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

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. © 2015 Elsevier B.V. All rights reserved.

-1 Fig. 9. The predicted PDR versus the measured PDR for comprised membrane B with one and two controlled defects. and adiabatic constant, will be known factors, so the membrane defect size would be calculated using the following equation: r breach vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u  1 u κ u V Á PDR Á p1 p2 u vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ δ3 Á u " u  κ−1 # u u 2κ κ p u t tπ Á p1 Á RT 1− 2 κ−1 p1 ð23Þ where rbreach is the equivalent size of the defect, δ3 is the size modified coefficient which needs lots of experiments to collect and determine for membrane modules. 4.5. Feasibility of application of prediction model In practical projects, the number of defects would be more than one and could not be decided in advance. In Eq. (23), rbreach is the equivalent size of the defect, showing the equivalent area of all the defects. Of course, if there are more than one defect on the membrane surface, the airflow would be discharge along porous pipe from these defects, so the flow rate would be different with that with only one defect. Here, the equation just presents the airflow dynamics from the equivalent leakage area, neglecting the effect of defect number and defect position. In theory, the defect would be flexible due to the elastic properties of ultrafiltration membrane, so the hold-up volume V and the defect size rbranch would change with the applied test pressure. The PDR should not be consistent, but variable in the PDT test process of dynamic change. In order to understand the effect of membrane deformation properties on the change of defect size, the defect size was measured using a Caikon DMM-400D metallurgical microscope without liquid phase at applied pressure of 0, 0.04, 0.08, 0.12 and 0.16 MPa. The image treatment is performed using the image processing software Image-J and the defect area is measured. Nevertheless, Fig. 11 shows that the equivalent defect does not expand obviously with an increase in applied pressure, so it is difficult to say with certainty that the defect size changed too much with the applied pressure at a certain range. In addition, the applied test pressure and the duration are often kept in a certain range in real projects, the PDR would keep in a limited scope (as descried in Section 4.3), so the effect of membrane deformation properties on defect size would be neglected. Of course, the used membrane in this experiment was made of modified PVC, its elastic properties are limited by the manufacturing processes. To describe the dynamic process of PDT at a flexible defect, it is necessary to characterize many kinds of membrane in terms of wetting critical surface tension, This study developed a prediction model of the membrane defect size with easily measurable components from a membrane integrity test using pressure decay test. Results from the comparison between predicted model and measured data with membrane A provided the basis for the demonstration of the feasibility. The measured data about nitrogen flow rate through controlled defects and PDR goes well with the similar trend with prediction model. Using the measured nitrogen flow rate and PDR, one can then determine the equivalent defect size with an acceptable degree of accuracy under certain applicative scope of applied pressures. For a certain membrane integrity test system, the parameters such as the hold-up volume, PDR, applied test pressure, downstream pressure, universal gas constant, temperature and adiabatic constant, will be known factors, so the membrane defect size would be calculated using deduced equation. By this method, the degree of membrane defect could be estimated in membrane filtration system. Of course, this paper was just based on the experiments with the variable of applied pressures, not including other variables like holdup volume, downstream pressure, universal gas constant, and temperature. The prediction model needs to be calibrated on lots of full-scale membrane modules to identify the size modified coefficient. Further work is underway to determine the true effect of water temperature and elastic properties of different membrane materials on the flow rate and PDR. In addition, since pressure decay test is always implemented under the condition of fully-submerged membrane system, future work should focus on the effect of submergence on the flow rate and PDR. Then the user-friendly model might be used as an automatic tool for defining an optimized membrane repairing schedule.