**4. Results and discussion**

#### **4.1 Bed porosity, specific surface area, and minimum fluidization velocity**

Using Eq. (10) and the procedure described in Section 3.1, the porosity of the bed has been determined in the fixed bed condition. The specific surface has been obtained based on the Ergun's modified equation. The size *dp* corresponds to particles *Experimental Investigation on Drying of Forest Biomass Particles in a Mechanically… DOI: http://dx.doi.org/10.5772/intechopen.113973*

**Figure 5.** *Axial temperature profile inside the bed, corresponding to seven profiles measured with an inlet temperature equal to 150°C.*


#### **Table 1.**

*Experiments for determination of* hgp *and* kgp *coefficients.*

obtained by means of ASTM E-11 sieving. **Table 2** shows the results on bed porosity and specific surface area of particles.

In the preliminary tests in an agitated fluidized bed, the range between 0 and 2 rev s �<sup>1</sup> has been chosen, to analyze the behavior of the bed in terms of its mobility, depending on the combination of the superficial velocity and agitation speeds parameters. Tests were carried out with a load of 2 kg of biomass particles of 1.44 mm in size and with a moisture content of 2.0 kg kg�<sup>1</sup> d.b.

**Figure 6** shows the behavior of the pressure drop in the bed as a function of superficial velocity, for a stirred bed with different stirring speeds. With 0.5 rev s�<sup>1</sup> (**Figure 6a**) it could be seen that at a speed of 1.12 m s�<sup>1</sup> (point A), the bed opens abruptly giving way to a sudden increase in the air flow through the bed, reaching a velocity of 1.35 m s�<sup>1</sup> (point B). The fluidization stabilizes from a velocity of 1.46 m s�<sup>1</sup> with a suspension of the particles equivalent to a *QF* = 0.78.

By increasing the turning speed to 1 rev s�<sup>1</sup> (**Figure 6b**), the transition from the fixed bed to the fluidized bed is more gradual with a transition speed of 1.18 m s�<sup>1</sup> (A) and a *QF* = 0.88, but then there tends to be a decrease in *QF* with increasing velocity. This phenomenon is significantly attenuated at higher turning speed and at 2 rev s�<sup>1</sup> (**Figure 6d**) at a superficial velocity of 0.91 m s�<sup>1</sup> (A) the transition from a fixed bed to a fluid bed occurs, reaching a *QF* = 0.95. A notable aspect of these tests was the minimal amount of particle carryover out of the dryer.


**Table 2.**

*Fixed bed porosity and specific surface area for dry and wet biomass particles.*

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

**Figure 6.** *Pressure drop across the bed as a function of superficial velocity with different stirring speeds for* dp *= 1.44 mm and* w *= 2.0 kg kg*�*<sup>1</sup> d.b.*

Once the objective of having a high-quality fluidized bed was achieved, the minimum fluidization velocity was determined. **Figure 7** shows a curve of pressure drop versus superficial velocity obtained with particles with equilibrium moisture and 1.85 mm size for an agitation velocity of 2.0 rev s�<sup>1</sup> . When carrying out tests with the other particle sizes, it was found that the qualitative behavior was similar, with obvious differences in the velocity values obtained, depending on the particle size, as shown in **Table 3**.

From the point of view of the quality of the fluidization of wet particles, it is found that mechanical agitation has an important effect when the particles have high moisture contents, taking into account that a bed of wet biomass is impossible to fluidize without mechanical agitation; in the case of low moisture particles, the effect of agitation is less.

The minimum fluidization velocities *Umf* were determined in a mechanically shaken fluidized bed with agitation velocity *N* = 2 rev s�<sup>1</sup> , for dry and wet biomass particles; it can be observed in **Table 3** that with dry biomass, fluidization velocities are smaller.

For the *Umf* velocity prediction, a new correlation is proposed based on a procedure reported in [18]. The initial correlation studied fits well with experimental data in the range of small particles. However, with large particle sizes, the prediction of experimental values of *Umf* was not successful and therefore the correlation had to be corrected to consider the variation of the *Umf* velocity with the particle size. To carry out this correction, a geometric factor (*dp*/*D0*) was used, where *dp* is the particle size obtained by sieving and *D0* is a reference size equal to 1 mm. Thus, the proposed correlation is:

**Figure 7.** *Pressure drop in an agitation-fluidized bed for* dp *= 1.85 mm and equilibrium moisture content;* N *= 2.0 rev s*�*<sup>1</sup> .*


**Table 3.**

*Variation of the minimum fluidization velocity* Umf *in m s*�*<sup>1</sup> , in relation to the particle size* dp *for dry and wet biomass;* N *= 2.0 rev s*�*<sup>1</sup> .*

$$Re\_{\eta f} = \left[ \left( 24.8^2 + 0.0444 GaM\_\rho \right)^{0.5} - 24.8 \right] \left( \frac{d\_p}{D\_0} \right)^{1/3} \tag{27}$$

The prediction of the velocity of minimum fluidization using Eq. (27) as observed in **Table 3**, it is acceptable; only in two tests the deviations were �12% and +15%.

#### **4.2 Heat and mass transfer**

#### *4.2.1 Thermal characterization of the bed of biomass particles*

From the point of view of the fluodynamic behavior of the particles in the fluidized bed, it is first important to guarantee the high quality of their suspension, reflected in a high value of the *QF* index of Eq. (11), as already indicated. From the thermal point of view itself, the high quality of fluidization has been evidenced in a high homogeneity of the bed temperature, according to the records of the eight thermocouples inserted inside the fluidized bed, as shown in **Figure 8**, which have been obtained during a drying experiment.

In addition, this excellent fluidization quality has been verified with the high value of the correlation coefficient *R<sup>2</sup>* for the drying curves, as will be seen in the drying

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

experiments. **Figure 9** shows one of the drying curves obtained and it can be seen that the process is carried out with a constant drying rate, therefore the ideal adjustment curve in this case would be a straight line with a high value for the explanatory variance *R<sup>2</sup>* .

On the other hand, in order to know the behavior of the biomass during the drying process, specifically in the range of temperatures normally used in dryers with atmospheric air, a thermogravimetric analysis has been carried out.

The experimental tests were carried out in a Cahn 2000 thermogravimetric equipment, 113 system, equipped with a programmable temperature control system.

**Figure 10** shows the TG diagram in an inert atmosphere, for two tests carried out with wet and dry biomass. This diagram shows the percentage of residual weight, with respect to the initial weight loaded, as a function of the sample during the test.

**Figure 8.** *Temperature profile at different points in the bed during biomass drying experiment.*

**Figure 9.** *Drying curve for biomass particles in an agitated fluidized bed;* R*<sup>2</sup> = 0.996.*

**Figure 10.** *Thermogravimetric (TG) of wet and dry biomass in an inert atmosphere depending on the temperature.*

It can be seen in **Figure 10**, how the absolute loss of volatiles in the wet biomass is less than in the dry one, for having introduced less dry mass into the sample, since part of it was water (moisture). If the relative value were calculated, it would give the same proportion.

**Figure 11** shows two curves obtained for the test carried out in an oxidizing atmosphere, showing good reproducibility, which gives a good degree of reliability in the results obtained. The weight variations between the original test and the replica were 5.3%.

**Table 4** contains a summary of the relevant parameters of the thermogravimetric analysis. The maximum rate of devolatilization and combustion is evaluated according to the following expression:

$$U\_{\text{max}} = -\frac{1}{m\_{\text{isc}}} \left( \frac{dm}{dt} \right)\_{\text{max}} \tag{28}$$

where *misc* corresponds to the initial mass of loaded biomass, on an ash-free basis and (d*m*/d*t*)máx represents the maximum slope of the TG curve (mass versus time).

**Figure 11.** *Thermogravimetric (TG) of biomass in an oxidant atmosphere and its replica.*

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


#### **Table 4.**

*Thermogravimetric parameters derived from TG and DTG curves of forest biomass.*

#### *4.2.2 Convective heat transfer coefficient*

The values obtained for the heat transfer coefficients are shown in **Table 5**, for each of the tests defined in **Table 1**. When using Eq. (15) in the calculation of the convective heat transport coefficient, the drying rate d*w*/d*t* shown in **Table 5** was introduced, which in turn is obtained from the experimental drying curve of each test (**Figure 9**). The value of *R2* indicated in the table corresponds to the correlation coefficient obtained in the fit of the straight line to the experimental data of moisture content of the solids versus time.

On the other hand, once the values of the heat transfer coefficient were known, in each test the Nusselt number was calculated using the first equality of Eq. (3) and then the correlation between the Nusselt number and the Reynolds number was obtained, which is proposed in Eq. (29). It has been verified that the rotation speed (*N*) does not


#### **Table 5.**

*Convective heat and mass transfer coefficients.*

influence the convective heat transfer coefficient, since the variations found in the *hgp* coefficient as a function of *N* are random as shown in **Table 5**, which is consistent with previously reported results [15].

$$Nu\_{\mathfrak{g}p} = 0.003 \, Re\_p \, ^{1.28}; 100 < Re\_p < 250; R^2 = 0.95\tag{29}$$

or by rearranging terms as,

$$h\_{\rm gp} = 0.003 \frac{k\_{\rm g}}{D\_{\rm p}} \left( \frac{\rho\_{\rm g} U D\_{\rm p}}{\mu\_{\rm g}} \right)^{1.28} \tag{30}$$

**Table 5** shows the values found for the *hgp* coefficient, which fluctuate between 13 and 25.7 W m�<sup>2</sup> K�<sup>1</sup> ; these values are in a range similar to that of 6 and 23 W m�<sup>2</sup> K�<sup>1</sup> reported by Botterill [19]. In another investigation [20], results on the drying of forest biomass particles are reported, with *hgc* values in the range between 10 and 60 W m�<sup>2</sup> K�<sup>1</sup> , to a dryer with superheated steam and operating temperatures up to 513 K. In a subsequent study by Salve et al. [21], higher *hgp* coefficient values (80– 220 W m�<sup>2</sup> K�<sup>1</sup> ) were found, obtained with superficial velocities as well as elevated (3–11 m s�<sup>1</sup> ) and using sand in the bed.

On the other hand, **Table 6** shows a comparison between the values of the Nusselt number, obtained through the experimental procedure of this research, and those predicted by Eq. (29) with *R*<sup>2</sup> equal to 0.95. Furthermore, the experimental results have been compared with values predicted by Eq. (31) reported by Reyes and Alvarez [22] and obtained for Reynolds numbers in the range between 33 and 150.

$$Nu\_{\rm gp} = 0.00116 \ Re\_p^{1.52} \tag{31}$$

The comparison is also made with Eq. (32) from Zabrodsky and Eq. (33) by Lykov, respectively, both reported in Ciesielczyk [15].


#### **Table 6.**

*Nusselt number: comparison of experimental values with the proposed equation and correlations from other authors.*

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

$$Nu\_{\rm gp} = 0.00195 \ Re\_p^{1.46} \tag{32}$$

$$Nu\_{\rm gp} = 0.0087 \ Re\_p^{0.84} \tag{33}$$

Finally, the results are compared with Eq. (34) from Rao and Sen Gupta and reported by Vyas and Nageshwar [23] with the Reynolds numbers in the range between 7 and 20.

$$Nu\_{\rm gp} = 0.000075 \ Re\_p^{1.61} \tag{34}$$

Of these correlations, those that are closest to Eq. (29) and the experimental values of this study are those of Reyes and Alvarez and that of Zabrodsky, Eqs. (31) and (32), respectively. The Rao and Sen Gupta equation is the one with the most deviations and is attributed to the fact that it is obtained for a very low range of the Reynolds number.

#### *4.2.3 Convective mass transfer coefficient*

The experimental values of the convective coefficient of mass transfer under the conditions already established are shown in **Table 7**. As in the phenomenon of heat transfer, it is verified that the rotation speed of the mechanical stirrer does not affect the mass transfer.

In Eq. (35) the correlation obtained by adjustment between the Sherwood number and the Reynolds number is shown.

$$Sh\_{gp} = 1.6 \text{\AA} \, 10^{-3} Re\_p \, ^{1.38}; \quad 100 < Re\_p < 250; \quad R^2 = 0.75 \tag{35}$$

or:

$$k\_{\rm gp} = 1.6 \times 10^{-3} \frac{D\_v}{D\_p} \left(\frac{\rho\_\text{g} U D\_p}{\mu\_\text{g}}\right)^{1.38} \tag{36}$$


#### **Table 7.**

*Sherwood number: comparison of experimental values with the proposed equation and correlations from other authors.*

**Table 7** shows a comparison between the values of the Sherwood number, obtained in this research, and those predicted by Eq. (35) with a correlation *R*<sup>2</sup> equal to 0.75. When comparing the experimental results with Eqs. (6), (7), and (9), unlike what happens with the heat transfer mechanism, in mass transport more significant differences are seen between our results and the Sherwood number values predicted by correlations obtained by other authors. Considering also that there are great differences between correlations already reported in the literature, it can be concluded that it is a more complex phenomenon to analyze and study experimentally. This is also verified in our research on mass transfer by observing that the value of *R*<sup>2</sup> from Eq. (35) is lower relative to the best correlation coefficient *R*<sup>2</sup> obtained in Eq. (29) for heat transfer.

The above implies that the information available in the specialized literature is not necessarily sufficient to predict heat and mass transfer coefficients, formulate mathematical modeling, and develop the thermal design of particulate forest biomass drying processes.

In the analysis of the discrepancies between experimental results with the values that predict equations reported in the literature, the characteristics of the solids of each system analyzed must be taken in consideration. It is also important to keep in mind the experimental procedures to determine the differences in temperatures and vapor concentrations between the fluidizing gas and the particles and the type of flow pattern in the fluidized bed (plug flow or complete mixing).

In this particular case, the system studied corresponds to a fluidized bed of coarse type D particles of the Geldart classification [24], which forces them to be fluidized with higher fluidization velocities and Reynolds numbers, which in this research ranged between 102 and 257.

Furthermore, Geldart type D biomass particles are solids with a high tendency to agglomerate as a result of cohesion forces between them, which are generated by surface water bridges. This is confirmed in this research with the lower values obtained for the specific surface area of wet particles *Sp*, compared to the values obtained when they are in a condition of low humidity *Sp,0* (**Table 2**).

Regarding the flow pattern of the fluidized bed, it can be said that a fluidized bed of biomass particles, as a result of the combination of the air flow and the effect of the mechanical agitator, it could be considered as a system with complete mixing. Thus, according to the experimental results obtained on the *QF* fluidization quality index and temperature profiles inside the bed.
