Page 96 - Handbook of Natural Gas Transmission and Processing Principles and Practices

(2.31)

It is, however, well known that cubic EoS provide inaccurate liquid densities. To fix the ideas, the
SRK and PR EoS predict the saturated-liquid volumes with an average deviation of about 16% and
8%, respectively (Le Guennec et al., 2016b). One method to overcome this shortcoming is the so-
called volume translation. Indeed, Péneloux et al. (1982) noticed that for a given component, the
notable difference between the experimental and the calculated saturated-liquid volume at a given
temperature was more or less constant when varying the temperature out of the critical region.
Consequently, translating all the calculated molar volumes by a temperature-independent amount c
significantly improves the description of the saturated liquid densities. The mathematical
expression of the translated EoS can thus be obtained by replacing v by and b by within
the untranslated (original) expression. As recently discussed by (Jaubert et al., 2016), such a
translation leaves unaffected the calculated vapor pressures, property changes on vaporization, and
heat capacities. It is thus possible to keep the same alpha function for both the translated and
untranslated EoS and to determine c to minimize the deviations between experimental and
calculated liquid densities. Following the previous work by Péneloux et al. (1982), Le Guennec et al.
(2016b) proposed to estimate the volume translation c from the following correlations which involve
the Rackett compressibility factor, z RA , defined by Spencer and Danner (1972) when they improved
the original Rackett equation (Rackett, 1970):

(2.32)
In a recent paper, Privat et al. (2016) highlighted that the volume-translation concept
could be straightforwardly extended to mixtures by using a linear mixing rule. It means that the
volume-translation parameter of the mixture is obtained by summing pure-component
volume-translation parameters weighted by their corresponding mole fractions:

(2.33)

2.3.2. General Presentation of Cubic Equations of State

All the cubic equations can be written under the following general form:

96