GB/T 21450-2008 Crude petroleum and petroleum products — Compressibility factors for hydrocarbons in the range of density 638kg/m³~1074kg/m³

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1. Method number / full title / English title / replacement relationship

• Standard number: GB/T 21450-2008
• Chinese full title: Crude petroleum and petroleum products — Compressibility factors for hydrocarbons in the range of density 638kg/m³~1074kg/m³
• English title: Crude petroleum and petroleum products—Compressibility factors for hydrocarbons in the range 638 kg/m³ to 1074 kg/m³
• Adoption relationship: Modified adoption of ISO 9770:1989 (MOD)
• Replacement relationship: This standard is formulated for the first time; this standard replaces Table II of Annex B in the withdrawn API 1101 (original text see Chapter 2)
• Publication/implementation: Published on 2008-02-13, implemented on 2008-09-01
• Responsible committee: Sinopec Research Institute of Petroleum Processing
• Drafting organizations: Sinopec Research Institute of Petroleum Processing (responsible); PetroChina Pipeline Company, Sinopec Pipeline Storage and Transportation Company (participating)
• Main drafters: Wei Jinxiang, Pang Yongqing, Xiao Yong, Wang Zhixue

2. Scope of application and non-applicability

• This standard provides the mathematical model, calculation steps and compressibility factor tables for obtaining the compressibility factors of crude petroleum and petroleum products, with the purpose of using the compressibility factor to correct the volume of hydrocarbons measured under pressure at the metering temperature to the corresponding volume at equilibrium pressure.
• The compressibility factor table is related to the metering temperature and the 15°C density of the metered medium; the temperature range is −30°C–90°C, and the density range is 638 kg/m³–1074 kg/m³.
• A compressibility factor table directly looked up from the metering temperature and 20°C density is also provided; the temperature range is −30°C–90°C, and the density range is 634 kg/m³–1074 kg/m³ (original text as such, suspected to be an error for 638, requires confirmation against the source standard (source-text extraction)).
• Not applicable: This standard does not include the compressibility factors of lubricating oils.
• Extrapolation note: The ranges covered by test data for density, temperature and pressure are, in order, 681 kg/m³–934 kg/m³, 0°C–150°C, 0 kPa–4902 kPa; after testing by COSM and COPM, the actual range of the standard can be extended to 638 kg/m³–1074 kg/m³, −30°C–90°C, 0 kPa–10300 kPa, therefore some parts of this standard are extrapolated results (Figure 1); for the extrapolated parts, the uncertainty analysis in 5.1 may be invalid.
• Increment intervals: The increment intervals for temperature and density are 0.25°C and 2 kg/m³ respectively; for smaller increments, interpolation is not recommended.
• 20°C density table lookup rule: When the 20°C density lies between two adjacent densities in the table, the density indicated by the arrow among the two adjacent densities shall be used for table lookup according to the different density ranges of the compressibility factor table and the arrow directions corresponding to different boundary densities.

3. Method principle

• The basic mathematical model involves the exponential relationship between the compressibility factor and temperature and the square of molar volume: F = EXP(A + B×T + C/P' + D×T/p) (Formula 2) Where: A, B, C, D are coefficients; T is temperature, °C; P15 is 15°C density (represented by RHO in the calculation program), g/cm³; 1/p is proportional to molar volume.
• The compressibility factor is the result of the mutual influence of two terms, molar volume and temperature; the reasoning of Formula (2) is consistent with the reasoning of the thermal expansion coefficient of hydrocarbons in API/2540 (Petroleum Measurement Standard Manual).
• The data basis (Table 1) is derived from Jessup, Downer and Gardiner as well as Downer, including 7 crude oil samples, 5 gasoline samples and 7 middle distillate and heavy distillate oil samples; lubricating oil data are not included (simulation results show that lubricating oils belong to a different data group, and including them would increase the uncertainty associated with the compressibility factor by a factor of 2; moreover, lubricating oils are generally metered at atmospheric pressure and do not require this standard).
• The compressibility factor (F) is used in the volume correction manner: Vb = Vm / [1 − F(pm − pe)] (original formula number not provided in the available source, requires confirmation against the source standard (source-text extraction)).

4. Reagents and materials (purity / preparation)

Not provided in the available source.

5. Instruments and equipment

Not provided in the available source (this standard is a table lookup/calculation method standard and does not list instrument and equipment clauses).

6. Recommended operating conditions

• Temperature range: −30°C~90°C.
• 15°C density range: 638 kg/m³~1074 kg/m³.
• 20°C density table lookup range: 634 kg/m³~1074 kg/m³ (original text as such, requires confirmation against the source standard (source-text extraction)).
• Temperature rounding interval: 0.25°C; density rounding interval: 2 kg/m³ (Annex A table lookup); Annex B table lookup density rounded to 0.1 kg/m³.
• The calculation program recommends that the computer operation precision have or exceed 6 floating-point digits.
• Pressure application range: basic data 0 kPa–4902 kPa; extended range 0 kPa–10300 kPa; when the working pressure exceeds 4902 kPa, the use of this standard may cause the uncertainty of the calculated volume to exceed the uncertainty based on existing data by a factor of 2.

7. Sampling and sample preparation

Not provided in the available source.

8. Analysis procedure

8.1 Calculation program (5.2)

Step 1: Initialize temperature (°C) T = XX.XX; −30.00 ≤ T ≤ 90.00, rounded to near 0.25°C:

• TT = INT(T) (truncated)
• DIF = T − TT
• If DIF ≥ 0 then SIGN = 1.0 else SIGN = −1.0
• DIFF = ABS(DIF) (absolute value)
• If DIFF ≤ 0.125 then T = TT
• If 0.125 ≤ DIFF < 0.375 then T = TT + 0.25×SIGN
• If 0.375 ≤ DIFF < 0.625 then T = TT + 0.50×SIGN (original text here has source-text extraction as 0.875/0.625, requires confirmation against the source standard (source-text extraction))
• If 0.625 ≤ DIFF < 0.875 then T = TT + 0.75×SIGN (original text has source-text extraction as 0.76, requires confirmation against the source standard (source-text extraction))
• If DIFF ≥ 0.875 then T = TT + 1.00×SIGN

Step 2: Initialize density (kg/m³) RHO = XXXX; 638 ≤ RHO ≤ 1074, rounded to 2:

• RHOH = INT(RHO/2.0)
• DIF = RHO − 2×RHOH
• If DIF ≥ 1.0 then RHO = 2 + 2×RHOH else RHO = 2×RHOH

Step 3: Calculate density (g/cm³) and the square of density

• RHO = RHO×0.001
• RHOSQR = RHO×RHO = X.XXXXX, rounded to 0.00001: RHOSQR = INT(RHOSQR×100000.0 + 0.5)×0.00001

Step 4: Calculate compressibility factor F = EXP(−1.62080 + 0.00021592×T + 0.87096/RHOSQR + 0.0042092×T/RHOSQR) Round each term to 0.00001:

• If T < 0 then SIGN = −1.0 else SIGN = 1.0
• TERM1 = −1.62080
• TERM2 = INT(21.592×T + 0.5×SIGN)×0.00001
• TERM3 = INT(87096.0/RHOSQR + 0.5)×0.00001
• TERM4 = INT(420.92×T/RHOSQR + 0.5×SIGN)×0.00001
• F = EXP(TERM1 + TERM2 + TERM3 + TERM4) = X.XXXX
• Then round F to 0.001: F = INT(F×1000.0 + 0.5)×0.001
• The rounded F is the value in the compressibility factor table.
• INT The function returns an integer by discarding all digits to the right of the decimal point; the exponential function EXP must return a result accurate to 0.0001.

8.2 Table Lookup Method

• Refer to Appendix A (look up the table using density at 15°C, round temperature to 0.25°C, round density to 2 kg/m³).
• Alternatively, refer to Appendix B (look up the table using density at 20°C, round temperature to 0.25°C, round density to 0.1 kg/m³).
• Appendix B boundary density and table lookup orientation annotation meanings:
  • “XXX.X” represents the boundary density; “||” represents the midpoint between adjacent densities; “→” represents the density orientation for table lookup.
  • “[XXX.X]→” indicates that when the lookup density is greater than or equal to the boundary density on the left side of the midpoint, the right-side density is used for table lookup.
  • “[||XXX.X]→” indicates that when the lookup density is greater than or equal to the boundary density on the right side of the midpoint, the right-side density is used for table lookup.
  • “[||]→” indicates that when the lookup density is greater than or equal to the midpoint, the right-side density is used for table lookup; otherwise, the left-side density is used for table lookup.
  • “←” indicates that when the lookup density lies between two adjacent densities, the left-side density is used for table lookup.

8.3 Application Examples (Chapter 4)

Example 1: For fuel oil with density 933.6 kg/m³ at 15°C, pressure 3450 kPa, temperature 37.85°C, metered volume 1000 m³, assuming pe = 0 kPa. After rounding density and temperature to 934 kg/m³ and 37.75°C, looking up Appendix A gives F = 0.649×10⁻⁶. Vb = 1000/(1 − 0.000000649×3450) = 1002.2 m³. Example 2: For crude oil with density 927.1 kg/m³ at 20°C, pressure 1450 kPa, temperature 41.35°C, metered volume 1000 m³, assuming pe = 0 kPa.

• Method One: Look up Petroleum Measurement Tables (crude oil section) Table E.1, from density 927.1 kg/m³ at 20°C obtain density 930.1 kg/m³ at 15°C, after rounding density and temperature to 930 kg/m³ and 41.25°C, looking up Appendix A gives F = 0.668×10⁻⁶.
• Method Two: Round density to 0.1 kg/m³ as 927.1 kg/m³, round temperature to 0.25°C as 41.25°C, directly look up Appendix B using density 927.1 kg/m³ at 20°C and temperature 41.25°C, density lies between 926 kg/m³ and 928 kg/m³, according to the annotation “[||XXX.7]→”, boundary density 927.7 kg/m³, lookup density 927.1 kg/m³ is less than the boundary density, use the left-side density 926 kg/m³ for table lookup, obtaining F = 0.668×10⁻⁶.
• Vb = 1000/(1 − 0.000000668×1450) = 1001.0 m³.
• Other examples and more details can be found in GB/T 9109.5 or ISO 4267-2.

9. Qualitative and Quantitative and Calculation Formulas

• Volume correction formula: Vb = Vm / [1 − F(pm − pe)] Where: F is the compressibility factor (from table lookup or calculation), unit kPa⁻¹; pe is the equilibrium pressure of the liquid at the metering temperature (gauge pressure), kPa; pm is the metering pressure of the liquid (gauge pressure), kPa; Vb is the volume at equilibrium pressure pe; Vm is the volume at metering pressure pm.
• Note 1: When the saturated vapor pressure of crude oil and petroleum products at the metering temperature is not greater than atmospheric pressure, the equilibrium pressure is the pressure specified by the reference conditions for petroleum liquid and gas metering 101.32 kPa, in which case the equilibrium pressure expressed as gauge pressure pe equals zero; otherwise, it is the saturated vapor pressure of crude oil and petroleum products at the metering temperature.
• Note 2: The compressibility factor table for density lookup at 20°C provides boundary densities and table lookup orientation annotations, with rules as given in 8.2.
• Mathematical model: F = EXP(A + B×T + C/P' + D×T/p) (Formula 2).
• Calculation program formula: F = EXP(−1.62080 + 0.00021592×T + 0.87096/RHOSQR + 0.0042092×T/RHOSQR).

10. Precision

• Using Formula (2) and the basic data, the maximum uncertainty of the compressibility factor is 6.5%, with a confidence level of 95%; in the worst case, the actual compressibility factor of a given substance may be higher by 6.5% or lower by 6.5% compared to the standard value. This uncertainty is only valid within the range of the basic data and may not be correct in extrapolated regions.
• Volume uncertainty analysis (Table 2):
  • Only correlation uncertainty (Algorithm A): For average compressibility 1.45×10⁻⁶ kPa⁻¹, at 3447 kPa it is 0.03%, at 6895 kPa it is 0.07%, at 10342 kPa it is 0.10%; for average compressibility 0.87×10⁻⁶ kPa⁻¹, at 3447 kPa it is 0.02%, at 6895 kPa it is 0.04%, at 10342 kPa it is 0.06%.
  • Correlation uncertainty + pressure uncertainty (Algorithm A+B): At 3447 kPa it is 0.05%, at 6895 kPa it is 0.12%, at 10342 kPa it is 0.21% (corresponding to 1.45×10⁻⁶ kPa⁻¹); at 3447 kPa it is 0.03%, at 6895 kPa it is 0.08%, at 10342 kPa it is 0.13% (corresponding to 0.87×10⁻⁶ kPa⁻¹).
  • The predicted value of the average compressibility correlation uncertainty is 6.5%; the average compressibility uncertainty due to pressure effects is 0.00073%/kPa.
  • Table 2 footnote: Typical compressibility factor values for jet fuel with density 720 kg/m³ at 15°C under 38°C, or for fuel oil with density 800 kg/m³ at 15°C under 93°C; typical compressibility factor values for gasoline with density 738 kg/m³ at 15°C under −7°C, or for crude oil with density 850 kg/m³ at 15°C under 38°C.
• The uncertainty of the measured volume depends on the operating conditions (Table 2, Algorithm A), should be within the range 0.02%~0.10%, and comply with the maximum uncertainty of 0.10% recommended in the reports of COSM and COPM.
• After combining the correlation uncertainty and possible pressure uncertainty, the volume uncertainty is within the range 0.03%~0.21% (Table 2, Algorithm A+B).

11. Report

not provided in the available source.

12. Normative References

• GB/T 1885—1998 Petroleum Measurement Tables
• GB/T 9109.5—1988 Dynamic Measurement of Crude Oil—Oil Quantity Calculation
• ISO 4267-2:1988 Petroleum and liquid petroleum products—Calculation of oil quantities—Part 2: Dynamic measurement
• References: [1] Jacobson, E. W., Ambrosius, E. E., Dashiell, J. W., and Crawford, C. L. "Second Progress Report on Study of Existing Data on Compressibility of Liquid Hydrocarbons," Report of the Central Committee on Pipe-Line Transportation, Vol. 2(1), p. 39-45, American Petroleum Institute, Washington, D.C., 1945. [2] Jessup, R. S., "Compressibility and Thermal Expansion of Petroleum Oils in the Range 0°C to 300°C," Bureau of Standards Journal of Research, Vol. 5, July to December 1930, p. 985-1039, National Bureau of Standards, Washington, D.C. [3] Downer, L., and Gardiner, K. E. S. "Bulk Oil Measurement Compressibility Measurements on Crude Oils Deviations from API Standard 1101," BP Research Centre Report No. 20587/M (8 pages), October 28, 1970. [4] Downer, L. "Bulk Oil Measurement Compressibility Data on Crude Oils and Petroleum Products Viewed as a Basis for Revised International Tables (API Standard 1101 Tables)," BP Research Centre Report No. 20639 (21 pages), January 17, 1972. [5] GB/T 9109.5—1988 Dynamic measurement of crude oil — Oil quantity calculation [6] ISO 4267-2:1988 Petroleum and liquid petroleum products—Calculation of oil quantities—Part 2: Dynamic measurement

13. Source and verification

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14. Quick Q&A Reference