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The NRTL-PR thermodynamic model

01/12/2010
The NRTL-PR model is available in ProSim thermodynamic library, therefore in most ProSim software.


It is an accurate model, used to represent water – hydrocarbons – glycol mixture behaviour. The interest of this kind of systems is linked to the fact that, for economical reasons, one tries to avoid the use of oil platforms for oil recovery in sea. One of the major consequences of this is the formation of solid hydrocarbons hydrates in pipes during the transportation to the refinery, in the sub-marine temperature and pressure conditions. To avoid hydrate formation, one option is to inject ethylene glycol; unfortunately, this leads to liquid phase splitting (demixtion) which needs to be represented by the thermodynamics models.

The NRTL-PR model, developed by the team of Professor Neau [ESC08], [NEA10a], [NEA10b] is an equation of state based on PR-78 [PEN78] and which approach is predictive by group contribution. It uses a mixing rule that uses a predictive model to compute the non athermal term of the Gibbs free energy. This mixing rule is written as a “complex” mixing rule, but it can also be written as a “kij” mixing rule:
1) Gibbs free energy mixing rule:



The mathematical expressions of the non-athermal term of the Gibbs free energy proposed by the authors are:


(except if one of the main group is water or glycol).


2) "kij" mixing rule



Just like for other group contribution predictive methods (UNIFAC type), two categories of groups are defined. First, the groups called “main groups”, which correspond to a type of interaction, therefore to a couple of given interaction parameters. The group "CH2" is an example. For the majority of these main groups, subgroups are defined. The latters differ one from the others by the values of the Bondi parameter Qk. The subgroups "CH3", "CH2”, “CH” and “C” are subgroups from the main group “CH2”.

The matrix of the binary interaction parameters between the groups defined in the NRTL-PR is given below:


The main group "CH2" corresponds to the alkane group and its sub-groups are "CH3", "CH2", "CH" and "C".
The main group "CY-C" corresponds to the cycloalkane group and its sub-groups are "c-CH2", "c-CH" and "c-C".
The main group "AC" corresponds to the aromatic group and its sub-groups are"ACH" and "AC".

Some comparisons of results obtained from NRTL-PR with experimental data are presented hereafter:






water, benzene, liquid-liquid equilibrium

 



References

- [ESC08] ESCANDELL J., “Mise au point d’une méthode predictive pour le calcul des équilibres de phases des systèmes eau – hydrocarbures – glycols”, phD Thesis, (2008).
- [NEA10a] NEAU E., ESCANDELL J., NICOLAS C., “Modeling of highly nonideal systems: 1. A generalized version of the NRTL equation for the description of low-pressure equilibria”, Ind. Eng. Chem. Res., 49, pp. 7580-7588 (2010).
- [NEA10b] NEAU E., ESCANDELL J., NICOLAS C., “Modeling of highly nonideal systems: 2. Prediction of high pressure phase equilibria with the groupe contribution NRTL-PR-EoS”, Ind. Eng. Chem. Res., 49, pp. 7589-7596 (2010).
- [PEN78] PENG D.Y., ROBINSON D.B., “The characterization of the heptanes and heavier fractions for the GPA Peng-Robinson programs”, Gas processors association, Research Report PR-28 (1978).