V ISTA DE CASOS DE  U SO :

S-REA 55°C Data 55°C S-REA 65°C Data 65°C

t(s) × 10⁴

280 290 300 310 320 330 340

Figure 3.4 Centre temperature profiles of mango tissues during convective drying at different drying air temperatures.[Reprinted from AIChE Journal, 59, Aditya Putranto, Xiao Dong Chen,

Spatial reaction engineering approach as an alternative for nonequilibrium multiphase mass-transfer model for drying of food and biological materials, 55–67, Copyright (2012), with

permission from John Wiley & Sons Inc.]

Reaction engineering approach II: S-REA 135

Table 3.2 R²and RMSE of convective drying of mango tissues using the S-REA.

Drying air temperature

(°C) R²for X RMSE for X R²for T RMSE for T

45 0.998 0.103 0.998 0.285

55 0.999 0.079 0.985 1.004

65 0.996 0.150 0.994 0.842

Moisture content (kg water/kg dry solids)

0 0.002 0.004 0.006 0.008 Half thickness (m)

0.01 0.012 0.014 t = 1000s t = 3000s t = 5000s t = 10 000s t = 20 000s t = 30 000s t = 35 000s 8

7 6 5 4 3 2 1 0 9 10

Figure 3.5 Spatial moisture content profiles of mango tissues during convective drying at drying air temperatures of 45°C. [Reprinted from AIChE Journal, 59, Aditya Putranto, Xiao Dong Chen, Spatial reaction engineering approach as an alternative for nonequilibrium multiphase mass-transfer model for drying of food and biological materials, 55–67, Copyright (2012), with

permission from John Wiley & Sons Inc.]

2009) indicate that the S-REA yields comparable, or even better, agreement towards the experimental data.

Figure 3.5shows the spatial profiles of the moisture content during convective drying of mango tissues at a drying air temperature of 45°C. The moisture content at the outer part of the samples is lower than that at the inner part, which indicates the effect of moisture removal. Initially, the gradient of moisture content inside the samples is relatively high but this decreases as the drying progresses. At the end of drying, no noticeable gradient of moisture content is observed, which indicates the equilibrium moisture content is nearly approached. If no liquid diffusion mechanism is used, the S-REA model would not be able to project this kind of liquid water profile (Kar and Chen,2010;2011).

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 Water vapour concentration (kg/m3)

Half thickness (m) 0

0.002 0.004 0.006 0.008 0.01 0.012

t = 1000s t = 3000s t = 5000s t = 10 000s t = 20 000s t = 30 000s t = 35 000s

Figure 3.6 Spatial water vapour concentration profiles of mango tissues during convective drying at drying air temperatures of 45°C. [Reprinted from AIChE Journal, 59, Aditya Putranto, Xiao Dong Chen, Spatial reaction engineering approach as an alternative for nonequilibrium multiphase mass-transfer model for drying of food and biological materials, 55–67, Copyright

(2012), with permission from John Wiley & Sons Inc.]

The S-REA can generate the spatial profiles of water vapour concentration. The spatial profiles of water vapour concentration during convective drying of mango tissues at a drying air temperature of 45°C are shown inFigure 3.6. The profiles of water vapour concentration are significantly affected by the local composition and structure of the samples being dried. Along drying, the concentration of water vapour achieves a maximum at a particular position inside the samples. This could be because, at the core of samples, the moisture content is higher than that of the outer part which makes the porosity of the core of samples lower. The lower porosity retards the evaporation rate at the sample core. At the outer part of the samples, the water extraction rate may be enhanced because of higher porosity but this seems to be balanced by high diffusive water vapour transfer as a result of higher porosity and temperature at the outer part of the samples. The S-REA seems to capture this physics well and can model the profiles of water vapour concentration well qualitatively.

The spatial profiles of temperature are presented inFigure 3.7. The temperature of the outer part of the samples is higher than that of the inner part because the sam-ples receive heat by convection from the drying air and this is used for vaporisation;

if any is left over as such, this would penetrate further inwards by conduction. How-ever, the gradient of temperature inside the samples is not large which may indicate that the temperature inside the samples is essentially uniform. This is in agreement

Reaction engineering approach II: S-REA 137

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Temperature (K)

Half thickness (m) 305

310 315 320 325 330

t = 1000s t = 3000s t = 5000s t = 10 000s t = 20 000s t = 30 000s t = 35 000s

Figure 3.7 Spatial temperature profiles of mango tissues during convective drying at drying air temperatures of 45°C. [Reprinted from AIChE Journal, 59, Aditya Putranto, Xiao Dong Chen,

Spatial reaction engineering approach as an alternative for nonequilibrium multiphase mass-transfer model for drying of food and biological materials, 55–67, Copyright (2012), with

permission from John Wiley & Sons Inc.]

with the prediction of the Chen–Biot number (Ch–Bi) (Chen and Peng,2005; Putranto et al., 2011a) which remains low (less than 0.3) during drying reported previously (Putranto et al.,2011a).

Figure 3.8indicates the local evaporation rate inside mango tissues during convective drying at a drying air temperature of 55°C. As drying proceeds, the evaporation rate at the inner part is smaller than that of the outer part, which could be due to high moisture content at the inner part of the sample. This means a lower porosity there that retards the evaporation rate. The observation is also in agreement with the intuitive explanation of profiles of water vapour concentration during drying by Chen (2007). As drying progresses, the evaporation rate increases as the temperature increases. However, the increase is observed up to a drying time of around 15 000 s. After this period, the evaporation rate decreases as the moisture content inside the samples is depleted. At the end of drying, essentially there is not much difference in evaporation rate inside the samples because the moisture content has nearly achieved equilibrium under the drying conditions.

Therefore, it can be said that the S-REA approach models the convective drying of mango tissues well and the original REA is a simple alternative approach to represent the local evaporation and condensation rates. In addition, the S-REA has been easily

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 Evaporation rate (kg water/(m3 s))

Half thickness (m) –0.2

0 0.2 0.4 0.6 0.8 1 1.2

t = 1000s t = 5000s t = 10 000s t = 15 000s t = 20 000s t = 30 000s t = 35 000s

Figure 3.8 Profiles of evaporation rates inside mango tissues during convective drying at a drying air temperature of 55°C. [Reprinted from AIChE Journal, 59, Aditya Putranto, Xiao Dong Chen,

Spatial reaction engineering approach as an alternative for nonequilibrium multiphase mass-transfer model for drying of food and biological materials, 55–67, Copyright (2012), with

permission from John Wiley & Sons Inc.]

operated to yield the profiles of water vapour concentration, local evaporation rate and local heat evaporation rate inside the mango tissues during drying.

3.3.4 Results of modelling of convective drying of potato tissues using the S-REA As mentioned earlier, the S-REA has also been implemented to model the convective drying of potato tissues. The relative activation energy is generated from one accurate drying run which is the convective drying at air temperature of 70°C. It is represented in Equation (3.3.16). Similar to the convective drying of mango tissues, the internal mass transfer coefficient (hm,in: on Equation 3.1.17) is chosen to be 0.01 m s⁻¹ as the sensitivity analysis indicates that hm,in of higher than 0.01 m s⁻¹does not give any noticeable differences in the profiles of moisture content and temperature. Nicely, this is also in the order of Dv/rp as suggested by Kar and Chen (2010;2011), hence hm,in

is a fundamental value. However, Dwo(in Equation3.2.7) is determined by sensitivity analysis and it is found that Dwoof 6.5× 10⁻⁶m²s⁻¹gives the best agreement against the experimental data. It is emphasised that the temperature dependence function for the liquid diffusivity in this case was obtained in isothermal drying experiments specially designed by Srikiatden and Roberts (2006), in contrast to many published studies that

Reaction engineering approach II: S-REA 139

0 0.5 1 1.5 2 2.5

Moisture content (kg water/kg dry solids)

t(s) × 10⁴

0 1 2 3 4 5 6

S-REA-core Data-core S-REA-cortex Data-cortex

Figure 3.9 Moisture content profiles in the core and cortex during convective drying of potato tissues with a diameter of 1.4 cm.[Reprinted from AIChE Journal, 59, Aditya Putranto, Xiao

Dong Chen, Spatial reaction engineering approach as an alternative for nonequilibrium multiphase mass-transfer model for drying of food and biological materials, 55–67, Copyright

(2012), with permission from John Wiley & Sons Inc.]

suggest the diffusivity in the material is related to drying air temperature instead (Chen, 2007).

Results of modelling convective drying of potato tissues are shown inFigures 3.9–

3.11.Figure 3.9shows the profiles of moisture content of each part of potato cylindrical tissue with the diameter of 1.4 cm during the convective drying. It can be shown that the results of modelling match well with the experimental data with a correlation coefficient R² of 0.98. Benchmarks against modelling implemented by Srikiatden and Roberts (2008) with the liquid diffusivity concept indicate that the S-REA yields comparable results.

In addition, the profiles of moisture content for each part of samples with the diameter of 2.8 cm are shown inFigure 3.10. Again, a good agreement towards the experimental data is observed (R²of 0.992). Indeed, the S-REA describes the moisture content pro-files accurately during convective drying of potato tissues with a diameter of 2.8 cm.

Benchmarks towards modelling implemented by Srikiatden and Roberts (2008) indicate that the REA yields comparable or even better results. It can be said that the S-REA can be used to model the profiles of moisture content very well.

Figure 3.11indicates the core temperature during convective drying of potato tissues with the diameter of 1.4 cm. The predictions of temperature using the S-REA match

0 1 2 3 4

Moisture content (kg water/kg dry solids)

0 0.5 1 1.5 2 2.5 3 3.5

t(s) × 10⁴

S-REA-core S-REA-cortex 1 S-REA-cortex 2 S-REA-cortex 3 Data-core Data-cortex 1 Data-cortex 2 Data-cortex 3

Figure 3.10 Moisture content profiles in the core and cortex during convective drying of potato tissues with a diameter of 2.8 cm.[Reprinted from AIChE Journal, 59, Aditya Putranto, Xiao

Dong Chen, Spatial reaction engineering approach as an alternative for nonequilibrium multiphase mass-transfer model for drying of food and biological materials, 55–67, Copyright

(2012), with permission from John Wiley & Sons Inc.]

295 305 300 310 315 320 325 335 330 340 345

Core temperature (K)

0 0.5 1 1.5 2 2.5

t(s) × 10⁴

Data S-REA

Figure 3.11 Core temperature profiles during convective drying of potato tissues with a diameter of 1.4 cm.[Reprinted from AIChE Journal, 59, Aditya Putranto, Xiao Dong Chen, Spatial reaction engineering approach as an alternative for nonequilibrium multiphase mass-transfer model for drying of food and biological materials, 55–67, Copyright (2012), with permission

from John Wiley & Sons Inc.]

Reaction engineering approach II: S-REA 141

Table 3.3 Scheme of intermittent drying of mango tissues (Vaquiro et al.,2009).

Drying air temperature (ºC)

Period of first heating (s)

Period of resting (at 27°C ± 1.6) (s)

Period of second heating (s)

45 16 200 10 800 36 360

55 9480 10 800 33 720

well with the experimental data with R²of 0.99. Benchmarks against modelling imple-mented by Srikiatden and Roberts (2008) indicate that the S-REA yields comparable results. Overall, S-REA seems to be a sound approach to modelling the details of spatial distributions of temperature, liquid water and water vapour concentration in the material being dried.

3.4 The S-REA for intermittent drying

The accuracy of the S-REA in modelling intermittent drying is validated by the exper-imental data of intermittent drying of mango tissues (Vaquiro et al.,2009). For better understanding of the modelling approach, the experimental details are summarised and reviewed in this section. The samples of mango tissues were cubes with initial side lengths of 2.5 cm, while the initial moisture content and temperature were 9.3 kg kg⁻¹ and 10.8ºC, respectively. The laboratory drier was described in Sanjuan et al. (2004).

During drying, the weight of the sample and the centre temperature were recorded. The drying air temperature and air velocity were controlled at preset values by PID control algorithms while air humidity was maintained constant during drying. The experimental setting for intermittent drying is shown inTable 3.3. During the resting period, the sam-ples stayed in an environment with an ambient temperature of 27± 1.6 °C and relative humidity of 60% (Vaquiro et al.,2009). Determination of density, thermal conductivity, heat capacity, equilibrium moisture content and shrinkage of samples being dried has been described previously (Putranto et al.,2011a).

3.4.1 The mathematical modelling of intermittent drying using the S-REA

In experiments reported by Vaquiro et al. (2009), the subject of interest, the samples were dried from three directions (x, y and z directions) so three-dimensional modelling of the S-REA for intermittent drying of mango tissues needs to be set up, which is represented next. The mass and heat balances of intermittent drying of mango tissues are similar to those of convective drying described in Section 3.3.1.

Similarly to the convective drying of mango tissues, the mass balance of water in liquid phase liquid water, the mass balance of water in the vapour phase (water vapour) and the heat balance are shown in Equations (3.3.1), (3.3.2) and (3.3.3), respectively, while the initial and boundary conditions for equations are shown in Equations (3.1.4)–

(3.1.16).

Table 3.4 R²and RMSE of intermittent drying of mango tissues.

R²for X RMSE for X R²for T RMSE for T

45°C 0.964 0.358 0.992 0.705

55°C 0.999 0.0774 0.994 0.874

The internal-surface water vapour concentration (Cv,s) and internal evaporation rate are evaluated using Equations (3.1.18) and (3.1.19), respectively. The liquid diffusivity (Dw) is shown in Equation (3.2.7) while the effective vapour diffusivity (Dv), tortuosity (τ), solid concentration (Cs) and porosity (ε) are deduced using Equations (3.2.1)–

(3.2.5). Similarly, the internal mass transfer coefficient (hm,in) is evaluated using the procedures explained in Section 3.2.

The relative activation energy implemented for modelling of convective drying of mango tissues shown in Equation (3.3.4) is used here to model the intermittent drying of mango tissues. For modelling the intermittent drying of these tissues, the equilib-rium activation (Ev,b) energy shown in Equation (2.1.7) is evaluated according to the corresponding drying air temperature and humidity in each drying period. It is also combined with the relative activation energy shown in Equation (3.3.4) to yield the local drying/condensation rate. In addition, the heat balance implements the corresponding drying air temperature in each drying period by using the corresponding drying air temperature in the boundary conditions indicated in Equations (3.1.10), (3.1.13) and (3.1.16). The solution procedures are similar to the one for convective drying of mango tissues, described in Section 3.3.1.

3.4.2 Results of modelling intermittent drying using the S-REA

The S-REA is implemented here to model the intermittent drying of mango tissues whose conditions are listed inTable 3.3. As mentioned before, for modelling of the intermittent drying, the equilibrium activation energy needs to be evaluated according to the corresponding drying settings in each drying period. Similarly, the heat balance implements the corresponding drying air temperature in each drying period. Solving Equations (3.3.9)–(3.3.11) in conjunction with the initial and boundary conditions shown in Equations (3.3.4) to (3.3.8) simultaneously yields the profiles of moisture content, concentration of water vapour and temperature during intermittent drying.Figures 3.12–

3.17show the results of modelling of the intermittent drying.

The profiles of moisture content during intermittent drying are shown inFigure 3.12.

A good agreement between the predicted and experimental data is observed and con-firmed by R²and RMSE listed inTable 3.4. The results of modelling match well with the experimental data of moisture content. The S-REA models the average moisture content during the intermittent drying at drying air temperature of 45°, 55° and 65 °C very well.

Benchmarks against modelling implemented by Vaquiro et al. (2009) revealed that the REA yields better results as Vaquiro et al. (2009) showed a slight underestimation in drying rate of intermittent drying at a drying air temperature at 45°C during drying

Reaction engineering approach II: S-REA 143

0 1 2 3 4 5 6 7

Moisture content (kg water/kg dry solids)

t(s) × 10⁴

0 1 2 3 4 5 6 7 8 9 10

S-REA 45°C