LAUSR

Batch kinetic experiments were performed for the sorption of nickel ions onto nanobentonite. The kinetic data were adjusted with pseudo-first-order and pseudo-second-order kinetics by linear and nonlinear regressions in addition to some fixed suggested fractional orders $$1/2 \le n \le 5/2$$1/2≤n≤5/2. The removal process was found to be well explained by nonlinear pseudo-second-order kinetic expression with 0.5222 mg $$\hbox {g}^{-1}$$g-1 standard deviation, whereas linear regression is improper method for obtaining the kinetic parameters of the studied models specially at lower order values. The kinetic rate constants were increased with the value of the prefixed reaction pseudo-order giving optimal pseudo-average order equal to 3.522 with standard deviation 0.0815 mg $$\text {g}^{-1}$$g-1. This optimal value is estimated at infinite time which is physically become closer to the reality of the studied system. Nevertheless, the theoretical removal capacity (22.95 mg $$\text {g}^{-1})$$g-1) calculated by optimal order value is greater than the experimental one (19.15 mg $$\text {g}^{-1})$$g-1). This behavior can be attributed to the rapidity of the process to reach the equilibrium state.