Parametric analysis of a heavy metal sorption isotherm based on fractional calculus

Abstract

Heavy metals are widely recognized as being hazardous to human health and environmentally aggressive. The literature reports different approaches for lead removal, for example, water hyacinths. Heavy metal sorption isotherm modeling represents an important tool towards the study of equilibrium conditions. Fractional calculus represents a novel approach and a growing research field for process modeling, based on derivatives of arbitrary order. Recently, a novel isotherm based on fractional calculus was proposed for lead sorption using water hyacinth (Eichhornia crassipes). This paper reports a general procedure on error analysis and its influence on parameter estimation. It was applied to mathematical models based on fractional differential equations, focusing on a heavy metal novel isotherm sorption model. Parameter variance was calculated by using two different approaches (with the complete Hessian matrix and with a simplified Hessian matrix), and joint parameter confidence regions were generated, being successfully able to show that the fractional nature of the model is statistically valid. © 2013 Enrico M. Gomes et al.