Fig. 1. (a) Moisture ratio vs. drying time at different air temperatures for the WS: (?) 313K, (?) 323K, (?) 333K, (?) 343K and (–) 353K; (b) Moisture ratio vs. drying time at different air temperatures for the CS: (?) 313K, (?) 323K, (?) 333K, (?) 343K and (–) 353K.

When drying of the whole seeds (Fig. 1a) and the crushed seeds (Fig.1b) of Jatropha, the moisture evaporation rate was faster at the beginning due to high level of water to be removed, and decreasing as the equilibrium moisture content approached. According to Sandeepa et al. (Sandeepa et al., 2013), in the drying experiment, the decreasing of drying rate from the starting (t = 0) to end of drying indicates the absence of constant drying rate period or presence of constant rate period for an insignificant period of time compared to the total drying time. The rate of drying is higher at the early stage of drying while the moisture content was high and reduces as the moisture content decreases.

The activation energy that is required for the onset of the drying process, namely water activation in the seed (Vo?a et al., 2007), could be determined using the Arrhenius equation. It is the energy barrier that must be overcome in order to activate moisture diffusion (Perea-Flores et al., 2012). The activation energies for the WS and CS of Jatropha were determined from the slopes of the plots of ln(k) versus T?1 for all the tested model. Fig. 2a and b show the plot of ln(k) versus T?1 for WS and CS of Jatropha, respectively at the five drying temperatures when Avhad and Marchetti model (Avhad and Marchetti, 2016) was used. The estimated value for the activation energies and pre-exponential factors for the four studied models are also presented in Table 1. The activation energy value for the whole seeds and crushed seeds of Jatropha varied from 23.67 to 36.06 and 32.88 to 45.75 KJ mol?1, respectively for all mathematical models used. The computed activation energies of WS and CS of Jatropha were in agreement with those reported for other agricultural products such as Sorghum (Resende et al., 2014), grape seeds (Roberts et al., 2008), sliced, and crushed Hass avocado seeds (Avhad and Marchetti, 2016) and castor oil seeds (Perea-Flores et al., 2012).

As it can be observed from Table 1, the activation energy of the CS was greater than that of the WS and this was unexpected as the rate of water evaporation in the crushed seed was faster than that of the WS. In the study of activation energy of water release rate from corn kernel, Vo?a, et al. (Vo?a et al., 2007) found that the drying rate constant k significantly increased with the increasing of drying air temperature, and described activation energy as the energy that needs to be supplied to kernels for initiating the moisture release. The authors concluded that if the activation energy is higher, moisture release from kernels would be slower. In general, high values of activation energy are related to the nature of materials where water is bounded more strongly to the structure and consequently more difficult to be removed it (Bezerra et al., 2015). The present result was in contrary to the finding of Avhad and Marchetti (Avhad and Marchetti, 2016) in which the activation energy of the crushed Hass avocado seeds (24-32 KJ mol?1) was found to be less than that of the sliced (34-36 KJ mol?1) and non-pretreated (43-129 KJ mol?1) seeds.

Fig. 2. (a) Arrhenius plot between ln(k) versus 1/T for the WS of Jatropha using Avhad and Marchetti model: (?) 313K, (?) 323K, (?) 333K, (?) 343K and (–) 353K; (b) Arrhenius plot between ln(k) versus 1/T for the CS of Jatropha: (?) 313K, (?) 323K, (?) 333K, (?) 343K and (–) 353K.

Table 1

Estimated activation energy and pre-exponential factor for the WS and CS of Jatropha

Models WS CS

Ea (KJ mol?1) A Ea (KJ mol?1) A

Lewis 35.5956 3.8372×103 42.333 8.253×104

Henderson and Pabis 36.063 3.891×103 45.753 2.563×105

Page 23.6706 2.8911×104 35.7759 3.468×104

Avhad and Marchetti 33.533 1.0064×104 32.885 1.288×104

Drying curves of the experimental data were fitted with four different mathematical models to select a suitable model for describing the drying process of the WS and CS of Jatropha. Fig. 3a–c and Fig. 4a–c show the comparison of the four drying mathematical models versus experimental data obtained for the WS of Jatropha and the CS of Jatropha, respectively at 313K (the lowest), 333K (medium) and 353 K (the highest) air temperatures of the experiments. As it could be seen from the graphical presentations, all the four models described the drying kinetics of the Jatropha seeds. However, the selection of the model that best fit to the experimental data was based on the values of the statistical parameters R2, X2, RMSE, MBE and MAE, and as it was aforementioned, the selection of best fit is primarily based on the values of R2 (Doymaz, 2010). In the mathematical modelling of castor oil seeds drying kinetics, Perea-Flores et al. (Perea-Flores et al., 2012) accepted the mathematical models with R2 values greater than 0.97 as fit models to the experimental data.

The calculated statistical parameters for the WS and CS of Jatropha for all the four models and the drying air temperatures (313–353K) is presented in Table 2. As it can be seed from Table 2, the values of R2, X2, RMSE, MBE and MAE for the WS of Jatropha for all the drying models and drying temperatures ranged from 0.9278 to 0.9969, 2.37×10-4 and 4.29×10-3, 0.01454 and 0.06427, 1.95×10-3and 2.97×10-2, and 0.01171 and 0.05559, respectively. In the CS of Jatropha, the R2, X2, RMSE, MBE and MAE values changed between 0.9361 and 0.9917, 4.18×10-4 and 4.01×10-3, 0.02039 and 0.06224, 3.64×10-3 and 0.04043, and 0.01639 and 0.05318, respectively.

From the four mathematical models, the Avhad and Marchetti model was found to show best fit to experimental data, with the values of coefficient of determination ranging from 0.9914 to 0.9969 and 0.9908 to 0.9917 for the WS and CS of Jatropha, respectively when analyzing all temperature ranges. In the drying of the WS, the values of R2 for Avhad and Marchetti model were the closest to 1 when compared to that of all other models used. The maximum value of R2 (0.9969) and the smallest values of X2 (2.37×10-4), RMSE (0.01454), MBE (1.95×10-3) and MAE (0.01171) were obtained when the whole seeds were dried at 313K and the Avhad and Marchetti mode (Avhad and Marchetti, 2016) was employed. Moreover, in the drying of crushed seeds of Jatropha, the maximum R2 value (0.9917) was obtained when the seeds were dried at 333K and Avhad and Marchetti model was used. The smallest values of ERMS (0.02039) and MBE (3.64×10-3) for crushed seeds were also found when Avhad and Marchetti model was used.

The Page model was found to have a satisfactory fitting with the experimental data as well. Although the fitness of Page model was comparable to that of Avhad and Marchetti, the latter model was found to be superior to fit to the experimental data. As it could be seen from Table 2, the value of R2 for Avhad and Marchetti model were slightly larger than that of Page model while the X2 and other statistical parameters for Avhad and Marchetti model were found to be smaller compared to that of the Page model.

Fig. 3. Comparison of the experimental and predicted moisture ratios using the four different drying mathematical models at (a) 313K, (b) 333K and (c) 353K for the WS of Jatropha: (?) Experimental data, (?) Lewis model, (?¬) Henderson and Pabis model, (?) Page model and (?) Avhad and Marchetti model.

Fig. 4. Comparison of the experimental and predicted moisture ratios using the four different drying mathematical models at (a) 313K, (b) 333K and (c) 353K for the CS of Jatropha: (?) Experimental data, (?) Lewis model, (?¬) Henderson and Pabis model, (?) Page model and (?) Avhad and Marchetti model.