## Chapter 3:

From Components

to Models

### Abstract

Read the abstract### Table of contents

See the table of contents### List of examples

- 3-1: Vapour pressure predictions of methane using different formulas
- 3-2: Quality evaluation of molar volume correlations
- 3-3: Evaluation of the ideal gas heat capacity equations for n-pentane
- 3-4: Quality evaluation of vapourisation enthalpy correlations
- 3-5: Comparison of second virial coefficient calculation methods
- 3-6: Comparison of critical points and acentric factor from different databases
- 3-7: Use of the group contribution methods of Joback and Gani
- 3.8: Diesel fuel characterization
- 3.9: Vapour pressures of di-alcohols
- 3.10: Find the parameters to fit the vapour pressure of ethyl oleate
- 3.11: Fitting of BIP coefficients for the mixture water + MEA with the NRTL model
- 3.12: Separation of n-butane from 1,3 butadiene at 333.15K using vapour-liquid equilibrium
- 3.13: Draw the heteroazeotropic isothermal phase diagram of the binary mixture of water and butanol at 373.15 K
- 3.14: Isothermal phase diagram using the Flory Huggins activity coefficient model
- 3.15: Use of an equation of state for pure component vapour pressure calculations

# Chapter 3 – Abstract

This chapter will discuss how the fluid composition affects the thermodynamic calculations. As already pointed out in the first chapter, discussion brings up both the issue of models as that of their parameters i.e. the fluid description. These two issues cannot be dissociated.

In table 1.1, it has been proposed to subdivide this analysis criterion into three sub-questions:

- What is the nature of the components? This question will lead us to investigate the pure component data, how they are presented, how they can be validated.
- What type of molecular interactions may occur between the components? This question will bring us to investigate how a component behaves when it is surrounded by other components. Many thermodynamic models attempt to describe these interactions.
- Finally, the concept of key component(s) will be introduced. In some cases, this is not crucial, but in the case where the fate of impurities is important, it will be shown how different the analysis becomes.

In order to help answering these questions, we shall stress that:

In one way or another, the model-parameter combination must always be compared (either for regression or for validation) to experimental data.

The first two sections are therefore devoted to the description of the type of data that may exist, the way they are presented and some discussions on how to evaluate their quality (pure components and mixtures). Figure 3.21 illustrates the regression procedure. The third section is entirely focused on the determination of model parameters by fitting on experimental data. The fourth section will discuss the thermodynamic models, focusing on their molecular construction, and hence how they provide the species behaviour in a mixture. Table 3.20 provides a summary for the activity coefficient models and table 3.26 for equations of state. Finally, in the fifth section, the concept of “key component” will be discussed and the mixture data to be evaluated will be first identified (it is often almost impossible to consider all binary data in a multicomponent mixture).

Predictive | Correlative | |

Enthalpic | Hildebrand | NRTL Margules Van Laar |

Entropic | Flory Staverman-Guggenheim |
Wilson |

Enthalpic + Entropic | UNIFAC Flory-Huggins |
UNIQUAC (Flory-Huggins)* |

* The Flory Huggins model is presented here as a predictive, but it is very often used with a correlated parameter for solvent-polymer mixtures.

Correlative | Corresponding states | Group contribution | ||
---|---|---|---|---|

Phaseequilibria |
Hydrocarbons | Cubic +α(T) | ||

Slightly non-ideal | Cubic + k_{ij} mixing rule |
Cubic + Jaubert k_{ij}PC-SAFT (Tihic) |
||

Strongly non-ideal (enthalpic) |
Cubic + G^{E}-type mixing ruleCPA (water, alcohols, gases) |
VR-γ-SAFT (Lymperiadis) GCA (bio-applications) |
||

Enthalpic + entropic non-ideality |
NRHB | GC-Lattice Fluid GC-PPC-SAFT (Passarello) |
||

Phaseproperties |
VR-SAFT MBWR |
Lee Kesler Starling - BWR |