Nernst-Planck analysis of reverse-electrodialysis with the thin-composite pore-filling membranes and its upscaling potential

To properly design reverse electrodialysis (RED) stacks, modeling of ion transport and prediction of power generation on the single RED stack are very important. Currently, the Nernst-Planck equation is widely adopted to simulate ion transport through IEMs. However, applying typical Nernst-Planck equation is not proper to analyze ion transport through the heterogeneous thin-composite pore-filling membrane because of the non-conductive site in the membrane matrix. Herein, we firstly introduced modified Nernst-Planck equation by addressing conductive traveling length (CTL) to simulate the ion transport through the thin-composite pore-filling membranes and the performance of a single RED stack with the same membranes. Also, 100 cell-pairs of RED stacks were assembled to validate modified Nernst-Planck equation according to the flow rate and membrane types. Under the OCV condition, the conductivity of the effluents was measured to validate the modified Nernst-Planck equation, and differences between modeling and experiments were less than 1.5 mS/cm. Theoretical OCV and current density were estimated by using modified Nernst-Planck equation. In particular, hydrophobicity on the surface of the heterogeneous membrane was considered to describe ion transport through the pore-filling membranes. Moreover, power generation from RED stacks was calculated according to the flow rate and the number of cell pairs.