The value of Remf number varies from 0.3 to 51.7. Particles with sizes dp = 0.225; 0.45 and 0.75

• The obtained values of minimum fluidization velocity (vmf) determined by the Kozeny-Carman and Kunii equations for particles with diameter greater than

(Vtmf > > Vemf). While, with particles having diameter smaller than 1 mm (dp < 1 mm), the result of calculation was nearly equal to the experimental values. Notably, the void fraction value of the minimum fluidization state from 0.4 to 0.5 (εmf = 0.4–0.5) the calculation result matches the experimental value.

• By using the correlation of Wen and Yu to calculate void fraction at (εmf)

• When using the correlation between Remf and Ar, the obtained values of minimum fluidization velocity fit quite well to experimental results. Reynolds

• The minimum fluidization velocity that was calculated according the

correlation between Remf and Ar number of Beayens and Geldart (Eq. (19))

• The obtained values by using the Goroshko and Todes formula in Eq. (28) were

• The calculated value of Vmf according to Beayens and Geldart was the lowest in

• The difference between the values of Remf calculated according to Goroshko and Ergun was lower than 10–20% for particles that lie in the range of Remf number from 0.28 to 43.7 (Remf = 0.28–43.7). The obtained values of velocity value (Vmf) for particles with diameter smaller than 0.9 mm (dp < 0.9 mm) were closer to the experimental value in comparison with particles with

• The minimum fluidization velocity that was calculated by Leva formula was only suitable for particles with diameter smaller than 0.75 mm (dp < 0.75 mm) and value of Remf number smaller than 10 (Remf < 10). The regime of air flow

• The calculation method of the minimum fluidization velocity according to the Kunii and Levenspiel equations was suitable for particle with diameter dp = (0.225; 0.45; 0.75 mm) and the results were appropriate under the conditions Remf < 20, and the calculation result was close to the experimental

**3.3 Determination of air velocity through the particle layer at the optimum**

The optimal fluidization velocity Vof was in the region from A to C (**Figure 2**). It

knowing the spherical properties of particle, we obtained values that were much smaller than the experimental value. The Remf number varied from 0.07 to 21.1.

1 mm (dp > 1 mm) were much larger than experimental values

had the tendency for laminar flow.

*Current Drying Processes*

values vary from 0.16 to 36.6.

comparison to other methods.

nearly equal to the experimental values.

diameter larger than 0.9 mm (dp > 0.9 mm).

through the particle layer is laminar flow.

value.

meets the conditions:

**100**

**fluidization regime (Vof)**

gave reasonable results.

From **Table 4** for the specific case: Vmf = 0.55 m/s and particle diameter was 0.953 mm.

$$\mathbf{V\_{hf1}} = (\mathbf{2} \div \mathbf{3}) \times \mathbf{V\_{mf}} = (\mathbf{2} \div \mathbf{3}) \times \mathbf{0.56} = (\mathbf{1.12} \div \mathbf{1.68}) \text{ m/s} \tag{44}$$

Both Vhf1 and Vhf2 met the conditions of the Eq. (38). Selecting the optimum velocity Vof:

$$\mathbf{V\_{of}} = (\mathbf{V\_{hf1}} + \mathbf{V\_{hf2}})/2 = (\mathbf{0.99} + \mathbf{1.66})/2 = \mathbf{1.33 m/s}$$

Re-calculating the standard Reynolds number at reasonable fluidization state (Reof) under the condition of optimum fluidization velocity (Vof = 1.33 m/s)

$$\mathbf{V}\_{\text{gf}} = \frac{\mu\_f.\,\text{Re}\_{\text{gf}}}{\rho\_f.d\_{\text{p}}} \tag{45}$$

From the calculation result of Remf of the minimum fluidization state (Remf = 10.032), this parameter of the air stream through the particle layer in the

*Determination on Fluidization Velocity Types of the Continuous Refined Salt Fluidized Bed Drying*

<sup>¼</sup> 4 2138 ð Þ � <sup>0</sup>*:*<sup>815</sup> <sup>9</sup>*:*<sup>81</sup> 3 � 0*:*815 � *CD*

With resistance coefficient (CD) (described in Wen-ChingYang) [27, 28] given by

So, the critical velocity at position C (**Figure 2**) in the specific case had the value:

In fact, during the drying process, to ensure the drying productivity and quality, the dryer operator must observe the fluidization particle layer and adjust the inlet doors of drying air capacity at appropriate the air velocity value in the range from A

We re-calculated the void fraction of particle layer with average particle diameter dp = ϕdm = 0.953 mm at the theoretical critical velocity in fluidization particle

Re � calculating Re cf : Re *cf* <sup>¼</sup> *<sup>ϕ</sup>dp:<sup>ρ</sup> <sup>f</sup> :Vof*

Using Eq. (46) to re-calculate the void fraction of particle layer at the complete

When the void fraction of particle layer was 1 (ε = 1), the fluidization particle

Re cf <sup>¼</sup> <sup>0</sup>*:*<sup>71</sup> � <sup>956</sup> � <sup>10</sup>�<sup>6</sup> � � � <sup>0</sup>*:*<sup>815</sup> � <sup>2</sup>*:*<sup>3</sup>

Re <sup>3</sup>*=*<sup>5</sup> <sup>¼</sup> <sup>18</sup>

<sup>0</sup>*:*<sup>71</sup> � <sup>0</sup>*:*<sup>953</sup> � �1*=*<sup>2</sup>

ð Þ <sup>10</sup>*:*<sup>032</sup> <sup>3</sup>*=*<sup>5</sup> <sup>¼</sup> <sup>4</sup>*:*<sup>5</sup> (50)

*μ f*

<sup>2</sup>*:*<sup>4</sup> � <sup>10</sup>�<sup>5</sup> <sup>¼</sup> <sup>0</sup>*:*53*:*

<sup>¼</sup> <sup>18</sup> � <sup>53</sup> <sup>þ</sup> <sup>0</sup>*:*<sup>36</sup> � ð Þ <sup>53</sup> <sup>2</sup> 8818*:*4 !<sup>0</sup>*:*<sup>21</sup>

¼ 2*:*3*m=s*

(49)

(51)

(52)

¼ 0*:*73

According to the equation of Haider and Levenspiel (described in Wen-ChingYang) [28, 29], the critical velocity was calculated by Eq. (49).

transition flow was in range 1 < Remf < 500.

*DOI: http://dx.doi.org/10.5772/intechopen.92077*

*ϕdp*

3 5

1*=*2

*CD* <sup>¼</sup> <sup>18</sup>

*ϕdp*

Substituting the above value into Eq. (52), we get:

*cf*

layer turned to the transport regime in the air stream (called pneumatic

3 5

1*=*2

<sup>0</sup>*:*<sup>71</sup> � <sup>956</sup> � <sup>10</sup>�<sup>6</sup> � � � �<sup>1</sup>*=*<sup>2</sup>

to C (**Figure 2**) and the correlation of velocity types Vmf < Vhf < Vcf.

4 *ρ<sup>p</sup>* � *ρ <sup>f</sup>* � �*<sup>g</sup>*

3*ρ fCD*

4 *ρ<sup>p</sup>* � *ρ <sup>f</sup>* � �*<sup>g</sup>*

3*ρ fCD*

<sup>¼</sup> 4 2138 <sup>ð</sup> � <sup>0</sup>*:*815Þ � <sup>9</sup>*:*<sup>81</sup> 3 � 0*:*815 � 4*:*5

*Vcf* ¼

*Vcf* ¼

layer condition.

fluidization state:

transportation).

**103**

*<sup>ε</sup>tf* <sup>¼</sup> 18 Re *cf* <sup>þ</sup> <sup>0</sup>*:*36 Re <sup>2</sup>

*Ar* !<sup>0</sup>*:*<sup>21</sup>

2 4

2 4

or

$$\mathrm{Re}\_{\circ f} = \frac{\phi d\_p \rho\_f V\_{\circ f}}{\mu\_f} = \frac{0.71 \left(0.956 \times 10^{-3}\right) 0.815 \times 1.33}{2.45 \times 10^{-5}} = 30$$

The value of optimum Reynolds number (Reof) was 30 (Reof = 30).

The void fraction of the particle layer at the reasonable fluidization state was determined by the Zabrodski formula (Eq. 46) (described in Lebedev, [21]).

$$\varepsilon\_{bf1} = \left(\frac{18\,\mathrm{Re}\_{obj} + 0.36\,\mathrm{Re}\_{obj}^2}{Ar}\right)^{0.21} = \left(\frac{18 \times 30 + 0.36(30)^2}{8818.4}\right)^{0.21} = 0.61 \quad \text{(46)}$$

Rehf2 could be recalculated according to the correlation between Rehf2 and Ar Eq. (47).

$$\text{Re}\_{hf2} = (0.22 \div 0.33) \text{Ar}^{0.52} = 0.275 \times (8818.4)^{0.52} = \mathfrak{A1} \tag{47}$$

Substituting value of Rehf2 into Eq. (46), we re-calculated the homogeneous fluidization void fraction (εhf) by Eq. (48).

$$\epsilon\_{\rm hf} = \left(\frac{18\,\mathrm{Re}\_{\rm hf} + 0.36\,\mathrm{Re}\_{\rm hf}^2}{Ar}\right)^{0.21} = \left(\frac{18 \times 31 + 0.36(31)^2}{8818.4}\right)^{0.21} = 0.62 \tag{48}$$

These two calculation methods generated almost identical results.

#### **3.4 Calculation of the critical air velocity flowing through the fluidization particle layer**

In order to have a basis for determining the reasonable dimension of separating chamber of fluidized bed dryer (the chamber was located above the fluidization particle drying tank) and to limit removal of materials from the drying chamber, we defined the theoretical critical velocity (also called the final velocity).

*Determination on Fluidization Velocity Types of the Continuous Refined Salt Fluidized Bed Drying DOI: http://dx.doi.org/10.5772/intechopen.92077*

From the calculation result of Remf of the minimum fluidization state (Remf = 10.032), this parameter of the air stream through the particle layer in the transition flow was in range 1 < Remf < 500.

According to the equation of Haider and Levenspiel (described in Wen-ChingYang) [28, 29], the critical velocity was calculated by Eq. (49).

$$\mathbf{V}\_{\mathcal{G}} = \left[\frac{4\left(\rho\_p - \rho\_f\right)\mathbf{g}}{3\rho\_f\mathbf{C}\_D}\phi d\_p\right]^{1/2} = \left[\frac{4(2138 - 0.815)9.81}{3 \times 0.815 \times \mathbf{C}\_D} 0.71 \times 0.953\right]^{1/2} \tag{49}$$

With resistance coefficient (CD) (described in Wen-ChingYang) [27, 28] given by

$$C\_D = \frac{18}{\text{Re}^{3/5}} = \frac{18}{\left(10.032\right)^{3/5}} = 4.5\tag{50}$$

So, the critical velocity at position C (**Figure 2**) in the specific case had the value:

$$\begin{aligned} V\_{\mathcal{G}} &= \left[ \frac{4\left(\rho\_p - \rho\_f\right)g}{3\rho\_f C\_D} \phi d\_p \right]^{1/2} \\\\ &= \left[ \frac{4(2138 - 0.815) \times 9.81}{3 \times 0.815 \times 4.5} (0.71 \times 956 \times 10^{-6}) \right]^{1/2} = 2.3 m/s \end{aligned} \tag{51}$$

In fact, during the drying process, to ensure the drying productivity and quality, the dryer operator must observe the fluidization particle layer and adjust the inlet doors of drying air capacity at appropriate the air velocity value in the range from A to C (**Figure 2**) and the correlation of velocity types Vmf < Vhf < Vcf.

We re-calculated the void fraction of particle layer with average particle diameter dp = ϕdm = 0.953 mm at the theoretical critical velocity in fluidization particle layer condition.

$$\text{Re } - \text{ calculating } \text{Re}\_{\text{cf}} : \text{Re}\_{\text{cf}} = \frac{\phi d\_{p} \cdot \rho\_{f} \cdot V\_{\text{of}}}{\mu\_{f}} \tag{52}$$

Substituting the above value into Eq. (52), we get:

$$\mathrm{Re}\_{\mathrm{cf}} = \frac{\mathbf{0.71} \times \left(\mathbf{956} \times \mathbf{10^{-6}}\right) \times \mathbf{0.815} \times \mathbf{2.3}}{2.4 \times \mathbf{10^{-5}}} = \mathbf{0.53}.$$

Using Eq. (46) to re-calculate the void fraction of particle layer at the complete fluidization state:

$$\varepsilon\_{\rm{f}} = \left(\frac{18\,\mathrm{Re}\_{\rm{cf}} + 0.36\,\mathrm{Re}\_{\rm{cf}}^2}{Ar}\right)^{0.21} = \left(\frac{18 \times 53 + 0.36 \times (53)^2}{8818.4}\right)^{0.21} = 0.73$$

When the void fraction of particle layer was 1 (ε = 1), the fluidization particle layer turned to the transport regime in the air stream (called pneumatic transportation).

From **Table 4** for the specific case: Vmf = 0.55 m/s and particle diameter was

Both Vhf1 and Vhf2 met the conditions of the Eq. (38). Selecting the optimum

Vof ¼ ð Þ Vhf1 þ Vhf2 *=*2 ¼ ð Þ 0*:*99 þ 1*:*66 *=*2 ¼ 1*:*33 m*=*s

Re-calculating the standard Reynolds number at reasonable fluidization state (Reof) under the condition of optimum fluidization velocity (Vof = 1.33 m/s)

> *Vof* <sup>¼</sup> *<sup>μ</sup> <sup>f</sup> :* Re *of ρ <sup>f</sup> :dp*

Rehf2 could be recalculated according to the correlation between Rehf2 and Ar

Substituting value of Rehf2 into Eq. (46), we re-calculated the homogeneous

The value of optimum Reynolds number (Reof) was 30 (Reof = 30). The void fraction of the particle layer at the reasonable fluidization state was determined by the Zabrodski formula (Eq. 46) (described in Lebedev, [21]).

*ohf*

*hf*

These two calculation methods generated almost identical results.

defined the theoretical critical velocity (also called the final velocity).

**3.4 Calculation of the critical air velocity flowing through the fluidization**

In order to have a basis for determining the reasonable dimension of separating chamber of fluidized bed dryer (the chamber was located above the fluidization particle drying tank) and to limit removal of materials from the drying chamber, we

Vhf1 ¼ ð Þ� 2÷3 Vmf ¼ ð Þ� 2÷3 0*:*56 ¼ ð Þ 1*:*12÷1*:*68 m*=*s (44)

<sup>¼</sup> <sup>0</sup>*:*71 0*:*<sup>956</sup> � <sup>10</sup>�<sup>3</sup> � �0*:*<sup>815</sup> � <sup>1</sup>*:*<sup>33</sup>

<sup>¼</sup> <sup>18</sup> � <sup>30</sup> <sup>þ</sup> <sup>0</sup>*:*36 30 ð Þ<sup>2</sup> 8818*:*4 !<sup>0</sup>*:*<sup>21</sup>

Re *hf* <sup>2</sup> <sup>¼</sup> ð Þ <sup>0</sup>*:*22÷0*:*<sup>33</sup> Ar0*:*<sup>52</sup> <sup>¼</sup> <sup>0</sup>*:*<sup>275</sup> � ð Þ <sup>8818</sup>*:*<sup>4</sup> <sup>0</sup>*:*<sup>52</sup> <sup>¼</sup> 31 (47)

<sup>¼</sup> <sup>18</sup> � <sup>31</sup> <sup>þ</sup> <sup>0</sup>*:*36 31 ð Þ<sup>2</sup> 8818*:*4 !<sup>0</sup>*:*<sup>21</sup>

<sup>2</sup>*:*<sup>45</sup> � <sup>10</sup>�<sup>5</sup> <sup>¼</sup> <sup>30</sup>

(45)

¼ 0*:*61 (46)

¼ 0*:*62 (48)

0.953 mm.

*Current Drying Processes*

velocity Vof:

or

Eq. (47).

Re *of* <sup>¼</sup> *<sup>ϕ</sup>dp<sup>ρ</sup> fVof μ f*

*Ar* !<sup>0</sup>*:*<sup>21</sup>

fluidization void fraction (εhf) by Eq. (48).

*Ar* !<sup>0</sup>*:*<sup>21</sup>

*<sup>ε</sup>hf* <sup>2</sup> <sup>¼</sup> 18 Re *hf* <sup>þ</sup> <sup>0</sup>*:*36 Re <sup>2</sup>

**particle layer**

**102**

*<sup>ε</sup>hf* <sup>1</sup> <sup>¼</sup> 18 Re *ohf* <sup>þ</sup> <sup>0</sup>*:*36 Re <sup>2</sup>

#### **4. Conclusions**

Most of the used correlations in the calculations and the formulas given by the authors, as mentioned above, were derived from the experiments with temperature close to the ambient temperature. So, when we use them in calculations in specific cases, they should consider the accuracy. The extrapolation should be used in the cases of the states at the temperature higher than the ambient temperature.

ε<sup>0</sup> void fraction at static particle layer Hmf minimum fluidization bed height, m

*DOI: http://dx.doi.org/10.5772/intechopen.92077*

ΔP pressure drop across the bed, N/m<sup>2</sup>

dp spherical particle diameter, m

ϕ sphericity degree, dimensionless

Fe Fedorov standard, dimensionless

g acceleration due to gravity, m/s<sup>2</sup> Vmf minimum fluidization velocity, m/s ρ<sup>p</sup> solid particle density, kg/m<sup>3</sup>

ρ<sup>b</sup> particle bulk density, kg/m<sup>3</sup>

Kcc Kozeny-Carman coefficient

mb mass of particles bulk, kg μ air dynamic viscosity, kg/ms Ss specific surface area, cm<sup>1</sup>

W weight of particle, mass, N

\*Address all correspondence to:

provided the original work is properly cited.

**Author details**

Bui Trung Thanh<sup>1</sup>

**105**

ρ<sup>f</sup> air density, kg/m<sup>3</sup>

mp mass of particles, kg

ϕdm equivalent spherical mean diameters, m

Re Reynolds number εtf terminal void fraction

εmf void fraction at minimum fluidization particle layer

εhf void fraction at homogeneous fluidization particle layer

*Determination on Fluidization Velocity Types of the Continuous Refined Salt Fluidized Bed Drying*

Remf Reynolds number at the minimum fluidization velocity Rehf Reynolds number at the homogeneous fluidization velocity

Recf Reynolds number at the fluidization terminal velocity

Reof Reynolds number at the optimum fluidization velocity

V bed surface velocity or superficial velocity, m/s

Vtmf theoretical minimum fluidization velocity, m/s

Vhf homogeneous fluidization velocity, m/s

Vcf terminal velocity or critical velocity, m/s

\* and Le Anh Duc2

1 Industrial University of Ho Chi Minh City, Vietnam

2 Nong Lam University, Ho Chi Minh City, Vietnam

buitrungthanh@iuh.edu.vn and leanhduc@hcmuaf.edu.vn

U cubic volume of particle layer, m<sup>3</sup>

Vemf experimental minimum fluidization velocity, m/s

Vohf optimum homogeneous fluidization velocity, m/s

, cm2 /g

\*

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

The mentioned theoretical calculations show the necessity for the determining of the minimum fluidization velocity of the solid particle layer with high accuracy. The sphericity of particle and void fraction of the particle layer were often not known, therefore it is required to get their values from the range of experimental variables. Empirically, the void fraction of the particles in the minimum fluidization layer at the ambient temperature is not the same as that in the increasing gas temperature.

The best method to determine the minimum fluidization velocity is to conduct the experiments. Firstly, we directly measured the pressure drop across the particle layer when the air velocity gradually decreased. Secondly, we built the graphs and read the results of the minimum fluidization velocity value.

However, if we were forced to find out the fluidization velocity without carrying out experiments to measure the pressure drop across the particle layer, the best way would be to determine the void fraction at the minimum fluidization velocity. Then we calculated the spherical property of the particle using the Ergun equations or correlation between Ar and Remf in Eqs. (10)–(12) to count out the minimum air velocity through the particle fluidization layer. This velocity value also had accuracy close to the experimental one.

The average particle diameter considered spherical degree of the particles of different sizes was 953 μm (dm = 953 μm). This diameter represented the size of the particles in dry grinding technology with the hammer crusher. It is also in the common size distribution range of the combined washing-grinding hydraulic-separation technology in Vietnam's market. Besides, the particle diameter of 953 μm (dp = 953 μm) is also used in calculating the value of all types of velocity, characterized for the medium particle size of the refined salt production technology in Vietnam.

We calculated the values of three characteristic velocity types of fluidized bed drying for particles with average size dm = dp = 953 μm, including the minimum fluidization velocity Vmf = 0.55 m/s with void fraction εmf = 0.56; reasonable fluidization velocity Vhf = 1.33 m/s corresponding to the void fraction of particle layer εhf = 0.615; and the critical velocity of the air flow through the particle bulk Vcf = 2.3 m/s with the void fraction value of fluidization particle layer εcf = 0.73.

In fact, during the drying process, to ensure the drying productivity and quality, the dryer operator must observe the fluidization particle layer and adjust the inlet doors of drying air capacity at appropriate air velocity value in the range from A to C (**Figure 2**) to make sure the correlation of velocity types Vmf < Vhf < Vcf.

#### **Nomenclature**


*Determination on Fluidization Velocity Types of the Continuous Refined Salt Fluidized Bed Drying DOI: http://dx.doi.org/10.5772/intechopen.92077*


### **Author details**

**4. Conclusions**

*Current Drying Processes*

temperature.

Vietnam.

**Nomenclature**

**104**

A cross sectional area of the bed m<sup>2</sup> area for gas distribution H height of the bed, m

H0 initial bed height, m

Ar Archimedes number, dimensionless

close to the experimental one.

Most of the used correlations in the calculations and the formulas given by the authors, as mentioned above, were derived from the experiments with temperature close to the ambient temperature. So, when we use them in calculations in specific cases, they should consider the accuracy. The extrapolation should be used in the cases of the states at the temperature higher than the ambient temperature.

The mentioned theoretical calculations show the necessity for the determining of the minimum fluidization velocity of the solid particle layer with high accuracy. The sphericity of particle and void fraction of the particle layer were often not known, therefore it is required to get their values from the range of experimental variables. Empirically, the void fraction of the particles in the minimum fluidization layer at the ambient temperature is not the same as that in the increasing gas

The best method to determine the minimum fluidization velocity is to conduct the experiments. Firstly, we directly measured the pressure drop across the particle layer when the air velocity gradually decreased. Secondly, we built the graphs and

However, if we were forced to find out the fluidization velocity without carrying out experiments to measure the pressure drop across the particle layer, the best way would be to determine the void fraction at the minimum fluidization velocity. Then we calculated the spherical property of the particle using the Ergun equations or correlation between Ar and Remf in Eqs. (10)–(12) to count out the minimum air velocity through the particle fluidization layer. This velocity value also had accuracy

The average particle diameter considered spherical degree of the particles of different sizes was 953 μm (dm = 953 μm). This diameter represented the size of the particles in dry grinding technology with the hammer crusher. It is also in the common size distribution range of the combined washing-grinding hydraulic-separation technology in Vietnam's market. Besides, the particle diameter of 953 μm (dp = 953 μm) is also used in calculating the value of all types of velocity, characterized for the medium particle size of the refined salt production technology in

We calculated the values of three characteristic velocity types of fluidized bed drying for particles with average size dm = dp = 953 μm, including the minimum fluidization velocity Vmf = 0.55 m/s with void fraction εmf = 0.56; reasonable fluidization velocity Vhf = 1.33 m/s corresponding to the void fraction of particle layer εhf = 0.615; and the critical velocity of the air flow through the particle bulk Vcf = 2.3 m/s with the void fraction value of fluidization particle layer εcf = 0.73. In fact, during the drying process, to ensure the drying productivity and quality, the dryer operator must observe the fluidization particle layer and adjust the inlet doors of drying air capacity at appropriate air velocity value in the range from A to C (**Figure 2**) to make sure the correlation of velocity types Vmf < Vhf < Vcf.

read the results of the minimum fluidization velocity value.

Bui Trung Thanh<sup>1</sup> \* and Le Anh Duc2 \*

1 Industrial University of Ho Chi Minh City, Vietnam

2 Nong Lam University, Ho Chi Minh City, Vietnam

\*Address all correspondence to: buitrungthanh@iuh.edu.vn and leanhduc@hcmuaf.edu.vn

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## **References**

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[2] Lewis WK, Gilliland ER, Bauer WC. Characteristics of fluidized particles. Industrial and Engineering Chemistry. 1949;**41**:1104-1117. DOI: 10.1021/ ie50497a059

[3] Zahed AH, Zhu JX, Grace JR. Modelling and simulation of batch and continuous fluidized bed dryers. Drying Technology. 1995;**13**:1-28. DOI: 10.1080/ 07373939508916940

[4] Han JW, Keum DH, Kim W, Duc LA, Cho SH, Kim H. Circulating concurrentflow drying simulation of rapeseed. Journal of Biosystems Engineering. 2010;**35**(6):401-407. DOI: 10.5307/JBE.2010.35.6.401

[5] Hong SJ, Duc LA, Han JW, Kim H, Kim YH, Keum DH. Physical properties of rapeseed (II). Journal of Biosystems Engineering. 2008;**33**(3):173-178. DOI: 10.5307/JBE.2008.33.3.173

[6] Duc LA, Han JW. The effects of drying conditions on the germination properties of rapeseed. Journal of Biosystems Engineering. 2009;**34**(1): 30-36. DOI: 10.5307/JBE.2009.34.1.030

[7] Abrahamsen AR, Gedart D. Behaviour of gas-fluidized beds of fine powders part I. Homogeneous expansion. Powder Technology. 1980; **26**:47-55. DOI: 10.1016/0032-5910(80) 85006-6

[8] Geldart D. The effect of particle size and size distribution on the behaviour of gas-fluidized beds. Powder Technology. 1972;**6**:201-215

[9] Geldart D. Types of gas fluidization. Powder Technology. 1973;**7**:285-292. DOI: 10.1016/0032-5910(73)80037-3

[10] Howard JR. Fluidized Bed Technology: Principles and Application. Publisher Taylor and Francis Group; 1989. p. 214

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[29] Yang WC. Flow through fixed beds. In: Yang W-C, editor. Handbook of Fluidization and Fluid-Particle System. New York: Marcel Dekker; 2003.

pp. 29-53

*Determination on Fluidization Velocity Types of the Continuous Refined Salt Fluidized Bed Drying*

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[21] Lebedev PD. Calculation and Design

Leningrad: Gosenergoizdat; 1963. p. 320

[22] Leva M. Fluidization. New York:

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[24] McCabe WE, Smith JC, Harriott P.

[25] Kunii D, Levenspiel O. Various kinds of contacting of a batch of solids by fluid. In: Fluidized Engineering. Huntington, NY: Robert E. Krieger Publishing Co.; 1977. pp. 24-56

Publishing House; 2002

(in Russian)

of Drying Equipmet. Moscow,

McGraw-Hill; 1959. p. 281

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[27] Ginzburg AS. Theoretical and Technical Basis of Drying Food Products. Moscow: Pishchevaya Promyshlennost; 1973. p. 528

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1991. p. 49

(in Russian)

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[19] Goroshko VD, Rozenbaum RB, Todes OM. Approximate laws of fluidized bed hydraulics and restrained fall. Izvestiya Vysshikh Uchebnykh Zavedenii, Neft i Gaz. 1958;**1**:125-131

[11] Rhodes M. Fluidization of particles by fluids. In: Educational Resources for Particles Technology. Melbourne, Australia: Monash University; 2001. pp. 1-39

[12] Ergun S. Fluid flow through packed columns. Chemical Engineering Progress. 1952;**48**:9-94

[13] Bui TT. Determination on geometrical parameters of refined salt particle applying of fluidized particle lay drying. Journal of Heat Science and Technology. 2009;**86**:10-13

[14] Bui TT. Determination on hydrodynamic parameters in fine salt drying in a model of fluidized bed dryer. Journal of Heat Science and Technology. 2009;**90**:13-17

[15] Bui TT. Researching and determining on basic physical parameters of refined salt particles to apply in the calculation and designing of continuous fluidized bed. Journal of Vietnam Mechanical Engineering. 2009; **146**:8-31 and 48

[16] Yates JG. Fundamentals of Fluidized-Bed Chemical Processes. 1st ed. Oxford: Butterworth-Heinemann; 1983. p. 236

[17] Wen CY, Yu YH. A generalized method for predicting the minimum fluidized velocity. AICHE Journal. 1966; **12**:610-612

[18] Baeyens J, Geldart D. Predictive calculations of flow parameters in gas fluidized bed and fluidization behavior of various powders. In: Proceedings of

*Determination on Fluidization Velocity Types of the Continuous Refined Salt Fluidized Bed Drying DOI: http://dx.doi.org/10.5772/intechopen.92077*

the International Symposiu on Fluidization and its Applications; 1973

**References**

ie50497a059

07373939508916940

Cho SH, Kim H. Circulating

10.5307/JBE.2010.35.6.401

10.5307/JBE.2008.33.3.173

[1] Tavoulareas S. Fluidized-bed combustion technology. Annual

[3] Zahed AH, Zhu JX, Grace JR. Modelling and simulation of batch and continuous fluidized bed dryers. Drying Technology. 1995;**13**:1-28. DOI: 10.1080/

[2] Lewis WK, Gilliland ER, Bauer WC. Characteristics of fluidized particles. Industrial and Engineering Chemistry. 1949;**41**:1104-1117. DOI: 10.1021/

[10] Howard JR. Fluidized Bed

1989. p. 214

pp. 1-39

Technology: Principles and Application. Publisher Taylor and Francis Group;

[11] Rhodes M. Fluidization of particles by fluids. In: Educational Resources for Particles Technology. Melbourne, Australia: Monash University; 2001.

[12] Ergun S. Fluid flow through packed

geometrical parameters of refined salt particle applying of fluidized particle lay drying. Journal of Heat Science and

hydrodynamic parameters in fine salt drying in a model of fluidized bed dryer. Journal of Heat Science and Technology.

parameters of refined salt particles to apply in the calculation and designing of continuous fluidized bed. Journal of Vietnam Mechanical Engineering. 2009;

columns. Chemical Engineering

[13] Bui TT. Determination on

Technology. 2009;**86**:10-13

2009;**90**:13-17

**146**:8-31 and 48

1983. p. 236

**12**:610-612

[14] Bui TT. Determination on

[15] Bui TT. Researching and determining on basic physical

[16] Yates JG. Fundamentals of

Fluidized-Bed Chemical Processes. 1st ed. Oxford: Butterworth-Heinemann;

[17] Wen CY, Yu YH. A generalized method for predicting the minimum fluidized velocity. AICHE Journal. 1966;

[18] Baeyens J, Geldart D. Predictive calculations of flow parameters in gas fluidized bed and fluidization behavior of various powders. In: Proceedings of

Progress. 1952;**48**:9-94

[4] Han JW, Keum DH, Kim W, Duc LA,

concurrentflow drying simulation of rapeseed. Journal of Biosystems

Engineering. 2010;**35**(6):401-407. DOI:

[5] Hong SJ, Duc LA, Han JW, Kim H, Kim YH, Keum DH. Physical properties of rapeseed (II). Journal of Biosystems Engineering. 2008;**33**(3):173-178. DOI:

[6] Duc LA, Han JW. The effects of drying conditions on the germination properties of rapeseed. Journal of Biosystems Engineering. 2009;**34**(1): 30-36. DOI: 10.5307/JBE.2009.34.1.030

[7] Abrahamsen AR, Gedart D.

powders part I. Homogeneous

85006-6

**106**

1972;**6**:201-215

Behaviour of gas-fluidized beds of fine

expansion. Powder Technology. 1980; **26**:47-55. DOI: 10.1016/0032-5910(80)

[8] Geldart D. The effect of particle size and size distribution on the behaviour of gas-fluidized beds. Powder Technology.

[9] Geldart D. Types of gas fluidization. Powder Technology. 1973;**7**:285-292. DOI: 10.1016/0032-5910(73)80037-3

Reviews. 1991;**16**:25-27

*Current Drying Processes*

[19] Goroshko VD, Rozenbaum RB, Todes OM. Approximate laws of fluidized bed hydraulics and restrained fall. Izvestiya Vysshikh Uchebnykh Zavedenii, Neft i Gaz. 1958;**1**:125-131

[20] Tran VP. Calculation and Designing on the Drying System. Hanoi: Education Publishing House; 2002

[21] Lebedev PD. Calculation and Design of Drying Equipmet. Moscow, Leningrad: Gosenergoizdat; 1963. p. 320 (in Russian)

[22] Leva M. Fluidization. New York: McGraw-Hill; 1959. p. 281

[23] Carman PC. Fluid flow through granular beds. Transactions, Institution of Chemical Engineers. 1937;**15**:150-166

[24] McCabe WE, Smith JC, Harriott P. Unit Operations of Chemical Engineering. 6th ed. New York: McGraw Hill; 2001. p. 1132

[25] Kunii D, Levenspiel O. Various kinds of contacting of a batch of solids by fluid. In: Fluidized Engineering. Huntington, NY: Robert E. Krieger Publishing Co.; 1977. pp. 24-56

[26] Kunii D, Levenspiel O. Fluidization engineering. 2nd ed. Boston: Butterworth-Heinemann; 1991. p. 49

[27] Ginzburg AS. Theoretical and Technical Basis of Drying Food Products. Moscow: Pishchevaya Promyshlennost; 1973. p. 528 (in Russian)

[28] Yang WC. Particle characterization and dynamics. In: Yang WC, editor. Handbook of Fluidization and Fluid-Particle System. New York: Marcel Dekker; 2003. pp. 1-29

[29] Yang WC. Flow through fixed beds. In: Yang W-C, editor. Handbook of Fluidization and Fluid-Particle System. New York: Marcel Dekker; 2003. pp. 29-53

**109**

Section 3

Novel Drying

Technologies

Section 3
