Model based statistical analysis of adsorption equilibrium data

A large group of separation problems can be solved using selective adsorption on suitable solids. A mathematical description of adsorption isotherms, which relate the equilibrium concentrations in the fluid phase to the loadings of the solid, could be used to design, observe and control such processes in an efficient way. However, the determination of the isotherms typically requires the identification of unknown parameters in postulated models from experimental data. While for the estimation of the parameters a number of tools and methods are available, a comprehensive analysis of the quality of the parameters is seldom performed. To estimate and characterize parameters obtained from adsorption measurements in this work a non-linear regression analysis was explored in combination with an extended statistical analysis. Hereby, the non-linearity method (“intrinsic” and “parameter-effect” non-linearity) proposed by Bates and Watts [1980. Relative curvature measures of non-linearity. Journal of the Royal Statistical Society: Series B (Methodological) 42, 1–25] was used to check the quality of parameters and the suitability of model/data combinations. The variances of the parameters are determined with the bootstrap method originally proposed by Efron and Tibshirani [1993. An Introduction to the Bootstrap. Chapman and Hall, CRC Press, London, Boca Raton.]. The later approach clearly overcomes some limitation of classical Fisher-information-matrix (FIM) method. By applying these statistical methods to different adsorption models and data sets, it was found that non-linearity method is a good tool to check the quality of the model/data combination. Furthermore, it was found that the confidence intervals of the parameters determined based on the bootstrap are larger than predicted by traditional methods.