## 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

# Example 3-5: Comparison of second virial coefficient calculation methods

A comparison of second virial coefficient for hydrocarbon is to be proposed. Differences between different correlations will be analysed. The various equations are the following:

### DIPPR form:

### Tsonopoulos form:

where

### Ambrose form:

In these relationships, the reduced temperature is defined as:. Coefficients for the different equations are:

T_{c} (K) |
Pc (kPa) |
ω |
---|---|---|

562.05 |
4895 |
0.2212 |

Equation |
A |
B |
C |
D |
E |
T_{min.}(K) |
T_{max}(K) |
---|---|---|---|---|---|---|---|

DIPPR |
0.1509 |
-186.94 |
-2.3146.10^{7} |
-7.05.10^{18} |
-6.88.10^{22} |
281 |
1500 |

Ambrose |
571.4 |
-348.4 |
526.6 |
- |
- |
290 |
600 |

Tsonopoulos |
From critical parameters |
281 |
1500 |

## Analysis:

- The properties are temperature and second virial coefficient.
- Component is benzene, which is a databank component.

## Solution:

### See complete results in file (xls):

Some help on nomenclature and tips to use this file can be found here.

A graph is constructed with the different equations: DIPPR, Tsonopoulos and Ambrose. The two former relations cover a large temperature range [281 – 1500 K], but the latter is related to a shorter temperature range and we have also extrapolated it to high temperature.

We have determined the Boyle’s temperature where the second virial coefficient is zero. Table 3 gives the values obtained from the three correlations.

Correlations | Boyle’s Temperature (K) |
---|---|

DIPPR form | 1327.11 |

Tsonopoulos form | 1313.84 |

Ambrose form | 1059.64 |

We can observe that the DIPPR and the Tsonopoulos forms are in agreement with a relative difference close to 1 %. This is not the cas with the Ambrose form, which is extrapolated, we obtain a lower Boyle’s temperature (less than 255 K). This example illustrates the risk of extrapolation outside of the defined temperature range of the correlation.

## References

R. L. Rowley, W. V. Wilding, J. L. Oscarson, Y. Yang, N. A. Zundel, T. E. Daubert, R. P. Danner, *DIPPR® Data Compilation of Pure Compound Properties*, Design Institute for Physical Properties, AIChE, New York, NY (2003).