Discrete Modeling Approach for Cluster-Based Excess Gibbs-Energy of Molecular Liquids.

The excess Gibbs-energy of a two-component liquid molecular mixture is modeled based on discrete clusters of molecules. These clusters preserve the three-dimensional geometric information about local molecule neighborhoods that inform the interaction energies of the clusters. In terms of a discrete Markov-chain, the clusters are used to hypothetically construct the mixture using sequential insertion steps. Each insertion step and, therefore, cluster is assigned a probability of occurring in an equilibrium system that is determined via the constrained minimization of the Helmholtz free energy. For this, informational Shannon entropy based on these probabilities is used synonymously with thermodynamic entropy. A first approach for coupling the model to real molecules is introduced in the form of a molecular sampling algorithm, which utilizes a force-field approach to determine the energetic interactions within a cluster. An exemplary application to four mixtures shows promising results regarding the description of a variety of excess Gibbs-energy curves, including the ability to distinguish between structural isomers.

Surrogates for Liquid-Liquid Extraction.

Fuel surrogates are mixtures that mimic the properties of real fuels with only a small number of components, simplifying the calculation and simulation of fuel-related processes. This work extends a previously published surrogate optimization algorithm toward the generation of fuel surrogates with a focus on liquid-liquid extraction characteristics. For this purpose, experimental liquid-liquid equilibrium data from batch extraction experiments are incorporated into the calculation procedure as an additional constraint. The use of the method is demonstrated by optimizing a surrogate for the catalytic reformate. Application of the surrogate to an extraction process and comparison with experimental data demonstrate that the resulting surrogate accurately depicts the properties of the real mixture with regard to liquid-liquid extraction performance. This demonstrates that the use of such surrogates is of particular interest for mixtures used as extracting agents for biofuels.

Cluster-Based Thermodynamics of Interacting Dice in a Lattice.

In this paper, a model for two-component systems of six-sided dice in a simple cubic lattice is developed, based on a basic cluster approach previously proposed. The model represents a simplified picture of liquid mixtures of molecules with different interaction sites on their surfaces, where each interaction site can be assigned an individual energetic property to account for cooperative effects. Based on probabilities that characterize the sequential construction of the lattice using clusters, explicit expressions for the Shannon entropy, synonymously used as thermodynamic entropy, and the internal energy of the system are derived. The latter are used to formulate the Helmholtz free energy that is minimized to determine thermodynamic bulk properties of the system in equilibrium. The model is exemplarily applied to mixtures that contain distinct isomeric configurations of molecules, and the results are compared with the Monte-Carlo simulation results as a benchmark. The comparison shows that the model can be applied to distinguish between isomeric configurations, which suggests that it can be further developed towards an excess Gibbs-energy, respectively, activity coefficient model for chemical engineering applications.