A reverse approach to evaluate membrane pore size distribution by the bubble gas transport method using fewer experimental data points

Abstract

Membrane technologies have been successfully developed as the separation and purification processes, such as desalination, wastewater treatment, gas separation and so forth. It is known that membrane pore size and pore size distribution (PSD) are the factors by which membrane performance is significantly affected. In this study, a novel mathematical model is presented to evaluate the PSD. Although the new model is based on the bubble gas transport method, it is different from the conventional approach since this model starts from the assumption of a distribution function, typically Gaussian normal distribution, for the PSD, and a flow rate versus pressure line is drawn theoretically based on the assumed PDS. Then, the mean pore size and standard deviation of the PSD are optimized by the best fit of the theoretical line to the experimental one using the nonlinear regression analysis. A unique feature of the proposed model is that fewer experimental data points are necessary to find the optimal PSD. In addition, experiments with the dry membrane are no longer required. The PSDs estimated by this model for three commercial membranes were compared with those obtained by the conventional method, and an excellent agreement was observed.