Combination of Two Experimental Designs to Optimize the Dimethylphthalate Elimination on Activated Carbon Elaborated from Arundo donax

This work aims to apply a combination of fractional factorial design (FFD) and Doehlert design to determine the operational conditions allowing to study the adsorption process applied for dimethylphthalate (DMP) elimination from aqueous solution. The Arundo donax stems plant are used to prepare various activated carbons. The investigated parameters and their levels are impregnation rate (r=2-4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r = 2{-}4$$\end{document}), activating agent concentration (Cact=30-50%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{{\mathrm{act}}} = 30{-}50\%$$\end{document}), activation time (tact\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${t}_{{\mathrm{act}}}$$\end{document} = 2-4h), carbonization temperature (Tcarb=300-500∘C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{\mathrm{carb}} = 300{-}500\,{^{\circ }}\hbox {C}$$\end{document}), mixture temperature (T=25-35∘C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T = 25{-}35\,{^{\circ }}\hbox {C}$$\end{document}), DMP concentration (C0=50-100mgL-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{0}= 50{-}100\,\hbox {mg}\,\hbox {L}^{-1})$$\end{document}, carbonization time (tcarb=1-2h\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${t}_{{\mathrm{carb}}} = 1{-}2\,\hbox {h}$$\end{document}), stirring speed (v=200-400rpm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v = 200{-}400\,\hbox {rpm}$$\end{document}) and activated carbon dose (mad=0.1-0.2gL-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${m}_{\mathrm{ad}} = 0.1{-}0.2\,\hbox {g}\,\hbox {L}^{-1})$$\end{document}. The FFD is applied for parameters screening. Two responses are defined: the activated carbon production yield (Yp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y_\mathrm{p}$$\end{document}) and DMP elimination yield (Ye\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y_\mathrm{e}$$\end{document}). When both responses are taken into account, according to the p value, the significant factors are (mad\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\mathrm{ad}$$\end{document}), (Tcarb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_\mathrm{carb}$$\end{document}), (Cact\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_\mathrm{act}$$\end{document}) with a value < 0.0001, and (tcarb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_\mathrm{carb}$$\end{document}) with a value of 0.0018. These parameters are considered in optimization process. To choose the most appropriate mathematical model, Mallows criterion, corrected Akaike information criterion, Bayesian information criterion, Amemiya Prediction Criterion and ANOVA are applied. This model presents a saddle point, so the optimal conditions are identified at the study field limits for each parameter, so the optimal values are mad=0.100±10-3gL-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${m}_\mathrm{ad} = 0.100 \pm 10^{-3}\,\hbox {g}\,\hbox {L}^{-1}$$\end{document}, Tcarb=357±5∘C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_\mathrm{carb} = 357 \pm 5\, {^{\circ }}\hbox {C}$$\end{document}; Cact=47±5%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_\mathrm{act} = 47 \pm 5\%$$\end{document}; tcar=0.209±0.083h\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {tcar} = 0.209 \pm \,0.083\,\hbox {h}$$\end{document}. Under these conditions, the removal efficiency exceeds 97±3%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$97 \pm 3\%$$\end{document} and the BET surface area of activated carbon optimal is 1315m2g-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1315\,\hbox {m}^{2}\,\hbox {g}^{-1}$$\end{document}.