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Correlations for Liquid Molar Volumes

by J. M. Haile

For estimating the molar volumes of liquids, we have two commonly used correlations: the Rackett equation [1] (used in the Property Calculator on this website) and the Lee-Kesler correlation [2] (described elsewhere on this site). The choice between these illustrates the usual engineering dilemma of balancing accuracy (Lee-Kesler) against computational simplicity (Rackett). Your decision is driven by the accuracy with which you need a value: if you only need a volume within about 3%, then the Rackett correlation will probably be good enough. But if you need a better value, Lee-Kesler should be used.

To illustrate, we compare results from these two correlations with experimental values for saturated liquid propane, as reported by Goodwin and Haynes [3]. For temperatures from the normal boiling point (231.1 K) to within 5 K of the critical point (Tc = 369.8 K), the results are given in the table below.

Note that, for this example, the Rackett correlation consistently underestimates the molar volume by about 2%. For these 15 points, the rms deviation is 2 cc/mol. In contrast, the Lee-Kesler correlation overestimates the volume at low temperatures, but underestimates it at temperatures within 20 degrees of the critical temperature (369.8 K). For these 15 points, the rms deviation in the Lee-Kesler values is about 1 cc/mol.

These results are probably typical, though details of the trends will differ for other fluids: magnitudes of the errors may reach 4-5% for the Rackett correlation and 3% for Lee-Kesler.

Molar volumes (cc/mol) for Saturated Liquid Propane

Experiment Rackett Lee-Kesler
T (K) vol [3] vol % Error vol % Error
231.07 75.89 74.56-1.876.84+1.2
240 77.29 75.93-1.8 78.34+1.4
250 78.96 77.59-1.7 80.11+1.5
260 80.78 79.38-1.7 82.00+1.5
270 82.77 81.34 -1.784.03+1.5
280 84.96 83.50-1.7 86.23+1.5
290 87.40 85.91 -1.788.64+1.4
300 90.15 88.62-1.791.33+1.3
310 93.32 91.72 -1.794.38+1.1
320 97.04 95.35-1.7 97.92+0.9
330 101.54 99.73 -1.8102.2+0.6
340 107.24 105.25-1.9 107.52+0.3
350 115.03 112.75-2.2 114.9-0.3
360 127.63 124.76-2.2 127.1-0.4
365 139.17 135.68-2.5 138.93-0.2

References

[ 1 ] B. E. Poling, J. M. Prausnitz, and J. P. O'Connell, The Properties of Gases and Liquids, 5th ed., McGraw-Hill, New York, 2001.

[ 2 ] B. I. Lee and M. G. Kesler, "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States," AIChE J, 21, 510 (1975).

[ 3 ] R. D. Goodwin and W. M. Haynes, "Thermophysical Properties of Propane from 85 to 700 K at Pressures to 70 MPa,"NBS Monograph 170, National Bureau of Standards, Washington, D. C., 1982.