Prediction of optimum equilibrium and kinetic models for U(VI) sorption onto rice husk: comparison of linear and nonlinear regression methods

Abstract

The use of empirical models in the research is a vital part of the inventions and investigations of civil and environmental engineering organizations. Linear regression is the most commonly used method for optimization and parameter estimation of different equilibrium and kinetic models for sorption. In addition, the usage of this analysis can be extended to a range of nonlinear error functions, subsequently in consent to broader mathematical approach to parameter estimation. The sorption behavior of U(VI) ions from aqueous solution was studied with untreated, treated, and immobilized rice husk by conducting batch-mode sorption experiments. The equilibrium experimental data were fitted to the Freundlich, Langmuir and Redlich–Peterson isotherms by linear and nonlinear regression methods. Kinetic modeling of U(VI) ions removal was also done using linear and nonlinear pseudo-first and second-order rate expressions. In the case of nonlinear regression method, six error functions, namely hybrid fractional error function, Marquardt’s percent standard deviation, average relative error, sum of the errors squared, sum of the absolute errors, and Chi-square test were used to predict the parameters involved in the two- and three-parameter isotherms, and also to predict the optimum isotherm. The results showed that nonlinear method could be a better way to obtain the parameters and get the most suitable fitted model for equilibrium and kinetic studies.