Strategy of screening and optimization of process parameters using experimental design: application to amoxicillin elimination by adsorption on activated carbon

• Pedicels dates can be converted to an efficient activated carbon.
• Seven factors of adsorption process are studied in one step by applying fractional factor design.
• Fractional factorial design and response surface methodology are combined to select the process parameters and the modeling.
• Optimal conditions were determined directly from the regression model, and were validated using statistical criterions.

A fractional factorial design (FFD) 27 − 3 was used as screening technique to verify the influence of the seven factors on the response variable (yield of Amoxicillin elimination: ye) by adsorption on activated carbon prepared from pedicels of dates. Factors studied are the impregnation ratio (r = 1.0–2.0), carbonization temperature (Tc = 300–500 °C), carbonization time (tc = 1.5–2.5 h), stirring rate (v = 200–400 rpm), dose of activated carbon ([AC] = 1–2 g·L− 1), pollutant concentration ([AMX] = 50–100 mg·L− 1), and medium temperature (T = 25–35 °C). As a result of FFD evaluation, the main influent factors are the Tc, [AC], [AMX] and T. The fitted quadratic regression model, including these parameters was developed using the central composite design (CCD) as the response surface methodology. Analysis of variance (ANOVA) of the preliminary fitted model was validated with a confidence level of > 95%. The final model is established on the basis of additional statistical analysis using other statistical criteria (coefficient of variation, adequate precision, Mallow's Cp statistic), the convenient results obtained, ensuring a satisfactory quadratic regression model, including all main parameters and their quadratic terms. Optimal conditions were determined using an analytic method, stationary point of model was determined, and the determinant values of Hessian matrix showed that the response (yield of AMX elimination) agrees a maximum solution corresponding to optimal conditions, Tc = 488 °C, T = 33.6 °C, [AMX] = 58.5 mg·L-1 and [AC] 1.178 g·L-1, at which the predictive value of the response is ye = 100 ± 3%.