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

*Bui Trung Thanh and Le Anh Duc*

#### **Abstract**

After the centrifugation stage, refined salt particles have rather high moisture content; therefore, the moist salt particles in contact with each other will stick together in a short time. In particular, the moist salt particles will stick together faster and tighter and form a larger unit when they are exposed to drying hot air. For this reason, the refined salt was dried by rotary drum dryers with vibrating balls distributed along the drum or a vibrating fluidized bed dryers. These drying methods make poor product sensory quality, low product recovery efficiency, while also lead to an increase of heat and electricity energy consumption. In order to increase the efficiency of refined salt drying technology by conventional continuous fluidized bed dryers, the chapter focuses on the study of aerodynamic properties of refined salt grains in the continuous fluidized particle layer. The content of the chapter presents theoretical and empirical methods to determine fluidization velocity types in designing a continuous fluidized bed dryer.

**Keywords:** refined salt, solid particles, aerodynamic, minimum fluidization velocity, homogeneous fluidization, bed fraction, fluidized bed dryer

#### **1. Introduction**

#### **1.1 Preface**

The phenomenon in which solid particles float in a gas stream and have a liquidlike property is called a fluidized bed. This phenomenon of fluidization in gas or liquid flow was discovered by Fritz Winkler in the 1920s [1]. This one was investigated by Lewis et al. and had been raised to fluidized theory [2]. The first commercial fluidized bed dryer was installed in USA in 1948 [3]. The fluidized bed technology is used for drying of bulk materials, includes examples such as: vibrating fluidized bed dryer, normal fluidized bed dryer without vibrating device and pulsed fluidized bed dryer.

Mathematical modeling and computer simulation of grain drying are now widely used and become an important tool for designing new dryers, for analyzing existing drying systems and for identifying drying conditions [4]. Identifying the drying conditions is necessary to establish the optimal protocol for ensuring seed quality [5]. To solve the simulation models, equations concerning aerodynamic properties such as the gas stream velocity and particle velocity are the most important components. The aerodynamic properties are affected by shape, density and size of particles [6].


**Table 1.**

*Relations and functions of gas interacting with solid particle in real production.*

In recent years, the fluidized bed technology has been concerned in the application in the sugar drying and refined salt drying in Vietnam. In the scope of this chapter, we discuss the issues related to the hydrodynamics of refined salt particles in the gas stream at ambient temperature and temperature equivalent to that of drying particle. The focus of this chapter is to determine the velocity values of the gas through the particle layer to form the minimum, homogeneous and critical fluidized layers.

**1.3 Basic concept of fluidized particle layer and principle of fluidized particle**

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

When the material layer is fluidized, its state is converted from a fixed bed to a dynamic state. The particle layer has liquid-like properties. The surface area of the particles contacting with the fluid increases, and therefore the heat transfer ability

In order for the fluidization phenomena to occur in the bulk material layer, the air stream must have sufficient pressure and velocity. The air stream flows upward,

By further raising the velocity of air stream to the critical value, the friction force between the particles and air is equal to the weight of particles. At this time, the vertical component of the compression pressure is eliminated, the upwardpulling force equals the downward gravity, causing the particle material to be suspended in the air stream. When the gas velocity reaches the critical value, the particle material layer will be converted to complete fluidization state, called the fluidization particle layer and having the liquid-like properties (position from A to

By further increasing the velocity of the gas, the bulk density of the particle layers continues to decrease, its fluidization becomes more violent, until the particles no longer form a bed and are swept up and fallen down in the fluidization motion (position from B to C, **Figure 2**). At this time, each particle material is covered with gas flow, the intensity of the heat and material transfer occurs violently. When granular material is fully fluidized, the bed will conform to the volume of the chamber, its surface remaining perpendicular to gravity; objects with a lower

passes through the particle materials (follow the linear increment) through uncountable air holes of the distributor, which are arranged at the bottom of the particle material layer. When the velocity of air stream is small, pressure exerted on particles is small, the particle layer maintains its original fixed bed (the state from 0 before point A, **Figure 2**). As the air velocity is increased further, the aerodynamic traction appears, which has opposite effect of the gravitational force of the particles, causing the expansion of particle layers in a volume, and the particles begin to move

**layer creation**

**Figure 1.**

B in **Figure 2**).

**87**

from fluid to particles rapidly rises.

*Diagram of the Geldart classification of particles [9, 10].*

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

apart from each other (at point A, **Figure 1**).

In industrial manufacturing practice, we often encounter the contact, interaction between solid-particle materials and gases. These interaction phenomena are described in **Table 1**.

#### **1.2 Applied materials in fluidized bed drying technology**

According to Abrahamsen and Geldart [7], the two most important factors affecting the fluidization characteristic of the particle layer are particle size and particle density.

Geldart [8] visually observed the various conditions and classified fluidizable particles into four groups: A, B, C and D. As a result, the classification was related to the influence of the average particle size and particle density on the properties of the fluidized layer, as depicted in **Figure 1** and **Table 2**.

According to the content of this chapter, we focus on approaching, researching and experimenting on the mechanism and principle of interaction between air and the applied material in fluidized bed drying. The approach method is to arrange a stream of heat-carrying air blowing from the bottom of the particle chamber through a gas distributor (the holes arranged at an angle to the cross section of the tank). Hot air stream is evenly distributed and touches the surface of particles in tank (the particle layer was on the gas distributor). The continuous air stream ensures that the contact of particle surfaces with the gas flow is consecutive. The nature of the gas flowing through the particle layer may be laminar, turbulent, or transition flow at the material contact surface. The inflow of hot air affects the velocity of the interaction between the gas stream and the material.

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

**Figure 1.** *Diagram of the Geldart classification of particles [9, 10].*

#### **1.3 Basic concept of fluidized particle layer and principle of fluidized particle layer creation**

When the material layer is fluidized, its state is converted from a fixed bed to a dynamic state. The particle layer has liquid-like properties. The surface area of the particles contacting with the fluid increases, and therefore the heat transfer ability from fluid to particles rapidly rises.

In order for the fluidization phenomena to occur in the bulk material layer, the air stream must have sufficient pressure and velocity. The air stream flows upward, passes through the particle materials (follow the linear increment) through uncountable air holes of the distributor, which are arranged at the bottom of the particle material layer. When the velocity of air stream is small, pressure exerted on particles is small, the particle layer maintains its original fixed bed (the state from 0 before point A, **Figure 2**). As the air velocity is increased further, the aerodynamic traction appears, which has opposite effect of the gravitational force of the particles, causing the expansion of particle layers in a volume, and the particles begin to move apart from each other (at point A, **Figure 1**).

By further raising the velocity of air stream to the critical value, the friction force between the particles and air is equal to the weight of particles. At this time, the vertical component of the compression pressure is eliminated, the upwardpulling force equals the downward gravity, causing the particle material to be suspended in the air stream. When the gas velocity reaches the critical value, the particle material layer will be converted to complete fluidization state, called the fluidization particle layer and having the liquid-like properties (position from A to B in **Figure 2**).

By further increasing the velocity of the gas, the bulk density of the particle layers continues to decrease, its fluidization becomes more violent, until the particles no longer form a bed and are swept up and fallen down in the fluidization motion (position from B to C, **Figure 2**). At this time, each particle material is covered with gas flow, the intensity of the heat and material transfer occurs violently. When granular material is fully fluidized, the bed will conform to the volume of the chamber, its surface remaining perpendicular to gravity; objects with a lower

In recent years, the fluidized bed technology has been concerned in the application in the sugar drying and refined salt drying in Vietnam. In the scope of this chapter, we discuss the issues related to the hydrodynamics of refined salt particles in the gas stream at ambient temperature and temperature equivalent to that of drying particle. The focus of this chapter is to determine the velocity values of the gas through the particle layer to form the minimum, homogeneous and critical fluidized layers. In industrial manufacturing practice, we often encounter the contact, interaction between solid-particle materials and gases. These interaction phenomena are

5 Agitation Materials do not react to gases Mixer of different materials in the

**Order Function of gases Function of solid materials Equipment in practice** 1 Heat carrier Materials do not react to gases • Heaters supply to materials

> • Activated material for chemical reactions • As inert material which is used in fluidized bed combustion of boiler

• Heat exchangers with heat

recovery

• The burner burns • Gasification equipment • Catalytic reconstitution • Oxidation equipment • Processing of metallurgical surfaces and annealing furnace

tank

Materials do not react to gases Pneumatic solid particle carrier

Materials do not react to gases Aerodynamic dryers

According to Abrahamsen and Geldart [7], the two most important factors affecting the fluidization characteristic of the particle layer are particle size and

Geldart [8] visually observed the various conditions and classified fluidizable particles into four groups: A, B, C and D. As a result, the classification was related to the influence of the average particle size and particle density on the properties of

According to the content of this chapter, we focus on approaching, researching and experimenting on the mechanism and principle of interaction between air and the applied material in fluidized bed drying. The approach method is to arrange a stream of heat-carrying air blowing from the bottom of the particle chamber through a gas distributor (the holes arranged at an angle to the cross section of the tank). Hot air stream is evenly distributed and touches the surface of particles in tank (the particle layer was on the gas distributor). The continuous air stream ensures that the contact of particle surfaces with the gas flow is consecutive. The nature of the gas flowing through the particle layer may be laminar, turbulent, or transition flow at the material contact surface. The inflow of hot air affects the

**1.2 Applied materials in fluidized bed drying technology**

*Relations and functions of gas interacting with solid particle in real production.*

the fluidized layer, as depicted in **Figure 1** and **Table 2**.

velocity of the interaction between the gas stream and the material.

described in **Table 1**.

**Table 1.**

2 Loading and

*Current Drying Processes*

3 Heat carrier and

transportation of particle materials

material loading and transportation

4 Chemical agents • Chemical reaction

particle density.

**86**


**2. Methodology**

**Figure 2.**

**89**

**2.1 Determination of the minimum fluidization velocity from publications**

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

When the air stream having sufficient pressure and velocity passes through the static spherical particle layers, they begin to expand (the particles become "flexible"). In this condition, it is called the minimum particulate fluidization state and is described by the modified equation of Ergun (see position A in **Figure 1**) [12].

*Vmf*

þ

For particles of arbitrary shapes, the pressure drop of air stream at the minimum fluidization state is represented by Eq. (2). The spherical value of particle material

> *μ fVmf* ð Þ *<sup>ϕ</sup>dm* <sup>2</sup> <sup>þ</sup> <sup>1</sup>*:*<sup>75</sup>

For the particle layer to be converted from a fixed state to a fluidization state, the pressure of air stream must be large enough to overcome the weight of the

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

In Eq. (3), it is considered that there was no interaction force between particles in layer and no interaction between particles and the wall of the tank. So, that did not cause the pressure increasing effect. Thus, the pressure drop of the air stream was constant while increasing the gas velocity from the smallest fluidization velocity to the value when the entrainment process of particles occurred (position C, **Figure 2**). In Eqs. (1) and (2), it is also shown that the pressure drop of the gas stream that is generated through the fluidized particle layer is depended on the particle size

<sup>1</sup>*:*75 1 � *<sup>ε</sup>mf <sup>ρ</sup> fVmf*

*εmf* <sup>3</sup>*dp*

<sup>1</sup> � *<sup>ε</sup>mf εmf* <sup>3</sup>

2

*ρ fVmf* 2

*ϕdm*

*<sup>g</sup>* (3)

C). According to Eq. (3), the

(1)

(2)

*2.1.1 Determination of Vmf using the Ergun equation*

<sup>¼</sup> <sup>150</sup>*<sup>μ</sup> <sup>f</sup>* <sup>1</sup> � *<sup>ε</sup>mf* <sup>2</sup>

<sup>1</sup> � *<sup>ε</sup>mf* <sup>2</sup> *εmf* <sup>3</sup>

<sup>Δ</sup>*<sup>p</sup>* <sup>¼</sup> *<sup>m</sup>*

*εmf* <sup>3</sup>*d*<sup>2</sup> *p*

Δ*P Hmf*

*Particle layer states with gas velocity changing [10].*

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

got in the Eq. (1) [10] is given by:

Δ*p Hmf*

¼ 150

particle layers and it is determined by Eq. (3) [10].

(dp), the bed voidage (ε) and the gas temperature (t°

#### **Table 2.**

*The classification of fluidization properties of particle groups according to Geldart [9, 11].*

density than the bed density will float on its surface, bobbing up and down, while objects with a higher density sink to the bottom of the bed.

Fluidization has many applications in many technologies of manufacturing practice, such as mixing different types of granular materials; fluidized bed drying; cooling grain after drying; supporting interaction between chemicals in the fluidized bed; granulation technology; film coating technology of medicine and pharmacy; manufacturing technology through the combined use of organic and inorganic fertilizers; and biomass fuel combustion technology in fluidized bed.

To clarify the dynamics of the fluidized beds for application in refined salt drying in the fluidized bed, the theoretical and experimental issues determining the velocity of gas through the particle layers to form different fluidized layers are described as follows.

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

**Figure 2.**

*Particle layer states with gas velocity changing [10].*

#### **2. Methodology**

#### **2.1 Determination of the minimum fluidization velocity from publications**

#### *2.1.1 Determination of Vmf using the Ergun equation*

When the air stream having sufficient pressure and velocity passes through the static spherical particle layers, they begin to expand (the particles become "flexible"). In this condition, it is called the minimum particulate fluidization state and is described by the modified equation of Ergun (see position A in **Figure 1**) [12].

$$\frac{\Delta P}{H\_{mf}} = \frac{150\mu\_f \left(1 - \varepsilon\_{mf}\right)^2 V\_{mf}}{\varepsilon\_{mf} ^3 d\_p^2} + \frac{1.75 \left(1 - \varepsilon\_{mf}\right) \rho\_f V\_{mf} r^2}{\varepsilon\_{mf} ^3 d\_p} \tag{1}$$

For particles of arbitrary shapes, the pressure drop of air stream at the minimum fluidization state is represented by Eq. (2). The spherical value of particle material got in the Eq. (1) [10] is given by:

$$\frac{\Delta p}{H\_{mf}} = 150 \frac{\left(\mathbf{1} - \varepsilon\_{mf}\right)^2}{\varepsilon\_{mf}^{-3}} \frac{\mu\_f V\_{mf}}{\left(\phi d\_m\right)^2} + \mathbf{1}.75 \frac{\left(\mathbf{1} - \varepsilon\_{mf}\right)}{\varepsilon\_{mf}^{-3}} \frac{\rho\_f V\_{mf}^2}{\phi d\_m} \tag{2}$$

For the particle layer to be converted from a fixed state to a fluidization state, the pressure of air stream must be large enough to overcome the weight of the particle layers and it is determined by Eq. (3) [10].

$$
\Delta p = \frac{m}{\rho\_p A} \left(\rho\_p - \rho\_f\right) \mathbf{g} \tag{3}
$$

In Eq. (3), it is considered that there was no interaction force between particles in layer and no interaction between particles and the wall of the tank. So, that did not cause the pressure increasing effect. Thus, the pressure drop of the air stream was constant while increasing the gas velocity from the smallest fluidization velocity to the value when the entrainment process of particles occurred (position C, **Figure 2**).

In Eqs. (1) and (2), it is also shown that the pressure drop of the gas stream that is generated through the fluidized particle layer is depended on the particle size (dp), the bed voidage (ε) and the gas temperature (t° C). According to Eq. (3), the

density than the bed density will float on its surface, bobbing up and down, while

**C group A group B group D group**

0–3 30 ≤ dp ≤ 100 100 ≤ dp ≤ 1000 ≥ 1000

• Easy fluidization • Dense phase expands stably before bubbling starts

• Milk flour • FCC granular

• The large bed expansion before bubbling is started • The minimum fluidization velocity is smaller than minimum bubbling

• It does not form bubble fluidization • There is a maximum bubble size

Very low High Solids' recirculation

Smallest 1400 400–4500 Lower than other

• Starting on bubble creation at the minimum fluidized velocity value

• The bubbles rise faster than the interstitial gas • Bubbles are large and grow rapidly and coalescence, as they rise through the bed

rates are smaller

upper layer

materials

• Construction sands • Pebbles in rice

Medium Difficult to fluidize

• The rough solid particles

• Coffee beans, wheat, lead shot

evenly (low)

• Bubbles rise more slowly than the rest of the gas percolating through the emulsion

Low

• It occurs

layers

• Only occur in under

Fluidization has many applications in many technologies of manufacturing practice, such as mixing different types of granular materials; fluidized bed drying;

cooling grain after drying; supporting interaction between chemicals in the fluidized bed; granulation technology; film coating technology of medicine and pharmacy; manufacturing technology through the combined use of organic and inorganic fertilizers; and biomass fuel combustion technology in fluidized bed. To clarify the dynamics of the fluidized beds for application in refined salt drying in the fluidized bed, the theoretical and experimental issues determining the velocity of gas through the particle layers to form different fluidized layers are

*The classification of fluidization properties of particle groups according to Geldart [9, 11].*

objects with a higher density sink to the bottom of the bed.

Spaying None None Only occurs in the

described as follows.

**88**

**Particle group characteristics**

*Current Drying Processes*

Particle size (μm)

Density (kg/m<sup>3</sup> )

The most obvious characteristics of group

Typical granulars

Particle layer expansion

Properties of air bubbles

Property of mixed solid particles

**Table 2.**

• Particles are cohesive and linked • Difficult fluidization

• Flour • Cement

• Channeling possibilities in the particles layer easily

• Do not form bubble

**Properties of fluidization layer**

pressure drop of the gas stream through the particle layers is dependent upon the material mass (m), the gas distributor grate area (A), particle density (ρp) and gas density (ρf). Thus, we could calculate the minimum fluidization velocity value (Vmf), which was based on Eqs. (1)–(3) for non-spherical particles by solving Eq. (4).

$$\frac{m.H\_{m\text{f}}}{\rho\_p A} \left(\rho\_p - \rho\_f\right) \mathbf{g} = \mathbf{150} \frac{\left(\mathbf{1} - \varepsilon\_{mf}\right)}{\varepsilon\_{mf}^3} \frac{\mu\_f V\_{mf}}{\left(\phi d\_p\right)^2} + \mathbf{1.75} \frac{\rho\_f V\_{mf}}{\varepsilon\_{mf}^3} \frac{\rho\_f V\_{mf}^2}{\phi d\_p} \tag{4}$$

Re *mf* <sup>¼</sup> *<sup>ρ</sup>mf :Vmf :dp:<sup>ϕ</sup> μ f*

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

Eq. (11) describes the correlation between Ar and Remf with void fraction at

Re *mf* þ

*<sup>g</sup> <sup>ϕ</sup>dp*

*μ*2 *f*

<sup>1</sup> � *<sup>ε</sup>mf ϕ*<sup>2</sup> *ε*<sup>3</sup> *mf*

Substituting physical parameters into the Eq. (12), which includes the particle density (ρp), the gas density at the temperature of minimum fluidization velocity (ρf), the air dynamic viscosity (μf), spherical degree of particle (ϕ), void fraction at the minimum fluidization velocity (εmf), mean particle diameter (dm) [13–15] and getting Ar number value into the Eq. (13). Then, we solved the quadratic equation to find out the root of equation Remf in Eq. (10), we got only the positive value. Thus, we calculated the minimum fluidization velocity (Vmf) from Eq. (10).

Kozeny-Carman gave the formula of calculation of the minimum fluidization velocity for a very small particle size with the Remf < 10 in Eq. (14) described in

> *εmf* <sup>3</sup> 1 � *εmf*

*ϕ*2 *d*2

*g ρ<sup>p</sup>* � *ρ <sup>f</sup>* 

150*μ <sup>f</sup>*

For spherical particles or sphericity equivalent, the bed voidage of the minimum

In case of the unavailability of the sphericity of particles, we determine the minimum fluidization velocity (Vmf) by using of the experimental correlation of Wen and Yu [17]. An empirical formula of calculation of the void fraction at minimum fluidization particle layers in Eq. (15) or Eq. (16) with the available sphericity degree of particle (ϕ) or the calculation of the sphericity degree of particle (ϕ) in case void fraction (εmf) at minimum fluidization particle layer is available, which was also described by Wen and Yu equation (cited in Howard,

1*:*75 *ϕε*<sup>3</sup> *mf*

<sup>3</sup>

Re *mf* þ

Re <sup>2</sup>

1*:*75 *ϕ ε*<sup>3</sup> *mf*

Re <sup>2</sup>

*<sup>p</sup>* (14)

*mf* (11)

<sup>1</sup> � *<sup>ε</sup>mf ϕ*<sup>2</sup> *ε*<sup>3</sup> *mf*

Archimeter (Ar) is determined by Eq. (12) for particles of any shape.

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

minimum fluidization particle layer (Vmf)

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

Set up Eq. (13):

Yates [16].

1989) [10].

**91**

fluidization εmf = 0.4 ÷ 0.45.

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

*<sup>g</sup> <sup>ϕ</sup>dp*

*μ*2 *f* *Ar* ¼ 150

*Ar* ¼

¼ 150

<sup>3</sup>

*2.1.3 Determination of Vmf by the Kozeny-Carman correlation*

*Vmf* ¼

*2.1.4 Determination of Vmf by correlation of Wen and Yu*

(10)

(12)

*mf* (13)

The minimum fluidization velocity (Vmf) is the root of Eq. (4), which is based on available parameters, such as the height of minimum fluidization bed (Hmf), the mass of particles in the air distributor (m), the area for gas distribution or called cross-sectional area of the bed (A), particle density (ρp), air density (ρf), mean particle diameter (dp), spherical degree of particles (ϕ) and void fraction at minimum fluidization particle layer (εmf).

Commonly, the sphere degree of particles (ϕ) must be determined in experiments [10]. The spherical degree of refined salt particles was found out by Bui [13–15]. Theoretically, in order to fluidize the particle layer, the actual weight of the solid particles must be equal to the force exerted on the particle layers and that is equal to the pressure drop across the bed (ΔP) multiplied by the cross-sectional area of the chamber (A). A minimum fluidization layer which must have determined layer thickness (Hmf), void fraction (εmf), then the expanded volume of the fluidized particles (U) has the value of the Eq. (5):

$$\mathbf{U} = (\mathbf{1} - \mathbf{e\_{mf}}) . \mathbf{A.H\_{mf}} \tag{5}$$

And the actual gravity of the particle mass has a value of:

$$\mathbf{W} = (\mathbf{1} - \varepsilon\_{\mathrm{mf}}) \left(\rho\_{\mathrm{p}} - \rho\_{\mathrm{f}}\right) \mathbf{A} \mathbf{A}\_{\mathrm{mf}\cdot\mathbf{g}} \mathbf{g} \tag{6}$$

The balance of the real gravity components of the particle mass and the upward force exerted on the particle mass of the gas flow was calculated according to

$$
\Delta \mathbf{P} = (\mathbf{1} - \varepsilon\_{\rm mf}) \left(\rho\_{\rm p} - \rho\_{\rm f}\right) \text{.H.g} \tag{7}
$$

Substituting Eq. (8) into Eq. (1) or Eq. (2) yields Eq. (9).

$$\left(\mathbf{1} - \varepsilon\_{\mathrm{mf}}\right) \left(\rho\_p - \rho\_f\right).\mathrm{H}\_{\mathrm{mf}}.\mathrm{g} = \mathbf{1} \mathrm{50} \frac{\left(\mathbf{1} - \varepsilon\_{\mathrm{mf}}\right)^2}{\varepsilon\_{\mathrm{mf}}^{-3}} \frac{\mu\_f V\_{\mathrm{mf}}}{\left(\phi d\_p\right)^2} + \mathbf{1}.\mathrm{75} \frac{\left(\mathbf{1} - \varepsilon\_{\mathrm{mf}}\right)}{\varepsilon\_{\mathrm{mf}}^{-3}} \frac{\rho\_f V\_{\mathrm{mf}}^2}{\phi d\_p} \tag{8}$$

$$\mathbf{150} \frac{\left(\mathbf{1} - \varepsilon\_{mf}\right)}{\phi^2 \varepsilon\_{mf}^3} \text{ Re}\_{mf} + \frac{\mathbf{1}.75}{\phi \,\varepsilon\_{mf}^3} \text{ Re}\_{mf}^2 = Ar \tag{9}$$

Giving physical parameters of particle and gas into the Eq. (8), velocity (Vmf) was found out. In case of very small particles, the gas stream regime through the particle layer was laminar flow and the minimum fluidization velocity should be calculated by the Ergun equation [12]. In case of Remf < 1, we use Eq. (9) to calculate the minimum fluidization velocity of gas.

#### *2.1.2 Determination of Vmf by the correlation of Remf and Archimeter (Ar)*

When gas passes through the particle bulk, which can have any shape, the minimum fluidization Reynolds coefficient (Remf) is determined by Eq. (10). *Determination on Fluidization Velocity Types of the Continuous Refined Salt Fluidized Bed Drying DOI: http://dx.doi.org/10.5772/intechopen.92077*

$$\mathrm{Re}\_{mf} = \frac{\rho\_{mf} \cdot V\_{mf} \, d\_p \, \phi}{\mu\_f} \tag{10}$$

Eq. (11) describes the correlation between Ar and Remf with void fraction at minimum fluidization particle layer (Vmf)

$$Ar = 150 \frac{\left(1 - \varepsilon\_{mf}\right)}{\phi^2 \varepsilon\_{mf}^3} \text{ Re}\_{mf} + \frac{1.75}{\phi \varepsilon\_{mf}^3} \text{ Re}\_{mf}^2 \tag{11}$$

Archimeter (Ar) is determined by Eq. (12) for particles of any shape.

$$Ar = \frac{\rho\_f \left(\rho\_p - \rho\_f\right) \lg\left(\phi d\_p\right)^3}{\mu\_f^2} \tag{12}$$

Set up Eq. (13):

pressure drop of the gas stream through the particle layers is dependent upon the material mass (m), the gas distributor grate area (A), particle density (ρp) and gas density (ρf). Thus, we could calculate the minimum fluidization velocity value (Vmf), which was based on Eqs. (1)–(3) for non-spherical particles by solving Eq. (4).

> 1 � *εmf εmf* 3

The minimum fluidization velocity (Vmf) is the root of Eq. (4), which is based on available parameters, such as the height of minimum fluidization bed (Hmf), the mass of particles in the air distributor (m), the area for gas distribution or called cross-sectional area of the bed (A), particle density (ρp), air density (ρf), mean particle diameter (dp), spherical degree of particles (ϕ) and void fraction at

Commonly, the sphere degree of particles (ϕ) must be determined in experiments [10]. The spherical degree of refined salt particles was found out by Bui [13–15]. Theoretically, in order to fluidize the particle layer, the actual weight of the solid particles must be equal to the force exerted on the particle layers and that is equal to the pressure drop across the bed (ΔP) multiplied by the cross-sectional area of the chamber (A). A minimum fluidization layer which must have determined layer thickness (Hmf), void fraction (εmf), then the expanded volume of the fluid-

*μ fVmf ϕdp*

<sup>2</sup> <sup>þ</sup> <sup>1</sup>*:*<sup>75</sup> *<sup>ε</sup>*<sup>3</sup>

U ¼ ð Þ 1 � εmf *:*A*:*Hmf (5)

*:*A*:*Hmf*::*g (6)

*:*H*:*g (7)

*mf* ¼ *Ar* (9)

*ρ fVmf* 2

*ϕdp*

(8)

1 � *εmf εmf* <sup>3</sup>

*mf*

*ρ fVmf* 2

*ϕdp*

(4)

*g* ¼ 150

*m:Hmf*

*Current Drying Processes*

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

minimum fluidization particle layer (εmf).

ized particles (U) has the value of the Eq. (5):

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

**90**

And the actual gravity of the particle mass has a value of:

Substituting Eq. (8) into Eq. (1) or Eq. (2) yields Eq. (9).

*:*H*mf :*g ¼ 150

1 � *εmf ϕ*<sup>2</sup> *ε*<sup>3</sup> *mf*

*2.1.2 Determination of Vmf by the correlation of Remf and Archimeter (Ar)*

150

calculate the minimum fluidization velocity of gas.

W ¼ ð Þ 1 � εmf ρ<sup>p</sup> � ρ<sup>f</sup>

force exerted on the particle mass of the gas flow was calculated according to

ΔP ¼ ð Þ 1 � εmf ρ<sup>p</sup> � ρ<sup>f</sup>

1 � *εmf* <sup>2</sup> *εmf* <sup>3</sup>

Re *mf* þ

When gas passes through the particle bulk, which can have any shape, the minimum fluidization Reynolds coefficient (Remf) is determined by Eq. (10).

Giving physical parameters of particle and gas into the Eq. (8), velocity (Vmf) was found out. In case of very small particles, the gas stream regime through the particle layer was laminar flow and the minimum fluidization velocity should be calculated by the Ergun equation [12]. In case of Remf < 1, we use Eq. (9) to

The balance of the real gravity components of the particle mass and the upward

*μ fVmf ϕdp* <sup>2</sup> <sup>þ</sup> <sup>1</sup>*:*<sup>75</sup>

1*:*75 *ϕ ε*<sup>3</sup> *mf*

Re <sup>2</sup>

$$\frac{\rho\_f \left(\rho\_p - \rho\_f\right) \mathbf{g} \left(\phi d\_p\right)^3}{\mu\_f^2} = \mathbf{150} \,\frac{\left(\mathbf{1} - \varepsilon\_{mf}\right)}{\phi^2 \varepsilon\_{mf}^3} \,\mathrm{Re}\_{mf} + \frac{\mathbf{1.75}}{\phi \varepsilon\_{mf}^3} \,\mathrm{Re}\_{mf}^2\tag{13}$$

Substituting physical parameters into the Eq. (12), which includes the particle density (ρp), the gas density at the temperature of minimum fluidization velocity (ρf), the air dynamic viscosity (μf), spherical degree of particle (ϕ), void fraction at the minimum fluidization velocity (εmf), mean particle diameter (dm) [13–15] and getting Ar number value into the Eq. (13). Then, we solved the quadratic equation to find out the root of equation Remf in Eq. (10), we got only the positive value. Thus, we calculated the minimum fluidization velocity (Vmf) from Eq. (10).

#### *2.1.3 Determination of Vmf by the Kozeny-Carman correlation*

Kozeny-Carman gave the formula of calculation of the minimum fluidization velocity for a very small particle size with the Remf < 10 in Eq. (14) described in Yates [16].

$$V\_{mf} = \frac{\text{g}\left(\rho\_p - \rho\_f\right)}{\text{150}\mu\_f} \frac{\varepsilon\_{mf}^{-3}}{\text{1} - \varepsilon\_{mf}} \phi^2 d\_p^2 \tag{14}$$

For spherical particles or sphericity equivalent, the bed voidage of the minimum fluidization εmf = 0.4 ÷ 0.45.

#### *2.1.4 Determination of Vmf by correlation of Wen and Yu*

In case of the unavailability of the sphericity of particles, we determine the minimum fluidization velocity (Vmf) by using of the experimental correlation of Wen and Yu [17]. An empirical formula of calculation of the void fraction at minimum fluidization particle layers in Eq. (15) or Eq. (16) with the available sphericity degree of particle (ϕ) or the calculation of the sphericity degree of particle (ϕ) in case void fraction (εmf) at minimum fluidization particle layer is available, which was also described by Wen and Yu equation (cited in Howard, 1989) [10].

$$\frac{1 - \varepsilon\_{mf}}{\phi^2 \varepsilon\_{mf}^3} \approx 11 \text{ or } \frac{1}{\phi \varepsilon\_{mf}^3} \approx 14\tag{15}$$

*a* Re <sup>2</sup>

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

*<sup>a</sup>* <sup>¼</sup> <sup>1</sup>*:*<sup>75</sup> *ϕ ε*<sup>3</sup> *mf*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *<sup>b</sup>*<sup>2</sup> <sup>þ</sup> <sup>4</sup>*aAr* � � <sup>p</sup>

Re *mf* <sup>¼</sup> *Ar <sup>b</sup>*

And its value was determined by Eq. (27) by Goroshko:

Eq. (27) is different from Eq. (26) by the added value *<sup>b</sup>*

we have a correlation equation, which is described in Eq. (28).

*2.1.7 Determination of Vmf following Goroshko and Todes equation*

Re *mf* ð Þ *Ergun*

from the Remf by Goroshko et al. in Eq. (29) [19].

Remf is calculated in Eq. (30) [21].

**93**

2 þ

Re *pmf* <sup>¼</sup> *Ar*

There is a difference in Remf value between the Goroshko equation and Ergun equation. The Repmf of Goroshko equation [Eq. (27)] is smaller than Remf of Ergun [Eq. (26)]. This deviation interval depends on the value of Archimeter (Ar). Thus,

Re *pmf* ð Þ *Goroshko* <sup>¼</sup> *<sup>b</sup>* <sup>þ</sup> ffiffiffiffiffiffiffiffiffi

Re *pmf* <sup>¼</sup> *Ar* 150 <sup>1</sup>�*εmf*

Re *mf* <sup>¼</sup> *Ar*

The minimum fluidization velocity **(**Vmf) of sphericity particles was defined

In case of non-spherical particles with different sizes, the Repmf value was error from 15–20% in case we use the Eq. (29) of calculation described in [20]. In the case of rapid calculation, we considered the bed voidage of the minimum fluidization state to be equal to the bed voidage at static particle layers (ε<sup>o</sup> = εmf = 0.4), and the

<sup>1400</sup> <sup>þ</sup> <sup>5</sup>*:*<sup>22</sup> ffiffiffiffiffiffi

*<sup>ε</sup>mf* <sup>3</sup> <sup>þ</sup> ffiffiffiffiffiffiffiffiffiffiffiffi 1*:*75 *ε*3 *mf*

< :

where

we have the Eq. (25).

Multiplying *b* þ

we have the Eq. (26)

*mf* þ *b* Re *mf* � *Ar* ¼ 0 (23)

by the numerator and denominator of Eq. (25),

�1

*aAr* <sup>p</sup> (27)

<sup>þ</sup> *aAr* <sup>¼</sup> *<sup>b</sup>*

2 � �<sup>2</sup>

*<sup>b</sup>=*<sup>2</sup> <sup>þ</sup> ð Þ *<sup>b</sup>=*<sup>2</sup> <sup>2</sup> <sup>þ</sup> *aAr* h i<sup>1</sup>*=*<sup>2</sup> � � (28)

*Ar* <sup>q</sup> (29)

*Ar* <sup>p</sup> (30)

*aAr* <sup>p</sup>

9 = ; (24)

(25)

(26)

<sup>2</sup> <sup>þ</sup> ffiffiffiffiffiffiffiffiffi *<sup>a</sup>:Ar* <sup>p</sup> .

and *<sup>b</sup>* <sup>¼</sup> 150 1 � *<sup>ε</sup>mf* � � *ϕ*<sup>2</sup> *ε*<sup>3</sup> *mf*

We get ϕ is 1.0 (ϕ = 1) then solving the Eq. (23) take the spherical degree value,

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

Re *mf* <sup>¼</sup> �*<sup>b</sup>* <sup>þ</sup> *<sup>b</sup>*<sup>2</sup> <sup>þ</sup> <sup>4</sup>*aAr* � �1*=*<sup>2</sup>

*b* 2 � �<sup>2</sup> <sup>þ</sup> *aAr* " #<sup>1</sup>*=*<sup>2</sup> <sup>8</sup>

*<sup>b</sup>* <sup>þ</sup> ffiffiffiffiffiffiffiffi

2*a*

We can use the calculation of the void fraction at minimum fluidization particle layers from the other correlation, which is also converted from Wen and Yu.

$$
\varepsilon\_{mf} = \left(\frac{0.071}{\phi}\right)^{1/3} \tag{16}
$$

It is based on the calculation of the void fraction (εmf) (at position A in **Figure 2**) of Eq. (15) or Eq. (16) and substituting the obtained εmf value into the Ergun Eq. (2), we have Eq. (17).

$$Ar = \text{1650 Re}\_{pmf} + \text{24.5 } \text{Re}\_{pmf}^2 \tag{17}$$

Using the calculated Ar number from Eq. (12) and substituting the Ar value into Eq. (17), we obtain Eq. (18) to calculate the particle Reynolds number at the minimum fluidization velocity (Remf).

$$\mathrm{Re}\_{mf} = \frac{-1650 \pm \left\{ 1650 + (4 \times 24.5 \, Ar) \right\}^{1/2}}{2 \times 24.5} \tag{18}$$

Taking the positive square root, we get Eq. (19):

$$\mathrm{Re}\_{mf} = \left( \mathbf{33.7}^2 + \mathbf{0.0408} \, Ar \right)^{1/2} - \mathbf{33.7} \tag{19}$$

It was applied to calculate for solid particles with size larger than 100 μm [10]. From the Remfvalue that was found out in the Eq. (19), Vmf is calculated according to Eq. (10). In case of solid particles with small size (C group of Geldart, 1973) in the specified temperature conditions, the Vmf value is calculated in Eq. (20) by Wen and Yu.

$$V\_{mf} = 7.90.10^{-3} d\_p^{1.82} \left(\rho\_p - \rho\_f\right) 0.94 \mu\_f^{-0.83} \tag{20}$$

#### *2.1.5 Determination of Vmf by the correlation of Beayens and Geldart*

For solid spherical particles with diameters ranging from 0.05 to 4 mm (0.05 mm < dp < 4 mm) and particle density ranging from 850 to 8810 kg/m<sup>3</sup> (850 kg/m<sup>3</sup> < ρ<sup>p</sup> < 8810 kg/m<sup>3</sup> ), the method of calculation of Vmf was proposed by Beayens and Geldart as shown in Eq. (21) [18].

$$Ar = \text{1823 } \text{Re}\_{\text{mf}}{}^{1.07} + \text{21.7 } \text{Re}\_{\text{mf}}^2 \tag{21}$$

Then the Vmf can be calculated from Eq. (22) in case of available solid particle and gas parameters.

$$\mathbf{V}\_{mf} = \frac{\mathbf{9.125} \times \mathbf{10^{-4}} \left( \left( \rho\_p - \rho\_f \right) \mathbf{g} \right)^{0.934} d\_p^{1.8}}{\mu\_f^{0.87} \rho\_p^{0.66}} \tag{22}$$

#### *2.1.6 Determination of Vmf by correlation of Goroshko*

The minimum fluidization velocity of spherical particles was determined by correlation shown in Eq. (23) by Goroshko described in Howard [10, 19].

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

$$a \text{ } \text{Re}^2\_{mf} + b \text{ } \text{Re}\_{mf} - Ar = 0 \tag{23}$$

where

1 � *εmf ϕ*<sup>2</sup> *ε*<sup>3</sup> *mf*

Eq. (2), we have Eq. (17).

*Current Drying Processes*

minimum fluidization velocity (Remf).

(850 kg/m<sup>3</sup> < ρ<sup>p</sup> < 8810 kg/m<sup>3</sup>

and gas parameters.

**92**

Beayens and Geldart as shown in Eq. (21) [18].

*Vmf* ¼

*2.1.6 Determination of Vmf by correlation of Goroshko*

Taking the positive square root, we get Eq. (19):

*Vmf* <sup>¼</sup> <sup>7</sup>*:*90*:*10�<sup>3</sup>

*2.1.5 Determination of Vmf by the correlation of Beayens and Geldart*

*Ar* ¼ 1823 Re *mf*

≈11 or

layers from the other correlation, which is also converted from Wen and Yu.

*<sup>ε</sup>mf* <sup>¼</sup> <sup>0</sup>*:*<sup>071</sup> *ϕ* <sup>1</sup>*=*<sup>3</sup>

of Eq. (15) or Eq. (16) and substituting the obtained εmf value into the Ergun

Eq. (17), we obtain Eq. (18) to calculate the particle Reynolds number at the

*Ar* <sup>¼</sup> 1650 Re *pmf* <sup>þ</sup> <sup>24</sup>*:*5 Re <sup>2</sup>

We can use the calculation of the void fraction at minimum fluidization particle

It is based on the calculation of the void fraction (εmf) (at position A in **Figure 2**)

Using the calculated Ar number from Eq. (12) and substituting the Ar value into

Re *mf* <sup>¼</sup> �<sup>1650</sup> � f g <sup>1650</sup> <sup>þ</sup> ð Þ <sup>4</sup> � <sup>24</sup>*:*<sup>5</sup> *Ar* <sup>1</sup>*=*<sup>2</sup>

It was applied to calculate for solid particles with size larger than 100 μm [10]. From the Remfvalue that was found out in the Eq. (19), Vmf is calculated according to Eq. (10). In case of solid particles with small size (C group of Geldart, 1973) in the specified temperature conditions, the Vmf value is calculated in Eq. (20) by Wen and Yu.

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

> > <sup>1</sup>*:*<sup>07</sup> <sup>þ</sup> <sup>21</sup>*:*7 Re <sup>2</sup>

*g* <sup>0</sup>*:*<sup>934</sup>

*d*<sup>1</sup>*:*<sup>82</sup>

For solid spherical particles with diameters ranging from 0.05 to 4 mm (0.05 mm < dp < 4 mm) and particle density ranging from 850 to 8810 kg/m<sup>3</sup>

Then the Vmf can be calculated from Eq. (22) in case of available solid particle

*μ*<sup>0</sup>*:*<sup>87</sup> *<sup>f</sup> ρ*<sup>0</sup>*:*<sup>66</sup> *p*

The minimum fluidization velocity of spherical particles was determined by

correlation shown in Eq. (23) by Goroshko described in Howard [10, 19].

<sup>9</sup>*:*<sup>125</sup> � <sup>10</sup>�<sup>4</sup> *<sup>ρ</sup><sup>p</sup>* � *<sup>ρ</sup> <sup>f</sup>*

1 *ϕ ε*<sup>3</sup> *mf*

≈14 (15)

*pmf* (17)

*<sup>f</sup>* (20)

*mf* (21)

(22)

<sup>2</sup> � <sup>24</sup>*:*<sup>5</sup> (18)

Re *mf* <sup>¼</sup> <sup>33</sup>*:*7<sup>2</sup> <sup>þ</sup> <sup>0</sup>*:*<sup>0408</sup> *Ar* <sup>1</sup>*=*<sup>2</sup> � <sup>33</sup>*:*<sup>7</sup> (19)

0*:*94*μ*�0*:*<sup>83</sup>

), the method of calculation of Vmf was proposed by

*d*<sup>1</sup>*:*<sup>8</sup> *p*

(16)

$$a = \frac{1.75}{\phi \, \varepsilon\_{mf}^3} \text{ and } b = \frac{150 \left(1 - \varepsilon\_{mf}\right)}{\phi^2 \, \varepsilon\_{mf}^3} \tag{24}$$

We get ϕ is 1.0 (ϕ = 1) then solving the Eq. (23) take the spherical degree value, we have the Eq. (25).

$$\mathrm{Re}\_{mf} = \frac{-b + \left(b^2 + 4aAr\right)^{1/2}}{2a} \tag{25}$$

Multiplying *b* þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *<sup>b</sup>*<sup>2</sup> <sup>þ</sup> <sup>4</sup>*aAr* � � <sup>p</sup> by the numerator and denominator of Eq. (25), we have the Eq. (26)

$$\text{Re}\_{mf} = Ar \left\{ \frac{b}{2} + \left[ \left( \frac{b}{2} \right)^2 + aAr \right]^{1/2} \right\}^{-1} \tag{26}$$

And its value was determined by Eq. (27) by Goroshko:

$$\mathrm{Re}\_{pmf} = \frac{Ar}{b + \sqrt{aAr}}\tag{27}$$

Eq. (27) is different from Eq. (26) by the added value *<sup>b</sup>* 2 � �<sup>2</sup> <sup>þ</sup> *aAr* <sup>¼</sup> *<sup>b</sup>* <sup>2</sup> <sup>þ</sup> ffiffiffiffiffiffiffiffiffi *<sup>a</sup>:Ar* <sup>p</sup> . There is a difference in Remf value between the Goroshko equation and Ergun equation. The Repmf of Goroshko equation [Eq. (27)] is smaller than Remf of Ergun [Eq. (26)]. This deviation interval depends on the value of Archimeter (Ar). Thus, we have a correlation equation, which is described in Eq. (28).

$$\frac{\operatorname{Re}\_{mf}\left(\operatorname{Egrun}\right)}{\operatorname{Re}\_{pmf}\left(\operatorname{Goroshko}\right)} = \frac{b + \sqrt{aAr}}{\left\{b/2 + \left[\left(b/2\right)^2 + aAr\right]^{1/2}\right\}}\tag{28}$$

#### *2.1.7 Determination of Vmf following Goroshko and Todes equation*

The minimum fluidization velocity **(**Vmf) of sphericity particles was defined from the Remf by Goroshko et al. in Eq. (29) [19].

$$\mathrm{Re}\_{pm^f} = \frac{Ar}{150 \frac{1 - \varepsilon\_{mf}}{\varepsilon\_{mf} \cdot ^\circ} + \sqrt{\frac{1.75}{\varepsilon\_{mf}^3} Ar}} \tag{29}$$

In case of non-spherical particles with different sizes, the Repmf value was error from 15–20% in case we use the Eq. (29) of calculation described in [20]. In the case of rapid calculation, we considered the bed voidage of the minimum fluidization state to be equal to the bed voidage at static particle layers (ε<sup>o</sup> = εmf = 0.4), and the Remf is calculated in Eq. (30) [21].

$$\mathrm{Re}\_{mf} = \frac{Ar}{1400 + 5.22\sqrt{Ar}}\tag{30}$$

#### *2.1.8 Determination of Vmf following Leva*

From the formula of Carman-Kozan *<sup>k</sup>* <sup>¼</sup> *<sup>g</sup>:<sup>ρ</sup> <sup>f</sup> :εmf <sup>μ</sup> <sup>f</sup> kcS* described in (as cited in Leva, [22]) yield the formula to define the minimum fluidization velocity [22, 23].

$$W\_{mf} = \frac{5 \times 10^{-3} \left(\phi d\_p\right)^2 \left(\rho\_p - \rho\_p\right) \text{g} \varepsilon\_{mf}{}^3}{\mu\_{mf} \left(1 - \varepsilon\_{mf}\right)}\tag{31}$$

The Leva formula is used in case of Reynolds to be smaller than 10 (Remf < 10). In case of Reynolds to be larger than 10 (Remf > 10), there is an adjustment factor added into this formula.

#### *2.1.9 Determination of Vmf according to Kunii-Levenspiel*

The formula of Kunii-Levenspiel was simplified from the Ergun formula and it gave out two cases of calculation of the minimum fluidization velocity. In the first case for solid particles of small size with Remf < 20, we have to use Eq. (32).

$$V\_{mf} = \frac{\left(\phi d\_p\right)^2}{150\mu\_f} \frac{\left(\rho\_p - \rho\_f\right)\text{g}\varepsilon\_{mf}^{-3}}{\left(1 - \varepsilon\_{mf}\right)}\tag{32}$$

**2.2 Physical model of experiment**

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

**2.3 Experimental equipment**

measurement of refined salt particles.

**No. Equipment/parts Technical parameter** 1 Drying air fan Flow: 0.63 m<sup>3</sup>

shown in **Figure 3**.

motor.

**Table 3.**

**95**

**Figure 3.**

Experimental arrangement of determining the minimum fluidization velocity is

*Model for determination of the minimum fluidization velocity. 1. Centrifugal fan; 2. air heater; 3. thermometer for surface particle temperature measurement; 4. pitot tube for measurement of dynamic pressure and total pressure of air; 5. U-manometer; 6. chamber of fluidization; 7. air distributor; 8. drying air inlet.*

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

In order to gradually increase the bed surface velocity of hot air via the particle layers, the air fan (1) is equipped with an inverter to change the rotation of the fan

The instruments in experiments include a moisture analyzer (Axis AGS100, Germany), measurement error 0.01%; a digital electronic scale (Satorius MA45, Germany), measurement error 0.001 g; an air velocity meter (Extech SDL350 Taiwan), measurement error 0.01 m/s and a digital thermometer (WIKA CTH6300, Germany), measurement accuracy 0.001°C. This instrument has two measuring rate modes including fast at 4/s and slow at 1/s; an inclined manometer (T10, UK), measured range is 0–280 mmwg with error 0.1% and a pitot pipe (PT6300, 304 Germany), measurement range is 0–400 mmwg with error 0.1%. For measurement on the bulk density and density of refined salt particles, we used instruments such as Graduated pipet, buret, graduated cylinder, all of them made in Germany with error measurement 0.01 ml. The HCl acid is used for density

2 Electrical heater Overall dimension (L W H): 600 630 275 mm;

3 Drying chamber Overall dimension (L W H): 1750 300 350 mm

4 Salt dust settling chamber Overall dimension (L W H): 1750 450 350 mm

*The basic parameters of the continuous fluidized bed dryer for experiment by authors.*

Fabrication material: SUS304

Fabrication material: SUS304

/s; total pressure: 1244 Pa; motor power: 2.2 kW

heating power: 1.0 kW; number of heater bars: 6

We have to use Eq. (33) for the larger particle size with Reynolds number larger than 1000 (Remf > 1000).

$$\left(V\_{mf}\right)^2 = \frac{\left(\phi d\_p\right)\left(\rho\_p - \rho\_f\right)\mathbf{g} \cdot \varepsilon\_{mf}\mathbf{}^3}{\mathbf{1.75}\rho\_f} \tag{33}$$

#### *2.1.10 Determination of Vmf based on the bed voidage problem*

There is a correlation equation of particle mass balance at the minimum fluidization state (fluidization without bubbles), which was created by Kunii and Levenspiel as shown in Eq. (34).

$$\lg H\_0(\mathbf{1} - \varepsilon\_0)\rho\_p A = (\mathbf{1} - \varepsilon\_{\rm mf})\rho\_p \mathbf{g}.\\ H\_{\rm mf} \tag{34}$$

Thus, we can obtain a correlation as shown in Eq. (35).

$$\frac{H\_{mf}}{H\_0} = \frac{(\mathbf{1} - \varepsilon\_0)}{\mathbf{1} - \varepsilon\_{mf}} \tag{35}$$

According to Ginzburg, described in [18], the bed voidage of minimum fluidization and height of particle layer are calculated by Eq. (36) and Eq. (37).

$$
\mathfrak{e}\_{\rm mf} = \mathfrak{e}\_0 \times \mathbf{10\%} \tag{36}
$$

$$\mathbf{H\_{mf}} = \mathbf{H\_0} \times \mathbf{10\%}\tag{37}$$

McCabe et al. proposed εmf = 0.4 ÷ 0.45 for the spherical particle [24]. The bed voidage of minimum fluidization particle layers was 0.5 (εmf = 0.5) for larger particle size. The bed voidage is equal to 1.0 (ε<sup>t</sup> = 1.0) when the particle layers are attracted to the gas stream (see position C in **Figure 2**).

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

#### **Figure 3.**

*2.1.8 Determination of Vmf following Leva*

added into this formula.

*Current Drying Processes*

than 1000 (Remf > 1000).

Levenspiel as shown in Eq. (34).

**94**

From the formula of Carman-Kozan *<sup>k</sup>* <sup>¼</sup> *<sup>g</sup>:<sup>ρ</sup> <sup>f</sup> :εmf*

*Vmf* ¼

*2.1.9 Determination of Vmf according to Kunii-Levenspiel*

*Vmf* <sup>¼</sup> *<sup>ϕ</sup>dp*

*Vmf* 2 ¼

*2.1.10 Determination of Vmf based on the bed voidage problem*

Thus, we can obtain a correlation as shown in Eq. (35).

attracted to the gas stream (see position C in **Figure 2**).

 <sup>2</sup> 150*μ <sup>f</sup>*

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

zation state (fluidization without bubbles), which was created by Kunii and

*g:H*0ð Þ 1 � *ε*<sup>0</sup> *ρp:A* ¼ 1 � *εmf*

*Hmf H*<sup>0</sup>

zation and height of particle layer are calculated by Eq. (36) and Eq. (37).

[22]) yield the formula to define the minimum fluidization velocity [22, 23].

<sup>2</sup>

*μmf* 1 � *εmf*

The Leva formula is used in case of Reynolds to be smaller than 10 (Remf < 10). In case of Reynolds to be larger than 10 (Remf > 10), there is an adjustment factor

The formula of Kunii-Levenspiel was simplified from the Ergun formula and it gave out two cases of calculation of the minimum fluidization velocity. In the first case for solid particles of small size with Remf < 20, we have to use Eq. (32).

> *ρ<sup>p</sup>* � *ρ <sup>f</sup>*

We have to use Eq. (33) for the larger particle size with Reynolds number larger

1*:*75*ρ <sup>f</sup>*

There is a correlation equation of particle mass balance at the minimum fluidi-

<sup>¼</sup> ð Þ <sup>1</sup> � *<sup>ε</sup>*<sup>0</sup> 1 � *εmf*

According to Ginzburg, described in [18], the bed voidage of minimum fluidi-

McCabe et al. proposed εmf = 0.4 ÷ 0.45 for the spherical particle [24]. The bed

voidage of minimum fluidization particle layers was 0.5 (εmf = 0.5) for larger particle size. The bed voidage is equal to 1.0 (ε<sup>t</sup> = 1.0) when the particle layers are

1 � *εmf*

*gεmf* <sup>3</sup>

*g:εmf* <sup>3</sup>

*ρ<sup>p</sup>* � *ρ<sup>p</sup>* 

<sup>5</sup> � <sup>10</sup>�<sup>3</sup> *<sup>ϕ</sup>dp*

*<sup>μ</sup> <sup>f</sup> kcS* described in (as cited in Leva,

(31)

(32)

*ρpg:Hmf* (34)

εmf ¼ ε<sup>0</sup> � 10% (36) Hmf ¼ H0 � 10% (37)

(33)

(35)

*gεmf* <sup>3</sup>

*Model for determination of the minimum fluidization velocity. 1. Centrifugal fan; 2. air heater; 3. thermometer for surface particle temperature measurement; 4. pitot tube for measurement of dynamic pressure and total pressure of air; 5. U-manometer; 6. chamber of fluidization; 7. air distributor; 8. drying air inlet.*

#### **2.2 Physical model of experiment**

Experimental arrangement of determining the minimum fluidization velocity is shown in **Figure 3**.

In order to gradually increase the bed surface velocity of hot air via the particle layers, the air fan (1) is equipped with an inverter to change the rotation of the fan motor.

#### **2.3 Experimental equipment**

The instruments in experiments include a moisture analyzer (Axis AGS100, Germany), measurement error 0.01%; a digital electronic scale (Satorius MA45, Germany), measurement error 0.001 g; an air velocity meter (Extech SDL350 Taiwan), measurement error 0.01 m/s and a digital thermometer (WIKA CTH6300, Germany), measurement accuracy 0.001°C. This instrument has two measuring rate modes including fast at 4/s and slow at 1/s; an inclined manometer (T10, UK), measured range is 0–280 mmwg with error 0.1% and a pitot pipe (PT6300, 304 Germany), measurement range is 0–400 mmwg with error 0.1%. For measurement on the bulk density and density of refined salt particles, we used instruments such as Graduated pipet, buret, graduated cylinder, all of them made in Germany with error measurement 0.01 ml. The HCl acid is used for density measurement of refined salt particles.


**Table 3.**

*The basic parameters of the continuous fluidized bed dryer for experiment by authors.*

#### **2.4 The materials of 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 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 analysis (**Table 3**) [14].

#### **3. Results and discussions**

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 combination with the correlation calculation or empirical formulas.

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 refined salt particles**

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

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

a. Calculation based on Ergun equations and correlations of pressure

Applying to calculate the minimum fluidization velocity (Vmf) for refined salt particles with the fixed bed height (H0) is 30 mm, the bed voidage (ε0) is 0.5 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 degree value of refined salt particle is 0.71 (ϕ = 0.71) and other parameters were taken from the **Table 5** which described in Bui (2009). Then we use the Ergun equations to calculate the minimum fluidization velocity. It is recommended that Remf had no limit [13–15].

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

In these two calculation methods, the parameters in the calculations are taken from the empirical results according to **Table 5**.

**Determination**

**97**

**No**

 **dh** **(mm)**

1

2

3

7 4

5

6

*The bold values in Table 4 refers to the common average particle size for commercial*

**Table 4.** *Theoretical*

 *calculation*

*experimental*

 *results of the physical model of author.*

 *results of minimum fluidization*

 *velocity for refined salt particles from equations and empirical correlation*

 *formulas of*

*published authors, which compare to the*

 0.225

 0.058

 0.029

 0.059

 0.45

 0.22

 0.115

 0.234

 0.75

 0.522

 0.298

 0.651

**0.953**

 **0.731**

 **0.445**

 1.05

 0.826

 0.518

 1.35

 1.094

 0.736

 2.108 1.275 **1.05**

**0.2209**

0.1416

0.0524

0.0132

 *refined salt in the Vietnamese market.*

 0.014

 0.0537

 0.054

 0.044

 0.05

 0.1863

 0.186

 0.176

 0.123

 0.4188

 0.419

 0.488

 **0.186**

 **0.586**

 **0.586**

 **0.788**

0.2625

 0.219

 0.6653

 0.665

 0.956

 1.65

 1.327

 0.939

 3.149

0.5414

0.4002

 0.331

 0.9022

 0.902

 1.581

 0.45

 1.1223

 1.122

 2.362

3.149 2.108 1.275 **1.05** 0.651 0.234 0.059

0.8

0.6

0.58

**0.55**

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

0.42

0.2

0.15

**Ergun**

 **Re andAr**

 **Ko and Ca**

 **Wen and Yu**

 **Gedar**

 **Go**

 **Todes**

 **Leva**

 **Kunii and Levenspiel**

 **Empirical methods**

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

 **of the minimum** 

**fluidization**

 **velocity according to theoretical**

 **and empirical methods**

**Minimum** 

**fluidization**

 **velocity**

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

According to Wen and Yu methods, the bed voidage of the refined salt particle layer at minimum fluidization state (εmf) was unknown, but we had


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

**Table**
