A simple mathematical analysis on the effect of sand in Cr(VI) reduction using zero valent iron

A simple mathematical model was proposed to analyze the enhancement of Cr(VI) reduction when sand materials are added to the zero valent iron (ZVI). Natural decay of Cr(VI) in a control experiment was analyzed by using a zero-order decay reaction. Adsorption kinetics of Cr(VI) to sand was modeled as a first-order reversible process, and the reduction rate by ZVI was treated as a first-order reaction. Natural decay of Cr(VI) was also included in other experiments, i.e., the adsorption to sand, the reduction by ZVI, and both adsorption and reduction when sand and ZVI are present together. The model parameters were estimated by fitting the solution of each model to the corresponding experimental data. To observe the effect of sand addition to ZVI, both adsorption and reduction rate models were considered simultaneously including the natural decay. The solution of the combined model was fitted to the experimental data to determine the first-order adsorption and reduction rate constants when sand as well as ZVI is present. The first-order reduction rate constant in the presence of sand was about 35 times higher than that with ZVI only.