Applicability of Sherwood correlations for natural organic matter (NOM) transport in nanofiltration (NF) membranes

A Sherwood correlation (mass transfer correlation) pertinent to natural organic matter–nanofiltration (NOM–NF) systems was established through the determination of the mass transfer coefficient (k) based on a combined film/thermodynamic approach, under laminar flow conditions. In this study, the NOM transport characteristics inside a NF membrane were quantitatively demonstrated through the pore Peclet number (Pe) calculated from experimental data. Transport experiments were performed, using a plate-and-frame crossflow test unit, at various feed flow rates, with a thin-channel type test cell that could be adjusted to different channel heights. The transport experimental results, with Suwannee River NOM (SRNOM), show that the transport of the SRNOM through the NF membrane (denoted as ESNA, MWCO of 200–250) was dominated by diffusion, which was further confirmed by the determined pore Pe (Pe < 1.0). The Sherwood correlation established for the SRNOM and NF membrane under ambient conditions (neither pH nor ionic strength adjustment) exhibited the standard form: Sh = 0.853Re^0.550Sc^0.363. The k values calculated by the correlations (k_Sh) were in good agreement with those determined from the experiments (k_exp). However, significant discrepancy between the k_Sh and k_exp was observed with alterations in the feed water chemistry. The k_Sh value increased with either decreasing pH or increasing ionic strength, as the experimentally determined diffusion coefficient of the SRNOM increased under these condition, whereas, the k_exp exhibited opposite trends, due to the decreased water permeation (or suction) rate, increased NOM transmission and decreased electrostatic repulsion. The k values for other source water NOM (but with the same membrane) were also estimated by the Sherwood correlation coupled with diffusion cell tests. The discrepancy between the k_Sh and k_exp values was less than 20%, and the discrepancy decreased with increased feed flow rate.