The infrared-heat drying of a mixture of polymer solutions modelled using the L-REA

The experimental data for validating the accuracy of the L-REA are derived from a study reported by Allanic et al. (2009). The experimental setup up is similar to that described in Section 2.5 but constant infrared-heat intensity is applied here. The velocity and

Reaction engineering approach I: L-REA 101

0

z

Product

Petri dish e(t)

Thermocouple

Long infrared Convection

Conduction Evaporation Diffusion

Figure 2.58 Heat transfer mechanisms of convective and infrared-heat drying.[Reprinted from Chemical Engineering and Processing: Process Intensification, 49, A. Putranto, X.D. Chen and

P.A. Webley, Infrared and convective drying of thin layer of polyvinyl alcohol (PVA)/glycerol/water mixture – The reaction engineering approach (REA), 348–357, Copyright

(2012), with permission from Elsevier.]

temperature of the drying medium were set to 1 m s⁻¹ and 35°C, respectively was fed into the canal. Constant infrared-heating with an intensity of 3.7 kW m⁻²was maintained throughout the experimental run (Allanic et al.,2009).

2.11.1 Mathematical modelling of the infrared-heat drying of a mixture of polymer solutions using the L-REA

The L-REA shown in Equation (2.1.4) is used for the mass balance here. For infrared heat-drying, the sample was heated by an infrared emitter which increased the temperature of the sample and the Petri dish (refer toFigure 2.58).

Because of the relatively low temperature of the drying air, the sample and the Petri dish actually release heat to the environment by convection. The heat is released from the upper side and bottom side due to forced and natural convection, respectively (refer toFigure 2.58). Hence, it can be written as:

d(ρCpeT )

dt = αQIR− htop(T− Tb)− Ubottom(T− Tb)+ms

A d X

dt HV(T ), (2.11.1) whereρ is sample density (kg m⁻³), Cpis sample heat capacity (J kg⁻¹K⁻¹), e is sample thickness (m), T is sample temperature (K), msis mass of dried product (kg), A is surface area of product (m²),Hv is vaporisation enthalpy of water (J kg⁻¹), htop is the heat

transfer coefficients on top of the sample (W m⁻² K⁻¹), Ubottomrepresents the overall heat transfer coefficient (W m⁻²K⁻¹) from the lower side, including convection along and conduction through the Petri dish, QIRis the intensity of radiation (W m⁻²) andα is the absorptivity of the product.

Rearranging Equation (2.11.1) results in:

d(ρCpeT )

dt = αQIR− Utotal(T− Tb)+ms

A d X

dt HV(T ). (2.11.2) It should be highlighted that the application of the L-REA requires accurate deter-mination of activation energy as a function of moisture content.Ev/Ev,b because characteristics of drying kinetics are used to describe the reduction of moisture content and temperature profiles. In convective drying, the product is heated by relatively high drying air temperatures and the maximum activation energyEv,bis determined using Equation (2.1.7). However, a different condition occurs when drying is conducted using infrared heating because the product temperature increases to above the drying air tem-perature so the product releases heat to the air instead of gaining heat from the air. If one maintains constant infrared power and lets drying continue until low water content is reached, the product temperature would reach a constant temperature determined by the balance between infrared power input and heat loss to the surroundings. The minor modifications of the L-REA are taken here as explained next.

The heat transfer coefficient should be determined from the final part of drying instead of using the initial constant rate period of drying because of the low evaporation rate at the final part of drying, so most of the heat adsorbed by the product from the infrared emitter is released to the air. In addition, at the final part of drying the product temperature is essentially constant as revealed by Allanic et al. (2009) indicating ‘thermal’ equilibrium has been reached. The heat balance for final part of drying can be written as:

αQIR= ms

A d X

dt HV(T )+ Utotal(T− Tb). (2.11.3) It is apparent that, for the final part of drying, the contribution of the first term on the right-hand side is low because of the low evaporation rate, thus the second term is dominant. Equation (2.11.3) can be simplified:

αQIR≈ Utotal(T− Tb), (2.11.4)

and Utotalcan be determined using Equation (2.11.3) by inserting T from the recorded final product temperature (Allanic et al.,2009). The predetermined Utotalis then used for modelling of moisture content and temperature profile. It is emphasised that Equation (2.11.4) only holds at this point.

In addition, a new definition of maximum activation energy (Ev,b) is introduced because the product is not heated only by air so the definition ofEv,bshown by Equation (2.1.7) is not appropriate. The relative activation energy generated from the convective drying run and shown in Equation (2.5.10) is used butEv,bhas been determined from the final product temperature and corresponding humidity of air instead of using drying air temperature. This can be written:

Ev,b= −RT ln(RHb), (2.11.5)

Reaction engineering approach I: L-REA 103

0 1 2 3 4 5 6 7 8

0 500 1000 1500

t(s)

X (kg water/kg dry solid)

2000 2500 3000

Model Data

Figure 2.59 Moisture content profile of convective and infrared drying at an air temperature of 35°C, air velocity of 1 m s⁻¹, air relative humidity of 18% and intensity of infrared drying of 3700 W m⁻².[Reprinted from Chemical Engineering and Processing: Process Intensification, 49, A. Putranto, X.D. Chen and P.A. Webley, Infrared and convective drying of thin layer of polyvinyl alcohol (PVA)/glycerol/water mixture – The reaction engineering approach (REA),

348–357, Copyright (2012), with permission from Elsevier.]

where T is the final product temperature (K) and RHbis the relative humidity at the final product temperature and the absolute humidity. For other drying conditions, as T is not known prior to drying experiments, T can be determined from heat balance between the infrared power input and heat loss to the surroundings as explained previously.

In order to yield the moisture content and temperature profiles, the mass and heat balances shown in Equations (2.1.4) and (2.11.1), respectively are solved simultaneously.

The equations are combined with the relative and equilibrium activation energy indicated in Equations (2.5.10) and (2.11.5), respectively. The results of modelling using the L-REA are validated towards the experimental data of Allanic et al. (2009).

2.11.2 The results of mathematical modelling of infrared-heat drying of a mixture of polymer solutions using the L-REA

The results of modelling are presented inFigures 2.59and2.60. It could be observed that the discrepancies between experimental and calculated data are reasonably small.

Statistical analysis showed that the R² and RMSE of the moisture content profile are 0.994 and 0.181, respectively. Overestimation of the drying rate between drying times of 600–2250 s was also predicted by the previous model (Allanic et al., 2009). The L-REA seems to model this case better and only shows slight overestimation in drying

360

2900 500 1000 1500

t(s)

Temperature (K)

2000 2500 3000

300 310 320 330 340 350

Model Data

Figure 2.60 Product temperature profile of convective and infrared drying at an air temperature of 35°C, air velocity of 1 m s⁻¹, air relative humidity of 18% and intensity of infrared drying of 3700 W m⁻².[Reprinted from Chemical Engineering and Processing: Process Intensification, 49, A. Putranto, X.D. Chen and P.A. Webley, Infrared and convective drying of thin layer of polyvinyl alcohol (PVA)/glycerol/water mixture – The reaction engineering approach (REA),

348–357, Copyright (2012), with permission from Elsevier.]

rates between drying times of 1350–2250 s. In addition, it is apparent that the REA can handle temperature profiles quite well as shown by the R² and RMSE of temperature profile, which are 0.992 and 1.712, respectively. Overestimation in the temperature profile of about 5°C during drying times of 150–1200 s was indicated by the previous model (Allanic et al.,2009). However, this overestimation is not observed by modelling using the L-REA.

It can be observed thatEv/Ev,bderived from convective drying combined with the new quantification ofEv,b shown in Equation (2.11.5) is appropriate for describing the drying kinetics of infrared-heat drying. It may be applied to other infrared-heating cases. In the case of drying, which exhibits product temperature higher than the drying air temperature, application of the modification ofEv,bshown by Equation (2.11.5) in conjunction with the generatedEv/Ev,bis shown to be appropriate.

2.12 The intermittent drying of a mixture of polymer solutions under