Development of a predictive equation of state


Leonhard, Kai


Kai Leonhard

Junior professor Model-Based Fuel Design


+49 241 80 98174




Zulkarnain, Ihsan Ahmad


Ihsan Ahmad Zulkarnain

Model-Based Fuel Design


+49 241 80 96412



An equation of state (EOS) is important for modelling fuel properties for injection in engine modelling in the cluster of excellence. An EOS can also be used in the design of separation and reaction processes as well as in the design of energy technology applications e.g. refrigeration. The objective is to develop a predictive equation of state based on PC-SAFT (Perturbed-Chain Statistical Associating Fluid Theory) and quantum mechanically obtained molecular information. It is used to predict thermodynamic properties of pure compounds and mixtures.


Non-hydrogen bonding parameters prediction

A scheme has been developed to determine EOS parameters from quantum mechanical (QM) calculations for non-hydrogen bonding compounds (1) and applied to predict the solubility of drug compounds (2). These EOS parameters were used to predict the surface tension of new potential fuel candidates along with other model compounds with a fully predictive model and with a 1-parameter model adjusted to the easily-obtainable normal boiling point (3).


Hydrogen bonding parameters prediction

We also investigated the prediction of PC-SAFT equation of state parameters of hydrogen bonding compounds. To reach this goal, thermochemical properties (enthalpies and entropies of association) of 1-alkanols are calculated by using efficient and accurate ab initio and statistical mechanical methods (3) and related to the PC-SAFT pure component association parameters (ε AB /k and Ƙ AB) (4). The remaining parameters (m, σ, ε/k) are predicted by the semi-empirical approach as described in ref. 4 and 5 (4 & 5). Further thermochemical property calculations are under progress for other hydrogen bonding compounds.


Improvement strategies to the predictive equation of state models

sigma surface of trichloromethane Copyright: Chair of Technical Thermodynamics, RWTH Aachen University Figure 1 sigma surface of trichloromethane, a multipolar substance that needs to be covered in the next predictive model

In order to improve the accuracy of the predictive equation of state models, we developed some strategies, those are: combining it with a minimal set of experimental property data (6); or combining it with a set of property data predicted from another predictive model, which is the Conductor-like Screening Model – Real Solvent (COSMO-RS) (7). Currently, we are working on developing some strategies by introducing new molecular descriptors from COSMO to simplify parameter prediction of hydrogen-bonding compounds and to improve parameterization accuracy of polar compounds, such as halogenated compounds (see figure 1).


Publications on this topic:

(1)Van Nhu Nguyen, Mahendra Singh und Kai Leonhard, Feelly Ruether, Kai Leonhard und Gabriele Sadowski
Quantum Mechanically Based Estimation of Perturbed-Chain Polar Statistical Associating Fluid Theory Parameters for Analyzing Their Physical Significance and Predicting Properties.
The Journal of Physical Chemistry B, 112(18):5693-5701, 2008.

(2) Jan Cassens, Feelly Ruether, Kai Leonhard und Gabriele Sadowski
Solubility calculation of pharmaceutical compounds – A priori parameter estimation using quantum-chemistry
Fluid Phase Equilibria, 299(1): 161 - 170, 2010.

(3) Alexander von Müller and Kai Leonhard
Surface Tension Calculations by Means of a PCP-SAFT-DFT Formalism Using Equation of State Parameters from Quantum Mechanics
Fluid Phase Equilibria, 356: 96-101, 2013.

(4) Muhammad Umer and Kai Leonhard
Ab Initio Calculations of Thermochemical Properties of Methanol Clusters
The Journal of Physical Chemistry A, 117(7):1569–1582, 2013.

(5) Muhammad Umer, Katja Albers, Gabriele Sadowski and Kai Leonhard
PC-SAFT parameters from ab-initio calculations
Fluid Phase Equilibria, 362(41-50) 2014.

(6) Sebastian Kaminski, André Bardow, and Kai Leonhard
The trade-off between experimental effort and accuracy for determination of PCP-SAFT parameters
Fluid Phase Equilibria, 428:182-189, 2016

(7) Sebastian Kaminski, Evagelos Kirgios, André Bardow, and Kai Leonhard
Improved Property Predictions by Combination of Predictive Models
Industrial Engineering Chemistry Research, 56(11):3098-3106, 2017