August 2015: How good are the predictions of sound velocity with an equation of state?
It was a major achievement when Peneloux et al in 1982 presented the method for volume correcting a cubic equation of state. It enabled liquid densities to be matched using a cubic equation, which was not possible with the equations in their original form. Prior to that time cubic equations had mainly been used to calculate phase amounts and compositions and to some extent gas Z-factors while liquid densities were calculated using external liquid density correlations. The volume correction made the empirical density correlation redundant.
The volume correction can be treated as a constant or as a function of temperature. PVTsim supports a volume correction, which varies linearly with temperature, which will enable a good match of the isobaric compressibility. The volume correction has only marginal influence on isothermal compressibility and velocity of sound. While the isothermal compressibility can be derived from routine PVT studies, the data material for the sound velocity of reservoir fluids is scarce. The sound velocity is defined as
M = Molecular weight
V = Molar volume
P = Pressure
S = Entropy
Acoustic techniques used in oil exploration are dependent on models providing an accurate sound velocities and sound velocity is a key property in dynamic flow simulations. Calsep regularly receives requests about the accuracy that can be expected with PVTsim for sound velocity. Following those requests Calsep conducted a literature search for sound velocity data for petroleum reservoir fluids. Sound velocity data was found for 4 reservoir fluids, two gas condensates and two oil mixtures. The data material covered temperatures from 0-180 oC and pressures from 1 – 1200 bar. The data was simulated using the volume corrected SRK and PR equations and the PC-SAFT equation and the results documented in a validation report available to PVTsim users upon request: “Validation of PVTsim sound velocity predictions using SRK-Peneloux, PR-Peneloux and PC-SAFT”.
For gas condensates PR-Peneloux was superior to the two other equations while for oil mixtures the better results were seen with the PC-SAFT equation. In general the sound velocity can be simulated within 10% by choosing the appropriate equation of state. Figures 1 and 2 plots exemplifying the deviations between simulated and experimental data.
Figure 1. Match of sound velocity data for gas condensate mixture with PR-Peneloux EoS. Series are pressures in bar.
Figure 2. Match of sound velocity data for oil mixture with PC-SAFT EoS. Series are pressures in bar.
REFERENCES TO EXPERIMENTAL DATA
A. Barreau, K. Gaillard, E. Béhar, J.L. Daridon, B. Lagourette, P. Xans. Volumetric properties, isobaric heat capacity and sound velocity of condensate gas measurements and modelling. Fluid Phase Equilibria, Volume 127, Issues 1–2, 15 January 1997, pp. 155-171.
J.L. Daridon et al. Petroleum characterization from ultrasonic measurement. Journal of Petroleum Science and Engineering 19,1998, pp. 281–293.
Wang, Z., Nur, A. M., & Batzle, M. L. (1990, February 1). Acoustic Velocities in Petroleum Oils. Society of Petroleum Engineers. doi:10.2118/18163-PA.