## 4 Results and Discussion
### Discussion  
From the model simulation and experimental verification, it was found that the pressure decay could be simulated by the model based on the microdefect bubble dynamic behavior, although there were some differences due to the selection parameters. These results prove that the pressure decay test process, which involves gas entering the wet microdefects and balancing the resistance, bubble formation and detachment, and then gas chamber pressure decay, is in essence a bubble dynamic process. The bubble dynamic behavior of microdefects on the membrane can therefore be used to analyze pressure decay characteristics in a membrane integrity test. The results show that the PDR decreases with time in the duration of the pressure decay test and changes due to the defect size, applied test pressure, and pressurized system volume.  
It is worth emphasizing that the model was developed on the basis of model assumptions and simulated under the present laboratory conditions. The model ignores the effects of thermodynamic parameters and the diffusion of membrane pores, and it has not been validated by engineering application. In the simulation experiments, the small defects (5-10 \(\upmu\)m) created by laser drilling in  
Figure 9: The correlation coefficients between parameters and the back-calculated diameter resolution (BDR).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Conditions**} & \(\mathbf{d_{eq}}\) & \begin{tabular}{c} **Percentage** \\ **Error** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Size-Modified** \\ **Coefficient** \\ **\(\upalpha\)** \\ \end{tabular} \\ \hline \(P_{g}=80\) kPa & \begin{tabular}{c} \(D_{0}=0.185\) mm \\ \(D_{0}=0.189\) mm \\ \(D_{0}=0.189\) mm \\ \(D_{0}=0.276\) mm \\ \end{tabular} & 0.165 & 10.81 & 1.15 \\ \(V_{g}=365.59\) mL & \
\begin{tabular}{c} \(D_{0}=0.189\) mm \\ \(D_{0}=0.276\) mm \\ \end{tabular} & 0.187 & 1.06 & 1.06 \\ \(H=30\) mm &
\begin{tabular}{c} \(D_{0}=0.276\) mm \\ \(D_{0}=0.352\) mm \\ \end{tabular} & 0.264 & 4.34 & 1.08 \\ \hline \multirow{4}{*}{\(V_{g}=365.59\) mL \(H=30\) mm} & \(P_{g}=40\) kPa, \(D_{0}=0.346\) mm & 0.388 & 12.14 & 0.90 \\  & \(P_{g}=60\) kPa, \(D_{0}=0.358\) mm & 0.376 & 5.03 & 0.98 \\ \(P_{g}=80\) kPa, \(D_{0}=0.352\) mm & 0.348 & 1.14 & 1.04 \\  & \(P_{g}=100\) kPa, \(D_{0}=0.345\) mm & 0.328 & 4.93 & 1.06 \\  & \(P_{g}=120\) kPa, \(D_{0}=0.350\) mm & 0.324 & 7.43 & 1.10 \\ \hline \(D_{0}=0.35\) mm & \(V_{g}=365.59\) mL & 0.348 & 1.14 & 1.04 \\ \(P_{g}=80\) kPa & \(V_{g}=690.72\) mL & 0.355 & 7.90 & 0.95 \\ \(H=30\) mm & \(V_{g}=1015.18\) mL & 0.361 & 5.86 & 0.97 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The back-calculated defect diameter and size-modified coefficient.  
the center of the membrane discs were too small to measure the actual equivalent diameter of the defect size under experimental conditions (the membrane was in the vessel and under water) using a Caikon DMM-400D metallurgical microscope, so the defects were made by different kinds of needles. In addition, the above experimental data was obtained using a flat membrane in a small vessel, so the model needs to be calibrated on lots of full-scale membrane modules. Subsequent model validation works should focus on other kinds of membrane modules and the engineering application aspect.