**3. Material and methods**

#### **3.1 Aerodynamics in an agitated fluidized bed of biomass particles**

The experiments were carried out in a laboratory equipment whose main section, the drying chamber, is shown in **Figure 1**; details of the equipment, which has also been used to carry out the experiment on heat and mass transfer, can be found in Moreno et al. [11]. **Figure 2** shows an overview of the equipment.

To develop the aerodynamic analysis of the fluidized bed, experiments were carried out to determine the pressure drop of the bed as a function of the superficial velocity of the air. The basis weight of the biomass samples was 2.0 kg d.b. The superficial velocity was gradually increased until reaching the *Umf* value in order to analyze the bed in its rest condition; the suspended bed condition was also guaranteed, for which the superficial velocities rose above the minimum fluidization velocity.

**Figure 1.** *Schematic diagram of experimental equipment.*

**Figure 2.** *Overview of the fluidized bed dryer of biomass particles.*

The *dp* particle size varied in the range of 0.51–3.56 mm. The tests were carried out first using particles with equilibrium moisture content (0.15 kg kg�<sup>1</sup> d.b.); subsequently, the bed was loaded with wet particles (2.0 kg kg�<sup>1</sup> of humidity d.b.), with which the density of the particles varied between 423 and 1044 kg m�<sup>3</sup> .

The experimental velocity data were obtained with a Pitot tube. On the other hand, the pressure drops of the bed were measured with a differential manometer for each superficial velocity tested. In addition, the rotation speed of the mechanical agitator was varied, seeking the best stability condition for the bed of wet particles, since wet biomass particles have a great tendency toward agglomeration as a result of surface forces generated by the water contained in them.

*Experimental Investigation on Drying of Forest Biomass Particles in a Mechanically… DOI: http://dx.doi.org/10.5772/intechopen.113973*

In a fixed bed of biomass particles, the bed porosity *ε* can be calculated with the values of the density of the particles *ρ<sup>p</sup>* and the density of the static bed *ρb*. Thus,

$$\varepsilon = \mathbf{1} - \frac{\rho\_b}{\rho\_p} \tag{10}$$

In order to analyze the quality of the fluidization of biomass particles, prior to the drying tests, the procedure used consists of determining the fraction of particles in the bed that are suspended by the ascending air flow; the fluidization quality index *QF* is used according to the Eq. (11). Thus, if the bed is completely fluidized, the pressure drop of the bed should be equal to the weight of solids per unit of cross-sectional area of the bed and otherwise the *QF* index is less than 1.

$$QF = \frac{\Delta p}{W/A} \tag{11}$$

#### **3.2 Fundamentals of gas-particle heat transfer**

Regarding the determination of the convective heat transfer coefficient in fluidized beds, in most of the works reported in the literature, the interfacial heat transfer analysis is carried out in batch processes and steady state, where the hot gas enters the bed and is then cooled by making contact with the cold particles. Thus, for a bed layer of thickness d*l*, the convective coefficient can be represented as:

$$-C\_{\rm g}U\rho\_{\rm g}\frac{dT\_{\rm g}}{dl} = h\_{\rm gp}S(T\_{\rm g} - T\_{p,s})\tag{12}$$

which, integrated for a height *l* in the bed, allows to obtain:

$$\ln \frac{T\_{\rm g,i} - T\_{p,s}}{T\_{\rm g,l} - T\_{p,s}} = \frac{h\_{\rm gp} \text{S}}{\rho\_{\rm g} U C\_{\rm g}} l \tag{13}$$

where *Tg,i* and *Tg,l* are the gas temperature at the inlet and at a height *l* of the bed.

Representing the first member of Eq. (13) as a function of *l*, based on the experimental data, then the value of *hgp* can be obtained through the slope plotted on a semilogarithmic graph. The slope can be variable if the local coefficient presents variations depending on the position inside the bed.

Eq. (13) has been obtained on the basis of the complete mixing of gas and particles, that is, assuming that the temperature of the particles in the bed is the same at all points, except for a region of the bed close to the distributor. The above is because temperature gradients and equilibrium between gas and particles are reached in this zone, as already reported by [8, 12, 13]. This means that the gas temperature variations must be measured in the area close to the distributor and that the temperature of the particles can be considered equal to that of the gas at the outlet of the bed. Some authors consider that a thermocouple inserted in the bed provides a measurement of the temperature of the solids, which, strictly speaking, is not the case. This experimental model assumes that heat losses to the environment are negligible.

For studies of heat transfer coefficients in drying systems in the period of constant drying rate, it can be assumed that the temperature of the surface particles *Tp,s* is equal to the wet bulb temperature *Twb* of the inlet air [14, 15], since in such a period the product shows a wet surface.

The analysis of the drying curves, obtained in Moreno [16] allows us to conclude that a large part of the process is carried out under a constant temperature regime and at a constant drying rate. In principle, the determination of the heat transfer coefficients should be carried out using Eq. (13). However, this procedure provides a local value of the convective heat transfer coefficient.

For design purposes, it is more appropriate to work with mean values of *hgp*. Thus, in an adiabatic regime, the heat balance equation can be written as:

$$-h\_{\text{f\S}} \rho\_{p,0} \frac{dw}{dt} = h\_{\text{gp}} \mathbf{S}\_p \Delta T\_{ml} \tag{14}$$

Thus, the *hgp* calculation can be carried out using the equation:

$$h\_{\rm gp} = \frac{h\_{\rm fg} \rho\_{p,0} \left(-\frac{dw}{dt}\right)}{\mathcal{S}\_p \Delta T\_{ml}} \tag{15}$$

In Eq. (14) the concept of logarithmic-mean temperature difference is introduced, which for its application in this drying process can be assumed that the surface temperature of the particles is equal to the temperature of the wet bulb of the air because the drying was carried out under the condition of constant rate. Thus:

$$
\Delta T\_{ml} = \frac{T\_{\text{g,i}} - T\_{\text{g,o}}}{\ln \left( \frac{T\_{\text{f,i}} - T\_{\text{ub}}}{T\_{\text{k}} - T\_{\text{ub}}} \right)} \tag{16}
$$

#### **3.3 Fundamentals of gas-particle mass transfer**

In analogy with the convective phenomenon of heat transfer between a solid particle and a fluid, which is governed by Newton's cooling equation, for a drying process the mass transfer between the wet particle and the air that receives the vapor released by solids is governed by a similar equation, that is:

$$
\dot{m}\_v = k\_{\text{gp}} A\_p (c\_{v,s} - c\_{v,\text{so}}) \tag{17}
$$

It can be assumed, in analogy with heat transfer, that the moisture concentration in the humid air *cv,*<sup>∞</sup> of Eq. (17), at a given bed height, is uniform across the cross section of the drying chamber and the transfer of matter is completed in a very small distance above the distributor.

By making a mass balance during the drying process in the constant drying rate period, for a differential fluidized bed element of thickness d*l*, the mass flow of water vapor at the particle surface, based on Eq. (17), can be determined. Thus:

$$d\dot{m}\_v = k\_{\text{gp}} (c\_{v,s} - c\_v) \text{SA} dl \tag{18}$$

The water vapor flow can be related to the moist content of the moist air through:

$$d\dot{m}\_v = \dot{m}\_{da} d\omega\_a \tag{19}$$

Then:

$$
\dot{m}\_{da} dw\_a = k\_{\text{gp}} (c\_{v,s} - c\_v) \text{SA} dl \tag{20}
$$

*Experimental Investigation on Drying of Forest Biomass Particles in a Mechanically… DOI: http://dx.doi.org/10.5772/intechopen.113973*

If incompressible flow is considered, then:

$$
\dot{m}\_{da} v\_a d\boldsymbol{c}\_v = k\_{\rm gp} (\boldsymbol{c}\_{v,s} - \boldsymbol{c}\_v) \text{SA} d\boldsymbol{l} \tag{21}
$$

When Eq. (21) is integrated from a point on the distributor, for a bed height *l*, the following is obtained:

$$\ln \frac{c\_{v,s} - c\_{v,i}}{c\_{v,t} - c\_{v,l}} = \frac{k\_{\text{gp}} \text{SA}}{\dot{m}\_{da} \upsilon\_a} l \tag{22}$$

On the other hand, using an average coefficient of *kgp*, the mass balance equation for the entire bed can be written as:

$$k\_{\rm gp} = \frac{\dot{m}\_v}{A\_p \Delta c\_{ml}} \tag{23}$$

where the logarithmic mean difference in moisture concentration is defined as:

$$
\Delta c\_{ml} = \frac{c\_{v,o} - c\_{v,i}}{\ln\left(\frac{c\_{v,l} - c\_{v,i}}{c\_{v,l} - c\_{v,o}}\right)}\tag{24}
$$

Since the equation applies to the entire bed, then *Ap = SpVp* and

$$k\_{\rm gp} = \frac{\dot{m}\_v}{\mathcal{S}\_p V\_p \Delta \mathcal{L}\_{ml}} \tag{25}$$

In terms of the drying rate (�d*w*/d*t*) Eq. (25) can be written as:

$$k\_{\xi p} = \frac{\rho\_{p,0} \left(-\frac{dw}{dt}\right)}{\mathcal{S}\_p \Delta \mathcal{c}\_{ml}}\tag{26}$$

Similarly, to what was assumed in the heat transfer analysis, in determining the surface mass transfer coefficient it was assumed that the concentration of water vapor on the wetted surface of the particles is equal to that of saturated air and evaluated at the wet bulb temperature of humid air [15].

#### **3.4 Experiments on heat and mass transfer**

The experimental dryer has a drying chamber with a diameter of 0.3 m. The biomass load, as in the fluodynamic tests, was 2.0 kg d.b., occupying an approximate height of 0.17 m. The mechanical stirrer was built with a vertical shaft and four blades in total.

To analyze the homogeneity of the bed and its temperature, 8 temperature sensors were installed, as shown in **Figures 1** and **3**, and connected to a Digi-Sense Cole-Parmer Instrument Company multichannel thermometer; it has a resolution of 0.1 K and � 0.5 K accuracy and an RS-232 output for connection to a PC. Data was collected every 4 s and analyzed using a ScanLink 2.0 software. An additional temperature sensor PT100 was placed at the entrance of the air flow to the dryer to control the operating temperature of the equipment.

#### **Figure 3.**

*Arrangement of thermocouples to measure temperature inside the bed.*

At the bed outlet, a Digi-Sense digital psychrometric digital recorder was used together with ScanLink 2.0 and PCDAC (Cole-Parmer Instrument Company) programs to collect data every 10 s.

The drying experiences were carried out with Pinus radiata sawdust particles. The operating temperature measured at the inlet of the hot air flow to the drying chamber was recorded, as well as the outlet temperature of the gas above the particle bed.

In determining the mean logarithmic difference of Eq. (16) and to avoid the error caused by the heat transferred from the air to the distributor plate, the temperature of the gas at the bed inlet *Tg,i* was measured at a point just above the air distributor. Thus, was verified that the air temperature, after passing through the distributor, drops sharply when it comes into contact with the particles. **Figure 4** shows a schematic diagram of the thermocouples to obtain the axial distribution of temperature in the bed. The homogenization of the temperature is reached at a height lower than 20 mm above the distributor, as shown in **Figure 5**, which agrees with the analysis of other authors [8, 12] and the experimental results of [13, 17].

The physical properties of the gas were evaluated at the mean temperature of the fluid film surrounding the particle, considering that the particle surface temperature is equal to the air wet bulb temperature.

In the heat and mass transfer experiments, three control factors (*U*, *dp* and *N*) were used. The experiments were carried out, considering each particle with an air velocity within the range in which its fluidization occurs according to the moisture content of the particles. In order to study possible variations of the *hgc* and *kgc* coefficients, at each level of (*dp*-*U*) the experiments were performed with two rotation speeds of the mechanical bed stirrer. **Table 1** shows the 10 trials with their respective levels; the operating temperature was 150°C in all cases.
