## 4 Discussion
### Comparison of the Steady-State Method and the Discharge Method  
Figure 12 compares the steady-state results and the calculated results with the determined coefficients by the discharge method. The calculated curves agree with the steady-state data points on the whole, indicating that the discharge method works well for obtaining the property coefficients. To evaluate the discharge method, the accuracies of the method are calculated and compared with that of the steady-state method, which was proven viable in a previous work [28]. The error \(E\) is expressed as  
\[E=\sqrt{\frac{\sum\left(G_{(\exp)i}-G_{(\text{ca})i}\right)^{2}}{\sum G_{(\exp) i}^{2}}}\times 100\%, \tag{11}\]  
where \(G_{(\exp)i}\) is for the steady-state flow rate, and \(G_{(\text{ca})i}\) is for the calculated flow rate. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Porous Medium**} & \multicolumn{2}{c}{**Group 1**} & \multicolumn{2}{c}{**Group 2**} & \multicolumn{2}{c}{**Group 3**} \\ \cline{2-7}  & \(K\) **(10\({}^{-12}\) m\({}^{2}\))** & \(\beta\) & \(K\) **(10\({}^{-12}\) m\({}^{2}\))** & \(\beta\) & \(K\) **(10\({}^{-12}\) m\({}^{2}\))** & \(\beta\) \\ \hline
7 mm & 1.96 & 0.411 & 3.71 & 0.562 & 5.03 & 0.468 \\
8 mm & 1.97 & 0.467 & 3.68 & 0.641 & 4.91 & 0.537 \\
9 mm & 2.12 & 0.509 & 3.63 & 0.658 & 4.98 & 0.582 \\
10 mm & 1.98 & 0.467 & 3.66 & 0.621 & 4.95 & 0.562 \\
11 mm & 2.08 & 0.574 & 3.54 & 0.739 & 5.01 & 0.621 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of fitting coefficients \(K\) and \(\beta\) by the discharge method. Figure 11: Permeability obtained by the discharge method in different pressure subsections for the five porous media of group 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Porous Medium**} & \multicolumn{2}{c}{**Group 1**} & \multicolumn{2}{c}{**Group 2**} & \multicolumn{2}{c}{**Group 3**} \\ \cline{2-7}  & \(K\) **(10\({}^{-12}\) m\({}^{2}\))** & \(\beta\) & \(K\) **(10\({}^{-12}\) m\({}^{2}\))** & \(\beta\) & \(K\) **(10\({}^{-12}\) m\({}^{2}\))** & \(\beta\) \\ \hline
7 mm & 2.15 & 0.512 & 3.73 & 0.522 & 5.02 & 0.608 \\
8 mm & 2.02 & 0.515 & 3.64 & 0.585 & 4.99 & 0.617 \\
9 mm & 2.02 & 0.486 & 3.65 & 0.613 & 4.86 & 0.588 \\
10 mm & 2.048 & 0.467 & 3.68 & 0.578 & 5.05 & 0.598 \\
11 mm & 2.095 & 0.491 & 3.55 & 0.623 & 4.93 & 0.615 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Permeability and inertia coefficients of the porous media by the steady-state method. The results in Table 5 show that the calculated results can achieve an accuracy within 3%. However, referring to one of the previous works of the authors, the calculated results with the property coefficients determined by the steady-state method can achieve an accuracy within 1% in the Forchheimer flow region. This is probably because the flow rate in the current work is obtained by differentiating the measured pressure with respect to time, and this treatment would magnify the noise and deteriorate the measuring accuracy. Taking one of the previous works by [PERSON] et al. as another example, the sonic conductance \(C\) determined by the discharge method following the ISO 6358 equation can achieve an accuracy within 2% while the permeability in the current work is 5-10%. Despite a larger deviation in the coefficients, the accuracy of the theoretical flow rate over the entire range is sufficient for most applications. The key point of the discharge method is that the isothermal chamber must remain isothermal during the measuring process. If the selected chamber has a very small volume, the isothermal condition cannot be maintained due to the rapidly changing pressure. Previous research [32] implies that the temperature variation can be limited within 3K when the pressure change is less than 100 kPa/s. That is, for group 2, the lower limit volumes for 7-11 mm samples are 0.28 L, 0.34 L, 0.43 L, 0.48 L and 0.62 L, respectively.