Forward Osmosis: Mass Transmission Coefficient–Based Models for Evaluation of Concentration Polarization under Different Conditions

In the past, forward osmosis (FO) models were developed to evaluate the effects of concentration polarization (CP), including external CP (ECP) and internal CP (ICP), on FO performance. However, these models are not clear about the reverse salt flux of FO membranes because they often assume the osmosis reflection coefficient $\sigma$ to be 1. In addition, these models need some empirical parameters that are difficult to obtain via experiments. In this study, a new set of FO models was developed, for the first time, on the basis of mass transmission coefficient (${\eta }_{\mathrm{MT}}$) and $\sigma$. These models were used to evaluate the impact of ECP and ICP on FO performance under the influence of different parameters and conditions. Data from previous studies were used to verify the models based on experimental and model-calculated ${\eta }_{\mathrm{MT}}$. Sensitivity analysis was conducted for these models to find the most sensitive parameters to ECP, ICP, ${\eta }_{\mathrm{MT}}$, and FO water flux ${\mathit{J}}_{\mathit{v}}$. Results indicate that $\sigma$ is the most relatively influential parameter to concentrative ECP or concentrative ICP, revealing the FO membrane’s reverse salt flux. The models developed can be used to analyze how ECP, ICP, and ${\eta }_{\mathrm{MT}}$ change under different FO systems and experimental conditions, including FO reactor configuration, mixing intensity, water velocity, FO membranes, and draw-solution concentration.