# 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:

where

### Ambrose form:

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

Table 1: Critical parameters for benzene
Tc (K) Pc (kPa) ω
562.05 4895 0.2212
Table 2: Parameters for various second virial coefficient for benzene
Equation A B C D E Tmin.(K) Tmax(K)
DIPPR 0.1509 -186.94 -2.3146.107 -7.05.1018 -6.88.1022 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.

Table 3: Estimated Boyle’s temperature for benzene
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).