ASTM D4784-23

Standard Specification for Liquefied Natural Gas Density Calculation Models

ABSTRACT
This specification covers LNG density calculation models for use in the calculation or prediction of the densities of saturated liquefied natural gas (LNG) mixtures at a specified temperature range given the pressure, temperature, and composition of the mixture. Composition restrictions for the LNGs are given for methane, nitrogen, n-butane, i-butane, and pentanes. It is assumed that hydrocarbons with carbon numbers of six or greater are not present in the LNG solution. The mathematical models presented here are the extended corresponding states model, hard sphere model, revised Klosek and McKinley model, and the cell model.
SCOPE
1.1 This specification covers Liquefied Natural Gas (LNG) density calculation models for use in the calculation or prediction of the densities of saturated LNG mixtures from 90K to 120K to within 0.1 % of true values given the pressure, temperature, and composition of the mixture.  
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 30-Apr-2023
• ICS: 75.060 - Natural gas
• Technical Committee: D03 - Gaseous Fuels
• Drafting Committee: D03.08 - Thermophysical Properties

Relations

• Refers: ASTM D4150-19 - Standard Terminology Relating to Gaseous Fuels
• Effective Date: 15-Dec-2019
• Refers: ASTM D4150-08(2016) - Standard Terminology Relating to Gaseous Fuels
• Effective Date: 01-Jul-2016
• Refers: ASTM D4150-08 - Standard Terminology Relating to Gaseous Fuels
• Effective Date: 01-Dec-2008
• Refers: ASTM D4150-03 - Standard Terminology Relating to Gaseous Fuels
• Effective Date: 10-Aug-2003
• Refers: ASTM D4150-00 - Standard Terminology Relating to Gaseous Fuels
• Effective Date: 10-Jun-2000

Overview

ASTM D4784-23: Standard Specification for Liquefied Natural Gas Density Calculation Models defines models and procedures for calculating or predicting the density of saturated Liquefied Natural Gas (LNG) mixtures. This standard is critical for ensuring accurate measurement and management of LNG storage, transport, and custody transfer operations. The models are optimized for LNG mixtures containing at least 60% methane, less than 4% nitrogen, less than 4% n- and i-butanes, and less than 2% total pentanes, with the explicit assumption that heavier hydrocarbons (carbon number six and above) are absent.

ASTM D4784-23 provides guidance on four validated mathematical models:

• Extended corresponding states model
• Hard sphere model
• Revised Klosek and McKinley model
• Cell model

These models have been optimized using extensive experimental data, and each achieves a density prediction accuracy within 0.1% of true values between 90K and 120K.

Key Topics

1. Applicability and Range

• Predicts the density of saturated LNG mixtures from 90K to 120K.
• Suitable for mixtures primarily composed of methane with defined limits on nitrogen, butanes, and pentanes.
• Designed for LNGs without significant amounts of heavy hydrocarbons.

2. Mathematical Models Provided

• Extended Corresponding States Model: Utilizes a reference fluid approach (methane) and modified equations of state for mixtures.
• Hard Sphere Model: Employs adjustable parameters for pressure, temperature, and composition; uses one-fluid theory for mixtures.
• Revised Klosek and McKinley Model: Calculates mixture volume based on mole fractions and correction factors.
• Cell Model: Uses a correlation approach, details of which are referenced in supporting documents.

3. Measurement Units

• All calculations and results are specified in SI units.

4. Safety and Regulatory Compliance

• Users are responsible for adhering to safety, health, and environmental protocols.
• Consideration of local and international regulatory requirements remains essential.

Applications

ASTM D4784-23 is widely used in the LNG industry for scenarios where accurate LNG density calculation is essential. Typical applications include:

• LNG Custody Transfer: Accurate density prediction is vital for transactional measurement and validation during LNG buying, selling, and transfer.
• Storage and Shipping: Ensures reliable inventory management and optimizes shipping calculations by providing precise LNG density values.
• Process Engineering: Supports design, simulation, and optimization of LNG processing facilities, including liquefaction, storage, and regasification terminals.
• Compliance & Quality Assurance: Helps companies meet industry regulations and standards for measurement accuracy in the LNG value chain.
• Research & Development: Provides a reliable foundation for developing new LNG mixtures or advancing cryogenic fluid technologies.

Related Standards

For comprehensive LNG measurement and analysis, the following standards may complement ASTM D4784-23:

• ASTM D4150 - Terminology Relating to Gaseous Fuels: Offers definitions used throughout LPG and LNG standards.
• Additional technical resources such as NBS Monograph 172 for background on density measurements and model development.

Keywords

Liquefied Natural Gas density, LNG density calculation, ASTM D4784-23, LNG measurement, LNG properties, extended corresponding states model, hard sphere model, Klosek and McKinley model, LNG composition, custody transfer, SI units, LNG standard, LNG shipping, Gaseous Fuels standards.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: D4784 − 23
Standard Specification for
Liquefied Natural Gas Density Calculation Models
This standard is issued under the fixed designation D4784; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 4. Summary of the Specification
4.1 The models in this specification can be used to calculate
1.1 This specification covers Liquefied Natural Gas (LNG)
the density of saturated liquid natural gas in the temperature
density calculation models for use in the calculation or
range 90K to 120K. The estimated uncertainty for the density
prediction of the densities of saturated LNG mixtures from
calculations is 60.1 %. The restrictions on composition of the
90K to 120K to within 0.1 % of true values given the pressure,
liquefied natural gas are:
temperature, and composition of the mixture.
methane 60 % or greater
1.2 The values stated in SI units are to be regarded as
nitrogen less than 4 %
standard. No other units of measurement are included in this n-Butane less than 4 %
i-butane less than 4 %
standard.
pentanes less than 2 %
1.3 This standard does not purport to address all of the
It is assumed that hydrocarbons with carbon numbers of six
safety concerns, if any, associated with its use. It is the
or greater are not present in the LNG solution.
responsibility of the user of this standard to establish appro-
5. Model Used
priate safety, health, and environmental practices and deter-
mine the applicability of regulatory limitations prior to use.
5.1 Extended Corresponding States—The extended corre-
1.4 This international standard was developed in accor-
sponding states method is defined by the following equations:
dance with internationally recognized principles on standard-
Z P,T 5 Z P h /f , T/f (1)
@ # @ #
i o ii,o ii,o ii,o
ization established in the Decision on Principles for the
G @P,T# 5 f G @P h /f , T/f # 2 RT ln h (2)
~ !
i ii,o o ii,o ii,o ii,o ii,o
Development of International Standards, Guides and Recom-
mendations issued by the World Trade Organization Technical
where:
Barriers to Trade (TBT) Committee.
Z = compressibility factor,
G = Gibbs free energy,
2. Referenced Documents
P = pressure,
2 T = temperature,
2.1 ASTM Standards:
o = reference fluid, and
D4150 Terminology Relating to Gaseous Fuels
i = fluid for which properties are to be obtained via the
equation of state for the reference fluid and the
3. Terminology
transformation functions f and h are introduced to
ii,o ii,o
3.1 Definitions:
allow extension of the method to mixtures.
3.1.1 For definitions of general terms used in D03 Gaseous
The two defining Eq 1 and Eq 2 are necessary since there are
Fuels standards, refer to Terminology D4150.
two transformation functions. In this case, an equation of state
3.2 Abbreviations:
for methane was chosen for the reference fluid. During the
3.2.1 LNG—Liquefied Natural Gas
course of the study it was necessary to modify the equation of
state to give a realistic vapor liquid phase boundary down to a
temperature of 43K. This modification was necessary to
accommodate the very low reduced temperatures of the heavier
This standard is under the jurisdiction of ASTM Committee D03 on Gaseous
hydrocarbons and was accomplished without changing the
Fuels and is the direct responsibility of Subcommittee D03.08 on Thermophysical
Properties.
performance of the equation of state above the triple point of
Current edition approved May 1, 2023. Published June 2023. Originally
methane. The f and h are defined as
ii,o ii,o
approved in 1988. Last previous edition approved in 2015 as D4784 – 93 (2015).
c c
DOI: 10.1520/D4784-23.
f 5 ~T /T ! θ T ,V (3)
~ !
ii,o ii o ii,o r r
i i
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
and
Standards volume information, refer to the standard’s Document Summary page on
c c
h 5 V /V φ T ,V (4)
~ ! ~ !
the ASTM website. ii,o ii,o o ii,o r r
i i
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D4784 − 23
where: c 1c
ii ij
c 5 (17)
ij
θ 5 11~w 2 w ! n 2 n ℓ n T 1 n 2 n /T V 2 n
@ ~ ! ~ !#
ii,o i o 1 2 r 3 4 r r 5
i i i
The parameters j and k are in this case the binary interac-
(5)
ij ij
tion parameters. The excess volume is now calculated using the
and
equation of state and
c
Z
o
¯ ¯
φ 5 11 w 2 w n V 2 n 2 n V 2 n ℓn T (6)
@ ~ ! @ ~ ! ~ ! ##
c V 5 V 2 V x (18)
ii,o i o 6 ri 7 8 ri 9 ri
E m i i
Z
i
¯ ¯
where V and V are calculated via Eq 11-17. The calculated
m i
The V and T are reduced temperature and volume (that is,
ri ri
value of V can now be used with measured values V x to give
c c
E i i
T 5T/T and V 5V/V ); each fluid requires a unique w which
ri ii ri ii i
an actual volume of the mixture. Then:
was estimated using pure fluid experimental data. A single set
of the n’s is used for all fluids. The n’s were estimated using all
V 5 V x 1V (19)
m ( i i E
i
of the pure fluid experimental data from the NBS Boulder
c c
Study. The Z /Z is the ratio of the compressibi
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: D4784 − 93 (Reapproved 2015) D4784 − 23
Standard Specification for
LNG Liquefied Natural Gas Density Calculation Models
This standard is issued under the fixed designation D4784; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
This specification is a description of four mathematical models of the equation of state for LNG-like
mixtures that were adopted in 1988. The four models include an extended corresponding states model,
a cell model, a hard sphere model, and a revised Klosek and McKinley model. Each of the models has
been optimized to the same experimental data set which included data for pure nitrogen, methane,
ethane, propane, iso and normal butane, iso and normal pentane, and mixtures thereof. For LNG-like
mixtures (mixtures of the orthobaric liquid state at temperatures of 120K or less and containing at least
60 % methane, less than 4 % nitrogen, less than 4 % each of iso and normal butane, and less than 2 %
total of iso and normal pentane), all of the models are estimated to predict densities to within 0.1 %
of the true value. These models were developed by the National Institute of Standards and Technology
(formerly the Bureau of Standards) upon culmination of seven years of effort in acquiring physical
properties data, performing extensive experimental measurements using specially developed
equipment, and in using these data to develop predictive models for use in density calculations.
1. Scope
1.1 This specification covers LNG Liquefied Natural Gas (LNG) density calculation models for use in the calculation or prediction
of the densities of saturated LNG mixtures from 9090K to 120K to within 0.1 % of true values given the pressure, temperature,
and composition of the mixture.
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety and healthsafety, health, and environmental practices and determine
the applicability of regulatory limitations prior to use.
1.4 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Significance and Use
2.1 The models in this specification can be used to calculate the density of saturated liquid natural gas in the temperature range
90 to 120K. The estimated uncertainty for the density calculations is 60.1 %. The restrictions on composition of the liquefied
natural gas are:
This standard is under the jurisdiction of ASTM Committee D03 on Gaseous Fuels and is the direct responsibility of Subcommittee D03.08 on Thermophysical Properties.
Current edition approved June 1, 2015May 1, 2023. Published July 2015June 2023. Originally approved in 1988. Last previous edition approved in 20102015 as
D4784 – 93 (2010).(2015). DOI: 10.1520/D4784-93R15.10.1520/D4784-23.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D4784 − 23
methane 60 % or greater
nitrogen less than 4 %
n-butane less than 4 %
i-butane less than 4 %
pentanes less than 2 %
It is assumed that hydrocarbons with carbon numbers of six or greater are not present in the LNG solution.
2. Referenced Documents
2.1 ASTM Standards:
D4150 Terminology Relating to Gaseous Fuels
3. Terminology
3.1 Definitions:
3.1.1 For definitions of general terms used in D03 Gaseous Fuels standards, refer to Terminology D4150.
3.2 Abbreviations:
3.2.1 LNG—Liquefied Natural Gas
4. Summary of the Specification
4.1 The models in this specification can be used to calculate the density of saturated liquid natural gas in the temperature range
90K to 120K. The estimated uncertainty for the density calculations is 60.1 %. The restrictions on composition of the liquefied
natural gas are:
methane 60 % or greater
nitrogen less than 4 %
n-Butane less than 4 %
i-butane less than 4 %
pentanes less than 2 %
It is assumed that hydrocarbons with carbon numbers of six or greater are not present in the LNG solution.
5. Models Model Used
5.1 Extended Corresponding States—The extended corresponding states method is defined by the following equations:
Z P,T 5 Z P h /f , T/f (1)
@ # @ #
i o ii,o ii,o ii,o
G @P,T# 5 f G @P h /f , T/f # 2 RT ln h (2)
~ !
i ii,o o ii,o ii,o ii,o ii,o
where:
Z = compressibility factor,
G = Gibbs free energy,
P = pressure,
T = temperature,
o = reference fluid, and
i = fluid for which properties are to be obtained via the equation of state for the reference fluid and the transformation
functions f and h are introduced to allow extension of the method to mixtures.
ii,o ii,o
The two defining Eq 1 and Eq 2 are necessary since there are two transformation functions. In this case, an equation of state
for methane was chosen for the reference fluid. During the course of the study it was necessary to modify the equation of state
to give a realistic vapor liquid phase boundary down to a temperature of 43K. This modification was necessary to accommodate
the very low reduced temperatures of the heavier hydrocarbons and was accomplished without changing the performance of the
equation of state above the triple point of methane. The f and h are defined as
ii,o ii,o
The formulation of the models and the supporting work was done by the National Bureau of Standards underFor referenced ASTM standards, visit the ASTM website,
www.astm.org, or contact ASTM Customer Service at [e-mail]. For the sponsorship of British GasAnnual Book of ASTM Standards Corp., Chicago Bridge and Iron
Co., Columbia Gas Service Corp., Distrigas Corp., Easco Gas LNG, Inc., El Paso Natural Gas, Gaz de France, Marathon Oil Co., Mobil Oil Corp., Natural Gas Pipeline Co.,
Phillips Petroleum Co., Shell International Gas, Ltd., Sonatrach, Southern California Gas Co., Tennessee Gas Pipeline, Texas Eastern Transmission Co., Tokyo Gas Co., Ltd.,
and Transcontinental Gas Pipe Line Corp., through a grant administered by the American Gas Association, Inc.volume information, refer to the standard’s Document Summary
page on the ASTM website.
D4784 − 23
c c
f 5 T /T θ T ,V (3)
~ !
ii,o ii o ii,o ~ r r !
i i
and
c c
h 5 V /V φ T ,V (4)
~ !
~ !
ii,o ii,o o ii,o r r
i i
where:
θ 5 11~w 2 w ! n 2 n ℓ n T 1 n 2 n /T V 2 n (5)
@ ~ ! ~ !#
ii,o i o 1 2 r 3 4 r r 5
i i i
and
c
Z
o
φ 5 @11~w 2 w ! @n ~V 2 n !2 n ~V 2 n ! ℓn T ## (6)
ii,o c i o 6 ri 7 8 ri 9 ri
Z
i
c c
The V and T are reduce
...