New modelling approach for nitrogen transfer and water passage in gas-permeable membranes for wastewater treatment

Gas-permeable membranes (GPM) have emerged as a promising technology for recovering total ammoniacal nitrogen (TAN) from wastewater. However, simultaneous transport of ammonia and water across hydrophobic membranes dilute the trapping solution and reduces its value. Additionally, water transport hinders nitrogen transfer analysis, which is used to assess membrane performance. Existing modelling approaches often rely on osmotic pressure estimates or assume constant volumes, which limits their applicability when treating real wastewaters. This study presents a new modelling approach to describe the coupled transport of ammonia and water across GPM using only experimentally measurable variables such as TAN concentration and solution volume. A key feature of this model is its capacity to capture dilution effects caused by water flux and accurately estimate TAN diffusion without requiring chemical speciation data. Laboratory experiments with synthetic and waste-derived effluents, including anaerobic digestion supernatant, acidogenic fermentation liquid, and industrial wastewater accurately reproduced TAN concentration over time. For synthetic wastewater, the mean ammonia permeability was 1.26·10^-6 m/s, while waste effluents showed broader values from 0.58·10^-6 to 1.83·10^-6 m/s due to matrix component interactions. This narrow distribution confirms the robustness of the model, as permeability is a membrane-intrinsic parameter. Water transport significantly increased trapping solution volume, up to 149% in synthetic media and 292% in high-strength effluents, increasing with the osmotic pressure gradient between solutions. The proposed model provides a practical tool to obtain membrane-intrinsic ammonia permeability and to model TAN recovery in GPM treating real effluents, helping to bridge the gap between theoretical transport models and experimental applications.