## 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 3-7: Evaluate critical temperatures using the group contribution methods of Joback and Gani

This example shows how to calculate a number of important properties using group contributions. One excel file is available for the Joback method, and one for the Marrero-Gani method (more complex). We shall discuss the example of the calculation of the critical temperature for n-octane, n-propyl-benzene and n-propyl-cyclohexane.

## Analysis:

- The components are known through their chemical structure
- The property required is critical temperature.

## Solution:

### Use the excel for the Joback method [1]:

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

### And for the Marrero-Gani method [2]:

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

### n-octane:

It is composed of 2 (CH3) groups and 6 (CH2) groups. It has no second order groups.

- using the Joback method, it is worth mentioning that a normal boiling temperature is requested. This temperature may come from the database (DIPPR provides 398.83 K), in which case the critical temperature is calculated to be 569.27 K (very close to the database value of 568.7 K). When the normal boiling temperature is itself calculated from the Joback group contribution (Tb = 382.44 K) then the calculated critical temperature is 545.88 K, which is rather far from the database value. It is therefore concluded that
**the Joback method is only partially predictive**: its result depends very much on the quality of the input values. - The Marrero-Gani method here requires only first order information, and is fully predictive. It yields 564.71 K to be compared with the database value of 568.7 K.

### n-propyl benzene:

**The group decomposition is different depending on the method.**

- For the Joback method, it is composed of 1 (CH
_{3}) group 2 (CH_{2}) groups, 5 cyclic (=CH-) groups and one branched cyclic (=C<) group. Again, the results is different depending on whether the database value is used for the normal boiling temperature (639.67 K), or its predicted value using the group contribution method (639.09 K). Because the normal boiling temperature is very well predicted by the Joback method in this case, the difference is small. - For the Marrero-Gani method, the component is decomposed as follows: 1 (CH
_{3}) group 1 (CH_{2}) group, 5 aromatic (CH) groups and one branched aromatic (C-CH_{2}) group. It has no second order groups. The resulting critical temperature is 643.32 K, which is rather close to the database value (638.5 K)

### n-propyl cyclohexane:

Again, the group decomposition depends on the method:

- Using the Joback method, it is composed of 1 (CH3) group, 2 (CH
_{2}) groups, 5 ring-groups (-CH_{2}-), and one ring-group (>CH-). When using the fully predictive Joback method, the value of Tc= 623.8 K is found, compared with the database value of 639.15 K. - the Marrero-Gani method allows the use of second order groups. The n-propyl cyclohexane provides an example of such groups, as illustrated in figure 1.

The final group decomposition of n-propyl cyclohexane is : 1^{st} order: 1 (CH_{3}) group, 2 (CH_{2}) groups, 5 cyclic (CH_{2}) groups and 1 cyclic (CH) group. On top of that, the second order group called ‘CHcyc-CH_{2}’ must be added. The resulting calculation is available on the excel sheet, with a final value of *Tc* = 630.89 K. If only first order had been used, the calculation would have given *Tc* = 625.06 K. The database value is 639.15K, showing that **the use of second order groups helps, but is not enough to make it a tool of great predictive quality**.

### References

[1] JOBACK K.G., REID R.C., Estimation of Pure Component Properties from Group Contributions, *Chemical Engineering Communications*, 1987, **57**, p. 233-243. http://dx.doi.org/10.1080/00986448708960487

[2] MARRERO J., GANI R., Group-contribution based estimation of pure component properties, *Fluid Phase Equilibria*, 2001, **183**, p. 183-208. http://dx.doi.org/10.1016/S0378-3812(01)00431-9