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Volume correction factors by velocity of sound

Profile image of Denis FITZGERALDDenis FITZGERALD

2004, Petroleum review

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Abstract

A recent study carried out by members of the HM-L-4B Oil Transportation Measurement Committee - supported by the Energy Institute (El) and the API - has confirmed the general accuracy of the existing IP/API/ASTM Petroleum Measurement Tables (1980). The tables are used to convert densities and volumes measured at ambient conditions to standard conditions. In addition, new, simple equations have been developed based on velocity of sound, which can provide improved precision over the existing tables. Paul Harrison*, Melverley Consultants, and Denis Fitzgerald**, H&D Fitzgerald, report.

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Analysis of these measurements has allowed development of two generalised equations:
Analysis of these measurements has allowed development of two generalised equations:
Due to the diverse molecular nature of hydrocarbon liquids there is no physical reason why a should be related to density alone and this is reflected in the above chart. The scattering of results was overcome in part by separating crude oils, products and lube oils and then using best-fit curves for each population. However results are fairly scattered around the curves as is seen from the crude oils and products curves shown above.
Due to the diverse molecular nature of hydrocarbon liquids there is no physical reason why a should be related to density alone and this is reflected in the above chart. The scattering of results was overcome in part by separating crude oils, products and lube oils and then using best-fit curves for each population. However results are fairly scattered around the curves as is seen from the crude oils and products curves shown above.
The test procedure ensured that each determination of temperature, density and velocity of sound (data triplet) was independent. Samples were injected against a simple weighted piston back pressure device which maintained the sample at 2.15 bara throughout the analysis. This stopped out-gassing, even with volatile gasolines and crude oils. Measured densities were corrected to allow for this small overpressure.
The test procedure ensured that each determination of temperature, density and velocity of sound (data triplet) was independent. Samples were injected against a simple weighted piston back pressure device which maintained the sample at 2.15 bara throughout the analysis. This stopped out-gassing, even with volatile gasolines and crude oils. Measured densities were corrected to allow for this small overpressure.
This shows damping value against temperature for 3 gasoline samples. They plot as fairly smooth curves where the slope is a function of the behaviour of the glass wall of the cell and the change in viscosity o the sample with temperature. Obviously no crystal formation is anticipated here. The following graphs illustrate this effect.
This shows damping value against temperature for 3 gasoline samples. They plot as fairly smooth curves where the slope is a function of the behaviour of the glass wall of the cell and the change in viscosity o the sample with temperature. Obviously no crystal formation is anticipated here. The following graphs illustrate this effect.
Five samples of Ekofisk crude have been analysed and damping value against temperature for these is shown in Fig 7.1.2 above. All show a consistent and stable damping value down to around 20°C when the value rises steeply with falling temperature. Ekofisk cloud point is typically 18-24°C.
Five samples of Ekofisk crude have been analysed and damping value against temperature for these is shown in Fig 7.1.2 above. All show a consistent and stable damping value down to around 20°C when the value rises steeply with falling temperature. Ekofisk cloud point is typically 18-24°C.
The following graph for three Statfjord samples show two samples with very little change at lower temperatures while the third sample from a different source shows a change in damping value from around 15°C. This could indicate that the samples have been treated differently, possibly with addition of inhibitors.
The following graph for three Statfjord samples show two samples with very little change at lower temperatures while the third sample from a different source shows a change in damping value from around 15°C. This could indicate that the samples have been treated differently, possibly with addition of inhibitors.
The plot of damping value against temperature has been used to define wax appearance temperature where appropriate for all the project samples. These plots are presented with the results in Appendix 2.
The plot of damping value against temperature has been used to define wax appearance temperature where appropriate for all the project samples. These plots are presented with the results in Appendix 2.
Table 8.1.3 shows a comparison of the VCFs calculated via each of the curve fitting methods with the experimental VCF.
Table 8.1.3 shows a comparison of the VCFs calculated via each of the curve fitting methods with the experimental VCF.
When the three equations were fitted to all 218 samples in the database, the average errors were as follows:
When the three equations were fitted to all 218 samples in the database, the average errors were as follows:
It is suggested that one possible advantage of using this method is that it is easy to convert an observed density or volume to another temperature, without having to go through a reference density.
It is suggested that one possible advantage of using this method is that it is easy to convert an observed density or volume to another temperature, without having to go through a reference density.
Table 11.2 tabulates the differences between the density calculated by applying the generalised d5p/d¢ derived from equation 11.1 to the observed data, and the experimental value, for a range of temperatures. This approach was outside the scope of the project but could provide a useful method with many applications. There are indications that further statistical analysis should be able to substantially reduce the residual standard deviation which already shows a small improvement over the PM Tables.
Table 11.2 tabulates the differences between the density calculated by applying the generalised d5p/d¢ derived from equation 11.1 to the observed data, and the experimental value, for a range of temperatures. This approach was outside the scope of the project but could provide a useful method with many applications. There are indications that further statistical analysis should be able to substantially reduce the residual standard deviation which already shows a small improvement over the PM Tables.
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    References (33)

    1. 0 Introduction ......................................................................................................................................
    2. 0 Acknowledgements .......................................................................................................................... 2.1 Finance..................................................................................................................................
    3. 2 Samples.................................................................................................................................
    4. 3 Software................................................................................................................................
    5. 0 Summary...........................................................................................................................................
    6. 0 Background.......................................................................................................................................
    7. 1 The Petroleum Measurement Tables ....................................................................................
    8. 2 The Concept of Velocity of Sound as a "correction factor" .................................................
    9. 3 The Characteristics of Pure hydrocarbons............................................................................
    10. 4 Initial tests on Hydrocarbon Mixtures ..................................................................................
    11. 0 Experimental Arrangements ............................................................................................................. 5.1 Equipment and Procedure.....................................................................................................
    12. 2 Temperature Traceability......................................................................................................
    13. 3 Density Traceability .............................................................................................................
    14. 4 Velocity of Sound Traceability.............................................................................................
    15. 5 Typical data ........................................................................................................................
    16. 0 Samples........................................................................................................................................... 6.1 Range ..................................................................................................................................
    17. 2 Sample Provenance.............................................................................................................
    18. 3 Sample Collection and Handling........................................................................................
    19. 4 Storage................................................................................................................................
    20. 0 Wax Appearance Temperature ....................................................................................................... 7.1 General................................................................................................................................
    21. 2 Viscous Samples.................................................................................................................
    22. 3 Conclusion..........................................................................................................................
    23. 0 Reference density ........................................................................................................................... 8.1 Comparison of Methods -linear, quadratic, API................................................................
    24. 0 Data available .................................................................................................................................
    25. 0 Predicting density 15 from Measured Density and VoS................................................................... 10.1 Crudes.................................................................................................................................
    26. 2 Products ..............................................................................................................................
    27. 3 Lubes .................................................................................................................................. 10.4
    28. Products & Lubes ............................................................................................................... 10.5 All Samples......................................................................................................................... 10.6 Influence of crystal formation ............................................................................................ 10.7 Sensitivity of the generalised equation ...............................................................................
    29. 0 Predicting δρ/δt from Measured Density and VoS .........................................................................
    30. 0 Unusual samples / Interferences ..................................................................................................... 12.1 Effect of Water Content...................................................................................................... 12.2 Unleaded Gasolines ............................................................................................................ 12.3 Oxygenates (from H&D earlier work)................................................................................ 12.4
    31. Biodiesel/FAME (from H&D earlier work) .......................................................................
    32. 0 Practical Application of Velocity of Sound Relationships ............................................................. 13.1
    33. VoS Standards ....................................................................................................................
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