In this article, a systematic approach is presented which allows the estimation of model parameters including isotherm parameters for equilibrium-dispersive and general rate models including a procedure for how to subsequently select the most appropriate isotherm and model for a given application. The approach consists of three parts: determination of feed concentration, parameter estimation, and model selection. Accurate modeling of any separation process depends on the starting point, i.e. the feed and the feed concentration, however, for many chromatographic separations, this concentration is unknown. The first part of this work therefore presents a systematic procedure for feed concentration determination. The estimation of isotherm or other model parameters is done using the simulation and optimization tool gPROMS. Finally, the predictions from each model alternative are then compared using fractionation and maximum purification diagrams. The estimation approach is successfully applied to three case studies, including purification of alcohol dehydrogenase from a yeast homogenate supernatant and gradient elution ion-exchange of myoglobin, which illustrate the approach and the relative suitability and range of application of the models in describing the behavior of complex chromatographic separations. It is found that, while the equilibrium-dispersive model is a good approximation in most cases, there are cases when the more detailed general rate model is required. (c) 2008 American Institute of Chemical Engineers.