Response surface modeling of Pb(II) removal from aqueous solution by Pistacia vera L.: Box-Behnken experimental design

A three factor, three-level Box-Behnken experimental design combining with response surface modeling (RSM) and quadratic programming (QP) was employed for maximizing Pb(II) removal from aqueous solution by Antep pistachio (Pistacia vera L.) shells based on 17 different experimental data obtained in a lab-scale batch study. Three independent variables (initial pH of solution (pH0) ranging from 2.0 to 5.5, initial concentration of Pb(II) ions (C0) ranging from 5 to 50 ppm, and contact time (tC) ranging from 5 to 120 min) were consecutively coded as x1, x2 and x3 at three levels (−1, 0 and 1), and a second-order polynomial regression equation was then derived to predict responses. The significance of independent variables and their interactions were tested by means of the analysis of variance (ANOVA) with 95% confidence limits (α = 0.05). The standardized effects of the independent variables and their interactions on the dependent variable were also investigated by preparing a Pareto chart. The optimum values of the selected variables were obtained by solving the quadratic regression model, as well as by analysing the response surface contour plots. The optimum coded values of three test variables were computed as x1 = 0.125, x2 = 0.707, and x3 = 0.107 by using a LOQO/AMPL optimization algorithm. The experimental conditions at this global point were determined to be pH0 = 3.97, C0 = 43.4 ppm, and tC = 68.7 min, and the corresponding Pb(II) removal efficiency was found to be about 100%.