This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API of API committee activities except with the approval of the of the Chairman of the of the committee having jurisdiction. Copyright API. All rights reserved
Manual of Petroleum Measurement Standards Chapter 11—Physical Properties Data
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Section 4—Properties of Reference Materials
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Part 1—Density of Water Water and Water Water Volumetric Correction Factors for Water Calibration of Volumetric Provers SECOND EDITION, 2016
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This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction. Copyright API. All rights reserved
CONTENTS Page 1
Introduction ......................................................................................................................... 1
2
Scope ..................................................................................................................................... 1
3
References ............................................................................................................................ 1
4
Definitions ............................................................................................................................ 1
5
Significance and Use .................................................................................................. 2
6
Implementation Procedures .............................................................................................. 2 Representative Density Values ........................................................................2 6.1 Absolute Density of Water ............................................................................... 3 6.2 Correction for Temperature on Water (CTL) .................................................. 3 6.3 6.4 Correction for Pressure on Water (CPL).......................................................4 Flowing Density (ρtp) ........................................................................................4 6.5 CTDW Correction Factor for Volumetric Provers .......................................... 5 6.6 6.7 Other Influence Factors on Water Density .................................................... 5
7
Discrimination ..................................................................................................................... 6
8
Examples .............................................................................................................................. 6 Water Density (USC Units) ............................................................................. 6 8.1 8.2 CTDW (USC Units).......................................................................................... 6 8.3 Water Density (SI Units) ................................................................................. 6 CTDW (SI Units) ..................................................................................................... 6 8.4
Annex A (Informative) Representative Density Values .................................................. 7 Annex B (Informative) Reference Standard Water......................................................... 9 Annex C (Informative) Basis for Water Density Equation Selection ........................... 10 Tables 1 Significant Digits ................................................................................................. 6
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This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction. Copyright API. All rights reserved
Chapter 11—Physical Properties Data Section 4—Properties of Reference Materials Part 1—Density of Water and Water Volumetric Correction Factors for Water Calibration of Volumetric Provers 1
Introduction This Standard specifies the density of water equation to be used in all applicable API MPMS Standards. It also specifies the volume correction factor equation for water and demonstrates its use for water calibration of provers and pycnometers.
2
Scope This Standard is applicable to all API Standards that use the density of water or its volume correction factors.
3
References The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. 1.) API MPMS Chapter 11.5 – 2009 (All parts), Density/Weight/Volume Intraconversions. 2.) H. Wagenbreth and H. Blanke, “The Density of Water in the International System of Units and in the International Practical Temperature Scale of 1968”, Mitteilungen der Physikalish-Technischen Bunde- sanstalt (PTB–Mitt), 412-415, June 1971. 3.) G.S. Kell, Journal of Chemical Engineering Data, 1967, 12,66-69;ibid,1975,20, 97-105. 4.) N. Bignell, “The Effect of Dissolved Air on the Density of Water”, Metrologia,1983,19,57-59. 5.) J.B. Patterson and E.C. Morris, “Measurement of Absolute Water Density”, Metrologia, 31, 277-288, 1994. 6.) M. Tanaka, G. Girard, R. Davis, A. Peuto and N. Bignell, “Recommended table for the density of water between 0 °C and 40 °C based on recent experimental reports”, Metrologia, 38, 301-309, 2001. 7.) W. Wagner and A Pruss, “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General Scientific Use”, Journal of Physical and Chemical Reference Data, 31, 2, 387-535, 2002. 8.) World Health Organization, Guidelines for Drinking-water Quality, 4th Edition, 2011. 9.) ASTM D1193 – 20061, Specification for Reagent Water.
4
Definitions 4.1 density, absolute The mass of a substance per unit of volume at a specified temperature and pressure.
NOTE 1
Absolute density is sometimes referred to as “true density”, “density”, “mass density” or as “density in vacuo.”
When reporting density, the reference conditions must be stated. In practice, the pressure, if not explicitly stated, is NOTE 2 assumed to be standard pressure.
1
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4.2 correction for temperature on liquid CTL Volume correction for the effect of temperature on the density of a liquid.
NOTE The CTL is defined as the ratio of the absolute density at specified temperature and reference pressure divided by the absolute density at reference temperature and pressure. 4.3 correction for pressure on liquid CPL Volume correction for the compressibility effect of pressure on the density of a liquid.
4.4 correction for temperature and pressure on liquid CTPL Volume correction for the effect of temperature and pressure on the density of a liquid (CTPL = CTL × CPL).
5
Significance and Use A prior standard (API MPMS 11.2.3, 1984), which the first edition of this Standard replaced, was based on the internationally accepted work of Wagenbreth and Blanke, which produced a density of 999.012 kg/m3 at 15.5556 °C (60 °F) and 101.325 kPa (14.696 psia). In 1994, Patterson and Morris published a paper proposing a new equation based on their laboratory data of VSMOW (see Annex B), which was accepted by the USA’s National Institute of Standards and Technology (NIST). This Standard, based on the Patterson and Morris work, is applicable between 1 °C and 40 °C (33.8 °F and 104 °F), at standard pressure; 101.325 kPa (14.696 psia). This Standard also provides an equation for the compressibility of water based on a compressibility equation contained in a 2001 Tanaka paper. The range of applicability is for gauge pressures of 0 kPa to 10,000 kPa (0 psig to 1450 psig) for water temperatures between 1 °C and 40 °C (33.8 °F and 104 °F). Specific applications include:
determination of base prover volumes (BPV)
determination of pycnometer base volumes (PBV)
conversions between liquid density units
calculation of water content based on fluid and water density
6
Implementation Procedures
6.1
Representative Density Values Representative density values are presented, at standard pressure [101.325 kPa (14.696 psia)], for U.S. customary (USC) and International System of Units (SI) units in Annex A for calculation verification purposes.
6.2
Absolute Density of Water This Standard is based on the Patterson and Morris work for water density at standard pressure, which is applicable for the temperature range 1 °C to 40 °C (33.8 °F to 104 °F). The following equation expresses the density of water, at standard pressure [101.325 kPa (14.696 psia)], as a function of temperature in degrees Celsius (°C): ρt
2
3
4
5
ρ 0 [1 ( A t B t C t D t E t )]
(1)
Where: t
=
density at temperature t and 101.325 kPa, in kg/m3
0
=
density at temperature t 0, 999.973 58 kg/m3
t
=
t – t 0
t
=
temperature, in °C
t 0
=
3.9818 °C
A
=
7.0134 × 10-8
B
=
7.926 504 × 10-6
C
=
-7.575 677 × 10-8
D
=
7.314 894 × 10-10
E
=
-3.596 458 × 10-12
For temperatures in degrees Fahrenheit (°F), calculate
t
(F 32 ) 1 .8
t 0
Where: °F =
temperature, in °F
t in
the above equation using equation (2):
(2)
Equation 1 produces the following results:
Table 1 – Reference Water Densities Description
SI
US Customary a
(kg/m3)
(lb/gal)
Symbol
Density at 60 °F (15.5556 °C)
ρw,60
999.016
8.337 19
Density at 15 °C (59 °F)
ρw,15
999.102
8.337 91
Density at 20 °C (68 °F)
ρw,20
998.206
8.330 43
NOTES: a.
The USC values were converted to pounds per gallon by multiplying by 0.008 345 404 452 (reference MPMS Chapter 11.5).
These values may be rounded further depending upon their ultimate use.
6.3
Correction for Temperature on Water (CTL) The liquid volume correction for temperature on water (CTL) with respect to a chosen reference temperature is the density at temperature t divided by the density of water at that reference temperature in consistent units of density. The CTL equation for water referenced to 60 °F (15.5556 °C) is:
CTL 60 F
ρ t
(3)
w , 60
The CTL equation for water referenced to 15 °C (59 °F) is:
CTL 15 C
ρ t
(4)
w,15
The CTL equation for water referenced to 20 °C (68 °F) is:
CTL 20 C 6.4
ρ t
(5)
w, 20
Correction for Pressure on Water (CPL) Equation 6 provides a correction for the effects of pressure on water. While it is effective at low pressures, at pressures of 800 kPa or so, the calculated value will exhibit biases relative to accepted water property predictive equations such as those provided by the International Association for the Properties of Water and Steam that are noticeable within the discrimination identified for CPL in Table 2. CPL is also affected by water temperature. The given equation is effective in the range of 0 °C to 40 °C (32 °F to 104 °F). Beyond these limits of pressure and temperature, the provided CPL calculation uncertainty and/or bias increases significantly and may not meet metrological requirements. The density of deaerated water has been given at an absolute pressure of 101.325 kPa (14.696 psia). Water is slightly compressible, so a correction must be made for pressures other than standard pressure.
Based on the work by Tanaka, the density at standard pressure should be multiplied by the equation for compressibility of water (CPL):
CPL 1 F p 1 (k 0 k 1t k 2 t 2 ) p
(6)
Where, in SI units: F
=
water compressibility factor in kPa-1
p =
p p std
p
absolute pressure in kilopascals (kPa)
=
p std =
standard pressure of 101.325 kPa
k 0
=
5.074 × 10
k 1
=
-3.26 × 10
k 2
=
4.16 × 10
t
=
temperature in C
-7
-9
-11
For USC units, perform the following conversions: For temperatures in degrees Fahrenheit (°F), calculate t in the above equation using equation (7):
t
(F 32 )
(7)
1 .8
Where: °F =
temperature in °F
For pressures in pounds per square inch (psia), calculate p in the above equation using equation (8):
p psia 6.894 757
(8)
Where: psia = absolute pressure in pounds per square inch (psia)
6.5
Correction for Temperature and Pressure on Liquid (CTPL) The combined correction for temperature and pressure on the density of water shall be calculated using the following equations:
CTPL
t
1 F p
w,ref
Where: ρt
= density as obtained using Equation 1
ρw,ref = density as obtained from Table 1
F
= water compressibility factor in kPa -1 as shown in Equation 6
(9)
CTPL is equivalent to the product of CTL and CPL without any intermediate rounding applied to the two factors.
6.6
Flowing Density (ρtp) The flowing density of water shall be calculated using one of the following equations: ρ tp
ρ b CTPL
(10)
ρ tp
ρ t CPL
(11)
Where: ρtp
= flowing density at t and p in kg/m3
ρb
= density at reference temperature and pressure in kg/m3
ρt
= density at t and 101.325 kPa (14.696 psia) in kg/m3
CTPL = Correction for Temperature and Pressure on Liquid CPL = Correction for Pressure on Liquid
6.7
CTDW Correction Factor for Volumetric Provers For waterdraw calibrations of volumetric provers, a Correction for the Temperature Difference of W ater (CTDW) between the test measure and the prover at 101.325 kPa (14.696 psia) is utilized. The CTDW is calculated as follows:
CTDW
ρ tm ρ p
(12)
Where: CTDW
=
Correction for the Effect of the Difference in Temperature of the Water between the Prover and the Test Measure during the Prover Calibration
tm
=
water density in the test measure at T tm and 101.325 kPa (14.696 psia)
p
=
water density in the prover at T p and 101.325 kPa (14.696 psia)
The densities tm and p are calculated from equation (1).
6.8 6.8.1
Other Influence Factors on Water Density Overview Besides pressure and temperature, the density of water is impacted by many other factors, not all of which are taken into account in typical petroleum industry applications. A brief discussion of the influence factors is given in the following paragraphs.
6.8.2
Water Aeration For petroleum industry applications, the impact of water aeration is assumed to be insignificant, or is controlled by defined procedures for water handling within the application.
6.8.3
Water Quality For petroleum industry applications, potable water is usually presumed to be acceptable unless indicated otherwise for the specific application. The World Health Organization Guidelines for Drinking-water Quality provides guidance on all aspects of potable water. For applications requiring more control, ASTM defines specifications for reagent water used in a laboratory environment in ASTM D1193. In developing water density equations, Vienna Standard Mean Ocean Water (VSMOW) may be referenced (See Annex B).
6.8.3.1
Isotopes While it is commonly accepted that water consists of only H 2O, in fact it also contains several related isotopes such as deuterium (heavy water). The isotopic composition varies around the world and has a small impact on water density. Variability of isotopic composition is not considered significant for petroleum industry applications.
6.8.3.2
Dissolved and Suspended Materials Salts and minerals can be dissolved in water and sediments can be suspended in unfiltered water. The presence of these materials has a significant impact on the density. For example, fresh water (potable water) has a density of approximately 1000 kg/m 3 at room temperature, while produced saltwater and seawater can have densities of 1150 kg/m 3 or more. For this reason, it is important to make use of potable water or water with more stringent specifications for petroleum industry applications to minimize the bias errors associated with dissolved and suspended materials.
7
Discrimination The number of significant figures for various terms is presented in Table 1. Discrimination for the input parameters for this standard, temperature and pressure, are defined by calculation standards in Chapter 12. For other applications, the discriminations in Table 1 may be appropriate. When the figure to the right of the last place to be retained is less than 5, the figure in the last place retained should be unchanged.
Table 2 – Significant Digits Term
Units
No. of Decimals
CPL CTL CTPL CTDW ρb
– – – – 3 kg/m 3 kg/m
X.xxx xxx X.xxx xxx X.xxx xxx X.xxx xxx XXXX.xxx XXXX.xxx
t ρtp T T P P F
8
Examples
8.1
Water Density (USC Units)
3
kg/m °F °C psi kPa -1 kPa
XXXX.xxx XXX.x XX.x5 XXX.0 XXX.0 0.xxx xxx xxx
Water is at a temperature of 78.0 °F and a pressure of 284.0 psig. The observed barometric pressure was 13.696 psia. What is the water density?
The density may be calculated using the method shown in equations (10) or (11). Using equations 10, 1, 2, 3, 6, 7, 8, a reference temperature (T b) of 60.0 °F, and, the appropriate rounding requirements stated in Table 2 the density is calculated as shown below: 3
ρtp = ρw,60 kg/m
× CTPL = X XXX.xxx kg/m3
T b = (°F – 32)/1.8 = XX.x5 °C t = (°F – 32)/1.8 = XX.x5 °C p = (psig + barometric pressure psia) × 6.894 757 = unrounded kPa Δ p = p – 101.325 kPa = X XXX.0 kPa
CTL = ρt / ρw,60 = X.xxx xxx F = 1 + (k 0 +k 1t + k 2t 2) = 0.xxx xxx xxx kPa-1 CPL = 1 + F Δ p = 1.xxx xxx CTPL = ρt / ρw,60 (1 + F Δ p) = X.xxx xxx Solving, t = 25.55 °C p = (284.0 psig + 13.696 psia) × 6.894 757 = 2052.541 579 kPa Δ p = 2052.541 579 – 101.325 = 1951.0 kPa ρt =
996.903 kg/m3
CTL = 996.903 / 999.016 = 0.997 885 F = 4.51 × 10-7 kPa-1 CPL = 1.000 880 CTPL = 0.998 763 ρtp =
999.016 kg/m3 × 0.998 763 = 997.780 kg/m 3
Alternately, using equation 11, the above results and appropriate rounding requirements stated in Table 2 the density is calculated as shown below: ρtp = ρt ×
CPL = X XXX.xxx kg/m 3
Solving, t = 25.55 °C Δ p = 1,951.0 kPa ρt =
996.903 kg/m3
F = 4.51 × 10-7 kPa-1 CPL = 1.000 880 ρtp = ρt ×
8.2
CPL = 997.780 kg/m3
CTDW (USC Units) During a waterdraw, the water in the prover is 80.7 °F and the water in a field standard test measure is 83.0 °F. What is the CTDW value? The CTDW term is calculated using equations 12, 1, 7, and, the appropriate rounding requirements stated in Table 2 as shown below: CTDW = ρtm / ρ p = X.xxx xxx t tm = (°F – 32)/1.8 = XX.x5 °C t p = (°F – 32)/1.8 = XX.x5 °C ρtm = ρ p =
X XXX.xxx kg/m3
X XXX.xxx kg/m3
Solving, t tm = 28.35 °C t p = 27.05 °C ρtm =
ρ p =
996.134 kg/m3
999.500 kg/m3
CTDW = 0.999 633
8.3
Water Density (SI Units) Water is at a temperature of 12.00 °C and a gauge pressure of 1405.0 kPa. The observed barometric pressure was 96.325 kPa. What is the water density? The density may be calculated using the method shown in equation 10 or 11. Using equations 10, 1, 4, 6, a reference temperature (T b) of 15.00 °C, and the appropriate rounding requirements stated in Table 2 the density is calculated as shown below: 3
ρtp = ρw,15 kg/m
× CTPL = X XXX.xxx kg/m3
t = XX.x5 °C p = kPa gauge + barometric pressure kPa = unrounded kPa Δ p = p – 101.325 kPa = X XXX.0 kPa
CTL = ρt / ρw,15 = X.xxx xxx F = 1 + (k 0 +k 1t + k 2t 2) = 0.xxx xxx xxx kPa-1 CPL = 1 + F Δ p = 1.xxx xxx CTPL = ρt / ρw,15 (1 + F Δ p) = X.xxx xxx Solving, t = 12.00 °C p = 1405.0 kPa gauge + 96.325 kPa = 1501.325 kPa Δ p = 1501.325 – 101.325 = 1400.0 kPa ρt =
999.500 kg/m3
CTL = 999.500 / 999.102 = 1.000 398 F = 4.743 × 10 -7 kPa-1 CPL = 1.000 664 CTPL = 1.001 063 ρtp =
999.102 kg/m3 × 1.001 063 = 1000.164 kg/m3
Alternately, using equation 11, the above results and appropriate rounding requirements stated in Table 2 the density is calculated as shown below: ρtp = ρt ×
CPL = X XXX.xxx kg/m 3
Solving, t = 12.00 °C Δ p = 1400.0 kPa ρt =
999.500 kg/m3
F = 44.743 × 10 -7 kPa-1 CPL = 1.000 664 ρtp = ρt ×
8.4
CPL = 1000.164 kg/m3
CTDW (SI Units) During a waterdraw, the water in the prover is 19.00 °C and the water in a field standard test measure is 18.40 °C. What is the value of CTDW? The CTDW term is calculated using equations 12, 1, and the appropriate rounding requirements stated in Table 2 as shown below: CTDW = ρtm / ρ p = X.xxx xxx
ρtm = ρ p =
X XXX.xxx kg/m3
X XXX.xxx kg/m3
Solving, t tm = 18.40 °C t p = 19.00 °C ρtm =
ρ p =
998.523 kg/m3
998.407 kg/m3
CTDW = 1.000 116
ANNEX A (Informative) Representative Density Values (°F Increments) °F
°C
kg/m3
°F
°C
kg/m3
33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
0.6 1.1 1.7 2.2 2.8 3.3 3.9 4.4 5.0 5.6 6.1 6.7 7.2 7.8 8.3 8.9 9.4 10.0 10.6 11.1 11.7 12.2 12.8 13.3 13.9 14.4 15.0 15.6 16.1 16.7 17.2 17.8 18.3 18.9 19.4 20.0
999.878 999.907 999.930 999.949 999.962 999.970 999.974 999.972 999.965 999.954 999.938 999.918 999.893 999.863 999.829 999.791 999.748 999.702 999.651 999.596 999.537 999.474 999.407 999.336 999.262 999.184 999.102 999.016 998.927 998.834 998.738 998.638 998.535 998.429 998.319 998.206
69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104
20.6 21.1 21.7 22.2 22.8 23.3 23.9 24.4 25.0 25.6 26.1 26.7 27.2 27.8 28.3 28.9 29.4 30.0 30.6 31.1 31.7 32.2 32.8 33.3 33.9 34.4 35.0 35.6 36.1 36.7 37.2 37.8 38.3 38.9 39.4 40.0
998.089 997.970 997.847 997.721 997.592 997.460 997.325 997.187 997.046 996.902 996.755 996.605 996.453 996.297 996.139 995.978 995.814 995.648 995.479 995.307 995.133 994.956 994.776 994.594 994.409 994.222 994.032 993.840 993.645 993.448 993.249 993.047 992.842 992.635 992.426 992.215
(°C Increments) °C
°F
kg/m3
°C
°F
kg/m3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
33.8 35.6 37.4 39.2 41.0 42.8 44.6 46.4 48.2 50.0 51.8 53.6 55.4 57.2 59.0 60.8 62.6 64.4 66.2 68.0
999.901 999.942 999.966 999.974 999.965 999.942 999.903 999.850 999.783 999.702 999.607 999.500 999.379 999.247 999.102 998.945 998.777 998.597 998.407 998.206
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
69.8 71.6 73.4 75.2 77.0 78.8 80.6 82.4 84.2 86.0 87.8 89.6 91.4 93.2 95.0 96.8 98.6 100.4 102.2 104.0
997.994 997.772 997.540 997.298 997.046 996.785 996.514 996.234 995.946 995.648 995.342 995.027 994.704 994.372 994.032 993.684 993.329 992.965 992.594 992.215
ANNEX B (Informative) Reference Standard Water The Patterson & Morris equation (1) is based on the isotopic composition of Vienna Standard Mean Ocean Water (VSMOW). VSMOW is so named because it is distributed by the International Atomic Energy Agency (IAEA) headquartered in Vienna . It should be noted that water obtained from other sources does not have the same isotopic composition and thus has slightly different densities. Evaporation or distillation shifts the isotopic composition as molecules with heavier isotopes of hydrogen and/or oxygen have slightly higher boiling points. Conversely, rain or snow tends to slightly concentrate molecules with the heavier isotopes, leaving more of the lighter molecules in the air. The result is that fresh water varies widely in isotopic composition around the earth. However, the isotopic composition of deep ocean water is reasonably constant everywhere. VSMOW is expensive and of limited availability. Current commercially available densitometers using water as a reference density standard are not sensitive enough to measure the density difference between distilled fresh water and VSMOW.
ANNEX C (Informative) Basis for Water Density Equation Selection The Patterson equation has a 1 sigma(σ)uncertainty of ±0.00064 kg/m3 at 60 °F. Listing the density at 60 °F and those equivalent to plus or minus one σ, each rounded to 3 places past the decimal, provides: 999.01666 999.017 999.01602 999.016 999.01538 999.015
Likewise, the Tanaka equation has a 1 sigma (σ)uncertainty of ± 0.00083 kg/m3 at 15.5556 °C (60 °F). This means that the calculated density of water of 999.01692 kg/m3 most likely lies between 999.01775 and 999.01609. Listing the values, each rounded to 3 places past the decimal, provides: 999.01775 999.018 999.01692 999.017 999.01609 999.016
The Wagner and Pruss equation has a 1 sigma(σ)uncertainty of ±0.000999 kg/m3 at 15.5556 °C (60 °F). Listing the values, each rounded to 3 places past the decimal, provides: 999.01808 999.018 999.01708 999.017 999.01608 999.016
When compared at reference temperature, the results of the three equations are within the experimental uncertainty of 0.001 kg/m 3. The difference is for all practical purposes insignificant. Thus, API has elected to use the Patterson & Morris equation until it can be shown that the prediction of the true density of water does not lie within the experimental uncertainty of the chosen equation.
