LNG Training Course – Density Calculationslngmetrology.info/.../10/Richter-EMRP_Workshop_DensityCalc_June20… · LNG Training Course – Density Calculations 4th International

RUHR-UNIVERSITÄT BOCHUM

LNG Training Course – Density Calculations 4th International Workshop “Metrology for LNG”

NPL, Teddington, UK | 2016/06/15

M. Richter, C. Tietz, R. Kleinrahm, R. Lentner, R. Span

2Richter et al. | 4th International Workshop “Metrology for LNG” | June 2016

LNG Custody Transfer

General Formula for Calculating the LNG Energy Transferred(According to GIIGNL - LNG Custody Transfer Handbook)

𝑬 = 𝑽𝐋𝐍𝐆 ' 𝝆𝐋𝐍𝐆 𝑻, 𝒑, 𝒙 ' 𝑯𝐒,𝐋𝐍𝐆 𝒙 𝐤𝐖𝐡

𝐸: the total net energy transferred from the loading facilities to the LNG carrier, or from the LNG carrier to the unloading facilities.

𝑉567: the volume of LNG loaded or unloaded in m3.

𝜌567: the density of LNG loaded or unloaded in kg/m3.

𝐻:,567: the gross calorific value of the LNG loaded or unloaded in MMBTU/kg.


LNG Density Calculation Methods – cf. CTH

_________________________________

GIIGNL _________________________________

LNG CUSTODY TRANSFER

HANDBOOK

FOURTH EDITION version 4.00

� GIIGNL 2015

GIIGNL – LNG CUSTODY TRANSFER HANDBOOK Fourth edition – version 4.0 – Uncontrolled when printed

42

chromatograph software it may be used to calculate these properties directly using temperature as an additional parameter. The set of LNG compositions provided by the gas chromatograph(s) during the Custody Transfer process must be managed to produce a representative composition for the whole LNG (un)loading operation. That is performed in two steps: processing and treatment. 8.2.1. Data processing

The aim of this step is to eliminate those LNG compositions which were produced by analyses in a period of time during which some operating parameters were outside preset limits.

For instance, when:

the sampling rate is lower than a preset value of regasified LNG flow (e.g. 1.0 m3(n)/h),

the pressure at the sampling point is lower than a preset value, e.g. 2 bar (gauge),

ship’s LNG cargo discharge pumping rate is lower than a preset value, e.g. 70% of nominal rate,

other criteria particular to the analyses.

After performing this data processing step, a subset of acceptable LNG compositions is ready for data treatment. 8.2.2. Data treatment

The aim of the data treatment is to obtain, from a statistical point of view, a robust and consistent result that best reflects the quality of the whole transferred LNG. This step consists of:

performing a statistical test for each analysis and each LNG component in order to determine the presence of outliers,

evaluating the elimination or not of the detected outliers (the whole analysis must be eliminated),

calculating the average composition from the analyses not being rejected,

normalizing the final LNG composition. There are different approaches to determine the presence of individual values in a set of data that may be inconsistent and may change the final result: graphical consistency technique and numerical outlier tests. These techniques are explained in ISO 57252 standard. One of the numerical tests recommended in this standard for dealing with outliers is the Grubbs’ test. Appendix 8 shows the procedure to apply this test as well as a numerical example. This data treatment step results in a final LNG molar composition, representative for the whole LNG (un)loading operation, from which the relevant LNG properties can be calculated.

9. DENSITY 9.1. GENERAL There are two ways of determining density:

the first consists of measuring its average value directly in the LNG carrier's tank by means of densitometers,

the second enables the density to be calculated on the basis of an average composition of LNG.

Insitu measurement with the help of a densitometer takes into account the LNG state of equilibrium and composition, which means that one no longer depends on product sampling and analysis. It would therefore seem to be the best method for measuring the LNG density. Unfortunately, technological progress has not reached the stage where it is possible for a reliable apparatus to be available on board a LNG carrier under normal operating conditions. This is why the second method, which enables the density to be calculated from the LNG average composition, is the one that has been selected here. 9.2. DENSITY CALCULATION

METHODS A variety of calculation methods exists [6], such as:

state equations in their integral form,

method of extended corresponding states,

hard sphere model method,

WATSON method,

ELFAQUITAINE method,

graphic method of RC MILLER,

HIZA method,

revised KLOSEKMcKINLEY method (k1 and k2 tables in Kelvin: K),

ISO 6578, also using the revised KLOSEKMcKINLEY method (k1, k2 tables in degrees Celsius: °C).

Validation of these density models by experimentation is ongoing (Ref [18]). In this handbook, the preferred method is the revised KLOSEKMcKINLEY method, as described in N.B.S. Technical note 1030 December 1980 [9] or in ISO 6578. It is easy to apply and only requires the LNG temperature and composition to be taken into account. The limits of the method also encompass the composition of most LNG produced. Its uncertainty is ±0.1%, when either the nitrogen or butane content does not exceed 5%. For these density calculations an electronic spreadsheet or a computer programme is often used. Comparison between the revised KLOSEK-McKINLEY method using tables in Kelvin (NBS) and tables in degrees Celsius (ISO 6578:1991) indicates that they are very similar with a relative difference of about 10-4. Tables according to NBS only mention


'5'=-/35'3ft-/-ZV7

NBS TECHNICAL NOTE1030

u.s. DEPARTMENT OF COMMERCE 'National Bureau of Standalds

LNG Density Calculation Methods – cf. McCarty

therefore requires twelve significant figures to insure the accuracy of the

calculated density. The other two models require only eight significant figures

to be carried along in the calculations.

7. CONCLUSIONS

On the basis of the performance of the four models given here and subject to

the composition and temperature restrictions already noted, it is estimated that

given the pressure, temperature and composition of LNG, any one of the four

models may be used to predict the density to within 0.1% of the true value. As

has already been mentioned (see section I) the above accuracy statement is

dependent entirely upon the accuracy of the experimental data in Haynes, et al.

[11], Haynes, et al. [13], Hiza, et al. [14], Haynes [g], Hiza and Haynes [15],

Miller and Hiza [25] and Haynes [10]. These data have been estimated by the

authors to be accurate to within 0.1% of the true value with a precision of a few

hundredths of a percent. The work on the models given here have provided no

basis for questioning the claims of the experimenters, in fact the ability of the

models to predict the densities of the multicomponent mixtures to within 0.1% of

the measured values tends to support the accuracy claims of the experimenters.

Interim results of this study were reported by Haynes, et al. [13] and

McCarty [23], both of which contain earlier versions of the mathematical models

given here. These earlier versions are only slightly different than the final

ones and for the purposes of calculating LNG densities either of the versions may

be used. The reader is, however, cautioned to read the limitations of each model

as defined in the earlier sections.

Computer programs for the four models are available at the Thermophysical

Properties Division of the National Bureau of Standards in Boulder, Colorado.

19

Models investigated by R. D. McCarty (1980):• extended corresponding states• hard sphere method• cell method• revised Klosek and McKinley method


LNG Density Calculation Methods – Wide Range

Modelling liquefied-natural-gas processes using highly accurate property models

Florian Dauber ⇑, Roland SpanRuhr-Universität Bochum, Thermodynamics, Universitätsstr. 150, 44780 Bochum, Germany

a r t i c l e i n f o

Article history:Received 27 June 2011Received in revised form 13 November 2011Accepted 14 November 2011Available online 7 December 2011

Keywords:GERG-2008VapourisationCAPE-OPENLiquefied natural gasLiquefactionTransport

a b s t r a c t

Accurate simulations are important for efficient design and operation of a process. Therefore, a preciserepresentation of thermophysical properties using an adequate property model is necessary. TheGERG-2008 by Kunz and Wagner [1] is the new reference equation of state for natural gases consistingof up to 21 specific compounds. It describes the gas and liquid phase as well as the super-critical regionand the vapour–liquid equilibrium. In order to model LNG processes with the highest accuracy available,software available for the new equation is implemented into various common simulation tools. To ensurestable and consistent simulations, the GERG-2008 Property Package has been developed, which meets theCAPE-OPEN standard. The influence of property models on the simulation of the most important pro-cesses of the LNG value chain is investigated. Results show the expected advantages in accuracy for sim-ulations using the new property model.

! 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Evaporation, transport and liquefaction are important processesin the LNG process chain. High expectations on the economic effi-ciency, the product quality and environmental safety result inincreasing demands on design and operation of these systems.Fundamental contributions to the optimisation of systems can beexpected from detailed and sufficiently accurate simulations ofthe processes. For these simulations an accurate representationof thermophysical properties is essential.

Results of process simulations are influenced by the propertymodel used. New, highly accurate equations of state represent anunused potential for process modelling. The GERG-2008 by Kunzand Wagner [1] is an equation of state that describes mixtures ofarbitrary composition consisting of up to 21 specific compounds.It covers the gas and liquid phase as well as the super-critical re-gion and the vapour–liquid equilibrium with the highest accuracyavailable. It was adopted by the GERG (Groupe Européen deRecherche Gazières) as new reference equation of state for naturalgases. The equation is under consideration to be adopted as an ISOStandard (ISO 20765-2 and ISO 20765-3) for natural gases. Ongo-ing projects aim at an improvement of the GERG-2008 e.g. forCO2-rich mixtures [2]. However in this article the original formula-tion by Kunz and Wagner [1] is used. In order to embed the newreference equation into various simulation tools, the softwareavailable for the GERG-2008 equation of state has been has been

implemented in a software component adhering to the CAPE-OPENstandard [3]. This standard defines rules and interfaces that allowComputer-Aided Process Engineering (CAPE) applications or com-ponents to interoperate. While the standard is supported by vari-ous commercial simulation tools, the developed GERG-2008Property Package is not limited to a single simulation softwarealone. The Property Package is a consistent collection of methodsand compounds for calculating any of a set of physical propertiesfor the different phases of a mixture or a pure compound. Usingthe Property Package allows consistent and stable calculations ofthermodynamic properties.

In order to examine the influence of different property modelson process simulation, cubic equations by Peng and Robinson [4]and by Redlich, Kwong and Soave [5] are taken into account. Fur-thermore, the modified Benedict–Webb–Rubin type equation ofstate by Lee and Kesler [6] in connection with the mixture modelby Plöcker et al. [7] is reviewed. For all these property models,the binary parameters of Knapp et al. [8] are used. For these typicalengineering equations of state, significant deviations were foundfrom the GERG-2008 model. In this article it is shown that thesedifferences result in uncertainties for simulations of natural gasliquefaction processes, LNG transport calculations and for mod-elled heat exchangers of a regasification terminal.

2. Comparing property models

As LNG is transported and stored in the saturated liquid phase,an accurate representation of thermodynamic properties in this re-gion is significant. The density is an essential thermal property forbilling of LNG and for modelling of partial vapourisation processes

0306-2619/$ - see front matter ! 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.apenergy.2011.11.045

⇑ Corresponding author. Tel.: +49 (0)176 24642997; fax: +49 (0)234 32 14163.E-mail addresses: [email protected] (F. Dauber), roland.span@thermo.

rub.de (R. Span).

Applied Energy 97 (2012) 822–827

Contents lists available at SciVerse ScienceDirect

Applied Energy

journal homepage: www.elsevier .com/ locate/apenergy

during a ship transport. Caloric properties must be considered e.g.for the simulation of heat exchangers. As the enthalpy needs a de-fined reference point that has an influence on the comparison ofproperty models by means of relative deviations, the isobaric heatcapacity is studied. The isobaric heat capacity cp describes thederivative of the enthalpy h with respect to temperature T at con-stant pressure p.

Low temperatures in the liquid phase of natural gases result inexperimental difficulties and ultimately in a lack of accurate exper-imental data for properties of LNG. However, the GERG-2008 equa-tion and the equations of Peng–Robinson [4], Redlich–Kwong–Soave [5] and Lee–Kesler–Plöcker [6,7] allow calculations of ther-modynamic properties for LNG.

Figs. 1 and 2 show deviations of calculated and measured den-sities and isobaric heat capacities from results of the GERG-2008equation. Calculations were conducted with different propertymodels along the saturated liquid line for a temperature rangefrom 110 to 195 K and for the LNG composition which is shownin Table 1. The plotted experimental data represent different com-positions, which were of course considered when deviations to theGERG-2008 equation were calculated. The LNG densities weremeasured at the National Bureau of Standards in the USA (today:National Institute of Standards and Technology, NIST) by Haynesand Hiza [9,10] with an uncertainty of Dq0/q0 6 0.1%. However,considering the additional uncertainty of the composition, the totaluncertainty in density amounts to approx. 0.3%. The experimentaldata for the isobaric heat capacities of a LNG mixture were mea-sured at the Koninklijke/Shell-Laboratory in Amsterdam, Nether-lands by van Kasteren and Zeldenrust [11]. The uncertainty isestimated by the authors with Dcp/cp 6 1%.

Saturated liquid densities calculated with the equation of Peng–Robinson deviate by more than 10% from results of the GERG-2008.

Maximum deviations of the Redlich–Kwong–Soave model areabove !7% for higher pressures. The Lee–Kesler–Plöcker model re-sults in deviations of !5% at a temperature of 195 K. For LNG mix-tures, the GERG-2008 equation accurately represents theexperimental data for densities within ±(0.06 ! 0.4)%. The devia-tions observed for the analysed property models exceed this uncer-tainty by far.

Measured isobaric heat capacities at saturated liquid conditionsare described by the reference equation within ±1% which is inagreement with the experimental uncertainty of the available data.Fig. 2 shows the poor quality of cubic equations for caloric proper-ties in the liquid phase. The maximum deviation exceeds theuncertainty of the GERG-2008 equation by a factor of 5. Significantdifferences can also be found for the Lee–Kesler–Plöcker model asdeviations increase to 8%.

For the representation of thermodynamic properties of LNG,significant deviations are shown depending on the quality of theproperty model used. Taking those uncertainties into accountproperty models have a crucial impact on the accuracy of processsimulations, which makes an implementation of the GERG-2008equation of state inevitable.

3. The GERG-2008 Property Package

Since the GERG-2008 equation of state describes the whole fluidregion of natural gases and similar mixtures with an accuracy thatis beyond those of industrially used equations of state, smalleruncertainties for process simulation can be expected as well. Animplementation of the GERG-2008 equation into simulation envi-ronments enables a consistent and stable calculation in the scien-tifically and industrially most often used process modelling

Nomenclature

BOR boil-off-rate (%/day)Calc calculatedcp isobaric heat capacityDev deviationEOS equation of stateexp experimentalf fugacityg gibbs free energyGCV gross calorific value (MJ/kg)h enthalpyKi K-factor of component iLNG liquefied natural gas_m mass flow

MCHE main cryogenic heat exchangerP powerp pressure (MPa)_Q heat flows entropyT temperature (K)V volume (m3)Z compressibility factorD difference@ partial derivativeui fugacity coefficient of component iq densityq 0 saturated liquid density

Fig. 1. Percentage deviations of saturated liquid densities of LNG measured by Hiza and Haynes [9] and Haynes [10] and calculated with different property models fromresults obtained with the GERG-2008.

F. Dauber, R. Span / Applied Energy 97 (2012) 822–827 823



© ISO 2015

Natural gas — Calculation of thermodynamic properties —Part 2: Single-phase properties (gas, liquid, and dense fluid) for extended ranges of applicationGaz naturel — Calcul des propriétés thermodynamiques —Partie 2: Propriétés des phases uniques (gaz, liquide, fluide dense) pour une gamme étendue d’applications

INTERNATIONAL STANDARD

ISO20765-2

First edition2015-01-15

Reference numberISO 20765-2:2015(E)

© ISO 2015



ISO20765-2



© ISO 2015



ISO20765-2



The GERG-2008 Wide-Range Equation of State for Natural Gases andOther Mixtures: An Expansion of GERG-2004O. Kunz† and W. Wagner*

Lehrstuhl fur Thermodynamik, Ruhr-Universitat Bochum, D-44780 Bochum, Germany

ABSTRACT: A new equation of state for the thermodynamic properties of naturalgases, similar gases, and other mixtures, the GERG-2008 equation of state, is presentedin this work. This equation is an expanded version of the GERG-2004 equation.GERG-2008 is explicit in the Helmholtz free energy as a function of density, temperature,and composition. The equation is based on 21 natural gas components: methane,nitrogen, carbon dioxide, ethane, propane, n-butane, isobutane, n-pentane, isopentane,n-hexane, n-heptane, n-octane, n-nonane, n-decane, hydrogen, oxygen, carbonmonoxide, water, hydrogen sulfide, helium, and argon. Over the entire compositionrange, GERG-2008 covers the gas phase, liquid phase, supercritical region, and vapor−liquid equilibrium states for mixtures of these components. The normal range ofvalidity of GERG-2008 includes temperatures from (90 to 450) K and pressures up to 35 MPa where the most accurateexperimental data of the thermal and caloric properties are represented to within their accuracy. The extended validity rangereaches from (60 to 700) K and up to 70 MPa. The given numerical information (including all of the sophisticated derivatives)enables the use of GERG-2008 for all of the various technical applications. Examples are processing, transportation throughpipelines or by shipping, storage and liquefaction of natural gas, and processes to separate gas components. Comparisons withother equations of state, for example, AGA8-DC92 and Peng−Robinson equation (P-R), are also presented. GERG-2008 will beadopted as an ISO Standard (ISO 20765-2/3) for natural gases.

1. INTRODUCTIONThe accurate knowledge of the thermodynamic properties ofnatural gases and other mixtures consisting of natural gascomponents is of indispensable importance for the basicengineering and performance of technical processes. Theprocessing, transportation, storage, and liquefaction of naturalgas are examples for technical applications where thethermodynamic properties of a variety of mixtures of naturalgas components are required.To meet pipeline-quality specifications or for commercial use

as a fuel, natural gas in its raw form in general needs to beprocessed ahead of the feed into gas-pipeline systems orliquefaction facilities. This involves the separation of a numberof components that are either undesirable (e.g., carbon dioxide,water, and hydrogen sulfide) or have more value on their ownthan when left in the natural gas (e.g., ethane, propane, butane,and heavier hydrocarbons and also helium).The processed natural gas is transported in gaseous form

through pipelines at pressures up to 12 MPa. Compressorstations placed periodically along the pipeline ensure that thenatural gas remains pressurized. In addition, metering stationsallow for monitoring and managing the natural gas in the pipes.Small differences in methods used to calculate flow rates in largescale metering can introduce large cost uncertainties. To matchsupply and demand, natural gas is injected at pressures up to30 MPa into underground storage facilities, such as depleted gasreservoirs, aquifers, and salt caverns.In situations where the economics of major gas-transmission

pipelines are not viable (primarily across oceans), natural gas iscooled and condensed into liquid form, known as liquefied

natural gas (LNG), thus making it transportable by specializedtanker ships. Modern and highly efficient liquefaction processesuse mixtures of natural gas components as refrigerants inprecooling, liquefaction, and subcooling cycles.For the applications described above, the design of

fractionation units, compressors, heat exchangers, and storagefacilities requires property calculations over wide ranges ofmixture compositions and operating conditions in thehomogeneous gas, liquid, and supercritical regions and forvapor−liquid equilibrium (VLE) states. These data can becalculated in a very convenient way from equations of state.The GERG-2004 wide-range equation of state for natural

gases and other mixtures developed by Kunz et al.1 is the onlyequation of state that is appropriate for nearly all of the technicalapplications described above and that satisfies the demands onthe accuracy in the calculation of thermodynamic properties overthe entire fluid region. Similar to other recent developments, theGERG-2004 equation of state is based on a multi-fluidapproximation. The mixture model uses accurate equations ofstate in the form of fundamental equations for each mixturecomponent along with functions developed for the binarymixtures of the components to take into account the residualmixture behavior. The GERG-2004 equation of state enables thecalculation of thermal and caloric properties for natural gases andother mixtures consisting of 18 components: methane, nitrogen,carbon dioxide, ethane, propane, n-butane, isobutane, n-pentane,

Received: June 17, 2012Accepted: August 2, 2012Published: October 31, 2012

Article

pubs.acs.org/jced

© 2012 American Chemical Society 3032 dx.doi.org/10.1021/je300655b | J. Chem. Eng. Data 2012, 57, 3032−3091

The GERG-2008 Wide-Range Equation of State for Natural Gases andOther Mixtures: An Expansion of GERG-2004O. Kunz† and W. Wagner*

Lehrstuhl fur Thermodynamik, Ruhr-Universitat Bochum, D-44780 Bochum, Germany

ABSTRACT: A new equation of state for the thermodynamic properties of naturalgases, similar gases, and other mixtures, the GERG-2008 equation of state, is presentedin this work. This equation is an expanded version of the GERG-2004 equation.GERG-2008 is explicit in the Helmholtz free energy as a function of density, temperature,and composition. The equation is based on 21 natural gas components: methane,nitrogen, carbon dioxide, ethane, propane, n-butane, isobutane, n-pentane, isopentane,n-hexane, n-heptane, n-octane, n-nonane, n-decane, hydrogen, oxygen, carbonmonoxide, water, hydrogen sulfide, helium, and argon. Over the entire compositionrange, GERG-2008 covers the gas phase, liquid phase, supercritical region, and vapor−liquid equilibrium states for mixtures of these components. The normal range ofvalidity of GERG-2008 includes temperatures from (90 to 450) K and pressures up to 35 MPa where the most accurateexperimental data of the thermal and caloric properties are represented to within their accuracy. The extended validity rangereaches from (60 to 700) K and up to 70 MPa. The given numerical information (including all of the sophisticated derivatives)enables the use of GERG-2008 for all of the various technical applications. Examples are processing, transportation throughpipelines or by shipping, storage and liquefaction of natural gas, and processes to separate gas components. Comparisons withother equations of state, for example, AGA8-DC92 and Peng−Robinson equation (P-R), are also presented. GERG-2008 will beadopted as an ISO Standard (ISO 20765-2/3) for natural gases.

1. INTRODUCTIONThe accurate knowledge of the thermodynamic properties ofnatural gases and other mixtures consisting of natural gascomponents is of indispensable importance for the basicengineering and performance of technical processes. Theprocessing, transportation, storage, and liquefaction of naturalgas are examples for technical applications where thethermodynamic properties of a variety of mixtures of naturalgas components are required.To meet pipeline-quality specifications or for commercial use

as a fuel, natural gas in its raw form in general needs to beprocessed ahead of the feed into gas-pipeline systems orliquefaction facilities. This involves the separation of a numberof components that are either undesirable (e.g., carbon dioxide,water, and hydrogen sulfide) or have more value on their ownthan when left in the natural gas (e.g., ethane, propane, butane,and heavier hydrocarbons and also helium).The processed natural gas is transported in gaseous form

through pipelines at pressures up to 12 MPa. Compressorstations placed periodically along the pipeline ensure that thenatural gas remains pressurized. In addition, metering stationsallow for monitoring and managing the natural gas in the pipes.Small differences in methods used to calculate flow rates in largescale metering can introduce large cost uncertainties. To matchsupply and demand, natural gas is injected at pressures up to30 MPa into underground storage facilities, such as depleted gasreservoirs, aquifers, and salt caverns.In situations where the economics of major gas-transmission

pipelines are not viable (primarily across oceans), natural gas iscooled and condensed into liquid form, known as liquefied

natural gas (LNG), thus making it transportable by specializedtanker ships. Modern and highly efficient liquefaction processesuse mixtures of natural gas components as refrigerants inprecooling, liquefaction, and subcooling cycles.For the applications described above, the design of

fractionation units, compressors, heat exchangers, and storagefacilities requires property calculations over wide ranges ofmixture compositions and operating conditions in thehomogeneous gas, liquid, and supercritical regions and forvapor−liquid equilibrium (VLE) states. These data can becalculated in a very convenient way from equations of state.The GERG-2004 wide-range equation of state for natural

gases and other mixtures developed by Kunz et al.1 is the onlyequation of state that is appropriate for nearly all of the technicalapplications described above and that satisfies the demands onthe accuracy in the calculation of thermodynamic properties overthe entire fluid region. Similar to other recent developments, theGERG-2004 equation of state is based on a multi-fluidapproximation. The mixture model uses accurate equations ofstate in the form of fundamental equations for each mixturecomponent along with functions developed for the binarymixtures of the components to take into account the residualmixture behavior. The GERG-2004 equation of state enables thecalculation of thermal and caloric properties for natural gases andother mixtures consisting of 18 components: methane, nitrogen,carbon dioxide, ethane, propane, n-butane, isobutane, n-pentane,

Received: June 17, 2012Accepted: August 2, 2012Published: October 31, 2012

Article

pubs.acs.org/jced

© 2012 American Chemical Society 3032 dx.doi.org/10.1021/je300655b | J. Chem. Eng. Data 2012, 57, 3032−3091

• For the binary mixtures methane−propane and methane−carbon dioxide, additional sound-speed data should bemeasured at pressures above 10 MPa.

• Since the heavier alkanes have a significant influence onthe sound speed of multi-component mixtures at lowertemperatures, accurate sound-speed data at supercriticaltemperatures should be measured for the binary mixturesmethane−n-butane, methane−isobutane, methane−n-pentane,methane−isopentane, and methane−n-hexane.

• For mixtures of important natural gas components, such asnitrogen−carbon dioxide and carbon dioxide−propane,only few data are available for caloric properties.

• Moreover, for most of the binary mixtures that consist ofsecondary natural gas components, including mixtureswith the three additional components considered for theexpansion of GERG-2004, no (accurate) caloric data areavailable.

Due to the lack of (very) accurate experimental data for binarymixtures that contain one of the three new componentsn-nonane, n-decane, and hydrogen sulfide, it is highly recom-mended to perform accurate measurements for various proper-ties for these mixtures over wide ranges of temperature, pressure,and composition. On the one hand, this recommendation refersto the binary combinations of the main natural gas componentswith the three new components. On the other hand, it also refersto mixtures of secondary components with the three newcomponents and especially to mixtures containing n-nonane.

4. THE GERG-2008 EQUATION OF STATE FORNATURAL GASES AND OTHER MIXTURES

The GERG-2008 equation of state is an expansion of the GERG-2004 equation of state.1 In addition to the 18 componentscovered by GERG-2004, the GERG-2008 equation of state alsoconsiders the three components n-nonane, n-decane, andhydrogen sulfide. These additional components add up to the21 components listed in Table 1. Thus, theGERG-2008 equationof state is valid for all of the mixtures that are covered by GERG-2004, and, in addition, it also covers all mixtures consisting of the18 components of GERG-2004 and the three additionalcomponents in any arbitrary combination or concentration.As shown in this section, the calculation of the thermodynamic

properties of multi-component mixtures from GERG-2008 isbased on equations developed for binary mixtures. In this sense,GERG-2004 covers 153 binary mixtures (formed from the 18pure components). The three additional components mentionedabove result in 57 additional binary mixtures. The 57 additionalmixtures add up to a total of 210 binary mixtures (formed fromthe 21 pure components) covered by the expanded modelGERG-2008. The numerical information given for the 153 binarymixtures of GERG-2004 remain almost entirely unchanged. Thenumerical values that characterize the 57 additional binarymixtures had to be added. Figure 1 shows how the 57 additionalbinary mixtures are formed.For the mixtures of the 18 components covered by GERG-

2004, the GERG-2008 equation of state yields virtually the sameresults as GERG-2004. Both equations are determined by thesame mathematical formalism; only the maximum value for N inthe corresponding summations is different.If one is only interested in the application of GERG-2008 and

not in the details of its development, sufficient information isgiven in Section 4.1.

4.1. Numerical Description of GERG-2008. The GERG-2008 equation of state for natural gases and other mixtures ofnatural gas components is based on a multi-fluid approximationexplicit in the reduced Helmholtz free energy

α δ τ α ρ α δ τ = + x T x x( , , ) ( , , ) ( , , )o r (8)

where the αo part represents the properties of the ideal-gasmixture at a given mixture density ρ, temperature T, and molarcomposition x according to

∑α ρ α ρ = +=

T x x T x( , , ) [ ( , ) ln ]i

N

i i io

1oo

(9)

The residual part αr of the reduced Helmholtz free energy of themixture is given by

∑ ∑ ∑α δ τ α δ τ α δ τ = += =

−

= +x x x x F( , , ) ( , ) ( , )

i

N

i ii

N

j i

N

i j ij ijr

1or

1

1

1

r

(10)

where δ is the reduced mixture density and τ is the inversereduced mixture temperature according to

δ ρρ τ=

=

xT x

T( )and

( )

r

r

(11)

and N = 21 is the total number of components in the mixture.Since the mixture model is not limited to the currentlyconsidered 21 components, the summation variable N iscontinuously used in this work to denote the maximum numberof components.Equation 10 takes into account the residual behavior of the

mixture at the reduced mixture variables δ and τ. The first sum inthis equation is the linear contribution of the reduced residualHelmholtz free energy of the pure substance equations of statemultiplied by the mole fractions xi. The double summation in eq10 is the departure function Δαr(δ,τ,x) (see also eqs 7 and 44),which is the summation over all binary specific and generalizeddeparture functions Δαij

r (δ,τ,x) developed for the respectivebinary mixtures (see eq 45).In eq 9, the dimensionless form of the Helmholtz free energy

in the ideal-gas state of component i is given by

∑

∑

α ρ ρρ= + * + +

+ ϑ

− ϑ

=

=

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜⎜

⎛⎝⎜

⎞⎠⎟

⎞⎠⎟⎟

⎛⎝⎜

⎛⎝⎜

⎞⎠⎟⎞⎠⎟

T RR

n nTT

nTT

nTT

nTT

( , ) ln [ ln

ln sinh

ln cosh ]

ii

i ii

ii

ki k i k

i

ki k i k

i

oo

c,o ,1o

o ,2o c,

o ,3o c,

4,6o ,o

o ,o c,

5,7o ,o

o ,o c,

(12)

where ρc,i and Tc,i are the critical parameters of the purecomponents (see Table A5 of Appendix A) and

= · ·− −R 8.314472 J mol K1 1 (13)

is the molar gas constant. This value corresponds to theinternationally accepted standard for R at the time when theequations GERG-2004 and GERG-2008 were developed.138 Theequations for αoi

o result from the integration of the cpo equations of

Jaeschke and Schley25 who used a different molar gas constantthan the one used in the developed mixture model. The ratioR*/R with R* = 8.314510 J·mol−1·K−1, used in ref 25, takes into

Journal of Chemical & Engineering Data Article

dx.doi.org/10.1021/je300655b | J. Chem. Eng. Data 2012, 57, 3032−30913040

Kunz et al.1 developed the GERG-2004 wide-range equationof state for natural gases and other mixtures. Similar to thedevelopments mentioned above, the GERG-2004 equation ofstate is based on a multi-fluid approximation. The equationcovers 18 natural gas components: methane, nitrogen, carbondioxide, ethane, propane, n-butane, isobutane, n-pentane,isopentane, n-hexane, n-heptane, n-octane, hydrogen, oxygen,carbon monoxide, water, helium, and argon. GERG-2004 isappropriate for various natural gas applications and satisfies thedemands on the accuracy in the calculation of thermodynamicproperties over the entire fluid region.2.2.1. General Structure ofMulti-Fluid Approximations.The

mixture models mentioned above and the new model for naturalgases, similar gases, and other mixtures presented here arefundamental equations explicit in the Helmholtz free energy awith the independent mixture variables density ρ, temperature T,and the vector of the molar composition x. The function a(ρ,T,x)is split into a part ao, which represents the properties of ideal-gasmixtures at given values for ρ, T, and x, and a part ar, which takesinto account the residual mixture behavior:

ρ ρ ρ = + a T x a T x a T x( , , ) ( , , ) ( , , )o r (1)

The use of the Helmholtz free energy in its dimensionless formα = a/(RT) results in the following equation (note that αo doesnot depend on δ and τ of the mixture, but on ρ and T)

α δ τ α ρ α δ τ = + x T x x( , , ) ( , , ) ( , , )o r (2)

where δ is the reduced mixture density and τ is the inversereduced mixture temperature according to

δ ρ ρ τ= = T T/ and /r r (3)

with ρr and Tr being the composition-dependent reducingfunctions for the mixture density and temperature:

ρ ρ= x( )r r (4)

= T T x( )r r (5)

The dimensionless form of the Helmholtz free energy for theideal-gas mixture αo is given by

∑α ρ α ρ = +=

T x x T x( , , ) [ ( , ) ln ]i

N

i i io

1oo

(6)

where N is the number of components in the mixture, αoio is the

dimensionless form of the Helmholtz free energy in the ideal-gasstate of component i (see eq 12), and the quantities xi arethe mole fractions of the mixture constituents. The term xilnxiaccounts for the entropy of mixing.In a multi-fluid approximation, the residual part of the reduced

Helmholtz free energy of the mixture αr is given by:

∑α δ τ α δ τ α δ τ = + Δ =

x x x( , , ) ( , ) ( , , )i

N

i ir

1or r

(7)

where αoir is the residual part of the reduced Helmholtz free

energy of component i (see eq 14), and Δαr is the so-calleddeparture function. The reduced residual Helmholtz free energyof each component depends on the reduced variables δ and τ ofthe mixture; the departure function additionally depends on themixture composition x.This general structure is used by the models of, for example,

Tillner-Roth,12 Lemmon and Jacobsen,21 and Kunz et al.,1 which

were developed to achieve an accurate description of thethermodynamic properties of nonideal mixtures.According to eq 7, the residual part of the reduced Helmholtz

free energy of the mixture αr is composed of two different parts,namely:

• the linear combination of the residual parts of allconsidered mixture components, and

• the departure function.In general, the contribution of the departure function to the

reduced residual Helmholtz free energy of themixture is less thanthe contribution of the equations for the pure components.Summarized, the development of mixture models based on a

multi-fluid approximation requires the following three elements:• pure substance equations of state for all considered mix-

ture components;• composition-dependent reducing functions ρr(x) and

Tr(x) for the mixture density and temperature;• a departure function Δαr depending on the reduced

mixture density, the inverse reduced mixture temperature,and the mixture composition.

3. EXPERIMENTAL DATAThe GERG-2008 wide-range equation of state for natural gases,similar gases, and other mixtures is based on pure substanceequations of state for each considered mixture component andcorrelation equations developed for binary mixtures consisting ofthese components (see Section 4). This allows for a suitablepredictive description of multi-component mixtures over a widerange of compositions, which means it is able to predict theproperties of a variety of natural gases and other multi-component mixtures. The basis for the development of suchan empirical equation of state is experimental data for severalthermodynamic properties. These data are used to determine thestructures, coefficients, and parameters of the correlationequations and to evaluate the behavior of the equation of statein different fluid regions. The quality and the extent of theavailable data limit the achievable accuracy of the equation.The database of experimental binary and multi-component

mixture data used in this work builds up on the comprehensivedatabase that has been used for the development of the GERG-2004 equation of state. This database has been continuouslyupdated and expanded to mixtures containing the threeadditional components n-nonane, n-decane, and hydrogensulfide. The updated and expanded database is also referred toin the following as the GERG-2008 database. Due to theextensive amount of data for a large number of different binaryand multi-component mixtures, only basic remarks on the datasets are given in this subsection. Additional details on the dataused to develop and evaluate the GERG-2004 equation of stateare given by Kunz et al.1 Details on the data used for theexpansion of GERG-2004 are given in Section 3.1.All collected data were assessed by means of comparisons to

values calculated from different equations of state. The dataclassified as “reliable” form an experimental basis for thedevelopment (i.e., fitting and structure optimization) of theGERG-2008 equation of state. Other data were only used forcomparisons. Many of the collected data do not meet presentquality standards. However, for several binary mixtures thesedata represent the only available experimental information.

3.1. Properties and Mixtures Covered by the GERG-2008 Database. The updated and expanded database containsmore than 125 000 experimental data for the thermal and caloric

Journal of Chemical & Engineering Data Article

dx.doi.org/10.1021/je300655b | J. Chem. Eng. Data 2012, 57, 3032−30913035

general structure of multi-fluid approx.

residual part à


• Cubic EOS of Redlingand Kwong (1949)

𝑝 = <'=>?@ −

B=C,D'>' >E@

• Cubic EOS of Peng and Robinson (1976)

𝑝 = <'=>?@ −

B>' >E@ E@' >?@ a, b: fluid spec. const.

• Modified BWR EOS of Lee and Kesler (1975) and Plöcker et al. (1978)

𝑍 = 1 +𝜔𝜔ref

𝑍P +𝜔𝜔ref

𝑍ref

𝑍ref/P =𝑝r𝑣r𝑅𝑇r

= 1+𝐵𝑣r+𝐶𝑣rW+𝐷𝑣rY+

𝑐[𝑇r\𝑣rW

𝛽 +𝛾𝑣rW

exp −𝛾𝑣rW

B, C, D are calculated by means of the critical parameters (as a function of the composition and pure substance parameters) and a binary specific mixture parameterthe equation contains 25 general constants, e.g., c4, γ, β (which are not fluid specific)



• COSTALD(corresponding states liquid density) by Hankinson and Thomson (1979)

𝑣 = 𝑣′ '1 − 𝐶 ln(𝐵 + 𝑝)

𝐵 + 𝑝s𝑣n = 𝑣∗ ' 𝑣Pr ' 1 − 𝜔 ' 𝑣pr

B and C are calculated by means of the critical parameters and the acentric factor (as a function of the composition and pure substance parameter à without specific mixture parameter)


Development of a special single-sinker densimeter for cryogenic liquidmixtures and first results for a liquefied natural gas (LNG)

Markus Richter ⇑, Reiner Kleinrahm, Rafael Lentner, Roland SpanLehrstuhl für Thermodynamik, Ruhr-Universität Bochum, D-44780 Bochum, Germany

a r t i c l e i n f o

Article history:Received 9 August 2015Received in revised form 22 September 2015Accepted 29 September 2015Available online 8 October 2015

Keywords:Cryogenic liquid mixturesDensity measurementSingle-sinker densimeterLiquefied natural gas (LNG)Magnetic suspension couplingSynthetic gas mixtures

a b s t r a c t

A special densimeter has been developed for accurate density measurements of liquid mixtures atcryogenic temperatures, e.g., liquefied natural gas (LNG). It covers the density range from (10 to 1000)kg !m"3, thus enabling density measurements in the supercritical region, in the homogeneous liquidregion, along the saturated liquid line as well as in the homogeneous gas region. The apparatus isdesigned for measurements over a temperature range from (90 to 300) K at pressures up to 12 MPa.The densimeter is based on the Archimedes (buoyancy) principle and is a single-sinker systemincorporating a magnetic suspension coupling. The density can be obtained directly without the needfor calibration fluids. The relative combined expanded uncertainty (k = 2) for density measurements inthe homogeneous liquid region (including the contribution resulting from the uncertainty of the samplegas analysis) was estimated to be 0.044%. First results for a synthetic five-component LNG mixture wereobtained at the temperatures T = (105, 115, 120, 125, and 135) K with pressures up to 8.1 MPa. The resultswere compared to the GERG-2008 reference equation of state for natural gases, which represents theexperimental values within 0.06%.

! 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Natural gas is an important energy source today and for thefuture. According to the International Energy Agency [1] the‘‘demand for natural gas grows by more than half, the fastest rateamong the fossil fuels, and increasingly flexible global trade inliquefied natural gas (LNG) offers some protection against the riskof supply disruptions.” In this context, the accurate determinationof LNG densities is gaining importance for the custody transfer pro-cess when determining the transferred energy and also for processsimulations, e.g., for modeling of economically and ecologicallyoptimized liquefaction and vaporization processes. Today, eventhe best available calculation models used for natural gas offer onlyrelatively large uncertainties of (0.1 to 0.5)% in the liquid phase. Toreduce these uncertainties, new accurate sets of experimental (p, q,T, x) data are essential.

For example, in Europe custody transfer calculations for LNG aremostly carried out according to the GIIGNL-LNG Custody TransferHandbook [2]. Therein, the revised Klosek and McKinley method[3] is given for determining densities of LNG. This empirical calcu-lation method can only be applied in a very limited temperature

and pressure range and was fitted to a comparatively smallnumber of experimental data. Within the present project, theuncertainty of these data, mostly measured by Miller and Hiza[4] as well as by Hiza and Haynes [5–7], was estimated to be upto about 0.3%. Thus, it can be stated that an uncertainty of 0.1%,given in Reference [3] for calculated densities, is probablyunderestimated.

Detailed studies at the thermodynamics institute ofRuhr-Universität Bochum have shown that comparisons betweendensity calculations with the revised Klosek and McKinley methodand the GERG-2008 wide-range reference equation of state for nat-ural gases of Kunz and Wagner [8] lead to deviations of up to 0.2%[9]. Currently no calculation model can be clearly recommendedfor the custody transfer of LNG. Furthermore, density calculationsin process simulations (e.g., with Aspen Plus or Hysys) have beenstudied. For such applications, thermodynamic models such asPeng–Robinson [10], Redlich–Kwong–Soave [11] and Lee–Kesler–Plöcker [12,13] are used. Comparisons between these models andthe GERG-2008 equation have shown deviations in density of upto 10% [14,15].

To verify the thermodynamic models used for the mentionedpurposes, accurate experimental data for densities of LNG overwide temperature and pressure ranges are needed. The data situa-tion for the relevant fluid regions (saturated liquid densities and

http://dx.doi.org/10.1016/j.jct.2015.09.0340021-9614/! 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +49 234 32 26395.E-mail address: [email protected] (M. Richter).

J. Chem. Thermodynamics 93 (2016) 205–221

Contents lists available at ScienceDirect

J. Chem. Thermodynamics

journal homepage: www.elsevier .com/locate / jc t

exp. data (this work) Rev. Klosek-McKinley COSTALD correlation

100

(ρ' ex

p−ρ'

GER

G)/ρ

' GER

G

0

0.1

0.2

0.3

0.4

T / K105 110 115 120 125 130 135

LNG (type: Norway), p = (0.07 to 0.5) MPa


𝜌567 =𝑀rst𝑣rst

⋅ 1 + 𝑝 − 𝑝v,wxyy ⋅ 4.06 ⋅ 10?[ ⋅𝑇}w

𝑇}w − 𝑇

~.��

𝑣rst = � 𝑥� ⋅ 𝑣��

− 𝑘~ + 𝑘W − 𝑘~ ⋅𝑥6W

0.0425 ⋅ 𝑥��[

𝑝v,wxyy = 𝑝v,��[ + 𝑥6W ⋅ 0.11MPa ⋅ 𝑇 − 90K − 𝑥�W�� ⋅ 0.05MPa ⋅ 𝑇 − 95K

𝑇}w =� 𝑥� ⋅ 𝑇w,��

(ERKM = Enhanced Revised Klosek and McKinley Method)

The original RKM-method:

A correction term for the saturation pressure:

A pseudo-critical temperature to avoiddeviations at higher temperatures:

Fitted constants

LNG Density Calculation Methods – ERKM


0.1%for100K ≤ 𝑇 < 115Kand𝑝v ≤ 𝑝 < 5MPa0.15%for115K ≤ 𝑇 ≤ 135Kand5MPa ≤ 𝑝 ≤ 10MPa

EstimatedUncertainties:

LNG Density Calculation Methods – Performance of ERKM


4

SUBROUTINE FOR THE CALCULATION OF ALL COMMON THERMODYNAMIC PROPERTIES

Temperature T K

ALLEOS

Density U� mol/m3 Pressure p MPa

Internal energy u J/mol Enthalpy h J/mol Entropy s J/mol/K

Gibbs free energy g = h - Ts J/mol Helmholtz free energy a = u -Ts J/mol Isobaric heat capacity cp J/mol/K

Isochoric heat capacity cv J/mol/K Speed of sound ws m/s

Second Virial coefficient B m3/mol Third Virial coefficient C m6/mol2

Ideal gas isobaric heat capacity cp0 J/mol/K

Quality (molar vapor fraction) E� mol/mol

The subroutine ALLEOS has the following call:

ALLEOS (INPUT;PROP1;PROP2;FLUIDS;MOLFRACTIONS;EOSTYPE;PATH)

In order to use the ALLEOS routine, a range of 15 cells needs to be selected. A click on the fx button

after typing “ALLEOS(“opens the optional context menu (see Figure 1). After finishing the inputs

Ctrl+Shift+ Enter need to be pushed at the time instead of just Enter or clicking ok. The 15 selected

cells will then be filled with T, D, P, U, H, S, G, A, CP, CV, WS, B, C, CP0 and Q, respectively.

Figure 1: ALLEOS routine

The input parameters must have the types according to Table 2:

REFPROP 3

3. OVERVIEW

This section presents a brief overview of the program and its main features. Please refer to the remaining sections in this User's Guide for more complete information.

3.1 Database Structure

REFPROP consists of a graphical user interface (GUI) and FORTRAN subroutines implementing a variety of fluid property models. The interface provides a convenient means to calculate and display thermodynamic and transport properties of pure fluids and mixtures. The property models are written in FORTRAN and accessed by the GUI through a dynamic link library (DLL). The property subroutines can also be used by other applications, such as spreadsheets, independently of the GUI, as described in Appendix B.

The high-level subroutines that carry out iterative saturation and flash calculations are independent of the fluid property models. Underlying these subroutines are sets of core routines for each of the models implemented in the program. The numerical coefficients to the property models for each fluid are stored in separate text files. The coefficients for the mixture departure functions are stored in a single text file. Additional files contain information specifying predefined or user-defined mixtures. This structure simplifies the addition of new fluids and additional models to future versions of the database and makes such additions almost totally transparent to the user.

3.2 Use of the Database

Start the REFPROP program by double-clicking on its icon. A banner screen displays the title, credits, and a legal disclaimer. Clicking the "Information" button calls up further details and credits through the help system. Clicking the "Continue" button starts the program. The program is controlled, in the usual fashion of a Windows application, by the use of pull-down menus displayed across the top of the application window.

3.3 Overview of the Menus

The File menu provides commands to save and print generated tables and plots. Individual items or entire sessions with multiple windows can be saved or recalled. The standard Print, Print Setup, and Exit commands are also present.

The Edit menu provides copy and paste commands, which allow selected data or plots to be exchanged with other applications.

REFPROP 17

The constant property (temperature or pressure) is entered at the upper left. The composition will be linearly varied from the condition indicated in the "Initial" column to that in the "Final" column using the number of points indicated at the upper right. With 11 points, the composition of the binary system shown in the example is varied from pure component 1 to pure component 2 with increments of 0.1 in mass fraction.

Clicking the OK button initiates the calculations. While the calculations are in progress, a small window appears indicating the status. To stop the calculations, click the Cancel button. When the calculations are complete, a table displaying the results appears.

LNG Density Calculation Methods – Software

à In industry often individual in-house solutions are used!


* not applicable for the RKM-method.

à Beside the ERKM-, the RKM-method was also implemented

Demonstration of current TREND 2 BETA Version(Software is only for demonstration and personal use! Do not distribute!)

LNG Density Calculation – e.g. TREND Package


Documents

LNG Training Course – Density Calculationslngmetrology.info/.../10/Richter-EMRP_Workshop_DensityCalc_June20… · LNG Training Course – Density Calculations 4th International