FITTING ION-EXCHANGE MODELS TO COMPLEX DATA BY MINIMIZING AITCHISON'S DISTANCE

Abstract

Ion-exchange reactions are one of the most common separation methods used in chemical processes. Ion-exchange models often predict the composition of one phase from the measured concentrations in another phase. Fitting models to these systems can be complicated because of the potentially large number of ions involved and because models must be fit iteratively. An objective function is required for iterative model fitting. Previous work has determined that Aitchison's Distance is the best measure of the difference between multicomponent compositions. Therefore, the present study argues that the minimum Aitchison's Distance between measured and predicted compositions is the most appropriate objective function. An example application of this fitting method is presented, where a log-ratio model is fit to ion-exchange data for the Na+-Ca2+-K+-Mg2+-illite system. The log-ratio model is found to fit this system well overall. These results demonstrate that excellent model coefficients can be obtained by minimizing Aitchison's Distance during model fitting.