Statistical Evaluation of Non-Linear Parameter Estimation Procedures for Adsorption Equilibrium Models

Adsorption equilibrium is a fundamental concept in the adsorption science and relates the equilibrium between the quantity of the adsorbed material and its concentration in the bulk phase. Several models have been proposed for prediction of adsorption equilibrium and all models depend on parameters whose values must be estimated from available experimental data. Although linear parameter estimation procedures can be used for model fitting, through transformation of available experimental data and model parameters, non-linear parameter estimation procedures lead to more reliable results and allow for direct comparison of results obtained with different adsorption equilibrium models. The main objective of this work is to present and compare different non-linear procedures for parameter estimation of adsorption equilibrium models, based on theoretical arguments and also on the numerical estimation of adsorption equilibrium parameters, using available experimental data for adsorption of methylene blue onto activated carbon. The results obtained indicate that the best parameter estimation procedure is the one that relies on available equilibrium concentrations in the bulk phase as a function of the fluid volume, adsorbent mass and initial concentrations in the bulk phase, without transformation of measured experimental values and model parameters. Besides, it is shown that parameter estimates should be obtained through proper minimization of weighted least-squares objective function, in accordance with maximum likelihood procedures.