## 3 Results and Discussion
### Influence of Self-Compaction on the Airflow Resistance
[38], who found a considerable increase in pressure drop \(\Delta P\) due to increase of \(\rho_{b}\) and reduction of \(\varepsilon\) obtained from the application of different filling methods and filling height. The same tendency has been also noted by [PERSON] et al. [64] for rapeseed, [PERSON] et al. [65] for maize and [PERSON] and [PERSON] [66] for rice. However, they used the mean pore volume \(\varepsilon\) for modeling the relationship between \(\Delta P\) and \(v_{a}\) and did not encounter the lateral variation of \(\varepsilon\) caused by self-compaction. Moreover, the results of this study are consistent with the outcomes of [PERSON] [67], who confirmed the effect of non-homogeneous bulk of wheat on the pressure drop per unit of bulk depth due to self-compaction. [PERSON] and [PERSON] [68] reported similar findings for soybeans. Despite consistency with published research, the effect of storage time \(t\) on \(\Delta P\) has not been reported so far. Figure 4: Variation of pore volume \(\varepsilon\) with bulk depth \(H_{b}\) and storage time \(t\). The grey plane indicates the default pore volume \(\epsilon_{0}\). A summary of adjusted pore volumes \(\varepsilon\) and statistical indicators attained from the fitting analysis is given in Table 5. The inspection of the statistical indicators revealed that the [PERSON] and Petersen [31] model was capable of depicting the course of \(\Delta P\) vs. \(v_{a}\) at a decent accuracy. Particularly, \(R^{2}\) between 0.983 and 0.996, \(RMSE\) between 15.18 and 123.77 Pa and \(MAPE\) between 8.21 and 16.16% were observed, respectively. However, a slight overestimation was observed at all predicted curves from 0.06 to 0.09 m\(\cdot\)s\({}^{-1}\). Furthermore, from Table 5 can be discerned an increase in bulk density \(\rho_{b}\) which goes along with the decrease of pore volume \(\varepsilon\). Particularly, a variation of 793.00-822.60 kg\(\cdot\)m\({}^{-3}\), 802.33-830.98 kg\(\cdot\)m\({}^{-3}\), 810.98-938.95 kg\(\cdot\)m\({}^{-3}\) and 825.03-851.65 kg\(\cdot\)m\({}^{-3}\) was observed for the bulk density \(\rho_{b}\) at the bulk depths \(H_{b}\) of 1.0 to 3.4 m and storage times \(t\) of 1, 65, 164, 236 h, respectively. Figure 6a presents the data from pooling all predicted \(\Delta P_{pred}\) and experimental \(\Delta P_{obs}\) from the fitting analysis. It can be seen that the experimental data were satisfactorily anticipated by the model since they fell around the line of \(\Delta P_{pred}=\Delta P_{obs}\), hence showing an appropriate accuracy of prediction of the Matthies and Pettersen model for the employed range of \(v_{a}\), \(H_{b}\) and \(t\) with an \(R^{2}=0.990\), \(RMSE=68.67\) Pa, \(MAPE=12.50\%\). Figure 5: Pressure drop \(\Delta P\) vs. airflow velocity \(v_{a}\) and storage time \(t\) predicted with the Matthies and Petersen model at bulk depths \(H_{b}\) of 1.0, 2.0, 3.0, 3.4 m (**a–d**). The frequency distribution of residuals is shown in Figure 6b. The results indicate that the residuals follow a random distribution. This distribution was found to be unbiased and homoscedastic with non-constant variance, hence a reasonably symmetric and unimodal distribution of residuals around 0 was observed, which supported the validity of the engaged model. The values of residuals ranged from \(-169.24\) to \(233.55\). However, \(55.0\%\) of data fell between \(-34.97\) and \(9.78\). According to the Shapiro-Wilk test, the residuals indicated a significant likelihood of non-normal distribution at \(p\leq 0.05\). Hence, a logistic model was employed to describe the distribution behavior of residuals. Figure 6: **(a)** Predicted pressure drop \(\Delta P_{prd}\) vs. observed pressure drop \(\Delta P_{obs}\) from pooled data of bulk depth \(H_{b}\) of 1.0, 2.0, 3.0, 3.4 m and storage times \(t\) of 1, 65, 164, 236 h; **(b)** Frequency distribution of residuals. Dashed-dotted line indicates the logistic probability distribution of residuals.