Multiple linear regression in adsorption capacity prediction: Application in plastic waste pyrolysis oil purification

Effectively removing heteroatom impurities from pyrolysis oil derived from waste plastic is essential for its use in petrochemical production. Adsorption is a cost-effective purification method; however, most studies that conduct adsorption experiments overlook variations in pyrolysis oil composition resulting from differences in plastic waste feedstocks and operating conditions within the pyrolysis reactor. To address this, we propose treating the adsorption system as a ternary system in which heteroatoms, pyrolysis oil composition, and activated carbon properties vary. Considering adsorption experiments across multiple ternary systems, statistical tools such as correlation matrix analysis and experimental design are applied to develop a predictive model based on multiple regression to describe the ternary system with four significant descriptors: Hansen solubility parameter distance (DHSP), heteroatom molecular weight (MW_heteroatom), activated carbon microporous surface area (S_micro), and activated carbon surface pH. Among the seven tested multiple regression models, the Quad-SQ model, a quadratic model with square root transformation, provides the best predictive performance (R_adjust² = 0.916, Q² = 0.712, TIC = 0.30). Our findings reveal that polar contaminants (e.g., benzoic acid and phenol) combined with saturated pyrolysis oil enhance adsorption capacity. However, this positive effect diminishes when paired with more basic activated carbon. In contrast, apolar contaminants, such as chlorobenzene, benefit more from neutral-surface activated carbon.