Determination of an adsorption isotherm is an important step in the design of adsorption/chromatographic separation processes. Several methods exist in the literature to measure adsorption equilibria. While many of the techniques are rigorous, they are at the same time elaborate and time-consuming. It is well known that a properly conducted breakthrough response from a packed column subjected to a step change in feed concentration at the inlet contains both equilibrium and kinetic information. However, to estimate the isotherm from such dynamic column breakthrough experiments, one must assume an adsorption isotherm model. Typically a simple isotherm model, such as Langmuir isotherm, is assumed, which may be able to approximately capture the trend and provide semi-empirical basis for limited process modeling. However, this approach is inadequate to understand the physics of adsorption for which the actual data rather than the trend is needed.
In this work, we present a new method for extracting a model-independent discredited equilibrium data from a set of column breakthrough experiment covering both adsorption and desorption in the desired concentration range. Instead of assuming an isotherm model, our approach represents the isotherm as a set of discrete points. For a given set of discrete fluid phase concentrations, we use an optimization method to determine the corresponding solid loadings that lead to the best-fit prediction of the experimental breakthrough profile. We describe the algorithm and demonstrate the effectiveness of our approach using several single-component case studies for type I (favourable), type II (unfavourable) and type III (with inflection points) isotherms. In addition, the efficacy of the method has been tested with experimental elution profiles. We also discuss guidelines for the mininmal number of experiments and the number of discretization points required to obtain satisfactory adsorption equilibrium data. We apply the technique to both simulated and experimental breakthrough curves and demonstrate its efficacy.