Modeling sorption kinetics in environmental separations: Advancing beyond traditional pseudo-order approaches

Accurate kinetic modeling is essential for elucidating sorption mechanisms and optimizing pollutant removal; however, the traditional pseudo-first-order (PFO) and pseudo-second-order (PSO) models are often misapplied due to linearization artifacts and limited statistical validation. This study establishes a comprehensive, statistically rigorous framework that integrates nonlinear least-squares regression, multi-criteria error analysis, information-theoretic model selection, and jackknife resampling for uncertainty quantification in kinetic parameters. Eight models—PFO, PSO, pseudo-mixed-order fractional (PMOF), mixed 1,2-order (MOM), Ritchie second-order (RSO), Elovich, Bangham, and intraparticle diffusion (IPD)—were evaluated across 40 sorbent–sorbate systems involving heavy metals, precious metals, radionuclides, dyes, and pharmaceuticals. Quantitatively, the PMOF model yielded the lowest mean average relative error ( ARE ≈ 2.1 %), Marquardt's percent standard deviation ( MPSD ≈ 4.2 %), and Akaike Information Criterion ( AIC = 4.5–22), outperforming PSO ( ARE ≈ 3.4 %, MPSD ≈ 6.5 %) and PFO ( ARE ≈ 6.8 %, MPSD ≈ 11.8 %). Multi-criteria ranking confirmed the order PMOF > RSO > PSO > MOM ≈ Elovich > Bangham > IPD > PFO. Jackknife resampling, introduced here for the first time in sorption kinetics, revealed that datasets with fewer than eight points increased parameter uncertainty by >25 %, whereas dense early-time sampling reduced deviation to <5 %. These findings demonstrate that the PMOF model bridges diffusion- and surface-reaction-controlled regimes via a fractional constant, offering a reliable and interpretable framework for kinetic analysis in environmental separation processes. Finally, a user-friendly Excel-based nonlinear fitting tool was developed to automate model fitting and statistical evaluation. • New framework integrates nonlinear fitting and advanced sorption kinetics analysis. • Pseudo-mixed order fractional model outperforms traditional kinetic approaches • Jackknife method enhances parameter uncertainty and sensitivity assessment. • Multi-criteria validation strengthens kinetic model reliability.