BAYESIAN PARAMETER ESTIMATION FOR SUSTAINABLE MULTICOMPONENT BIOSORPTION USING ALGINATE EXTRACTION RESIDUE FROM Sargassum filipendula

Alginate extraction residue from the brown seaweed Sargassum filipendula is a promising low-cost biosorbent for removing toxic metals from aqueous streams while supporting biomass valorization and circular-economy practices. This study applied Bayesian inference to estimate mass-transfer coefficients and quantify their uncertainty during the competitive biosorption of Cu(II), Ni(II), and Zn(II) in a fixed-bed column. The analysis used previously published breakthrough data and the corresponding phenomenological model for four ternary feed compositions (Cu-Ni-Zn: 1.00-1.00-1.00, 0.50-0.50-0.50, 0.65-0.65-0.80, and 0.80-0.35-0.65 mmol L⁻¹). Experiments were conducted at pH 4 and 25 °C with a flow rate of 3 mL min⁻¹, a bed height of 12 cm, and 2 g of biosorbent. Competitive equilibrium was described by the multicomponent Langmuir isotherm, and the dynamic model was solved numerically using the Method of Lines. Sensitivity analysis showed low correlations among the mass-transfer coefficients (0.332-0.400), supporting their simultaneous estimation. Bayesian estimation employed the Metropolis-Hastings Markov chain Monte Carlo algorithm with 10,000 states and an average acceptance rate of approximately 30%. Predictions based on posterior mean values satisfactorily reproduced the experimental breakthrough curves and the competitive behavior of the metal ions. The model described the overshoot of Ni(II) and Zn(II) under most conditions, although it underestimated the experimental overshoot for the 0.80-0.35-0.65 mmol L⁻¹ feed. For the equimolar 1.00-1.00-1.00 mmol L⁻¹ condition, the posterior mean mass-transfer coefficients were 1.76, 1.51, and 1.54 min⁻¹ for Cu(II), Ni(II), and Zn(II), respectively, with 95% credible intervals of 1.45-2.06, 1.23-1.80, and 1.23-1.84 min⁻¹. Across all conditions, previously reported reference coefficients fell within the corresponding 95% credible intervals, confirming consistency with the deterministic estimates. By explicitly quantifying parameter uncertainty, the Bayesian framework provides a more reliable basis for simulation, optimization, and scale-up of sustainable fixed-bed remediation systems.