comparison of calculation standards of ngl and lpg

02.02.2009

BCP 10A / BCG 10A

Temperature

corrections for NGL &

LPG

An analysis of different

standards used for calculations

of NGL and LPG volumes -

comparison with GPA TP-27

Comparison of calculation standards for NGL & LPG 2/

Notes:

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Contents

BCP 10A / BCG 10A ..................................................................................................................... 1

TEMPERATURE CORRECTIONS FOR NGL & LPG ................................................................... 1

Notes: ............................................................................................................................... 2

Contents ........................................................................................................................... 3

Introduction ....................................................................................................................... 5

1. Types of calculations .................................................................................................... 6

1.1. Calculation of an appropriate base density .................................................. 6

1.2. Calculation of a CTL factor............................................................................. 6

2. Standards currently in use ............................................................................................ 7

2.1. GPA Technical Publication TP-27 ................................................................ 7

2.2. Petroleum Measurement Tables, ASTM D 1250-80 .................................... 7

2.3. Petroleum Measurement Tables 33 and 34, ASTM D 1250-80 Volume XII. 9

3. Comparison between standards ................................................................................. 10

3.1. Ranges and accuracy/rounding of the standards ....................................... 10

3.2. Statistics of the comparison ........................................................................ 13

3.3. Analysis of the comparison statistics .......................................................... 13

3.4. Dependencies between density, temperature and accuracy ..................... 14

4. Conclusion .................................................................................................................. 15

The QuantityWare Recommendation: ............................................................... 15

5. References ................................................................................................................. 16

Appendix 1 ...................................................................................................................... 17


ASTM D 1250-80 table 23B against GPA TP-27 table 23E .............................. 17







Introduction

For custody transfer purposes, NGL (Natural Gas Liquid) and LPG (Liquefied Petroleum Gas)

measurements are stated at a fixed base temperature and saturation pressure; however most

volume transfers occur at temperatures and pressures other than the defined base conditions.

In these cases, such volumes must be adjusted to base conditions through the use of correction

factors. A full correction can be performed using a correction factor for temperature (CTL) and a

correction factor for pressure (CPL).

Different standards are used for the calculation of these factors.

Pressure correction factors are not within the scope of this paper, but can be calculated using

the American Petroleum Institute Manual of Petroleum Measurement Standards (MPMS)

Chapter 11.1-2004/2007.

This paper analyzes the ranges and limits of different standards for the calculation of CTL factors

as well as the density at base conditions, and compares the results against the most modern

available standard.


1. Types of calculations

Two types of calculations can be distinguished:

1.1. Calculation of an appropriate base density

The calculation of an appropriate base density, at the defined base temperature, relies on a

measured density, at an observed temperature. Such calculation procedures generally also

make use of CTL calculations (see chapter 1.2. herein).

In daily business, the base density is usually determined in a laboratory using a product sample,

instead of it being calculated separately for each business transaction using a standard’s tables

or procedures.

1.2. Calculation of a CTL factor

The calculation of a factor to correct the volume measured at any observed temperature to the

volume at basis temperature.

These tables and procedures are widely used in custody transfer processes.


2. Standards currently in use

Although NGL and LPG CTL can be calculated using a single modern standard f based on

equations for the base temperatures of:

- 60 degree Fahrenheit - 60°F

- 15 degree Celsius -15°C and

- 20 degree Celsius -20 °C,

Several historical standards are still in use, globally.

This paper provides an analysis of the most common, but superseded standards, and provides

a comparison of their calculated results against the standard currently recommended by the

relevant standards organization.

2.1. GPA Technical Publication TP-27

GPA TP-27 is the current and most accurate standard for CTL calculations, which are utilized for

volume quantity adjustments of NGL and LPG.

It was released in September 2007 and supersedes all other standards, including

GPA TP-25.

Similar to ASTM D 1250-04/07 the calculation procedures based on 15°C and 20°C are based

upon the 60°F procedures. This guaranties uniform, accurate results.

GPA TP-27 contains two pairs of procedures (still called “tables”) for the three supported base

temperatures:

- Tables 23E, 24E 60 °F / relative density

- Tables 53E, 54E 15 °C / density in kg/m3

- Tables 59E, 60E 20 °C / density in kg/m3

2.2. Petroleum Measurement Tables, ASTM D 1250-80

This standard clearly states that it is not to be used for NGL and LPG, however it contains

equations instead of printed tables and supports base temperatures of 60 °F and 15 °C. Later

extensions (tables 59 and 60) provide support for base temperatures of 20 °C. Tables 59 and

60 are modified versions of the of the 15 °C equations.


The following tables are still widely in use for calculations of NGL and LPG:

- Table 23B, 24B 60 °F / relative density

- Table 53B, 54B 15 °C / density in kg/m3

- Table 59B, 60B 20 °C / density in kg/m3

The letter B stands for the product type “refined products” (e.g. jet fuel, gasoline, heating oil).

Even the lowest densities of gasoline cannot support the densities required for NGL and LPG.

However, since this standard is based on equations and software implementations exist, it is

possible to extend the ranges by simply modifying the density and temperature range checks.

The QuantityWare BCP 10A solution allows such range changes to be made via solution-

specific “SAP customizing” (a process known and understandable by projects, business and

audit bodies), instead of forcing changes in source coding. As the QuantityWare solution is a

fully integrated SAP Certified Solution, if calculations take place in customised ranges, a

warning will appear in the application and also be stored in the appropriate material document.

However, as QuantityWare’s BCP 10A is a complete calculations solution, GPA TP-27 is

provided in the same package as the multiple ASTM D1250 implementations and should be

used for NGL and LPG calculations where possible.

Note that standard ASTM D 1250 has not been developed nor designed to

support calculations outside of the supported ranges required for NGL and

LPG. Accuracy cannot be guaranteed if ranges are extended. In this document

we will analyze and document the differences between ASTM D 1250 with

extended ranges and the GPA TP-27.

More information about ASTM D 1250-80 can be found here:

http://www.quantityware.com/_data/ASTM_D_1250_-

__Historical_and_technical_overview_v3.pdf

The impact on business processes by using the ASTM D 1250-80 standard with extended

ranges has been analyzed in the following document:

QuantityWare Case Study: LPG measurement standard selection

http://www.quantityware.com/_data/ASTM_D_1250_-__Historical_and_technical_overview_v3.pdf

http://www.quantityware.com/_data/ASTM_D_1250_-__Historical_and_technical_overview_v3.pdf


2.3. Petroleum Measurement Tables 33 and 34, ASTM D 1250-80 Volume XII

These are printed tables which were released as part of ASTM D1250 in 1952.

The values are taken from the historic tables 23 and 24.

Table 33 and 34 support a base temperature of 60 °F and relative density values.

They were developed over a half-a-century ago for the convenience of the American liquefied

petroleum gas and natural gasoline industries and are still in use owing to old agreements,

although technically superseded.


3. Comparison between standards

Since GPA TP-27 is the most modern, accurate and recommended standard for NGL and LPG

calculations, we will calculate data for the complete supported ranges of the superseded

standards, and compare the results against those of GPA TP-27.

3.1. Ranges and accuracy/rounding of the standards

The tables of GPA TP-27 support the widest ranges with the highest degree of accuracy.

Tables 33 and 34 are printed tables and have to be used as such. Interpolation of table 33 has

been defined in the standard and is used accordingly.

The values provided by those both tables are compared against GPA TP-27 results. A

comparison outside the ranges of tables 33 and 34 is not possible.

The ASTM D1250-80 tables are provided as equations. These tables can only be used for NGL

and LPG calculations when the temperature and density ranges have been extended. We will

compare the whole range of GPA TP-27 against the extended ranges of ASTM D 1250-80.

The table below shows the ranges and the accuracy/rounding of the standards compared:


Calculation based on 60 degree Fahrenheit:

Standard Temperature

(°F)

Temp.

increment

(°F)

Density (rel.) Dens.

increment

Rounding

/ accuracy

Calculate base density at 60 °F and relative density

GPA TP-27

table 23E -50.8 to 199.4 0.1

0.3500 to

0.6880 0.0001 0.0001

ASTM table 33 30 to 90 1 0.490 to 0.650 0.01

0.001 interp. 0.001

ASTM D1250-

80 table 23B 0 to 200 0.1

0.6535 to

1.0760 0.0005 0.0001

Calculate volume correction factors CTL (observed to 60 °F) and relative density

GPA TP-27

table 24 E

-50.8 to 199.4 0.1

0.3500 to

0.6880

0.0001 0.00001

ASTM table 34 -20 to 120 1 0.495 to 0.604 0.005 0.001

ASTM D1250-

80 table 24B 0 to 200 0.1

0.6535 to

0.7795 0.0005

0.00001

0.0001

Note: There are some gaps in the ranges of the ASTM tables 33 and 34. For more information,

please refer to the standards.


Calculation based on 15 degree Celsius:


(°C)

Temp.

increment

(°C)

Density

(kg/m3)

Dens.

increment

Rounding

/ accuracy

Calculate base density at 15 °C and density in kg/m3

GPA TP-27

table 53E -46 to 93 0.05 210.0 to 740.0 0. 1 0. 1

ASTM D1250-

80 table 53B -18 to 90 0.05 653.6 to 779.3 0. 5 0. 1

Calculate volume correction factors CTL observed to 15 °C at density in kg/m3

GPA TP-27

table 54E -46 to 93 0.05 352.1 to 688.5 0. 1 0. 1

ASTM D1250-

80 table 54B -18 to 95 0.05 653.6 to 778.8 0. 5 0. 1

Calculation based on 20 degree Celsius:


(°C)

Temp.

increment

(°C)

Density

(kg/m3)

Dens.

increment

Rounding

/ accuracy

Calculate base density at 15 °C and density in kg/m3

GPA TP-27

table 53E -46 to 93 0.05 210.0 to 740.0 0. 1 0. 1

ASTM D1250-

80 table 53B -18 to 90 0.05 653.6 to 779.3 0. 5 0. 1

Calculate volume correction factors CTL observed to 15 °C at density in kg/m3

GPA TP-27

table 54E -46 to 93 0.05 352.1 to 688.5 0. 1 0. 1

ASTM D1250-

80 table 54B -18 to 95 0.05 653.6 to 778.8 0. 5 0. 1


Note: There are some gaps in the ranges of the ASTM tables. For more information, refer to the

original standards documents. The density has been converted from kg/m3 to relative density for

comparability.

3.2. Statistics of the comparison

We compared all supported density and temperature pairs of the superseded standards used

for NGL and LPG calculations with the results of the corresponding tables of GPA TP-27.

The differences are calculated in percent. “Plus” means that the superseded table provide a

larger result than GPA TP-27 and “Minus” that the result of the superseded table is smaller than

that provided by GPA TP-27.

Table Compared

calls

Number

of

differences

Average

+% Max +%

Average

-% Max -%

tab33 9.521 8.501 0,0345 1,9865 0,0200- 0,2657-

tab34 1.551 1.539 0,0600 1,2720 0,0620- 0,4872-

tab23b 1.429.923 1.408.763 0,7049 17,4000 1,4178- 13,4701-

tab24b 1.516.179 1.514.218 1,8802 88,6814 1,1240- 11,4943-

tab53b 9.480.361 9.383.997 0,5872 16,9463 3,8485- 33,7464-

tab54b 8.373.033 8.362.456 1,9005 87,0966 1,0832- 11,2294-

tab59b 10.071.095 9.977.902 0.7228 22.0012 4.0414 34.2454

tab60b 8.680.842 8.670.623 1,7343 92,7909 1,4864- 13,5735-

3.3. Analysis of the comparison statistics

- Tables 33 and 34

The average differences of these printed tables are in a range that can generally be

accepted. If buyer and seller agree to the ranges, accuracy and intervals of the values,

these tables could still be used.

- ASTM D 1250-80, tables 23b, 24b, 53b and 54b

The average and maximum differences are in a range which we would not recommend

accepting in a custody transfer. Major differences start to appear when mainly the density

(but also the temperature) is outside of the supported ranges.


To decide whether these standards may be used or not, we must check the expected ranges

of density and temperature at which custody transfers can take place.

This will be done in the next chapter.

- ASTM D 1250-80, tables 58b and 60b

The results are similar to the tables 53b and 54b for 15 °C. However these tables are a

simple modification of the 15 °C equations and not a “soft conversion”; thus the differences

are slightly larger than at 15 °C.

3.4. Dependencies between density, temperature and accuracy

While tables 33 and 34 may still be acceptable, usage of the ASTM D 1250-80 tables tested

above may be critical - dependent on the pressure and temperature ranges being used.

- ASTM D 1250-80 all tables with extended ranges

In general, no differences should occur at the basis temperature, however when the

observed temperature is different from the basis temperature, considerable differences start

to emerge.

Lower density has a high impact on the accuracy of calculations when compared to TP-27

and the differences increase with increasing distance to the base temperature.

Thus the calculation using ASTM D 1250-80 will produce the biggest negative difference

(smaller values) at the lowest density and temperature, and the biggest positive difference at

the lowest density and highest temperatures.

In other words:

- Lower temperatures leads to lower results than GPA TP-27

- Higher temperatures leads to higher results than GPA TP-27

- These differences increases as the base density values decreases

We have made a general comparison over the entire ranges to show this density and

temperature dependent behaviour.

The results are listed in Appendix 1 of this document.


4. Conclusion

The values provided by ASTM tables 33 and 34 are similar to those calculated using GPA TP-

27; however the ranges supported by the tables are limited by density, temperature and printed

intervals. This analysis is already present in great detail in GPA TP-27.

As long as the provided values can coherently reflect the calculations needs of a specific

business, and buyer and seller agree, these tables can still be used and the parties can expect

to receive relatively realistic calculations results, if change to the new GPA TP-27 appears to

costly. However, as recommended by the relevant standards organizations, new computer

systems should use the most modern available standards.

The ASTM D 1250 tables can theoretically only be used for calculation of NGL and LPG when

their ranges are extended outside of the officially published limits to much lower densities and

lower temperatures.

The major issue when using ASTM D 1250 tables for NGL and LNG is that the calculations

inaccuracy increases, the farther density and temperature distance themselves from the original

standard ranges.

This is easily seen by studying the tables in Appendix 1.

The QuantityWare Recommendation:

Usage of ASTM tables 33 and 34 does not reflect the accuracy that one would expect in the 21st

century, but is still acceptable as long as the ranges are practicable for the business situation,

both business parties and regulatory bodies agree to the standards usage, and the wording of

existing contracts does not assume the usage of the latest available standards.

Usage of a “manipulated“ ASTM D 1250-80 standard is very difficult to justify because of the

inaccuracies in calculation and the existence of an alternate modern, proven standard .

Thus, “manipulated” ASTM D 1250-80 implementations should be replaced by usage of the

GPA TP-27.

More information about the impact on the custody transfer can be found here:

QuantityWare Case Study: LPG measurement standard selection


5. References

1. GPA Technical Publication TP-27.

2. Manual of Petroleum Measurement Standards, Chapter 11 – Physical Properties Data

Section 1 - Temperature and Pressure Volume Correction Factors for Generalized Crude Oils,

Refined Products, and Lubricating Oils, API 2004

3. Manual of Petroleum Measurement Standards Chapter 11.1, Volume X – Background.

4. ASTM D1250-80 Petroleum Measurement Tables, Volume XII, Tables 33 & 34.

5. ASTM D1250 – Historical Edition 1952

5. THE USE OF THE PETROLEUM MEASUREMENT TABLES – Manual of Petroleum

Measurement Standards, Chapter 11.1 (API Std. 2540, ASTM D1250, IP200, ISO 91-1), revised

October 1995, API 1995


Appendix 1

ASTM D 1250-80 table 23B against GPA TP-27 table 23E


Temperature (°F)

Rel. density 60 °F/60 °F

0.35 0.4 0.45 0.5 0.55 0.6 0.65

-58

-48 9.6232 4.621 1.9522 0.4421

-38 7.9832 3.9187 1.6072 0.3197

-28 6.7405 3.2426 1.2906 0.1998

-18 5.6613 2.6751 1.0557 0.1154

-8 10.3477 4.5361 2.1888 0.8449 0.0653

2 7.2718 3.5347 1.7787 0.675 0.0162

12 5.3815 2.7139 1.3222 0.4738 0

22 3.9216 2.0373 0.9575 0.3122 -0.0794

32 6.6048 2.7175 1.3877 0.6418 0.2059 -0.0787

42 3.312 1.6485 0.8462 0.3723 0.1188 -0.078

52 1.2847 0.6793 0.365 0.147 0.0504 -0.031

62 -0.678 -0.2732 -0.1549 -0.0797 -0.0363 -0.0166 0.0154

72 -3.205 -1.6133 -0.8873 -0.4707 -0.2149 -0.0329 0.061

82 -4.9948 -2.7602 -1.5261 -0.811 -0.354 -0.0653 0.121

92 -3.691 -2.0578 -1.0845 -0.4724 -0.097 0.1952

102 -7.7053 -4.4696 -2.5704 -1.3133 -0.571 -0.0961 0.2684

112 -8.893 -5.1923 -3.0254 -1.5544 -0.6335 -0.0477 0.3553

122 -9.7017 -5.8436 -3.4462 -1.7531 -0.6947 0.0158 0.4559

132 -10.4153 -6.371 -3.7231 -1.929 -0.738 0.0469 0.5405

142 -11.075 -6.8409 -3.9549 -2.1186 -0.7641 0.1086

152 -11.7087 -7.3132 -4.1808 -2.1999 -0.7897 0.1693

162 -12.1501 -7.7332 -4.4011 -2.2973 -0.815 0.2292

172 -12.6143 -7.9442 -4.5979 -2.3756 -0.8238 0.3186

182 -13.0625 -8.1504 -4.7903 -2.4191 -0.8165 0.4067

192 -13.3607 -8.3333 -4.9786 -2.4456 -0.7307 0.4936




Temperature (°F)

Relative density 60 °F/60 °F

0.35 0.4 0.45 0.5 0.55 0.6 0.65

-58

-48 -11.3834 -6.4912 -4.138 -2.4422 -1.1198 -0.2136 0.4398

-38 -10.9971 -6.2188 -3.9322 -2.3075 -1.0596 -0.1979 0.4159

-28 -10.5877 -5.916 -3.7082 -2.1675 -0.9866 -0.1857 0.3926

-18 -10.1281 -5.5835 -3.4695 -2.0201 -0.9177 -0.1761 0.3595

-8 -9.5991 -5.2122 -3.2031 -1.8542 -0.843 -0.1597 0.3184

2 -8.9857 -4.7907 -2.9118 -1.667 -0.7518 -0.145 0.2786

12 -8.2467 -4.2963 -2.5705 -1.4643 -0.6607 -0.131 0.2305

22 -7.3159 -3.7089 -2.1884 -1.2319 -0.5581 -0.1167 0.1855

32 -6.1362 -2.9951 -1.7354 -0.9646 -0.434 -0.0925 0.1341

42 -4.5736 -2.1359 -1.2076 -0.6674 -0.3032 -0.0658 0.0868

52 -2.4117 -1.0553 -0.5865 -0.3227 -0.1455 -0.0357 0.0348

62 0.751 0.303 0.1597 0.0873 0.0351 0.008 -0.013

72 5.9149 2.063 1.0631 0.5544 0.2499 0.0678 -0.0545

82 17.194 4.4178 2.1566 1.1098 0.4942 0.1248 -0.0977

92 7.7436 3.5226 1.7631 0.7727 0.2119 -0.1344

102 12.8596 5.2312 2.533 1.0925 0.3103 -0.1718

112 22.4255 7.4471 3.449 1.47 0.4227 -0.1983

122 10.4105 4.5612 1.9151 0.572 -0.2148

132 14.6063 5.9126 2.4289 0.7412 -0.2178

142 21.2176 7.5962 3.0353 0.9335 -0.2187

152 34.7524 9.737 3.7518 1.1744 -0.2035

162 12.5316 4.591 1.448 -0.1716

172 16.3886 5.5919 1.7607 -0.1314

182 22.2045 6.7986 2.1401 -0.0591

192 32.9599 8.268 2.5864 0.0248




Temp

°C

Density ( kg/m3)

210 260 310 360 410 460 510 560 610 660 710

-46 8.3928 4.0851 1.6333 0.2672 -0.5181

-41 7.2872 3.479 1.3571 0.1655 -0.5596

-36 6.3324 2.9766 1.124 0.0984 -0.5855

-31 13.8106 5.3662 2.5306 0.9503 0.0325 -0.5666

-26 9.4818 4.3713 2.1382 0.7627 0 -0.5332

-21 7.2699 3.5549 1.7171 0.5966 -0.048 -0.5002

-16 5.7071 2.8602 1.3662 0.4341 -0.1427 -0.4532

-11 4.4623 2.2776 1.0442 0.3266 -0.1573

-6 8.6648 3.4269 1.7155 0.7874 0.2213 -0.1561

-1 5.219 2.5122 1.2348 0.537 0.1349 -0.124

4 3.0737 1.5916 0.8104 0.3477 0.0836 -0.0923

9 1.4888 0.8014 0.439 0.181 0.0331 -0.0611

14 0.5609 0.2207 0.1309 0.0787 0.0179 0 -0.0152

19 -1.7468 -0.8835 -0.4711 -0.2327 -0.1062 -0.0163 0.0301

24 -3.4232 -1.8859 -1.0305 -0.5165 -0.2103 -0.0323 0.1048

29 -9.6343 -4.7715 -2.6849 -1.4885 -0.7554 -0.3122 -0.032 0.1785

34 -32.0353 -20.0822 -10.9239 -3.4283 -1.9117 -0.9698 -0.3779 0 0.2513

39 -32.0704 -20.7937 -12.112 -7.0362 -4.0776 -2.3219 -1.1609 -0.4425 0.0316 0.3232

44 -32.2239 -21.509 -13.1624 -7.9622 -4.6601 -2.7197 -1.3477 -0.4722 0.0783 0.4089

49 -32.4176 -22.2332 -14.132 -8.6584 -5.1825 -2.9543 -1.4944 -0.5348 0.1244

54 -32.7123 -22.9182 -15.0523 -9.2854 -5.6289 -3.2023 -1.6382 -0.5467 0.1699

59 -33.0204 -23.6266 -15.6009 -9.8877 -6.06 -3.4072 -1.7445 -0.5749 0.2455

64 -33.1581 -23.9782 -16.1276 -10.4272 -6.458 -3.6068 -1.8315 -0.5864 0.3048

69 -33.2516 -24.3183 -16.6739 -10.8574 -6.791 -3.8028 -1.8829 -0.5977 0.3634

74 -33.3769 -24.686 -17.1822 -11.2742 -6.988 -3.9759 -1.9504 -0.609 0.4362

79 -33.5389 -25.0635 -17.553 -11.6763 -7.1811 -4.1456 -1.9834 -0.5251 0.5232

84 -33.68 -25.3472 -17.9095 -12.0496 -7.3516 -4.3122 -1.9997 -0.474 0.6092

89 -25.6598 -18.309 -12.1918 -7.5377 -4.4076 -2.032 -0.4235 0.6941




Temperature (°C)

Density (kg/m3)

350 400 450 500 550 600 650

-46 -6.5046 -4.1467 -2.4485 -1.1209 -0.2124 0.4375

-36 -5.997 -3.7734 -2.2034 -1.0084 -0.1879 0.3972

-26 -5.3955 -3.3448 -1.9348 -0.8795 -0.1618 0.3389

-16 -4.6543 -2.8232 -1.6087 -0.7284 -0.1405 0.2647

-6 -3.665 -2.1675 -1.2145 -0.544 -0.11 0.1866

4 -2.2818 -1.2993 -0.7179 -0.325 -0.0746 0.1005

14 -0.2505 -0.1364 -0.0708 -0.0369 -0.007 0.009

24 2.9351 1.4864 0.7695 0.3381 0.0884 -0.0739

34 8.5672 3.8288 1.8984 0.8285 0.2238 -0.1429

44 22.2358 7.4175 3.4403 1.4658 0.4196 -0.2025

54 13.5418 5.5869 2.3128 0.6908 -0.2269

64 27.385 8.7565 3.4261 1.0588 -0.2178

74 13.789 4.9402 1.5486 -0.1668

84 23.4403 7.0076 2.1961 -0.0637




Temp.°C Density (kg/m3)

210 260 310 360 410 460 510 560 610 660 710

-46 10.0887 4.7599 1.8599 0.3202 -0.5831

-41 8.7494 4.0657 1.5961 0.2003 -0.6242

-36 7.631 3.4811 1.3204 0.1158 -0.6498

-31 18.385 6.4858 2.9988 1.1242 0.0656 -0.6303

-26 12.2705 5.3444 2.5523 0.9324 0.0163 -0.5962

-21 9.37 4.3959 2.0982 0.727 -0.0322 -0.5626

-16 7.4122 3.6243 1.6774 0.5438 -0.1438 -0.5149

-11 5.9207 2.9495 1.3274 0.3992 -0.1744

-6 13.1286 4.6921 2.2998 1.0253 0.2922 -0.1887

-1 7.9921 3.6004 1.7581 0.7687 0.2043 -0.1717

4 5.1053 2.5122 1.2557 0.537 0.1349 -0.1394

9 3.1274 1.6147 0.8308 0.3661 0.0836 -0.1077

14 4.0249 1.5653 0.8239 0.439 0.181 0.0331 -0.0611

19 0.5045 0.2453 0.1309 0.0787 0.0179 0 -0.0152

24 -1.7468 -0.9308 -0.4925 -0.2327 -0.1062 -0.0163 0.0452

29 -7.5143 -3.4733 -1.9088 -1.0305 -0.5165 -0.2103 -0.0323 0.1048

34 -31.3225 -18.6047 -9.4887 -2.7519 -1.5089 -0.7554 -0.2949 -0.016 0.1785

39 -31.7866 -19.8845 -11.0234 -6.2014 -3.4928 -1.9719 -0.9884 -0.3779 0.0318 0.2661

44 -32.1667 -20.8995 -12.3413 -7.2813 -4.1612 -2.4005 -1.1793 -0.4425 0.0473 0.3379

49 -32.5348 -21.8168 -13.5348 -8.0932 -4.7843 -2.7006 -1.3656 -0.489 0.094

54 -32.9186 -22.6824 -14.6156 -8.8268 -5.2841 -2.9738 -1.5302 -0.5181 0.14

59 -33.2932 -23.4845 -15.2829 -9.5091 -5.7467 -3.2215 -1.656 -0.5467 0.1854

64 -33.4971 -23.9489 -15.9014 -10.1465 -6.1943 -3.4444 -1.7448 -0.5586 0.2455

69 -33.6295 -24.3604 -16.4973 -10.6441 -6.5923 -3.6622 -1.8318 -0.6027 0.3201

74 -33.7997 -24.7792 -17.0695 -11.1065 -6.8119 -3.8568 -1.9002 -0.5978 0.3938

79 -33.9905 -25.2048 -17.4979 -11.5338 -7.0461 -4.0474 -1.9339 -0.5453 0.4665

84 -34.1587 -25.5534 -17.9126 -11.968 -7.2561 -4.2335 -1.9841 -0.4936 0.5384

89 -25.8923 -18.3516 -12.1481 -7.443 -4.3478 -2 -0.4584 0.6243




Temperature (°F)

Density (kg/m3)

350 400 450 500 550 600 650

-46 -11.0966 -6.7938 -4.2934 -2.564 -1.1502 -0.1821 0.5056

-41 -10.8128 -6.5768 -4.1317 -2.4575 -1.0995 -0.1643 0.4856

-36 -10.518 -6.3448 -3.9611 -2.3424 -1.048 -0.16 0.4645

-31 -10.1988 -6.0947 -3.7797 -2.2269 -0.9876 -0.152 0.4431

-26 -9.8536 -5.8281 -3.5852 -2.1014 -0.9335 -0.1485 0.4121

-21 -9.4566 -5.5241 -3.3639 -1.9627 -0.8684 -0.1393 0.3711

-16 -8.9929 -5.1746 -3.1218 -1.8095 -0.7994 -0.1338 0.3316

-11 -8.4509 -4.778 -2.8542 -1.6393 -0.7255 -0.1311 0.2925

-6 -7.7974 -4.3225 -2.5452 -1.4497 -0.6455 -0.1206 0.2452

-1 -6.9881 -3.7759 -2.1981 -1.2462 -0.5497 -0.1033 0.2002

4 -5.9777 -3.1363 -1.7947 -1.0064 -0.4443 -0.0866 0.1575

9 -4.6793 -2.3583 -1.3249 -0.7362 -0.3289 -0.0706 0.1074

14 -2.9532 -1.4263 -0.7851 -0.4303 -0.1904 -0.0445 0.0615

19 -0.5832 -0.2595 -0.1394 -0.0728 -0.0379 -0.007 0.01

24 2.9061 1.1863 0.6133 0.325 0.1423 0.0332 -0.0372

29 8.7204 3.0583 1.5201 0.7903 0.3432 0.0854 -0.079

34 22.8857 5.5281 2.612 1.3346 0.577 0.1436 -0.1255

39 8.9846 3.9388 1.9623 0.839 0.2279 -0.1542

44 14.2187 5.5807 2.6906 1.1443 0.3086 -0.1864

49 23.8879 7.6657 3.5512 1.4973 0.4195 -0.2202

54 10.397 4.5652 1.8961 0.5414 -0.2346

59 14.1254 5.7961 2.3579 0.6886 -0.2502

64 19.6663 7.2674 2.8933 0.8611 -0.2427

69 29.4299 9.1012 3.5036 1.052 -0.2458

74 11.4111 4.2143 1.288 -0.224

79 14.4558 5.0464 1.5506 -0.1876

84 18.6663 6.0262 1.8535 -0.1461

89 25.1603 7.1864 2.2048 -0.076

comparison of calculation standards of ngl and lpg

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