Statistical optimization, Bayesian Information Criterion (BIC) guided kinetics, and nonlinear isotherm modeling for heavy metal removal using a magnetic Spirulina‑banana peel biosorbent

This study presents the initial statistically guided optimization of a magnetic Spirulina-banana peel biosorbent (SP/MBP) utilizing Box–Behnken response surface methodology (RSM) in conjunction with Bayesian Information Criterion (BIC)-based kinetic model selection, a methodological innovation seldom employed in biosorption of Pb (II), Cu (II), and Cr (III) ions from aqueous solutions. RSM framework was optimised using three independent variables: initial metal ion concentration (50–150 mg/L), SP/MBP dosage (1–10 g/L), and contact time (30–120 min). Quadratic models were confirmed by analysis of variance (ANOVA), with high coefficients of determination (R 2 > 0.96) and adequate precision (> 15). Under optimal conditions (134.9 mg/L, 10 g/L, 120 min), removal efficiencies reached 92.91% for Cu (II), 88.70% for Pb (II), and 91.73% for Cr (III). In contrast to traditional batch studies that depend only on R 2 comparisons, BIC meticulously differentiates between pseudo-first order and pseudo-second order kinetics (ΔBIC: Cr = 16.6, Pb = 7.5, Cu = 3.0), indicating that Pb (II) and Cr (III) adsorption adheres to physisorption (PFO), but Cu (II) conforms to chemisorption (PSO). The nonlinear Freundlich isotherm accurately characterized the equilibrium data (R 2 > 0.997), indicating heterogeneous surface adsorption. The statistically validated models establish a solid foundation for the scalability of SP/MBP in continuous-flow magnetic separation systems, connecting batch optimization with practical wastewater treatment.