Hybrid Response Surface–Particle Swarm Optimisation of Donnan Dialysis Processes for Aluminium Recovery from Water Treatment Sludge

Sustainable recovery of aluminium from water treatment plant sludge (WTPS) offers a promising route for resource valorisation and waste reduction. In this study, Donnan dialysis (DD) is evaluated as a separation technique for recovering aluminium from a synthetic hydroxide-based feed simulating WTPS. A Box–Behnken design coupled with response surface methodology (BBD–RSM) was employed to model and quantify the effects of key operating parameters, namely feed pH, flow rate, initial aluminium concentration, runtime, and sweep solution concentration. Particle Swarm Optimisation (PSO) was integrated with the RSM framework to enhance global optimisation. The PSO approach predicted a maximum aluminium recovery of 99.1% under optimal conditions (pH 4.74, flow rate 98.60%, feed concentration 1313.3 ppm, runtime 21.5 h, and sweep concentration 0.25 M). Experimental validation yielded a recovery efficiency of 90.4%, corresponding to a deviation of 9.2% at a 95% confidence level with R2 = 0.9632 and predicted R2 = 0.9072. The results demonstrate that DD is an effective and scalable approach for recovering aluminium from hydroxide-rich sludge matrices, while PSO provides a robust optimisation strategy to address the nonlinearities inherent in membrane-based separation processes. This hybrid modelling framework advances process optimisation methodologies and supports the development of sustainable sludge-to-resource technologies in water treatment systems.