Error function analysis in nonlinear parameter estimation method for kinetic and equilibrium sorption models

A robust method for parameter estimation is required in determining the governing model in kinetic and equilibrium sorption modeling. In nonlinear method, parameters are estimated using a trial and error procedure to minimize an error function. In this study the effect of different error functions on estimated parameters of kinetic models (Pseudo First and second order) and equilibrium models (Langmuir and Freundlich) were examined. Best error function was determined using 239 series of kinetic data and 129 series of equilibrium data which are extracted from 100 previous studies. Using various error functions shows a lot of changes in estimated parameters, so that the largest changes for parameters is about 100%. using normalized error method based on experimental data, best error functions respectively are Errsq, Hybrd and Mpsd with average normal error of 3 and 3.4 and 3.6. Ef and Crm methods have the maximum normalized error according to the experimental data.