Estimation of Langmuir Adsorption Isotherm Parameters Using Nonlinear Optimization Method

Accurate parameter estimation of non-linear mathematical models is one of the most important calculations in science and engineering. Different methods based on linearization or optimization are applied to find the parameters of the equations. In this article, a new method for parameter estimation in Langmuir adsorption isotherm has been developed. In this method, the structure of the mentioned equation was investigated similarly to the linear curve fitting method and a nonlinear single variable optimization problem was obtained. Results of Methylene blue adsorption by bentonite were used as experimental data sets and the method was compared with other linearization methods. This comparison was based on three statistical methods including Coefficient of determination, Root means square error and Normalized standard deviation, and the Langmuir isotherm parameters were considered. Compared to the linearization nature that makes errorsin mathematical calculations, the proposed nonlinear method provides better results and can be used in other similar equations.