Predicting reverse electrodialysis performance in the presence of divalent ions for renewable energy generation

Reverse electrodialysis (RED) is an electro-membrane process to harvest renewable energy from salinity gradients. RED process models have been developed in the past, but they mostly assume that only NaCl is present in the feedwaters, which results in unrealistically high predictions. In the present work, an existing simple model is extended to accommodate the presence of magnesium ions and sulfate in the feedwaters, and potentially even more complex mixtures. All power loss mechanisms deriving from the presence of multivalent ions are included in the new model: increased membrane electrical resistance, uphill transport of multivalent ions from the river to the seawater compartment, and membrane permselectivity loss. This new model is validated with experimental and literature data of membrane electrical resistance (at 10 mol. % MgCl₂ for the CEMs and 25 mol. % Na₂SO₄ for the AEMs), RED stack performance (up to 50 mol. % MgCl₂ or Na₂SO₄ in the feedwaters), and ion transport (at 10 mol. % MgCl₂ or Na₂SO₄ in the feedwaters) showing very good agreement between model predictions and experimental data. Finally, we showed that the developed model not only describes experimental data but can also predict RED performances under a variety of conditions and cross-flow configurations (single-stage with and without electrode segmentation, multi-stage in co-current and counter-current mode) and feedwater compositions (only NaCl, with Na₂SO₄, with MgCl₂, and with MgSO₄). It thus provides a very valuable tool to design and evaluate RED process systems.