Optimal design of experiments for parameter identification in electrodialysis models

The Nernst-Planck approach, previously used to model the electrodialytic recovery of uni-, di or tri-valent electrolytes, was used to accomplish the desalination of concentrated brines with an initial NaCl concentration up to 4.6 kmol m−3. The complexity of the proposed model is such that an extensive experimentation is required for a statistically sound estimation of the relevant model parameters, including solute (tB) and water (tW) transport numbers through the ion-selective membranes; solute (LB) and water (LW) transport rate by diffusion; average electro-membrane resistance (R). A model-based design of experiments (MBDoE) approach is proposed in this paper to minimise the number of trials and resources required for model identification. The use of this approach in an experimental case study allowed for a dramatic reduction of the experimentation time from 1080 min (corresponding to a classical experimentation with multiple batch desalination trials) to 30-60 min corresponding to a single optimal batch desalination experiment. The results obtained show the potential of MBDoE for quick development and assessment of electrodialysis models, where highly predictive capability can be achieved with the minimum experimental time and waste of resources.