Quantification of the defect size of ultrafiltration membrane system using mathematical model

• A prediction model was developed to calculate the membrane defect size.
• The measured data goes with similar trend with the prediction model.
• The mathematical model could estimate the defect size as a function of applied pressure and pressure decay rate.

The estimation of the damaged part size could be conducted by using a relationship between the value of pressure decay rate and the size of the damaged part, since pressure decay rate performs as a good indicator for the molar flow of air leakage or diffusion airflow. This study presents the development of a predictive model for estimating the air leakage through a defect and its contribution to pressure decay, and develops a prediction model of the size of membrane damage to evaluate the size of the defect. The results obtained from nitrogen flow rate measurement and pressure decay rate (PDR) allowed for the consistent determination of membrane defect size. The results also indicated that nitrogen flow rate and PDR are relatively dependent on holdup volume and independent on membrane area for a specific membrane under certain margin of applied pressure with the same water temperature. The experimental results demonstrated that the mathematical model could estimate the defect size as a function of applied pressure and pressure decay rate.