A storage-state-based reduced-order electrochemical model for cyclic adsorption-desorption dynamics in membrane capacitive deionization

초록

Membrane capacitive deionization (MCDI) inherently operates through repeated short-term adsorption-desorption switching cycles, making cyclic state evolution, residual storage memory, and carry-over behavior essential characteristics of the process. However, existing MCDI models often struggle to simultaneously preserve cyclic state continuity, electrochemical interpretability, and computational tractability during long-horizon operation. In this study, a storage-state-based reduced-order electrochemical model was developed to describe cyclic adsorption-desorption dynamics through continuous evolution of internal electrochemical storage states. The model combines a modified-Donnan-informed storage-state formulation with four-zone hydraulic transport, current-limited state transfer, residual storage memory, and excess storage relaxation without separate adsorption/desorption fitting. Continuous non-reset simulations were performed over 12,000 s under five initial feed EC conditions ranging from approximately 223 to 4000 mu S cm(-1). The proposed model reproduced cyclic carry-over behavior, adsorption-desorption continuity, and post-switch desorption peak evolution across the tested initial EC range. Quantitatively, the model achieved a mean all-window weighted absolute percentage error (WAPE) of 13.10%, mean desorption WAPE of 12.04%, mean Nash-Sutcliffe efficiency (NSE) of 0.942 for normalized C/C0 dynamics, and mean Kling-Gupta efficiency (KGE) of 0.889. These results indicate that key cyclic MCDI dynamics can be captured using an interpretable and computationally tractable electrochemical backbone model, supporting continuous-state simulation and long-horizon analysis of cyclic MCDI operation.