Maximizing Adsorption Involving Three Solutes on Enhanced Adsorbents Using the Mixture-Process Variable Design

Unmodified (UN), acid-treated (AT) and microwave-acid-treated (MAT) activated carbons were optimized for their solute removal efficacies by adjusting feed mixture compositions and process conditions. Acetaminophen, benzotriazole, and caffeine were used either individually or as binary/ternary mixtures in this study. The process conditions considered were the pH, adsorbent dosage, and type of adsorbent. Experimental responses such as total adsorbent loading ( q total ) and total percentage removal (PR total ) were fitted with empirical models that had high adjusted R 2 (>0.95), insignificant lack of fit ( p -value > 0.22), and high model predictive R 2 (>0.93). Mixture compositions of the feed were found to interact significantly not only among themselves but with process variables as well. Hence, adsorption optimization must simultaneously consider mixture as well as process variables. The conventional response surface methodology for mixtures, termed as ridge analysis, optimizes mixture compositions at specified values of process variables. An improved steepest ascent method which considers mixture and process variables simultaneously was developed in this work. This could track the path of steepest ascent toward globally optimal settings, from any arbitrary starting point within the design space. For the chosen adsorbent, optimal settings for feed mixture compositions and pH were found to change along this steepest ascent path. The feed compositions, pH, and adsorbent dosage identified for maximum adsorbent utilization were usually quite different from those identified for maximum total percentage removal. When both these objectives were optimized together, the most favorable compromise solutions for q total and PR total were, respectively, 264.1 mg/g and 43.4% for UN, 294.9 mg/g and 52.5% for AT, and 336.6 mg/g and 55.9% for MAT.