Removing multiplicities from activity coefficient models

It is well known that the widely used activity coefficient models NRTL and UNIQUAC are not unique: a given pair of activity coefficients can be represented by different pairs of interaction parameters. This strict pointwise non-uniqueness must not be confused with the practical non-uniqueness commonly encountered when fitting data sets, which refers to the existence of regions in parameter space that yield practically equivalent descriptions of the data. We show that strict multiplicity poses additional challenges for model parameterization and has direct consequences for the robustness of predictions. In this work, we present an in-depth analysis of the nature of the strict pointwise multiplicities and identify the regions in parameter space where they occur by addressing their root cause. We show that, although all solutions yield exactly the same results at the training point, they differ strongly in their predictive behavior, and that a single solution stands out which can be considered the desired one. Based on these insights, we develop a strategy to eliminate multiplicities by selecting this desired solution without restricting the range of activity coefficients the models can represent. Thus, a one-to-one mapping between activity coefficients and parameters is established, resulting in unique NRTL and UNIQUAC models, being otherwise identical to their parent models. Finally, we discuss how the unique models can be applied to parameter fitting and illustrate the resulting advantages.