# Example 3-2: Quality evaluation of molar volume correlations

A comparison of liquid molar volume for various hydrocarbons is to be proposed. Differences between the DIPPR correlation and the Racket prediction will be analysed. Parameter values for the different components are found in the following table:

Table 1: Critical constant and parameters for liquid molar volume of some hydrocarbons (DIPPR [1])
Component Tc(K) Pc (kPa) ω A B C D
Ethane 305.32 4872 0.099493 1.9122 0.27937 305.32 0.29187
n-Hexane 507.6 3025 0.301261 0.70824 0.26411 507.6 0.27537
Cyclohexane 553.8 4080 0.208054 0.88998 0.27376 553.8 0.28571
Benzene 562.05 4895 0.2103 1.0259 0.26666 562.05 0.28394
n-Decane 617.7 2110 0.492328 0.41084 0.25175 617.7 0.28571

The Rackett and DIPR equations for liquid molar volume are given (see chapter 3, section 1.1.2.4):

(1)
(2)

ZRa is calculated using equation (3):

(3)

## Analysis:

• The property given is temperature, or preferably a range of temperatures on the saturation curve.
• Components are all hydrocarbons of different molar mass and different families.
• The phase of interest is liquid along the saturation curve.

## Model requirement:

Two different correlations are compared: the DIPPR correlation and the Rackett prediction. The relative deviation between the Rackett equation and the DIPPR saturated liquid volume correlation has been evaluated for a number of hydrocarbons.

## Solution:

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

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

The typical uncertainty on volume measurements is close to 3%. We can therefore can conclude that, especially for light hydrocarbons, the Rackett equation is very useful. The deviation is larger for heavier hydrocarbons. The equation is not suitable for non-hydrocarbons. If the calculation is carried out with the optimised value of ZRa, the error is less than 1%.

It is very easy to implement a short enhancement to the formula using an optimized value of ZRA. In the file, a choice can be made between two different values using a 1 or 0 value in cell B15 (remember that the values in blue are the values introduced by user). You can change this cell to 0 and then optimize the value in violet to minimize the RMSE (in brown).

## 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).