Statistical Thermodynamic Models: Non-random Two-liquid (NRTL) models¶

The next sections will give an overview of different thermodynamic models ranging from implicit solvation models to Non-random Two-liquid (NRTL) and group contribution (GC) models. Many of these models found on common theory and can even be combined to obtain fine-tuned parameter sets.

Currently the Cebule engine supports the following models:

COSMO-RS & COSMO-SAC
Non-random Two-liquid (NRTL, eNRTL) and Wilson models
Group contribution (GC) models including UNIQUAC, Original UNIFAC, UNIFAC (Dortmund), UNIFAC (Lyngby), UNIFAC 2.0 (Kaiserslautern) and Predictive Soave-Redlich Kwong (PSRK)
Hybrid models: UNIFAC-VISCO, COSMO-NRTL

Non-random Two-liquid (NRTL) models¶

Wilson¶

The binary interaction parameters for the Wilson model are defined as:

\[ A_{ij} = \frac{V_j}{V_i}exp(\frac{-(\lambda_{ij} - \lambda_{ji})}{RT}) \]

\(V_j\) and \(V_i\) are the molar volumes of component \(j\) and \(i\) in the liquid phase whereas \(\lambda_{ij}\) and \(\lambda_{ji}\) are the binary energy parameters. The liquid activity coefficient is defined with the following expression:

\[ ln \gamma_k = - \sum_{j=1}^N x_j A_{kj} + 1 - \sum_{i=1}^N \frac{x_i A_{ik}}{\sum_{j=1}^N x_j A_{ij}} \]

NRTL¶

eNRTL¶

eNRTL parameter table¶

https://doi.org/10.1021/ie100689g

Nonrandomness Factor of \(\alpha\) = 0.2

| Molecule (1) | Water | Hexane | Methanol | | Electrolyte (2) | NaCl | NaCl | NaCl | |-----------------|------------|------------|------------| | \(tau_{12}\) | 8.885 (a) | 15.000 (b) | 3.624 (c) | | \(tau_{21}\) | -4.549 (a) | 5.000 (b) | -0.789 (c) |

(a) Chen et al.

(b) Chen and Song

(c) Yang and Lee