D-optimal experimental designs for precise parameter estimation of adsorption equilibrium models

Abstract

D-optimal experimental designs were obtained for Langmuir, Freundlich, Jovanovich, Sips, Redlich-Peterson and BET isotherms using two different approaches. In the first one, it is assumed that liquid solution equilibrium concentration is the independent system variable and solid equilibrium concentration is the dependent variable, which is the usual procedure for parameter estimation of adsorption isotherm models. In the second approach, initial liquid solution concentration, liquid solution volume and adsorbent mass are the independent variables and liquid solution equilibrium concentration is the dependent variable, which is closer to what actually occurs in adsorption experiments. In both cases, one of the designed conditions is an experiment using the maximum concentration value in the experimental range, while other conditions are functions of one or more isotherm parameter. When using equilibrium concentration as the independent variable, the linear parameter of the equilibrium model did not affect the experimental design. In this case, analytical solutions for 2-parameter equilibrium isotherm were obtained, while only numerical solutions were obtained for 3-parameter equilibrium models. When considering the initial concentration as the independent variable, with a constant liquid solution volume to adsorbent mass ratio, it was possible to observe that the experimental conditions of the optimum design depend on all model parameters, for all isotherms evaluated. Additionally, as liquid solution volume to adsorbent mass ratio increases, the experimental design obtained using the initial concentration as the independent variable approaches the one obtained when equilibrium concentration is assumed to be independent variable; therefore, this approach is just a particular case of the first one.