Modeling Heavy Metal Sorption Kinetics Using Fractional Calculus

Heavy metals are commonly regarded as environmentally aggressive and hazardous to human health. Among the different metals, lead plays an important economic role due to its large use in the automotive industry, being an essential component of batteries. Different approaches have been reported in the literature aimed at lead removal, and among them a very successful one considers the use of water hyacinths for sorption-based operation. The modeling of the metal sorption kinetics is a fundamental step towards in-depth studies and proper separation equipment design and optimization. Fractional calculus represents a novel approach and a growing research field for process modeling, which is based on the successful use of derivatives of arbitrary order. This paper reports the modeling of the kinetics of lead sorption by water hyacinths ( Eichhornia crassipes ) using a fractional calculus. A general procedure on error analysis is also employed to prove the actual fractional nature of the proposed model by the use of parametric variance analysis, which was carried out using two different approaches (with the complete Hessian matrix and with a simplified Hessian matrix). The joint parameter confidence regions were generated, allowing to successfully show the fractional nature of the model and the sorption process.